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"\"xxx\""
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| 0.1 |
<!DOCTYPE HTML>
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
<link rel="stylesheet" href="../slick.grid.css" type="text/css"/>
<link rel="stylesheet" href="../css/smoothness/jquery-ui-1.8.16.custom.css" type="text/css"/>
<link rel="stylesheet" href="examples.css" type="text/css"/>
<link rel="stylesheet" href="../controls/slick.columnpicker.css" type="text/css"/>
<style>
.slick-cell-checkboxsel {
background: #f0f0f0;
border-right-color: silver;
border-right-style: solid;
}
</style>
</head>
<body>
<div style="position:relative">
<div style="width:600px;">
<div id="myGrid" style="width:100%;height:500px;"></div>
</div>
<div class="options-panel">
<h2>Demonstrates:</h2>
<ul>
<li>Checkbox row select column</li>
</ul>
<h2>View Source:</h2>
<ul>
<li><A href="https://github.com/mleibman/SlickGrid/blob/gh-pages/examples/example-checkbox-row-select.html" target="_sourcewindow"> View the source for this example on Github</a></li>
</ul>
</div>
</div>
<script src="../lib/firebugx.js"></script>
<script src="../lib/jquery-1.7.min.js"></script>
<script src="../lib/jquery-ui-1.8.16.custom.min.js"></script>
<script src="../lib/jquery.event.drag-2.2.js"></script>
<script src="../slick.core.js"></script>
<script src="../plugins/slick.checkboxselectcolumn.js"></script>
<script src="../plugins/slick.autotooltips.js"></script>
<script src="../plugins/slick.cellrangedecorator.js"></script>
<script src="../plugins/slick.cellrangeselector.js"></script>
<script src="../plugins/slick.cellcopymanager.js"></script>
<script src="../plugins/slick.cellselectionmodel.js"></script>
<script src="../plugins/slick.rowselectionmodel.js"></script>
<script src="../controls/slick.columnpicker.js"></script>
<script src="../slick.formatters.js"></script>
<script src="../slick.editors.js"></script>
<script src="../slick.grid.js"></script>
<script>
var grid;
var data = [];
var options = {
editable: true,
enableCellNavigation: true,
asyncEditorLoading: false,
autoEdit: false
};
var columns = [];
$(function () {
for (var i = 0; i < 100; i++) {
var d = (data[i] = {});
d[0] = "Row " + i;
}
var checkboxSelector = new Slick.CheckboxSelectColumn({
cssClass: "slick-cell-checkboxsel"
});
columns.push(checkboxSelector.getColumnDefinition());
for (var i = 0; i < 5; i++) {
columns.push({
id: i,
name: String.fromCharCode("A".charCodeAt(0) + i),
field: i,
width: 100,
editor: Slick.Editors.Text
});
}
grid = new Slick.Grid("#myGrid", data, columns, options);
grid.setSelectionModel(new Slick.RowSelectionModel({selectActiveRow: false}));
grid.registerPlugin(checkboxSelector);
var columnpicker = new Slick.Controls.ColumnPicker(columns, grid, options);
})
</script>
</body>
</html>
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| 0 |
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"pile_set_name": "Pile-CC"
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| 0.051282 |
XXXX XXX
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{
"pile_set_name": "Enron Emails"
}
| 0.125 |
878 F.2d 1441
Johnsonv.Alabama Power Co.*
NO. 88-7402
United States Court of Appeals,Eleventh Circuit.
JUN 05, 1989
1
Appeal From: N.D.Ala.
2
AFFIRMED.
*
Fed.R.App.P. 34(a); 11th Cir.R. 34-3
|
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"pile_set_name": "FreeLaw"
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| 0 |
Stephen Easton
Stephen Easton (born 12 August 1959) is a former Australian rules footballer who played with North Melbourne and Carlton in the Victorian Football League (VFL). He later played for Port Melbourne in the Victorian Football Association.
Stephen's father Kevin Easton was a former North Melbourne player and a Club Secretary for Geelong Football Club.
In 1975 the North Melbourne Under 19's side were stripped of 58 points on the eve of the finals by the league for illegally fielding Easton in 17 matches during the Home & Away season. It was found he was residentially tied to Geelong. This meant the North side who had finished second on the ladder were relegated to eleventh when the penalty was handed out and missed the finals.
North Melbourne paid Geelong $10,000 to obtain his clearance in 1976.
References
External links
Stephen Easton's profile at Blueseum
Category:1959 births
Category:Carlton Football Club players
Category:North Melbourne Football Club players
Category:Australian rules footballers from Victoria (Australia)
Category:Living people
Category:Port Melbourne Football Club players
|
{
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| 0 |
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{
"pile_set_name": "OpenWebText2"
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| 0.052632 |
Determination of doripenem penetration into human prostate tissue and assessment of dosing regimens for prostatitis based on site-specific pharmacokinetic-pharmacodynamic evaluation.
Prostatic hypertrophy patients prophylactically received a 0.5-hour infusion of doripenem (250 or 500 mg) before transurethral resection of the prostate. Doripenem concentrations in plasma and prostate tissue were measured chromatographically, and analysed pharmacokinetically using a three-compartment model. The approved doripenem regimens were assessed based on the time above the minimum inhibitory concentration for bacteria (T>MIC, % of 24 hours), an indicator for antibacterial effects, at the prostate. The prostate tissue/plasma ratios were 17.3% for the maximum drug concentration and 18.7% for the area under the drug concentration-time curve, and they were irrespective of the dose. Against Escherichia coli and Klebsiella species isolates, 500 mg once daily achieved a >90% probability of attaining the bacteriostatic target (20% T>MIC) in prostate tissue, and 500 mg twice daily achieved a >90% probability of attaining the bactericidal target (40% T>MIC) in prostate tissue.
|
{
"pile_set_name": "PubMed Abstracts"
}
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{
"pile_set_name": "OpenWebText2"
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| 0.056338 |
The forum is frozen forever - but it won't die; it'll stay for long in search engine results and we hope it would keep helping newbies in some way or other - cheers!
garage4hackers
CSIS Security Group A/S has uncovered a new trojan-banker family which we have named Tinba (Tiny Banker) alias “Zusy”.
Tinba is a small data stealing trojan-banker. It hooks into browsers and steals login data and sniffs on network traffic. As several sophisticated banker-trojan it also uses Man in The Browser (MiTB) tricks and webinjects in order to change the look and feel of certain webpages with the purpose of circumventing
...
Here we are providing a detail Analysis about Netravelr APT team based on the data we collected over the past 1 year.
In 2014 the actors behind global cyber espionage campaign “Operation NetTraveler” celebrate ten years of activity. NetTraveler has targeted more than 350 high-profile victims in 40 countries. So it is high time we make our research public . This is not an individual research, instead this was part of efforts of various Garage4hackers
...
GameoverZeus was brought down and it reincarnated again. The Gameover Zeus is a very authentic contender in our DGA series. So let us analyse it and try to reverse its DGA just like we did in case of PushDO in last article.http://www.garage4hackers.com/entry.php?b=3080
We got lot of request whether we could have a tutorial on reverse engineering DGA codes. So in this series we would
...
|
{
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| 0 |
Q:
Flask streaming doesn't return back response until finished
So I am trying to stream the chunks of data returned back from the sql database. The chunks seem to be streamed, however when I hit the endpoint, it shows the response at the very end when the request is completed, instead of showing the streamed data chunk by chunk. I know there are already questions about this but adding mimetype doesn't seem to work for me. I have the following code:
Any help is highly appreciated!
def generate_chunks():
result = _get_query_service(repo_url, True).stream_query(qry)
chunk_counter = 0
while True:
chunk = result.fetchmany(5)
chunk_counter += 1
if not chunk:
break
for value in chunk:
yield str(chunk)
return Response(stream_with_context(generate_chunks()), content_type='application/json', status=200)
A:
Actually it was a small thing. The above code works.
But tools like Postman and Insomnia do not support streaming data.
If you want to see your data streamed in action, use CURL or python requests.
For CURL, you need to add --no-buffer option to see the streamed data.
curl --no-buffer -v http://localhost:8082/healthy
For Python requests, you need to add stream=True. Example:
r = requests.post('http://localhost:8082/stream_query', json=dc, stream=True)
r.encoding = 'utf-8'
for line in r.iter_content(chunk_size=10): # prints the streamed data in chunks
print(line)
|
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| 0 |
Pet Age & Birthday Tracker for 200+ Breeds1.2
Publisher Description
This app tracks your pet's age as you watch, and also finds their next birthdays!
Clean interfaces allow easy setup with customizable pet photo and background, and then it's easy to plan a special treat for their next birthday.
Pet Age Tracker has accurate age calculations for 200+ breeds of pet, including:
- 61 dogs including four weight classes of mixed-breed dog
- 42 cats including a general mixed-breed cat
- 41 birds including many breeds of cockatoo, macaw & parrot
- 40 freshwater & saltwater fish
- 14 reptiles including many breeds of snake, lizard and turtle
- 13 amphibians including many breeds of gecko, frog, newt and toad
- 14 other pets
- 7 rodents including gerbil, hamster and mouse
Here's how we calculate the age of your pet - a cat's age is calculated as:
- 15 pet years old after the first human year
- 25 pet years old after the second human year
- 29 pet years old after the third human year
- Breed-specific aging is used after the third human year
A dog's age is calculated as:
- 10.5 pet years old after the first human year
- 21 pet years old after the second human year
- Breed-specific or weight-specific aging is used after the third human year
Breed-specific aging for alpaca, cow, emu, horse, llama, ostrich and rabbit. Details are available within the app.
Pet Age & Birthday Tracker for 200+ Breeds is a free software application from the Food & Drink subcategory, part of the Home & Hobby category.
The app is currently available in English and it was last updated on 2016-03-24. The program can be installed on iOS.
Pet Age & Birthday Tracker for 200+ Breeds (version 1.2) has a file size of 39.32 MB and is available for download from our website.
Just click the green Download button above to start. Until now the program was downloaded 0 times.
We already checked that the download link to be safe, however for your own protection we recommend that you scan the downloaded software with your antivirus.
Program Details
General
Category
System requirements
Operating systems
ios
Download information
File size
39.32 MB
Total downloads
0
Pricing
License model
Free
Price
N/A
Version History
Here you can find the changelog of Pet Age & Birthday Tracker for 200+ Breeds since it was posted on our website on 2016-10-15.
The latest version is 1.2 and it was updated on soft112.com on 2018-03-28.
See below the changes in each version:
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| 0 |
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| 0.088889 |
Novell, Inc. is a global software and services company based in Waltham, Massachusetts. The company specializes in
enterprise operating systems, such as SUSE Linux Enterprise and Novell NetWare; identity, security, and systemsmanagement solutions; and collaboration solutions, such as Novell Groupwise and Novell Pulse. Novell was instrumentalin making the Utah Valley a focus for technology and software development. Novell technology contributed to theemergence of local area networks, which displaced the dominant mainframe computing model and changed computingworldwide. Today, a primary focus of the company is on developing open source software for enterprise clients.
============================3) Technical details============================The vulnerability is caused due to an integer overflow error in GroupWise Internet Agent (gwia.exe)when copying request data and can be exploited to cause a heap-based buffer overflow by e.g.sending a specially crafted request with the "Content-Length" header value set to "-1" to the web-basedadministration interface (TCP port 9850). Successful exploitation may allow execution of arbitrary code.
|
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| 0.061538 |
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| 0.060606 |
Q:
Extracting argument of a specific functions in a large expression
I have a large expression, for example
Cos[x]Sin[y]Sqrt[1+z]/(1+x^2)-1/(1+y)
I wish to extract the argument inside Sqrt function, namely 1+z. I thought of using /.Sqrt[x_]->(h=x), but executing
Cos[x]Sin[y]Sqrt[1+z]/(1+x^2)-1/(1+y)/.Sqrt[x_]->(h=x);h
returns x but not 1+z, why? Is there a way to achieve my goal?
In my expressions, there will only be one Sqrt, but many other different heads as well. There is a similar question, but it is only applicable to very simple expression like Sqrt[1+z].
A:
Clear["Global`*"]
expr = Cos[x] Sin[y] Sqrt[1 + z]/(1 + x^2) - 1/(1 + y) Sqrt[1 - z];
Cases[expr, Sqrt[t_] :> t, Infinity]
(* {1 - z, 1 + z} *)
To ensure that all of the terms are real
And @@ Thread[% >= 0] // Simplify
(* -1 <= z <= 1 *)
Or more directly,
And @@ Cases[expr, Sqrt[t_] :> (t >= 0), Infinity] // Simplify
(* -1 <= z <= 1 *)
Better yet,
FunctionDomain[expr, z]
(* -1 <= z <= 1 *)
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| 0.055556 |
Rates and tariffs
Dear partners, current rates and tariffs on services of “Kedentransservice” JSC are represented in this section. If there is necessary information missing for you in this section or you have other questions, we ask you to send written requests to sales@kdts.kz and logistics@kdts.kz. Contacts with phone numbers are listed here.
At the same time, “Kedentransservice” JSC (hereinafter — the Company) in accordance with points 4.1.2 and 5.1. of the Agreement for the services of carriages operator when reloading containers through border crossings Dostyk, Altynkol in international traffic (import, transit) reports the change from January 1, 2017 of “The rates for the services of carriages operator when reloading containers through border crossings Dostyk, Altynkol in the international traffic (import, transit)”.
Since October 19, 2015 in the performing reloading of oversized cargo from wagon to wagon it is obligatory to be guided by the tariff policy of railways of participating States of the Commonwealth of Independent States on transportation of cargoes in the international message (the CIS-TP):
1) collecting tariffs for reloading of oversized cargo in accordance with the TA CIS rates applying the coefficient of 2;
2) collecting tariffs in performing reloading to the 8-axle rolling stock in accordance with the TA CIS rates applying the coefficient of 2;
3) collecting tariffs in performing reloading to the 8-axle rolling stock in accordance with the TA CIS rates applying the coefficient of 4.
Notification of the conclusion of contracts for 2017 for all forwarding companies!
|
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Accreditation of endocrine surgery units.
A key measure to maintain and improve the quality of healthcare is the formal accreditation of provider units. The European Society of Endocrine Surgeons (ESES) therefore proposes a system of accreditation for endocrine surgical centers in Europe to supplement existing measures that promote high standards in the practice in endocrine surgery. A working group analyzed the current healthcare situation in the field of endocrine surgery in Europe. Two surveys were distributed to ESES members to acquire information about the structure, staffing, caseload, specifications, and technology available to endocrine surgery units. Further data were sought on tracer diagnoses for quality standards, training provision, and research activity. Existing accreditation models related to endocrine surgery were included in the analysis. The analysis of existing accreditation models, available evidence, and survey results suggests that a majority of ESES members aspire to a two-level model (termed competence and reference centers), sub-divided into those providing neck endocrine surgery and those providing endocrine surgery. Criteria for minimum caseload, number and certification of staff, unit structure, on-site collaborating disciplines, research activities, and training capacity for competence center accreditation are proposed. Lastly, quality indicators for distinct tracer diagnoses are defined. Differing healthcare structures, existing accreditation models, training models, and varied case volumes across Europe are barriers to the conception and implementation of a pan-European accreditation model. However, there is consensus on accepted standards required for accrediting an ESES competence center. These will serve as a basis for first-stage accreditation of endocrine surgery units.
|
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| 0 |
5
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|
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"pile_set_name": "Github"
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| 0.049689 |
The present invention relates to a device for mechanical and electrical lockout of a remote control unit for a modular circuit breaker, this remote control unit being provided with a handle having two stable positions respectively open and closed and means for making and breaking the electrical power supply to this unit.
German Patent application DE-3,711,138A1 describes a remote control unit associated with a modular circuit breaker, the handles of the two units being rigidly coupled by means of a connecting bar. The remote control unit mechanism comprises two transmission rods fitted between a base of the handle and a cog-wheel of the speed reducer coupled to the motor. The end of one of the rods is engaged in an oblong opening of the base, which enables manual control of the circuit breaker independently from the remote control unit. The remote control unit is in addition equipped with switches coupled to the handle to supply, when applicable, a make or break signal.
On installations comprising remote control units associated to modular circuit breakers, the advantage, and even the necessity, of providing a device performing both mechanical and electrical lockout of the system has proved essential for user safety reasons.
The object of the present invention is to provide a solution to achieve this function which is both efficient, economical and easy to implement.
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| 0 |
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| 0.083333 |
Q:
UITableViewCell contentView custom disclosure image frame issue
Disclaimer: I've been working too late. But, I'm determined to get through this one tonight.
I have an app where I support different color themes. The dark cell backgrounds have been problematic.
I've been poking around trying to find a formidable way to draw the accessory disclosure icon in uitableviewcells with black backgrounds.
I decided to try overriding setAccessoryType to inherit the functionality for my 50+ views:
-(void) addWhiteDisclosureImage {
UIImageView *disclosureView = (UIImageView*) [self.contentView viewWithTag:kDisclosureReplacementImageTag];
if(!disclosureView) {
[super setAccessoryType:UITableViewCellAccessoryNone];
disclosureView = [[UIImageView alloc] initWithImage:self.whiteDisclosureImage];
disclosureView.tag = kDisclosureReplacementImageTag;
disclosureView.autoresizingMask = UIViewAutoresizingFlexibleRightMargin | UIViewAutoresizingFlexibleLeftMargin;
DebugLog(@"%f, %f", self.frame.size.width, self.frame.size.height);
[self.contentView addSubview:disclosureView];
[self.contentView bringSubviewToFront:disclosureView];
[disclosureView release];
}
}
- (void)setAccessoryType:(UITableViewCellAccessoryType)accessoryType {
if(accessoryType == UITableViewCellAccessoryDisclosureIndicator) {
if ([self.viewController isKindOfClass:[ViewControllerBase class]]) {
ViewControllerBase *view = (ViewControllerBase*) self.viewController;
if(view.colorTheme && view.colorTheme.controlBackgroundColor) {
if([ViewColors colorAverage:view.colorTheme.controlBackgroundColor] < 0.2) { //substitute white disclosure indicator
[self addWhiteDisclosureImage];
return;
} else { //not dark enough
[self removeWhiteDisclosureImage];
[super setAccessoryType:accessoryType];
return;
}
} else { //no colorTheme.backgroundColor
[self removeWhiteDisclosureImage];
[super setAccessoryType:accessoryType];
return;
}
} else { //viewController is not type ViewControllerBase
[self removeWhiteDisclosureImage];
[super setAccessoryType:accessoryType];
return;
}
}
UIView *disclosureView = [self.contentView viewWithTag:kDisclosureReplacementImageTag];
if(disclosureView)
[disclosureView removeFromSuperview];
[super setAccessoryType:accessoryType];
}
This override is typically called in cellForRowAtIndexPath.
It seemed like a good option until I drill down and come back. For some cells, the cell frame will be a great deal larger than the first time through. This consistently happens to the same cell in a list of 6 that I've been testing against. There's clearly something unique about this cell: it's frame.size.
Here is the size of the cell that I log for the first tableview load (in some cases every load/reload):
320.000000, 44.000000
This is the difference in what I get for some (not all) of the cells after call to reloadData:
759.000000, 44.000000
Does anyone know why this might happen?
Update: the suspect cell's custom accessory disclosure view almost acts like it's autoresizing flag is set to none. I confirmed this by setting all to none. I say almost because I see it line up where it should be after reloadData. A split second later it moves clear over to the left (where they all end up when I opt for no autoresizing).
A:
Don't mess around with subviews and calculating frames.
Just replace the accessoryView with the new imageView. Let iOS do the work.
|
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Dark star (dark matter)
A dark star is a type of star that may have existed early in the universe before conventional stars were able to form. The stars would be composed mostly of normal matter, like modern stars, but a high concentration of neutralino dark matter within them would generate heat via annihilation reactions between the dark-matter particles. This heat would prevent such stars from collapsing into the relatively compact sizes of modern stars and therefore prevent nuclear fusion among the normal matter atoms from being initiated.
Under this model, a dark star is predicted to be an enormous cloud of hydrogen and helium ranging between 4 and 2000 astronomical units in diameter and with a surface temperature low enough that the emitted radiation would be invisible to the naked eye.
In the unlikely event that dark stars have endured to the modern era, they could be detectable by their emissions of gamma rays, neutrinos, and antimatter and would be associated with clouds of cold molecular hydrogen gas that normally would not harbor such energetic particles.
Notes
Bibliography
Category:Star types
Star
|
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| 0 |
---
abstract: 'We propose a new modeling paradigm for large dimensional aggregates of stochastic systems by Generalized Factor Analysis (GFA) models. These models describe the data as the sum of a [*flocking*]{} plus an uncorrelated [*idiosyncratic* ]{} component. The flocking component describes a sort of collective orderly motion which admits a much simpler mathematical description than the whole ensemble while the idiosyncratic component describes weakly correlated noise. We first discuss static GFA representations and characterize in a rigorous way the properties of the two components. For wide-sense stationary sequences the character and existence of GFA models is completely clarified. The extraction of the flocking component of a random field is discussed for a simple class of separable random fields.'
author:
- 'Giulio Bottegal and Giorgio Picci[^1]'
bibliography:
- 'generalized\_factor\_models.bib'
title: '**Flocking and Generalized Factor Analysis** '
---
Introduction
============
[*Flocking*]{} is a commonly observed behavior in gregarious animals by which many equal individuals tend to group and follow, at least approximately, a common path in space. The phenomenon has similarities with many scenarios observed in artificial/technological and biological environments and has been studied quite actively in recent years [@Brockett_10; @Veerman-etal-05; @Olfati_06; @Cucker-S-07]. A few examples are described below.
The mechanism of [*formation*]{} of flocks is also called [*convergence to consensus*]{} and has been intensely studied in the literature, see e.g. [@Fagnani-Z-08; @Olfati-F-M-07; @Tahbaz-J-10], and there is now a quite articulated theory addressing the convergence to consensus under a variety of assumptions on the communication strategy among agents etc..
In this paper we want to address a different issue: given observations of the motion of a large set of equal agents and assuming statistical steady state, decide whether there is a flocking component in the collective motion and estimate its structural characteristics. The reason for doing this is that the very concept of flocking implies an [*orderly motion*]{} which must then admit a much simpler mathematical description than the whole ensemble. Once the flocking component (if present) has been separated, the motion of the ensemble splits naturally into flocking plus a random term which describes local random disagreements of the individual agents or the effect of external disturbances. Hence extracting a flocking structure is essentially a parsimonious modeling problem.
Detection of emitters
---------------------
In this scenario we suppose there is an unknown number, say $q$, of emitters, each of them broadcasting radio impulse trains at a fixed common frequency. Such impulses are received by a large array of $N$ antennas spread in space. The measurement of each antenna is corrupted by noise, generated by measurement errors or local disturbances, possibly correlated with that of neighboring antennas. The set up can be described mathematically, by indexing each antenna by an integer $i=1,2,\ldots, N$ and denoting by ${\mathbf y}_i(t)$ the signal received at time $t$ by antenna $i$. Then the following model can be used to describe the received signal $$\label{Antennas}
{\mathbf y}_i(t) = f_{i1} x_1(t) + \ldots + f_{iq} x_q(t) + \tilde {\mathbf y}_i(t) \,,$$ where:
- $x_j(t)$ is the signal sent by the $j$-th emitter at time $t$;
- $f_{ij}$ is a coefficient related to the distance between $j$-th emitter and antenna $i$;
- $\tilde {\mathbf y}_i(t)$ is the disturbance affecting antenna $i$ at time $t$.
The goal is to detect the number of emitters $q$ and possibly estimate the signal components $x_j(t)$ impinging on the antenna array. Let ${\mathbf y}(t),\,{\mathbf x}(t),\, \tilde {\mathbf y}(t)$ denote vector valued quantities in the model of respective dimensions $N,\,q$ and $N$. The model can be compactly written as $$\label{Antennas1}
{\mathbf y}(t) = F {\mathbf x}(t) + \tilde {\mathbf y}(t) \,,$$ where ${\mathbf y}$ is the $N$-dimensional random process of observables; ${\mathbf x}(t)= [{\mathbf x}_1(t) \, \ldots \, {\mathbf x}_q(t)\,]^\top$ is the unobservable vector of random signals generated by the emitters; $F= \{f_{ij}\} \in \mathbb{R}^{N \times q}$ is an unknown matrix of coefficients and $\tilde {\mathbf y}$ is a $N$-dimensional random process of disturbances, uncorrelated with ${\mathbf x}$, describing the local disturbance on the $i$-th antenna.
Note that in the model there are several hidden (non-measurable) variables, including the dimension $q$. In our setting $N$ is assumed to be very large; ideally we shall assume $N \rightarrow \infty$.
We may identify $F {\mathbf x}(t) $ as the flocking component of ${\mathbf y}(t)$. In a primitive statistical formulation all signals in the model are i.i.d. process, and the sample values $\{y(t)\}$ are interpreted as random samples generated by a underlying static model of the form $$\label{Antennas2}
{\mathbf y}= F {\mathbf x}+ \tilde {\mathbf y}\,.$$ One should observe that estimation of this model from observations $\{y(t)\}$ of ${\mathbf y}$, consists first of estimating the model parameters, say $F$ and the covariance matrix of $\tilde {\mathbf y}$ but also in constructing the hidden random quantities ${\mathbf x}$ and $\tilde {\mathbf y}$. The covariance matrix of ${\mathbf y}$, say $\Sigma \in {\mathbb R}^{N\times N}$ may be obtained from the data by standard procedures.
A problem leading to models of similar structure is automated speaker detection. This is the problem of detecting the speaking persons (emitters) in a noisy environment at any particular time, from signals coming from a large array of $N$ microphones distributed in a room. Here the number of emitters is generally small but could be varying with time. Robustly solving this problem is useful in areas such as surveillance systems, and human-machine interaction.
In the model specification it is customary to assume that the noise vector $ \tilde {\mathbf y}$ has uncorrelated components. In this case the model , is a [*(static) Factor Analysis Model*]{}. Statistical inference on these models leads in general to ill-posed problems and to resolve the issue it is often imposed that the variances of the scalar components of $ \tilde {\mathbf y}$ should all be equal. The problem can then be solved by computing the smallest eigenvalue of the covariance matrix of ${\mathbf y}$, following an old idea [@Pisarenko-73] which has generated an enormous literature. The assumption of uncorrelated noise and, especially, of equal variances is however rather unrealistic in many instances.
Inference on gene regulatory networks
-------------------------------------
In Systems Biology, an important task is the inference on gene regulatory networks in order to understand cell physiology and pathology. Genes are known to interact among each other forming a network, and their expression is directly regulated by few transcription factors (TFs). Typically, TFs and genes are modeled as two distinct networks of interactions which are able also to interact with each other. While methods for measuring the gene expressions using microarray data are extremely popular, there are still problems in understanding the action of TFs and the scientific community is currently working on computational methods for extraction of the action of the TFs from the available measurements of gene expression. To this end, a simplification of the interaction between genes and TFs is commonly accepted and consists in projecting the TFs network on the “gene space” [@brazhnik_2002].
Denoting by a random variable ${\mathbf y}_i$ the measured expression profile of the $i$-th gene of the network, usually the model is also proposed in this framework. In this case:
- The $N$ dimensional vector ${\mathbf y}$ represents all the gene expressions. The experimenter can usually observe a large amount of genes, and it is reasonable to assume that $N \rightarrow \infty$.
- Each component of the random vector ${\mathbf x}$ is associated with a TF. The number $q$ of TF’s is a priori unknown; furthermore $N \gg q$.
- The $N \times q$ matrix $F$ models the strength of the TFs effect on each gene.
- The vector $ \tilde {\mathbf y}$ describes the interaction of connected genes.
Factor Analysis models (see Section \[classicFA\]) have been considered to deal with this problem, see e.g. [@pournara_2007; @fa_chap_2010]; in such a case, the vector $
\tilde {\mathbf y}$ is assumed to have uncorrelated components. However, in the context of gene regulatory networks the latter assumption may be relaxed, since it is well-known that there are interactions among genes that are not determined by TFs. Then, a possible assumption is that $ \tilde {\mathbf y}$ admits some [“weak correlation”]{} among its components.
Modeling energy consumption
---------------------------
In this example, we may want to model the energy consumption (or production) of a network of $N$ users distributed geographically in a certain area, say a city or a region. The energy consumption ${\mathbf y}_i(t)$ of user $i$ is a random variable which can be seen as the sum of two contributions $$\label{Energy}
{\mathbf y}_i(t)= f_i^\top {\mathbf x}(t) + \tilde {\mathbf y}_i(t)\,.$$ where the term $f_i^\top {\mathbf x}(t)$ represents a linear combination of $q$ hidden variables ${\mathbf x}_i(t)$ which model different factors affecting the energy consumption (or production) of the whole ensemble; say heating or air conditioning consumption related to seasonal climatic variations, energy production related to the current status of the economy etc. The factor vector ${\mathbf x}(t)$ determines the average time pattern of energy consumption/production of each unit, the importance of each scalar factor being determined by a $q$-ple of constant weight coefficients $f_{i,k}$.\
One may identify the component $F{\mathbf x}(t)$ as the flocking component of the model . The terms $\tilde {\mathbf y}_i(t)$, represent local random fluctuations which model the consumption due to devices that are usually activated randomly, for short periods of time. They are assumed uncorrelated with the process ${\mathbf x}$. The covariance ${{\mathbb E}\,}\tilde {\mathbf y}_i(t) \tilde {\mathbf y}_j(t)$ could be non zero for neighbouring users but is reasonable to expect that it decays to zero when $|i-j|\to \infty$.\
To identify such a model one should start from real data of energy consumption collected from a large amount of units. A possible application for such a model is the forecasting of the average requirement of energy in a certain geographical area.
Dynamic modeling in computer vision
-----------------------------------
Large-dimensional time series occur often in signal processing applications, typically for example, in computer vision and dynamic image processing. The role of identification in image processing and computer vision has been addressed by several authors. We may refer the reader to the recent survey [@Chiuso-P-08] for more details and references. One starts from a signal ${\mathbf y}(t) := {\rm vec}({\mathbf I}(\cdot,t))$, obtained by vectorizing at each time $t$, the intensities ${\mathbf I}(\cdot,t)$ at each pixel of an image, into a vector, say ${\mathbf y}(t) \in \mathbb{R}^N$, with a “large” number (typically tens of thousands) of components. We may for instance be interested in modeling (and in identification methodologies thereof) of “dynamic textures” (see [@DynamicTexture]), by linear state space models or in extracting classes of models describing rigid motions of objects of a scene. Most of these models involve hidden variables, say the state of linear models of textures, or the displacement-velocity coordinates of the rigid motions of objects in the scene. The purpose is of course to compress high dimensional data into simple mathematical structures. Note that the number of samples that can be used for identification is very often of the same order (and sometimes smaller) than the data dimensionality. For instance, in dynamic textures modeling, the number of images in the sequences is of the order of a few hundreds while $N$ (which is equal to the number of pixels of the image) is certainly of the order of a few hundreds or thousands [@DynamicTexture; @BissaccoCSPAMI2007].
Factor Analysis {#classicFA}
---------------
Factor Analysis has a long history; it has apparently first been introduced by psychologists [@spearman-904; @burt_1909] and successively been studied and applied in various branches of Statistics and Econometrics [@Ledermann-37; @Ledermann-39; @Bekker-L-87; @Lawley-M-71]. With a few exceptions however, [@KalmanDFM1983; @JVSDFM1986; @Picci-1987; @picci_pinzoni_86; @Deistler-Z-07; @Georgiou-N-011], little attention has been payed to these models in the control engineering community. Dynamic versions of factor models have also been introduced in the econometric literature, see e.g. [@geweke_1977; @PenaBox1987; @PenaBoxModel2004] and references therein.\
Recently, we have been witnessing a revival of interest in these models, motivated on one hand by the need of modeling very large dimensional vector time series. Vector AR or ARMA models are inadequate for modeling signals of large cross-sectional dimension, because they involve a huge number of parameters to estimate which may sometime turn out to be larger than the sample size. On the other hand, an interesting generalization of dynamic factor analysis models allowing the cross-sectional dimension of the observed time series to go to infinity, has been proposed by Chamberlain, Rothschild, Forni, Lippi and collaborators in a series of widely quoted papers [@chamberlain_1983; @Chamberlain-R-83; @Forni_2000; @forni_lippi_2001]. This new modeling paradigm is attracting a considerable attention also in the engineering system identification community [@Deistler-A-F-Z-010; @anderson_deistler_2008; @Deistler-Z-07; @PenaJSPI2006]. These models, called *Generalized Dynamic Factor Models* are motivated by economic and econometric applications. We shall argue that, with some elaboration, they may be quite useful also in engineering applications.
Problem statement and scope of the paper {#ProblemSect}
----------------------------------------
[*Notations:* ]{} in this paper boldface symbols will normally denote random arrays, either finite or infinite. All random variables will be real, zero-mean and with finite variance. In the following we shall denote by the symbol $H({\mathbf v})$ the standard inner-product space of random variables linearly generated by the scalar components $\{{\mathbf v}_1,\ldots,{\mathbf v}_n,\ldots \}$ of a (possibly infinite) random string ${\mathbf v}$.
Let ${\mathbf y}(k,t)$ be a second order finite variance random field depending on a space variable $k$ and on a time variable $t$. The variable $k$ is indexing a large ensemble of space locations where equal “agents” produce at each time $t$ the measurement, ${\mathbf y}(k,t)$, of a scalar quantity, say the received voltage signal of the $k$-th antenna or the expression level of the $k$-th cell in a cell array. We shall assume that $k$ varies on some ordered index set of $N$ elements and let $t \in {\mathbb Z}$ or ${\mathbb Z}_{+}$, depending on the context. Eventually we shall be interested in problems where $N=\infty$. We shall denote by ${\mathbf y}(t)$ the random (column) vector with components $\{{\mathbf y}(k,t)\,;\, k=1,2,\ldots,N\}$. Suitable mathematical assumptions on this process will be specified in due time.
A [**(random) flock**]{} is a random field having the multiplicative structure $\hat{{\mathbf y}}(k,t)= \sum_{i=1}^{q} \,f_i(k) {\mathbf x}_{i}(t)$, or equivalently, $$\hat{{\mathbf y}}(t)= \sum_{i=1}^{q} \,f_i {\mathbf x}_{i}(t)$$ where $f_i= {\left[ \begin{matrix}}f_i(1) & f_i(2)& \ldots & f_i(N){\end{matrix} \right]}^{\top},\, i=1,2,\ldots,q$ are nonrandom $N$-vectors and ${\mathbf x}(t):= {\left[ \begin{matrix}}{\mathbf x}_{1}(t) & \ldots&{\mathbf x}_{q}(t){\end{matrix} \right]}^{\top}$ is a random processes with orthonormal components depending on the time variable only; i.e. $ {{\mathbb E}\,}{\mathbf x}(t){\mathbf x}(t)^{\top}= I_q \,,{\quad}t \in {\mathbb Z}\, $.\
The idea is that a flock is essentially a deterministic geometric configuration of $N$ points in a $q$-dimensional space moving rigidly in a random fashion. The main goal of this paper is to investigate when a second order random field has a flocking component and study the problem of extracting it from sample measurements of ${\mathbf y}(k,t)$. This means that one should be searching for decompositions of the type: $${\mathbf y}(t)= \sum_{i=1}^{q} \,f_i {\mathbf x}_{i}(t) +\tilde{{\mathbf y}}(t)$$ where $q \geq 1$ and $\tilde{{\mathbf y}}(t)$ is a “random noise” field which should not contain flocking components. Naturally for the problem to be well-defined one has to specify conditions making this decomposition [*unique*]{}.
A generalization of this setting where ${\mathbf y}$ may take vector values is possible, but for the sake of clarity we shall here restrict to scalar-valued processes.\
The organization of the paper is as follows: In Section \[Sec:FA\] we review static finite-dimensional Factor Analysis; in Section \[Sec:AggrIdio\] we discuss the basic ideas leading to representations of infinite dimensional strings of variables by Generalized Factor Analysis (GFA) models. The problem of representation by GFA models is discussed in Section \[GFA\]. The restriction to stationary sequences is discussed in Section \[Sec:Wold\]; the relation of GFA with the Wold decomposition, the main theme of this section is believed to be completely original. Also original is the content of Section \[Sec:RandFields\] where the extraction of the flocking component for a class of space-time random is finally discussed.\
Some of the material of this paper has been presented in a preliminary form to conferences [@Bottegal-P-11; @Picci-012].
A review of Static Factor Analysis models {#Sec:FA}
=========================================
A (static) [*Factor Analysis*]{} model is a representation $${\mathbf y}=F{\mathbf x}+{\mathbf e}, \label{FA}$$ of $N$ observable random variables ${\mathbf y}=[\,{\mathbf y}_1\,\ldots\,{\mathbf y}_N\,]^{\top}$, as linear combinations of $q$ [*common factors*]{} ${\mathbf x}=[\,{\mathbf x}_1\,\ldots\,{\mathbf x}_q\,]^{\top}$, plus uncorrelated “noise" or “error" terms ${\mathbf e}=[\,{\mathbf e}_1\,\ldots\,{\mathbf e}_N\,]^{\top}$. An essential part of the model specification is that the $N$ components of the error ${\mathbf e}$ should be (zero-mean and) mutually uncorrelated random variables, i.e. $${{\mathbb E}\,}{\mathbf x}{\mathbf e}^{\top}=0\,, \qquad {{\mathbb E}\,}{\mathbf e}{\mathbf e}^{\top}={\mathrm{diag}}\{\sigma^{2}_1,\ldots,\sigma^{2}_N\}\,.$$ The aim of these models is to provide an “explanation" of the mutual interrelation between the observable variables ${\mathbf y}_i$ in terms of a small number of common factors, in the sense that, setting: $ \hat{{\mathbf y}}_i:=f_{i}^{\top}{\mathbf x}$, where $f_{i}^{\top}$ is the $i$-th row of the matrix $F$, one has exactly ${{\mathbb E}\,}{\mathbf y}_i {\mathbf y}_j={{\mathbb E}\,}\hat{{\mathbf y}}_i\hat{{\mathbf y}}_j$, for all $i\neq j$. This property is just [*conditional orthogonality*]{} (or conditional independence in the Gaussian case) of the family of random variables $\{{\mathbf y}_1,\ldots,{\mathbf y}_N\}$ [*given*]{} ${\mathbf x}$ and is a characteristic property of the factors. It is in fact not difficult to see that ${\mathbf y}$ admits a representation of the type (\[FA\]) if and only if ${\mathbf x}$ renders $\{{\mathbf y}_1,\ldots,{\mathbf y}_N\}$ pairwise conditionally orthogonal given ${\mathbf x}$, [@Picci-1987; @Bartholomew-84]. We stress that conditional orthogonality given ${\mathbf x}$ is actually [*equivalent*]{} to the orthogonality (uncorrelation) of the components of the noise vector ${\mathbf e}$.
Unfortunately these models, although providing a quite natural and useful data compression scheme, in many circumstances, suffer from a serious non-uniqueness problem. In order to clarify this issue we first note that the property of making $\{{\mathbf y}_1,\ldots,{\mathbf y}_N\}$ conditionally orthogonal is really a property of the subspace of random variables linearly generated by the components of the vector $\hat{{\mathbf y}}:=F{\mathbf x}$, denoted $X:=H(\hat{{\mathbf y}})$ and it will hold for any set of generators of $X$. Any set of generating variables for $X$ can serve as a common factors vector and there is no loss of generality to choose the generating vector ${\mathbf x}$ for $X$ of minimal cardinality (a basis) and normalized, i.e. such that $ {{\mathbb E}\,}{\mathbf x}{\mathbf x}^{\top} = I,
$ which we shall always do in the following. A subspace $X$ making the components of ${\mathbf y}$ conditionally independent is called a [*splitting subspace*]{} for $\{{\mathbf y}_1,\ldots,{\mathbf y}_N\}$. The so-called “true" variables $\hat{{\mathbf y}}_i$ are then just the orthogonal projections $\hat{{\mathbf y}}_i ={{\mathbb E}\,}[{\mathbf y}_i \mid X]$.
We may then call $q=\dim {\mathbf x}=\dim X$ the dimension of the model. Hence a model of dimension $q$ will automatically have ${\mathrm{rank}\,}F=q$ as well. Two F.A. models for the same observable ${\mathbf y}$, whose factors span the same splitting subspace $X$ are [*equivalent*]{}. This is a trivial kind of non-uniqueness since two equivalent F.A. models will have factor vectors related by a real orthogonal transformation matrix.
The serious non-uniqueness comes from the fact that there are in general many (possibly infinitely many) minimal splitting subspaces for a given family of observables $\{{\mathbf y}_1,\ldots,{\mathbf y}_N\}$. This is by now well known [@Picci-1987; @LPBook]. Hence there are in general many nonequivalent minimal F.A. models (with normalized factors) representing a fixed $N$-tuple of random variables ${\mathbf y}$. For example, one can choose, for each $k\in\{1,\ldots,N\}$, a splitting subspace of the form $X:={\mathrm{span}\,}\{\,{\mathbf y}_1\,\ldots\,{\mathbf y}_{k-1}\,\,{\mathbf y}_{k+1}\,\ldots\,{\mathbf y}_N\,\}$, and thereby obtain $N$ “extremal" F.A. models called [*elementary regressions*]{} which are clearly non equivalent.\
Note that a Factor Analysis representation induces a decomposition of the covariance matrix $\Sigma$ of ${\mathbf y}$ as $$\Sigma= F F^{\top} + {\mathrm{diag}}\{\sigma_{{\mathbf e}_1}^2,\ldots,\sigma_{{\mathbf e}_N}^2\}$$ which can be seen as a special kind of *low rank plus sparse* decomposition of a covariance matrix [@Chandra-etal-011], a diagonal matrix being, in intuitive terms, as sparse as one could possibly ask for.
The inherent nonuniqueness of F.A. models is called “factor indeterminacy", or unindentifiability in the literature and the term is usually referred to parameter unidentifiability as it may appear that there are always “too many" parameters to be estimated. It may be argued that once a model, in essence, a splitting subspace, is selected, it can always be parametrized in a one-to-one (and hence identifiable) way. Unfortunately, the classification of all possible minimal F.A. representations and an explicit characterization of minimality are, to a large extent, still an open problem. The difficulty is indeed a serious one.\
Since, as we have argued, in essence non-uniqueness is just a consequence of uncorrelation of the noise components, one may try to get uniqueness by giving up or mitigating the requirement of uncorrelation of the components of ${\mathbf e}$. This however tends to make the problem ill-defined as the basic goal of uniquely splitting the external signal into a noiseless component plus “additive noise” is made vacuous, unless some extra assumptions are made on the model and on the very notion of “noise”. Quite surprisingly, as we shall see, for models describing an [*infinite* ]{} number of observables a meaningful weakening of the uncorrelation property can be introduced, so as to guarantee the uniqueness of the decomposition.
Aggregate and idiosyncratic sequences {#Sec:AggrIdio}
=====================================
In this section we shall review the main ideas of Generalized Factor Analysis, drawing quite heavily on the papers [@Chamberlain-R-83; @forni_lippi_2001] although with some non-trivial original contributions. We shall restrict for now to the [*static case*]{}.\
Consider a zero-mean finite variance stochastic process ${\mathbf y}:=\{{\mathbf y}(k),\,k \in {\mathbb Z}_+\}$, which we shall normally represent as a random column vector with an infinite number of components. The index $k$ will later have the interpretation of a space variable. We shall normally work on the standard Hilbert space $H({\mathbf y})$ linearly generated by the components of ${\mathbf y}$ and convergence shall always mean convergence in the norm topology of this space.\
We want to describe the process as a linear combination of a finite number of common random components plus “ noise”, i.e. $$\label{GFAD}
{\mathbf y}(k) = \sum_{i=1}^{q}f_i(k) {\mathbf x}_i + \tilde{{\mathbf y}}(k)\,,{\qquad}k=1,2, \ldots$$ where the random variables ${\mathbf x}_i\,,\, i=1,\ldots,q$ are the [*common factors*]{} and the deterministic vectors $f_i$ are the [*factor loadings*]{}. The ${\mathbf x}_i$ can be taken, without loss of generality, to be orthonormal so as to form a q-dimensional random vector ${\mathbf x}$ with ${{\mathbb E}\,}\,{\mathbf x}{\mathbf x}^{\top} =I_q$. The $\tilde{{\mathbf y}}(k)$’s are zero mean random variables orthogonal to ${\mathbf x}$. We shall list the linear combinations $ \hat{{\mathbf y}}(k):=\sum f_i(k){\mathbf x}_i$ as the components of an infinite random vector $\hat{{\mathbf y}}$ and likewise for the noise terms $\tilde{{\mathbf y}}(k)$ so that can be written ${\mathbf y}=\hat {{\mathbf y}} + \tilde{{\mathbf y}}$ for short. Which specific characteristics qualify the process $\tilde{{\mathbf y}}$ as “noise” is a nontrivial issue which will be one of the the main themes of this section and will be made precise later (see the definition of idiosyncratic noise below).\
The infinite covariance matrix of the vector ${\mathbf y}$ is formally written as $\Sigma := \mathbb{E} \{ {\mathbf y}{\mathbf y}^{\top} \}$. We let $\Sigma_n$ indicate the top-left $n \times n$ block of $\Sigma$, equal to the covariance matrix of the first $n$ components of ${\mathbf y}$, the corresponding $n$-dimensional vector being denoted by ${\mathbf y}^{n}$. The inequality $\Sigma > 0$ means that all submatrices $\Sigma_n$ of $\Sigma$ are positive definite, which we shall always assume in the following.\
Letting $\hat{\Sigma} := \mathbb{E}\hat{{\mathbf y}} \hat{{\mathbf y}} ^{\top}$ and $\tilde{\Sigma} := \mathbb{E}\tilde{{\mathbf y}} \tilde{{\mathbf y}} ^{\top}$, the orthogonality of the noise term and the factor components implies that $$\label{FADecomp}
\Sigma = \hat{\Sigma} + \tilde{\Sigma}\,,$$ that is, $\Sigma_n = \hat{\Sigma}_n + \tilde{\Sigma}_n \,, \quad
\forall n \in \mathbb{N}\,$. Even imposing $\hat{\Sigma}$ of low rank, this is a priori a highly non unique decomposition. There are situations/examples in which the $\tilde{\Sigma}$ is diagonal as in the static Factor Analysis case, but these situations are exceptional.
Let $\ell^2(\Sigma)$ denote the Hilbert space of infinite sequences $a:= \{a(k),\,k \in {\mathbb Z}_+\}$ such that $\|
a \|^2_\Sigma := a^{\top} \Sigma a < \infty$. When $\Sigma =I$ we use the standard symbol $\ell^2$, denoting the corresponding norm by $\|\cdot\|_2$.
\[Idiosync\] A sequence of elements $\{a_n\}_{n \in {\mathbb Z}_+} \subset \ell^2 \cap \ell^2(\Sigma)$ is an [*averaging sequence*]{} (AS) for ${\mathbf y}$, if $\lim_{n\rightarrow\infty} \| a_n \|_2 = 0$.\
We say that a sequence of random variables ${\mathbf y}$ is [**idiosyncratic**]{} if $\lim_{n\rightarrow\infty} a_n^{\top} {\mathbf y}= 0$ for any averaging sequence $a_n \in \ell^2 \cap \ell^2(\Sigma)$.
Whenever the covariance $\Sigma$ is a bounded operator on $\ell^2$ one has $\ell^2(\Sigma) \subset \ell^2$; in this case an AS can be seen just as a sequence of linear functionals in $\ell^2 $ converging strongly to zero.\
[*Examples :*]{} The sequence of elements in $\ell^2$ $$\label{Aritmean}
a_n = \frac{1}{n} [\,\underbrace{1 \, \ldots
\,1}_{n}\,0\,\ldots\, ]^{\top}$$ is an averaging sequence for any $\Sigma$. On the other hand, let $P_n $ denote the compression of the $n$-th power of the left shift operator to the space $\ell^2$; i.e. $[P_n a] (k)= a(k-n) $ for $k \geq n$ and zero otherwise. Then $\lim _{n \to \infty}\, P_n a=0$ for all $a\in \ell^2$ [@Halmos-61] so that $\{P_n a\}_{n \in {\mathbb Z}_+}$ is an AS for any $a \in \ell^2$.
Let ${\mathbf 1}\!\!1$ be an infinite column vector of $1$’s and let ${\mathbf x}$ be a scalar random variable uncorrelated with $ \tilde{{\mathbf y}}$, a zero-mean weakly stationary ergodic sequence. Consider the process $${\mathbf y}= {\mathbf 1}\!\!1 {\mathbf x}+ \tilde{{\mathbf y}}\,$$ and the averaging sequence . Since $\lim_{n \to \infty}\, \dfrac{1}{n} \sum_{k=1}^n \tilde{{\mathbf y}}(k) = {{\mathbb E}\,}\tilde{{\mathbf y}}(k)= 0$ (limit in $L^2$) we have $
\lim_{n \to \infty}\, \dfrac{1}{n} \sum_{k=1}^n {\mathbf y}(k) = {\mathbf x}\,;
$ hence we can recover the latent factor by averaging. More generally, if $ \tilde{{\mathbf y}}$ is idiosyncratic $\lim_{n\rightarrow \infty} a_n^{\top} \tilde{{\mathbf y}} = 0$ for any averaging sequence and one could recover ${\mathbf x}$ from AS’s such that $\lim_{n\rightarrow \infty} a_n^{\top} {\mathbf 1}\!\!1$ exists and is non zero. $\Box$
The following definition is meant to capture the phenomenon described in the example.
Let ${\mathbf z}\in H({\mathbf y})$. The random variable ${\mathbf z}$ is an [*aggregate (of ${\mathbf y}$)*]{} if there exists an AS $\{a_n\}$ such that $\lim_{n\rightarrow\infty} a_n^{\top}{\mathbf y}={\mathbf z}$. The set of all aggregate random variables in $H({\mathbf y})$ is denoted by $\mathcal{G}({\mathbf y})$.
It is straightforward to check that $\mathcal{G}({\mathbf y})$ is a closed subspace. It is called the [*aggregation subspace*]{} of $H({\mathbf y})$. Clearly, if ${\mathbf y}$ is an idiosyncratic sequence then $\mathcal{G}({\mathbf y}) = \{0\}$. In general it is possible to define an orthogonal decomposition of the type $${\mathbf y}= \mathbb{E}[{\mathbf y}\mid \mathcal{G}({\mathbf y})] + {\mathbf u}\,,$$ where all components $ {\mathbf u}(k)$ are uncorrelated with $\mathcal{G}({\mathbf y})$. The idea behind this decomposition is that, in case $ \mathcal{G}({\mathbf y})$ is finite dimensional, say generated by a q-dimensional random vector ${\mathbf x}$, one may naturally capture a unique decomposition of ${\mathbf y}$ of the type .
Unfortunately however, in general $\mathcal{G}({\mathbf y}) = \{0\}$ does not imply that ${\mathbf y}$ is idiosyncratic. See the example below, inspired to a similar one in [@forni_lippi_2001].
\[Ex2\] Consider a sequence ${\mathbf y}$ with ${\mathbf y}(j) \bot {\mathbf y}(h) \, \forall \, j~\neq~h$ (a possibly non-stationary white noise), and let ${\mathbf z}$ be an aggregate random variable, so that there is an AS $\{a_n\}$ such that $${\mathbf z}= \lim_{n\rightarrow\infty} a_n^{\top}{\mathbf y}=
\lim_{n\rightarrow\infty} \sum_{j=1}^\infty a_{n}(j) {\mathbf y}_j \,.$$ Note that, being ${\mathbf z}\in H({\mathbf y})$ and ${\mathbf y}$ an orthogonal basis of this space, we can uniquely express ${\mathbf z}$ as $${\mathbf z}= \sum_{j=1}^\infty b(j){\mathbf y}(j) \,,$$ and, by uniqueness of the representation, it follows that $\lim_{n\rightarrow\infty} a_{n}(j) = b(j) \, \forall j $. On the other hand, being $a_n$ an AS, the limits of $a_{n}(j) $ must be zero, so that $b(j) = 0$. Hence ${\mathbf z}=0$. Thus a white noise process has always $\mathcal{G}({\mathbf y}) = \{0\}$.\
However if $\{{\mathbf y}(k)\}$ has unbounded variance, the sequence is not idiosyncratic. For example if $\| {\mathbf y}(k) \|^2 = k$, given the AS $$d_n = \frac{1}{\sqrt{n}} [\,\underbrace{0 \, \ldots
\,0\,1}_{n}\,0\,\ldots\, ]^{\top} \,,$$ we have $\| d^{\top}_n {\mathbf y}\| = 1 \, \forall n $. Hence in this case ${\mathbf y}$ is neither aggregate nor idiosyncratic. On the other hand, when $\|{\mathbf y}(k)\| \leq M <\infty$ for all $k$, we have $$\| a_n^{\top} {\mathbf y}\|^2= \sum_{k=0}^{\infty} a_n(k)^2 \|{\mathbf y}(k)\|^2\leq M^2 \|a_n\|_2^2 \rightarrow 0$$ for $n \to \infty$. Hence a white noise process [*with a uniformly bounded variance*]{} (has a trivial aggregation subspace and) is idiosyncratic. $\Box$
The nature of an idiosyncratic sequence is related to certain properties of its covariance matrix. To explain this point, we need to introduce some notations and facts about the eigenvalues of sequences of covariance matrices. Denote by $\lambda_{n,k}(\Sigma)$ the k–th eigenvalue of the $n \times n$ upper left submatrix $\Sigma_n$ of $\Sigma$. The $\lambda_{n,k}(\Sigma)$ are real nonnegative and can be ordered by decreasing magnitude. By Weyl’s theorem [@Stewart-S-90 p. 203], see also [@forni_lippi_2001 Fact M], the k–th eigenvalue of $\Sigma_n$ is a non decreasing function of $n$ and hence has a limit, $\lambda_k(\Sigma)$, which may possibly be equal to $+\infty$. Each such limit is called an [*eigenvalue of $\Sigma$*]{}. These limits however are in general not true eigenvalues, as it is well-known that $\Sigma$ may not have eigenvalues. For example, a bounded symmetric Toeplitz matrix has a purely continuous spectrum [@Hartman-W-54]. Anyway since $\Sigma$ is symmetric and positive, its spectrum lies on the positive half line and its elements can also be ordered. Henceforth we shall denote by $\lambda_1(\Sigma)$ the maximal eigenvalue of $\Sigma$, as defined above, with the convention that $\lambda_1(\Sigma)=+\infty $ when there are infinite eigenvalues. The following result will be instrumental in understanding the structure of idiosyncratic processes.
\[th:Boundedness\] If $\lambda_1(\Sigma)$ is finite, then $\Sigma$ is a bounded operator on $\ell^2$.
Let $\lambda_1(\Sigma_n)$ be the maximal eigenvalue of $\Sigma_n$. Denote the string of the first $n$ elements of an infinite sequence $a$ by $a^n$. Since $$\Sigma_n \leq \lambda_1(\Sigma_n)I_n \leq \lambda_1(\Sigma) I_n$$ where $I_n$ is the $n \times n$ identity matrix and $\lambda_1(\Sigma) <\infty$ by assumption, it follows that for all sequences $x, y \in \ell^2$ $$x^n \Sigma_n y^n \leq \lambda_1(\Sigma) \|x^n\|_2\, \|y^n\|_2\,, {\qquad}n=1,2, \ldots$$ Then the result follows from the theorem in [@Akhiezer-G-61 p. 53].
A strong characterization of idiosyncratic sequences is stated in the following theorem, inspired by [@forni_lippi_2001] after some obvious simplifications. For completeness we shall provide a proof.
\[th:idiosyncratic\] The sequence ${\mathbf y}$ is idiosyncratic if and only if $\lambda_1(\Sigma)$ is finite; equivalently, if and only if its covariance matrix defines a bounded operator on $\ell^2$.
Assume first that $\lim_{n\rightarrow\infty} \lambda_{n,1}(\Sigma) =
+\infty$. Since $\Sigma_n > 0$ is symmetric it has a spectral represenattion $$\label{Diagonaliz}
U^\top_n\Sigma_n U_n = D_n \,,$$ where $U_n$ is orthonormal and $D_n = {\mathrm{diag}}\{\,\lambda_{n,1}(\Sigma),\, \ldots ,\, \lambda_{n,n}(\Sigma) \,\}$. Consider the first column of $U_n$, say $u_1^n$, which is the eigenvector of $\lambda_{n,1}(\Sigma)$ and define the sequence of elements in $\ell^2 \cap \ell^2(\Sigma)$ constructed as $$a_n := \frac{1}{\sqrt{\lambda_{n,1}(\Sigma)}}\begin{bmatrix} ( u_1^{n}) ^{\top} & 0 & \ldots \end{bmatrix}^\top \,, {\qquad}n=1,2,\ldots\,.$$ Since $\lim_{n\rightarrow\infty} \lambda_{n,1}(\Sigma) = +\infty$, this is an AS, for which $$\|a_n^\top {\mathbf y}\|^2 = \frac{1}{ \lambda_{n,1}(\Sigma) } \,(u_1^{n}) ^{\top} \Sigma_n u_1^{n} = 1$$ for every $n$ and hence the sequence ${\mathbf y}$ cannot be idiosyncratic.
Conversely, suppose that $\lambda_1(\Sigma) < +\infty$ and again use the diagonalization . Let $a_n$ be an arbitrary AS and consider the random variable ${\mathbf z}= \lim_{n \rightarrow \infty} a_n^{\top} {\mathbf y}= \lim_{n \rightarrow \infty} a_n^{n\top} {\mathbf y}^{n}$, which has variance $${\mathrm{var}}[{\mathbf z}] = \lim_{n\rightarrow\infty} (a_n^{n})^{\top} U_nD_n U_n^{\top}
a^{n}_n := (d_n^{\,n})^{\top} D_n\, d_n^{\,n} \,,$$ where the vector $d_n^{\,n} := U_n^{\top} a_n^{n}$ is used to form the first $n$ elements of an infinite string, say $d_n$, whose remaining entries are taken equal to those of $a_n$; i.e. $d_n(k)= a_n(k)$ for $k >n$. Clearly $d_n$ is an AS.\
Since $(d_n^{\,n})^{\top} D_n\, d_n^{\,n}= \sum_{k=1}^n \lambda_{n,k}(\Sigma)
d_{n}(k)^2$, one can write $$\begin{aligned}
{\mathrm{var}}[{\mathbf z}] & = \lim_{n\rightarrow\infty} \sum_{i=1}^n \lambda_{n,k}(\Sigma) d_{n}(k)^2 \leq \lim_{n\rightarrow\infty} \lambda_1(\Sigma) \sum_{k=1}^n d_{n}(k)^2 = \lim_{n\rightarrow\infty}\, \lambda_1(\Sigma) \| d_n \|_2^2 = 0\end{aligned}$$ which shows that ${\mathbf y}$ is idiosyncratic.
In particular, since the covariance of a white noise process is diagonal, the covariance of a white noise can be bounded (and therefore ${\mathbf y}$ can be idiosyncratic) only if the variances $\|{\mathbf y}(k)\|^2$ are uniformly bounded. This completes the discussion in Example \[Ex2\].
Let $q$ be a finite integer. A sequence ${\mathbf y}$ is [*purely deterministic of rank $q$*]{} (in short $q$-PD) if $H({\mathbf y})$ has dimension $q$.
Clearly a $q$-PD sequence ${\mathbf y}$ can be seen as a (in general non-stationary) purely deterministic process in the classical sense of the term, see e.g. [@Cramer-61]. Let ${\mathbf x}= {\left[ \begin{matrix}}{\mathbf x}_1 & \ldots & {\mathbf x}_q {\end{matrix} \right]}^{\top}$ be an orthonormal basis in $H({\mathbf y})$. Obviously ${\mathbf y}$ is a $q$-PD random sequence if and only if there is $\infty \times q$ matrix $F= {\left[ \begin{matrix}}f_1&f_2& \ldots& f_q{\end{matrix} \right]}$, such that $$\label{qAggrProc}
{\mathbf y}(k)\, = \sum_{i=1}^{q} \, f_i(k)\, {\mathbf x}_i\,,\qquad
k\in {\mathbb Z}_+\,,$$ where the columns $f_1,\,f_2,\,\ldots f_q$ must be linearly independent, for otherwise the rank of ${\mathbf y}$ would be smaller than $q$.\
We want to relate this concept to the idea of aggregation subspace of ${\mathbf y}$, as defined earlier. In particular we would like to identify ${\mathbf x}$ as an orthonormal basis in $\mathcal{G}({\mathbf y}) $. Quite unfortunately however, there are nontrivial sequences representable in the form which are idiosyncratic (or contain idiosyncratic sequences). See the Example below.
\[Ex3\] Consider a sequence ${\mathbf y}$ whose $k-$th element is $${\mathbf y}(k) = \lambda^k {\mathbf x}\quad,\,|\lambda| < 1,$$ where ${\mathbf x}$ is a zero–mean random variable of positive variance $\sigma^2$. Clearly, ${\mathbf y}$ is 1-PD, its spanned subspace $H({\mathbf y})$ being the one-dimensional space $H({\mathbf x})$. The covariance matrix of the first $n$ components of ${\mathbf y}$ is $$\Sigma_n = \mathbb{E}{\mathbf y}_{n}{\mathbf y}_{n}^{\top} = \sigma^2 \begin{bmatrix}\lambda^2 & \lambda^3 & \ldots & \lambda^{n+1} \\ \lambda^3 & \lambda^4 & \ldots & \lambda^{n+2} \\ \vdots & \vdots &\ddots& \vdots \\
\lambda^{n+1}&\lambda^{n+2} &\ldots & \lambda^{2n} \end{bmatrix}$$ Since ${\mathrm{rank}\,}(\Sigma_n) = 1$ for every $n$, we have $$\begin{aligned}
\lambda_1(\Sigma) = \lim_{n\rightarrow \infty} {\mathrm{tr}}(\Sigma_n) = \lim_{n\rightarrow \infty} \sigma^2\sum_{k=1}^n
\lambda^{2k} = \frac{\sigma^2\lambda^2}{1-\lambda^2} \,,\end{aligned}$$ thus, in force of Theorem \[th:idiosyncratic\], ${\mathbf y}$ is idiosyncratic. Hence there are (non-stationary) $q-$PD sequences which are idiosyncratic.
This is a possibility which we clearly must exclude if the decomposition has to be unique. The question is which properties need to be satisfied by the functions $f_1,\,
f_2,\,\ldots f_q$ for ${\mathbf y}$ to be a $q$-aggregate sequence. One necessary condition is easily found: the $f_i$ [*cannot be in $\ell^2$*]{} since otherwise any sequence of functionals $\{a_n\}$ in $\ell^2$ converging to zero would lead to $$\lim_{n\to \infty} \, a_n^{\top} f_i =0$$ so that $\lim_{n\to \infty} \, a_n^{\top} {\mathbf y}=0$ as well. This is clearly the problem with Example \[Ex3\].\
We shall call a sequence ${\mathbf y}$ [**$q$-aggregate**]{} if its covariance matrix has $q$ nonzero eigenvalues, i.e. ${\mathrm{rank}\,}\, \Sigma_n =q,\; \forall n$, and $\lim_{n \to \infty} \lambda_{n,k}(\Sigma) = +\infty$ for $k=1,\ldots,q$. In short, all nonzero eigenvalues of $\Sigma$ are [*infinite*]{}.\
This condition guarantees uniqueness of the decomposition when $\hat {\mathbf y}$ is $q$-aggregate and $\tilde {\mathbf y}$ is idiosyncratic.
\[Prop:uniqueness\] A $q$-aggregate sequence $\hat {\mathbf y}$ can be idiosyncratic only if it is the zero sequence.
This follows trivially from Theorem \[th:idiosyncratic\]. If $q>0$ the maximal eigenvalue of the covariance matrix of $\hat {\mathbf y}$ is $+\infty$ by definition.
Of course the question is under what conditions the $q$ eigenvalues of $\hat{\Sigma}$ may tend to infinity. Theorem \[Thm:Strong\] below provides an answer.
Let $$\label{eq:condition_tilde}
\tilde{f}_i^n := f_i^n - \Pi[\, f_i^n \,|\,\mathcal{F}_i^n]$$ where $\Pi$ is the orthogonal projection onto the Euclidean space $ \mathcal{F}^n_i = {\mathrm{span}\,}\{f_j^n ,\,j\neq i \, \} $ of dimension $q-1$.\
The vectors $f_i, \,i=1,\ldots,q$ in ${\mathbb R}^{\infty}$ are [**strongly linearly independent**]{} if $$\label{eq:condition}
\lim_{n\rightarrow\infty}\|\tilde{f}_i^n\|_2 = +\infty\,{\qquad}\,i=1,\ldots,q\,.$$
In a sense, the tails of two strongly linearly independent vectors in ${\mathbb R}^{\infty}$ cannot get “too close” asymptotically.
\[Thm:Strong\] Let ${\mathbf y}$ be a $q-$PD sequence, i.e. let $${\mathbf y}(k)\, = \sum_{i=1}^{q} \, f_i(k)\, {\mathbf x}_i\,,\qquad
k\in {\mathbb Z}_+\,;$$ then ${\mathbf y}$ is $q-$aggregate if and only if, the vectors $f_i, \,i=1,\ldots,q$ are strongly linearly independent.
First we prove the sufficiency of condition . Let $k$ be a fixed positive constant and let $f_1$ be such that $$\lim_{n\rightarrow\infty}\| f_1^n -
\Pi [f_1^n\,|\,\mathcal{F}_1^n] \|_2 = k^{\frac{1}{2}} < +\infty \,.$$ Let $$\label{alphas}
\tilde{f}_1^n = f_1^n - \Pi[f_1^n\,|\,\mathcal{F}_1^n] = f_1^n - \alpha_2^n f_2^n - \ldots - \alpha_q^n f_q^n \,;$$ whence, defining $\tilde{F}^n := \begin{bmatrix} \tilde{f}_1^n
& f_2^n & \ldots & f_q^n \end{bmatrix}$, one can write $\tilde{F}^n = F^n T^n$, with $T^n$ is a full rank matrix of the form $$\label{eq:matrixT}
T^n = \begin{bmatrix} 1 & 0 \\ -\alpha_n &I_{q-1} \end{bmatrix} \,,$$ where $\alpha_n := \begin{bmatrix} \alpha_2^n & \ldots& \alpha_q^n
\end{bmatrix}^\top$. Since $\tilde{f}_1^n \bot f_i^n $, $i \neq 1$, the Gramian matrix of $\tilde{F}^n$ is block diagonal, $$\tilde{F}^{n\top}\tilde{F}^n = \begin{bmatrix}
\|\tilde{f}_1^n \|^2 & 0 \\ 0 & A_n \end{bmatrix} \,,$$ where $A_n$ is a positive definite matrix whose eigenvalues tend to infinity as $n$ increases. Note that the spectrum of $\tilde{F}^{n\top}\tilde{F}^n $ contains the eigenvalue $\|\tilde{f}_1^n \|^2$, which, for $n \rightarrow \infty$, converges to $k < +\infty$. Now, let us compute the trace of both sides of the identity $T^n(\tilde{F}^{n\top}\tilde{F}^n)^{-1}T^{n \top}=(F^{n\top}F^n)^{-1}$ obtaining $$\begin{aligned}
{\mathrm{tr}}\left[(F^{n\top}F^n)^{-1}\right] & ={\mathrm{tr}}\left[T^n(\tilde{F}^{n\top}\tilde{F}^n)^{-1}T^{n\top}\right]
= {\mathrm{tr}}\left[T^{n\top} T^n(\tilde{F}^{n\top}\tilde{F}^n)^{-1}\right] \nonumber \\
& = {\mathrm{tr}}\begin{bmatrix} 1 + \| \alpha_n \|^2 & -\alpha_n^\top \nonumber\\
-\alpha_n & I_{q-1} \end{bmatrix} \begin{bmatrix} k^{-1} & 0 \\ 0 &
A_n^{-1} \end{bmatrix} \nonumber\\
& = {\mathrm{tr}}\begin{bmatrix} k^{-1}(1+\|\alpha_n\|^2) & -\alpha_n^\top A_n^{-1} \\ - \alpha_n k^{-1} & A_n^{-1} \end{bmatrix}
=k^{-1}(1+\|\alpha_n\|^2) + {\mathrm{tr}}\left[A_n^{-1}\right]\end{aligned}$$ Since the eigenvalues of $A_n$ tend to infinity, those of $A_n^{-1}$ tend to zero, while, for every $n$ we have $k^{-1}(1+\|\alpha_n\|^2) >0$. Thus, one eigenvalue of $(F^{n\top}F^n)^{-1}$ is bounded below by a fixed constant as $n$ tends to infinity. Hence we conclude that one eigenvalue of $F^{n\top}F^n$ remains bounded as $
n$ tends to infinity, which is a contradiction.
For the necessity, we define $f_i^{n_1,n_2}:=\begin{bmatrix}f_i(n_1)&\ldots&f_i(n_2)\end{bmatrix}^\top$ and observe that condition implies that $$\lim_{n\rightarrow\infty}\| f_i^{n_1,n} -
\Pi[f_i^{n_1,n}\,|\,\mathcal{F}_i^{n_1,n}] \|_2 = +\infty \,,$$ for every index $i = 1,\,\ldots,\,q$ and natural number $n_1$. Moreover, by definition of limit, we have that for every $n_1 \in
\mathbb{N}$ and $K \in \mathbb{R}_{+}$ there exists an integer $n_2$ such that the inequality (with an obvious meaning of the symbols) $$\label{eq:ineq}
\| f_i^{n_1,n_2} - \Pi[f_i^{n_1,n_2}\,|\,\mathcal{F}_i^{n_1,n_2}]
\|^2_2 \geq K$$ holds for every $i = 1,\,\ldots,\,q$.
Now, consider the sequence generated by the $q$-th eigenvalue of the matrix $F^{n\top}F^n$, say $\{\lambda_q^n\,;\,n\in\mathbb{N}\}$. Our goal is to show that for every natural $n_1$ and arbitrary constant $c > 0$ there exists a natural number $n_2$ such that $\lambda_q^{n_2} \geq \lambda_q^{n_1} + c$, so that $\lim_{n\rightarrow\infty} \lambda_q^n = +\infty$. To this end, fix $c$ and, for a generic $n_1$, consider the normalized eigenvector of the $q$-th eigenvalue of the matrix $F^{n_2\top}F^{n_2}$, say $v_q^{n_2}$. Since for every $n_2 > n_1$ it holds that $$F^{n_2\top}F^{n_2} = F^{n_1\top}F^{n_1} + F^{n_1,n_2\top}F^{n_1,n_2}
\,,$$ we can write $$\lambda_q^{n_2} = v_q^{n_2 \top} F^{n_1\top}F^{n_1} v_q^{n_2} +
v_q^{n_2 \top} F^{n_1,n_2\top}F^{n_1,n_2} v_q^{n_2} \,.$$ Consider the first term on the right side of this identity; expressing $v_q^{n_2}$ as a linear combination of the eigenvectors of $F^{n_1\top}F^{n_1}$, i.e. $v_q^{n_2} = \alpha_1 v_1^{n_1} +
\ldots + \alpha_q v_q^{n_1}$, the orthogonality of these eigenvectors implies that $$v_q^{n_2 \top} F^{n_1\top}F^{n_1} v_q^{n_2} = \lambda_1^{n_1}
\alpha_1^2 + \ldots + \lambda_q^{n_1} \alpha_q^2
\geq \lambda_q^{n_1} \sum_{i=1}^q \alpha_i^2 = \lambda_q^{n_1} \,,$$ so that $$\label{eq:parziale}
\lambda_q^{n_2} \geq \lambda_q^{n_1} + v_q^{n_2 \top}
F^{n_1,n_2\top}F^{n_1,n_2} v_q^{n_2} \,.$$ Now we have to show that we can always find an integer $n_2$ such that the quantity $$v_q^{n_2 \top} F^{n_1,n_2\top}F^{n_1,n_2}
v_q^{n_2}$$ can be chosen arbitrarily large, i.e. greater or equal to the previously fixed constant $c$ . To this end, take $n_2$ such that for every $i = 1,\,\ldots,\,q$ the inequality holds, with $K = c\sqrt{q}$. Then, there is an index $i$ such that the $i$-th component of the norm one vector $ v_q^{n_2} =
\begin{bmatrix} w_1 & \ldots & w_q \end{bmatrix}^\top$, satisfies the inequality $w_i \geq \frac{1}{\sqrt{q}}$. Without loss of generality we may and shall assume that $i = 1$. Let $\alpha_2 \ldots \alpha_q$ be defined as in and set $$\label{eq:cambio_base}
\tilde{f}_1^{n_1,n_2} := f_1^{n_1,n_2} - \alpha_2 f_2^{n_1,n_2} -
\ldots - \alpha_q f_q^{n_1,n_2} \,,$$ so that we have $$\label{eq:prod}
v_q^{n_2 \top} F^{n_1,n_2\top}F^{n_1,n_2} v_q^{n_2} = v_q^{n_2 \top}
T^{n \top} \begin{bmatrix} \|\tilde{f}_1^{n_1,n_2} \|^2 & 0 \\ 0 & A_n \end{bmatrix} T^n v_q^{n_2} \,,$$ where $T^n$ has the same structure as in . Now, observe that $$T^n v_q^{n_2} = \begin{bmatrix} w_1 & -\alpha_2 w_1 + w_2 & \ldots &
-\alpha_q w_1 + w_q \end{bmatrix}^\top \,,$$ which implies that is equal to $w_1^2
\|\tilde{f}_1^{n_1,n_2} \|^2 + Q ,$ where $Q$ is a positive constant. Hence, from we have $v_q^{n_2
\top} F^{n_1,n_2\top}F^{n_1,n_2} v_q^{n_2} > c$ and hence, recalling , $$\lambda_q^{n_2} \geq \lambda_q^{n_1} + c \,.$$ which proves the theorem.
Consider the following $2-$PD sequence $
{\mathbf y}(k) := \sum_{i=1}^{2} \, f_i(k)\, {\mathbf x}_i
$\
with $$f_1(k) = 1 \quad \mbox{for all } k \,,\quad\quad f_2(k) = 1 - \left(\frac{1}{2}\right)^k$$ It is not difficult to check that this sequence does not satisfy condition . We shall show that this sequence is not 2-aggregate. The Gramian matrix of the functions $f_1,f_2$ restricted to $[1,\, n]$ is $$F^{n\top} F^n = \begin{bmatrix} \|f_1^n\|_2^2 & \langle f_1^n,\,f_2^n \rangle_2 \\
\langle f_1^n,\,f_2^n \rangle_2 & \|f_2^n\|_2^2 \end{bmatrix}$$ and it can be seen that as $n \rightarrow \infty$, the second eigenvalue converges to $\frac{5}{3}$. Hence one eigenvalue of the covariance matrix of ${\mathbf y}$ is finite and the sequence is not 2-aggregate. $\Box$
GFA representations: Existence and uniqueness {#GFA}
==============================================
We eventually come to a precise definition of the basic object of our study. The following is the static version of a similar definition of [@forni_lippi_2001] for the dynamic setting.
A random sequence ${\mathbf y}$ is a [**$q-$factor sequence** ]{} ($q-$FS) if it can be written as an orthogonal sum $$\label{genFA}
{\mathbf y}(k) = \sum_{i=1}^{q} f_i(k){\mathbf x}_i + \tilde{{\mathbf y}}(k)\,,{\qquad}\, k= 0,1,2, \ldots$$ where $\hat {\mathbf y}:= \sum f_i {\mathbf x}_i $ is a $q$-aggregate sequence and $\tilde{{\mathbf y}}$ is idiosyncratic and orthogonal to ${\mathbf x}$. The representation is called a [**Generalized Factor Analysis (GFA) representation of ${\mathbf y}$ with $q$ factors.**]{}
The crucial question is now which random sequences are $q-$FS. A first step is to discuss the problem for covariance matrices.
The covariance $\Sigma$ has a GFA decomposition of rank $q$ if it can be decomposed as the sum of a matrix $\tilde{\Sigma}$ which is a bounded operator in $\ell^2$ and a ${\mathrm{rank}\,}\; q$ perturbation $\hat{\Sigma}=F F^{\top}$ where $F\in {\mathbb R}^{\infty \times q}$ has strongly linearly independent columns.
Chamberlain and Rothschild [@Chamberlain-R-83 Theorem 4] provide a criterion for a GFA decomposition based on separating the bounded from the unbounded eigenvalues of $\Sigma$. The criterion has been extended by Forni and Lippi [@forni_lippi_2001] to the dynamic case.
\[Chamberlain-Rothschild\]\[CovCond\] If and only if for $n\to \infty$, $\Sigma_n$ has $q$ [**unbounded eigenvalues**]{} and $\lambda_{q+1}(\Sigma_n)$ stays bounded, then $\Sigma$ has a GFA decomposition of rank $q$: $$\label{CovGFA}
\Sigma=F F^{\top} + \tilde{\Sigma}\,,{\qquad}\text{with} {\quad}F= {\left[ \begin{matrix}}f_1&\ldots &f_q{\end{matrix} \right]}\,,\;\; f_i \in {\mathbb R}^{\infty}$$ The GFA decomposition of $\Sigma$ is unique.
Note that there may well be sequences (of positive symmetric) $\Sigma_n$ for which [*all eigenvalues*]{} tend to infinity. In this case there is no GFA decomposition. When it applies, the criterion can be seen as a limit of the well-known rule of separating “large” from “small” eigenvalues in Principal Components Analysis. Let $f^{n}_{i} \in {\mathbb R}^{n}\,;\, i=1,\ldots,q$ be the eigenvectors corresponding to the $q$ (ordered) eigenvalues of $\Sigma_n$ which increase without bound when $n\to \infty$. We normalize these eigenvectors in such a way that $F_n:= {\left[ \begin{matrix}}f^{n}_{1} & \ldots & f^{n}_{q}{\end{matrix} \right]}$ yields $\hat{\Sigma}_n = F_nF_n^{\top}$. Then $$\lim_{n\to \infty} F_nF_n^{\top}= F F^{\top}\,.$$ Although the usual orthogonality of the $f^{n}_{i}$ in PCA does not make sense in infinite dimensions as the limit eigenvectors do not belong to $\ell^2$, one may however interpret the strong linear independence condition as a limit of the orthogonality holding for finite $n$. Hence we can (asymptotically) get $q$ and $F$ by a limit PCA procedure on the sequence $ \Sigma_n$.
Trivially, if a random sequence ${\mathbf y}$ admits a GFA representation then its covariance matrix has a GFA decomposition. On the other hand, assume we are given a GFA decomposition $\hat{\Sigma}+\tilde{\Sigma}$ of an infinite covariance $\Sigma$. How do we find the hidden variables in the representation ${\mathbf y}= F{\mathbf x}+\tilde {\mathbf y}$?\
We can answer this question under the constraint that both ${\mathbf x}$ and $\tilde{{\mathbf y}}$ belong to $H({\mathbf y})$. Models of this kind are called [*internal*]{} in stochastic realization.
Assume that its covariance matrix $\Sigma$ has a GFA decomposition of rank $q$. Then ${\mathbf y}$ has a GFA representation with $q$ factors where both ${\mathbf x}$ and $\tilde {\mathbf y}$ have components in $H({\mathbf y})$.
By a standard Q-R factorization we can orthogonalize the columns of $F_n$, $${\left[ \begin{matrix}}f_1^{n} &f_2^{n}& \ldots&f_q^{n}{\end{matrix} \right]}= {\left[ \begin{matrix}}g_1^n & g_2^n & \ldots & g_q^n{\end{matrix} \right]}{\left[ \begin{matrix}}1& r_{1,2}& r_{1,3}& \ldots & r_{1,q}\\
0 & 1 & r_{2,3}& \ldots & r_{2,q}\\
0 & 0 &1 & \ddots & r_{3,q} \\
\dots & \dots & \dots &\ddots &\dots \\
0 & 0 & 0& \ldots & 1{\end{matrix} \right]}$$ which we shall write compactly as $$\label{Q-Rfact}
F_n = Q_n R_n$$ where $Q_n := \begin{bmatrix} g_1^n & g_2^n & \ldots & g_q^n \end{bmatrix}$ has orthogonal columns. It is well-known that each $g_{i}^n$ can be obtained by a sequential Gram-Schmidt orthogonalization procedure as the difference of $f_i^{n} $ with its projection onto the subspace $ {\mathrm{span}\,}\{f_j^n ,\,j< i \, \} \subset \mathcal{F}^n_i $. Hence $\|g_{i}^n\| \geq \|\tilde{f}_i^{n}\|$ and hence, by assumption, tends to $\infty$ when $n\to \infty$.\
Next, define $$a_{i,n}^{\top}:= {{\displaystyle\frac{1}{\| g_i^n\|_2^2}}}\, {\left[ \begin{matrix}}g_i^n(1) & g_i^n (2) & \ldots& g_i^n(n) & 0& \ldots{\end{matrix} \right]}$$ where the $g_i^n$’s are as defined above. Since $\|g_i^n\|_2 \to \infty$ with $n$, we have $\| a_{i,n}\|_2= 1/\|g_i^n\|_2 \, \rightarrow 0$ as $n \to \infty$. Hence $a_{i,n}$ is an AS.\
Note that we can express each $f_i^{n}$ as $ f_i^{n} = g_i^n +\sum_{j=1}^{i-1} r_{j,i} g_j^n$ so that $$a_{i,n}^{\top} f_i= {{\displaystyle\frac{1}{\| g_i^n\|_2^2}}}\,\| g_i^n\|_2^2 \,=\,1$$ for all $n$ large enough and by a similar calculation one can easily check that $a_{i,n}^{\top} f_j= 0 $, for all $j<i$. With these $a_{i,n}$ construct a sequence of $q \times \infty$ matrices $$A_n := {\left[ \begin{matrix}}a_{1,n}^{\top} \\ \dots \\ a_{q,n}^{\top} {\end{matrix} \right]}$$ which provides an asymptotic left-inverse of $F$, in the sense that $\lim _{n \to \infty}\, A_n F= R$, where $R $ is the limit of a sequence of $q\times q$ matrices all of which are upper triangular with ones on the main diagonal. Next, define the random vector ${\mathbf z}_n := A_n {\mathbf y}$ which converges as $n \to \infty$ to a $q$-dimensional ${\mathbf z}$ whose components must belong to $ \mathcal{G}({\mathbf y})$. These $q$ components form in fact a basis for $ \mathcal{G}({\mathbf y})$ as the covariance ${{\mathbb E}\,}{\mathbf z}_n {\mathbf z}_n^{\top}$ converges to $RR^{\top}$ which is non singular. From this, one can easily get an orthonormal basis ${\mathbf x}$, in $H(\hat {\mathbf y})$. Hence, since $F$ is known, we can form $\hat {\mathbf y}= F {\mathbf x}$ and letting $\tilde {\mathbf y}:= {\mathbf y}- \hat {\mathbf y}$ does yield a GFA representation of ${\mathbf y}$ inducing the given GFA decomposition of $\Sigma$. Uniqueness is then guaranteed in force of Proposition \[Prop:uniqueness\].
Short and long distance interaction {#short-and-long-distance-interaction .unnumbered}
-----------------------------------
At this point we have collected enough information on the model structure to suggest an interpretation of GFA models. We shall imagine a scenario of an ensemble of infinitely many agents distributed in space generating the random variables $\{{\mathbf y}(k)= \hat{{\mathbf y}}(k) + \tilde{{\mathbf y}}(k)\;;\; k=1,2,\ldots\}$ and interacting in a random fashion.\
The idiosyncratic covariances $ \tilde\sigma(k,j)= {{\mathbb E}\,}\tilde{\mathbf y}(k) \tilde{\mathbf y}(j)\, $ measure the mutual influence of neighboring units noises $\tilde{\mathbf y}(k),\,\tilde{\mathbf y}(j)$. Since $ \tilde{\Sigma}$ is a bounded operator in $\ell^2$, it is a known fact [@Akhiezer-G-61 Section 26] that $ \tilde\sigma(k,j)\rightarrow 0$ as $|k-j|\rightarrow \infty$ so in a sense the idyosincratic component $\tilde{\mathbf y}$ of a GFA representation models only [*short range* ]{} interaction among the agents, as $\tilde\sigma(k,j)$ is decaying with distance. Agents which are far away from each other essentially do not resent of mutual influence.\
On the other hand, ${{\mathbb E}\,}\hat{{\mathbf y}}(k)\hat{{\mathbf y}}(j)= \sum_{i} f_i(k)f_i(j)$ and the elements of the column vectors $f_i $ cannot be in $\ell^2$. In particular, as stated in the proposition below, if the variances of the random variables ${\mathbf y}(k)$ are uniformly bounded $f_i \in \ell^{\infty}$.
\[BddVar\] If ${\mathbf y}$ is a $q-$FS and has uniformly bounded variance, then the $f_i$’s are uniformly bounded sequences (i.e. belong to the space $\ell^{\infty}$).
The statement follows since $\|\hat{{\mathbf y}}(k)\|^2\leq M^2$, which is the same as $ \sum_{i=1}^{q} f_i(k)^2 \leq M^2$ and hence $|f_i(k)|\leq M$ for all $k$’s.
Hence since the components $f_i(k)$ do not decay with distance, the products $f_i(k)f_i(j)$ generically do not vanish when $|k-j|\rightarrow \infty$. Therefore the factor loadings describe “long range” correlation between the factor components and the $\hat{{\mathbf y}}$ component of ${\mathbf y}$ can be interpreted as variables modeling the [*long range interaction*]{} among agents. In this sense $\hat{{\mathbf y}}$ models a [*collective behavior*]{} of the ensemble.
Stationary sequences and the Wold decomposition {#Sec:Wold}
===============================================
As we have just seen, non-stationarity may bring in some pathologies which seem to be difficult to rule out. We consider now the special case in which the sequence ${\mathbf y}$, defined on ${\mathbb Z}_{+}$, is (weakly) stationary; i.e. $\mathbb{E}{\mathbf y}(k) {\mathbf y}(j) =\sigma(k-j)$ for $k,j \geq 0$. Let $H_{k}({\mathbf y})$ be the closed linear span of all random variables $\{{\mathbf y}(s)\,;\, s \geq k\}$. Introducing the [*remote future subspace*]{} of ${\mathbf y}$: $$\label{InfFut}
H_{\infty}({\mathbf y}) = \bigcap_{k \geq 0} H_{k}({\mathbf y})\,,$$ the sequence of orthogonal wandering subspaces $E_k := H_{k}({\mathbf y}) \ominus H_{k+1}({\mathbf y})$ and their orthogonal direct sum $$\check{H} ({\mathbf y})= \bigoplus_{k\geq 0}\, E_k\,,$$ it is well known, see e.g. [@Doob-53; @Rozanov-67; @Halmos-61], that one has the orthogonal decomposition $$\label{InfFut}
{\mathbf y}=\hat {{\mathbf y}} + \check{{\mathbf y}}\,,\qquad \hat {{\mathbf y}}(k) \in H_{\infty}({\mathbf y})\,{\quad}\check{{\mathbf y}}(k) \in \check{H} ({\mathbf y})$$ for all $k \in {\mathbb Z}_{+}$, the component $ \hat {{\mathbf y}}$ being the purely deterministic (PD), while $\check{{\mathbf y}}$ the purely non-deterministic (PND) components. The two sequences are orthogonal and uniquely determined. Furthermore, it is well known that $\check{{\mathbf y}}$ has an absolutely continuous spectrum with a spectral density function, say $S_y(\omega)$ satisfying the log-integrability condition $\int \log S_y(\omega)\, d\omega> -\infty$, while the spectral distribution of $\hat {{\mathbf y}}$ is singular with respect to Lebesgue measure (for example consisting only of jumps) possibly together with a spectral density such that $\int \log S_y(\omega)\, d\omega= -\infty$, compare e.g. [@Rozanov-67].
In this section we want to give an interpretation of the decomposition in the light of the Wold decomposition. First we prove the following two lemmas.
\[theo:PND\_idio\] Let ${\mathbf y}$ be stationary and assume it has an absolutely continuous spectrum with a bounded spectral density; i.e. $$\label{BoundedSpec}
S_y(\omega) \in L^\infty([-\pi,\,\pi])\,.$$ Then ${\mathbf y}$ is idiosyncratic. In particular, PND sequences with a bounded spectral density are idiosyncratic sequences.
By a well known theorem of Szegö [@Grenander-S-84 p.65] se also [@Hartman-W-54], $\Sigma$ is a bounded Toeplitz operator, thus for any AS $a_n$, $$\|a_n^{\top} {\mathbf y}\|^2 = \|a_n \|^2_\Sigma = a_n^{\top}\Sigma a_n \leq
\|\Sigma\|\, \|a_n\|_2^2 \,.$$ and since $ \|a_n\|_2^2 \rightarrow 0$, $\|a_n^{\top} {\mathbf y}\|^2\rightarrow 0$, and ${\mathbf y}$ is idiosyncratic.
Let ${\mathbf y}$ be a stationary sequence with a bounded spectral density, then $$\mathcal{G}({\mathbf y}) \subseteq H_\infty({\mathbf y}) \,.$$
Assume that ${\mathbf z}\in \mathcal{G}({\mathbf y})$. Then there exists an AS $a_n$ such that ${\mathbf z}= \lim_n a_n^{\top} {\mathbf y}$. Applying the Wold decomposition we obtain $${\mathbf z}= \lim_{n\rightarrow \infty} a_n^{\top} {\mathbf y}= \lim_{n\rightarrow \infty} a_n^{\top} \hat{{\mathbf y}} + \lim_{n\rightarrow \infty} a_n^{\top} \check{{\mathbf y}} \,.$$ By Lemma \[theo:PND\_idio\], the PND part vanishes as $n$ tends to infinity, thus ${\mathbf z}\in H_\infty({\mathbf y})$.
Note that the statement holds in particular for PD processes with a singular spectrum, as in this case $S_y(\omega)\equiv 0$. The converse inclusion, i.e. $ H_\infty({\mathbf y}) \subseteq \mathcal{G}({\mathbf y})$, is in general not true. However, for stationary sequences with a [*finite dimensional remote future*]{}, we can state the following.
\[MainThm\] Assume that ${\mathbf y}$ is a stationary sequence with a bounded spectral density and that $\dim
H_\infty({\mathbf y})~< ~\infty$. Then $H_\infty({\mathbf y}) \equiv \mathcal{G}({\mathbf y})$.
It is sufficient to show that $ H_\infty({\mathbf y}) \subseteq
\mathcal{G}({\mathbf y})$.\
Let $\dim \,H_\infty({\mathbf y})= q$. By assumption $H_{k}({\mathbf y}) \supseteq H_\infty({\mathbf y})$ has dimension greater than or equal to $q$ for all $k \geq 0$. It follows that for any $k$, the random variables $ {\mathbf y}(k+1),\ldots,{\mathbf y}(k+q)$ must be linearly independent. For otherwise the $q\times q$ covariance matrix $$\Sigma_q := {{\mathbb E}\,}{\left[ \begin{matrix}}{\mathbf y}(k+1)\\ \dots \\ {\mathbf y}(k+q){\end{matrix} \right]}{\left[ \begin{matrix}}{\mathbf y}(k+1)\\ \dots \\ {\mathbf y}(k+q){\end{matrix} \right]}^{\top}$$ would be singular of rank $r <q$ and hence, because of the Toeplitz structure, one would have ${\mathrm{rank}\,}\Sigma_n=r <q$ for all $n\geq q$, which implies that one can extract only $r$ linearly independent random variables from an arbitrarily long string of random variables of the process. This in turn would imply $\dim H_\infty({\mathbf y})=r <q$ contrary to our assumption. Therefore $${\mathrm{span}\,}\{{\mathbf y}(k+1),\ldots,{\mathbf y}(k+q)\} \supseteq H_\infty({\mathbf y})\,,{\qquad}\text {for all}\;\; k$$ and for any ${\mathbf z}\in H_\infty({\mathbf y})$ there is a nonzero $b_k \in {\mathbb R}^{q}$ such that $${\mathbf z}= b_k^{\top} \, {\left[ \begin{matrix}}\hat {\mathbf y}(k+1)\\ \dots \\ \hat {\mathbf y}(k+q){\end{matrix} \right]}\,,$$ where $\hat {\mathbf y}(k+1),\,\ldots,\,\hat {\mathbf y}(k+q)$ are the projections of ${\mathbf y}(k+1),\,\ldots,\,{\mathbf y}(k+q)$ onto $H_\infty({\mathbf y})$. Furthermore, the Euclidean norm $\|b_k\| $ is the same for all $k$ because of stationarity. Hence, choosing $k=0, q, 2q , \ldots,(n-1)q$, one also has $${\mathbf z}= {{\displaystyle\frac{1}{n}}} \,[\,\underbrace { \begin{matrix} b_0^{\top}& b_1^{\top}& \ldots &b_{n-1}^{\top}\end{matrix}}_{n} \begin{matrix} 0& \ldots& 0\end{matrix} \,]\,\hat {\mathbf y}\,:= a_n ^{\top}\,\hat {\mathbf y}$$ where the sequence $\{a_n,\,n \in{\mathbb Z}_+\}$ is clearly an AS. It follows that $$a_n^{\top}{\mathbf y}= \lim_{n\rightarrow \infty} a_n^{\top}{\mathbf y}= \lim_{n\rightarrow \infty} a_n^{\top} \hat {\mathbf y}+ \lim_{n\rightarrow \infty} a_n^{\top} \check {\mathbf y}= {\mathbf z}\,,$$ where the last identity is a consequence of Lemma \[theo:PND\_idio\]. Therefore ${\mathbf z}\in \mathcal{G}({\mathbf y})$.
Hence,
\[mainThm1\] Every stationary sequence with a bounded spectral density and remote future space of dimension $q$ is a $q-$factor sequence. It admits a unique generalized factor analysis representation where $\hat {\mathbf y}$ is the purely deterministic and $\tilde {\mathbf y}$ is the purely non-deterministic component of ${\mathbf y}$.
Note in particular that the spectral density of $\tilde {\mathbf y}$ must necessarily satisfy the log-integrability condition.\
When $H_\infty({\mathbf y})$ is finite dimensional, the PD component of a stationary process has a special structure, namely $$\label{PDsignal}
\hat {\mathbf y}(k) = \sum_{i=1}^\nu {\mathbf v}_i \cos \omega_i k + {\mathbf w}_i \sin \omega_i k \,,$$ where $e^{\pm j\omega_i}\,,\, i=1,2,\ldots,q $ are the $q$ eigenvalues of the unitary shift operator of the process [@Rozanov-67]. The $\omega_i$ are distinct real frequencies in $[0,\, \pi)$ and ${\mathbf v}_i$ and ${\mathbf w}_i$ are mutually uncorrelated zero-mean random variables with ${\mathrm{var}}[{\mathbf v}_i] = {\mathrm{var}}[{\mathbf w}_i]$ which span the subspace $H(\hat {\mathbf y})\equiv H_\infty({\mathbf y})$.
In the following proposition, we show how to construct AS’s that generate a basis in the finite-dimensional remote future space.
The latent factors of a stationary $q$-factor sequence can be recovered using averaging sequences $\{a_{i,n}\}_{n \in
\mathbb{N}}$ of the type $$\label{eq:sin}
a_{i,n}(k) = \left\{\begin{array}{ll}\dfrac{1}{n} \sin \omega_i k & k \leq n \\
0 & k > n \end{array} \right.$$ or $$\label{eq:cos}
a_{i,n}(k) = \left\{\begin{array}{ll}\dfrac{1}{n} \cos \omega_i k & k \leq n \\
0 & k > n \end{array} \right. \,,$$ by letting $\omega_i$ vary on the set of proper frequencies of the signal .
Consider the AS $\{a_n\}_{n \in \mathbb{N}}$ of , with a fixed frequency $\omega_i = \omega_p$, $p \in \{1,\,\ldots,\,\nu\}$ and apply it to the sequence ${\mathbf y}$. While the idiosyncratic (PND) part vanishes asymptotically, the $q$-aggregate (PD) component yields the sequence of random variables $$\begin{aligned}
{\mathbf z}_n & = a_n^\top \hat {\mathbf y}= \sum_{k=1}^n
a_n(k) \hat {\mathbf y}(k) = \frac{1}{n} \sum_{k=1}^n \Big[ \sin \omega_pk \sum_{i=1}^\nu ({\mathbf v}_i \cos \omega_ik + {\mathbf w}_i \sin \omega_ik)\Big]\\
& = \frac{1}{n} \sum_{k=1}^n \Big[\sum_{i=1,i\neq p}^{\nu} ({\mathbf v}_i \sin \omega_pk \cos \omega_ik + {\mathbf w}_i \sin \omega_pk \sin \omega_ik) + {\mathbf v}_p \sin \omega_pk \cos \omega_pk+ {\mathbf w}_p \sin^2 \omega_pk \Big] \nonumber\end{aligned}$$ It is well-known and not difficult to check directly, using elementary trigonometric identities such as $\sin \alpha \cos \beta= \sin(\alpha + \beta) + \sin(\alpha-\beta)$ and the formula $$\left| \frac{1}{n} \sum_{k=1}^n e^{j\omega k}\right| = \frac{1}{n} \left|e^{j\omega }{{\displaystyle\frac{1-e^{j\omega n}}{1- e^{j\omega }}}}\right|\leq \frac{1}{n} \left| {{\displaystyle\frac{1 }{\sin \omega/2 }}} \right|$$ that all time averages of products of $\sin$ and $\cos$ functions in this sum vanish asymptotically except for the $ \sin^2$ term, which has the limit $$\lim_{n\rightarrow \infty} \frac{1}{n} \sum_{k=1}^n {\mathbf w}_p \sin^2 \omega_pk =
\frac{{\mathbf w}_p}{ 2} \,,$$ which is one of the latent factors. Similarly, the random variables ${\mathbf v}_i$, associated with cosine-type oscillations, can be recovered using averaging sequences of the type .
Obviously one can obtain arbitrary linear combinations $ \sum_{i=1}^\nu c_i {\mathbf v}_i + d_i {\mathbf w}_i $ by properly combining the AS’s and .
Discussion {#discussion .unnumbered}
----------
We have shown that there is a natural interpretation of generalized factor analysis models in terms of the Wold decomposition of stationary sequences. A stationary sequence admits a generalized factor analysis representation if and only if its spectral density is bounded and the remote future space is finite dimensional. Both conditions are necessary since a PD stationary process has a finite factor representation if and only if its remote future has finite dimension. On the other hand there are stationary processes with a finite dimensional remote future space, whose PND component has an unbounded spectral density. It follows from Szegö’s theorem that $\tilde \Sigma$ is an unbounded operator and these processes are neither aggregate nor idiosyncratic.
In the classical papers [@Chamberlain-R-83; @forni_lippi_2001], stationarity with respect to the cross-sectional (space) index is not assumed. However without stationarity, there may be random sequences which fail to satisfy the eigenvalue conditions of Theorem \[CovCond\] and do not admit a generalized factor analysis representation. A precise characterization of which class of non-stationary sequences admits a GFA representation seems still to be an open problem.
GFA models of Random Fields {#Sec:RandFields}
===========================
We come back to the question raised in section \[ProblemSect\] namely when does a second order random field have a flocking component and how to extract it from sample measurements of ${\mathbf y}(k,t)$. A simple class of random fields for which this question can be answered positively is the class of separable space-time processes $$\label{multRF}
{\mathbf y}(k,t)= {\mathbf v}(k) {\mathbf u}(t)$$ which are the product of a space, ${\mathbf v}(k)$, and time component, ${\mathbf u}(t)$, both zero mean and with finite variance. This model can be generalized, for example making both ${\mathbf v}(k)$ and ${\mathbf u}(t)$ vector-valued but this would require extending our static theory in the preceding sections to vector-valued processes as well. Although this is quite straightforward involving no new concepts but just more notations, for the sake of clarity we shall restrain to the scalar case.\
The model needs to be specified probabilistically, as the dynamics of the “time” process $\{{\mathbf u}(t)\}$ may well be space dependent and dually, the distribution of ${\mathbf v}(k)$ may be a priori time-dependent. The following assumption specifies in probabilistic terms the multiplicative structure of the random field ${\mathbf y}(k,t)$.
[**Assumption :**]{} The space and time evolutions of ${\mathbf y}(k,t)$ are [*multiplicatively uncorrelated*]{} in the sense that $$\label{condExp}
{{\mathbb E}\,}\{ {\mathbf v}(k_1) {\mathbf v}(k_2)\mid {\mathbf u}(t_1){\mathbf u}(t_2)\}= {{\mathbb E}\,}_{{\mathbf v}}\{ {\mathbf v}(k_1) {\mathbf v}(k_2)\}$$ where the first conditional expectation is made with respect to the conditional probability distribution of ${\mathbf v}$ given the random variables ${\mathbf u}(t_1),\,{\mathbf u}(t_2)$, while the second expectation is with respect to the marginal distribution of ${\mathbf v}$.
From the multiplicative uncorrelation one gets $$\label{ProdCov}
{{\mathbb E}\,}\{ {\mathbf v}(k_1) {\mathbf v}(k_2) {\mathbf u}(t_1){\mathbf u}(t_2)\}= {{\mathbb E}\,}\{ {\mathbf v}(k_1) {\mathbf v}(k_2)\} \, {{\mathbb E}\,}\{ {\mathbf u}(t_1){\mathbf u}(t_2)\}= \sigma_{{\mathbf v}}(k_1,k_2) \, \sigma_{{\mathbf u}}(t_1,t_2)$$ where $\sigma_{{\mathbf v}}$ and $\sigma_{{\mathbf u}}$ are the covariance functions of the two processes. Hence the covariance function of the random field inherits the separable structure of the process. If ${\mathbf v}$ and ${\mathbf u}$ are jointly Gaussian, the multiplicative uncorrelation property follows if the two components are uncorrelated; namely their joint covariance is separable. This is a structure which is often assumed in the literature, see [@Li-G-S-08] and references therein. Assume now that the space process has a nontrivial GFA representation with $q$ factors $$\label{SpaceGFA}
{\mathbf v}(k)= \sum_{i=1}^{q}\, f_{i}(k) {\mathbf z}_i + \tilde{{\mathbf v}}(k)$$ where $\hat {\mathbf v}(k):=\sum_{i} f_{i}(k) {\mathbf z}_i $ is the aggregate and $\tilde {\mathbf v}(k)$ the idiosyncratic component of ${\mathbf v}(k)$. Then setting ${\mathbf x}_{i}(t)= {\mathbf z}_i {\mathbf u}(t)$ and $ \tilde{{\mathbf y}}(k,t):= \tilde{{\mathbf v}}(k){\mathbf u}(t)$ one can represent the random field by a dynamic GFA model, $$\label{TimeGFA}
{\mathbf y}(k,t)= \sum_{i=1}^{q}\, f_{i}(k) {\mathbf x}_i(t) + \tilde{{\mathbf y}}(k,t):= \hat{{\mathbf y}}(k,t) + \tilde{{\mathbf y}}(k,t)$$
If the processes ${\mathbf v}$ and ${\mathbf u}$ are multiplicatively uncorrelated then the two terms $\hat{{\mathbf y}}(k,t)$ and $\tilde{{\mathbf y}}(h,s)$ in the GFA model are uncorrelated for all $k, h$ and $t,s$. Hence a separable random field satisfying the multiplicative uncorrelation property has a flocking component if and only if its space process ${\mathbf v}$ has a nontrivial aggregate component.
We have $${{\mathbb E}\,}\{ \hat{{\mathbf y}}(k,t) \tilde{{\mathbf y}}(h,s)\}= \sum_{i=1}^{q}\, f_{i}(k) \, {{\mathbb E}\,}\{ {\mathbf z}_i {\mathbf u}(t)\tilde{{\mathbf v}}(h){\mathbf u}(s)\}$$ where the expectation in the last term can be written as $${{\mathbb E}\,}\{ {\mathbf z}_i \tilde{{\mathbf v}}(h){\mathbf u}(t){\mathbf u}(s)\}= {{\mathbb E}\,}\{{{\mathbb E}\,}_{{\mathbf v}} [ {\mathbf z}_i \tilde{{\mathbf v}}(h)\mid {\mathbf u}(t){\mathbf u}(s)]\,{\mathbf u}(t){\mathbf u}(s)\}= {{\mathbb E}\,}\{{{\mathbb E}\,}_{{\mathbf v}} [ {\mathbf z}_i \tilde{{\mathbf v}}(h)\,] {\mathbf u}(t){\mathbf u}(s)\}=0$$ since the ${\mathbf z}_i$’s are random variables in $H(\hat{{\mathbf v}})$ and $ \tilde{{\mathbf v}}(h)$ is orthogonal to this space. The last statement then follows directly.
Let now ${\mathbf v}$ be second-order weakly stationary satisfying the conditions of Theorem \[mainThm1\]. Here is probably the simplest nontrivial example of decomposition .
Consider the case of a [*(weakly) exchangeable*]{} space process ${\mathbf v}$; i.e. a process whose second order statistics are invariant with respect to all index permutations of locations $(k,j)$. Clearly the covariances $\sigma_{{\mathbf v}}(k,j)={{\mathbb E}\,}{\mathbf v}(k){\mathbf v}(j)$ must be independent of $k,\,j$ for $k\neq j$ and $\sigma_{{\mathbf v}}(k,k)= \sigma^2>0$ must be independent of $k$ [@Aldous-85]. Letting $\rho:= \sigma_{{\mathbf v}}(k,j),\,k\neq j$, one has $$\Sigma_{{\mathbf v}}= {\left[ \begin{matrix}}\sigma^2& \rho& \rho& \rho &\ldots\\
\rho & \sigma^2 & \rho& \rho &\ldots\\
\ldots & & \ddots& &\ldots {\end{matrix} \right]}$$ where $\sigma^2 > |\rho|$ for positive definitness. Letting $f$ denote an infinite column vector with components all equal to $\rho$, one can decompose $\Sigma_{{\mathbf v}}$ as $$\Sigma_{{\mathbf v}} = f f^{\top} + (\sigma^2 - \rho) I$$ where here $I$ denotes an infinite identity matrix. This is a Factor Analysis decomposition of rank $q=1$ of $\Sigma_{{\mathbf v}}$ with $\tilde {\Sigma}_{{\mathbf v}}$ a diagonal matrix. Hence a weakly exchangeable space process is a 1-factor process with an idiosyncratic component which is actually white. In the GFA representation there is just one factor ${\mathbf z}$ and the factor loading vector $f$ does not depend on the space coordinate.\
Consider a random field with the multiplicative structure , then the flocking component $$\hat{{\mathbf y}}(k,t)= f {\mathbf x}(t)\,,{\qquad}{\mathbf x}(t) ={\mathbf z}{\mathbf u}(t)$$ describes a constant, space independent, configuration moving randomly in time.
Statistical estimation
----------------------
Assume that the space component of the random field is stationary and we have a snapshot of the system at certain time $ t_0$; that is we have observations of a “very large” portion of the process $\{{\mathbf y}(k,t_0),\, k=1,2,\ldots,N\}$ at some fixed time $t_0$. With these sample data we may form the sample covariance estimates $$\hat{\sigma}_N(h,t_0):= {{\displaystyle\frac{1}{N}}} \sum_{k=1}^{N} y(k+h,t_0)y(k,t_0)= {{\displaystyle\frac{1}{N}}} \sum_{k=1}^{N} v(k+h)v( k)\, u(t_0)^2\,,{\qquad}h=0,1,2, \ldots \,$$ which also have the multiplicative structure $\hat{\sigma}_N(h,t_0)= \hat{\sigma}_{{\mathbf v},\,N}(h) u(t_0)^2$, where $ \hat{\sigma}_{{\mathbf v},\,N}(h)$ is the sample covariance estimate of the ${\mathbf v}$ process based on $N$ data. Now by the assumptions made on the space-process ${\mathbf v}$ the limit $\lim_{N\to \infty} \hat{\sigma}_N(h,t_0)$ exists (although it may be sample dependent for the PD part), so the sample matrix covariance estimate, which has the form $$\hat{\Sigma}_N(t_0):= {\left[ \begin{matrix}}\hat{\sigma}_N(0,t_0) &\hat{\sigma}_N(1,t_0)& \ldots& & \hat{\sigma}_N(N-1,t_0)\\
\hat{\sigma}_N(1,t_0)& \hat{\sigma}_N(0,t_0) &\hat{\sigma}_N(1,t_0)& \ldots& \hat{\sigma}_N(N-2,t_0)\\
\ldots & \ldots & & \ldots & \ldots\\
\hat{\sigma}_N(N-1,t_0)&\ldots & &\hat{\sigma}_N(1,t_0)& \hat{\sigma}_N(0,t_0) {\end{matrix} \right]}\, =
u(t_0)^2 \,\hat{\Sigma}_{{\mathbf v},N}$$ will converge to a limit for $N\to \infty$.\
Following [@Chamberlain-R-83; @forni_lippi_2001] the idea is now to do PCA on the covariance estimate for increasing N and isolate $q$ eigenvalues which tend to grow without bound as $N\to \infty$ while the others stay bounded. The $q$ corresponding eigenvectors will tend as $N\to \infty$ to the $q$ factor loadings $f_1,\ldots,f_q$ and therefore provide asymptotically the F.A. decomposition of the $\Sigma_{{\mathbf v}}$ matrix $$\Sigma_{{\mathbf v}} = FF^{\top} +\tilde{\Sigma}_{{\mathbf v}} \,.$$ After $F$ and $\tilde{\Sigma}_{{\mathbf v}}$ are estimated, the stochastic realization procedure of Sect. \[GFA\] permits to construct the factor vector ${\mathbf z}$ and the idiosyncratic component $\tilde{{\mathbf v}}$ of the GFA representation of ${\mathbf v}$ as in . The reconstruction of the time varying factor variables ${\mathbf x}_i(t)= {\mathbf z}_i {\mathbf u}(t)$ of ${\mathbf y}$ from the observations ${\mathbf y}(k,t)= {\mathbf v}(k) {\mathbf u}(t)$ can be done, in several equivalent ways, by averaging on the space variable.
Conclusions
===========
We have proposed a new modeling paradigm for large dimensional aggregates of random systems by the theory of Generalized Factor Analysis models. We have discussed static GFA representations and characterized in a rigorous way the properties of the [*aggregate*]{} and [*idiosyncratic*]{} components of these models. For wide-sense stationary sequences the character and existence of these models has been completely clarified in the light of the Wold decomposition. The extraction of the flocking component of a random field has been discussed for a simple class of separable random fields.
[^1]: G. Bottegal and G. Picci are with the Department of Information Engineering, University of Padova, Italy [bottegal@dei.unipd.it]{}, [picci@dei.unipd.it]{}
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Characterization of the cone-rod dystrophy retinal phenotype caused by novel homozygous DRAM2 mutations.
Cone-rod dystrophies (CRD) are a group of Inherited Retinal Dystrophies (IRD) characterized by the primary involvement of cone photoreceptors, resulting in the degeneration of the central retina, or macula. Although there are more than 55 CRD genes, a considerable percentage of cases remain unsolved. In this context, the present study aimed to describe and characterize the phenoptype and the genetic cause of 3 CRD families from a cohort of IRD cases. Clinical evaluation in each patient was supported by a complete ophthalmological examination, including visual acuity measurement, fundus retinography, fundus autofluorescence imaging, optical coherence tomography and full-field electroretinography. Molecular diagnoses were performed by whole exome sequencing analyzing a group of 279 IRD genes, and cosegregation of the identified pathogenic variants was confirmed by Sanger sequencing. Three novel homozygous mutations in the autophagy gene DRAM2 were identified as the molecular cause of disease in the three families: c.518-1G>A, c.628_629insAG and c.693+2T>A. Clinical data revealed that the 3 patients presented a shared CRD phenotype with adult-onset macular involvement and later peripheral degeneration, although the age of onset, evolution and severity were variable. In order to characterize the transcription effects of these variants, mRNA expression studies were performed. The results showed alterations in the DRAM2 transcription, including alternative splicing forms and lower levels of mRNA, which correlated with the phenotypic variability observed between patients. For instance, frameshift mutations were related to a less severe phenotype, with circumscribed mid-peripheral involvement, and lower levels of mRNA, suggesting an activation of the nonsense-mediated decay (NMD) pathway; while a more severe and widespread retinal degeneration was associated to the inframe alternative splicing variant reported, possibly due to a malfunctioning or toxicity of the resulting protein. Following these findings, DRAM2 expression was assessed in several human tissues by semi-quantitative RT-PCR and two isoforms were detected ubiquitously, yet with a singular tissue-specific pattern in retina and brain. Altogether, although the unique retinal phenotype described did not correlate with the ubiquitous expression, the retinal-specific expression and the essential role of autophagy in the photoreceptor survival could be key arguments to explain this particular DRAM2 phenotype.
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{
"pile_set_name": "PubMed Abstracts"
}
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Cum Whore Strapped Up for the Fucking Machine
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"pile_set_name": "OpenWebText2"
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HD 12:26 loading preview
Fuck my Face and Cum in my Pussy
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"pile_set_name": "OpenWebText2"
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Students to enroll in high schools nearest to their homes in Turkey’s new system
ANKARA
A central high school entrance exam will only be held at specific schools, Education Minister İsmet Yılmaz has said, announcing that Turkey’s new education system will be based upon the principle of students enrolling at the nearest school available.
“With this new system, students will be admitted to the nearest school to where they live. That is the basic point,” Yılmaz told state-run Anadolu Agency on Nov. 5.
Revealing details of the new system called “System of Educational District and Regional Enrollment,” Yılmaz said there will be a new examination only for “project schools,” the list of which will be announced soon.
“It will be an optional exam. We are currently preparing the questions. All the examinations will be held in the province where the student lives. It will be a central exam that is executed locally. All the questions will be prepared by the Ministry,” Yılmaz said.
“We will hold this exam in the first weekend of June,” he said, adding that the exam will be a multiple-choice test system.
“It will feature 60 questions and students will have 90 minutes to answer them,” Yılmaz stated.
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"pile_set_name": "OpenWebText2"
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Related BBC sites
Why are Swiss bankers called gnomes?
They've been called many things in recent months, but "gnomes" is one moniker for bankers - particularly Swiss ones - that has a long history, says the BBC's Chris Bowlby.
There's been a lot of name calling when it comes to those who work in the world of finance recently, most of it unprintable.
But the current financial turmoil in Europe, as well as news that London's best bankers are considering moving to Switzerland to avoid stricter regulation and public hostility, has resurrected an ancient and intriguing phrase - the "gnomes of Zurich".
First coined by British politicians facing a currency crisis in the 1960s, the phrase has lurked ever since whenever speculators are suspected of destabilising a country. But why gnomes? And why Zurich?
Labour politician George Brown coined the phrase
Forget kitschy garden ornaments. These gnomes emerged from medieval fascination with the secrets of wealth, especially gold, buried underground and mined by mysterious beings. Goethe writes about them in his epic Faust - ambiguous characters creating wealth which others, depending on their morals, use for good or evil.
So as the secretive world of Swiss banking took shape, centred on Zurich, and based on underground vaults with anonymous numbered accounts in a fiercely independent, mountainous country, you can see why the idea of gnomes sprang to mind.
Armed with bars of gold, currency trading accounts containing very large sums and the utmost discretion, Swiss bankers were admired - and feared. But in the 20th Century their reputation, especially among those on the political left, darkened.
The secretive Swiss were seen as helping ruthless international capitalists and dictators avoid taxes and protect their wealth. In World War II, neutral Switzerland appeared to help Nazi Germany financially, while taking deposits from Jewish victims of the Holocaust. It failed to return many of the assets after the war and in recent years some Swiss banks have agreed multi-million pound settlements with families to avoid being sued.
Mischievous
When post-war Labour politicians worried about whether speculation against sterling would undermine their economic plans for Britain, those financiers in Zurich made a convenient scapegoat.
Disparaging references to Swiss bankers had already been heard in Britain in the 1950s. But it was the intervention of the leading Labour politician George Brown in November, 1964, that made headlines. Emerging from a crisis meeting at which the Labour government discussed the plummeting pound, Brown snapped: "The gnomes of Zurich are at work again."
Mr Brown, famous for forthright utterances, had created a new catchphrase. Soon it was on many other lips, including those of the prime minister at the time, Harold Wilson, promising to resist the gnomes' "sinister" power.
Swiss banking is viewed as a secretive world
The Swiss were unrepentant. "In the world it is not the image, but the substance behind the image which counts," sniffed top banker Paul Rossy at the time.
When they heard news of Mr Brown's hostility, they were perhaps reminded of a great local scandal in 1958 when a Briton also named Brown dared to hold up a Zurich bank and was arrested by an angry mob before the police needed to intervene.
Some Zurich bankers took to answering the phone to British callers with "hello, gnome speaking". Others retaliated mischievously by suggesting that trade union power - "the gnomes of Transport House" - rather than currency speculation, was weakening the British economy.
One enterprising, and courageous, Zurich banker moved to London to set up in business, where he was promptly dubbed "the gnome of Notting Hill".
The Americans took up the phrase too, with the Wall Street Journal mentioning the Zurich gnomes alongside the military-industrial complex, the Establishment and the Illuminati, as the people who allegedly ran the world.
Hostility
It may all have been hugely exaggerated, but such was the secrecy surrounding Swiss banking, no one could tell. There were, as Donald Rumsfeld might have put it, so many "gnome unknowns".
However great their influence really was, the Zurich money men seemed to lose influence in more recent decades. Gnomes in modest, discreet buildings were dwarfed, so to speak, by the skyscrapers of the City of London, New York and, more recently, Dubai and Shanghai.
But they are still there, still holding enormous private and commercial fortunes. And Jurg Conzett, of the Zurich Money Museum, where they proudly display a Swiss gnome sculpture, says today's bankers sometimes see the gnome label as "almost a noble title".
Goethe wrote about gnomes in his epic Faust
He says the global crisis has led to an intense debate in Switzerland, as elsewhere, about the role of bankers. The inventors of apparently miraculous new products like derivatives or sub-prime loan packages are viewed like those medieval gnomes conjuring gold, he adds.
Today's bankers, like Goethe's gnomes, say they are not to blame if others act irresponsibly with their creations. Those Swiss financiers may become still more confident if they acquire new recruits from the enemy territory of Britain.
Bankers currently based in London, fearful of higher taxes, stricter regulation and public hostility, are said to considering moving in large numbers to Switzerland where banking, the humorist George Mikes once said, is "the state religion".
And what if they then start speculating against sterling during a crisis? How might British politicians react to such apparent treachery?
A new hostile catchphrase, perhaps, which will then remain, stored in the underground vaults of our subconscious, ready for when we next need someone, somewhere, to blame for a crisis.
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Trucking company failures are rising as faltering freight demand exposes operators unprepared for a downturn after last year’s red-hot shipping market.
Approximately 640 carriers went out of business in the first half of 2019, up from 175 for the same period last year and more than double the total number of trucker failures in 2018, according to transportation industry data firm Broughton Capital LLC.
This week, Denver-based HVH Transportation Inc. abruptly shut down, stranding about 150 drivers and loads out on the road. The closure adds to a 2019 tally that includes Ohio truckload company Falcon Transport Co. and regional less-than-truckload carriers New England Motor Freight Inc. and LME Inc.
Former HVH Chief Executive John Kenneally said he is negotiating with the carrier’s bank on steps to help get the drivers’ fuel cards reactivated so they can deliver their loads and get home. The company has about 380 trucks, including those tied to a related Canadian company, FTI Transportation, which also shut this week, Mr. Kenneally said. That company also belonged to HVH’s owner, private-equity firm HCI Equity Partners.
The increasing number of closures come as trucking companies that boosted driver pay and plowed last year’s profits into record orders for new equipment now are wrestling with a tougher pricing environment and slackening demand.
In 2018, “demand was so strong, rates were so strong, it was virtually impossible to fail,” said Donald Broughton, Broughton Capital’s managing partner.
Newsletter Sign-up The Logistics Report Top news and in-depth analysis on the world of logistics, from supply chain to transport and technology. PREVIEW
Trucking rates stalled out in July, falling 0.1% from the prior year after a 27-month run of annual increases, according to the Cass Truckload Linehaul Index, which measures per-mile pricing for truckload carriers. Prices on trucking’s spot market, where shippers book last-minute transportation, were down nearly 19% last month compared with 2018, according to online freight marketplace DAT Solutions LLC.
That swing has hurt transport operators that shifted more business to the spot market last year to take advantage of surging rates. That also has proved painful for smaller operators that depend more on trucking’s spot market and may not have the leverage big trucking companies have with shipping customers to build higher prices into their contract rates.
Some trucking companies say rising insurance costs also are weighing on the business. Mr. Kenneally said HVH’s monthly insurance bill more than doubled this year, to about $368,000 from $150,000 in 2018.
Some trucking executives believe the recent spate of smaller carrier bankruptcies will give “larger carriers added control and pricing power in the marketplace,” Cowen & Co. transportation analyst Jason Seidl wrote in a research note last month.
Many big operators both bolstered their balance sheets during last year’s freight surge and deepened their ties to shipping customers with a broader array of services.
This week, Iowa-based truckload operator Heartland Express Inc. bought trucker Millis Transfer Inc. for about $150 million. Heartland last month reported its net profit jumped 25.6% in the second quarter despite declining revenue, and cash on the truckload carrier’s balance sheet jumped more than 27% from the end of 2018 to June 30, to $205.6 million.
Write to Jennifer Smith at jennifer.smith@wsj.com
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Menu
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Did you know? You can easily access AAP Policy Statements, Clinical Practice Guidelines, and Clinical and Technical Reports with the AAP Policy & Collections link in the black header bar above (or the 3-line menu button on a mobile device), or by clicking here.
Hospital Discharge of the High-Risk Neonate—Proposed Guidelines
Abstract
This policy statement is the first formal statement of the American Academy of Pediatrics on the issue of hospital discharge of the high-risk neonate. It has been developed, to the extent possible, on the basis of published, scientifically derived information. Four categories of high risk are identified: 1) the preterm infant, 2) the infant who requires technological support, 3) the infant primarily at risk because of family issues, and 4) the infant whose irreversible condition will result in an early death. The unique home care issues for each are reviewed within a common framework. Recommendations are given for four areas of readiness for hospital discharge: infant, home care planning, family and home environment, and the community and health care system. The need for individualized planning and physician judgment is emphasized.
The decision about timing of hospital discharge of an infant after neonatal intensive care is complex. It is made even more difficult because of cost-containment issues and rigid definitions of medical necessity as determining influences on the length of hospitalization. Because of the pressure to discharge high-risk neonates at the earliest possible opportunity, it is important that guidelines are based on a review and analysis of current evidence. Shortening the length of a hospital stay may benefit the infant and family because decreasing the period of separation from the parents may lessen the subsequent adverse effect on parenting.1,2The risks for hospital-acquired morbidity may be reduced.3-6 However, the overriding concern is that infants may be placed at risk for increased mortality and morbidity related to discharge before physiologic stability is established. Multiple investigators have found that preterm low birth weight infants who required neonatal intensive care experience a much higher rate of hospital readmission and death during the first year after birth compared with appropriate for gestational age, healthy term infants.7-13 Adequate time for preparation of the family to provide care in a home setting and for mobilization of community resources to provide support services is necessary before discharge. With advances in neonatal intensive care and changes in the economic and societal forces, the complexity of posthospital care issues has increased. A single set of criteria for discharge readiness is no longer adequate. These guidelines, therefore, address four broad categories of high-risk situations: 1) the preterm infant, 2) the infant who requires technological support, 3) the infant primarily at risk because of family issues, and 4) the infant whose irreversible condition will result in an early death.
REVIEW OF THE LITERATURE
The Preterm Infant
The traditional approach to determining discharge readiness was the achievement of a preset weight, historically 5 or 5½ lb. During the past three decades several observational,14-17 nonrandomized,18-21and randomized, controlled22-24 studies have been published that analyzed outcomes of preterm infants who were discharged after certain criteria were met. Although the population characteristics, the nature and results of the outcome measures, and the content of the early discharge programs varied, the common elements included:
A sustained pattern of weight gain rather than a specific achieved weight,
Physiologic stability defined as the ability to suckle feed and maintain normal body temperature in an open environment,
An active program of parental involvement and preparation for posthospital care,
Predischarge on-site home assessment,
An active program of parental support after discharge of the very low birth weight (VLBW) infant,
Frequent outpatient follow-up to assure adequate weight gain for the smallest infants in the weeks immediately after discharge,
An organized program of postdischarge tracking and surveillance.
The safety of discharge after a shorter than usual hospital stay was supported by adequacy of weight gain and no increase in the number of acute care visits, unscheduled hospital readmissions, or early infant deaths in randomized studies with matched control cohorts. Each of these study designs included a program of parent education and infant follow-up.22-24 In the studies that addressed cost savings specifically,19,20,22,23 effectiveness was documented even with the inclusion of costs for coordination of care and services, home visiting, transportation, sibling care, and in-home support for the family, although in no single study were all of the aforementioned ancillary services provided. The success of the early discharge programs that incorporated specialized home care and follow-up surveillance indicates that the care required by the preterm infant and the support needed by families exceed that after discharge at a later postnatal age.
The three physiologic competencies that are generally recognized as essential before hospital discharge are the ability to maintain a normal body temperature fully clothed in an open bed with normal ambient temperature, the ability to coordinate suckle feeding, swallowing, and breathing while ingesting an adequate volume of feeding, and the ability to grow at an acceptable rate. These competencies are achieved by most preterm infants between 34 and 36 weeks postmenstrual age. Equally essential is the ability to maintain stable cardiorespiratory function. Data about maturation of breathing control and feeding behavior are more direct,25-38whereas the maturational timing of the ability to maintain body temperature can only be inferred.39-41 Although interrelated, not all competencies are achieved at the same postnatal age in a given infant. The pace of maturation is further influenced by the birth weight, the gestational age at birth, and the degree and chronicity of neonatal illnesses.
For infants with delayed maturation of respiratory control, use of home cardiorespiratory monitoring has been reported.42-44 The National Institutes of Health Consensus Development Conference45 and the Canadian Pediatric Society policy statement46 included prematurity with unresolved apnea as a potential indication for home monitoring. The success of home monitoring for unresolved apnea in reducing hospital stay without undue family stress has been observed.43,44 However, infant deaths associated with the lack of proper monitor use have been reported.47 The predischarge clinical course and abnormal cardiorespiratory polygraphic findings have not correlated with subsequent alarm events requiring parental intervention42and apnea of prematurity and risk of sudden infant death syndrome.45 Thus, the decision to use home cardiorespiratory monitoring and predischarge polygraphic studies of cardiorespiratory function remains a matter of individual clinical judgment.
The Infant With Special Health Care Needs or the Technology-dependent Infant
In the past two decades, increasing numbers of children with unresolved and/or special health care needs have been discharged to home care with varying requirements for technologic dependence and/or support.48 For newborn infants, the three broad groupings or categories of special care requirements are as follows: 1) those requiring special or assistive feeding techniques, 2) those requiring respiratory assistance, and 3) those with complex congenital anomalies requiring supportive and assistive devices. Only the first two categories are addressed because the population of the third group is very diverse and to our knowledge no data from controlled studies of home care have been published.
Gavage feeding as the primary mode of enteral feeding of sick and premature infants is a common practice in the hospital setting. There is no reported clinical experience of its use in home care of young infants from which conclusions about safety, efficacy, and clinical appropriateness can be reached. Another approach for infants requiring long-term assistive feeding is placement of a gastrostomy; however, no clinical series of newborns with long-term home gastrostomy feeding has been reported. In the only reported series of home intravenous nutritional support of infants,49 one death from catheter-related sepsis was noted. Somatic growth was maintained at normal rates, and six of the eight infants had normal developmental progress.
Infants with tracheostomies placed for various airway abnormalities have been cared for at home in recent years.50-52 The underlying reason for the tracheostomy is reported to be the most important factor affecting the outcome, although airway accidents have been a major factor in adverse morbidity.
To date, no clinical trials have been reported that compare outcomes of home oxygen therapy in infants with bronchopulmonary dysplasia with those after prolonged hospitalization. Multiple observational studies have been conducted, however,53-55 the more recent of which have noted relative safety, ease of implementation, and cost-effectiveness.56-58 Prolonged oxygen supplementation is further supported by reported observations about its role in limiting progression to cor pulmonale,59 facilitating normal growth rates,60,61 and avoiding unrecognized hypoxic episodes.62,63
Reports of home ventilatory support of infants with chronic respiratory failure64,65 emphasize the need for continuous cardiorespiratory monitoring, disconnect alarms for mechanical support devices, and qualified personnel to provide bedside care to reduce the risk of death from airway accidents. Maintaining safe and adequate care is complex, emotionally demanding, and consumes the time and resources of families.46,65
The Infant at Risk Because of Family Issues
Preterm birth and prolonged hospitalization were first reported as risk factors for subsequent child abuse in 1971.66 In subsequent studies,67,68 infant risk factors found to be significant were VLBW, prolonged hospital stay, and congenital defects. Maternal factors included lower educational level, lack of social support, marital instability, and fewer prenatal care visits. Significantly fewer family visits during the stay in the neonatal intensive care unit had occurred for infants in whom subsequent maltreatment was documented.67
The increase in substance use among the childbearing age group has created a large population of children at risk for a variety of adverse medical and psychosocial outcomes.69 Sequelae such as attachment disturbances, behavioral and developmental disorders, and child maltreatment have been observed frequently among children born to substance abusers.70-72 Strategies to reduce the risks of adverse outcomes in infants at high risk because of psychosocial concerns that have been adequately studied have focused primarily on home visitation with or without additional social support services.73-79 The likelihood of success increased when an intervention program for maternal substance abuse included addiction treatment for the parents.80
The Infant With Anticipated Early Death
The concept of hospice care for neonates was first introduced in the pediatric literature in an editorial in 198281 and in reports of a specialized in-hospital program.82,83Although hospice care at home or in an alternative setting for older children has been reported,84-87 such studies are lacking for neonates. However, the components of pediatric hospice care as expounded by Corr and Corr88 are theoretically as equally applicable for infants, including 1) involvement of skilled professionals, 2) care directed toward control of distressing symptoms and provision of physical comfort, 3) coordination of services and a multidisciplinary approach, 4) adequate social supports to meet family needs, and 5) provision of follow-up and bereavement care. Enhancing the quality of the remaining life for the infant and family is more important than the site of care delivery.
DISCHARGE PLANNING
The care of each high-risk neonate after discharge must be carefully coordinated to provide ongoing multidisciplinary support of the family. The discharge planning team should include parents, the primary care physician, the neonatologist, neonatal nurses, and the social worker. Other professionals, such as surgical specialists and pediatric subspecialists, pediatric occupational, physical, speech, and respiratory therapists, infant educators, nutritionists, home health care liaisons, and a case manager selected by the team and family, may be included as needed.
The initiation of discharge planning should begin when it is evident that recovery is certain, although the exact date of discharge may not be predictable. The goal of the discharge plan is to assure successful transition to home care. Essential elements are a physiologically stable infant, a family who can provide the necessary care without undue strain and with appropriate support services in place within the community, and a primary care physician who is prepared to assume the responsibility with appropriate back up from specialist physicians and other professionals as needed.
Six critical components must be included in discharge planning.
1. Parental Education.
Parental contact and involvement in the care of the infant should have been encouraged from the time of admission. The participation of the parents in giving care as early as feasible in the neonatal course has been shown to have a positive effect on their confidence in handling the infant and readiness to assume full responsibility for the infant's care at home.89
The development of an individualized teaching plan aids parents in acquiring the skills and judgment required for the appropriate care of their infant. Having a written checklist or outline of the specific areas and tasks to be mastered increases the likelihood that both parents will receive complete instructions and experience. Caregivers and parents must understand that if an infant is discharged from the hospital before complete physiological maturation and resolution of all complications of high-risk birth, the infant's care requirements will continue at home. Furthermore, the level of care being asked of the parents is beyond that of the usual parental role. Thus, ample time for teaching the parents and caregivers the techniques and the rationale for each item in the care plan is essential. Return demonstrations, parent rooming-in, and telephone follow-up have all been reported to facilitate parental education and adaptation to their infant's care.15-17,21,89,90
In so far as possible, at least two caregivers, one of whom is a responsible adult, should be identified and taught for each infant. The demands of home care can be physically and emotionally draining, especially at first, for infants requiring frequent feeding. Young mothers who do not live with a parent or the father of the baby have been shown to be vulnerable to the strains of home care.67Even in a two-parent family, the primary caregiver may become ill and need relief.
2. Implementation of Primary Care.
Preparing the infant for transition to primary care begins early in the hospitalization with administration of immunizations at the recommended ages,91 completion of metabolic screening,92,93 and assessment of hearing by an acceptable electronic measurement.94 For the infants at risk, appropriate funduscopic examination for retinopathy of prematurity should be performed by an ophthalmologist skilled in the evaluation of the retina of the preterm infant as recommended in the AAP policy statement.95 Assessment of hematologic status is recommended for all infants because of the high prevalence of anemia after neonatal intensive care. Because VLBW infants and those who have received parenteral nutrition for prolonged periods may be at risk for hypoproteinemia, vitamin deficiencies, and bone mineralization abnormalities, screening for nutritional or metabolic deficiencies may be indicated.
3. Evaluation of Unresolved Medical Problems.
Review of the hospital course and the active problem list of each infant and careful physical assessment will reveal unresolved medical issues and areas of physiologic function that have not reached full maturation for the infant. From such a review, the diagnostic studies required to document the current clinical status of the infant can be identified and alterations in management instituted. The intent should be to assure implementation of appropriate home care and follow-up plans.
4. Development of the Home Care Plan.
Although the content of the home care plan may vary among the four categories of infants, the common elements include the following: 1) identification and preparation of the in-home caregivers, 2) development of a comprehensive listing of required equipment and supplies and accessible sources, 3) identification and mobilization of necessary and qualified home care personnel and community support services, 4) assessment of the adequacy of the physical facilities within the home, 5) development of an emergency care and transport plan as indicated, and 6) assessment of available financial resources to assure the capability to finance home care costs. Specific details of planning home care for the technology-dependent infant are included in the AAP policy statement,96 in a consensus report48 and, for hospice care, in Corr and Corr.97 The input of the primary care physician in formulating the home care plan of the technology-dependent infant is essential. Many infants, particularly the VLBW and technology-dependent infants, require continued care by multiple surgical specialists and pediatric subspecialists, each of whom should be included in the predischarge assessment and discharge planning.
5. Identification and Mobilization of Surveillance and Support Services.
The psychosocial characteristics of each family should be reviewed, noting those risk factors that may contribute to an adverse infant outcome. The availability of social support is essential to the success of every parent's adaptation to the home care of a high-risk infant.98 Before discharge and periodically thereafter, a review of the family's needs, coping skills, use of available resources, financial problems, and progress toward goals in the home care of their infant should be evaluated. After the social support needs of the family have been identified, an appropriate, individualized intervention plan using available community programs, surveillance, or alternative care placement may be implemented.
6. Determination and Designation of Follow-up Care.
In general, the attending neonatologist has the responsibility for coordination of follow-up care, although in an individual institution, the tasks may be delegated to other professionals. A primary care physician should be identified as early as possible to facilitate the coordination of follow-up care planning between the primary care setting and the subspecialty center-based discharge planning staff. Pertinent information about the nursery course and home care plan should be given to that individual before the infant's discharge. It is highly desirable that the primary care physician meet the parents before the discharge and, if possible, examine the infant in the hospital. In specialty center units, the primary care attending physician should work together with the neonatologist in coordinating the discharge planning.
Arrangements for an initial appointment with the primary care physician should be initiated before discharge. Specific follow-up appointments with each involved surgical specialist and pediatric subspecialist should be made as indicated in advance of discharge, giving attention to grouping these as much as possible to enhance compliance and to decrease the inconvenience of the family.
Periodic evaluation of the developmental progress of every infant is essential to identify deviations in neurodevelopmental progress at the earliest possible point, thereby facilitating entry into early intervention programs (Public Law 99–457).99 The primary care physician with appropriate skills, the pediatric subspecialist, or clinic personnel may provide longitudinal developmental follow-up. When input from multiple disciplines is identified before discharge, a center-based clinic providing multidisciplinary care may be the least cumbersome option for the family.
SPECIAL CONSIDERATIONS
With networking among nurseries that provide different levels of care, increasing numbers of infants are transported back to community hospitals for convalescent care. In these hospitals, the discharge planning process should follow the same principles as those outlined above for an infant being discharged from a subspecialty center. Appropriate follow-up during the most critical periods for infants at risk for adverse sensorineural outcomes, ie, the VLBW infant for progression of retinopathy and for all high-risk infants whose hearing status or type of hearing deficit still needs evaluation.
Innovative programs based on community resources, both public and private, should be encouraged. The goal should be to provide coordinated care and family support. Efficient teamwork by health care professionals is imperative. Programs should be modified to accommodate different demographic needs and to achieve efficient use of all funding resources.
For optimal support of parents and surveillance of the status of a high-risk infant after discharge it is important that experienced nurses who are qualified to perform specialized assessments are utilized for home nursing visits. It is essential that previous performance and existing quality control programs be considered when choosing a home health care agency to provide personnel for in-home care of the technology-dependent infant.
RECOMMENDATIONS
The following recommendations are offered as a framework for consideration as each individual infant and caregiving situation is evaluated and the discharge decision made. It is prudent that each institution establish guidelines allowing for individual physician judgment and flexibility.
Infant Readiness for Hospital Discharge
In the judgment of the responsible physician there has been:
A sustained pattern of weight gain of sufficient duration;
Adequate maintenance of normal body temperature with the infant fully clothed in an open bed with normal ambient temperature (24°C to 25°C);
Competent suckle feeding, breast or bottle, without cardiorespiratory compromise; and
Hematologic status has been assessed and appropriate therapy instituted as indicated;
Nutritional risks have been assessed and therapy and dietary modification instituted as indicated;
Sensorineural assessments, hearing and funduscopy, have been completed as indicated;
Review of hospital course has been completed, unresolved medical problems identified, and plans for treatment instituted as indicated.
Home Care Plan Readiness
An individualized home care plan has been developed with input from all the appropriate disciplines. The plan for infants with complex multiple system problems, and particularly for those requiring technological assistance, must be specific and detailed. For infants at psychosocial risk, arrangement for appropriate psychosocial surveillance and family support is essential.
Family and Home Environmental Readiness
Assessments of the family caregiving capabilities, resource requirements, and home physical facilities have been completed.
Identification of at least two family caregivers, one of whom is an adult, and assessment of their ability, availability, and commitment;
Psychosocial assessment for parenting risks;
A home environmental assessment that may include an on-site evaluation;
Review of available financial resources and identification of adequate financial support.
An on-site assessment documenting availability of 24-hour telephone access, electricity, and an in-house water supply and heating and detailed financial assessment and planning are essential in preparation for home care of the technology-dependent infant.
Parents and caregivers have demonstrated the necessary capabilities to provide all components of care including:
Feeding, whether breast, bottle, or an alternative technique, including formula preparation as required;
Assessment of clinical status, including understanding and detection of the general early signs and symptoms of illness, as well as the signs and symptoms specific to the infant's condition;
Infant safety precautions including proper infant positioning during sleep and use of car seats100-102;
Specific safety precautions for an artificial airway, feeding tube, ostomy, infusion pump, and other mechanical and prosthetic devices as indicated;
Administration of medications, specifically proper dosage and timing, storage, and recognition of the signs and symptoms of toxicity;
Equipment operation, maintenance, and problem-solving for each mechanical support device required;
The appropriate technique for each special care procedure required, including special dressings for infusion entry site, ostomy, or healing wounds, maintenance of an artificial airway, chest physiotherapy, oropharyngeal and tracheal suctioning, and infant stimulation and physical therapy, as indicated.
Specific modification of home facilities as required by home care system needs have been completed.
Community and Health Care System Readiness
An emergency intervention and a transportation plan have been developed and emergency services providers identified and notified as indicated.
Follow-up care needs have been determined, appropriate providers identified, and appropriate communication exchanged including the following:
Home nursing visits for assessment and parent support arranged as indicated by the complexity of the infant's clinical status and family capability and the home care plan transmitted to home health agency.
The determination of readiness for care at home of an infant after neonatal intensive care is complex. Careful balancing of infant safety and well-being with family needs and capabilities is required while giving consideration to the availability and adequacy of community resources and support services. The final decision, which is the responsibility of the attending physician, must be tailored for the unique constellation of issues posed by each situation.
Committee on Fetus and Newborn, 1997 to 1998
James A. Lemons, MD, Chairperson
Lillian R. Blackmon, MD
Avroy A. Fanaroff, MD
Hugh M. MacDonald, MD
Carol A. Miller, MD
Lu-Ann Papile, MD
Warren Rosenfeld, MD
Craig T. Shoemaker, MD
Michael E. Speer, MD
Liaison Representatives
Patrician Johnson, RN, MS, NNP
American Nurses Association
Association of Women's Health, Obstetric, and Neonatal Nurses
National Association of Neonatal Nurses
Michael F. Greene, MD
American College of Obstetricians and Gynecologists
Douglas D. McMillan, MD
Canadian Paediatric Society
Solomon Iyasu, MBBS, MPH
Centers for Disease Control and Prevention
Linda L. Wright, MD
National Institute of Child Health and Human Development
Section Liaison
Jacob C. Langer, MD
Section on Surgery
David K. Stevenson, MD
Section on Perinatal Pediatrics
Consultants
Irwin Light, MD
William Oh, MD
Footnotes
The recommendations in this statement do not indicate an exclusive course of treatment or serve as a standard of medical care. Variations, taking into account individual circumstances, may be appropriate.
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Lately I’ve noticed some Democratic politicians defending the current healthcare system by saying it preserves “choice” for Americans. As a former health insurance exec who helped draft this talking point, I need to come clean on its back story, and why it's wrong and a trap 1/11
When I worked in the insurance industry, we were instructed to talk about “choice,” based on focus groups and people like Frank Luntz (who wrote the book on how the GOP should communicate with Americans). I used it all the time as an industry flack. But there was a problem. 2/11
As a health insurance PR guy, we knew one of the huge *vulnerabilities* of the current system was LACK of choice. In the current system, you can’t pick your own doc, specialist, or hospital without huge “out of network” bills. So we set out to muddy the issue of "choice." 3/11
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Dohertyorsidis dohertyi
Dohertyorsidis dohertyi is a species of beetle in the family Cerambycidae. It was described by Stephan von Breuning in 1960, originally under the genus Pseudorsidis.
References
Category:Lamiinae
Category:Beetles described in 1960
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PFOA is associated with diabetes and metabolic alteration in US men: National Health and Nutrition Examination Survey 2003-2012.
Exposure to perfluoroalkyl substances (PFAS) is associated with a range of adverse health effects. However, it remains unclear whether PFAS at environmentally relevant exposure levels are related to diabetes and metabolite concentrations in adults. Using cross-sectional data from 7904 adults (age≥20years) in the 2003-2012 National Health and Nutrition Examination Survey (NHANES), we examined the association of PFAS with the prevalence of diabetes and metabolite concentrations. A multivariate logistic regression was applied to investigate the associations of diabetes prevalence with serum perfluorooctanoate (PFOA), perfluorooctane sulfonate (PFOS), perfluorohexane sulfonate (PFHxS) and perfluorononanoate (PFNA) levels. A multivariate generalised linear regression was further performed to investigate the associations between PFAS exposure and some metabolites. We identified a strong positive association between serum PFOA and diabetes prevalence in men with an adjusted model (OR: 2.66, 95% CI: 1.63-4.35; P for trend=0.001). No significant association between serum PFOA and diabetes prevalence was observed in women (OR: 1.47, 95% CI: 0.88-2.46; P for trend=0.737). Furthermore, diabetes was not related to PFOS, PFHxS and PFNA, regardless of gender. In the gender-stratified generalised linear models, men and women with the highest PFOA levels demonstrated a 1.43% (95% CI: 0.62%-2.34%) and a 1.07% (95% CI: 0.27%-1.97%) greater increase in serum total cholesterol (P for trend=0.006 and 0.001) compared to those with the lowest PFOA levels. There were no significant associations between serum PFOA and other metabolites. These results provide epidemiological evidence that environment-related levels of serum PFOA may be positively associated with the prevalence of diabetes in men and with total cholesterol in adults. Further clinical and animal studies are urgently needed to elucidate putative causal relationships and shed light on the potential mode of action involved.
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Directions
Sift or whisk together the flour, sugar, cocoa, baking soda, and salt into a bowl. In a separate bowl, mix the coconut milk, oil, vinegar, vanilla, and espresso powder until smooth. Pour the wet mixture into the dry mixture and mix with a fork or small whisk. Divide the batter evenly among the prepared cupcake liners. The cups should be filled about 2/3-full, and bake until a toothpick inserted in the center comes out clean, about 20 to 22 minutes for the mini cupcakes and about 25 minutes for the regular-size cupcakes. Cool the cupcakes in the pans for 5 minutes and then transfer to a rack to cool completely.
Slice off the top 1/3 of each cupcake and slather with frosting and sliced strawberries. Place the top of the cupcake back on top and add an additional bit of frosting and sliced strawberries. Dust with confectioners sugar, if using.
Frosting:
Combine the confectioners' sugar, margarine, and vanilla extract in the bowl of a stand mixer. Beat on medium-high speed until combined. With the mixer running, add 1 tablespoon of water at a time, until the desired buttercream consistency.
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King started the panel asking the crow of they had read Heroes in Crisis? Most audience members replied with a loud cheer, so he then asked “who loved it?” another cheer – “who is mad about it?” another loud noise – who “both loved it and is really mad about it” a less loud cheer came from the crowd “so there is not a complete overlap – I do have a bodyguard with me, I just want you to know” said King.
He also noted that more people are dead in kill zone than have been revealed – the spinoffs will show who these characters are.
Eza then noted that Mister Miracle had just won best series at The Ringos – and they showed the award itself. King then noted that he had won the Eisner for best writer (Gerads clarified that he actually shared the award with Marjorie Liu). Gerads had won best artist so King was sure they would win best series – ‘what else is left but just coloring and lettering? we can’t lose!”. When they didn’t get the award he joked he felt like “my letterer has some explaining to do!”
King was asked about what he has coming up in Batman – he joked “hmm are there any Titans left that I could shoot”? and that he has a 12 issue arc lined up “The Death of Aqualad – where he is slowly falling off a building for 12 issues chanting “Ihope there is water at the bottom, I hope there is water at the bottom”.
Actually he has an arc coming up featuring KGBeast that will be drawn by Mark Buckingham – the impetus for the story came about because sometimes “I just want to punch Russians – no offense to Russians” the crowd laughed at this statement and King caught himself and made the first mention (of many in this panel) to this illustrious website “Oh great I can’t wait for the Bleeding Cool headline: Tom King wants to punch Russians” – thanks for the idea Tom!
Batman #54 cover by Matt and Brennan Wagner
Mitch Gerads then talked about how he is returning to Batman to do an arc and he apologized to the audience – it was his idea to use the villain Professor Pyg “I am sorry now we all have to deal with a Tom King Professor Pyg story – it is truly disgusting”
King was asked “Why do you hate sidekicks?”
“I don’t! – Oh wait I just killed 3 of them“. He then started talking about his refusal to kill Robinas has been covered in another post on this site. He had decided that killing Robin was too easy and obvious and discussed that with some writer colleagues – including Steve Orlando – who all agreed.
Then when he went to the Batman creative summit the editors asked the creators “who thinks we should kill Tim “Red Robin” Drake” and every writer – except King – but including Orlando put up their hand “I was like “et tu, Steve Orlando?””
So the decision was made – Drake was for the chop and in the bar afterwards King indiscreetly bitched about it to all and sundry. The story made its way back to this site which spoiled the development, which led DC to change their plans and angrily ask the creators “who is responsible for this leak!?” – ”I said it was Steve Orlando” joked King as the panel wound up.
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PHOENIX – Starting left-hander Brett Lilek tossed his first career complete game to power No. 9 Sun Devil Baseball to a victory against No. 2 UCLA, 2-1, in the series finale on Sunday at Phoenix Municipal Stadium.
Lilek (4-2) did not give up an earned run in the longest outing of his career and allowed just five base runners on three hits, a walk and a hit batter. He retired the first 14 batters of the game before his no-hit bid was broken up with a two-out single in the fifth inning. His seven strikeouts tied a season-high as he threw 68 of his 108 pitches for strikes.
The Sun Devils (30-17, 15-9) notched their nation-leading 53rd consecutive 30-win season to continue a streak that began in 1963. It is two more than the next closest Div. I team, Florida State, and Arizona State has had just one losing season in the program's 57 years.
Center fielder Johnny Sewald drove in both of ASU's runs with a single in the fifth and a double in the seventh, and finished the weekend with seven hits, two runs and three RBI.
ASU took a 1-0 lead in the bottom of the fifth behind a double from designated hitter RJ Ybarra and a two-out RBI single from Sewald. The Devils added to their advantage in the seventh inning behind a leadoff walk, a single by second baseman Andrew Snow and a RBI double by Sewald to right field.
The Bruins (36-12, 18-6) cut ASU's lead in half, 2-1, with an unearned run in the top of the eighth. Shortstop Kevin Kramer followed a hit batter with a two-out single that slipped under the glove of left fielder Andrew Shaps and allowed both runners to move into scoring position. Left fielder Ty Moore grounded out to ASU shortstop Colby Woodmansee in the next at-bat, but the lead runner scored from third before Woodmansee was able to throw Kramer out at second base.
UCLA starting left-hander Hunter Virant (0-1) was lifted in the fifth inning after he gave up a one-out double that resulted in the first run of the game. He was responsible for one run on three hits in 4 1/3 innings in the loss.
Notes
The Devils notched their 11th win over a ranked opponent, including their fourth over a top-five team…ASU moved to 15-6 in one-run games this season, including 9-3 in Pac-12 play...ASU is 22-6 when leading after six innings and 22-2 when leading after eight…Phoenix Muni has drawn 98,482 fans this season.
Up Next
The Sun Devils head to Albuquerque, N.M., for a midweek game with New Mexico on May 12 at 5 p.m. PT, before heading home for the final three-game Pac-12 series of the season vs. Washington State May 14-16. First pitch on Thursday is set for 7 p.m., with Friday slated for a 4 p.m. start and Saturday at 7 p.m. All three homes will be televised by the Pac-12 Networks and broadcast on NBC Sports Radio AM 1060.
Family Section, Family Four Pack
The Family Section, located in Section 20 on the third-base line near the picnic area, does not permit alcohol or inappropriate language. A general admission ticket is the only requirement to gain entry into the section. Family Four Pack's include four tickets to the game, four big hot dogs and four 32 oz. fountain drinks, and start at just $60. Family Four Packs are available for all home mid-week and Sunday games. Click here to purchase.
2015 Flex and Mini Plans
Flex and Mini Plans are available now for the 2015 season at Phoenix Municipal Stadium. A Flex Plan allows fans to receive discounted prices up to 46 percent without having to choose games in advance. Fans will receive nine ticket vouchers that are redeemable for any game, in any quantity, in the infield reserved seating sections. Mini Plans offer fans the opportunity to pick and choose any five games this season. Click here to view Flex and Mini Plan options.
Transitioning The Legacy Campaign
Season ticket holders also have an opportunity to make a capital campaign commitment towards the Phoenix Muni renovations. All gifts, no matter the size, are important and appreciated, and can be a one-time gift or a five-year pledge. Fans interested in naming opportunities at Phoenix Muni can contact the Sun Devil Club at 480-727-7700. All commitments are tax-deductible through the Sun Devil Club. Join our community and own a piece of our hometown team.
Join the conversation all season
Twitter: @ASU_Baseball | Facebook: Sun Devil Baseball | Instagram: ASU_Baseball
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Silent Minute
The Silent Minute was an historic movement begun in the United Kingdom by Major Wellesley Tudor Pole O.B.E. in 1940. It continues today as a London-based charity following its revival by Dorothy Forster. During the Second World War people would unite in meditation, prayer or focus (each according to their own belief) and consciously will for peace to prevail. This dedicated minute received the direct support of King George VI, Sir Winston Churchill and his Parliamentary Cabinet. It was also recognized by U.S. President Franklin D. Roosevelt and observed on land and at sea on the battlefields, in air raid shelters and in hospitals. With Churchill’s support, the BBC, on Sunday, November 10, 1940, began to play the bells of Big Ben on the radio as a signal for the Silent Minute to begin.
History
The idea was developed in Britain in the Second World War, initially from an idea by Major Wellesley Tudor Pole. People were asked to devote one minute of prayer for peace at nine o’clock each evening. He said:
“There is no power on earth that can withstand the united cooperation on spiritual levels of men and women of goodwill everywhere. It is for this reason that the continued and widespread observance of the Silent Minute is of such vital importance in the interest of human welfare.”
The Silent Minute began in 1940 during The Blitz on the UK when Major Wellesley Tudor-Pole perceived
an inner request from a high spiritual source that there be a Silent Minute of Prayer for Freedom, at 9pm each evening during the striking of Big Ben. If enough people joined in this gesture of dedicated intent, the tide would turn and the invasion of England would be diverted.
Tudor-Pole went to the King and Prime Minister with his request and won both their support.
An anecdote emphasizes the profound power of the group meditation of the Silent Minute. In 1945 a British intelligence officer was interrogating a high Nazi official. He asked him why he thought Germany lost the war. His reply was, “During the war, you had a secret weapon for which we could find no counter measure, which we did not understand, but it was very powerful. It was associated with the striking of the Big Ben each evening. I believe you called it the ‘Silent Minute.’
The Silent Minute in the 21st Century
The Silent Minute was revived by Dorothy Forster and gained a new following of people after the 9/11 terrorist attack on the World Trade Center and the commencement of the wars in Iraq and Afghanistan. It continues as a small charitable organisation based in London, but with a worldwide list of participants. Some people had continued the habit of the 9 p.m. prayer ever since the Second World War, but diverting their focus to the different areas of the World wherever there were conflicts currently ongoing. Apart from these few people, the practice had been largely forgotten by the British public for almost half a century until it was revived.
The trustees maintain that there is always war going on somewhere in the World and that uniting in a collective will for peace may have some beneficial effect for humankind, whether or not there is any direct effect upon the conflict. At the heart of the effort there is a community united from people of all ages, races and backgrounds, and a focus on our collective humanity and the benefits of peace in society.
The Silent Minute does not have any political affiliations and receives no funding, but runs entirely on donations from the general public.
See also
Moment of silence
Two-minute silence
References
External links
Silent Minute website
Major Wellesley Tudor-Pole biography
Remembrance History
Category:Commemoration
Category:Silence
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Eid Ul Adha Mubarak Best Wishes Greetings 2015
Beneficial visitors have look by means of hottest selection of Eid Ul Adha Mubarak Best Wishes Greetings 2015 needs status and Eid ul Adha Greeting Graphics and Quotes in the good execution of pictures. Now throughout the globe a time and energy to choose between the ideal Statements that’s one hundred forty text in duration and go it for your joyful brothers and family to pals which can be continues to be waiting around to your hottest pleased Eid ul Adha wishes which will improve the like they hold their own individual heart in your case. As we create Eid ul Adha is the vacation that remind u.s. of america the sacrifices on the prophet Ebrahim in history but possessing the exactly the same emotions inside your individual heart so is definitely ordinarily great to perform not ignore that sacrifices for Almighty manufactured the Prophet Ebrahim and system your loving employees now.
Eid Ul Adha Mubarak Best Wishes Greetings 2015
May perhaps Allah take your very good deeds;
Forgive your transgressions;
And relieve your worldy sufferings.
Would like you an exceptionally joyous and peaceful Eid!
E-Embrace with open up coronary heart
I-Inculcate very good deeds
D-Distribute & share Allah’s bounties with the underprivileged
Eid Mubarak!
Allah rewards all those who fast religiously during the holy month of Ramadan. He showers them with countless blessings. May well He give you the strength and the character to remember Him at all times. Eid ul-Fitr is an example of His benevolence and abundance showered on the rich as well as the poor. Could you be the blessed one on this Eid!
Content Eid ul-Fitr!
When my arms can’t reach people who are close to my coronary heart, I always hug them with my prayers.
May well Allah be always with you and give you peace, abundant happiness and contentment!
Eid Mubarak!
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Sulfate reduction at low pH to remediate acid mine drainage.
Industrial activities and the natural oxidation of metallic sulfide-ores produce sulfate-rich waters with low pH and high heavy metals content, generally termed acid mine drainage (AMD). This is of great environmental concern as some heavy metals are highly toxic. Within a number of possibilities, biological treatment applying sulfate-reducing bacteria (SRB) is an attractive option to treat AMD and to recover metals. The process produces alkalinity, neutralizing the AMD simultaneously. The sulfide that is produced reacts with the metal in solution and precipitates them as metal sulfides. Here, important factors for biotechnological application of SRB such as the inocula, the pH of the process, the substrates and the reactor design are discussed. Microbial communities of sulfidogenic reactors treating AMD which comprise fermentative-, acetogenic- and SRB as well as methanogenic archaea are reviewed.
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Knoji reviews products and up-and-coming brands we think you'll love. In certain cases, we may receive a commission from brands mentioned in our guides. Learn more.
Seniors, Senior Citizen and the elderly are the common terms for a person who comes with the retirement age. Retirement age at which an individual can retire from his or her job position and receive all the benefits guaranteed under a retirement plan. A major part of life is working so hard, and the time has come to enjoy the fruits of labor. Now, what comes next ? Life continues with the retirees, here are ways how to get more out of life during retirement age :
Stay positive. Although anxiety usually comes in with the elderly, try to counteract the worries and enjoy life instead. Every morning is a new day, do something that would keep the spirit alive.
Explore new horizons. Travelling is one of the most enjoyable and enriching activity after years of hardwork since taking a vacation is often missed because of end to end schedules. An exploration of new environment gives an opportunity to see more of the beauty of the world, increase knowledge, widens perspective, and able to meet people of different culture.
Pursue and widen interests. In younger days, personal interests and hobbies are being neglected because the main focus are generating income and taking care of the family. Now is the time to pursue personal pastimes like writing, gardening, painting, playing a musical instrument, go into sports, learn new things in the computer such as joining social media groups and other networking sites. Browse the web with subjects of interest and discover untold wealth of information. It is never too late to learn and keep up with the new generation.
youtube video courtesy of havelah
Keep the heart,mind and body healthy.
• Avoid heated arguments and emotional conflicts. Have a regular cardiovascular check-up with the family doctor.
• Quit smoking and drink alcohol moderately. Too much alcohol is bad for arthritis, overweight, and cardiovascular diseases.
• Exercise regularly by doing light exercises or taking a brisk walk around the neighborhood. Walking stimulates the senses and it gets the blood circulating.
• Eat plenty of protein,iron,ascorbic acid and calcium.
• Drink plenty of plain water without sugar or caffeine and other liquids with chemicals. Water can keep the body balance and help maintain healthy weight. It also reduces drowsiness and fatigue.
• Cut down on butter, fats and oil.
• Our body needs exercise so as our mind. Continue to be updated with the latest news and keep the habit of reading books. Reading helps largely in sharpening memory.
Build Relationships. Spend quality moments with family and enjoy being around with grandchildren as well as taking time to have some coffee moments with valued friends who had been there through the years. Build new relationships by joining a group which brings a sense of belongingness and worthiness. One example is do volunteering in church or joining charity activities which are opportunities to share oneself in giving time to those in need.
Reconnect with yourself. Have a regular schedule of giving yourself alone without the noisy distractions around. Take time to reconnect with your own self and just enjoy the serenity by meditating peacefully in silence. Keep the religious faith within and reconnect soul to the divine spirit. Meditation and prayer can keep the mind healthy and rejuvenates the soul.
More articles :
Things People Normally Forget
Home Improvement Planning And Cost Saving Tips
Home Safety 101: How To Prevent Accidents Inside The House
How to balance housekeeping tasks with your career life without burning out
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Q:
Overlay while loading page into QWebView
Let's say we have a barebones QWebView:
#include <QApplication>
#include <QWebView>
int main(int argc, char** argv)
{
QApplication app(argc, argv);
QWebView view;
view.show();
view.setUrl(QUrl("http://google.com"));
return app.exec();
}
How can I display a graphic overlay, preferably fullscreen with transparency and minimal animation (like timer/beachball/etc.) from when the page starts loading till it's finished? Should also be triggered when url changes from within the QWebView.
A:
You can use the LoadingOverlay class provided in this answer to draw an overlay over any QWidget. In your case, show the overlay on top of the QWebView when the signal loadStarted is triggered and hide it, when the signal loadFinished is triggered.
The following code should get you started. I put the code from the linked answer into overlay.h, the subclass of QWebView which handles the showing/hiding of the overlay is in webview.h:
webview.h
#include "overlay.h"
#include <QWebView>
class WebView : public QWebView
{
Q_OBJECT
public:
WebView(QWidget * parent) : QWebView(parent)
{
overlay = new LoadingOverlay(parent);
connect(this,SIGNAL(loadFinished(bool)),this,SLOT(hideOverlay()));
connect(this,SIGNAL(loadStarted()),this,SLOT(showOverlay()));
}
~WebView()
{
}
public slots:
void showOverlay()
{
overlay->show();
}
void hideOverlay()
{
overlay->hide();
}
private:
LoadingOverlay* overlay;
};
main.cpp
#include <QApplication>
#include "overlay.h"
#include "webview.h"
int main(int argc, char *argv[])
{
QApplication a(argc, argv);
ContainerWidget base;
Webview w(&base);
base.show();
w.load(QUrl("http://google.com"));
return a.exec();
}
|
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"pile_set_name": "StackExchange"
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<?xml version="1.0" encoding="utf-8"?>
<selector xmlns:android="http://schemas.android.com/apk/res/android">
<item android:state_pressed="true" android:color="@color/lesdk_green_dark"/>
<item android:color="@color/sdk_green"/>
</selector>
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| 0.067797 |
I. Introduction
===============
A Drug Utilization Review (DUR) system prevents drug side effects and helps reduce the use of problematic medicine and medical supplies by preventing the prescription and preparation of inappropriate drugs \[[@B1]\]. Although the United States implemented such a system in 1990, South Korea developed the DUR, and it was subsequently implemented in all recuperation centers in the country \[[@B2]\]. Korea\'s DUR system can be largely divided into inspection \"within and between prescriptions.\" It contains various types of information, such as restrictions on combined intake, restrictions for certain age groups, restrictions for pregnant women, medicines prepared in low-content multiples, medicines suspended for safety reasons, and overlapping prescriptions with the same ingredients administered through the same injection routes \[[@B3]\]. In some cases, warning pop-ups appear during the prescription process, flagging restrictions on combined intake, restrictions for certain age groups, restrictions for pregnant women, and overlapping prescription drugs with the same ingredients. To proceed with such a prescription, a physician must provide a reason for prescription of the alerted medicine \[[@B4]\].
The prohibition on combined use is intended to prevent drug--drug interactions (DDIs) \[[@B5]\]. Patients can sometimes be prescribed more than 2 administered drugs during their treatments, which can cause DDIs. In a DDI, 2 administered drugs interact and change the absorption speed, proteinbinding site, biotransformation, or excretion speed of one or both drugs \[[@B6]\]. Such changes manifest as additive, synergistic, or antagonistic reactions, and can cause severe side effects and toxicity. Although DDIs occur frequently \[[@B7][@B8]\], a considerable number can be prevented through use of a DUR system \[[@B9]\].
South Korea has the advantage that a single DUR system is used in all medical institutions and recuperation centers except in oriental medicine institutes. For the Korean DUR system to work effectively, it must be continually monitored and improved. However, there has been limited research on this system since 2010; in particular, no study has analyzed cases of alert overrides with overlapping prescription codes and reasons for override (i.e., free-text entry), even though these are the key elements of the DUR system. To fill this gap in the research, we examined all such cases among outpatients in a tertiary medical institution from the past 10 months and analyzed the current use of existing overlapping prescription codes and free-text exception reasons. Based on our findings, we were able to propose new alert override codes that improve upon the existing codes.
1. DUR System and Overlapping Prescription Codes
------------------------------------------------
South Korea\'s DUR system involves 1) self-inspection within and cross-inspection between prescriptions, 2) prescription and preparation of medicines in accordance with the inspection results, and 3) entry of reasons and transmission completion. The first is a check for any prohibitions on combined use, ingredient overlap, restrictions for certain age groups, and restrictions for pregnant women within the same prescription. The second is a crosscheck of the information from self-inspection, which was automatically transmitted to the central server of the Health Insurance Review and Assessment Service (HIRA), with that of prescriptions of another medicine currently taken by the patient. The cross-inspection involves 1) comparison of prescriptions of medicines before preparation and 2) comparison of preparations for medicines already being taken. If a medicine prohibited from prescription is ultimately prescribed for medical and pharmaceutical reasons in a medical institution, the corresponding reason is entered into the system to complete the processing. When the reason is entered, the type and side effects of the relevant medicine must be explained to the patient, and the reason code or details must be input and sent to the HIRA. The reasons are entered differently depending on the inspection grades; they can be omitted if the inspection grade is A, but must be entered for grade B. For grade C, the drug must not be prescribed because it is prohibited, while for grade D, the reason entry is optional. Apart from inspection grades, there are 11 types of overlapping prescription codes already established, including A--C, F--K, and P. Overlapping prescription reasons related to combined use, age, or pregnancy can be entered as free text. The overlapping prescription codes, which were devised by the HIRA, are entered when
A: a patient must receive a prescription before exhausting the existing medicine or medical supplies due to a long-term business trip or travel;
B: specific ingredients cannot be sorted for separate prescriptions among existing prescribed medicines due to preparation in powder form;
C: a medicine is destroyed or altered for reasons not attributable to the patient (e.g., vomiting during drug intake);
F: the prescription and administration dates differ;
G: a medicine is administered weekly or monthly;
H: overlapping or combined drug use occurs by a change of only the method of intake or volume;
I: overlapping or combined medicine use occurs due to a change of only the number of administration dates;
J: a patient does not take the existing prescription or prepared medicine (voluntarily);
K: a patient cannot reach the prescribing doctor or preparing pharmacists via phone;
L: a patient is not permitted to take the existing prescribed medicine (by the doctor); and
P: a medicine is administered pro re nata (PRN).
II. Methods
===========
1. Study Material
-----------------
This study examined all alert override cases in the DUR system among outpatients of a tertiary medical institution from April 1, 2012 to January 15, 2013. The data cover only cases in which an alert override occurred and do not contain any private or health-related patient or health professional information.
### 2. Code and Free-Text Analysis Methodology
While the alert override cases assigned an overlapping prescription code can be readily used in analysis, the free-text reasons comprise a large, diverse, and irregular body of free text including Korean and English text, meaningless symbols, and numbers. This makes automated analysis impossible. Therefore, all free-text data were classified manually by two researchers (JC, KBY) and evaluated by RWP. In this study, the exception processing codes of Grizzle et al. \[[@B10]\] and Ahn et al. \[[@B11]\] were referenced in classification. Grizzle et al. \[[@B10]\] developed 14 categories for overriding DDI alerts and prescribers classified their messages into the categories after excluding duplicated messages from ambulatory pharmacy dispensing records. Ahn et al. \[[@B11]\] was modified from the study of Grizzle et al. \[[@B10]\] and simplified according to the subject data.
### 3. Statistical Analysis Methods
This study did not require statistical evaluation, as the classification results were merely recorded. For data extraction and classification, MS-SQL 2012 (Microsoft, Redmond, WA, USA) was used.
III. Results
============
According to an analysis of the system log file of all outpatient DDIs in the target medical institution, there were 28,606 alert override cases. Among the 7,879 cases with overlapping prescription codes, we excluded 48 with missing data and 59 involving an unknown drug; this resulted in a 7,772 cases. Among the 20,727 free-text cases, we excluded 102 with missing data and 442 involving an unknown drug, thereby leaving 20,183 cases for analysis. In total, 27,955 cases were included in the analysis ([Figure 1](#F1){ref-type="fig"}).
The most frequently appearing overlapping prescription code was F, at 2,519 cases (32.4%), followed by A, at 2,428 cases (31.2%). The least frequent code was K, which occurred only once ([Table 1](#T1){ref-type="table"}).
An analysis of the free-text reasons entered for alert override prescriptions revealed 15 classifications. The most frequently occurring reason was \"prescribing a medicine to control a patient\'s symptom,\" with 5,665 cases (28.1%) followed by \"meaningless/no meaning (e.g., ㅋㅋㅋ, aaa),\" with 4,263 cases (21.1%). \"Prescribing out of necessity\" occurred in 3,719 cases (18.4%). For a number of cases, the reasons did not match any existing overlapping prescription codes, including 290 cases (1.4%) for \"prescribing out of necessity before and after an operation or examination\" and 458 cases (2.3%) of \"emergency situations.\" Among these 15 classifications, 8,626 cases (42.8%) could be classified using the 11 HIRA codes; 11,537 cases (57.2%) could not. Notably, the need for new codes describing operations and emergency situations was identified when these unclassifiable cases were analyzed and classified ([Table 2](#T2){ref-type="table"}).
The results of the free-text classification were compared with the HIRA override prescription codes. This led to the identification of 6 new alert override codes ([Table 3](#T3){ref-type="table"}). Previous codes P and G were combined into J1. Previous code L was revised as J3. The 6 codes describing drug nonadministration situations (A, C, F, H, I, and J) were thought to be overly descriptive of surrounding situations in which drugs were not being administered; thus, these 6 codes were combined into J4: \"patient was not taking/will not take the medications involved in the DDI.\" The cases made up of meaningless symbols and characters were classified as \"prescriber provided no reason for override\" (n = 4,263, 21.1%) and were not included in the new classification system. Codes B (0.8%) and K (0%) were rarely used and thus were classified as \"rarely used reasons\" (n = 65, 0.8%); they were also not included in the new classification system.
Using the new classification structure, we reanalyzed the 20,183 alert override cases with free-text reasons. Of the free-text reasons, code J2 (\"prescriber provided clinical justification\") was the most frequent, with 6,449 cases (32.0%), followed by J1 (\"PRN \[as needed\] or intermittent medication\"), with 3,968 cases (19.7%). \"Prescription according to patient request\" (77 cases, 0.4%) was found to be too general and unclear, and thus was not included in the new system.
On the basis of the new classification, J4 was the most frequently occurring reason at 9,551 cases (34.2%), followed by J2, with 6,449 cases (23.1%), and then J1, with 4,669 cases (16.7%).
IV. Discussion
==============
We analyzed and classified DUR alert override cases occurring among outpatients in a tertiary medical institution and codified the results to improve existing codes for overlapping prescription reasons, and based on our findings, we introduced a new coding system. The main purpose of the DUR system is to help physicians administer drugs safely and with minimal side effects. For the DUR system to be successfully implemented in accordance with this purpose, research on its effects and means of improvement is required in many areas, including strategy, cost, stability, and convenience. This study sought to identify appropriate methods of improvement by analyzing override reasons. Specifically, we analyzed the frequency of overlapping prescription codes and free-text reasons. In the process, the free-text content was classified into 15 different categories based on similarity of content as found by the researcher; these 15 categories were compared with the existing overlapping prescription codes, resulting in the creation of 6 new alert override codes.
This study utilized the entire set of DDI data on outpatients of a tertiary medical institution from April 1, 2012 to January 15, 2013. We minimized recall and selection biases by analyzing all prescription cases within the system log file, and minimized the classification errors for all 20,183 cases involving free-text override reasons via manual evaluation and classification.
To create the new override reason codes, we consulted a previous study \[[@B11]\]; previous code P was revised and renamed J1; codes J2 and J4 were adopted from a previous study by Grizzle et al. \[[@B10]\]; and codes J3, J5, and J6 were created by the researcher. The main contribution of this study is the recommendation of an improved coding system for override reasons based on existing overlapping prescription codes and free-text reasons. Although one previous study \[[@B11]\] performed some analysis of overlapping prescription codes for hospitalized patients, there have been almost no studies that have conducted comparative analysis of these codes and free-text reasons. Therefore, the current study makes a meaningful contribution by conducting a systematic comparison of overlapping prescription codes and free-text reasons as the basis for developing an improved coding system.
In analyzing the overlapping prescription reason codes, the most frequent was F (32.4%), followed by A (31.2%). Code F (\"when the prescription and administration dates differ\") seems irrelevant to the prevention of DDIs caused by overlapping prescriptions.
Moreover, code A (\"when a patient has to receive a prescription before exhausting the existing medicine or medical supplies due to a long-term business trip or travel\") also seems irrelevant to the prevention of DDIs caused by overlapping prescriptions, as it seems a very reasonable reason for overlapping prescriptions from the patient\'s perspective. In contrast, codes B (\"when specific ingredients cannot be sorted for separate prescriptions among existing prescribed medicines due to preparation in powder form\") and K (\"when a patient cannot reach the prescribing doctor or preparing pharmacists via phone\") were very rarely used by the prescribing physician, and seem inappropriate from a researcher\'s perspective; they were thus classified as rarely used reasons (n = 65, 0.8%). Clinically irrelevant codes are known as the main source of alert fatigue \[[@B12]\] and most can be ignored \[[@B13][@B14]\].
Codes A, C, F, H, I, and J were thought to be overly descriptive of a situation wherein a drug is not being administered; thus, they are difficult to distinguish in practice. To prevent confusion among physicians, we merged these codes into a new code, J4: \"patient was not taking/will not take the medications involved in the DDI.\"
According to the analysis of the free-text cases that could not be classified using existing codes, we noted many occurrences of \"prescription relating to operation\" and \"emergency situations.\" This led to our creating two additional codes (J5 and J6). The most frequently occurring reason among the free-text cases was \"prescribing a medicine to control a patient\'s symptoms,\" with 5,665 cases (28.1%); this reason was mapped onto J2. The second most frequently occurring reason was \"meaningless/no meaning (e.g., ㅋㅋㅋ, aaa)\" with 4,263 cases (21.1%). However, such cases were difficult to codify; therefore, they were processed as \"prescriber provided no reason for override\" (n = 4,263, 21.1%). \"Prescribing out of necessity\" also frequently occurred, at 3,719 cases (18.4%), and was subsequently mapped onto code J1.
We considered establishing code G (\"when a medicine is administered weekly or monthly\") as a separate item but decided to merge it with J1 because it was rarely used (6.3%) and the code itself means that the medicine is administered rarely. Ultimately, the analysis of the existing 11 overlapping prescription codes resulted in 6 codes being merged into a single code, 2 codes being deleted, and 2 codes being created, resulting in 6 new alert override codes. When this new set of codes was applied to the cases, we found that 23,550 (84.2%) of the total 27,955 cases could be codified.
This study had the following limitations. First, this was a case study of DUR alert override reasons from a single tertiary medical institution over a period of approximately 10 months. This could have resulted in selection bias. Second, we excluded prescriptions for hospitalized patients; if prescription patterns differ between inpatients and outpatients, the results of this study may not reflect the actual clinical environment. Third, the prescription analysis was limited to drugs prescribed over a certain period of time within the same hospital, and the number of alerts in this study cannot be considered to reliably represent all DDI cases. Finally, our own subjective standards may have influenced the codifying of the free-text, the mapping of the existing codes and freetext reasons onto new codes, and the deletion of existing codes.
These new codes will facilitate the use of drug--drug interactions alert override in the current DUR system. For further studies, an appropriate evaluation should be conducted with prescribing clinicians and the reason \"meaningless/no meaning (e.g., ㅋㅋㅋ, aaa)\" in free text needs to be identified.
**Conflict of Interest:** No potential conflict of interest relevant to this article was reported.
{#F1}
###### Frequency of overlapping prescription codes of the health insurance review and assessment service
###### Frequencies of override reasons in free text
###### Frequency of alert override reasons using new classification system
Code J1 was taken from the HIRA codes. Codes J2 and J4 were from Grizzle et al. \[[@B10]\] and Ahn et al. \[[@B11]\]. Codes J3, J5, and J6 were newly proposed in this study.
HIRA: Health Insurance Review and Assessment Service, PRN: pro re nata, DDI: drug--drug interaction.
|
{
"pile_set_name": "PubMed Central"
}
| 0 |
Jack of no clubs
Sharing a picture of his pet, he wrote: "I am using Instagram for help. I have lost this parrot in the San Siro area (of Milan) he has a red ring with the number 23 on. He is one of my children and I urge you to contact me with any information".
Action Images
Philippe Mexes won 29 caps for France in a 10-year international career
Mexes fires in an amazing overhead kick for AC Milan against Anderlecht
Centre-back Mexes celebrates his wondergoal with Kevin-Prince Boateng
Mexes retired in 2016 after finishing his career with a five-year stint at Milan.
He previously played for Roma - where he established himself as one of Europe's top defenders - and Auxerre in his homeland.
The Frenchman won 29 caps in a 10-year career in international football -scoring his only goal against Luxembourg in 2011.
|
{
"pile_set_name": "Pile-CC"
}
| 0 |
You can suck a dick if you want... Just suck that dick like a man
333 shares
|
{
"pile_set_name": "OpenWebText2"
}
| 0.051948 |
// Copyright Louis Dionne 2013-2017
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/equal.hpp>
#include <boost/hana/length.hpp>
#include <boost/hana/maximum.hpp>
#include <boost/hana/ordering.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
int main() {
static_assert(
hana::maximum.by(hana::ordering(hana::length), hana::make_tuple(
hana::make_tuple(),
hana::make_tuple(1, '2'),
hana::make_tuple(3.3, nullptr, 4)
))
== hana::make_tuple(3.3, nullptr, 4)
, "");
}
|
{
"pile_set_name": "Github"
}
| 0 |
Bleeding edge tutorials and news for game developers working with Dart
Tuesday, July 30, 2013
SIMD on the Web July 2013 Update (ARM, JavaScript, and AVX-512)
Accessing the SIMD instruction sets available in both desktop and mobile CPUs can greatly speedup 3D graphics (and other) applications . Until recently, web programmers have been unable to access this part of the CPU losing out on performance and battery savings. In the six months since I gave my talk, Bringing SIMD to the Web via Dart, a lot of things have happened. Read on for a complete status update on SIMD on the web including the latest on ARM, JavaScript, and AVX-512 support.
The Dart to JavaScript compiler fully supports the Float32x4, Uint32x4, and Float32x4List types. When compiled to JavaScript the types are implemented in software and do not give speedups. A flag will be introduced allowing your program to detect when SIMD will be slow. If your program executing on an ARM CPU without NEON (most current generation smart phones have NEON support, but older ones may not.) support or via JavaScript it is recommend that you use non-SIMD code paths.
4. What about JavaScript acceleration?
I've proposed these types for ECMAScript 7. I've created a polyfill for those interested in what the API will look like. Time will tell how serious the ECMAScript members are about SIMD and how fast the JavaScript engines can implement support for it.
5. What about AVX and AVX-512?
For those of you who don't follow the latest CPU instruction sets, AVX is the successor to SSE and has 256-bit wide registers (YMM). AVX-512 is a follow up to AVX and adds 512-bit wide registers (ZMM) and doubles (32 instead of 16) the number of register names available. Exciting stuff. AVX exists in the wild and I plan on implementing Float32x8 later this year. AVX-512 was only just announced and no chips support it (yet), once AVX-512 becomes closer to reality Dart will get a Float32x16 type.
|
{
"pile_set_name": "Pile-CC"
}
| 0 |
Q:
How to place the checkBox In between rows of tableview
My Problem is I want to place the checkbox in between the rows of the tableview.
A:
HI... There is nothing like check box friend and for showing that you have to use custom cell and use imageview in it that showing that check box.. you have to change the image when user click on it with tick image and if again clcik on the same hen it change with cross or disappear...
if( check == 0 )
{
UIButton *selectedButton = (UIButton *)sender;
if (editCount%2 == 0) {
[(UIButton *)[self.view viewWithTag:160] setImage:[UIImage imageWithContentsOfFile:[[NSBundle mainBundle] pathForResource:[NSString stringWithFormat:@"YOUR TICK IMAGE",[selectedButton tag]] ofType:@"png"]] forState:UIControlStateNormal];
} else {
[(UIButton *)[self.view viewWithTag:160] setImage:[UIImage imageWithContentsOfFile:[[NSBundle mainBundle] pathForResource:[NSString stringWithFormat:@"YOUR CROSS IMAGE",[selectedButton tag]] ofType:@"png"]] forState:UIControlStateNormal];
editCount++;
}
}
|
{
"pile_set_name": "StackExchange"
}
| 0 |
Vin de pays
Vin de pays (, "country wine") is a French wine classification that is above the vin de table classification, but below the appellation d'origine contrôlée classification, as well as the former vin délimité de qualité supérieure classification. Legislation on the Vin de pays terminology was created in 1973 and passed in 1979, allowing producers to distinguish wines that were made using grape varieties or procedures other than those required by the AOC rules, without having to use the simple and commercially non-viable table wine classification. Unlike table wines, which are only indicated as being from France, Vin de pays carries a geographic designation of origin, the producers have to submit the wine for analysis and tasting, and the wines have to be made from certain varieties or blends. Regulations regarding varieties and labelling practices are typically more lenient than the regulations for AOC wines. In 2009, the Vin de pays classification was replaced by the new Indication Géographique Protégée (IGP, "Protected Geographical Region") designation.
Taxonomy
There are three tiers of Vin de Pays: regional, departmental and local.
There are six regional Vins de Pays, which cover large areas of France. The most voluminous contributor to this category of wines is Vin de Pays d'Oc, from the Languedoc-Roussillon area in Mediterranean France. The second largest volume of Vin de Pays wines is produced as Vin de Pays de la Loire, a designation that applies to wines from the whole Loire Valley. The others are: Vin de Pays du Comté Tolosan (south-west), Vin de Pays de Méditerranée (south-east, Provence and Corsica) and Vin de Pays des Comtés Rhodaniens (Rhone valley). Two further regional Vin de Pays designations, Vin de Pays de l'Atlantique (Bordeaux and Charentes (Cognac)) and Vin de Pays Vignobles de France (all of wine-making France) were approved by French authorities in 2007, but (together with Vin de Pays de Gaules for the Beaujolais region) remain disputed and as of July 2009, they remained unpublished in the Official Journal of the European Union due to actions taken by other French wine producers. The Vin de Pays Vignobles de France has now been replaced by a table wine designation Vin de France, launched in August 2009.
Each regional Vin de Pays is divided into several departmental Vins de Pays, of which there are about 50. The names are derived from the French departments in question and the limits exactly the same as the department's borders. For example, Vin de Pays du Gard is one of the Vins de Pays produced within Vins de Pays d'Oc using grapes from the Gard department and the Vin de Pays de Charente-maritime is produced in the Cognac area. Approximately one third of the French departments don't produce Vin de Pays, for example Côte d'Or in Burgundy and Gironde in Bordeaux, or because the climate is not suited to produce wine at all, like the Bretagne, Normandy and Nord-Pas de Calais regions.
The local, or zone-defined Vins de pays are numerous, and may take their name from some historical or geographical phenomenon, such as Vin de Pays des Marches de Bretagne or Vin de Pays des Coteaux de l'Ardeche, or even a more locally specific variant. The boundaries of a zone may reflect a consistent terroir, rather than an administrative convenience, and could potentially in the long run achieve the status of an AOC.
Production rules
The conditions to respect to be allowed to use the classification Vin de pays are the following:
The yield must be less than 90 hectoliters per hectare for white wines, and less than 85 hl for red and rosé wines.
Only wine producers with a total yield of less than 100 hl/ha can qualify.
The minimum alcoholic strength depends on the region and is 10% in Le Midi, 9.5% in South-west France area and the Centre East area, and 9% for the Loire Valley and the East area.
The allowed amounts of sulfur dioxide allowed in the wines are 125 mg/l for red wines and 150 mg/l for white and rosé wines. For wines with sugar content of at least 5 g/l, the quantity of sulfur dioxide is slightly higher: 150 mg/l for red wines and 175 mg/l for white and rosé wines.
The acidity in terms of pH values is also regulated, with some Vin de Pays areas having stricter rules than others.
The wines must be kept and produced separately from other wines (e.g., production for table wines) and are subject to quality monitoring by an official regional committee.
Economic effects
In terms of volume, Vins de Pays d'Oc and Vin de Pays du Val de Loire (previously known as Vins de Pays du Jardin de France) are responsible for the majority of French exports.
Originally, Vin de Pays designation was commonly viewed as inferior to an AOC Appellation, often being ascribed to thin and simple wines. However, since the late 1980s, an increase in demand for varietal wines has led some French producers and cooperatives to produce more Vin de Pays, especially Vin de Pays d'Oc, to make varietal wines with some form of designation, while turning away from the highly restrictive AOC classification which often requires very specific blends of grape varieties.
This can be seen as a response to the increasing sales success of varietal New World wines from Australia, New Zealand, the United States, South Africa and Chile. As well as varietal wines (such as Cabernet Sauvignon or Merlot), Vin de Pays is being used to produce non-traditional blends which do not meet the requirements of AOC or VDQS regulations. Some of these wines are considered much better, and command higher prices, than AOC or VDQS wines from the same region, or even the same winemakers.
See also
Indicazione Geografica Tipica of Italy
Vino de la Tierra of Spain
Vinho Regional of Portugal
German wine classification Landwein of Germany
Tájbor of Hungary
References
Category:French wine
Category:Wine classification
|
{
"pile_set_name": "Wikipedia (en)"
}
| 0 |
Exclusive Promotions
Location
Consult the map and directions below to explore the location of the Ambassador Hotel Tulsa – conveniently situated just minutes from Tulsa Oklahoma attractions like City Hall, the Performing Arts Center and the entertainment and shopping districts of Brady, Brookside and Cherry Street.
For guests arriving by car, the hotel is easily accessible by three major highways leading into the downtown area.
Guests arriving by air are welcome to take advantage of our complimentary Cadillac Escalade service to and from the airport. This service is available between 7:00 am and 11:00 pm and can be arranged by calling the front desk.
|
{
"pile_set_name": "Pile-CC"
}
| 0 |
Hardcore Bondage and BDSM in the dungeon
|
{
"pile_set_name": "OpenWebText2"
}
| 0.075 |
Cum in my new panties after fuck me baby !!!
|
{
"pile_set_name": "OpenWebText2"
}
| 0.068182 |
PUSSY AND CLIT LICKING UNTIL SHE CUMS – REAL WET ORGASM
|
{
"pile_set_name": "OpenWebText2"
}
| 0.054545 |
Bethany Benz Loves Some Cock In Her Ass
|
{
"pile_set_name": "OpenWebText2"
}
| 0.051282 |
5:55
Pissing on her face and fucking her ass from behind
|
{
"pile_set_name": "OpenWebText2"
}
| 0.052632 |
She Fuck Him In Ass Hole
|
{
"pile_set_name": "OpenWebText2"
}
| 0.083333 |
// Generated by the capnpc-rust plugin to the Cap'n Proto schema compiler.
// DO NOT EDIT.
// source: record.capnp
pub mod record {
#[derive(Copy, Clone)]
pub struct Owned;
impl <'a> ::capnp::traits::Owned<'a> for Owned { type Reader = Reader<'a>; type Builder = Builder<'a>; }
impl <'a> ::capnp::traits::OwnedStruct<'a> for Owned { type Reader = Reader<'a>; type Builder = Builder<'a>; }
impl ::capnp::traits::Pipelined for Owned { type Pipeline = Pipeline; }
#[derive(Clone, Copy)]
pub struct Reader<'a> { reader: ::capnp::private::layout::StructReader<'a> }
impl <'a,> ::capnp::traits::HasTypeId for Reader<'a,> {
#[inline]
fn type_id() -> u64 { _private::TYPE_ID }
}
impl <'a,> ::capnp::traits::FromStructReader<'a> for Reader<'a,> {
fn new(reader: ::capnp::private::layout::StructReader<'a>) -> Reader<'a,> {
Reader { reader: reader, }
}
}
impl <'a,> ::capnp::traits::FromPointerReader<'a> for Reader<'a,> {
fn get_from_pointer(reader: &::capnp::private::layout::PointerReader<'a>, default: ::std::option::Option<&'a [::capnp::Word]>) -> ::capnp::Result<Reader<'a,>> {
::std::result::Result::Ok(::capnp::traits::FromStructReader::new(reader.get_struct(default)?))
}
}
impl <'a,> ::capnp::traits::IntoInternalStructReader<'a> for Reader<'a,> {
fn into_internal_struct_reader(self) -> ::capnp::private::layout::StructReader<'a> {
self.reader
}
}
impl <'a,> ::capnp::traits::Imbue<'a> for Reader<'a,> {
fn imbue(&mut self, cap_table: &'a ::capnp::private::layout::CapTable) {
self.reader.imbue(::capnp::private::layout::CapTableReader::Plain(cap_table))
}
}
impl <'a,> Reader<'a,> {
pub fn reborrow(&self) -> Reader<> {
Reader { .. *self }
}
pub fn total_size(&self) -> ::capnp::Result<::capnp::MessageSize> {
self.reader.total_size()
}
#[inline]
pub fn get_ts(self) -> f64 {
self.reader.get_data_field::<f64>(0)
}
#[inline]
pub fn get_hostname(self) -> ::capnp::Result<::capnp::text::Reader<'a>> {
::capnp::traits::FromPointerReader::get_from_pointer(&self.reader.get_pointer_field(0), ::std::option::Option::None)
}
pub fn has_hostname(&self) -> bool {
!self.reader.get_pointer_field(0).is_null()
}
#[inline]
pub fn get_facility(self) -> u8 {
self.reader.get_data_field::<u8>(8)
}
#[inline]
pub fn get_severity(self) -> u8 {
self.reader.get_data_field::<u8>(9)
}
#[inline]
pub fn get_appname(self) -> ::capnp::Result<::capnp::text::Reader<'a>> {
::capnp::traits::FromPointerReader::get_from_pointer(&self.reader.get_pointer_field(1), ::std::option::Option::None)
}
pub fn has_appname(&self) -> bool {
!self.reader.get_pointer_field(1).is_null()
}
#[inline]
pub fn get_procid(self) -> ::capnp::Result<::capnp::text::Reader<'a>> {
::capnp::traits::FromPointerReader::get_from_pointer(&self.reader.get_pointer_field(2), ::std::option::Option::None)
}
pub fn has_procid(&self) -> bool {
!self.reader.get_pointer_field(2).is_null()
}
#[inline]
pub fn get_msgid(self) -> ::capnp::Result<::capnp::text::Reader<'a>> {
::capnp::traits::FromPointerReader::get_from_pointer(&self.reader.get_pointer_field(3), ::std::option::Option::None)
}
pub fn has_msgid(&self) -> bool {
!self.reader.get_pointer_field(3).is_null()
}
#[inline]
pub fn get_msg(self) -> ::capnp::Result<::capnp::text::Reader<'a>> {
::capnp::traits::FromPointerReader::get_from_pointer(&self.reader.get_pointer_field(4), ::std::option::Option::None)
}
pub fn has_msg(&self) -> bool {
!self.reader.get_pointer_field(4).is_null()
}
#[inline]
pub fn get_full_msg(self) -> ::capnp::Result<::capnp::text::Reader<'a>> {
::capnp::traits::FromPointerReader::get_from_pointer(&self.reader.get_pointer_field(5), ::std::option::Option::None)
}
pub fn has_full_msg(&self) -> bool {
!self.reader.get_pointer_field(5).is_null()
}
#[inline]
pub fn get_sd_id(self) -> ::capnp::Result<::capnp::text::Reader<'a>> {
::capnp::traits::FromPointerReader::get_from_pointer(&self.reader.get_pointer_field(6), ::std::option::Option::None)
}
pub fn has_sd_id(&self) -> bool {
!self.reader.get_pointer_field(6).is_null()
}
#[inline]
pub fn get_pairs(self) -> ::capnp::Result<::capnp::struct_list::Reader<'a,crate::record_capnp::pair::Owned>> {
::capnp::traits::FromPointerReader::get_from_pointer(&self.reader.get_pointer_field(7), ::std::option::Option::None)
}
pub fn has_pairs(&self) -> bool {
!self.reader.get_pointer_field(7).is_null()
}
#[inline]
pub fn get_extra(self) -> ::capnp::Result<::capnp::struct_list::Reader<'a,crate::record_capnp::pair::Owned>> {
::capnp::traits::FromPointerReader::get_from_pointer(&self.reader.get_pointer_field(8), ::std::option::Option::None)
}
pub fn has_extra(&self) -> bool {
!self.reader.get_pointer_field(8).is_null()
}
}
pub struct Builder<'a> { builder: ::capnp::private::layout::StructBuilder<'a> }
impl <'a,> ::capnp::traits::HasStructSize for Builder<'a,> {
#[inline]
fn struct_size() -> ::capnp::private::layout::StructSize { _private::STRUCT_SIZE }
}
impl <'a,> ::capnp::traits::HasTypeId for Builder<'a,> {
#[inline]
fn type_id() -> u64 { _private::TYPE_ID }
}
impl <'a,> ::capnp::traits::FromStructBuilder<'a> for Builder<'a,> {
fn new(builder: ::capnp::private::layout::StructBuilder<'a>) -> Builder<'a, > {
Builder { builder: builder, }
}
}
impl <'a,> ::capnp::traits::ImbueMut<'a> for Builder<'a,> {
fn imbue_mut(&mut self, cap_table: &'a mut ::capnp::private::layout::CapTable) {
self.builder.imbue(::capnp::private::layout::CapTableBuilder::Plain(cap_table))
}
}
impl <'a,> ::capnp::traits::FromPointerBuilder<'a> for Builder<'a,> {
fn init_pointer(builder: ::capnp::private::layout::PointerBuilder<'a>, _size: u32) -> Builder<'a,> {
::capnp::traits::FromStructBuilder::new(builder.init_struct(_private::STRUCT_SIZE))
}
fn get_from_pointer(builder: ::capnp::private::layout::PointerBuilder<'a>, default: ::std::option::Option<&'a [::capnp::Word]>) -> ::capnp::Result<Builder<'a,>> {
::std::result::Result::Ok(::capnp::traits::FromStructBuilder::new(builder.get_struct(_private::STRUCT_SIZE, default)?))
}
}
impl <'a,> ::capnp::traits::SetPointerBuilder<Builder<'a,>> for Reader<'a,> {
fn set_pointer_builder<'b>(pointer: ::capnp::private::layout::PointerBuilder<'b>, value: Reader<'a,>, canonicalize: bool) -> ::capnp::Result<()> { pointer.set_struct(&value.reader, canonicalize) }
}
impl <'a,> Builder<'a,> {
pub fn into_reader(self) -> Reader<'a,> {
::capnp::traits::FromStructReader::new(self.builder.into_reader())
}
pub fn reborrow(&mut self) -> Builder<> {
Builder { .. *self }
}
pub fn reborrow_as_reader(&self) -> Reader<> {
::capnp::traits::FromStructReader::new(self.builder.into_reader())
}
pub fn total_size(&self) -> ::capnp::Result<::capnp::MessageSize> {
self.builder.into_reader().total_size()
}
#[inline]
pub fn get_ts(self) -> f64 {
self.builder.get_data_field::<f64>(0)
}
#[inline]
pub fn set_ts(&mut self, value: f64) {
self.builder.set_data_field::<f64>(0, value);
}
#[inline]
pub fn get_hostname(self) -> ::capnp::Result<::capnp::text::Builder<'a>> {
::capnp::traits::FromPointerBuilder::get_from_pointer(self.builder.get_pointer_field(0), ::std::option::Option::None)
}
#[inline]
pub fn set_hostname(&mut self, value: ::capnp::text::Reader) {
self.builder.get_pointer_field(0).set_text(value);
}
#[inline]
pub fn init_hostname(self, size: u32) -> ::capnp::text::Builder<'a> {
self.builder.get_pointer_field(0).init_text(size)
}
pub fn has_hostname(&self) -> bool {
!self.builder.get_pointer_field(0).is_null()
}
#[inline]
pub fn get_facility(self) -> u8 {
self.builder.get_data_field::<u8>(8)
}
#[inline]
pub fn set_facility(&mut self, value: u8) {
self.builder.set_data_field::<u8>(8, value);
}
#[inline]
pub fn get_severity(self) -> u8 {
self.builder.get_data_field::<u8>(9)
}
#[inline]
pub fn set_severity(&mut self, value: u8) {
self.builder.set_data_field::<u8>(9, value);
}
#[inline]
pub fn get_appname(self) -> ::capnp::Result<::capnp::text::Builder<'a>> {
::capnp::traits::FromPointerBuilder::get_from_pointer(self.builder.get_pointer_field(1), ::std::option::Option::None)
}
#[inline]
pub fn set_appname(&mut self, value: ::capnp::text::Reader) {
self.builder.get_pointer_field(1).set_text(value);
}
#[inline]
pub fn init_appname(self, size: u32) -> ::capnp::text::Builder<'a> {
self.builder.get_pointer_field(1).init_text(size)
}
pub fn has_appname(&self) -> bool {
!self.builder.get_pointer_field(1).is_null()
}
#[inline]
pub fn get_procid(self) -> ::capnp::Result<::capnp::text::Builder<'a>> {
::capnp::traits::FromPointerBuilder::get_from_pointer(self.builder.get_pointer_field(2), ::std::option::Option::None)
}
#[inline]
pub fn set_procid(&mut self, value: ::capnp::text::Reader) {
self.builder.get_pointer_field(2).set_text(value);
}
#[inline]
pub fn init_procid(self, size: u32) -> ::capnp::text::Builder<'a> {
self.builder.get_pointer_field(2).init_text(size)
}
pub fn has_procid(&self) -> bool {
!self.builder.get_pointer_field(2).is_null()
}
#[inline]
pub fn get_msgid(self) -> ::capnp::Result<::capnp::text::Builder<'a>> {
::capnp::traits::FromPointerBuilder::get_from_pointer(self.builder.get_pointer_field(3), ::std::option::Option::None)
}
#[inline]
pub fn set_msgid(&mut self, value: ::capnp::text::Reader) {
self.builder.get_pointer_field(3).set_text(value);
}
#[inline]
pub fn init_msgid(self, size: u32) -> ::capnp::text::Builder<'a> {
self.builder.get_pointer_field(3).init_text(size)
}
pub fn has_msgid(&self) -> bool {
!self.builder.get_pointer_field(3).is_null()
}
#[inline]
pub fn get_msg(self) -> ::capnp::Result<::capnp::text::Builder<'a>> {
::capnp::traits::FromPointerBuilder::get_from_pointer(self.builder.get_pointer_field(4), ::std::option::Option::None)
}
#[inline]
pub fn set_msg(&mut self, value: ::capnp::text::Reader) {
self.builder.get_pointer_field(4).set_text(value);
}
#[inline]
pub fn init_msg(self, size: u32) -> ::capnp::text::Builder<'a> {
self.builder.get_pointer_field(4).init_text(size)
}
pub fn has_msg(&self) -> bool {
!self.builder.get_pointer_field(4).is_null()
}
#[inline]
pub fn get_full_msg(self) -> ::capnp::Result<::capnp::text::Builder<'a>> {
::capnp::traits::FromPointerBuilder::get_from_pointer(self.builder.get_pointer_field(5), ::std::option::Option::None)
}
#[inline]
pub fn set_full_msg(&mut self, value: ::capnp::text::Reader) {
self.builder.get_pointer_field(5).set_text(value);
}
#[inline]
pub fn init_full_msg(self, size: u32) -> ::capnp::text::Builder<'a> {
self.builder.get_pointer_field(5).init_text(size)
}
pub fn has_full_msg(&self) -> bool {
!self.builder.get_pointer_field(5).is_null()
}
#[inline]
pub fn get_sd_id(self) -> ::capnp::Result<::capnp::text::Builder<'a>> {
::capnp::traits::FromPointerBuilder::get_from_pointer(self.builder.get_pointer_field(6), ::std::option::Option::None)
}
#[inline]
pub fn set_sd_id(&mut self, value: ::capnp::text::Reader) {
self.builder.get_pointer_field(6).set_text(value);
}
#[inline]
pub fn init_sd_id(self, size: u32) -> ::capnp::text::Builder<'a> {
self.builder.get_pointer_field(6).init_text(size)
}
pub fn has_sd_id(&self) -> bool {
!self.builder.get_pointer_field(6).is_null()
}
#[inline]
pub fn get_pairs(self) -> ::capnp::Result<::capnp::struct_list::Builder<'a,crate::record_capnp::pair::Owned>> {
::capnp::traits::FromPointerBuilder::get_from_pointer(self.builder.get_pointer_field(7), ::std::option::Option::None)
}
#[inline]
pub fn set_pairs(&mut self, value: ::capnp::struct_list::Reader<'a,crate::record_capnp::pair::Owned>) -> ::capnp::Result<()> {
::capnp::traits::SetPointerBuilder::set_pointer_builder(self.builder.get_pointer_field(7), value, false)
}
#[inline]
pub fn init_pairs(self, size: u32) -> ::capnp::struct_list::Builder<'a,crate::record_capnp::pair::Owned> {
::capnp::traits::FromPointerBuilder::init_pointer(self.builder.get_pointer_field(7), size)
}
pub fn has_pairs(&self) -> bool {
!self.builder.get_pointer_field(7).is_null()
}
#[inline]
pub fn get_extra(self) -> ::capnp::Result<::capnp::struct_list::Builder<'a,crate::record_capnp::pair::Owned>> {
::capnp::traits::FromPointerBuilder::get_from_pointer(self.builder.get_pointer_field(8), ::std::option::Option::None)
}
#[inline]
pub fn set_extra(&mut self, value: ::capnp::struct_list::Reader<'a,crate::record_capnp::pair::Owned>) -> ::capnp::Result<()> {
::capnp::traits::SetPointerBuilder::set_pointer_builder(self.builder.get_pointer_field(8), value, false)
}
#[inline]
pub fn init_extra(self, size: u32) -> ::capnp::struct_list::Builder<'a,crate::record_capnp::pair::Owned> {
::capnp::traits::FromPointerBuilder::init_pointer(self.builder.get_pointer_field(8), size)
}
pub fn has_extra(&self) -> bool {
!self.builder.get_pointer_field(8).is_null()
}
}
pub struct Pipeline { _typeless: ::capnp::any_pointer::Pipeline }
impl ::capnp::capability::FromTypelessPipeline for Pipeline {
fn new(typeless: ::capnp::any_pointer::Pipeline) -> Pipeline {
Pipeline { _typeless: typeless, }
}
}
impl Pipeline {
}
mod _private {
use capnp::private::layout;
pub const STRUCT_SIZE: layout::StructSize = layout::StructSize { data: 2, pointers: 9 };
pub const TYPE_ID: u64 = 0xe106_8a6a_ee02_baba;
}
}
pub mod pair {
#[derive(Copy, Clone)]
pub struct Owned;
impl <'a> ::capnp::traits::Owned<'a> for Owned { type Reader = Reader<'a>; type Builder = Builder<'a>; }
impl <'a> ::capnp::traits::OwnedStruct<'a> for Owned { type Reader = Reader<'a>; type Builder = Builder<'a>; }
impl ::capnp::traits::Pipelined for Owned { type Pipeline = Pipeline; }
#[derive(Clone, Copy)]
pub struct Reader<'a> { reader: ::capnp::private::layout::StructReader<'a> }
impl <'a,> ::capnp::traits::HasTypeId for Reader<'a,> {
#[inline]
fn type_id() -> u64 { _private::TYPE_ID }
}
impl <'a,> ::capnp::traits::FromStructReader<'a> for Reader<'a,> {
fn new(reader: ::capnp::private::layout::StructReader<'a>) -> Reader<'a,> {
Reader { reader: reader, }
}
}
impl <'a,> ::capnp::traits::FromPointerReader<'a> for Reader<'a,> {
fn get_from_pointer(reader: &::capnp::private::layout::PointerReader<'a>, default: ::std::option::Option<&'a [::capnp::Word]>) -> ::capnp::Result<Reader<'a,>> {
::std::result::Result::Ok(::capnp::traits::FromStructReader::new(reader.get_struct(default)?))
}
}
impl <'a,> ::capnp::traits::IntoInternalStructReader<'a> for Reader<'a,> {
fn into_internal_struct_reader(self) -> ::capnp::private::layout::StructReader<'a> {
self.reader
}
}
impl <'a,> ::capnp::traits::Imbue<'a> for Reader<'a,> {
fn imbue(&mut self, cap_table: &'a ::capnp::private::layout::CapTable) {
self.reader.imbue(::capnp::private::layout::CapTableReader::Plain(cap_table))
}
}
impl <'a,> Reader<'a,> {
pub fn reborrow(&self) -> Reader<> {
Reader { .. *self }
}
pub fn total_size(&self) -> ::capnp::Result<::capnp::MessageSize> {
self.reader.total_size()
}
#[inline]
pub fn get_key(self) -> ::capnp::Result<::capnp::text::Reader<'a>> {
::capnp::traits::FromPointerReader::get_from_pointer(&self.reader.get_pointer_field(0), ::std::option::Option::None)
}
pub fn has_key(&self) -> bool {
!self.reader.get_pointer_field(0).is_null()
}
#[inline]
pub fn get_value(self) -> crate::record_capnp::pair::value::Reader<'a> {
::capnp::traits::FromStructReader::new(self.reader)
}
}
pub struct Builder<'a> { builder: ::capnp::private::layout::StructBuilder<'a> }
impl <'a,> ::capnp::traits::HasStructSize for Builder<'a,> {
#[inline]
fn struct_size() -> ::capnp::private::layout::StructSize { _private::STRUCT_SIZE }
}
impl <'a,> ::capnp::traits::HasTypeId for Builder<'a,> {
#[inline]
fn type_id() -> u64 { _private::TYPE_ID }
}
impl <'a,> ::capnp::traits::FromStructBuilder<'a> for Builder<'a,> {
fn new(builder: ::capnp::private::layout::StructBuilder<'a>) -> Builder<'a, > {
Builder { builder: builder, }
}
}
impl <'a,> ::capnp::traits::ImbueMut<'a> for Builder<'a,> {
fn imbue_mut(&mut self, cap_table: &'a mut ::capnp::private::layout::CapTable) {
self.builder.imbue(::capnp::private::layout::CapTableBuilder::Plain(cap_table))
}
}
impl <'a,> ::capnp::traits::FromPointerBuilder<'a> for Builder<'a,> {
fn init_pointer(builder: ::capnp::private::layout::PointerBuilder<'a>, _size: u32) -> Builder<'a,> {
::capnp::traits::FromStructBuilder::new(builder.init_struct(_private::STRUCT_SIZE))
}
fn get_from_pointer(builder: ::capnp::private::layout::PointerBuilder<'a>, default: ::std::option::Option<&'a [::capnp::Word]>) -> ::capnp::Result<Builder<'a,>> {
::std::result::Result::Ok(::capnp::traits::FromStructBuilder::new(builder.get_struct(_private::STRUCT_SIZE, default)?))
}
}
impl <'a,> ::capnp::traits::SetPointerBuilder<Builder<'a,>> for Reader<'a,> {
fn set_pointer_builder<'b>(pointer: ::capnp::private::layout::PointerBuilder<'b>, value: Reader<'a,>, canonicalize: bool) -> ::capnp::Result<()> { pointer.set_struct(&value.reader, canonicalize) }
}
impl <'a,> Builder<'a,> {
pub fn into_reader(self) -> Reader<'a,> {
::capnp::traits::FromStructReader::new(self.builder.into_reader())
}
pub fn reborrow(&mut self) -> Builder<> {
Builder { .. *self }
}
pub fn reborrow_as_reader(&self) -> Reader<> {
::capnp::traits::FromStructReader::new(self.builder.into_reader())
}
pub fn total_size(&self) -> ::capnp::Result<::capnp::MessageSize> {
self.builder.into_reader().total_size()
}
#[inline]
pub fn get_key(self) -> ::capnp::Result<::capnp::text::Builder<'a>> {
::capnp::traits::FromPointerBuilder::get_from_pointer(self.builder.get_pointer_field(0), ::std::option::Option::None)
}
#[inline]
pub fn set_key(&mut self, value: ::capnp::text::Reader) {
self.builder.get_pointer_field(0).set_text(value);
}
#[inline]
pub fn init_key(self, size: u32) -> ::capnp::text::Builder<'a> {
self.builder.get_pointer_field(0).init_text(size)
}
pub fn has_key(&self) -> bool {
!self.builder.get_pointer_field(0).is_null()
}
#[inline]
pub fn get_value(self) -> crate::record_capnp::pair::value::Builder<'a> {
::capnp::traits::FromStructBuilder::new(self.builder)
}
#[inline]
pub fn init_value(self, ) -> crate::record_capnp::pair::value::Builder<'a> {
self.builder.set_data_field::<u16>(0, 0);
self.builder.get_pointer_field(1).clear();
self.builder.set_bool_field(16, false);
self.builder.set_data_field::<f64>(1, 0f64);
self.builder.set_data_field::<i64>(1, 0i64);
self.builder.set_data_field::<u64>(1, 0u64);
::capnp::traits::FromStructBuilder::new(self.builder)
}
}
pub struct Pipeline { _typeless: ::capnp::any_pointer::Pipeline }
impl ::capnp::capability::FromTypelessPipeline for Pipeline {
fn new(typeless: ::capnp::any_pointer::Pipeline) -> Pipeline {
Pipeline { _typeless: typeless, }
}
}
impl Pipeline {
pub fn get_value(&self) -> crate::record_capnp::pair::value::Pipeline {
::capnp::capability::FromTypelessPipeline::new(self._typeless.noop())
}
}
mod _private {
use capnp::private::layout;
pub const STRUCT_SIZE: layout::StructSize = layout::StructSize { data: 2, pointers: 2 };
pub const TYPE_ID: u64 = 0xb4a6_8d38_a716_233d;
}
pub mod value {
pub use self::Which::{String,Bool,F64,I64,U64,Null};
#[derive(Copy, Clone)]
pub struct Owned;
impl <'a> ::capnp::traits::Owned<'a> for Owned { type Reader = Reader<'a>; type Builder = Builder<'a>; }
impl <'a> ::capnp::traits::OwnedStruct<'a> for Owned { type Reader = Reader<'a>; type Builder = Builder<'a>; }
impl ::capnp::traits::Pipelined for Owned { type Pipeline = Pipeline; }
#[derive(Clone, Copy)]
pub struct Reader<'a> { reader: ::capnp::private::layout::StructReader<'a> }
impl <'a,> ::capnp::traits::HasTypeId for Reader<'a,> {
#[inline]
fn type_id() -> u64 { _private::TYPE_ID }
}
impl <'a,> ::capnp::traits::FromStructReader<'a> for Reader<'a,> {
fn new(reader: ::capnp::private::layout::StructReader<'a>) -> Reader<'a,> {
Reader { reader: reader, }
}
}
impl <'a,> ::capnp::traits::FromPointerReader<'a> for Reader<'a,> {
fn get_from_pointer(reader: &::capnp::private::layout::PointerReader<'a>, default: ::std::option::Option<&'a [::capnp::Word]>) -> ::capnp::Result<Reader<'a,>> {
::std::result::Result::Ok(::capnp::traits::FromStructReader::new(reader.get_struct(default)?))
}
}
impl <'a,> ::capnp::traits::IntoInternalStructReader<'a> for Reader<'a,> {
fn into_internal_struct_reader(self) -> ::capnp::private::layout::StructReader<'a> {
self.reader
}
}
impl <'a,> ::capnp::traits::Imbue<'a> for Reader<'a,> {
fn imbue(&mut self, cap_table: &'a ::capnp::private::layout::CapTable) {
self.reader.imbue(::capnp::private::layout::CapTableReader::Plain(cap_table))
}
}
impl <'a,> Reader<'a,> {
pub fn reborrow(&self) -> Reader<> {
Reader { .. *self }
}
pub fn total_size(&self) -> ::capnp::Result<::capnp::MessageSize> {
self.reader.total_size()
}
pub fn has_string(&self) -> bool {
if self.reader.get_data_field::<u16>(0) != 0 { return false; }
!self.reader.get_pointer_field(1).is_null()
}
#[inline]
pub fn which(self) -> ::std::result::Result<WhichReader<'a,>, ::capnp::NotInSchema> {
match self.reader.get_data_field::<u16>(0) {
0 => {
::std::result::Result::Ok(String(
::capnp::traits::FromPointerReader::get_from_pointer(&self.reader.get_pointer_field(1), ::std::option::Option::None)
))
}
1 => {
::std::result::Result::Ok(Bool(
self.reader.get_bool_field(16)
))
}
2 => {
::std::result::Result::Ok(F64(
self.reader.get_data_field::<f64>(1)
))
}
3 => {
::std::result::Result::Ok(I64(
self.reader.get_data_field::<i64>(1)
))
}
4 => {
::std::result::Result::Ok(U64(
self.reader.get_data_field::<u64>(1)
))
}
5 => {
::std::result::Result::Ok(Null(
()
))
}
x => ::std::result::Result::Err(::capnp::NotInSchema(x))
}
}
}
pub struct Builder<'a> { builder: ::capnp::private::layout::StructBuilder<'a> }
impl <'a,> ::capnp::traits::HasStructSize for Builder<'a,> {
#[inline]
fn struct_size() -> ::capnp::private::layout::StructSize { _private::STRUCT_SIZE }
}
impl <'a,> ::capnp::traits::HasTypeId for Builder<'a,> {
#[inline]
fn type_id() -> u64 { _private::TYPE_ID }
}
impl <'a,> ::capnp::traits::FromStructBuilder<'a> for Builder<'a,> {
fn new(builder: ::capnp::private::layout::StructBuilder<'a>) -> Builder<'a, > {
Builder { builder: builder, }
}
}
impl <'a,> ::capnp::traits::ImbueMut<'a> for Builder<'a,> {
fn imbue_mut(&mut self, cap_table: &'a mut ::capnp::private::layout::CapTable) {
self.builder.imbue(::capnp::private::layout::CapTableBuilder::Plain(cap_table))
}
}
impl <'a,> ::capnp::traits::FromPointerBuilder<'a> for Builder<'a,> {
fn init_pointer(builder: ::capnp::private::layout::PointerBuilder<'a>, _size: u32) -> Builder<'a,> {
::capnp::traits::FromStructBuilder::new(builder.init_struct(_private::STRUCT_SIZE))
}
fn get_from_pointer(builder: ::capnp::private::layout::PointerBuilder<'a>, default: ::std::option::Option<&'a [::capnp::Word]>) -> ::capnp::Result<Builder<'a,>> {
::std::result::Result::Ok(::capnp::traits::FromStructBuilder::new(builder.get_struct(_private::STRUCT_SIZE, default)?))
}
}
impl <'a,> ::capnp::traits::SetPointerBuilder<Builder<'a,>> for Reader<'a,> {
fn set_pointer_builder<'b>(pointer: ::capnp::private::layout::PointerBuilder<'b>, value: Reader<'a,>, canonicalize: bool) -> ::capnp::Result<()> { pointer.set_struct(&value.reader, canonicalize) }
}
impl <'a,> Builder<'a,> {
pub fn into_reader(self) -> Reader<'a,> {
::capnp::traits::FromStructReader::new(self.builder.into_reader())
}
pub fn reborrow(&mut self) -> Builder<> {
Builder { .. *self }
}
pub fn reborrow_as_reader(&self) -> Reader<> {
::capnp::traits::FromStructReader::new(self.builder.into_reader())
}
pub fn total_size(&self) -> ::capnp::Result<::capnp::MessageSize> {
self.builder.into_reader().total_size()
}
#[inline]
pub fn set_string(&mut self, value: ::capnp::text::Reader) {
self.builder.set_data_field::<u16>(0, 0);
self.builder.get_pointer_field(1).set_text(value);
}
#[inline]
pub fn init_string(self, size: u32) -> ::capnp::text::Builder<'a> {
self.builder.set_data_field::<u16>(0, 0);
self.builder.get_pointer_field(1).init_text(size)
}
pub fn has_string(&self) -> bool {
if self.builder.get_data_field::<u16>(0) != 0 { return false; }
!self.builder.get_pointer_field(1).is_null()
}
#[inline]
pub fn set_bool(&mut self, value: bool) {
self.builder.set_data_field::<u16>(0, 1);
self.builder.set_bool_field(16, value);
}
#[inline]
pub fn set_f64(&mut self, value: f64) {
self.builder.set_data_field::<u16>(0, 2);
self.builder.set_data_field::<f64>(1, value);
}
#[inline]
pub fn set_i64(&mut self, value: i64) {
self.builder.set_data_field::<u16>(0, 3);
self.builder.set_data_field::<i64>(1, value);
}
#[inline]
pub fn set_u64(&mut self, value: u64) {
self.builder.set_data_field::<u16>(0, 4);
self.builder.set_data_field::<u64>(1, value);
}
#[inline]
pub fn set_null(&mut self, _value: ()) {
self.builder.set_data_field::<u16>(0, 5);
}
#[inline]
pub fn which(self) -> ::std::result::Result<WhichBuilder<'a,>, ::capnp::NotInSchema> {
match self.builder.get_data_field::<u16>(0) {
0 => {
::std::result::Result::Ok(String(
::capnp::traits::FromPointerBuilder::get_from_pointer(self.builder.get_pointer_field(1), ::std::option::Option::None)
))
}
1 => {
::std::result::Result::Ok(Bool(
self.builder.get_bool_field(16)
))
}
2 => {
::std::result::Result::Ok(F64(
self.builder.get_data_field::<f64>(1)
))
}
3 => {
::std::result::Result::Ok(I64(
self.builder.get_data_field::<i64>(1)
))
}
4 => {
::std::result::Result::Ok(U64(
self.builder.get_data_field::<u64>(1)
))
}
5 => {
::std::result::Result::Ok(Null(
()
))
}
x => ::std::result::Result::Err(::capnp::NotInSchema(x))
}
}
}
pub struct Pipeline { _typeless: ::capnp::any_pointer::Pipeline }
impl ::capnp::capability::FromTypelessPipeline for Pipeline {
fn new(typeless: ::capnp::any_pointer::Pipeline) -> Pipeline {
Pipeline { _typeless: typeless, }
}
}
impl Pipeline {
}
mod _private {
use capnp::private::layout;
pub const STRUCT_SIZE: layout::StructSize = layout::StructSize { data: 2, pointers: 2 };
pub const TYPE_ID: u64 = 0x8a99_4a2a_ad4d_9204;
}
pub enum Which<A0> {
String(A0),
Bool(bool),
F64(f64),
I64(i64),
U64(u64),
Null(()),
}
pub type WhichReader<'a,> = Which<::capnp::Result<::capnp::text::Reader<'a>>>;
pub type WhichBuilder<'a,> = Which<::capnp::Result<::capnp::text::Builder<'a>>>;
}
}
|
{
"pile_set_name": "Github"
}
| 0 |
Added: 2 years ago
Watch this horny white slut beg me to stop fucking her ass with my big black cock
|
{
"pile_set_name": "OpenWebText2"
}
| 0.049505 |
Seasonal Training Load and Wellness Monitoring in a Professional Soccer Goalkeeper.
The purpose of this investigation was to (1) quantify the training load practices of a professional soccer goalkeeper and (2) investigate the relationship between the training load observed and the subsequent self-reported wellness response. One male goalkeeper playing for a team in the top league of the Netherlands participated in this case study. Training load data were collected across a full season using a global positioning system device and session-RPE (rating of perceived exertion). Data were assessed in relation to the number of days to a match (MD- and MD+). In addition, self-reported wellness response was assessed using a questionnaire. Duration, total distance, average speed, PlayerLoad™, and load (derived from session-RPE) were highest on MD. The lowest values for duration, total distance, and PlayerLoad™ were observed on MD-1 and MD+1. Total wellness scores were highest on MD and MD-3 and were lowest on MD+1 and MD-4. Small to moderate correlations between training load measures (duration, total distance covered, high deceleration efforts, and load) and the self-reported wellness response scores were found. This exploratory case study provides novel data about the physical load undertaken by a goalkeeper during 1 competitive season. The data suggest that there are small to moderate relationships between training load indicators and self-reported wellness response. This weak relation indicates that the association is not meaningful. This may be due to the lack of position-specific training load parameters that practitioners can currently measure in the applied context.
|
{
"pile_set_name": "PubMed Abstracts"
}
| 0 |
Out now! http://bit.ly/TalentEPVol2
Revealed Recordings is back with its concept Talent Revealed, revealing new talents and supporting the younger generation through the EP’s. Back in 2011 the opening volume brought us Dyro’s first release with his track ‘Daftastic’. Since then Dyro has grown from one of the emerging names in the EDM scene to become one of the hottest artists on the planet and is still strongly connected to Revealed. This second EP gives a diversity in tracks going from melodic breakdowns to more electro influences, all matching the sound of Revealed. This EP brings you exclusive tracks by the likes of Julian Calor, Row Rocka and Lush & Simon. Out October 14th on Revealed Recordings.
Row Rocka - Gate 9
Unleash the gates with the new track from 16-year old Dutch talent Row Rocka. As premiered by Hardwell during his EDC set, ‘Gate 9’ is all about melodic breakdowns and a huge drop. With already a successful release on Flashover, get ready for impact with his debut on Revealed Recordings.
Out October 14th on Revealed Recordings
More info:
http://www.revealedrecordings.com
http://facebook.com/revealedrecordings
http://twitter.com/revealedrec
http://www.soundcloud.com/revealed-recordings
http://www.facebook.com/djRowRocka
http://www.twitter.com/RowRocka
http://www.soundcloud.com/RowRocka
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FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU FUCK YOU 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Neve Shalom, Israel
The music blared in Arabic as a knot of women twirled slowly around the bride-to-be. Well-dressed onlookers, some in traditional Muslim head scarves, clapped and swayed.
On this evening of celebration, the fireworks sizzled, sweets beckoned and jubilant guests congratulated the Arab bride’s parents with a double kiss and hearty “Mazel tov!”
Mazel tov?
“It’s very normal,” said Nava Sonnenschein, one of the Jews clapping at the edge of the dance circle. “For here.”
The usual rules of the Middle East often don’t apply in Neve Shalom, founded in the 1970s as a utopian village on a hilltop in Israel’s midsection. For nearly three decades, its inhabitants have sought to defy the polarizing tugs of politics and nationalism.
Though most Jews and Arabs in Israel are kept apart by segregated communities and long years of mutual mistrust, Neve Shalom and its 250 residents -- half Jews, half Arab citizens of Israel -- represent a living experiment in integration.
The tree-shaded hamlet, whose name means “Oasis of Peace,” is defiantly mixed, its bougainvillea-splashed lanes a mishmash of stone Arab-style houses and boxy, modern Jewish homes.
Schoolchildren learn Hebrew and Arabic together, a rarity in Israel, and play at one another’s homes. Residents enjoy an equal say in running affairs and have elected Jews and Arabs as mayor. They also share management of the 120-pupil elementary school, which draws many students from outside the village, and a separate School for Peace, a well-known training center for activists.
The community’s name is in both languages. In Arabic, it is Wahat al Salam (though the Israeli government has never recognized that part).
“We don’t go out and protest in the classic way,” said Ahmad Hijazi, a 40-year-old Arab who moved from northern Israel with his wife in 1992 and is now Neve Shalom’s development director. “We live, and put into practice, what we want to see.”
A half-hour’s drive from Jerusalem, Neve Shalom is both a functioning community and a peace movement showcase. It has a website -- https://nswas.org -- and a parking lot for buses.
But this is no theme park. The affections and hurts are real, the gains and setbacks intimately felt. Alongside its taboo-breaking, the community has shown how hard it can be for Jews and Arabs to fully understand each other, even when they are trying.
Few know better than Abdessalam Najjar, a 55-year-old village leader with a balding head and pencil-thin beard tracing his jawline. Najjar, the father of the bride, moved to Neve Shalom in 1979 with a new wife, Ayshe, and a heart full of hope.
He was 27 and willing to take a chance, she 19 and in need of some persuading. Najjar, a devout Muslim, had been involved in discussion groups with Jews while studying at a branch of Hebrew University in nearby Rehovot. Clashes between Arab demonstrators and Israeli authorities a few years earlier that left six Arabs dead had generated new urgency over trying to improve relations.
The Najjars were the first Arab family to join Neve Shalom. Almost 30 years later, they are mainstays, well-liked and respected across the community. Najjar has been mayor and is working with a Jewish colleague in developing the community’s new spiritual center for interfaith conferences, lectures on peace topics and prayer.
The couple built a life and home in Neve Shalom, “slowly, brick after brick,” Najjar said. After the arrival a year later of the first of their four children, Ayshe watched over the village’s growing crop of babies -- Jews and Arabs -- and he turned his efforts to helping start the village’s bilingual school. He was one of two teachers.
He says residents have succeeded in creating an environment for raising tolerant children. For the grown-ups too there have been learning opportunities and innumerable debates, important and petty. Najjar, for example, has argued with his mostly secular Jewish neighbors over his right to pray at work and over whether he could keep a few sheep at home, as many rural Palestinians do. (He lost that one.)
Najjar said he once believed that conflicts break out only “between bad people.” No more.
“This conflict can be between two good guys,” he said.
Neve Shalom’s residents, mostly left-leaning professionals and academics, have been tested by two Palestinian uprisings, war in Lebanon and a steep deterioration in relations between Jews and Arabs in Israel. At times, the two groups here triumphed over those divisive pressures. At others, they fell prey.
To much of the rest of Israel, Neve Shalom is a harmless if worthy novelty. But Jewish extremists once declared the Jews here traitors and sprinkled nails on the road to pop tires. The village’s Arab residents, who refer to themselves as Palestinian citizens of Israel, often are asked by fellow Arabs if they really believe that Jews can accept them as equals.
The village today carries tempered aspirations and scars from past political fights. Not all of these are over yet.
Jewish and Arab residents spar over whether Neve Shalom Jews should perform compulsory service in the Israeli army. Arabs in Israel are not summoned to serve, and many object to residents of a “peace village” enlisting in the army.
They disagree too on some of the issues at the heart of the Israeli-Palestinian conflict, such as what to do about Palestinian refugees who fled homes in present-day Israel during the 1948 war and their descendants.
Arab residents are resentful that, despite the talk of equality, Hebrew is the village’s lingua franca. While the Arabs learned Hebrew by attending Israeli schools, few grown Jews in Neve Shalom have mastered Arabic.
Some residents from both groups, now in middle age, fear that the village has lost some of its political daring. It is perhaps telling that the burning issue these days is not potential peace talks but whether Neve Shalom residents can formalize their hold on the plots where they built homes years ago on land that was shared without private ownership.
“There are so many things we don’t talk about,” said Ayelet Ophir-Auron, 51, a Jewish special-education consultant who moved to the village with her family four years ago.
But residents say it may be success enough that Neve Shalom has managed to sustain its vision of mutual tolerance in a society with deep inequities between Jews and minority Arabs, who make up a fifth of Israel’s population.
They assert that the project still has drawing power, even if it is from the fringe of Israeli society, and point to a waiting list of potential newcomers. The village is full but hopes to begin adding 90 families in the next year or so by turning some of the vacant land surrounding it into housing lots.
“It is enough that we are here,” said Rayek Rizek, 52, an Arab former mayor who with his wife runs a cafe and gift shop at the entrance to the village. “It will never maybe bring the solution to the conflict. But there is still a small idea that maybe it is a candle in the midst of a big darkness.”
Neve Shalom, a short drive off the main highway between Jerusalem and Tel Aviv, looks from its hilltop over a panorama of rural tranquillity -- a sloping, rock-strewn plain turned paper-dry by late summer, and groves of almond and olive trees. The village is arrayed around an oval drive, shaded by evergreen trees and other plantings that have swaddled a once-barren hilltop.
Village business takes place in the two-story administration building. Two resident committees run the village and, separately, the elementary school, School for Peace and spiritual center. Key decisions, such as passing the budget and picking new residents, are voted upon by village members in the style of a town meeting.
Neve Shalom has no stores other than the cafe-gift shop, though it sports a 39-room guest house. Its swimming pool is frequented by visitors from as far away as Jerusalem. Most of the community’s middle-class residents commute to jobs in Tel Aviv and elsewhere.
The village is a far cry from the rough encampment that Rizek and his wife, Dyana Shaloufe-Rizek, encountered when they arrived in 1984.
Neve Shalom had been founded a decade earlier by a Dominican priest, Bruno Hussar, on a thistle-covered hill leased from a nearby Roman Catholic monastery. Father Bruno, who was born to Jewish parents, envisioned a place where people of different faiths could live together, though without a fixed political ideology.
Neve Shalom’s first young couples arrived in 1978, motivated by the chance to craft an egalitarian way of life between Jews and Arabs. The village looks out over the site of a key battle in the 1948 war that broke out with Israel’s independence.
Shaloufe-Rizek, who had been a student activist at Haifa University, was invited to teach at Neve Shalom’s peace school, which she had attended after its establishment in 1979. Newly married, she brought her husband.
“There was nothing. No paved roads. A lot of flies and mosquitoes,” Rayek Rizek recalled.
But it was an exhilarating place for Jews and Arabs to confront their yawning ignorance about one another.
Dorit Shippin, a Jew, arrived with her husband, Howard, the same year as the Rizeks after searching for a community that was, she said, “pluralistic enough and open-minded.” She recalled being stunned to learn that Israel’s Independence Day was treated as a historical catastrophe by her new Arab neighbors.
“My father participated in the 1948 war, and especially for this generation, the stories that they have are not stories of destruction and deportation of Palestinians, but they are stories of conquering, freeing, friendships and survival,” Shippin said. “It was quite shocking to hear the other side of the picture.”
For their part, Arab residents began to assume the burden of shared leadership and to confront a fuller portrait of Jews than the unflattering images many had grown up with.
The community’s discussions were earnest, often heated. But the outbreak of the first intifada in 1987 drove home for many residents the fundamental gap that remained in how each side viewed the world.
“The Palestinians saw it mostly as a kind of legitimate struggle of the people under occupation, and the Israelis saw it as an unnecessary kind of uprising that threatens their life, and their existence here,” Rizek said.
Some residents wonder, though, whether the community too often has steered around explosive issues to preserve neighborly harmony.
“As the years went by, it became more and more challenging to talk about the difficult issues,” said Boaz Kitain, a Jew who has been mayor and run the elementary school and School for Peace. “We stopped talking about the difficult things.”
The community was thrown into turmoil when Kitain’s 20-year-old son, Tom, an Israeli soldier, died in a helicopter collision en route to Lebanon in 1997.
The Kitain family asked to put up a memorial. But some Arab residents found it unthinkable that a community dedicated to peace would commemorate a soldier on a military mission, even one who had grown up in their midst. The debate grew bitter. To the Kitains, it only aggravated their grief.
Despite an eventual compromise -- a plaque on the village basketball court saluting a “son of peace, killed in war” -- the episode proved damaging. Kitain’s wife, Daniella, once active as fundraiser for the village, withdrew from community affairs. She has never rejoined.
Community relations have fared better since then, despite the buffeting effects of the second intifada, which further worsened Jewish-Arab relations in Israel, and the nation’s war against the Shiite Muslim militia Hezbollah in Lebanon last year.
Both times, Neve Shalom’s residents threw themselves into common action. After the second intifada broke out in 2000, they formed a motorcade to show support for families of 13 Arabs killed during rioting and delivered medical aid to Palestinians in the West Bank, a big swath of which sits within a 30-minute drive.
“This is when residents felt even more that we have to come together and try to do something for the outside,” said Hijazi, the development director.
There is also much thinking here about the future.
The community plans to keep up its education efforts, mainly through the School for Peace, which over the years has provided training workshops for 40,000 peace and human rights activists and others. Supported heavily by foreign donations, it has served as an incubator for the Israeli and Palestinian peace movements, with alumni sprinkled among important activist groups on both sides.
A planned residential expansion, which would nearly triple the number of families to almost 150, could lend the project more symbolic clout by increasing its size.
Some residents are urging a more activist role for the community in Israeli politics at a moment when polls show abysmal relations between Jews and Arabs.
“It’s time for us to go out more, even if they don’t want to hear us,” Dorit Shippin said. “We have to stop apologizing, really, and be relevant.”
The community claims a tangible accomplishment in rearing a generation of children to have friends across lines of religion and ethnic origin. Those young people have at times been unnerved by how much the egalitarian ideals of Neve Shalom clash with the stark realities of wider Israeli society.
“It’s like a dream,” said Sama Daoud, a 19-year-old Arab who lives with her parents in Neve Shalom. “It’s different from the outside.”
Tali Sonnenschein, 15, said she and her friends were well aware of the tensions and stereotypes that cleave the world outside Neve Shalom.
She sees no reason, though, why that should stop her little community from seeking some way out of the mess.
“I get to live in this place and have a different opinion -- that everybody can learn to live together,” she said. “It’s a little cheesy, maybe. But that’s what I learned.”
--
ellingwood@latimes.com
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"pile_set_name": "OpenWebText2"
}
| 0 |
Undefeated 2014 Spring Collection
Undefeated presents a look at its 2014 spring collection. This season brings back a selection of streetwear staples including hoodies, sweats, tees, and button-ups as well as some light vests and sports jersey-inspired crewnecks. Color schemes are kept simple, bold and solid with few patterns popping up save for a special printed photo graphic on a matching set of shirt and shorts. Look for the collection soon at Undefeated and select stockists including the HYPEBEAST Store.
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{
"pile_set_name": "Pile-CC"
}
| 0 |
Black slut with bound tits playing with her pussy
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{
"pile_set_name": "OpenWebText2"
}
| 0.061224 |
High-efficiency dye-sensitized solar cells of up to 8.03% by air plasma treatment of ZnO nanostructures.
By using the simple but effective method-air plasma to treat the precursor Zn(OH)2, the hydrogen-related defects in ZnO, which lead to increased charge carrier recombination, have been reduced. Successfully, a photoelectric conversion efficiency of 8.03% for pure ZnO-based DSSCs has been achieved, which is the highest one up to now.
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{
"pile_set_name": "PubMed Abstracts"
}
| 0 |
# gitserver
Mirrors repositories from their code host. All other Sourcegraph services talk to gitserver when they need data from git. Requests for fetch operations, however, go through repo-updater.
gitserver exposes an "exec" API over HTTP for running git commands against
clones of repositories. gitserver also exposes APIs for the management of
clones.
The management of clones comprises most of the complexity in gitserver since:
- We want to avoid concurrent clones and fetches of the same repository.
- We want to limit the number of concurrent clones and fetches.
- When adding/removing/modifying a clone, concurrent attempts to run commands
needs to be gracefully dealt with.
- We need to be robust against the many ways git clones can degrade. (gc,
interrupted clones)
Additionally we have invested heavily in the observability of
gitserver. Nearly every operation Sourcegraph does runs one or more git
commands. So we have detailed oberservability in prometheus, net/event,
jaeger, honeycomb and stderr logs.
We normalize repository names when storing them on disk. Always use
`protocol.NormalizeRepo`. The `$GIT_DIR` of a repository is at
`reposRoot/normalized_name/.git`.
When doing an operation on a file or directory which may be concurrently
read/written please use atomic filesystem patterns. This usually involves
heavy use of `os.Rename`. Search for existing uses of `os.Rename` to see
examples.
#### Scaling
gitserver's memory usage consists of short lived git subprocesses.
This is an IO and compute heavy service since most Sourcegraph requests will trigger 1 or more git commands. As such we shard requests for a repo to a specific replica. This allows us to horizontally scale out the service.
The service is stateful (maintaining git clones). However, it only contains data mirrored from upstream code hosts.
|
{
"pile_set_name": "Github"
}
| 0 |
---
abstract: 'The bifurcation sets of polynomial functions have been studied by many mathematicians from various points of view. In particular, Némethi and Zaharia described them in terms of Newton polytopes. In this paper, we will show analogous results for rational functions.'
address:
- 'Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Road, Cau Giay District, Hanoi, Vietnam.'
- 'Institute of Mathematics, University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki, 305-8571, Japan.'
- 'Institute of Mathematics, University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki, 305-8571, Japan. '
author:
- '[Tat Thang Nguyen]{}'
- '[Takahiro SAITO]{}'
- '[Kiyoshi Takeuchi]{}'
bibliography:
- 'refrat.bib'
title: The bifurcation set of a rational function via Newton polytopes
---
Introduction
============
Let $f(z) \in {\mathbb{C}}[z_1, \ldots, z_n]$ be a polynomial of $n$ ($\geq 2$) variables. Then for the function $f \colon {\mathbb{C}}^n
\longrightarrow {\mathbb{C}}$ defined by it there exists a finite subset $B \subset {\mathbb{C}}$ such that the restriction $$\begin{aligned}
{\mathbb{C}}^n \setminus f^{-1}(B) \longrightarrow
{\mathbb{C}}\setminus B\end{aligned}$$ of $f$ is a $C^{\infty}$ locally trivial fibration. We denote by ${\mathrm{B}}_f$ the smallest subset $B \subset {\mathbb{C}}$ satisfying this property. Let ${\rm Sing} f \subset {\mathbb{C}}^n$ be the set of the critical points of $f \colon {\mathbb{C}}^n \longrightarrow {\mathbb{C}}$. Then by the definition of ${\mathrm{B}}_f$, obviously we have $$\begin{aligned}
f( {\rm Sing} f) \subset {\mathrm{B}}_f.\end{aligned}$$ The elements of ${\mathrm{B}}_f$ are called bifurcation values of $f$. The description of the bifurcation set ${\mathrm{B}}_f \subset {\mathbb{C}}$ is a fundamental problem and was studied by many mathematicians e.g. [@Broughton], [@C-D-T-T], [@H-L], [@H-N], [@Is] [@N-Z1], [@Nguyen], [@P], [@T], [@Ta], [@Tibar-book] and [@Zaharia] etc. The essential difficulty lies in the fact that in general $f$ has a lot of singularities at infinity. In [@N-Z1], Némethi and Zaharia succeeded in describing ${\mathrm{B}}_{f}$ in terms of the Newton polytope of $f$ (for the generalizations to polynomial maps $f=(f_1, \ldots, f_k): {\mathbb{C}}^n \rightarrow {\mathbb{C}}^k$ for $n \geq k \geq 1$, see [@C-D-T-T], [@KOS] and [@Nguyen]).
In this paper, we will show that analogous results hold for rational functions. Let $P(z), Q(z) \in {\mathbb{C}}[z_1, \ldots, z_n]$ be polynomials of $n$ ($\geq 2$) variables. Assume that they are coprime each other. Let $$\begin{aligned}
f(z)= \frac{P(z)}{Q(z)} \qquad
(z \in {\mathbb{C}}^n \setminus Q^{-1}(0))\end{aligned}$$ be the rational function defined by them and consider the map $f \colon {\mathbb{C}}^n \setminus Q^{-1}(0)
\longrightarrow {\mathbb{C}}$ associated to it. Then as in the case of polynomial maps we can define the bifurcation set ${\mathrm{B}}_f \subset {\mathbb{C}}$ of $f$ such that $f( {\rm Sing} f) \subset {\mathrm{B}}_f$ (see [@G-L-M]). After the pioneering paper [@G-L-M] of Gusein-Zade, Luengo and Melle-Hernández, the local and global properties of rational functions were studied from various points of view by [@B-P], [@B-P-S], [@Thang], [@N-T] and [@Raibaut] etc.
In order to introduce our main results, from now we prepare some notations. Let ${\mathrm{N}}(P), {\mathrm{N}}(Q) \subset {\mathbb{R}}_{\geq 0}^n$ be the Newton polytopes of $P, Q$ respectively and $$\begin{aligned}
{\mathrm{N}}(f):={\mathrm{N}}(P)+{\mathrm{N}}(Q)\end{aligned}$$ their Minkowski sum. Recall that for a vector $u$ in the dual vector space of ${\mathbb{R}}^n$ we can define its supporting faces in ${\mathrm{N}}(f)$, ${\mathrm{N}}(P)$ and ${\mathrm{N}}(Q)$ (see Definition \[supface\] for the details). Then for a face $\gamma \prec {\mathrm{N}}(f)$ there exist faces $\gamma (P) \prec {\mathrm{N}}(P)$ and $\gamma (Q) \prec {\mathrm{N}}(Q)$ such that $$\begin{aligned}
\gamma = \gamma (P)+ \gamma (Q)\end{aligned}$$ (see Section \[prelim\] for the details.). We shall say that a face $\gamma \prec {\mathrm{N}}(f)$ is of type I if it is supported by a vector $u \in {\mathbb{R}}^n \setminus {\mathbb{R}}_{\geq 0}^n$ and the affice span ${\rm Aff}( \gamma (P)- \gamma (Q)) \simeq
{\mathbb{R}}^{\dim \gamma}$ of the polytope $\gamma (P)- \gamma (Q) \subset {\mathbb{R}}^n$ in ${\mathbb{R}}^n$ contains the origin $0 \in {\mathbb{R}}^n$. Clearly, if $Q(z)=1$ and $f(z)=P(z)$ is a polynomial, this notion corresponds to that of bad faces of ${\mathrm{N}}(f)= {\mathrm{N}}(P)$ defined by Némethi and Zaharia [@N-Z1] (cf. [@Saito], [@T] and [@T-T] for a slightly different one). We denote the set of faces of ${\mathrm{N}}(f)$ of type I by $\mathscr{F}_{I}$. For $\gamma
\in \mathscr{F}_{I}$ by using the Laurent polynomials $P_{\gamma (P)}(z)$ and $Q_{\gamma (Q)}(z)$ on the torus $T=( {\mathbb{C}}^*)^n$ we define a function $f_{\gamma}: T \setminus Q_{\gamma (Q)}^{-1}(0)
\longrightarrow {\mathbb{C}}$ by $$\begin{aligned}
f_{\gamma}(z)=
\frac{P_{\gamma (P)}(z)}{Q_{\gamma (Q)}(z)}
\qquad
(z \in T \setminus Q_{\gamma (Q)}^{-1}(0))\end{aligned}$$ Then our main result is as follows.
\[MTM\] Assume that the divisor $P^{-1}(0)
\cup Q^{-1}(0) \subset {\mathbb{C}}^n$ is normal crossing in a neighborhood of $P^{-1}(0) \cap Q^{-1}(0)$ and $f(z)= \frac{P(z)}{Q(z)}$ is non-degenerate (see Definition \[nondeg\]). Then we have $$\begin{aligned}
\label{th11inc}
{\mathrm{B}}_f \subset f( {\rm Sing} f) \cup \{ 0 \}
\cup \Bigl(
\bigcup_{\gamma \in \mathscr{F}_{I}}
f_{\gamma}( {\rm Sing} f_{\gamma})
\Bigr).\end{aligned}$$
Note that the first assumption of this theorem is satisfied by generic polynomials $P(x)$ and $Q(x)$ such that $P(0) \not= 0$ and $Q(0) \not= 0$. Moreover, in the two dimensional case $n=2$ the same is true also for generic $P(z)$ and $Q(z)$. For $n \geq 2$, if the intersection of ${\mathrm{N}}(Q)$ and each coordinate axis of ${\mathbb{R}}^n$ is equal to $\{ 0 \} \subset {\mathbb{R}}^n$ then the the first assumption of Theorem \[MTM\] is satisfied by generic $P(z)$ and $Q(z)$. Indeed, for such $Q(z)$ we have $$\begin{aligned}
Q^{-1}(0) \subset T=( {\mathbb{C}}^*)^n \subset {\mathbb{C}}^n.\end{aligned}$$ This is the case when $Q(z)=1$ and $f(z)=P(z)$ is a polynomial. If $f(z)=P(z)$ is non-degenerate (at infinity) and convenient, by a result of Broughton [@Broughton] the polynomial map $f: {\mathbb{C}}^n \rightarrow {\mathbb{C}}$ is tame at infinity and $$\begin{aligned}
{\mathrm{B}}_f = f( {\rm Sing} f).\end{aligned}$$ However, for rational functions $f(z)= \frac{P(z)}{Q(z)}$, by Theorem \[MTM\] and the analogues of the results in [@T] and [@Zaharia] for rational functions (which can be proved by toric compactifications of ${\mathbb{C}}^n$), even if $P(z)$ and $Q(z)$ are convenient there might be some type I faces of ${\mathrm{N}}(f)$ and hence we do not have the equality ${\mathrm{B}}_f = f( {\rm Sing} f)$ in general. See Section \[2-dim case\] for the details. As in Gusein-Zade, Luengo and Melle-Hernández [@G-L-M], our non-degeneracy condition in Definition \[nondeg\] is inspired from the classical one for polynomial functions over complete intersection subvarieties in ${\mathbb{C}}^n$ used by many authors such as [@M-T-1] and [@Oka] etc. For the proof of Theorem \[MTM\] we also need to refine the methods of Némethi and Zaharia in [@N-Z1]. Finally, note that the monodromies of rational functions over ${\mathbb{C}}^n$ were studied by [@G-L-M] and [@N-T].
Preliminary notions and results {#prelim}
===============================
Let $P(z), Q(z)\in {\mathbb{C}}[z_{1},\dots,z_{n}]$ be polynomials of $n(\geq 2)$-variables with coefficients in ${\mathbb{C}}$. We define a rational function $f(z)$ by $$f(z)=\dfrac{P(z)}{Q(z)}
\qquad
(z \in {\mathbb{C}}^n \setminus Q^{-1}(0)).$$ We will study the map from ${\mathbb{C}}^n\setminus Q^{-1}(0)$ to ${\mathbb{C}}$ defined by $f$. Let us set ${\mathrm{I}}(f)=P^{-1}(0) \cap Q^{-1}(0) \subset {\mathbb{C}}^n$. If $P$ and $Q$ are coprime, then ${\mathrm{I}}(f)$ is nothing but the set of the indeterminacy points of $f$. In fact, the set ${\mathrm{I}}(f)$ depends on the pair $(P(z), Q(z))$ of polynomials representing $f(z)$. For example, if we take a non-zero polynomial $R(z)$ on ${\mathbb{C}}^n$ and set $$\begin{aligned}
g(z)= \frac{P(z)R(z)}{Q(z)R(z)} \qquad (z \in {\mathbb{C}}^n), \end{aligned}$$ then the set ${\mathrm{I}}(g)={\mathrm{I}}(f) \cup R^{-1}(0)$ might be bigger than ${\mathrm{I}}(f)$. In this way, we distinguish $f(z)= \frac{P(z)}{Q(z)}$ from $g(z)= \frac{P(z)R(z)}{Q(z)R(z)}$ even if their values coincide over an open dense subset of ${\mathbb{C}}^n$. This is the convention due to Gusein-Zade, Luengo and Melle-Hernández [@G-L-M] etc. Hereafter, we assume that $P(z)$ and $Q(z)$ are coprime.
We say that $c\in {\mathbb{C}}$ is an atypical value of $f$ if for any open neighborhood $U$ of $c$, the restriction $f^{-1}(U)\cap ({\mathbb{C}}^n\setminus Q^{-1}(0))\to U$ of $f$ is not a $C^{\infty}$ trivial fibration. The bifurcation set ${\mathrm{B}}_{f}\subset {\mathbb{C}}$ is the set of all the atypical values of $f$.
For a polynomial or rational function $g$ on ${\mathbb{C}}^n$ as in [@Milnor], we set $$\begin{aligned}
{\mathrm{grad}}{g}(z):=\left(
\overline{\dfrac{\partial g}{\partial z_{1}}(z)},
\ldots, {\overline{\dfrac{\partial g}{\partial z_{n}}(z)}}\right), \end{aligned}$$ where $\overline{a}$ is the complex conjugate of $a\in {\mathbb{C}}$. For $z=(z_{1},\dots,z_{n}), w=(w_{1},\dots,w_{n})\in {\mathbb{C}}^n$, $\langle z,w\rangle$ stands for the Hermite inner product of $z$ and $w$, i.e. $\langle z,w\rangle=\sum_{i=1}^{n}z_{i}{\overline{w_{i}}}$. Moreover, for $z \in {\mathbb{C}}^n$ we set $\begin{Vmatrix}z\end{Vmatrix}:=\sqrt{\langle z,z\rangle}
\in {\mathbb{R}}_{\geq 0}$.
\[defmf\]
1. We define a subset ${\mathrm{M}}_f\subset {\mathbb{C}}^n$ by $$\begin{aligned}
{{\mathrm{M}}_f:=\{z\in {\mathbb{C}}^n\setminus Q^{-1}(0)\ |\
\mbox{there exists $\lambda\in {\mathbb{C}}$ such that ${\mathrm{grad}}{f} (z)=\lambda z$}\}}\end{aligned}$$
2. We define a subset ${\mathrm{S}}_{f}\subset {\mathbb{C}}$ by $$\begin{aligned}
{\mathrm{S}}_f:=\left\{ s_0 \in {\mathbb{C}}\ \middle|\
\begin{array}{l}
\mbox{there exists a sequence
$\{z^{k}\}_{k=0}^{\infty}\subset {\mathrm{M}}_f$ such that}\\
\mbox{$\lim_{k\to \infty}\begin{Vmatrix}z^{k}
\end{Vmatrix}=\infty$ and $\lim_{k\to \infty}f(z^k)= s_0$.}
\end{array}
\right\}\end{aligned}$$
<!-- -->
1. Let $g(z)=\sum_{\alpha\in {\mathbb{Z}}^n}
a_{\alpha}z^{\alpha}\in {\mathbb{C}}[z_{1}^{\pm},\dots,z_{n}^{\pm}]$ be a Laurent polynomial with coefficients in ${\mathbb{C}}$. Then the Newton polytope ${\mathrm{N}}(g)\subset {\mathbb{R}}^n$ of $g$ is the convex full of the set $\mathrm{supp}(f)
:=\{\alpha\in {\mathbb{Z}}^n\ |\ a_{\alpha}\neq 0\}$ in ${\mathbb{R}}^n$.
2. Let $P(z), Q(z)\in {\mathbb{C}}[z_{1},\dots,z_{n}]$ be polynomials and $f(z)$ the rational function $\frac{P(z)}{Q(z)}$ defined by them on ${\mathbb{C}}^n$. Then the Newton polytope ${\mathrm{N}}(f)\subset {\mathbb{R}}^n$ of $f$ is the Minkowski sum of ${\mathrm{N}}(P)$ and ${\mathrm{N}}(Q)$. Namely we set $${\mathrm{N}}(f):=\{x+y\in {\mathbb{R}}^n\ |\ x\in {\mathrm{N}}(P),\ y\in {\mathrm{N}}(Q)\}.$$
For real vectors $u=(u_{1},\dots,u_{n}),
v=(v_{1},\dots,v_{n})\in {\mathbb{R}}^n$, we set $\langle u,v\rangle:=\sum_{i=1}^{n}u_{i}v_{i}$.
\[supface\]
1. Let $S$ be a polytope in ${\mathbb{R}}^n$. For a vector $u\in {\mathbb{R}}^n$, we set $d^{u}_{S}:=
\mathrm{min}_{w\in S}\langle u,w\rangle\in {\mathbb{R}}$. Moreover, for a real vector $u\in {\mathbb{R}}^n$, the supporting face $\gamma^{u}_{S}$ of $S$ by $u$ is a polytope defined by $$\gamma^{u}_{S}:=\{v\in S\ |\
\langle u,v\rangle =
\mathrm{min}_{w\in S}\langle u,w\rangle
\}.$$
2. For a Laurent polynomial $g(z)\in {\mathbb{C}}[z_{1}^{\pm},\dots,z_{n}^{\pm}]$ and a real vector $u\in {\mathbb{R}}^n$ we set $d^{u}_{g}:=d^{u}_{{\mathrm{N}}(g)}$ and $\gamma^{u}_{g}:=\gamma^{u}_{{\mathrm{N}}(g)}$.
3. For a rational function $f(z)=\frac{P(z)}{Q(z)}$ on ${\mathbb{C}}^n$ and a real vector $u\in {\mathbb{R}}^n$, we set $d^{u}_{f}:=d^{u}_{P}-d^{u}_{Q}$ and $\gamma^{u}_{f}:=\gamma^{u}_{{\mathrm{N}}(f)}$.
Let $\frac{P(z)}{Q(z)}$ be a rational function on ${\mathbb{C}}^n$.
1. We say that a face $\gamma\prec {\mathrm{N}}(f)$ of ${\mathrm{N}}(f)$ is of type I if there exists a vector $u\in {\mathbb{R}}^n\setminus
{\mathbb{R}}^{n}_{\geq 0}$ such that $\gamma^{u}_{f}=\gamma$ and for any such $u$ we have $d_{f}^{u}(=d^{u}_{P}-d^{u}_{Q})=0$. We denote the set of all the type I faces of ${\mathrm{N}}(f)$ by $\mathscr{F}_{\mathrm{I}}$.
2. We say that a face $\gamma\prec {\mathrm{N}}(f)$ of ${\mathrm{N}}(f)$ is of type II, if it is not of type I but there exists $u\in {\mathbb{R}}^n\setminus {\mathbb{R}}^n_{\geq 0}$ such that $\gamma^{u}_{f}=\gamma$. We denote the set of all the type II faces of ${\mathrm{N}}(f)$ by $\mathscr{F}_{\mathrm{II}}$.
For a Laurent polynomial $g(z)=
\sum_{\alpha\in {\mathbb{Z}}^n}a_{\alpha}z^{\alpha}
\in {\mathbb{C}}[z_{1}^{\pm},\dots,z_{n}^{\pm}]$ and a face $\gamma\prec {\mathrm{N}}(g)$, we set $g_{\gamma}(z):=\sum_{\alpha\in \gamma}a_{\alpha}z^{\alpha}$. We regard it as a function on $T=( {\mathbb{C}}^*)^n$. Let $f(z)=\frac{P(z)}{Q(z)}$ be a rational function. Then for a face $\gamma\prec {\mathrm{N}}(f)$ and a real vector $u\in {\mathbb{R}}^n$ such that $\gamma_f^u= \gamma$, the faces $\gamma_P^u \prec {\mathrm{N}}(P)$ and $\gamma_Q^u \prec {\mathrm{N}}(Q)$ do not depend on $u$. By taking such $u$ we set $$\begin{aligned}
\gamma(P)= \gamma_P^u, \qquad
\gamma(Q)= \gamma_Q^u. \end{aligned}$$ Then we have $$\begin{aligned}
\gamma = \gamma (P)+ \gamma (Q).\end{aligned}$$ Let ${\rm Aff}( \gamma (P)- \gamma (Q)) \simeq
{\mathbb{R}}^{\dim \gamma}$ be the affice span of the polytope $\gamma (P)- \gamma (Q) \subset {\mathbb{R}}^n$ in ${\mathbb{R}}^n$. Then the face $\gamma\prec {\mathrm{N}}(f)$ is of type I iff it is supported by a vector $u\in {\mathbb{R}}^n\setminus
{\mathbb{R}}^{n}_{\geq 0}$ and $$\begin{aligned}
0 \in {\rm Aff}( \gamma (P)- \gamma (Q)). \end{aligned}$$
Let the Newton polytopes of $P(z)$ and $Q(z)$ be as in Figures \[fig1\] and \[fig2\]. In this case, ${\mathrm{N}}(f)$ is a polytope as in Figure \[fig3\]. Then, the lines ${\overline{OA}}$, ${\overline{OD}}$ and ${\overline{AB}}$ and the points $O$ and $A$ are of type I, and the other faces of ${\mathrm{N}}(f)$ are of type II.
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(-1,-1) grid (6,5); (0,0) –(2,3)–(5,3)–(0,0)–cycle; (0,-1)–(0,5); (-1,0)–(6,0); (2.5,2) node[${\mathrm{N}}(P)$]{}; (-1,-1) grid (6,5); (0,0) –(2,3)–(4,1)–(0,0)–cycle; (0,-1)–(0,5); (-1,0)–(6,0); (2.2,1.5) node[${\mathrm{N}}(Q)$]{}; (-1,-1) grid (10,7); (0,0) –(4,6)–(7,6)–(9,4)–(4,1)–(0,0)–cycle; (0,-1)–(0,7); (-1,0)–(10,0); (0,0) node\[below left\][$O$]{}; (4,6) node\[above\][$A$]{}; (7,6) node\[above\][$B$]{}; (9,4) node\[right\][$C$]{}; (4,1) node\[below\][$D$]{};
(0,0) circle (0.1); (2,3) circle (0.1); (5,3) circle (0.1); (0,0) circle (0.1); (2,3) circle (0.1); (4,1) circle (0.1); (0,0) circle (0.1); (4,6) circle (0.1); (7,6) circle (0.1); (9,4) circle (0.1); (4,1) circle (0.1);
(4.6,3) node[${\mathrm{N}}(f)$]{};
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For a face $\gamma\prec {\mathrm{N}}(f)$ ($\gamma \not= {\mathrm{N}}(f)$) by using the Laurent polynomials $P_{\gamma (P)}(z)$ and $Q_{\gamma (Q)}(z)$ on the torus $T=( {\mathbb{C}}^*)^n$ we define a function $f_{\gamma}: T \setminus Q_{\gamma (Q)}^{-1}(0)
\longrightarrow {\mathbb{C}}$ by $$\begin{aligned}
f_{\gamma}(z)=
\frac{P_{\gamma (P)}(z)}{Q_{\gamma (Q)}(z)}
\qquad
(z \in T \setminus Q_{\gamma (Q)}^{-1}(0))\end{aligned}$$
\[nondeg\] Let $f(z)=\frac{P(z)}{Q(z)}$ be a rational function on ${\mathbb{C}}^n$. Then we say that $f$ is non-degenerate if ${\mathrm{grad}}P_{\gamma(P)}(z)$ (resp. ${\mathrm{grad}}Q_{\gamma(Q)}(z)$) does not vanish on $P^{-1}_{\gamma(P)}(0)\setminus Q^{-1}_{\gamma(Q)}(0)
\subset T$ (resp. $Q^{-1}_{\gamma(Q)}(0)\setminus P^{-1}_{\gamma(P)}(0)
\subset T$) for any face $\gamma\prec {\mathrm{N}}(f)$ of type II, and the two vectors ${\mathrm{grad}}P_{\gamma(P)}(z)$ and ${\mathrm{grad}}Q_{\gamma(Q)}(z)$ are linearly independent on $P^{-1}_{\gamma(P)}(0)\cap Q^{-1}_{\gamma(Q)}(0) \subset T$ for any face $\gamma\prec {\mathrm{N}}(f)$ of type I or II.
\[type2sing\] Let $f(z)=\frac{P(z)}{Q(z)}$ be a rational function. Assume that a face $\gamma\prec {\mathrm{N}}(f)$ is of type II. Then we have $f_{\gamma}( {\mathrm{Sing}}{f_{\gamma}})\subset \{0\}$. If moreover $f$ is non-degenerate in the sense of Definition \[nondeg\], we have $f_{\gamma}( {\mathrm{Sing}}{f_{\gamma}})=\emptyset$.
By the definition of faces of type II, we can take a vector $u=(u_{1},\dots,u_{n})
\in {\mathbb{R}}^n\setminus {\mathbb{R}}^n_{\geq 0}$ such that $\gamma^{u}_{f}=\gamma$ and $d_{f}^{u}= d_{P}^{u}-d_{Q}^{u} \neq 0$. Define a ${\mathbb{C}}^*$-action $l_{c}\colon T\overset{\sim}{\to}
T$ ($c\in {\mathbb{C}}^*$) by $$\begin{aligned}
(z_{1},\dots,z_{n}) \longmapsto (c^{u_{1}}z_{1},\dots,c^{u_{n}}z_{n}). \end{aligned}$$ Then we have $$\begin{aligned}
l_{c}^*P_{\gamma(P)}(z):=
P_{\gamma(P)}(l_{c}(z))=c^{d_{P}^{u}}P_{\gamma(P)}(z)\end{aligned}$$ and $$\begin{aligned}
l_{c}^*Q_{\gamma(Q)}(z):=
Q_{\gamma(Q)}(l_{c}(z))=c^{d_{Q}^{u}}Q_{\gamma(Q)}(z).\end{aligned}$$ We thus obtain $$\begin{aligned}
l_{c}^*f_{\gamma}(z):=f_{\gamma}(l_{c}(z))=c^{d_{f}^{u}}f_{\gamma}(z). \end{aligned}$$ Since $d_{f}^{u}\neq 0$, this implies that the fibers $f_{\gamma}^{-1}(s)$ ($s \in {\mathbb{C}}^*$) of $f_{\gamma}$ are isomorphic to $f_{\gamma}^{-1}(1)$. Since the set of the critical values of $f_{\gamma}$ is discrete, we obtain the first assertion. The second assertion is now clear since if $f$ is non-degenerate, the central fiber $f^{-1}_{\gamma}(0)=
P^{-1}_{\gamma(P)}(0)\setminus Q^{-1}_{\gamma(Q)}(0)$ is also smooth.
We will use the following lemma.
\[cvsel\] Let $f_{1}(x),\dots, f_{s}(x)$, $g_{1}(x),\dots,
g_{t}(x)$, $h_{1}(z),\dots,h_{u}(x)\in {\mathbb{R}}[x_{1},\dots,x_{n}]$ be polynomials with real coefficients. Let $U=\{x\in {\mathbb{R}}^m\ |\ f_{i}(x)=0,\ 1\leq i \leq s\}$ and $W=\{x\in {\mathbb{R}}^m\ |\ g_{i}(x)>0,\ 1\leq
i\leq t\}$. Suppose that there exists a sequence $\{x^{k}\}_{k=0}^{\infty}\subset U\cap W$ such that $\lim_{k\to \infty}\begin{Vmatrix}x^{k}\end{Vmatrix}=\infty$ and for all $1\leq i\leq u$, $\lim_{k\to \infty}h_{i}(x^{k})=0$. Then, there exists a real analytic curve $p\colon (0,1)\to U\cap W$ of the form $p(t)=at^{\alpha}+a_{1}
t^{\alpha+1}+\dots$ with $a\in {\mathbb{R}}^m\setminus \{0\}$ and $\alpha<0$ such that $\lim_{t\to 0}\begin{Vmatrix}p(t)\end{Vmatrix}=\infty$ and $\lim_{t\to 0}h_{i}(p(t))=0$ for any $1\leq i\leq u$.
By the proof of the above lemma in [@N-Z2], we see moreover that $\alpha$ is a half integer.
Main theorems
=============
\[NST\] Let $f(z)=\frac{P(z)}{Q(z)}$ be a rational function ${\mathbb{C}}^n\setminus Q^{-1}(0)\to {\mathbb{C}}$. Assume that the divisor $P^{-1}(0)
\cup Q^{-1}(0) \subset {\mathbb{C}}^n$ is normal crossing in a neighborhood of $P^{-1}(0) \cap Q^{-1}(0)$. Then we have $$\begin{aligned}
{\mathrm{B}}_f \subset f({\rm Sing} f) \cup {\mathrm{S}}_{f}.\end{aligned}$$
First, let us consider the simplest case where $P^{-1}(0), Q^{-1}(0) \subset {\mathbb{C}}^n$ are smooth and intersect transversally. For $R>0$ we set $S_R= \{ z \in {\mathbb{C}}^n | \begin{Vmatrix}z\end{Vmatrix} =R \}$. Let $\mathcal{S}$ be the coarsest Whitney stratification of the normal crossing divisor $P^{-1}(0)
\cup Q^{-1}(0)$. Then there exists $R_0 \gg 0$ such that for any $R>R_0$ the sphere $S_R$ intersects each stratum in $\mathcal{S}$ transversally. Now let $s_0 \in {\mathbb{C}}$ be a point such that $s_0 \notin f({\rm Sing} f) \cup {\mathrm{S}}_{f}$ and $D \subset {\mathbb{C}}$ a small open disc centered at $s_0$ satisfying the condition $$\begin{aligned}
\overline{D} \subset {\mathbb{C}}\setminus \{
f({\rm Sing} f) \cup {\mathrm{S}}_{f} \}.\end{aligned}$$ Then by an analogue of Némethi and Zaharia [@N-Z1 Lemma 3] for rational functions, there exists $R_1 \geq R_0$ such that $$\begin{aligned}
f^{-1}(D) \cap {\mathrm{M}}_f \cap
\{ z \in {\mathbb{C}}^n | \begin{Vmatrix}z\end{Vmatrix} > R_1 \} = \emptyset.\end{aligned}$$ This implies that for any $R>R_1$ the sphere $S_R$ intersects the fiber $f^{-1}(s)$ transversally for any $s \in D$. Let $\pi : \widetilde{{\mathbb{C}}^n}
\rightarrow {\mathbb{C}}^n$ be the blow-up of ${\mathbb{C}}^n$ along $P^{-1}(0) \cap Q^{-1}(0)$ and $E= \pi^{-1} \{ P^{-1}(0) \cap Q^{-1}(0) \}$ the exceptional divisor in it. Then the meromorphic extension $g:=f \circ \pi$ of $f$ to $\widetilde{{\mathbb{C}}^n}$ has no point of indeterminacy and for any $s \in {\mathbb{C}}$ its fiber $g^{-1}(s)$ intersects $E$ transversally. Moreover for $R>R_0$ we see that the closure $$\begin{aligned}
\widetilde{S_R}:= \overline{
\pi^{-1} [ S_R \setminus
\{ P^{-1}(0) \cap Q^{-1}(0) \} ] }
\subset \widetilde{{\mathbb{C}}^n}\end{aligned}$$ is a smooth real hypersurface of the complex manifold $\widetilde{{\mathbb{C}}^n}$. For $s \in {\mathbb{C}}$ let $\mathcal{S}_s$ be the coarsest Whitney stratification of the normal crossing divisor $g^{-1}(s)
\cup E$. Then for any $R>R_1$ the real hypersurface $\widetilde{S_R}$ intersects each stratum in $\mathcal{S}_s$ transversally. This implies that for any point of $g^{-1}(s) \cap E \cap \widetilde{S_R}$ and a local coordinate system $\zeta =( \zeta_1, \zeta_2, \ldots,
\zeta_n)$ of $\widetilde{{\mathbb{C}}^n}$ around it such that $E= \{ \zeta_1=0 \}$ we can find locally a smooth real vector field $v( \zeta )$ on $\widetilde{{\mathbb{C}}^n}$ such that $$\begin{aligned}
v( \zeta ) \zeta_1 \equiv 0, \qquad
v( \zeta ) g( \zeta ) \equiv 1\end{aligned}$$ and $v( \zeta )$ is tangent to the real hypersurface $\widetilde{S_{ \begin{Vmatrix} \pi ( \zeta ) \end{Vmatrix} }}$ passing through the point $\zeta$. By the first (resp. third) condition on $v( \zeta )$, its integral curves do not go into the exceptional divisor $E$ (resp. at infinity) in finite time. Now by our choice of $D$ and the construction of the blow-up $\pi$, the morphisim $g^{-1}(D) \rightarrow D$ induced by $g$ is a (non-proper) holomorphic submersion. Moreover the boundary of the closure $$\begin{aligned}
\overline{g^{-1}(D)}= \overline{
\pi^{-1} f^{-1} (D) }
\subset \widetilde{{\mathbb{C}}^n}\end{aligned}$$ is smooth and intersects $E$ transversally. Then as in the proof of Némethi and Zaharia [@N-Z1 Theorem 1], by using a partition of unity we can construct a smooth real vector field $\tilde{v}$ globally defined on $g^{-1}(D)$ such that $$\begin{aligned}
\tilde{v} g \equiv 1\end{aligned}$$ whose integral curves do not go into the exceptional divisor $E$ or at infinity in finite time. By the restriction $u$ of $\tilde{v}$ to $f^{-1}(D) = g^{-1}(D) \setminus E \subset {\mathbb{C}}^n$ and its multiple $iu$ ($i:= \sqrt{-1}$) we can prove that the morphism $f^{-1}(D) \rightarrow D$ is a $C^{\infty}$ trivial fibration over $D$. Finally, let us consider the general case. We can construct a composition $\pi : \widetilde{{\mathbb{C}}^n}
\rightarrow {\mathbb{C}}^n$ of several blow-ups of ${\mathbb{C}}^n$ over $P^{-1}(0) \cap Q^{-1}(0)$ so that the meromorphic extension $g:=f \circ \pi$ of $f$ to $\widetilde{{\mathbb{C}}^n}$ has no point of indeterminacy (see e.g. the proof of [@M-T-2 Theorem 3.6] and [@M-T-3 Section 3]). Then the proof proceeds similarly to the one in the previous case. This completes the proof.
Note that the assumption of this theorem are satisfied by generic polynomials $P(z)$ and $Q(z)$ such that $P(0) \not= 0$ and $Q(0) \not= 0$. Moreover, in the two dimensional case $n=2$ the same is true also for generic $P(z)$ and $Q(z)$. For $n \geq 2$, if the intersection of ${\mathrm{N}}(Q)$ and each coordinate axis of ${\mathbb{R}}^n$ is equal to $\{ 0 \} \subset {\mathbb{R}}^n$ then the assumption of Theorem \[NST\] is satisfied by generic $P(z)$ and $Q(z)$. Indeed, for such $Q(z)$ we have $$\begin{aligned}
Q^{-1}(0) \subset T=( {\mathbb{C}}^*)^n \subset {\mathbb{C}}^n.\end{aligned}$$ This is the case when $Q(z)=1$ and $f(z)=P(z)$ is a polynomial.
\[main2\] Let $f(z)=\frac{P(z)}{Q(z)}$ be a rational function ${\mathbb{C}}^n\setminus Q^{-1}(0)\to {\mathbb{C}}$. Assume that $f$ is non-degenerate in the sense of Definition \[nondeg\]. Then, we have $$\begin{aligned}
\label{main2cont}
{\mathrm{S}}_{f} \subset \{0\}\cup
\Bigl( \bigcup_{\gamma\in
\mathscr{F}_{\mathrm{I}}}f_{\gamma}({\mathrm{Sing}}{f_{\gamma}})
\Bigr).\end{aligned}$$
Our proof is inspired from that of [@N-Z1 Theorem 2]. Assume that $s_0 \in {\mathrm{S}}_{f}$. Then, by the definition of ${\mathrm{S}}_{f}$, there exists a sequence $\{z^{k}\}_{k=0}^{\infty}$ in ${\mathrm{M}}_{f}$ such that $\lim_{k\to \infty}\begin{Vmatrix}z^{k}\end{Vmatrix}
=\infty$ and $\lim_{k\to \infty}f(z^{k})= s_0$. By the curve selection lemma (Lemma \[cvsel\]), we can take an analytic curve $h(t)\colon (0,1)\to {\mathbb{C}}^n$ of the form $$\begin{aligned}
\label{hexp}
h(t)=at^{\alpha}+a_{1}t^{\alpha+1}+
\cdots\quad (\mbox{$a\neq 0$ and $\alpha<0$}),\end{aligned}$$ satisfying the conditions:
$$\left\{\begin{array}{l}
h(t)\in {\mathrm{M}}_f \quad (t\in (0,1)),\\
\lim_{t\to 0}
\begingroup
\renewcommand{{1.6}}{1}
\begin{Vmatrix}p(t)\end{Vmatrix}=\infty,
\endgroup
\\
\lim_{t\to 0}f(h(t))=s_0.
\end{array}\right.$$ By the definition of ${\mathrm{M}}_{f}$, there is an analytic function $\lambda(t)
\colon (0,1)\to {\mathbb{C}}$ such that $$\begin{aligned}
\label{iden3}
{\mathrm{grad}}{f}(h(t))=\lambda(t)h(t).\end{aligned}$$ We will use the identities: $$\begin{aligned}
\label{iden1}
\dfrac{df(h(t))}{dt}={\left\langle \dfrac{dh}{dt}(t),
{\mathrm{grad}}{f}(h(t))\right\rangle}.\end{aligned}$$ If ${\mathrm{grad}}{f}(h(t))\equiv 0\ (t\in (0,1))$, the identity (\[iden1\]) implies that $\frac{df(h(t))}{dt}\equiv 0$ and $f(h(t))$ is a constant function. Hence $\sigma=\lim_{t\to 0}f(h(t))$ is in $\mathrm{Sing}{f}$. Therefore, we can assume ${\mathrm{grad}}{f}(h(t))
\not\equiv 0$. If $f(h(t))\equiv 0$, the identities (\[iden1\]) and (\[iden3\]) imply that $${\overline{\lambda(t)}}{\left\langle \dfrac{dh}{dt}(t),h(t)\right\rangle}\equiv 0.$$ By (\[hexp\]), we have $${\left\langle \dfrac{dh}{dt}(t),h(t)\right\rangle}=|a|^2\alpha t^{2\alpha-1}+\cdots.$$ Here $\cdots$ stands for higher order terms. In particular, ${\left\langle \frac{dh}{dt}(t),h(t)\right\rangle}\not\equiv 0$ and we thus obtain $\lambda(t)\equiv 0$, which is in contradiction with ${\mathrm{grad}}{f}(h(t))(=\lambda(t)h(t))\not\equiv 0$. So, we will also assume $f(h(t))\not\equiv 0$.
Let the expansions of $f(h(t)), {\mathrm{grad}}(f(h(t)))$ and $\lambda(t)$ be of the following forms:
[align]{}f(h(t))=bt\^+ ,\
[f]{}(h(t))=ct\^+ ,\
(t)=\_[0]{} t\^+ ,
where $b \in {\mathbb{C}}, c \in {\mathbb{C}}^n, \lambda_{0} \in {\mathbb{C}}$ are not zero. Note that the assumption $\lim_{t\to 0}f(h(t))=s_0
\in {\mathbb{C}}$ implies $\beta\geq 0$. By considering the expansions of both sides of (\[iden3\]), we have $$\begin{aligned}
\rho&=\delta+\alpha, \quad \mbox{and}\\
c&=\lambda_{0}a.\end{aligned}$$ Hence, we have ${\left\langle a,c\right\rangle}\neq 0$. For an analytic function $g(t)=g_{0}t^{\eta}+
\cdots \cdots$ ($g_0 \not= 0$), we denote by ${\mathrm{deg}}{g(t)}$ its degree with respect to $t$. Namely we set ${\mathrm{deg}}{g(t)}=\eta$. Then the degree of the right hand side of (\[iden1\]) is equal to $\alpha-1+\rho$. By (\[iden1\]), we thus obtain $$\alpha-1+\rho\ (=\beta-1)\geq -1,$$ which implies $\rho>0$ since we have $\alpha<0$. Moreover, we have $$\delta=\rho-\alpha>0.$$
We may assume that $$\begin{aligned}
\label{ht}
h(t)=(w_{1}^{0}t^{\nu_{1}}+w_{1}^{1}t^{\nu_{1}+1}+
\cdots, \dots, w_{k}^{0}t^{\nu_{k}}+w_{k}^{1}t^{\nu_{k}+1}+\cdots,0,\dots,0),\end{aligned}$$ where $w_{1}^{0}\neq 0,\dots, w_{k}^{0}\neq 0$ and $\alpha=\nu_{1}\leq \nu_{2}\leq \dots \leq \nu_{k}$. We identify $$\{(x_{1},\dots,x_{n})\in {\mathbb{R}}^n\ |\ x_{k+1}=\dots=x_{n}=0\}$$ with ${\mathbb{R}}^{k}$. Then, we will consider the supporting face $\gamma\subset {\mathbb{R}}^k(\subset {\mathbb{R}}^n)$ of ${\mathrm{N}}(f)\cap {\mathbb{R}}^k(={\mathrm{N}}(P)\cap {\mathbb{R}}^k+{\mathrm{N}}(Q)\cap {\mathbb{R}}^k)$ by the vector $(\nu_{1},\dots,
\nu_{k})\in {\mathbb{R}}^k$. Since $f(h(t))\not\equiv 0$, we have ${\mathrm{N}}(P)\cap {\mathbb{R}}^k\neq \emptyset$ and ${\mathrm{N}}(Q)\cap {\mathbb{R}}^k\neq \emptyset$. Let $m(<0)$ be a real number smaller than the (non-positive) integer $$\begin{aligned}
\min\{\nu_{1}w_{1}+\dots+\nu_{k}w_{k}\in
{\mathbb{R}}\ |\ (w_{1},\dots,w_{n})\in {\mathrm{N}}(f)\}&
\\-\min\{\nu_{1}w_{1}+\dots+\nu_{k}w_{k}\in
{\mathbb{R}}&\ |\ (w_{1},\dots,w_{k})\in {\mathrm{N}}(f)\cap {\mathbb{R}}^k\} \end{aligned}$$ and set $$\begin{aligned}
\nu:=(\nu_{1},\dots,\nu_{k}, -m,\dots,-m) \in {\mathbb{R}}^n. \end{aligned}$$ Then $\gamma$ is the supporting face of ${\mathrm{N}}(f)(\subset {\mathbb{R}}_{\geq 0}^{n})$ by $\nu \in {\mathbb{R}}^n$. Recall that by using the decomposition $\gamma=\gamma(P)+
\gamma(Q)\ (\gamma(P)\prec {\mathrm{N}}(P), \gamma(Q)\prec {\mathrm{N}}(Q))$ we defined $f_{\gamma}(z):=\frac{P_{\gamma(P)}(z)}{Q_{\gamma(P)}(z)}$ and $d_{f}^{\nu}=d_{P}^{\nu}-d_{Q}^{\nu}$. Set $$w^{0}:=(w_{1}^{0},\dots,w_{k}^{0},1,\dots,1)\in T=( {\mathbb{C}}^*)^n.$$ Then, for $j=1,\dots,k$ we have
[align]{}P(h(t))&=P\_[(P)]{}(w\^[0]{})t\^[d\_[P]{}\^]{}+,\
(h(t))&= ( w\^[0]{})t\^[d\_[P]{}\^-\_[j]{}]{}+,
[align]{}Q(h(t))&=Q\_[(Q)]{}(w\^[0]{})t\^[d\_[Q]{}\^]{}+,\
(h(t))&=(w\^[0]{}) t\^[d\_[Q]{}\^-\_[j]{}]{}+.
We set
[align]{}e\_[P]{}&:=[P(h(t))]{},\
e\_[Q]{}&:=[Q(h(t))]{}.
Namely the expansions of $P(h(t))$ and $Q(h(t))$ are of the form:
$$\left\{\begin{array}{l}
P(h(t))=P_{e_{P}}t^{e_{P}}+ \cdots \cdots, \\
Q(h(t))=Q_{e_{Q}}t^{e_{Q}}+ \cdots \cdots,
\end{array}
\right.$$ with $P_{e_{P}}\neq 0$ and $Q_{e_{P}}\neq 0$. Note that $$\begin{aligned}
\label{bigstar}\tag{$\bigstar$}
\left\{\begin{array}{l}
e_{P}\geq d_{P}^{\nu}, \\
e_{Q}\geq d_{Q}^{\nu}.
\end{array}
\right.\end{aligned}$$ Since $\lim_{t\to 0}f(h(t))=
\sigma\in {\mathbb{C}}$, we have $e_{P}\geq e_{Q}$. If $e_{P}>e_{Q}$, the value $s_0=\lim_{t\to 0}f(h(t))$ is $0$ and contained in the right hand side of (\[main2cont\]). So we will assume $e:=e_{P}=e_{Q}$ in the following.
We set $$l:=\min\{d_{P}^{\nu}, d_{Q}^{\nu}\}.$$ We will use the obvious identity: $$\begin{aligned}
\label{iden4}
{\overline{Q(h(t))}}{\mathrm{grad}}{P}(h(t))-{\overline{P(h(t))}}
{\mathrm{grad}}{Q}(h(t))={\overline{Q^2(h(t))}}{\mathrm{grad}}{f}(h(t)).\end{aligned}$$ By (\[iden3\]) and (\[ht\]), the $j(>k)$-th entry of the right hand side of (\[iden4\]) is zero. Note also that for $1\leq j\leq k$ the degree of the $j$-th entry of the left hand side of (\[iden4\]) is larger than or equal to $e+l-\nu_{j}$. We set
$$\begin{aligned}
\label{pti}
{\widetilde{P_{e}}}&:=\left\{
\begin{array}{ll}
P_{e}&(\mbox{if $l=d_{Q}^{\nu}$})\\
0&(\mbox{otherwise}).
\end{array}
\right.
\\
{\widetilde{Q_{e}}}&:=\left\{
\begin{array}{ll}
Q_{e}&(\mbox{if $l=d_{P}^{\nu}$})\\
0&(\mbox{otherwise}).
\end{array}
\right.\label{qti}\end{aligned}$$
Note that at least one of ${\widetilde{P_{e}}}$ and ${\widetilde{Q_{e}}}$ is not zero. For $1 \leq j \leq k$ let $A_{j} \in {\mathbb{C}}$ be the coefficient of $t^{e+l-\nu_{j}}$ in the $j$-th entry of the left hand side of (\[iden4\]). Then its complex conjugate ${\overline{A_{j}}}$ is expressed as $${\overline{A_{j}}}={\widetilde{Q_{e}}}
\dfrac{\partial
P_{\gamma(P)}}{\partial z_{j}}(w^{0})-
{\widetilde{P_{e}}}\dfrac{\partial Q_{\gamma(Q)}}{\partial z_{j}}(w^{0}).$$ Namely we have $$\begin{aligned}
\label{key}
\left(
\begin{array}{c}
{\overline{A_{1}}} \\
{\overline{A_{2}}} \\
\vdots \\
{\overline{A_{k}}}
\end{array}
\right)
= {\widetilde{Q_{e}}}
\left(
\begin{array}{c}
\frac{\partial P_{\gamma(P)}}{\partial z_{1}}(w^{0}) \\
\frac{\partial P_{\gamma(P)}}{\partial z_{2}}(w^{0}) \\
\vdots \\
\frac{\partial P_{\gamma(P)}}{\partial z_{k}}(w^{0})
\end{array}
\right)
- {\widetilde{P_{e}}}
\left(
\begin{array}{c}
\frac{\partial Q_{\gamma(Q)}}{\partial z_{1}}(w^{0}) \\
\frac{\partial Q_{\gamma(Q)}}{\partial z_{2}}(w^{0}) \\
\vdots \\
\frac{\partial Q_{\gamma(Q)}}{\partial z_{k}}(w^{0})
\end{array}
\right).\end{aligned}$$ We set $$\begin{aligned}
\label{ai}
J:=\{1\leq j\leq k\ |\ A_{j}\neq 0\},\mbox{\ and}\\
j_{0}:=\min J \mbox{\ (when $J\neq \emptyset$)}.\label{jzero}\end{aligned}$$ If $J \not= \emptyset$ and $A_{j}\neq 0$ for $j \in J$, by (\[iden3\]) and (\[iden4\]), we have $$\begin{aligned}
\label{jisuu}
e+l-\nu_{j}=&2e+\delta+\nu_{j},\mbox{\ and}\\
{\overline{A_{j}}}=&Q_{e}^2{\overline{\lambda_{0}}}{\overline{w^{0}_{j}}}.\label{cj}\end{aligned}$$ Therefore, we have $$\nu_{j}=\dfrac{1}{2}(-e+l-\delta)$$ and in particular $\nu_{j}=\nu_{j_{0}}\ (j\in J)$. Moreover, since $e\geq l$ and $\delta>0$, we have $$\begin{aligned}
\nu_{j}<0 \label{nuineq}\end{aligned}$$ for such $j$.
\[NZlem5\] If $J\neq \emptyset$, we have the equality $$\begin{aligned}
\label{iden5}
Q_{e}^2\nu_{j_{0}}{\overline{\lambda_{0}}}\sum_{j\in J}|w^{0}_{j}|^2=
{\widetilde{Q_{e}}}d_{P}^{\nu}P_{\gamma(P)}(w^{0})
-{\widetilde{P_{e}}}d_{Q}^{\nu}Q_{\gamma(Q)}(w^{0}).\end{aligned}$$ In particular, the right hand side of (\[iden5\]) is not $0$.
Assume $J\neq \emptyset$. By Euler’s equality for quasi-homogeneous polynomials, we have $$\begin{aligned}
\label{EulP}
\sum_{1\leq j\leq k}\nu_{j}w^{0}_{j}
\dfrac{\partial P_{\gamma(P)}}{\partial z_{j}}(w^{0})
=&d_{P}^{\nu}P_{\gamma(P)}(w^{0}), \mbox{\ and}\\
\sum_{1\leq j\leq k}\nu_{j}w^{0}_{j}
\dfrac{\partial Q_{\gamma(Q)}}{\partial z_{j}}(w^{0})
=&d_{Q}^{\nu}Q_{\gamma(Q)}(w^{0}).\label{EulQ}\end{aligned}$$ Then we have $$\begin{aligned}
\sum_{j\in J}w_{j}^{0}\nu_{j}{\overline{A_{j}}}
=&\sum_{1\leq j\leq k}w_{j}^{0}\nu_{j}{\overline{A_{j}}}\notag\\
=&\sum_{1\leq j\leq k}w_{j}^{0}\nu_{j} \Bigl\{
{\widetilde{Q_{e}}}\dfrac{\partial P_{\gamma(P)}}{\partial
z_{j}}(w^{0})-{\widetilde{P_{e}}}\dfrac{\partial
Q_{\gamma(Q)}}{\partial z_{j}}(w^{0}) \Bigr\} \notag \\
=&{\widetilde{Q_{e}}}d_{P}^{\nu}P_{\gamma(P)}(w^{0})-
{\widetilde{P_{e}}}d_{Q}^{\nu}Q_{\gamma(Q)}(w^{0})
\quad (\mbox{by (\ref{EulP}) and (\ref{EulQ})}). \label{sumI1}\end{aligned}$$ On the other hand, by (\[cj\]), we have $$\begin{aligned}
\label{sumI2}
\sum_{j\in J}w_{j}^{0}\nu_{j}{\overline{A_{j}}}=
Q_{e}^2\nu_{j_{0}}{\overline{\lambda_{0}}}\sum_{j\in J}|w^{0}_{j}|^2.\end{aligned}$$ Combining (\[sumI1\]) and (\[sumI2\]), we obtain the desired equality.
The second assertion follows from the facts: $Q_{e}\neq 0$, $\lambda_{0}\neq 0$, $w^{0}_{j}\neq 0$ and (\[nuineq\]).
Now, let us finish the proof of Theorem \[main2\].\
\
(**Case 1**) We first assume that $P_{\gamma(P)}(w^{0})\neq 0$ and $Q_{\gamma(Q)}(w^{0})\neq 0$. In this case, we have $e=e_{P}=d_{P}^{\nu}$ and $e=e_{Q}=d_{Q}^{\nu}$, and hence $$l=d_{P}^{\nu}=d_{Q}^{\nu} \mbox{\ and\ } d_{f}^{\nu}=0.$$ Therefore, we have $$\begin{aligned}
(\mbox{RHS\ of (\ref{iden5})})
&=d_{P}^{\nu} \Bigl\{ {\widetilde{Q_{e}}}P_{\gamma(P)}(w^{0})
-{\widetilde{P_{e}}}Q_{\gamma(Q)}(w^{0}) \Bigr\}
\mbox{\quad (since $d_{P}^{\nu}=d_{Q}^{\nu}$)}\\
&=0 \mbox{\quad (since ${\widetilde{P_{e}}}=P_{\gamma(P)}
(w^{0})$ and ${\widetilde{Q_{e}}}=Q_{\gamma(Q)}(w^{0})$)}.\end{aligned}$$ If $J\neq \emptyset$, this contradicts the second assertion of Lemma \[NZlem5\]. Therefore, we have $J= \emptyset$ i.e. $A_{j}=0\ (1\leq j\leq k)$. Moreover, for $1\leq j\leq k$, we have $${\overline{A_{j}}}=Q_{\gamma(Q)}(w_{0})\dfrac{\partial
P_{\gamma(P)}}{\partial z_{j}}(w^{0})-P_{\gamma(P)}(
w^{0})\dfrac{\partial Q_{\gamma(Q)}}{\partial
z_{j}}(w^{0}), \mbox{\ and hence}$$ $$\dfrac{\partial f_{\gamma}}{\partial z_{j}}(w^{0})=
\dfrac{{\overline{A_{j}}}}{{Q_{\gamma(Q)}^2(w^{0})}}=0.$$ Therefore, we have $w^{0}\in {\mathrm{Sing}}{f_{\gamma}}$. Since $\nu \in {\mathbb{R}}^n \setminus {\mathbb{R}}^n_{\geq 0}$ the face $\gamma$ is of type I or II. But Lemma \[type2sing\] implies that $\gamma$ is of type I and hence $$\begin{aligned}
s_0 = \lim_{t\to 0}f(h(t))
= f_{\gamma}(w^0)\in f_{\gamma}({\mathrm{Sing}}{f_{\gamma}})\end{aligned}$$ is contained in the right hand side of (\[main2cont\]).\
\
(**Case 2**) Next, we assume that $P_{\gamma(P)}(w^{0})= 0$ and $Q_{\gamma(Q)}(w^{0})\neq 0$. In this case, we have $e=e_{P}>d^{\nu}_{P}$ and $e=e_{Q}=d_{Q}^{\nu}$ and hence $$l=d^{\nu}_{P}<d^{\nu}_{Q}.$$ Moreover by $d_f^{\nu} \not= 0$ the face $\gamma$ is of type II. Therefore, for $1\leq j\leq k$ we have $${\overline{A_{j}}}=Q_{\gamma(Q)}(w^0)\dfrac{\partial
P_{\gamma(P)}}{\partial z_{j}}(w^{0}).$$ Since $P_{\gamma(P)}(w^0)=0$ and $\gamma$ is of type II, by the non-degeneracy condition (Definition \[nondeg\]), $\frac{\partial P_{\gamma(P)}}{\partial z_{j}}(w^0)\neq 0$ for some $1\leq j\leq k$. Hence, $J$ is not empty. On the other hand, in this case we have $$\begin{aligned}
(\mbox{RHS\ of (\ref{iden5})})=Q_{\gamma(Q)}(w^{0})
d_{P}^{\nu}P_{\gamma(P)}(w^0)=0.\end{aligned}$$ But, this contradicts the second assertion of Lemma \[NZlem5\].\
\
(**Case 3**) Similarly, we assume that $P_{\gamma(P)}(w^{0})\neq 0$ and $Q_{\gamma(Q)}(w^{0})= 0$. In this case, we have $e=e_{P}=d^{\nu}_{P}$ and $e=e_{Q}>d_{Q}^{\nu}$ and hence $$l=d^{\nu}_{Q}<d^{\nu}_{P}.$$ Moreover by $d_f^{\nu} \not= 0$ the face $\gamma$ is of type II. Therefore, for $1\leq j\leq k$ we have $${\overline{A_{j}}}=-P_{\gamma(P)}(w^{0})\dfrac{\partial
Q_{\gamma(Q)}}{\partial z_{j}}(w^0).$$ Since $Q_{\gamma(Q)}(w^0)=0$ and $\gamma$ is of type II, by the non-degeneracy condition, $\frac{\partial Q_{\gamma(Q)}}{\partial z_{j}}(w^0)
\neq 0$ for some $1\leq j\leq k$. Hence, $J$ is not empty. On the other hand, we have $$(\mbox{RHS of (\ref{iden5})})=-P_{\gamma(P)}(
w_{0})d_{Q}^{\nu}Q_{\gamma(Q)}(w^0)=0.$$ But, this contradicts the second assertion of Lemma \[NZlem5\].\
\
(**Case 4**) Finally, we assume that $P_{\gamma(P)}(w^{0})= 0$ and $Q_{\gamma(Q)}(w^{0})= 0$. In this case, we have $e=e_{P}>d^{\nu}_{P}$ and $e=e_{Q}>d^{\nu}_{Q}$. Since $\nu \in {\mathbb{R}}^n \setminus {\mathbb{R}}^n_{\geq 0}$ the face $\gamma$ is of type I or II. Then by $P_{\gamma(P)}(w^{0})= 0$, $Q_{\gamma(Q)}(w^{0})= 0$ and the non-degeneracy condition, the complex vectors ${\mathrm{grad}}{P_{\gamma(P)}}(w^0)$ and ${\mathrm{grad}}{Q_{\gamma(Q)}}(w^{0})$ are linearly independent. Therefore, by we get $J\neq \emptyset$. On the other hand, we have $$(\mbox{RHS of (\ref{iden5})})={\widetilde{Q_{e}}}
d_{P}^{\nu}P_{\gamma(P)}(w^{0})-{\widetilde{P_{e}}}
d_{Q}^{\nu}Q_{\gamma(Q)}(w^{0})=0.$$ But, this contradicts the second assertion of Lemma \[NZlem5\].
This completes the proof.
Combining Theorems \[NST\] and \[main2\], we obtain Theorem \[MTM\]. We will consider the following condition: $$\begin{aligned}
\tag{$*$}
\mbox{For any vector $u\in {\mathbb{R}}^n\setminus
{\mathbb{R}}^n_{\geq 0}$, we have $d^{u}_{Q}\geq d^{u}_{P}$.}\end{aligned}$$ It is satisfied if $P(0) \not= 0$, $Q(0) \not= 0$ and ${\mathrm{N}}(Q) \subset {\mathrm{N}}(P)$. This is the case in particular when $Q(z)=1$ (i.e. $f(z)=P(z)$ is a polynomial) and $P(0)=f(0) \not= 0$.
\[conthm\] In the situation in Theorem \[MTM\], assume moreover the condition ($*$). Then we have $${\mathrm{B}}_{f}\subset f({\mathrm{Sing}}{f})\cup \Bigl(
\bigcup_{\gamma\in \mathscr{F}_{\mathrm{I}}}
f_{\gamma}({\mathrm{Sing}}{f_{\gamma}}) \Bigr).$$
Assume that a point $s_0 \in {\mathrm{S}}_{f}\setminus f({\mathrm{Sing}}{f})$ is not contained in $\cup_{\gamma\in \mathscr{F}_{\mathrm{I}}}
f_{\gamma}({\mathrm{Sing}}{f_{\gamma}})$. It is enough to get a contradiction only for $s_0=0$. Let us assume $s_0=0$. We will use the notations and the results before ($\bigstar$) in the proof of Theorem \[main2\]. Then, we have $e_{P}>e_{Q}$. Therefore, if $P_{\gamma(P)}(w^{0})\neq 0$, we have $e_{P}=d_{P}^{\nu}$ and hence $d_{P}^{\nu}>e_{Q}\geq d^{\nu}_{Q}$, which contradicts the condition ($*$). Therefore, we have $$\begin{aligned}
P_{\gamma(P)}(w^{0})=0. \end{aligned}$$ By the condition ($*$), for $1\leq j\leq k$ the degree of the $j$-th entry of the left hand side of (\[iden4\]) is larger than or equal to $e_{Q}+d_{P}^{\nu}-\nu_{j}$. Let $A_j \in {\mathbb{C}}$ be the coefficient of $t^{e_{Q}+d_{P}^{\nu}-\nu_{j}}$ in it. Then its complex conjugate ${\overline{A_{j}}}$ is expressed as $${\overline{A_{j}}}=Q_{e_{P}}\dfrac{\partial
P_{\gamma(P)}}{\partial z_{j}}(w^{0}).$$ We define $J$ and $j_{0}$ as (\[ai\]) and (\[jzero\]). Since $\nu \in {\mathbb{R}}^n \setminus {\mathbb{R}}^n_{\geq 0}$ the face $\gamma$ is of type I or II. If $\gamma$ is of type I, $Q_{\gamma(Q)}(w^0) \not= 0$ and $J= \emptyset$, we have $w^0 \in {\mathrm{Sing}}{f_{\gamma}}$ and $$\begin{aligned}
s_0 =0 =f_{\gamma}(w^0) \in
f_{\gamma}({\mathrm{Sing}}{f_{\gamma}}). \end{aligned}$$ This is a contradiction. So, in the case where $\gamma$ is of type I and $Q_{\gamma(Q)}(w^0) \not= 0$, we have $J \not= \emptyset$. Also in the other cases (where $\gamma$ is of type II or $P_{\gamma(P)}(w^{0})=Q_{\gamma(Q)}(w^{0})=0$), by $P_{\gamma(P)}(w^{0})= 0$ and the non-degeneracy condition we have $\frac{\partial
P_{\gamma(P)}}{\partial z_{j}}(w^{0})\neq 0$ for some $1 \leq j \leq k$ and hence $J\neq \emptyset$. Similarly to the argument in the proof of Theorem \[main2\], by using $e_Q \geq d_Q^{\nu} \geq d_P^{\nu}$ we obtain $\nu_{j}=\nu_{j_{0}}$ for any $j\in J$ and $\nu_{j_{0}}<0$. Moreover, in this situation, we have an equality similar to (\[iden5\]): $$\begin{aligned}
Q_{e_{Q}}\nu_{j_{0}}\sum_{j\in J}|w_{j}^{0}|^2=
d_{P}^{\nu}P_{\gamma(P)}(w^{0}).\end{aligned}$$ The right hand side is $0$. Since the left hand side is not zero, this is a contradiction.
(Némethi and Zaharia [@N-Z1 Theorem 2]) In the situation in Theorem \[MTM\], assume moreover that $Q(z)=1$ (i.e. $f(z)=P(z)$ is a polynomial) and $P(0)=f(0) \not= 0$. Then we have $${\mathrm{B}}_{f}\subset f({\mathrm{Sing}}{f})\cup \Bigl(
\bigcup_{\gamma\in \mathscr{F}_{\mathrm{I}}}
f_{\gamma}({\mathrm{Sing}}{f_{\gamma}}) \Bigr).$$
In this corollary, for the face $\gamma = \{ 0 \}
\prec {\mathrm{N}}(f)$ of type I we have $\gamma(P)= \gamma(Q)= \{ 0 \}$, $f_{\gamma}(z)=f(0) \not= 0$ and $$\begin{aligned}
f_{\gamma}({\mathrm{Sing}}{f_{\gamma}}) =
\{ f(0) \}. \end{aligned}$$
The two dimensional case and examples {#2-dim case}
=====================================
In this section, we show that in the two dimensional case $n=2$ the inclusion $$\begin{aligned}
{\mathrm{B}}_{f}\subset f({\mathrm{Sing}}{f})\cup \{0\}\cup
\Bigl( \bigcup_{\gamma\in
\mathscr{F}_{\mathrm{I}}}f_{\gamma}({\mathrm{Sing}}{f_{\gamma}}) \Bigr)\end{aligned}$$ in Theorem \[MTM\] is indeed an equality outside a finite subset of ${\mathbb{C}}$ and give some examples. Let $\gamma \prec {\mathrm{N}}(f)$ be a $0$-dimensional face of type I. Then $\gamma (P) \prec {\mathrm{N}}(P)$ and $\gamma (Q) \prec {\mathrm{N}}(Q)$ are also $0$-dimensional, $\gamma (P)= \gamma (Q)$ and $$\begin{aligned}
f_{\gamma}=
\frac{P_{\gamma (P)}}{Q_{\gamma (Q)}}:
T \setminus Q_{\gamma (Q)}^{-1}(0) \longrightarrow {\mathbb{C}}\end{aligned}$$ is a non-zero constant function on $T \setminus Q_{\gamma (Q)}^{-1}(0)
=T$ (here $Q_{\gamma (Q)}$ is a monomial). We denote its value by $c( \gamma ) \in {\mathbb{C}}$. Then we define a subset ${\mathrm{C}}_f \subset {\mathbb{C}}$ by $$\begin{aligned}
{\mathrm{C}}_f:= \{ c( \gamma ) \in {\mathbb{C}}\ | \
\gamma \in \mathscr{F}_{\mathrm{I}}, \ \dim \gamma =0 \} \subset {\mathbb{C}}. \end{aligned}$$
\[main-3\] In the situation of Theorem \[MTM\], assume moreover that $n=2$. Then we have an equality $$\begin{aligned}
\label{main-3cont}
{\mathrm{B}}_{f} \setminus ( \{ 0 \} \cup {\mathrm{C}}_f) =
\Bigl\{ f({\mathrm{Sing}}{f}) \cup
\Bigl( \bigcup_{\gamma\in
\mathscr{F}_{\mathrm{I}}}f_{\gamma}({\mathrm{Sing}}{f_{\gamma}}) \Bigr)
\Bigr\} \setminus ( \{ 0 \} \cup {\mathrm{C}}_f).\end{aligned}$$
We follow the proof of [@T Theorem 4.3]. Since $f( {\rm Sing} f) \subset {\mathrm{B}}_f$, it suffices to show the inclusion $$\begin{aligned}
\Bigl( \bigcup_{\gamma\in
\mathscr{F}_{\mathrm{I}}}f_{\gamma}({\mathrm{Sing}}{f_{\gamma}}) \Bigr)
\setminus \left( f({\mathrm{Sing}}{f}) \cup \{ 0 \} \cup {\mathrm{C}}_f \right)
\subset {\mathrm{B}}_{f}.\end{aligned}$$ Let $s_0 \in {\mathbb{C}}$ be a point in the left hand side. We define a ${\mathbb{Z}}$-valued function $\chi_c: {\mathbb{C}}\longrightarrow {\mathbb{Z}}$ on ${\mathbb{C}}$ by $$\chi_c(s)= \sum_{j \in {\mathbb{Z}}} (-1)^j \dim
H^j_c ( f^{-1}(s); {\mathbb{C}}) \qquad (s \in {\mathbb{C}})$$ and its jump $E_f( \sigma ) \in {\mathbb{Z}}$ at $s_0 \in {\mathbb{C}}$ by $$E_f( s_0 )= - \left\{ \chi_c( s_0 + \varepsilon )
- \chi_c( s_0 ) \right\} \in {\mathbb{Z}},$$ where $\varepsilon >0$ is sufficiently small. Then it is enough to show that $E_f( s_0 ) \not= 0$. From now, we will use the terminologies in [@Dimca], [@H-T-T] and [@K-S] etc. For the point $s_0 \in {\mathbb{C}}$ define a function $h: {\mathbb{C}}\longrightarrow
{\mathbb{C}}$ on ${\mathbb{C}}$ by $h(s)=s- s_0$ so that we have $h^{-1}(0)= \{ s_0 \}$. Then we have $$E_f( s_0 )= -
\sum_{j \in {\mathbb{Z}}} (-1)^j \dim
H^j \phi_h(R f_! {\mathbb{C}}_{{\mathbb{C}}^2 \setminus Q^{-1}(0)})_{s_0},$$ where $\phi_h: \mathrm{D^{b}_{c}} ({\mathbb{C}}) \longrightarrow
\mathrm{D^{b}_{c}} ( \{ s_0 \} )$ is Deligne’s vanishing cycle functor associated to $h$. Now we introduce an equivalence relation $\sim$ on (the dual vector space of) ${\mathbb{R}}^2$ by $u \sim u^{\prime} \Longleftrightarrow
\gamma_f^u = \gamma_f^{u^{\prime}}$. We can easily see that for any face $\gamma \prec {\mathrm{N}}(f)$ of ${\mathrm{N}}(f)$ the closure of the equivalence class associated to it in ${\mathbb{R}}^2$ is an $(2- \dim \gamma )$-dimensional rational convex polyhedral cone $\sigma (\gamma )$ in ${\mathbb{R}}^2$. Moreover the family $\{ \sigma (\gamma ) \ | \
\gamma \prec {\mathrm{N}}(f) \}$ of cones in ${\mathbb{R}}^2$ thus obtained is a subdivision of ${\mathbb{R}}^2$. We call it the dual subdivision of ${\mathbb{R}}^2$ by ${\mathrm{N}}(f)$. If $\dim {\mathrm{N}}(f)=2$ it satisfies the axiom of fans (see [@Fulton] and [@Oda] etc.). We call it the dual fan of ${\mathrm{N}}(f)$. Let $\Sigma_0$ be a complete fan in ${\mathbb{R}}^2$ obtained by subdividing the dual subdivision. Note that all the cones in it are proper and convex. Let $\Sigma$ be a smooth and complete fan in ${\mathbb{R}}^2$ containing all the $1$-dimensional cones $\tau
\simeq {\mathbb{R}}^1_{\geq 0}$ in $\Sigma_0$ such that $\tau \cap {\mathbb{R}}^2_{\geq 0} = \{ 0 \}$ and satisfying the condition ${\mathbb{R}}^2_{\geq 0} \in \Sigma$. Let $X_{\Sigma}$ be the toric variety associated to it. Then $X_{\Sigma}$ is a smooth compactification of ${\mathbb{C}}^2$. This construction of $X_{\Sigma}$ is inspired from the one in Zaharia [@Zaharia]. Recall that the torus $T=( {\mathbb{C}}^*)^2$ acts on $X_{\Sigma}$ and the $T$-orbits in it are parametrized by the cones $\tau$ in $\Sigma$. For a cone $\tau \in \Sigma$ denote by $T_{\tau} \simeq ({\mathbb{C}}^*)^{2-\dim
\tau}$ the corresponding $T$-orbit. If $\tau \in \Sigma$ is not contained in ${\mathbb{R}}^2_{\geq 0}$ and its relative interior is contained in that of the cone $\sigma (\gamma )$ for a type II face $\gamma$ of ${\mathrm{N}}(f)$, then by the non-degeneracy condition the closures $\overline{P^{-1}(0)}, \overline{Q^{-1}(0)}
\subset X_{\Sigma}$ of $P^{-1}(0), Q^{-1}(0) \subset {\mathbb{C}}^2$ respectively in $X_{\Sigma}$ intersect $T_{\tau}$ transversally. At such intersection points, (the meromorphic extension) of $f$ to $X_{\Sigma}$ may have indeterminacy. Moreover for $n=2$ we have $$\begin{aligned}
(\overline{P^{-1}(0)} \cap T_{\tau}) \cap
(\overline{Q^{-1}(0)} \cap T_{\tau}) = \emptyset. \end{aligned}$$ If $\tau \in \Sigma$ is not contained in ${\mathbb{R}}^2_{\geq 0}$ and its relative interior is contained in that of the cone $\sigma (\gamma )$ for a type I face $\gamma$ of ${\mathrm{N}}(f)$ such that $\dim \gamma =1$, then the order of the meromorphic extension of $f$ to $X_{\Sigma}$ along the $T$-divisor $\overline{T_{\tau}} \subset X_{\Sigma}$ is zero. Moreover, by the non-degeneracy condition we have $$\begin{aligned}
(\overline{P^{-1}(0)} \cap T_{\tau}) \cap
(\overline{Q^{-1}(0)} \cap T_{\tau}) = \emptyset. \end{aligned}$$ As in [@T Section 3], by constructing a tower of blow-ups $\pi : \widetilde{X_{\Sigma}}
\longrightarrow X_{\Sigma}$ of $X_{\Sigma}$ to eliminate the indeterminacy of $f$ we obtain a commutative diagram: $$\begin{CD}
{\mathbb{C}}^2 \setminus Q^{-1}(0) @>{\iota}>> \widetilde{X_{\Sigma}}
\\
@V{f}VV @VV{g}V
\\
{\mathbb{C}}@>>{j}> {\mathbb{P}}^1
\end{CD}$$ of holomorphic maps, where $\iota : {\mathbb{C}}^2 \setminus Q^{-1}(0)
\hookrightarrow \widetilde{X_{\Sigma}}$ and $j : {\mathbb{C}}\hookrightarrow {\mathbb{P}}^1$ are the inclusion maps and $g$ is proper. By this construction, if $\tau \in \Sigma$ is not contained in ${\mathbb{R}}^2_{\geq 0}$ and its relative interior is contained in that of the cone $\sigma (\gamma )$ for a type I face $\gamma$ of ${\mathrm{N}}(f)$, then $\pi$ induced an isomorphism $\pi^{-1}(T_{\tau}) \simeq T_{\tau}$. So we regard $T_{\tau}$ as a subset of $\widetilde{X_{\Sigma}}$. Since $g$ is proper, by [@Dimca Proposition 4.2.11] and [@K-S Exercise VIII.15] we thus obtain an isomorphism $$\phi_h(R f_! {\mathbb{C}}_{{\mathbb{C}}^2 \setminus Q^{-1}(0)})_{s_0} \simeq
R \Gamma (g^{-1}( s_0 ); \phi_{h \circ g}
( \iota_! {\mathbb{C}}_{{\mathbb{C}}^2 \setminus Q^{-1}(0)})).$$ By our choice of the point $s_0 \in {\mathbb{C}}$, the support of $\phi_{h \circ g}( \iota_! {\mathbb{C}}_{{\mathbb{C}}^2 \setminus Q^{-1}(0)})
\in \mathrm{D^{b}_{c}} ( g^{-1}( s_0 ) )$ is contained in the (non-empty) finite subset of $g^{-1}( s_0 ) \subset {\widetilde{X_{\Sigma}}}$ consisting of the points $q \in T_{\sigma (\gamma)}$ for $1$-dimensional type I faces $\gamma$ of ${\mathrm{N}}(f)$ such that $q \in {\mathrm{Sing}}{f_{\gamma}}$ and $s_0 = f_{\gamma}(q)$. Here we naturally regard $f_{\gamma}$ as a rational function on $T_{\sigma (\gamma)} \simeq {\mathbb{C}}^*$. In a neighborhood of the point $q \in T_{\sigma (\gamma)}$ it coincides with the restriction of $g$ to $T_{\sigma (\gamma)} \subset
\widetilde{X_{\Sigma}}$. For one $q \in T_{\sigma (\gamma)}$ of such points, let $\mu_q \geq 0$ be the Milnor number of the (possibly singular) complex hypersurface $g^{-1}( s_0 )$ (in fact, it is an algebraic curve having at most an isolated singular point at $q$) of $\widetilde{X_{\Sigma}}$ at $q$. Denote by $m_q \geq 2$ the multiplicity of the zeros of the function $f_{\gamma}- s_0$ at $q$. Note that in a neighborhood of the point $q$ in $\widetilde{X_{\Sigma}}$ the sequence $$\begin{aligned}
0 \rightarrow {\mathbb{C}}_{{\mathbb{C}}^2 \setminus Q^{-1}(0)} \rightarrow
{\mathbb{C}}_{\widetilde{X_{\Sigma}}} \rightarrow
{\mathbb{C}}_{T_{\sigma (\gamma)}} \rightarrow 0\end{aligned}$$ is exact. Then as in the final part of the proof of [@T Theorem 4.3] we obtain $$\begin{aligned}
\chi ( \phi_{h \circ g}( \iota_!
{\mathbb{C}}_{{\mathbb{C}}^2 \setminus Q^{-1}(0)})_q ) =
- \mu_q -(m_q-1) <0. \end{aligned}$$ Consequently, we get $E_f( s_0 )>0$. This completes the proof.
By Theorems \[conthm\] and \[main-3\] we obtain the following result.
In the situation of Theorem \[MTM\], assume moreover the condition ($*$) and that $n=2$. Then we have an equality $$\begin{aligned}
\label{main-3cont}
{\mathrm{B}}_{f} \setminus {\mathrm{C}}_f =
\Bigl\{ f({\mathrm{Sing}}{f}) \cup
\Bigl( \bigcup_{\gamma\in
\mathscr{F}_{\mathrm{I}}}f_{\gamma}({\mathrm{Sing}}{f_{\gamma}}) \Bigr)
\Bigr\} \setminus {\mathrm{C}}_f.\end{aligned}$$
Similarly, also in higher dimensions $n \geq 3$ we obtain results similar to the ones in [@T] and [@Zaharia]. We leave their precise formulations to the readers. If $Q(z)=1$ and $f(z)=P(z)$ is a polynomial which is non-degenerate (at infinity) and convenient, then by a result of Broughton [@Broughton] the polynomial map $f: {\mathbb{C}}^n \rightarrow {\mathbb{C}}$ is tame at infinity and $$\begin{aligned}
{\mathrm{B}}_f = f( {\rm Sing} f).\end{aligned}$$ However, for rational functions $f(z)= \frac{P(z)}{Q(z)}$, by Theorems \[MTM\] and \[main-3\], even if $P(z)$ and $Q(z)$ are convenient there might be some type I faces of ${\mathrm{N}}(f)$ and hence we do not have the equality ${\mathrm{B}}_f = f( {\rm Sing} f)$ in general.
For the value $0$, let us consider the following example.
\[ex1\]
Let $f=
\frac{x^2+y}{x+y}.$ It is easy to check that $f$ is non-degenerate in the sense of Definition \[nondeg\]. Let us consider the value $0\in {\mathbb{C}}$. For a small disc $D\subset {\mathbb{C}}$ centered at it, we have $$f^{-1}(D)=\left\{(x, \frac{x^2-tx}{1-t})\ | \ x
\in {\mathbb{C}}\setminus \{0, 1\}, t\in D\right\}.$$ It is easy to check that the restriction map $f: f^{-1}(D)\to D$ is a trivial fibration. This means $0\notin {\mathrm{B}}_f.$
Moreover, by [@Thang Theorem 1.2] we have: $${\mathrm{B}}_f= {\mathrm{B}}_{\infty}\cup f({\mathrm{Sing}}f)\cup \mathrm{K}_1(f),$$ see [@Thang Definition 2.2] for the definition of the set $\mathrm{K}_1(f)$, while ${\mathrm{B}}_{\infty}(f)$ is the set of critical value at infinity of $f$. One can easily check that in this example $f({\mathrm{Sing}}f)
= \mathrm{K}_1(f)=\emptyset$. Therefore ${\mathrm{B}}_f={\mathrm{B}}_{\infty}(f)$. Let us consider the polynomial $$g_t(x,y):= x^2+y- t(x+y)$$ and $\delta(y,t)$ to be the discriminant of $g_t(x,y)$ with respect to the variable $x$. Then $$\delta(y,t)=4(1-t)y-t^2.$$ Hence by [@Thang Corollary 3.7] we get ${\mathrm{B}}_f={\mathrm{B}}_{\infty}(f)=\{1\}.$
On the other hand, for the set on the right hand side of the inclusion (\[th11inc\]) in Theorem \[MTM\], the only non-empty set among those of $\bigcup_{\gamma\in
\mathscr{F}_{\mathrm{I}}}
f_{\gamma}({\mathrm{Sing}}{f_{\gamma}})$ comes from the face function $\frac{y}{y}$ which again provides us the value $1.$
Regarding the set ${\mathrm{C}}_f$, we will see from the example below that in general ${\mathrm{C}}_f$ is not a subset of ${\mathrm{B}}_f$.
[Let $f:= \frac{x+y}{x+2y}$. Then ${\mathrm{C}}_f=\{1/2, 1\}$. For any small neighborhood $D$ of $1/2$ (such as $D$ contains $1/2$ and does not contain $1$), we have $f^{-1}(D)= \{( - \frac{1-2t}{1-t}y,y) :
y\in {\mathbb{C}}^{*}\}$. Hence the restriction $f: f^{-1}(D)\to D$ is a locally trivial fibration. This means $1/2\notin {\mathrm{B}}_f$. Similarly $1\notin {\mathrm{B}}_f$. ]{}
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Whose nipple do I have to suck to get a nipple to suck
1,099 shares
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| 0.058824 |
A 27-year-old man has been arrested by Greek police for what the authorities called “malicious blasphemy,” according to a HuffPost translation of a press release.
Police allege that the man managed a Facebook page that lampooned the deceased Eastern Orthodox monk Elder Paisios, a widely popular religious figure, using the name “Gerontas (Elder) Pastitsios.”
Pastitsios is a Greek pasta dish, and the page parodied the monk and his work in the vein of Pastafarianism, a lighthearted, satirical movement that promotes irreligion. In a screen shot of the group’s Facebook page, which now appears to have been removed from the social network, Elder Paisios is shown with a plate of pastitsios.
The unidentified man was arrested at his home in Athens on Friday following complaints received by the Greek police’s “Cyber Crimes” bureau. Police confiscated the man’s laptop and “determined that he was indeed the person who created and managed” the Facebook page, according to a HuffPost translation of the Greek police press release.
According to Reddit user “DeSaad,” who posted a thread about the arrest to the social news site, the manager of the page used it to publish satirical images and articles about the Greek Orthodox faith and Elder Paisios. The Redditor claimed that this angered members of the Greek right-wing political party Golden Dawn, who called for the man’s arrest under Greece’s anti-blasphemy laws.
However, a Digital Journal translation of a Greek news source claims that the Facebook page was under investigation prior to the political party’s condemnation of it.
The arrest has sparked outrage across the Internet. The hashtag #FreeGeronPastitios trended strongly on the Greek Twittersphere, Business Insider reports.
A petition addressed to the Greek parliament demands the immediate release of the accused man and the abolishment of anti-blasphemy laws in Greece.
Blasphemy in Greece carries a fine of up to 3,000 euros (about $3,800), and up to 2 years imprisonment, according to Change.org.
Pastafarianism, also known as the Church of the Flying Spaghetti Monster, is a parody religion founded in the United States that opposes, among other things, the teaching of intelligent design and creationism in public schools.
Blasphemy laws are a specific restriction on free speech for the benefit of religion which traditionally has opposed free speech. Laws are meant to protect people not ideas, therefore it is very strange to me, an American, that an idea may have legal protection. If religion is able to have a law passed to protect itself from insults then in the interest of consistency and fairness legal protection from insults of any kind against anyone or anything should be able to be passed. Have fun figuring out the legal definition of “insult” and who gets to define it and when to define it.
As an atheist I could have fun with laws against insults and my first target would be religion, but a person bringing a case against an idea would be just as silly as an idea bringing a case against a person. Good luck working that one out, Greece.
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"pile_set_name": "Pile-CC"
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Saturday, March 19, 2011
Last month I posted about this "mystery babe", post, and was trying to figure out who she was exactly. We know she's hot, Latina and got naughty on camera, but other than that....no clue. I got a few more photos of this alluring young woman, but the mystery deepens. Who is she???
Sites I like and DO get paid on. :-D
I do not claim ownership of any pictures included on this blog. If you see a picture here that you own, and you want it removed from the site, Contact me and include a link to the image. It will be taken care of immediately.
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{
"pile_set_name": "Pile-CC"
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| 0 |
ddir = 'xx'
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{
"pile_set_name": "Github"
}
| 0.083333 |
British big tits bdsm Porn Videos
All the best big tits bdsm British Porn videos from all over the world featuring charming sexy beauties who ready to do anything for big tits bdsm sex movies. On the big tits bdsm search on Free British Porn Tube.
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{
"pile_set_name": "Pile-CC"
}
| 0.052419 |
A novel key performance indicator oriented hierarchical monitoring and propagation path identification framework for complex industrial processes.
As the first protective layer for modern complex industrial processes, process monitoring and fault diagnosis (PM-FD) systems play a vital role in ensuring product quality, overall equipment effectiveness and process safety, which have recently become one of the hotspots both in academic research and practical application domains. Different from previous frameworks, this paper dedicates on industrial practices and theoretical methods for hierarchical monitoring and propagation path identification of key performance indicator (KPI) oriented faults in complex industrial processes, which can not only help field engineers to timely and purposefully keep track of the state of the process, but also help them to take appropriate remedial actions to remove the abnormal behaviors from the process. For these purposes, firstly, a new data-driven gap metric approach is proposed for monitoring KPI oriented faults in the block level. Then, Bayesian fusion is implemented to form monitoring decisions from the plant-wide level. After that, a neural network architecture-based Granger causality analysis method is developed for propagation path identification of KPI oriented faults. Finally, the proposed methods are validated in Tennessee Eastman process, where detailed simulation processes are presented and better performance is shown compared with the existing approaches.
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{
"pile_set_name": "PubMed Abstracts"
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| 0 |
ene sucks
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{
"pile_set_name": "Enron Emails"
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| 0.111111 |
Comprehensive evaluation of solution nuclear magnetic resonance spectroscopy sample preparation for helical integral membrane proteins.
The preparation of high quality samples is a critical challenge for the structural characterization of helical integral membrane proteins. Solving the structures of this diverse class of proteins by solution nuclear magnetic resonance spectroscopy (NMR) requires that well-resolved 2D 1H/15N chemical shift correlation spectra be obtained. Acquiring these spectra demands the production of samples with high levels of purity and excellent homogeneity throughout the sample. In addition, high yields of isotopically enriched protein and efficient purification protocols are required. We describe two robust sample preparation methods for preparing high quality, homogeneous samples of helical integral membrane proteins. These sample preparation protocols have been combined with screens for detergents and sample conditions leading to the efficient production of samples suitable for solution NMR spectroscopy. We have examined 18 helical integral membrane proteins, ranging in size from approximately 9 kDa to 29 kDa with 1-4 transmembrane helices, originating from a number of bacterial and viral genomes. 2D 1H/15N chemical shift correlation spectra acquired for each protein demonstrate well-resolved resonances, and >90% detection of the predicted resonances. These results indicate that with proper sample preparation, high quality solution NMR spectra of helical integral membrane proteins can be obtained greatly enhancing the probability for structural characterization of these important proteins.
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{
"pile_set_name": "PubMed Abstracts"
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| 0 |
Risky Public Outdoor Hardcore Fucking and Deepthroat Blowjob in the Woods.
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{
"pile_set_name": "OpenWebText2"
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| 0.054054 |
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