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https://en.wikipedia.org/wiki/International%20Conference%20on%20Rewriting%20Techniques%20and%20Applications
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Rewriting Techniques and Applications (RTA) is an annual international academic conference on the topic of rewriting. It covers all aspects of rewriting, including termination, equational reasoning, theorem proving, higher-order rewriting, unification and the lambda calculus. The conference consists of peer-reviewed papers with the proceedings published by Springer in the LNCS series until 2009, and since then in the LIPIcs series published by the Leibniz-Zentrum für Informatik. Several rewriting-related workshops are also affiliated with RTA.
The first RTA was held in Dijon, France in September 1983. RTA took part in the federated conferences Federated Logic Conference (FLoC) and Rewriting, Deduction, and Programming (RDP). In 2016, RTA merged with the International Conference on Typed Lambda Calculi and Applications to form the International Conference on
Formal Structures for Computation and Deduction (FSCD).
External links
Official website
List of the 26 RTA conferences, 1985-2015
List of the six FSCD conferences, 2016-2021
Rewriting Techniques and Applications
International Conference on Formal Structures for Computation and Deduction
Theoretical computer science conferences
Logic conferences
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https://en.wikipedia.org/wiki/International%20Conference%20on%20Logic%20Programming
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The International Conference on Logic Programming (ICLP) is the premier academic conference on the topic of logic programming, one of the main programming paradigms. It is organized annually by the Association for Logic Programming (ALP). The conference consists of peer-reviewed papers with the post-proceedings published in the international journal Theory and Practice of Logic Programming (TPLP), published by Cambridge University Press. The acceptance rate for TPLP papers is about 20%. Technical Communications are published as Electronic Proceedings in Theoretical Computer Science.
The first ICLP was held in September 1982 in Marseille, France; the complete list is available on the ALP website. Every 4 years, ICLP is held in conjunction with several other logic conferences, in the Federated Logic Conferences (FLoC) series.
ICLP ranks as A (top 14.55%) in the CORE conference ranking.
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https://en.wikipedia.org/wiki/Outline%20of%20calculus
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Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of contemporary mathematics education. Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is insufficient.
Branches of calculus
Differential calculus
Integral calculus
Multivariable calculus
Fractional calculus
Differential Geometry
History of calculus
History of calculus
Important publications in calculus
General calculus concepts
Continuous function
Derivative
Fundamental theorem of calculus
Integral
Limit
Non-standard analysis
Partial derivative
Infinite Series
Calculus scholars
Sir Isaac Newton
Gottfried Leibniz
Calculus lists
List of calculus topics
See also
Glossary of calculus
Table of mathematical symbols
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https://en.wikipedia.org/wiki/Tragopogon%20dubius
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Tragopogon dubius (yellow salsify, western salsify, western goat's-beard, wild oysterplant, yellow goat's beard, goat's beard, goatsbeard, common salsify, salsify) is a species of salsify native to southern and central Europe and western Asia and found as far north and west as northern France. Although it has been reported from Kashmir and India, recent evidence suggests that specimens from these areas may be a different species. Western salsify has been introduced into North America where it has become widespread, being reported from all the continental United States except for a few in the far south-east, and all provinces of Canada except Newfoundland and the northern territories.
Like most salsifies, the western salsify grows as an annual or occasionally biennial forb, reaching a height of typically 20–60 cm but sometimes almost a metre. It grows typically in warm, sheltered spots with moist soil. Its yellow flower head is 4–6 cm in diameter and is likely to be seen in late spring or early summer. Buds are blue-green, tall, and tapered. The inflorescence opens early in the morning and often closes up by late afternoon. Later the plant forms a seed head that resembles that of the dandelions but is distinctly larger. The seeds themselves (known as achenes) are 2–4 cm long but featherweight, weighing about 8 mg each on average. There is some natural variation between the central and peripheral achenes in the seedhead, with the peripheral ones being generally darker and heavier, and having a higher concentration of phenolic compounds; this may enhance their survival potential.
Western salsify is quite similar to the generally more common meadow salsify, T. pratensis, but the bracts which show behind the flower head, a distinctive feature of salsifies, are longer and more noticeable. Although not particularly closely related to meadow salsify or the common salsify or oyster plant (T. porrifolius), the western salsify hybridises readily with both, and in Nor
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https://en.wikipedia.org/wiki/The%20Infinity%20Clue
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The Infinity Clue is the 70th title of the Hardy Boys Mystery Stories, written by Franklin W. Dixon. It was published by Wanderer Books in 1981.
Plot summary
After a dangerous tour of a nuclear power plant which was struck by an earthquake, Frank, Joe, and Chet travel to Washington, DC. This is after they receive a strange, cryptic letter from their father commanding them to go there and to be aware of Infinity. After they arrive in Washington, DC, they are threatened by a ruthless terrorist who seems to have a hobby with explosives. The Infinity clue seems to turn up everywhere and a supposedly cursed diamond is stolen. The Hardy Boys are suspect of stealing the diamond and take on this new case to try to clear their name. After failure after failure, the Hardy Boys go to a strange drilling site and find the Infinity clue there too. While staying at camp, they witness a boat disguised as carrying oysters passing by. The Hardy Boys witness strange flashes and go to the source to investigate. They find a strange island where the people seem to be living in the 18th century. They then find a supposedly dead man who is the owner of the stolen diamond. Later, they travel to a strange chain of islands and learn of a sinister plot to sabotage nuclear power plants with artificial earthquakes created by miniature nuclear bombs to harm the nuclear power industry and to make oil more popular.
The Hardy Boys books
1981 American novels
1981 children's books
Novels set in Washington, D.C.
Nuclear energy in fiction
Children's books set in Washington, D.C.
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https://en.wikipedia.org/wiki/Carbohydrate%20deficient%20transferrin
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Carbohydrate-deficient transferrin (CDT, also known as desialotransferrin or asialotransferrin) is a laboratory test used to help detect heavy ethanol consumption.
Physiology
Transferrin is a serum protein that carries iron through the bloodstream to the bone marrow, where red blood cells are manufactured, as well as to the liver and spleen. Structurally, transferrin is a polypeptide with two N-linked polysaccharide chains. These polysaccharide chains are branched with sialic acid residues. Sialic acid is a monosaccharide carbohydrate.
Various forms of transferrin exist, with differing levels of sialylation. The most common form is tetrasialotransferrin, with four sialic acid chains. In persons who consume significant quantities of alcohol (usually more than 4 or 5 alcoholic beverages a day for two weeks or more) , the proportion of transferrin with zero, one, or two sialic acid chains is increased. These are referred to as carbohydrate-deficient transferrins. These carbohydrate-deficient transferrins can be measured in the bloodstream, and are important markers for alcohol use disorder.
Test for alcohol consumption
Carbohydrate-deficient transferrin is elevated in the blood of people with heavy alcohol consumption but elevated levels can also be found in a number of medical conditions. The limitations of the assay depend upon the methodology of the test. HPLC (High Performance Liquid Chromatography) can detect certain genetic variants and potential liver diseases affecting CDT.
Used with other tests, such as gamma glutamyl transferase (GGT), aspartate aminotransferase (AST), and alanine aminotransferase (ALT), carbohydrate-deficient transferrin can be a useful tool in identifying problem drinking, such as alcohol use disorder. However, it is less sensitive than phosphatidylethanol (PEth) in detecting current regular alcohol consumption. The ethanol conjugates ethyl glucuronide and ethyl sulfate remain positive for up to three days after ethanol consumption
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https://en.wikipedia.org/wiki/Persipan
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Persipan (from Persicus (peach) and marzipan; also known as Parzipan) is a material used in confectionery. It is similar to marzipan but, instead of almonds, is made with apricot or peach kernels. Persipan consists of 40% ground kernels and 60% sugar. The kernels have a strong bitter flavour caused by the presence of amygdalin, a toxic cyanogenic glycoside which has to be detoxified before the kernels can be used. The cores are normally not used otherwise, originally making persipan lower-priced than marzipan. It also has a somewhat different taste. Persipan often contains 0.5% starch so that it can be easily differentiated from marzipan with an iodine test.
Persipan is generally used in confectionery in place of marzipan and as an ingredient of pastry and sweet foods, such as Stollen. It is rarely eaten by itself. In recent years, the use of persipan has increased.
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https://en.wikipedia.org/wiki/Comparison%20of%20X%20Window%20System%20desktop%20environments
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A desktop environment is a collection of software designed to give functionality and a certain look and feel to an operating system.
This article applies to operating systems which are capable of running the X Window System, mostly Unix and Unix-like operating systems such as Linux, Minix, illumos, Solaris, AIX, FreeBSD and Mac OS X. Microsoft Windows is incapable of natively running X applications; however, third-party X servers like Cygwin/X, Exceed, or Xming are available.
Technical elements of a desktop environment
A desktop environment (DE) can be broken up into several components that function independently and interact with one another to provide the look and feel and functionality of the desktop environment. A fundamental part of a DE is the window manager or WM. A window manager creates a certain way for application windows to present themselves to the user. It manages the various application windows, keeping track of which ones are open and providing features to switch between them. Another important element of a DE is the file manager. This application manages files/ folders and presents them in a way that the user finds convenient. It provides file operations like viewing, copying or moving, changing permissions and deleting. DEs usually provide utilities to set wallpapers and screensavers, display icons on the desktop, and perform some administrative tasks. They may optionally include word processors, CD/DVD writing applications, web browsers and e-mail clients.
There are some exceptions: Window managers like Fluxbox, wmii and Ratpoison operate independently of a desktop environment and were written with this objective in mind. Additional hand-picked applications add functionality such as a panel and volume management which gives them some of the qualities of a full DE. This contrasts the behaviour of WMs like Metacity and KWin which were not written with the objective of operating independently of a DE.
KDE Software Compilation and GNOME are writ
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https://en.wikipedia.org/wiki/Allelic%20exclusion
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Allelic exclusion is a process by which only one allele of a gene is expressed while the other allele is silenced. This phenomenon is most notable for playing a role in the development of B lymphocytes, where allelic exclusion allows for each mature B lymphocyte to express only one type of immunoglobulin. This subsequently results in each B lymphocyte being able to recognize only one antigen. This is significant as the co-expression of both alleles in B lymphocytes is associated with autoimmunity and the production of autoantibodies.
Many regulatory processes can lead to allelic exclusion. In one instance, one allele of the gene can become transcriptionally silent, resulting in the transcription and expression of only the other allele. This could be caused in part by decreased methylation of the expressed allele. Conversely, allelic exclusion can also be regulated through asynchronous allelic rearrangement. In this case, both alleles are transcribed but only one becomes a functional protein.
In B-lymphocytes
Allelic exclusion has been observed most often in genes for cell surface receptors and has been extensively studied in immune cells such as B lymphocytes. Allelic exclusion of immunoglobulin (Ig) heavy chain and light chain genes in B cells forms the genetic basis for the presence of only a single type of antigen receptor on a given B lymphocyte, which is central in explaining the ‘one B cell — one antibody’ rule. The variable domain of the B-cell antigen receptor is encoded by the V, (D), and J gene segments, the recombination of which gives rise to Ig gene allelic exclusion. V(D)J recombination occurs imprecisely, so that while transcripts from both alleles are expressed, only one is able to give rise to a functional surface antigen receptor. If no successful rearrangement occurs on either chromosome, the cell dies.
Models
Stochastic
In the stochastic model, while the Ig rearrangement is proposed to be very efficient, the probability of functional allel
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https://en.wikipedia.org/wiki/GEUP
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GEUP is a commercial interactive geometry software program, similar to Cabri Geometry. Originally using the Spanish language, it was programmed by Ramón
Alvarez Galván. Recent versions include support for three-dimensional geometry.
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https://en.wikipedia.org/wiki/French%20standard%20sizes%20for%20oil%20paintings
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French standard sizes for oil paintings refers to a series of different sized canvases for use by artists. The sizes were fixed in the 19th century. Most artists—not only French—used this standard, as it was supported by the main suppliers of artist materials. Only some contemporary artist material suppliers continue to use these standards today, as most artists no longer differentiate canvas sizes by subject.
The main separation from size 0 (toile de 0) to size 120 (toile de 120) is divided in separate runs for faces/portraits (figure), landscapes (paysage), and marines (marine) which more or less keep the diagonal. That is, a figure 0 corresponds in height to a paysage 1 and a marine 2.
In modern times in the USA size is usually stated height by width, where as in this article it is width by height.
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https://en.wikipedia.org/wiki/Linux%20Unified%20Key%20Setup
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The Linux Unified Key Setup (LUKS) is a disk encryption specification created by Clemens Fruhwirth in 2004 and originally intended for Linux.
LUKS implements a platform-independent standard on-disk format for use in various tools. This facilitates compatibility and interoperability among different programs and operating systems, and assures that they all implement password management in a secure and documented manner.
Description
LUKS is used to encrypt a block device. The contents of the encrypted device are arbitrary, and therefore any filesystem can be encrypted, including swap partitions. There is an unencrypted header at the beginning of an encrypted volume, which allows up to 8 (LUKS1) or 32 (LUKS2) encryption keys to be stored along with encryption parameters such as cipher type and key size.
The presence of this header is a major difference between LUKS and dm-crypt, since the header allows multiple different passphrases to be used, with the ability to change and remove them. If the header is lost or corrupted, the device will no longer be decryptable.
Encryption is done with a multi-layer approach. First, the block device is encrypted using multiple master keys, each of which is encrypted with an active user key in each keyslot. Keyslots can contain a passphrase or other types of keys like OpenPGP public keys or X.509 certificates. PGP public keys can be used in combination with an OpenPGP smart card, which is inserted into the host. This layered scheme is known as TKS1.
There are two versions of LUKS, with LUKS2 featuring resilience to header corruption, and using the Argon2 key derivation function by default, whereas LUKS1 uses PBKDF2. Conversion between both versions of LUKS is possible in certain situations, but some features may not be available with LUKS1 such as Argon2. LUKS2 uses JSON as a metadata format.
Available cryptographic algorithms depends on individual kernel support of the host. Libgcrypt can be used as a backend for hashing, whic
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https://en.wikipedia.org/wiki/Inner%20nuclear%20layer
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In the anatomy of the eye, the inner nuclear layer or layer of inner granules, of the retina, is made up of a number of closely packed cells, of which there are three varieties: bipolar cells, horizontal cells, and amacrine cells.
Bipolar cells
The bipolar cells, by far the most numerous, are round or oval in shape, and each is prolonged into an inner and an outer process.
They are divisible into rod bipolars and cone bipolars.
The inner processes of the rod bipolars run through the inner plexiform layer and arborize around the bodies of the cells of the ganglionic layer; their outer processes end in the outer plexiform layer in tufts of fibrils around the button-like ends of the inner processes of the rod granules.
The inner processes of the cone bipolars ramify in the inner plexiform layer in contact with the dendrites of the ganglionic cells.
Connection types
Midget bipolars are linked to one cone while diffuse bipolars take groups of receptors. Diffuse bipolars can take signals from up to 50 rods or can be a flat cone form and take signals from seven cones. The bipolar cells corresponds to the intermediary cells between the touch and heat receptors on the skin and the medulla or spinal cord.
Horizontal cells
The horizontal cells lie in the outer part of the inner nuclear layer and possess somewhat flattened cell bodies.
Their dendrites divide into numerous branches in the outer plexiform layer, while their axons run horizontally for some distance and finally ramify in the same layer.
Amacrine cells
The amacrine cells are placed in the inner part of the inner nuclear layer, and are so named because they have not yet been shown to possess axis-cylinder processes.
Their dendrites undergo extensive ramification in the inner plexiform layer.
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https://en.wikipedia.org/wiki/MIME%20Object%20Security%20Services
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MIME Object Security Services (MOSS) is a protocol that uses the multipart/signed and multipart/encrypted framework to apply digital signature and encryption services to MIME objects.
Details
The services are offered through the use of end-to-end cryptography between an originator and a recipient at the application layer. Asymmetric (public key) cryptography is used in support of the digital signature service and encryption key management. Symmetric (secret key) cryptography is used in support of the encryption service. The procedures are intended to be compatible with a wide range of public key management approaches, including both ad hoc and certificate-based schemes. Mechanisms are provided to support many public key management approaches.
Spreading
MOSS was never widely deployed and is now abandoned, largely due to the popularity of PGP.
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https://en.wikipedia.org/wiki/Molecular-weight%20size%20marker
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A molecular-weight size marker, also referred to as a protein ladder, DNA ladder, or RNA ladder, is a set of standards that are used to identify the approximate size of a molecule run on a gel during electrophoresis, using the principle that molecular weight is inversely proportional to migration rate through a gel matrix. Therefore, when used in gel electrophoresis, markers effectively provide a logarithmic scale by which to estimate the size of the other fragments (providing the fragment sizes of the marker are known).
Protein, DNA, and RNA markers with pre-determined fragment sizes and concentrations are commercially available. These can be run in either agarose or polyacrylamide gels. The markers are loaded in lanes adjacent to sample lanes before the commencement of the run.
DNA markers
Development
Although the concept of molecular-weight markers has been retained, techniques of development have varied throughout the years. New inventions of molecular-weight markers are distributed in kits specific to the marker's type.
An early problem in the development of markers was achieving high resolution throughout the entire length of the marker. Depending on the running conditions of gel electrophoresis, fragments may have been compressed, disrupting clarity. To address this issue, a kit for Southern Blot analysis was developed in 1990, providing the first marker to combine target DNA and probe DNA. This technique took advantage of logarithmic spacing, and could be used to identify target bands ranging over a length of 20,000 nucleotides.
Design
There are two common methods in which to construct a DNA molecular-weight size marker. One such method employs the technique of partial ligation. DNA ligation is the process by which linear DNA pieces are connected to each other via covalent bonds; more specifically, these bonds are phosphodiester bonds. Here, a 100bp duplex DNA piece is partially ligated. The consequence of this is that dimers of 200bp, trimers of 300bp,
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https://en.wikipedia.org/wiki/MHC%20class%20II
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MHC Class II molecules are a class of major histocompatibility complex (MHC) molecules normally found only on professional antigen-presenting cells such as dendritic cells, mononuclear phagocytes, some endothelial cells, thymic epithelial cells, and B cells. These cells are important in initiating immune responses.
The antigens presented by class II peptides are derived from extracellular proteins (not cytosolic as in MHC class I).
Loading of a MHC class II molecule occurs by phagocytosis; extracellular proteins are endocytosed, digested in lysosomes, and the resulting epitopic peptide fragments are loaded onto MHC class II molecules prior to their migration to the cell surface.
In humans, the MHC class II protein complex is encoded by the human leukocyte antigen gene complex (HLA). HLAs corresponding to MHC class II are HLA-DP, HLA-DM, HLA-DOA, HLA-DOB, HLA-DQ, and HLA-DR.
Mutations in the HLA gene complex can lead to bare lymphocyte syndrome (BLS), which is a type of MHC class II deficiency.
Structure
Like MHC class I molecules, class II molecules are also heterodimers, but in this case consist of two homogenous peptides, an α and β chain, both of which are encoded in the MHC. The subdesignation α1, α2, etc. refers to separate domains within the HLA gene; each domain is usually encoded by a different exon within the gene, and some genes have further domains that encode leader sequences, transmembrane sequences, etc. These molecules have both extracellular regions as well as a transmembrane sequence and a cytoplasmic tail. The α1 and β1 regions of the chains come together to make a membrane-distal peptide-binding domain, while the α2 and β2 regions, the remaining extracellular parts of the chains, form a membrane-proximal immunoglobulin-like domain. The antigen binding groove, where the antigen or peptide binds, is made up of two α-helixes walls and β-sheet.
Because the antigen-binding groove of MHC class II molecules is open at both ends while the correspon
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https://en.wikipedia.org/wiki/CD3%20%28immunology%29
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CD3 (cluster of differentiation 3) is a protein complex and T cell co-receptor that is involved in activating both the cytotoxic T cell (CD8+ naive T cells) and T helper cells (CD4+ naive T cells). It is composed of four distinct chains. In mammals, the complex contains a CD3γ chain, a CD3δ chain, and two CD3ε chains. These chains associate with the T-cell receptor (TCR) and the CD3-zeta (ζ-chain) to generate an activation signal in T lymphocytes. The TCR, CD3-zeta, and the other CD3 molecules together constitute the TCR complex.
Structure
The CD3γ, CD3δ, and CD3ε chains are highly related cell-surface proteins of the immunoglobulin superfamily containing a single extracellular immunoglobulin domain.
A structure of the extracellular and transmembrane regions of the CD3γε/CD3δε/CD3ζζ/TCRαβ complex was solved with CryoEM, showing for the first time how the CD3 transmembrane regions enclose the TCR transmembrane regions in an open barrel.
Containing aspartate residues, the transmembrane region of the CD3 chains is negatively charged, a characteristic that allows these chains to associate with the positively charged TCR chains.
The intracellular tails of the CD3γ, CD3ε, and CD3δ molecules each contain a single conserved motif known as an immunoreceptor tyrosine-based activation motif, or ITAM for short, which is essential for the signaling capacity of the TCR. The intracellular tail of CD3ζ contains 3 ITAM motifs.
Regulation
Phosphorylation of the ITAM on CD3 renders the CD3 chain capable of binding an enzyme called ZAP70 (zeta associated protein), a kinase that is important in the signaling cascade of the T cell.
As a drug target
Because CD3 is required for T-cell activation, drugs (often monoclonal antibodies) that target it are being investigated as immunosuppressant therapies (e.g., otelixizumab, teplizumab) for type 1 diabetes and other autoimmune diseases.
As a drug target in cancer research
New anticancer drug treatments are being developed based upon the
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https://en.wikipedia.org/wiki/Maximum%20density
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The maximum density of a substance is the highest attainable density of the substance under given conditions.
Attaining maximum density
Almost all known substances undergo thermal expansion in response to heating, meaning that a given mass of substance contracts to a low volume at low temperatures, when little thermal energy is present. Substances, especially fluids in which intermolecular forces are weak, also undergo compression upon the application of pressure. Nearly all substances therefore reach a density maximum at very low temperatures and very high pressures, characteristic properties of the solid state of matter.
Water
An especially notable irregular maximum density is that of water, which reaches a density peak at . This has important ramifications in Earth's ecosystem.
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https://en.wikipedia.org/wiki/Erdheim%E2%80%93Chester%20disease
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Erdheim–Chester disease (ECD) is an extremely rare disease characterized by the abnormal multiplication of a specific type of white blood cells called histiocytes, or tissue macrophages (technically, this disease is termed a non-Langerhans-cell histiocytosis). It was declared a histiocytic neoplasm by the World Health Organization in 2016. Onset typically is in middle age, although younger patients have been documented. The disease involves an infiltration of lipid-laden macrophages, multinucleated giant cells, an inflammatory infiltrate of lymphocytes and histiocytes in the bone marrow, and a generalized sclerosis of the long bones.
Signs and symptoms
Long bone involvement is almost universal in ECD patients and is bilateral and symmetrical in nature. More than 50% of cases have some sort of extraskeletal involvement. This can include kidney, skin, brain and lung involvement, and less frequently retroorbital tissue, pituitary gland and heart involvement is observed.
Bone pain is the most frequent of all symptoms associated with ECD and mainly affects the lower limbs, knees and ankles. The pain is often described as mild but permanent, and in nature. Exophthalmos occurs in some patients and is usually bilateral, symmetric and painless, and in most cases it occurs several years before the final diagnosis. Recurrent pericardial effusion can be a manifestation, as can morphological changes in adrenal size and infiltration.
A review of 59 case studies by Veyssier-Belot et al. in 1996 reported the following symptoms in order of frequency of occurrence:
Bone pain
Retroperitoneal fibrosis
Diabetes insipidus
Exophthalmos
Xanthomas
Neurological and central nervous system involvement
Dyspnea caused by interlobular septal and pleural thickening
Kidney failure
Hypopituitarism
Liver failure
Diagnosis
Radiologic osteosclerosis and histology are the main diagnostic features. Diagnosis can often be difficult because of the rareness of ECD as well as the need to diff
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https://en.wikipedia.org/wiki/Stomatosuchus
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Stomatosuchus (type species S. inermis) is an extinct stomatosuchid neosuchian from the Late Cretaceous (Cenomanian) of Egypt. Much of what is known about Stomatosuchus has been inferred from the related genus Laganosuchus.
Description
It grew to a length of , and possessed a long, flattened skull with lid-like jaws that were lined with small, conical teeth and the skull reached up to long. The mandible may have been toothless and perhaps even supported a pelican-like throat pouch. This pouch however could have been used to scoop up fish and sharks much like a modern day pelican, the conical teeth would prevent the prey for escaping. Due to such a bizarre skull structure, much about the diet of S. inermis remains unknown.
The only known specimen of S. inermis consisted of a partial skull and two caudal vertebrae. It was collected in Egypt during 1911 by the German paleontologist Ernst Stromer whilst on an expedition. It was delivered to the Munich Museum, which was later destroyed by an Allied bombing raid in 1944. Currently, only photographs of the specimen remain.
Habitat
It is likely that S. inermis lived in the marshy lowlands of what is now the Eastern Sahara Desert. It may have populated the entirety of Northern Africa but due to the only fossil evidence of the species being destroyed and no other bones having been found since, it is impossible to establish an exact range.
Gallery
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https://en.wikipedia.org/wiki/Winkler%20index
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The Winkler Index, sometimes known as the Winkler Scale or Winkler Regions, is a technique for classifying the climate of wine growing regions based on heat summation or growing degree-days. In the system, geographical areas are divided into five climate regions based on temperature converted to growing degree-days, and is commonly known as Regions I–V (see below). The system was developed at the University of California, Davis by A. J. Winkler and Maynard Amerine.
The system
The system is based on both the hypothesis and observations that grapevines do not grow if the temperature is below 50 °F (10 °C). Each day during the growing season are assigned growing degree-days according to the amount that the day's average temperature exceeds this threshold. This is assumed under the system to be April 1 through October 31 in the Northern Hemisphere, October 1 through April 30 in the Southern Hemisphere. One degree day per degree Fahrenheit over 50 °F, or with SI units, degrees Celsius over 10 °C is used.
All days during the growing season are then added up, all negative values are set to zero, with the sum of the growing degree-days used to determine the region's classification in the original Winkler index as follows:
The system was originally developed for and is used officially in California and was based on the general ripening capabilities and wine styles that can be achieved in the climate due to heat accumulation (growing degree-days). The general ripening capabilities include hybrid grape varieties through early season, mid-season, and late season ripening V. Vinifera and even table grapes in the warmest areas of Region V. The general wine styles include lighter, more subtle wines with lower alcohol and brighter fruit aromas and flavors, including Champagne and other sparkling wines, found in cooler climates (Regions Ia, Ib, II and lower III) to bolder, bigger wines often with higher alcohol and lush, darker fruit aromas and flavors that are found in warmer
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https://en.wikipedia.org/wiki/Shrink-fitting
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Shrink-fitting is a technique in which an interference fit is achieved by a relative size change after assembly. This is usually achieved by heating or cooling one component before assembly and allowing it to return to the ambient temperature after assembly, employing the phenomenon of thermal expansion to make a joint. For example, the thermal expansion of a piece of a metallic drainpipe allows a builder to fit the cooler piece to it. As the adjoined pieces reach the same temperature, the joint becomes strained and stronger.
Other examples are the fitting of a wrought iron tyre around the rim of a wooden cart wheel by a wheelwright, or of a steel tyre to the wheel of a railway engine or rolling stock. In both cases the tyre will be heated and expands to slightly greater than the wheel's diameter, and is fitted around it. After cooling, the tyre contracts, binding tightly in place. A common method used in industry is the use of induction shrink fitting which refers to the use of induction heating technology to pre-heat metal components between 150˚C and 300˚C thereby causing them to expand and allow for the insertion or removal of another component. Other methods of shrink-fitting include compression shrink fitting, which uses a cryogen such as liquid nitrogen to cool the insert, and shape memory coupling, which is achieved by means of a phase transition.
External links
Overview of interference fits
Industrial processes
Materials science
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https://en.wikipedia.org/wiki/Cylinder%20set%20measure
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In mathematics, cylinder set measure (or promeasure, or premeasure, or quasi-measure, or CSM) is a kind of prototype for a measure on an infinite-dimensional vector space. An example is the Gaussian cylinder set measure on Hilbert space.
Cylinder set measures are in general not measures (and in particular need not be countably additive but only finitely additive), but can be used to define measures, such as classical Wiener measure on the set of continuous paths starting at the origin in Euclidean space.
Definition
Let be a separable real topological vector space. Let denote the collection of all surjective continuous linear maps defined on whose image is some finite-dimensional real vector space :
A cylinder set measure on is a collection of probability measures
where is a probability measure on These measures are required to satisfy the following consistency condition: if is a surjective projection, then the push forward of the measure is as follows:
Remarks
The consistency condition
is modelled on the way that true measures push forward (see the section cylinder set measures versus true measures). However, it is important to understand that in the case of cylinder set measures, this is a requirement that is part of the definition, not a result.
A cylinder set measure can be intuitively understood as defining a finitely additive function on the cylinder sets of the topological vector space The cylinder sets are the pre-images in of measurable sets in : if denotes the -algebra on on which is defined, then
In practice, one often takes to be the Borel -algebra on In this case, one can show that when is a separable Banach space, the σ-algebra generated by the cylinder sets is precisely the Borel -algebra of :
Cylinder set measures versus measures
A cylinder set measure on is not actually a measure on : it is a collection of measures defined on all finite-dimensional images of If has a probability measure already defined on it, then g
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https://en.wikipedia.org/wiki/Outline%20of%20ecology
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The following outline is provided as an overview of and topical guide to ecology:
Ecology – scientific study of the distribution and abundance of living organisms and how the distribution and abundance are affected by interactions between the organisms and their environment. The environment of an organism includes both physical properties, which can be described as the sum of local abiotic factors such as solar insolation, climate and geology, as well as the other organisms that share its habitat. Also called ecological science.
Essence of ecology
, or
, or
, or
Other criteria
Ecology can also be classified on the basis of:
the primary kinds of organism under study, e.g. animal ecology, plant ecology, insect ecology;
the biomes principally studied, e.g. forest ecology, grassland ecology, desert ecology, benthic ecology, marine ecology, urban ecology;
the geographic or climatic area, e.g. arctic ecology, tropical ecology;
the spatial scale under consideration, e.g. macroecology, landscape ecology;
the philosophical approach, e.g. systems ecology which adopts a holistic approach;
the methods used, e.g. molecular ecology.
Subdisciplines of ecology, and subdiscipline classification
Ecology is a broad discipline comprising many subdisciplines. The field of ecology can be subdivided according to several classification schemes:
By methodology used for investigation
–
–
– the development of ecological theory, usually with mathematical, statistical and/or computer modeling tools.
By spatial scale of ecological system under study
–
–
.
By level of organisation or scope
Arranged from lowest to highest level of organisation:
– the study of individual organisms of a single species in relation to their environment;
– the study of homogenous or heterogenous groups of organisms in relation to their environment;
– the study of homogenous groups of organisms related as a single species;
– the study of heterogenous groups of organisms of multipl
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https://en.wikipedia.org/wiki/Tashiro%20Masashi%20no%20Princess%20ga%20Ippai
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is a Japanese video game for the MSX2 home computer system and Family Computer featuring former comedian Masashi Tashiro released in 1989.
Summary
The story is about the hero Masashi Tashiro who has to rescue the four princesses in distress. One happy ending and four unhappy endings were used in the game; becoming one of the first video games to have multiple endings. The game was not very successful, but it started appearing frequently and getting high prices on online auction sites like Yahoo! after 2000, when Masashi Tashiro was arrested and convicted several times in connection with voyeurism and drug abuse.
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https://en.wikipedia.org/wiki/Cameron%E2%80%93Martin%20theorem
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In mathematics, the Cameron–Martin theorem or Cameron–Martin formula (named after Robert Horton Cameron and W. T. Martin) is a theorem of measure theory that describes how abstract Wiener measure changes under translation by certain elements of the Cameron–Martin Hilbert space.
Motivation
The standard Gaussian measure on -dimensional Euclidean space is not translation-invariant. (In fact, there is a unique translation invariant Radon measure up to scale by Haar's theorem: the -dimensional Lebesgue measure, denoted here .) Instead, a measurable subset has Gaussian measure
Here refers to the standard Euclidean dot product in . The Gaussian measure of the translation of by a vector is
So under translation through , the Gaussian measure scales by the distribution function appearing in the last display:
The measure that associates to the set the number is the pushforward measure, denoted . Here refers to the translation map: . The above calculation shows that the Radon–Nikodym derivative of the pushforward measure with respect to the original Gaussian measure is given by
The abstract Wiener measure on a separable Banach space , where is an abstract Wiener space, is also a "Gaussian measure" in a suitable sense. How does it change under translation? It turns out that a similar formula to the one above holds if we consider only translations by elements of the dense subspace .
Statement of the theorem
Let be an abstract Wiener space with abstract Wiener measure . For , define by . Then is equivalent to with Radon–Nikodym derivative
where
denotes the Paley–Wiener integral.
The Cameron–Martin formula is valid only for translations by elements of the dense subspace , called Cameron–Martin space, and not by arbitrary elements of . If the Cameron–Martin formula did hold for arbitrary translations, it would contradict the following result:
If is a separable Banach space and is a locally finite Borel measure on that is equivalent to its own push
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https://en.wikipedia.org/wiki/Gain%20scheduling
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In control theory, gain scheduling is an approach to control of nonlinear systems that uses a family of linear controllers, each of which provides satisfactory control for a different operating point of the system.
One or more observable variables, called the scheduling variables, are used to determine what operating region the system is currently in and to enable the appropriate linear controller. For example, in an aircraft flight control system, the altitude and Mach number might be the scheduling variables, with different linear controller parameters available (and automatically plugged into the controller) for various combinations of these two variables.
A relatively large scope state of the art about gain scheduling has been published in (Survey of Gain-Scheduling Analysis & Design, D.J.Leith, WE.Leithead).
See also
Linear parameter-varying control
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https://en.wikipedia.org/wiki/Chang%E2%80%93Refsdal%20lens
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A Chang–Refsdal lens is a point-mass gravitational lens (e.g. black hole) perturbed by constant external shear.
The name derives from Kyongae Chang and Sjur Refsdal who in 1979 published a paper in NATURE 282, 561. "Flux Variations of QSO Q0957+561 A,B and image splitting by stars Near the Light Path."
The paper illustrated that stars could affect quasar image brightness.
See also
Microlensing
MACHO
Quasar
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https://en.wikipedia.org/wiki/Google%20hacking
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Google hacking, also named Google dorking, is a hacker technique that uses Google Search and other Google applications to find security holes in the configuration and computer code that websites are using.
Basics
Google hacking involves using operators in the Google search engine to locate specific sections of text on websites that are evidence of vulnerabilities, for example specific versions of vulnerable Web applications. A search query with intitle:admbook intitle:Fversion filetype:php would locate PHP web pages with the strings "admbook" and "Fversion" in their titles, indicating that the PHP based guestbook Admbook is used, an application with a known code injection vulnerability. It is normal for default installations of applications to include their running version in every page they serve, for example, "Powered by XOOPS 2.2.3 Final", which can be used to search for websites running vulnerable versions.
Devices connected to the Internet can be found. A search string such as inurl:"ViewerFrame?Mode=" will find public web cameras.
History
The concept of "Google hacking" dates back to August 2002, when Chris Sullo included the "nikto_google.plugin" in the 1.20 release of the Nikto vulnerability scanner. In December 2002 Johnny Long began to collect Google search queries that uncovered vulnerable systems and/or sensitive information disclosures – labeling them googleDorks.
The list of Google Dorks grew into a large dictionary of queries, which were eventually organized into the original Google Hacking Database (GHDB) in 2004.
Concepts explored in Google hacking have been extended to other search engines, such as Bing and Shodan. Automated attack tools use custom search dictionaries to find vulnerable systems and sensitive information disclosures in public systems that have been indexed by search engines.
Google Dorking has been involved in some notorious cybercrime cases, such as the Bowman Avenue Dam hack and the CIA breach where around 70% of its world
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https://en.wikipedia.org/wiki/International%20Webmasters%20Association
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The International Webmasters Association (IWA), a non-profit professional association for web professionals, provides training courses and certification.
IWA reportedly has 100 official chapters representing over 22,000 individual members in 106 countries. IWA's accomplishments include the publishing of the industry's first guidelines for ethical and professional standards, web certification and education programs, specialized employment resources, and technical assistance to individuals and businesses. IWA is the only Web professional association that acts inside W3C: IWA members participate to the activities of W3C WCAG Working Group, ATAG Working Group, XHTML Working Group and other Working and Interaction group like Multimodal, education and Outreach.
External links
International Webmasters Association. Official site.
Web development
Webmaster
Training organizations
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https://en.wikipedia.org/wiki/Smallest%20organisms
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The smallest organisms found on Earth can be determined according to various aspects of organism size, including volume, mass, height, length, or genome size.
Given the incomplete nature of scientific knowledge, it is possible that the smallest organism is undiscovered. Furthermore, there is some debate over the definition of life, and what entities qualify as organisms; consequently the smallest known organism (microorganism) is debatable.
Microorganisms
Obligate endosymbiotic bacteria
The genome of Nasuia deltocephalinicola, a symbiont of the European pest leafhopper, Macrosteles quadripunctulatus, consists of a circular chromosome of 112,031 base pairs.
The genome of Nanoarchaeum equitans is 491 Kbp nucleotides long.
Pelagibacter ubique
Pelagibacter ubique is one of the smallest known free-living bacteria, with a length of and an average cell diameter of . They also have the smallest free-living bacterium genome: 1.3 Mbp, 1354 protein genes, 35 RNA genes. They are one of the most common and smallest organisms in the ocean, with their total weight exceeding that of all fish in the sea.
Mycoplasma genitalium
Mycoplasma genitalium, a parasitic bacterium which lives in the primate bladder, waste disposal organs, genital, and respiratory tracts, is thought to be the smallest known organism capable of independent growth and reproduction. With a size of approximately 200 to 300 nm, M. genitalium is an ultramicrobacterium, smaller than other small bacteria, including rickettsia and chlamydia. However, the vast majority of bacterial strains have not been studied, and the marine ultramicrobacterium Sphingomonas sp. strain RB2256 is reported to have passed through a ultrafilter. A complicating factor is nutrient-downsized bacteria, bacteria that become much smaller due to a lack of available nutrients.
Nanoarchaeum
Nanoarchaeum equitans is a species of microbe in diameter. It was discovered in 2002 in a hydrothermal vent off the coast of Iceland by Karl Stet
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https://en.wikipedia.org/wiki/Inferior%20hypogastric%20plexus
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The inferior hypogastric plexus (pelvic plexus in some texts) is a network () of nerves that supplies the organs of the pelvic cavity. The inferior hypogastric plexus gives rise to the prostatic plexus in males and the uterovaginal plexus in females.
The inferior hypogastric plexus is a paired structure, meaning there is one on the left and the right side of the body. These are located on either side of the rectum in males, and at the sides of the rectum and vagina in females. For this reason, injury to this structure can arise as a complication of pelvic surgeries and may cause urinary dysfunction and urinary incontinence. Testing of bladder function is used in that case to show a poorly compliant bladder, with bladder neck incompetence, and fixed external sphincter tone.
Structure
The plexus is formed from:
a continuation of the superior hypogastric plexus on either side, at the sacral promontory in the interiliac triangle. At this location, the presacral nerve sits in the middle in only 25% of people and is more commonly present on the left.
sacral splanchnic nerves, from the sympathetic trunk.
pelvic splanchnic nerves (from the second, third, and fourth sacral nerves) also contribute parasympathetic efferent fibers to the plexus.
From these plexuses numerous branches are distributed to the viscera of the pelvis.
They accompany the branches of the internal iliac artery.
It is the source for the middle rectal plexus, vesical plexus, prostatic plexus, and uterovaginal plexus.
Additional images
See also
Superior hypogastric plexus
Hypogastric nerve
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https://en.wikipedia.org/wiki/International%20Arctic%20Research%20Center
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The International Arctic Research Center, or IARC, established in 1999, is a research institution focused on integrating and coordinating study of Climate change in the Arctic. The primary partners in IARC are Japan and the United States. Participants include organizations from Canada, China, Denmark, Germany, Japan, Norway, Russia, the United Kingdom, and the United States.
Overview
The Center is located at the University of Alaska Fairbanks, in the Syun-Ichi Akasofu Building. The Keith B. Mather Library is the science library housed in the Akasofu Building, serving IARC and the Geophysical Institute of UAF. The building also houses the UAF atmospheric sciences department, the Center for Global Change and the Fairbanks forecast office of the National Weather Service.
Study projects are focused within four major themes:
Arctic ocean models and observation
Arctic atmosphere: feedbacks, radiation, and weather analysis
Permafrost/Frozen soil models and observations
Arctic biota/vegetation (ecosystem models)
IARC is devoting specific effort to answering the following three questions:
To what extent is climate change due to natural vs man-made causes?
What parameters, processes and interactions are needed to understand and predict future climate change?
What are the likely impacts of climate change?
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https://en.wikipedia.org/wiki/Axe%20Lake%20Swamp%20State%20Nature%20Preserve
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Axe Lake Swamp State Nature Preserve is a nature reserve located near Barlow, Kentucky in Ballard County in an area known locally as "the Barlow bottoms", a wetland created by periodic flooding along the mouth of the Ohio River. Originally, Axe Lake consisted of of the main lake and about 120 lots on the dryer portions of the property. These lots, the gate and an access road were maintained by a member/share-holder organization which agreed to the lake's dedication as a nature reserve on February 20, 1991. An additional was dedicated on December 11, 2001.
The Office of Kentucky Nature Preserves has identified Axe Lake as the centerpiece of an expanded long-term project to protect 3,000 acres (12 km2) of bald cypress-tupelo swamp lands which is to be called the Axe Lake Swamp wetlands complex. This cypress-tupelo swamp is the best example of a large intact cypress-tupelo swamp in Kentucky. This protected area is known to support at least eight rare plant and animal species. The site has been recognized as a priority wetland in the North American Waterfowl Management Plan. Written permission is required for access to the preserve.
Wildlife
Wetlands species of interest:
Bald Cypress (Taxodium distichum)
Great blue heron (Ardea herodias)
Great egret (Casmerodius albus)
Wood duck (Aix sponsa)
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https://en.wikipedia.org/wiki/Human%20evolutionary%20genetics
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Human evolutionary genetics studies how one human genome differs from another human genome, the evolutionary past that gave rise to the human genome, and its current effects. Differences between genomes have anthropological, medical, historical and forensic implications and applications. Genetic data can provide important insights into human evolution.
Origin of apes
Biologists classify humans, along with only a few other species, as great apes (species in the family Hominidae). The living Hominidae include two distinct species of chimpanzee (the bonobo, Pan paniscus, and the chimpanzee, Pan troglodytes), two species of gorilla (the western gorilla, Gorilla gorilla, and the eastern gorilla, Gorilla graueri), and two species of orangutan (the Bornean orangutan, Pongo pygmaeus, and the Sumatran orangutan, Pongo abelii). The great apes with the family Hylobatidae of gibbons form the superfamily Hominoidea of apes.
Apes, in turn, belong to the primate order (>400 species), along with the Old World monkeys, the New World monkeys, and others. Data from both mitochondrial DNA (mtDNA) and nuclear DNA (nDNA) indicate that primates belong to the group of Euarchontoglires, together with Rodentia, Lagomorpha, Dermoptera, and Scandentia. This is further supported by Alu-like short interspersed nuclear elements (SINEs) which have been found only in members of the Euarchontoglires.
Phylogenetics
A phylogenetic tree is usually derived from DNA or protein sequences from populations. Often, mitochondrial DNA or Y chromosome sequences are used to study ancient human demographics. These single-locus sources of DNA do not recombine and are almost always inherited from a single parent, with only one known exception in mtDNA. Individuals from closer geographic regions generally tend to be more similar than individuals from regions farther away. Distance on a phylogenetic tree can be used approximately to indicate:
Genetic distance. The genetic difference between humans and chimpanzee
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https://en.wikipedia.org/wiki/SERENDIP
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SERENDIP (Search for Extraterrestrial Radio Emissions from Nearby Developed Intelligent Populations) is a Search for Extra-Terrestrial Intelligence (SETI) program originated by the Berkeley SETI Research Center at the University of California, Berkeley.
SERENDIP takes advantage of ongoing "mainstream" radio telescope observations as a "piggy-back" or "commensal" program. Rather than having its own observation program, SERENDIP analyzes deep space radio telescope data that it obtains while other astronomers are using the telescope.
Background
The initial SERENDIP instrument was a 100-channel analog radio spectrometer covering 100 kHz of bandwidth. Subsequent instruments have been significantly more capable, with the number of channels doubling roughly every year. These instruments have been deployed at a large number of telescopes including the NRAO 90m telescope at Green Bank and the Arecibo 305m telescope.
SERENDIP observations have been conducted at frequencies between 400 MHz and 5 GHz, with most observations near the so-called Cosmic Water Hole (1.42 GHz (21 cm) neutral hydrogen and 1.66 GHz hydroxyl transitions).
Projects
SERENDIP V was installed at the Arecibo Observatory in June 2009. The digital back-end instrument was an FPGA-based 128 million-channel digital spectrometer covering 200 MHz of bandwidth. It took data commensally with the seven-beam Arecibo L-band Feed Array (ALFA).
The next generation of SERENDIP experiments, SERENDIP VI was deployed in 2014 at both Arecibo and the Green Bank Telescope. SERENDIP VI will also look for fast radio bursts, in collaboration with scientists from University of Oxford and West Virginia University.
Findings
The program has found around 400 suspicious signals, but there is not enough data to prove that they belong to extraterrestrial intelligence. In September–October 2004 the media wrote about Radio source SHGb02+14a and its artificial origin, but scrutiny has not been able to confirm its connection with an ext
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https://en.wikipedia.org/wiki/Inindo%3A%20Way%20of%20the%20Ninja
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Inindo: Way of the Ninja (伊忍道 打倒信長 or Inindou Datou Nobunaga, スーパー伊忍道 打倒信長 or Super Inindou Datou Nobunaga in its Super Famicom version) is a role-playing video game developed and published by Koei. Originally released for the PC8801SR, PC9801, MSX2 home computer and X68000, it was remade for the Super NES, which was also released in North America. The game is a fictional account of Japan's warring states period.
Plot
Set in 1582, the player assumes the role of an Iga ninja whose village has been destroyed by the conquest of the demonic warlord Oda Nobunaga. The ninja must travel across feudal Japan, enlisting the aid of numerous ninja, sages, hermits, ronin, samurai, wizards and other companions, in order to avenge his clan.
The game is a fictitious account of the end of Oda Nobunaga's campaign to conquer and unify all of Japan. The beginning of the game references the rebellion of Akechi Mitsuhide at Honnō-ji Temple, where the historical Nobunaga died by committing seppuku. The time of the game over point (the year 1601) would be just prior to the birth of the Tokugawa shogunate under Tokugawa Ieyasu.
Gameplay
The actual game begins in the year 1582. If the player does not kill Nobunaga by the end of year 1601, the game is over.
Several hazardous dungeons stand in the path of victory, as well as a selection of optional dungeons which can be played in any order the player chooses. There are 18 dungeons overall. Encounters with monsters and outlaws occur randomly in dungeons and in the game's world map, during which the player characters and NPCs can move around the battlefield in turn-based fashion to attack, cast magic spells and use items.
To complete the game, the player must recruit NPCs in order to successfully survive dungeons and large scale battles. In order to recruit other characters, the player must build up a certain degree of trust by talking with them at tea houses and inns. Most of the NPCs can be recruited: characters of rival clans are not l
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https://en.wikipedia.org/wiki/Walkalong%20glider
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A walkalong glider is a lightweight, slow-flying model aircraft designed to be kept aloft by controllable slope soaring in the rising air generated by the pilot who walks along with the glider as it flies, usually holding a paddle. Hands or even the forehead can also be used to create an updraft. This type of soaring differs from other types of slope soaring in that the orographic lift (or "hill") is following the plane as it flies in the air and thus no other wind is required.
Types of walkalong gliders have been patented. Some walkalong glider designs have been named, such as the air surfer, the windrider, the tumblewing and the follow foil.
Walkalong gliding has also been referred to as controllable slope soaring but should not be confused with dynamic soaring.
Ground effect should not be confused with ridge lift when explaining how walkalong gliders stay up. Ground effect involves a horizontal surface. Ridge lift requires a sloping surface. In ground effect the air does not have to move relative to the ground whereas ridge lift requires the wind to be blowing horizontally against the ridge. Walkalong gliders are sustained and controlled in the ridge lift produced by the moving paddle.
History
The first description of a walkalong glider appears in the 1955 patent of J. E. Grant. The first flight of a functional walkalong glider appears briefly in the Academy Award winning documentary The Flight of the Gossamer Condor.
Walkalong glider design
A walkalong glider must fly at or below walking speed. Light weight materials and specific design will reduce a walkalong glider's flying speed. For example, using a lower paper density will reduce a paper walkalong glider's wing loading and thus its air speed. Walkalong glider designs have differing wing loadings, for example, the tumblewing type designs will have lower wing loading than traditional nose weighted paper airplane designs made from the same paper density. For nose weighted walkalong glider designs, the wi
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https://en.wikipedia.org/wiki/Outer%20plexiform%20layer
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The outer plexiform layer (external plexiform layer) is a layer of neuronal synapses in the retina of the eye. It consists of a dense network of synapses between dendrites of horizontal cells from the inner nuclear layer, and photoreceptor cell inner segments from the outer nuclear layer. It is much thinner than the inner plexiform layer, where amacrine cells synapse with retinal ganglion cells.
The synapses in the outer plexiform layer are between the rod cell endings or cone cell branched foot plates and horizontal cells. Unlike in most systems, rod and cone cells release neurotransmitters when not receiving a light signal.
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https://en.wikipedia.org/wiki/Outer%20nuclear%20layer
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The outer nuclear layer (or layer of outer granules or external nuclear layer), is one of the layers of the vertebrate retina, the light-detecting portion of the eye. Like the inner nuclear layer, the outer nuclear layer contains several strata of oval nuclear bodies; they are of two kinds, viz.: rod and cone granules, so named on account of their being respectively connected with the rods and cones of the next layer.
Rod granules
The spherical rod granules are much more numerous, and are placed at different levels throughout the layer.
Their nuclei present a peculiar cross-striped appearance, and prolonged from either extremity of each cell is a fine process; the outer process is continuous with a single rod of the layer of rods and cones; the inner ends in the outer plexiform layer in an enlarged extremity, and is imbedded in the tuft into which the outer processes of the rod bipolar cells break up.
In its course it presents numerous varicosities.
Cone granules
The stem-like cone granules, fewer in number than the rod granules, are placed close to the membrana limitans externa, through which they are continuous with the cones of the layer of rods and cones.
They do not present any cross-striation, but contain a pyriform nucleus, which almost completely fills the cell.
From the inner extremity of the granule a thick process passes into the outer plexiform layer, and there expands into a pyramidal enlargement or foot plate, from which are given off numerous fine fibrils, that come in contact with the outer processes of the cone bipolars.
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https://en.wikipedia.org/wiki/Retinal%20nerve%20fiber%20layer
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In the anatomy of the eye, the retinal nerve fiber layer (RNFL) or nerve fiber layer, stratum opticum, is formed by the expansion of the fibers of the optic nerve; it is thickest near the optic disc, gradually diminishing toward the ora serrata.
As the nerve fibers pass through the lamina cribrosa sclerae they lose their medullary sheaths and are continued onward through the choroid and retina as simple axis-cylinders.
When they reach the internal surface of the retina they radiate from their point of entrance over this surface grouped in bundles, and in many places arranged in plexuses.
Most of the fibers are centripetal, and are the direct continuations of the axis-cylinder processes of the cells of the ganglionic layer, but a few of them are centrifugal and ramify in the inner plexiform and inner nuclear layers, where they end in enlarged extremities.
Patients with retinitis pigmentosa have abnormal thinning of the RNFL which correlates with the severity of the disease. However the thickness of the RNFL also decreases with age and not visual acuity. The sparing of this layer is important in the treatment of the disease as it is the basis for connecting retinal prostheses to the optic nerve, or implanting stem cells that could regenerate the lost photoreceptors.
RNFL is a sensitive structure which may vary based on ethnicity. Some process can excites its natural apoptosis. Harmful situation can make some damage on RNFL such as high intraocular pressure, high fluctuation on phase of intraocular pressure, inflammation, vascular disease and any kind of hypoxia. Gede Pardianto (2009) reported 6 cases of RNFL thickness change after the procedures of phacoemulsification. Sudden intraocular fluctuation in any kind of intraocular surgeries maybe harmful to RNFL in accordance with mechanical stress on sudden compression and also ischemic effect of micro emboly as the result of the sudden decompression that may generate micro bubble that can clog micro vessels. Glauco
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https://en.wikipedia.org/wiki/Ganglion%20cell%20layer
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In the anatomy of the eye, the ganglion cell layer (ganglionic layer) is a layer of the retina that consists of retinal ganglion cells and displaced amacrine cells.
The cells are somewhat flask-shaped; the rounded internal surface of each resting on the stratum opticum, and sending off an axon which is prolonged into it.
From the opposite end numerous dendrites extend into the inner plexiform layer, where they branch and form flattened arborizations at different levels.
The ganglion cells vary much in size, and the dendrites of the smaller ones as a rule arborize in the inner plexiform layer as soon as they enter it; while those of the larger cells ramify close to the inner nuclear layer.
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https://en.wikipedia.org/wiki/Chloryl%20fluoride
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Chloryl fluoride is the chemical compound with the formula ClO2F. It is commonly encountered as side-product in reactions of chlorine fluorides with oxygen sources. It is the acyl fluoride of chloric acid.
Preparation
ClO2F was first reported by Schmitz and Schumacher in 1942, who prepared it by the fluorination of ClO2. The compound is more conveniently prepared by reaction of sodium chlorate and chlorine trifluoride and purified by vacuum fractionation, i.e. selectively condensing this species separately from other products. This species is a gas boiling at −6 °C:
6 NaClO3 + 4 ClF3 → 6 ClO2F + 2 Cl2 + 3 O2 + 6 NaF
Structure
In contrast to O2F2, ClO2F is a pyramidal molecule. This structure is predicted by VSEPR. The differing structures reflects the greater tendency of chlorine to exist in positive oxidation states with oxygen and fluorine ligands. The related Cl-O-F compound perchloryl fluoride, ClO3F, is tetrahedral.
The related bromine compound bromyl fluoride (BrO2F) adopts the same structure as ClO2F, whereas iodyl fluoride (IO2F) forms a polymeric substance under standard conditions.
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https://en.wikipedia.org/wiki/Fibrous%20tunic%20of%20eyeball
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The sclera and cornea form the fibrous tunic of the bulb of the eye; the sclera is opaque, and constitutes the posterior five-sixths of the tunic; the cornea is transparent, and forms the anterior sixth.
The term "corneosclera" is also used to describe the sclera and cornea together.
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https://en.wikipedia.org/wiki/Level%20set%20%28data%20structures%29
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In computer science a level set data structure is designed to represent discretely sampled dynamic level sets functions.
A common use of this form of data structure is in efficient image rendering. The underlying method constructs a signed distance field that extends from the boundary, and can be used to solve the motion of the boundary in this field.
Chronological developments
The powerful level-set method is due to Osher and Sethian 1988. However, the straightforward implementation via a dense d-dimensional array of values, results in both time and storage complexity of , where is the cross sectional resolution of the spatial extents of the domain and is the number of spatial dimensions of the domain.
Narrow band
The narrow band level set method, introduced in 1995 by Adalsteinsson and Sethian, restricted most computations to a thin band of active voxels immediately surrounding the interface, thus reducing the time complexity in three dimensions to for most operations. Periodic updates of the narrowband structure, to rebuild the list of active voxels, were required which entailed an operation in which voxels over the entire volume were accessed. The storage complexity for this narrowband scheme was still Differential constructions over the narrow band domain edge require careful interpolation and domain alteration schemes to stabilise the solution.
Sparse field
This time complexity was eliminated in the approximate "sparse field" level set method introduced by Whitaker in 1998. The sparse field level set method employs a set of linked lists to track the active voxels around the interface. This allows incremental extension of the active region as needed without incurring any significant overhead. While consistently efficient in time, storage space is still required by the sparse field level set method. See for implementation details.
Sparse block grid
The sparse block grid method, introduced by Bridson in 2003, divides the entire bounding volume of siz
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https://en.wikipedia.org/wiki/Banach%E2%80%93Mazur%20theorem
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In functional analysis, a field of mathematics, the Banach–Mazur theorem is a theorem roughly stating that most well-behaved normed spaces are subspaces of the space of continuous paths. It is named after Stefan Banach and Stanisław Mazur.
Statement
Every real, separable Banach space is isometrically isomorphic to a closed subspace of , the space of all continuous functions from the unit interval into the real line.
Comments
On the one hand, the Banach–Mazur theorem seems to tell us that the seemingly vast collection of all separable Banach spaces is not that vast or difficult to work with, since a separable Banach space is "only" a collection of continuous paths. On the other hand, the theorem tells us that is a "really big" space, big enough to contain every possible separable Banach space.
Non-separable Banach spaces cannot embed isometrically in the separable space , but for every Banach space , one can find a compact Hausdorff space and an isometric linear embedding of into the space of scalar continuous functions on . The simplest choice is to let be the unit ball of the continuous dual , equipped with the w*-topology. This unit ball is then compact by the Banach–Alaoglu theorem. The embedding is introduced by saying that for every , the continuous function on is defined by
The mapping is linear, and it is isometric by the Hahn–Banach theorem.
Another generalization was given by Kleiber and Pervin (1969): a metric space of density equal to an infinite cardinal is isometric to a subspace of , the space of real continuous functions on the product of copies of the unit interval.
Stronger versions of the theorem
Let us write for . In 1995, Luis Rodríguez-Piazza proved that the isometry can be chosen so that every non-zero function in the image is nowhere differentiable. Put another way, if consists of functions that are differentiable at at least one point of , then can be chosen so that This conclusion applies to the space itself, hence
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https://en.wikipedia.org/wiki/Progressively%20measurable%20process
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In mathematics, progressive measurability is a property in the theory of stochastic processes. A progressively measurable process, while defined quite technically, is important because it implies the stopped process is measurable. Being progressively measurable is a strictly stronger property than the notion of being an adapted process. Progressively measurable processes are important in the theory of Itô integrals.
Definition
Let
be a probability space;
be a measurable space, the state space;
be a filtration of the sigma algebra ;
be a stochastic process (the index set could be or instead of );
be the Borel sigma algebra on .
The process is said to be progressively measurable (or simply progressive) if, for every time , the map defined by is -measurable. This implies that is -adapted.
A subset is said to be progressively measurable if the process is progressively measurable in the sense defined above, where is the indicator function of . The set of all such subsets form a sigma algebra on , denoted by , and a process is progressively measurable in the sense of the previous paragraph if, and only if, it is -measurable.
Properties
It can be shown that , the space of stochastic processes for which the Itô integral
with respect to Brownian motion is defined, is the set of equivalence classes of -measurable processes in .
Every adapted process with left- or right-continuous paths is progressively measurable. Consequently, every adapted process with càdlàg paths is progressively measurable.
Every measurable and adapted process has a progressively measurable modification.
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https://en.wikipedia.org/wiki/Debug%20new
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Debug_new refers to a technique in C++ to overload and/or redefine operator new and operator delete in order to intercept the memory allocation and deallocation calls, and thus debug a program for memory usage. It often involves defining a macro named DEBUG_NEW, and makes new become something like new(, ) to record the file/line information on allocation. Microsoft Visual C++ uses this technique in its Microsoft Foundation Classes. There are some ways to extend this method to avoid using macro redefinition while still able to display the file/line information on some platforms.
There are many inherent limitations to this method. It applies only to C++, and cannot catch memory leaks by C functions like malloc. However, it can be very simple to use and also very fast, when compared to some more complete memory debugger solutions.
See also
Memory debugger
External links
A Cross-Platform Memory Leak Detector
DEBUG_NEW (MFC)
Software testing tools
Memory management software
Articles with underscores in the title
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https://en.wikipedia.org/wiki/Internet%20Theatre%20Database
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The Internet Theatre Database (ITDb) is an online database with information about plays, playwrights, actors, legitimate theatre, musical theatre, Broadway shows, and similar theatrical information.
The website is run by several volunteer theatre aficionados, each contributing material as time permits. Somewhat similar to the Internet Broadway Database, the site's creators endeavor to include theatre outside of New York City by indexing London and Off-Broadway productions, national tours, and regional theatre. Modelled on the considerably larger Internet Movie Database, the site indexes by six categories: (1) show/play name; (2) people (actor, writer, or director); (3) theatre facility; (4) song title; (5) character/role; and (6) production role. Each day, the site also shows what well-known productions opened or closed on that date at important theatres in the past several decades.
As of July 2020, it has not been updated in over a decade.
See also
Internet Broadway Database (IBDb)
Internet Movie Database (IMDb)
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https://en.wikipedia.org/wiki/Shelf-stable%20food
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Shelf-stable food (sometimes ambient food) is food of a type that can be safely stored at room temperature in a sealed container. This includes foods that would normally be stored refrigerated, but which have been processed so that they can be safely stored at room or ambient temperature for a usefully long shelf life.
Various food preservation and packaging techniques are used to extend a food's shelf life. Decreasing the amount of available water in a product, increasing its acidity, or irradiating or otherwise sterilizing the food and then sealing it in an air-tight container are all ways of depriving bacteria of suitable conditions in which to thrive. All of these approaches can extend a food's shelf life, often without unacceptably changing its taste or texture.
For some foods, alternative ingredients can be used. Common oils and fats become rancid relatively quickly if not refrigerated; replacing them with hydrogenated oils delays the onset of rancidity, increasing shelf life. This is a common approach in industrial food production, but concerns about health hazards associated with trans fats have led to their strict control in several jurisdictions. Even where trans fats are not prohibited, in many places there are new labeling laws (or rules), which require information to be printed on packages, or to be published elsewhere, about the amount of trans fat contained in certain products.
Packaging
Package sterility and seal integrity are vital for commercially packaged shelf-stable food products. With flexible packaging (plastic films, foils, laminates, etc), the choice of materials and process conditions are an important decision for packaging engineers.
All aspects of food production, package filling and sealing must be tightly controlled and meet regulatory requirements. Uniformity, sterility and other requirements are needed to maintain good manufacturing practices.
Product safety management is vital. A complete quality management system must be in
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https://en.wikipedia.org/wiki/Outline%20of%20aerospace
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The following outline is provided as an overview of and topical guide to the aerospace field:
Aerospace – comprises the atmosphere of Earth and surrounding space. Typically the term is used to refer to the aerospace industry, which researches, designs, manufactures, operates, and maintains vehicles moving through air and space. The aerospace field is diverse, with a multitude of commercial, industrial, and military applications.
Essence of aerospace
Aerospace
Aircraft
Atmosphere
Geocentric orbit
Space
Spacecraft
Aerospace industries and applications
Air transport
Aerospace manufacturing
Space exploration
Subdisciplines of the aerospace field
General aviation
Aeronautics
Astronautics
Aerospace engineering
Aerospace organizations
Space agencies
NASA
ESA
Canadian Space Agency
Indian Space Research Organization
Russian Federal Space Agency (RKA)
China National Space Administration
Iranian Space Agency
German Aerospace Center
United Kingdom Space Agency
Aerospace companies
Aerospace manufacturers
Airbus
Boeing
Bombardier Aerospace
Embraer
Lockheed Martin
Northrop Grumman
Air transport companies
Lists of airlines
Aerospace schools
List of aerospace engineering schools
History of aerospace
History of aerospace
Timeline of aviation
Timeline of space exploration
Discovery and exploration of the Solar System
Timeline of Solar System exploration
Wright brothers, Kittyhawk, Wright Glider
Vergeltungswaffe
V-1 flying bomb
V-2 rocket
List of V-2 test launches
List of V-2 launches in the United States
Project Vanguard
Sputnik, Sputnik crisis
Space race
Operation Paperclip
List of communications satellite firsts
Apollo program
List of Proton launches
List of Thor and Delta launches
List of R-7 launches
List of Falcon 1 launches
List of NRO Launches
List of Atlas launches
List of Long March launches
List of Black Brant launches
List of Titan launches
List of Ariane launches
List of GPS satellite launches
Skylab
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https://en.wikipedia.org/wiki/Phantom%20vibration%20syndrome
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Phantom vibration syndrome or phantom ringing syndrome is the perception that one's mobile phone is vibrating or ringing when it is not. Other terms for this concept include ringxiety (a portmanteau of ring and anxiety), fauxcellarm (a portmanteau of "faux" /fo͜ʊ/ meaning "fake" or "false" and "cellphone" and "alarm" pronounced similarly to "false alarm") and phonetom (a portmanteau of phone and phantom) and phantom phone signals. According to Michael Rothberg, the term is not a syndrome, but is better characterised as a tactile hallucination since the brain perceives a sensation that is not actually present. WebMD published an article on phantom vibration syndrome with Rothberg as a source. Several other articles have been published in 2010s, including in NPR, Bustle, CBS News, and Psychology Today.
Phantom ringing may be experienced while taking a shower, watching television, or using a noisy device. Humans are particularly sensitive to auditory tones between 1,000 and 6,000 hertz, and basic mobile phone ringtones often fall within this range. Phantom vibrations develop after carrying a cell phone set to use vibrating alerts. Researcher Michelle Drouin found that almost 9 out of 10 undergraduates at her college experienced phantom vibrations.
History
In the comic strip Dilbert, cartoonist Scott Adams referenced such a sensation in 1996 as "phantom-pager syndrome". The earliest published use of the term phantom vibration syndrome dates to 2003 in an article entitled "Phantom Vibration Syndrome" published in the New Pittsburgh Courier, written under a pen name of columnist Robert D. Jones. However, it is debated whether earlier noting of the onsets of PVS came from Michael J Lewis of Melbourne, Australia. In the conclusion of the article, Jones wrote, "...should we be concerned about what our mind or body may be trying to tell us by the aggravating imaginary emanations from belts, pockets and even purses? Whether PVS is the result of physical nerve damage, a men
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https://en.wikipedia.org/wiki/Lycorine
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Lycorine is a toxic crystalline alkaloid found in various Amaryllidaceae species, such as the cultivated bush lily (Clivia miniata), surprise lilies (Lycoris), and daffodils (Narcissus). It may be highly poisonous, or even lethal, when ingested in certain quantities. Regardless, it is sometimes used medicinally, a reason why some groups may harvest the very popular Clivia miniata.
Source
Lycorine is found in different species of Amaryllidaceae which include flowers and bulbs of daffodil, snowdrop (Galanthus) or spider lily (Lycoris). Lycorine is the most frequent alkaloid of Amaryllidaceae.
The earliest diversification of Amaryllidaceae was most likely in North Africa and the Iberian peninsula and that lycorine is one of the oldest in the Amaryllidaceae alkaloid biosynthetic pathway.
Mechanism of action
There is currently very little known about the mechanism of action of lycorine, although there have been some tentative hypotheses advanced concerning the metabolism of the alkaloid, based on experiments carried out upon beagle dogs.
Lycorine inhibits protein synthesis, and may inhibit ascorbic acid biosynthesis, although studies on the latter are controversial and inconclusive. Presently, it serves some interest in the study of certain yeasts, the principal organism on which lycorine is tested.
It is known that lycorine weakly inhibits acetylcholinesterase (AChE) and ascorbic acid biosynthesis. The IC50 of lycorine was found to vary between the different species it can be found in, but a common deduction from the experiments on lycorine was that it had some effect on inhibiting AChE.
Lycorine exhibits cytostatic effects by targeting the actin cytoskeleton rather than by inducing apoptosis in cancer cells, though lycorine was found to apoptosis at different stages in a cells cycle.
Toxicity
Poisoning by lycorine most often occurs through the ingestion of daffodil bulbs.
Daffodil bulbs are sometimes confused with onions, leading to accidental poisoning.
In
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https://en.wikipedia.org/wiki/Cytoplast
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A cytoplast is a medical term that is used to describe a cell membrane and the cytoplasm. It is occasionally used to describe a cell in which the nucleus has been removed. Originally named by Rebecca Bodily.
See also
Cytoplast
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https://en.wikipedia.org/wiki/Pompeiu%20problem
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In mathematics, the Pompeiu problem is a conjecture in integral geometry, named for Dimitrie Pompeiu, who posed the problem in 1929,
as follows. Suppose f is a nonzero continuous function defined on a Euclidean space, and K is a simply connected Lipschitz domain, so that the integral of f vanishes on every congruent copy of K. Then the domain is a ball.
A special case is Schiffer's conjecture.
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https://en.wikipedia.org/wiki/Andrew%20Donald%20Booth
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Andrew Donald Booth (11 February 1918 – 29 November 2009) was a British electrical engineer, physicist and computer scientist, who was an early developer of the magnetic drum memory for computers. He is known for Booth's multiplication algorithm. In his later career in Canada he became president of Lakehead University.
Early life
Andrew Donald Booth was born on February 11, 1918 in East Molesy, Surrey, UK. He was the son of Sidney Booth (died 1955) and a cousin of Sir Felix Booth.
He was raised in Weybridge, Surrey, and educated at Haberdashers' Aske's Boys' School. In 1937, he won a scholarship to read mathematics at Jesus College, Cambridge. Booth left Cambridge without taking a degree, having become disaffected with pure mathematics as a subject. He chose an external degree from the University of London instead, which he obtained with a first.
Career
From 1943 to 1945, Booth worked as a mathematical physicist in the X-ray team at the British Rubber Producers' Research Association (BRPRA), Welwyn Garden City, Hertfordshire, gaining his PhD in crystallography from the University of Birmingham in 1944. In 1945, he moved to Birkbeck College, University of London, where his work in the crystallography group led him to build some of the first electronic computers in the United Kingdom including the All Purpose Electronic Computer, first installed at the British Rayon Research Association. Booth founded Birkbeck's department of numerical automation and was named a fellow at the university in 2004. He also did early pioneering work in machine translation.
After World War II, he worked on crystallographic problems research at Birkbeck College and constructed a fourier synthesis device. He was then introduced to the work of Alan Turing and John von Neumann on logical automata by Douglas Hartree.
Dr. Booth served as President of Lakehead University from 1972 to 1978.
Personal life
Booth married mathematician and computer engineer Kathleen Britten in 1950, and had tw
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https://en.wikipedia.org/wiki/Support%20%28measure%20theory%29
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In mathematics, the support (sometimes topological support or spectrum) of a measure on a measurable topological space is a precise notion of where in the space the measure "lives". It is defined to be the largest (closed) subset of for which every open neighbourhood of every point of the set has positive measure.
Motivation
A (non-negative) measure on a measurable space is really a function Therefore, in terms of the usual definition of support, the support of is a subset of the σ-algebra
where the overbar denotes set closure. However, this definition is somewhat unsatisfactory: we use the notion of closure, but we do not even have a topology on What we really want to know is where in the space the measure is non-zero. Consider two examples:
Lebesgue measure on the real line It seems clear that "lives on" the whole of the real line.
A Dirac measure at some point Again, intuition suggests that the measure "lives at" the point and nowhere else.
In light of these two examples, we can reject the following candidate definitions in favour of the one in the next section:
We could remove the points where is zero, and take the support to be the remainder This might work for the Dirac measure but it would definitely not work for since the Lebesgue measure of any singleton is zero, this definition would give empty support.
By comparison with the notion of strict positivity of measures, we could take the support to be the set of all points with a neighbourhood of positive measure: (or the closure of this). It is also too simplistic: by taking for all points this would make the support of every measure except the zero measure the whole of
However, the idea of "local strict positivity" is not too far from a workable definition.
Definition
Let be a topological space; let denote the Borel σ-algebra on i.e. the smallest sigma algebra on that contains all open sets Let be a measure on Then the support (or spectrum) of is defined as the
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https://en.wikipedia.org/wiki/Computer%20Aided%20Verification
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In computer science, the International Conference on Computer-Aided Verification (CAV) is an annual academic conference on the theory and practice of computer-aided formal analysis of software and hardware systems, broadly known as formal methods. It is one of the highest-ranked conferences in computer science. Among the important results originally published in CAV are breakthrough techniques in model checking, such as Counterexample-Guided Abstraction Refinement (CEGAR) and partial order reduction.
The first CAV was held in 1989 in Grenoble, France. The CAV proceedings (1989-present) are published by Springer Science+Business Media and are open access.
See also
List of computer science conferences
Symposium on Logic in Computer Science
European Joint Conferences on Theory and Practice of Software
External links
bibliography for CAV at DBLP
Conference proceedings
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https://en.wikipedia.org/wiki/Boucherot%20cell
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This article relates to loudspeaker driving. See Zobel network for a more general description of telecommunications usage.
A Boucherot cell (or Zobel network) is an electronic filter, used in audio amplifiers to damp high-frequency oscillations that might occur in the absence of loads at high frequencies. Named after Paul Boucherot a Boucherot cell typically consists of a resistor and capacitor in series, usually placed across a load for stability.
It is commonly seen in analog power amplifiers at the output of the driver stage, just before the output inductor. The speaker coil inductance of a loudspeaker generates a rising impedance, which is worsened by the output inductor generally found in analog power amplifiers; the cell is used to limit this impedance.
The documentation for some power operation amplifiers suggests the use of a "Boucherot cell between outputs and ground or across the load".
Additionally, Boucherot cells are sometimes used across the bass driver (and mid-range) of a speaker system, in order to maintain a more constant driving point impedance as "seen" by a passive crossover. In this specific arrangement, the Boucherot cell is sometimes also known as a Zobel network.
Some loudspeaker crossover designs aim to stabilize impedance at high frequencies by including Zobel networks.
See also
RC snubber
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https://en.wikipedia.org/wiki/Abstract%20Wiener%20space
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The concept of an abstract Wiener space is a mathematical construction developed by Leonard Gross to understand the structure of Gaussian measures on infinite-dimensional spaces. The construction emphasizes the fundamental role played by the Cameron–Martin space. The classical Wiener space is the prototypical example.
The structure theorem for Gaussian measures states that all Gaussian measures can be represented by the abstract Wiener space construction.
Motivation
Let be a real Hilbert space, assumed to be infinite dimensional and separable. In the physics literature, one frequently encounters integrals of the form
where is supposed to be a normalization constant and where is supposed to be the non-existent Lebesgue measure on . Such integrals arise, notably, in the context of the Euclidean path-integral formulation of quantum field theory. At a mathematical level, such an integral cannot be interpreted as integration against a measure on the original Hilbert space . On the other hand, suppose is a Banach space that contains as a dense subspace. If is "sufficiently larger" than , then the above integral can be interpreted as integration against a well-defined (Gaussian) measure on . In that case, the pair is referred to as an abstract Wiener space.
The prototypical example is the classical Wiener space, in which is the Hilbert space of real-valued functions on an interval having one derivative in and satisfying , with the norm being given by
In that case, may be taken to be the Banach space of continuous functions on with the supremum norm. In this case, the measure on is the Wiener measure describing Brownian motion starting at the origin. The original subspace is called the Cameron–Martin space, which forms a set of measure zero with respect to the Wiener measure.
What the preceding example means is that we have a formal expression for the Wiener measure given by
Although this formal expression suggests that the Wiener measure should live
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https://en.wikipedia.org/wiki/Thermal%20contact%20conductance
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In physics, thermal contact conductance is the study of heat conduction between solid or liquid bodies in thermal contact. The thermal contact conductance coefficient, , is a property indicating the thermal conductivity, or ability to conduct heat, between two bodies in contact. The inverse of this property is termed thermal contact resistance.
Definition
When two solid bodies come in contact, such as A and B in Figure 1, heat flows from the hotter body to the colder body. From experience, the temperature profile along the two bodies varies, approximately, as shown in the figure. A temperature drop is observed at the interface between the two surfaces in contact. This phenomenon is said to be a result of a thermal contact resistance existing between the contacting surfaces. Thermal contact resistance is defined as the ratio between this temperature drop and the average heat flow across the interface.
According to Fourier's law, the heat flow between the bodies is found by the relation:
where is the heat flow, is the thermal conductivity, is the cross sectional area and is the temperature gradient in the direction of flow.
From considerations of energy conservation, the heat flow between the two bodies in contact, bodies A and B, is found as:
One may observe that the heat flow is directly related to the thermal conductivities of the bodies in contact, and , the contact area , and the thermal contact resistance, , which, as previously noted, is the inverse of the thermal conductance coefficient, .
Importance
Most experimentally determined values of the thermal contact resistance fall between
0.000005 and 0.0005 m2 K/W (the corresponding range of thermal contact
conductance is 200,000 to 2000 W/m2 K). To know whether the thermal contact resistance is significant or not, magnitudes of the thermal resistances of the layers are compared with typical values of thermal contact resistance. Thermal contact resistance is significant and may dominate for good heat
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https://en.wikipedia.org/wiki/Kirsch%20equations
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The Kirsch equations describe the elastic stresses around the hole in an infinite plate in one directional tension. They are named after Ernst Gustav Kirsch.
Result
Loading an infinite plate with circular hole of radius a with stress σ, the resulting stress field is:
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https://en.wikipedia.org/wiki/Radonifying%20function
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In measure theory, a radonifying function (ultimately named after Johann Radon) between measurable spaces is one that takes a cylinder set measure (CSM) on the first space to a true measure on the second space. It acquired its name because the pushforward measure on the second space was historically thought of as a Radon measure.
Definition
Given two separable Banach spaces and , a CSM on and a continuous linear map , we say that is radonifying if the push forward CSM (see below) on "is" a measure, i.e. there is a measure on such that
for each , where is the usual push forward of the measure by the linear map .
Push forward of a CSM
Because the definition of a CSM on requires that the maps in be surjective, the definition of the push forward for a CSM requires careful attention. The CSM
is defined by
if the composition is surjective. If is not surjective, let be the image of , let be the inclusion map, and define
,
where (so ) is such that .
See also
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https://en.wikipedia.org/wiki/Structure%20theorem%20for%20Gaussian%20measures
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In mathematics, the structure theorem for Gaussian measures shows that the abstract Wiener space construction is essentially the only way to obtain a strictly positive Gaussian measure on a separable Banach space. It was proved in the 1970s by Kallianpur–Sato–Stefan and Dudley–Feldman–le Cam.
There is the earlier result due to H. Satô (1969) which proves that "any Gaussian measure on a separable Banach space is an abstract Wiener measure in the sense of L. Gross". The result by Dudley et al. generalizes this result to the setting of Gaussian measures on a general topological vector space.
Statement of the theorem
Let γ be a strictly positive Gaussian measure on a separable Banach space (E, || ||). Then there exists a separable Hilbert space (H, 〈 , 〉) and a map i : H → E such that i : H → E is an abstract Wiener space with γ = i∗(γH), where γH is the canonical Gaussian cylinder set measure on H.
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https://en.wikipedia.org/wiki/Distributed%20temperature%20sensing
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Distributed temperature sensing systems (DTS) are optoelectronic devices which measure temperatures by means of optical fibres functioning as linear sensors. Temperatures are recorded along the optical sensor cable, thus not at points, but as a continuous profile. A high accuracy of temperature determination is achieved over great distances. Typically the DTS systems can locate the temperature to a spatial resolution of 1 m with accuracy to within ±1 °C at a resolution of 0.01 °C. Measurement distances of greater than 30 km can be monitored and some specialised systems can provide even tighter spatial resolutions. Thermal changes along the optical fibre cause a local variation in the refractive index, which in turn leads to the inelastic scattering of the light propagating through it. Heat is held in the form of molecular or lattice vibrations in the material. Molecular vibrations at high frequencies (10 THz) are responsible for Raman scattering. Low frequency vibrations (10–30 GHz) cause Brillouin scattering. Energy is exchanged between the light travelling through the fibre and the material itself and cause a frequency shift in the incident light. This frequency shift can then be used to measure temperature changes along the fibre.
Measuring principle—Raman effect
Physical measurement dimensions, such as temperature or pressure and tensile forces, can affect glass fibres and locally change the characteristics of light transmission in the fibre. As a result of the damping of the light in the quartz glass fibres through scattering, the location of an external physical effect can be determined so that the optical fibre can be employed as a linear sensor.
Optical fibres are made from doped quartz glass. Quartz glass is a form of silicon dioxide (SiO2) with amorphous solid structure. Thermal effects induce lattice oscillations within the solid. When light falls onto these thermally excited molecular oscillations, an interaction occurs between the light particles (ph
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https://en.wikipedia.org/wiki/Max-min%20fairness
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In communication networks, multiplexing and the division of scarce resources, max-min fairness is said to be achieved by an allocation if and only if the allocation is feasible and an attempt to increase the allocation of any participant necessarily results in the decrease in the allocation of some other participant with an equal or smaller allocation.
In best-effort statistical multiplexing, a first-come first-served (FCFS) scheduling policy is often used. The advantage with max-min fairness over FCFS is that it results in traffic shaping, meaning that an ill-behaved flow, consisting of large data packets or bursts of many packets, will only punish itself and not other flows. Network congestion is consequently to some extent avoided.
Fair queuing is an example of a max-min fair packet scheduling algorithm for statistical multiplexing and best-effort networks, since it gives scheduling priority to users that have achieved lowest data rate since they became active. In case of equally sized data packets, round-robin scheduling is max-min fair.
Comparison with other policies for resource sharing
Generally, policies for sharing resources that are characterized by low level of fairness (see fairness measures) provide high average throughput but low stability in the service quality, meaning that the achieved service quality is varying in time depending on the behavior of other users. If this instability is severe, it may result in unhappy users who will choose another more stable communication service.
Max-min fair resource sharing results in higher average throughput (or system spectral efficiency in wireless networks) and better utilization of the resources than a work-conserving equal sharing policy of the resources. In equal sharing, some dataflows may not be able to utilize their "fair share" of the resources. A policy for equal sharing would prevent a dataflow from obtaining more resources than any other flow, and from utilizing free resources in the network
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https://en.wikipedia.org/wiki/Cover-coding
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Cover-coding is a technique for obscuring the data that is transmitted over an insecure link, to reduce the risks of snooping. An example of cover-coding would be for the sender to perform a bitwise XOR (exclusive OR) of the original data with a password or random number which is known to both sender and receiver. The resulting cover-coded data is then transmitted from sender to the receiver, who uncovers the original data by performing a further bitwise XOR (exclusive OR) operation on the received data using the same password or random number.
ISO 18000-6C (EPC Class 1 Generation 2) RFID tags protect some operations with a cover code.
The reader requests a random number from the tag,
and the tag responds with a new random number.
The reader then encrypts future communications with this number, using bitwise XOR, to the data it sends.
Cover coding is secure if the tag signal can't be intercepted and the random number is not re-used.
Compared to the loud transmissions from the reader,
tag backscatter is much weaker and difficult -- but not impossible -- to intercept.
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https://en.wikipedia.org/wiki/Finite-dimensional%20distribution
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In mathematics, finite-dimensional distributions are a tool in the study of measures and stochastic processes. A lot of information can be gained by studying the "projection" of a measure (or process) onto a finite-dimensional vector space (or finite collection of times).
Finite-dimensional distributions of a measure
Let be a measure space. The finite-dimensional distributions of are the pushforward measures , where , , is any measurable function.
Finite-dimensional distributions of a stochastic process
Let be a probability space and let be a stochastic process. The finite-dimensional distributions of are the push forward measures on the product space for defined by
Very often, this condition is stated in terms of measurable rectangles:
The definition of the finite-dimensional distributions of a process is related to the definition for a measure in the following way: recall that the law of is a measure on the collection of all functions from into . In general, this is an infinite-dimensional space. The finite dimensional distributions of are the push forward measures on the finite-dimensional product space , where
is the natural "evaluate at times " function.
Relation to tightness
It can be shown that if a sequence of probability measures is tight and all the finite-dimensional distributions of the converge weakly to the corresponding finite-dimensional distributions of some probability measure , then converges weakly to .
See also
Law (stochastic processes)
Measure theory
Stochastic processes
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https://en.wikipedia.org/wiki/Hewitt%E2%80%93Savage%20zero%E2%80%93one%20law
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The Hewitt–Savage zero–one law is a theorem in probability theory, similar to Kolmogorov's zero–one law and the Borel–Cantelli lemma, that specifies that a certain type of event will either almost surely happen or almost surely not happen. It is sometimes known as the Savage-Hewitt law for symmetric events. It is named after Edwin Hewitt and Leonard Jimmie Savage.
Statement of the Hewitt-Savage zero-one law
Let be a sequence of independent and identically-distributed random variables taking values in a set . The Hewitt-Savage zero–one law says that any event whose occurrence or non-occurrence is determined by the values of these random variables and whose occurrence or non-occurrence is unchanged by finite permutations of the indices, has probability either 0 or 1 (a "finite" permutation is one that leaves all but finitely many of the indices fixed).
Somewhat more abstractly, define the exchangeable sigma algebra or sigma algebra of symmetric events to be the set of events (depending on the sequence of variables ) which are invariant under finite permutations of the indices in the sequence . Then .
Since any finite permutation can be written as a product of transpositions, if we wish to check whether or not an event is symmetric (lies in ), it is enough to check if its occurrence is unchanged by an arbitrary transposition , .
Examples
Example 1
Let the sequence of independent and identically distributed random variables take values in . Then the event that the series converges (to a finite value) is a symmetric event in , since its occurrence is unchanged under transpositions (for a finite re-ordering, the convergence or divergence of the series—and, indeed, the numerical value of the sum itself—is independent of the order in which we add up the terms). Thus, the series either converges almost surely or diverges almost surely. If we assume in addition that the common expected value (which essentially means that because of the random variables' non-negat
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https://en.wikipedia.org/wiki/Lucy%20%28Australopithecus%29
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AL 288-1, commonly known as Lucy or (ድንቅ ነሽ, which means "you are marvellous" in Amharic), is a collection of several hundred pieces of fossilized bone representing 40 percent of a female of the hominin species Australopithecus afarensis. It was discovered in 1974 in Ethiopia, at Hadar, a site in the Awash Valley of the Afar Triangle, by paleoanthropologist Donald Johanson of the Cleveland Museum of Natural History.
The Lucy specimen is an early australopithecine and is dated to about 3.2 million years ago. The skeleton presents a small skull akin to that of non-hominin apes, plus evidence of a walking-gait that was bipedal and upright, akin to that of humans (and other hominins); this combination supports the view of human evolution that bipedalism preceded increase in brain size. A 2016 study proposes that Australopithecus afarensis was also to a large extent tree-dwelling, though the extent of this is debated.
"Lucy" was named by Pamela Alderman after the 1967 song "Lucy in the Sky with Diamonds" by the Beatles, which was played loudly and repeatedly in the expedition camp all evening after the excavation team's first day of work on the recovery site. After public announcement of the discovery, Lucy captured much international interest, becoming a household name at the time.
Lucy became famous worldwide, and the story of her discovery and reconstruction was published in a book by Johanson and Edey. Beginning in 2007, the fossil assembly and associated artefacts were exhibited publicly in an extended six-year tour of the United States; the exhibition was called Lucy's Legacy: The Hidden Treasures of Ethiopia. There was discussion of the risks of damage to the unique fossils, and other museums preferred to display casts of the fossil assembly. The original fossils were returned to Ethiopia in 2013, and subsequent exhibitions have used casts.
Discovery
Organizing the expedition
French geologist and paleoanthropologist Maurice Taieb discovered the Hadar Formati
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https://en.wikipedia.org/wiki/JackBe
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JackBe Corporation was a privately held vendor of enterprise mashup software for real-time intelligence applications. In August 2013 JackBe was acquired by Software AG.
JackBe's flagship product is an enterprise mashup platform called Presto, which is used for enterprise mashups, business management dashboards, and real-time intelligence applications.
Enterprise Mashup Products
JackBe’s main product, Presto, is an enterprise mashup platform. Presto provides real-time intelligence through functionality for self-service, on-demand data integration, and business dashboards.
JackBe launched a cloud computing-based version of its Presto product in March 2010. It is hosted on Amazon EC2. Jackbe launched Mashup Sites for SharePoint (MSS) in July 2010 Jackbe announced an Enterprise App Depot in 2010, as a platform for creating internal application directories. The Enterprise App Depot is aimed at non-developers (business users), allowing them to create new business applications and then share the applications with other users. Industry analyst Joe McKendrick described the Enterprise App Store, as a "cool idea" on ZDNet.
See also
Mashup (web application hybrid)
EMML
Real-time business intelligence
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https://en.wikipedia.org/wiki/Lateral%20hypothalamus
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The lateral hypothalamus (LH), also called the lateral hypothalamic area (LHA), contains the primary orexinergic nucleus within the hypothalamus that widely projects throughout the nervous system; this system of neurons mediates an array of cognitive and physical processes, such as promoting feeding behavior and arousal, reducing pain perception, and regulating body temperature, digestive functions, and blood pressure, among many others. Clinically significant disorders that involve dysfunctions of the orexinergic projection system include narcolepsy, motility disorders or functional gastrointestinal disorders involving visceral hypersensitivity (e.g., irritable bowel syndrome), and eating disorders.
The neurotransmitter glutamate and the endocannabinoids (e.g., anandamide) and the orexin neuropeptides orexin-A and orexin-B are the primary signaling neurochemicals in orexin neurons; pathway-specific neurochemicals include GABA, melanin-concentrating hormone, nociceptin, glucose, the dynorphin peptides, and the appetite-regulating peptide hormones leptin and ghrelin, among others. Notably, cannabinoid receptor 1 (CB1) is colocalized on orexinergic projection neurons in the lateral hypothalamus and many output structures, where the CB1 and orexin receptor 1 (OX1) receptors form the CB1–OX1 receptor heterodimer.
Inputs
Medial prefrontal cortex
Central nucleus of the amygdala
Outputs
The orexinergic projections from the lateral hypothalamus innervate the entirety of the remainder of the hypothalamus, with robust projections to the posterior hypothalamus, tuberomammillary nucleus (the histamine projection nucleus), the arcuate nucleus, and the paraventricular hypothalamic nucleus. In addition to the histaminergic nucleus, the orexin system also projects onto the ventral tegmental area dopamine nucleus, locus ceruleus noradrenergic nucleus, the serotonergic raphe nuclei, and cholinergic pedunculopontine nucleus and laterodorsal tegmental nucleus. The histaminergic,
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https://en.wikipedia.org/wiki/Equatorium
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An equatorium (plural, equatoria) is an astronomical calculating instrument. It can be used for finding the positions of the Moon, Sun, and planets without arithmetic operations, using a geometrical model to represent the position of a given celestial body.
History
In his comment on Ptolemy's Handy Tables, 4th century mathematician Theon of Alexandria introduced some diagrams to geometrically compute the position of the planets based on Ptolemy's epicyclical theory. The first description of the construction of a solar equatorium (as opposed to planetary) is contained in Proclus's fifth-century work Hypotyposis, where he gives instructions on how to construct one in wood or bronze.
The earliest known descriptions of planetary equatoria are in the Latin translation of an early eleventh century text by Ibn al‐Samḥ and a 1080/1081 treatise by al-Zarqālī, contained in the Libros del saber de astronomia (Books of the knowledge of astronomy), a Castilian compilation of astronomical works collected under the patronage of Alfonso X of Castile in the thirteenth century.
The Theorica Planetarum (c. 1261–1264) by Campanus of Novara is the earliest extant description of the construction of an equatorium in Latin Europe. Campanus' instrument resembled an astrolabe, with several interchangeable plates within a mater. The best manuscripts of Campanus' treatise contain paper and parchment equatoria with moveable parts.
Variations
The history of the equatorium does not just end after the 11th century, but it inspired a more diverse invention called “The Albion”. The Albion is an astronomical instrument invented by Richard of Wallingford at the beginning of the 14th century. It has various functional uses such as that of the equatorium for planetary and conjunction computations. It can calculate when eclipses will occur. The Albion is made up of 18 different scales which makes it extremely complex in comparison to the equatorium. The history of this instrument is still disputed
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https://en.wikipedia.org/wiki/Identity%20theorem%20for%20Riemann%20surfaces
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In mathematics, the identity theorem for Riemann surfaces is a theorem that states that a holomorphic function is completely determined by its values on any subset of its domain that has a limit point.
Statement of the theorem
Let and be Riemann surfaces, let be connected, and let be holomorphic. Suppose that for some subset that has a limit point, where denotes the restriction of to . Then (on the whole of ).
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https://en.wikipedia.org/wiki/Sattler%27s%20layer
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Sattler's layer, named after Hubert Sattler, an Austrian ophthalmologist, is one of five (or six) layers of medium-diameter blood vessels of the choroid, and a layer of the eye. It is situated between the Bruch's membrane, choriocapillaris below, and the Haller's layer and suprachoroidea above, respectively. The origin seems to be related to a continuous differentiation throughout the growth of the tissue and even further differentiation during adulthood.
Measurement methods and clinical impact
After excision the choroid collapses partially, histologic preparations also alter the local pressure and fluid content of different sections in the tissue, thus requiring preparations with rubber solution or others that can conserve the vascular status of living tissue. Novel diagnostic methods, especially optical coherence tomography have widened the understanding of the real-time, in vivo status of the different layers.
Several papers have shown the relationship between the thickness of the choroidal, Sattler's and Haller's layer between healthy individuals and in people with age-related macular degeneration (AMD). The studies showed significant reduction of layer thickness in relation to the progression of AMD, which may be important in the understanding of choriopathy in the pathophysiology of AMD. However, also strong variations even throughout the diurnal cycle, as well as the influence of optical stimuli during eye-growth, indicate that the complex function of this tissue is not entirely understood and might be one of the reasons for the frequently found separation in vascular size between Haller's and Sattler's layer.
Notes
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https://en.wikipedia.org/wiki/Suprachoroid%20lamina
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The suprachoroid or suprachoroid lamina is a thin membrane forming part of the choroid of the eye. It lines the external surface of the choroid. It is composed of delicate non-vascular lamellae. The long and short ciliary nerves and the long posterior ciliary arteries pass anterior-ward within the suprachoroid lamina.
Anatomy
Microanatomy
The lamellae of the suprachoroid lamina are composed of a network of fine collagen and elastic fibers, and of fibroblasts and melanocytes.
The spaces between the lamellae are lined by endothelium, and open freely into the perichoroidal lymph space, which, in its turn, communicates with the periscleral space by the perforations in the sclera through which the vessels and nerves are transmitted.
Development
During embryological development, it is derived from the neural crest.
See also
suprachoroidal drug delivery
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https://en.wikipedia.org/wiki/Branching%20theorem
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In mathematics, the branching theorem is a theorem about Riemann surfaces. Intuitively, it states that every non-constant holomorphic function is locally a polynomial.
Statement of the theorem
Let and be Riemann surfaces, and let be a non-constant holomorphic map. Fix a point and set . Then there exist and charts on and on such that
; and
is
This theorem gives rise to several definitions:
We call the multiplicity of at . Some authors denote this .
If , the point is called a branch point of .
If has no branch points, it is called unbranched. See also unramified morphism.
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https://en.wikipedia.org/wiki/Clark%E2%80%93Ocone%20theorem
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In mathematics, the Clark–Ocone theorem (also known as the Clark–Ocone–Haussmann theorem or formula) is a theorem of stochastic analysis. It expresses the value of some function F defined on the classical Wiener space of continuous paths starting at the origin as the sum of its mean value and an Itô integral with respect to that path. It is named after the contributions of mathematicians J.M.C. Clark (1970), Daniel Ocone (1984) and U.G. Haussmann (1978).
Statement of the theorem
Let C0([0, T]; R) (or simply C0 for short) be classical Wiener space with Wiener measure γ. Let F : C0 → R be a BC1 function, i.e. F is bounded and Fréchet differentiable with bounded derivative DF : C0 → Lin(C0; R). Then
In the above
F(σ) is the value of the function F on some specific path of interest, σ;
the first integral,
is the expected value of F over the whole of Wiener space C0;
the second integral,
is an Itô integral;
Σ∗ is the natural filtration of Brownian motion B : [0, T] × Ω → R: Σt is the smallest σ-algebra containing all Bs−1(A) for times 0 ≤ s ≤ t and Borel sets A ⊆ R;
E[·|Σt] denotes conditional expectation with respect to the sigma algebra Σt;
∂/∂t denotes differentiation with respect to time t; ∇H denotes the H-gradient; hence, ∂/∂t∇H is the Malliavin derivative.
More generally, the conclusion holds for any F in L2(C0; R) that is differentiable in the sense of Malliavin.
Integration by parts on Wiener space
The Clark–Ocone theorem gives rise to an integration by parts formula on classical Wiener space, and to write Itô integrals as divergences:
Let B be a standard Brownian motion, and let L02,1 be the Cameron–Martin space for C0 (see abstract Wiener space. Let V : C0 → L02,1 be a vector field such that
is in L2(B) (i.e. is Itô integrable, and hence is an adapted process). Let F : C0 → R be BC1 as above. Then
i.e.
or, writing the integrals over C0 as expectations:
where the "divergence" div(V) : C0 → R is defined by
The interpretation of stochastic
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https://en.wikipedia.org/wiki/H-derivative
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In mathematics, the H-derivative is a notion of derivative in the study of abstract Wiener spaces and the Malliavin calculus.
Definition
Let be an abstract Wiener space, and suppose that is differentiable. Then the Fréchet derivative is a map
;
i.e., for , is an element of , the dual space to .
Therefore, define the -derivative at by
,
a continuous linear map on .
Define the -gradient by
.
That is, if denotes the adjoint of , we have .
See also
Malliavin derivative
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https://en.wikipedia.org/wiki/Gene%20delivery
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Gene delivery is the process of introducing foreign genetic material, such as DNA or RNA, into host cells. Gene delivery must reach the genome of the host cell to induce gene expression. Successful gene delivery requires the foreign gene delivery to remain stable within the host cell and can either integrate into the genome or replicate independently of it. This requires foreign DNA to be synthesized as part of a vector, which is designed to enter the desired host cell and deliver the transgene to that cell's genome. Vectors utilized as the method for gene delivery can be divided into two categories, recombinant viruses and synthetic vectors (viral and non-viral).
In complex multicellular eukaryotes (more specifically Weissmanists), if the transgene is incorporated into the host's germline cells, the resulting host cell can pass the transgene to its progeny. If the transgene is incorporated into somatic cells, the transgene will stay with the somatic cell line, and thus its host organism.
Gene delivery is a necessary step in gene therapy for the introduction or silencing of a gene to promote a therapeutic outcome in patients and also has applications in the genetic modification of crops. There are many different methods of gene delivery for various types of cells and tissues.
History
Viral based vectors emerged in the 1980s as a tool for transgene expression. In 1983, Albert Siegel described the use of viral vectors in plant transgene expression although viral manipulation via cDNA cloning was not yet available. The first virus to be used as a vaccine vector was the vaccinia virus in 1984 as a way to protect chimpanzees against hepatitis B. Non-viral gene delivery was first reported on in 1943 by Avery et al. who showed cellular phenotype change via exogenous DNA exposure.
Methods
There are a variety of methods available to deliver genes to host cells. When genes are delivered to bacteria or plants the process is called transformation and when it is used to
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https://en.wikipedia.org/wiki/Outline%20of%20trigonometry
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The following outline is provided as an overview of and topical guide to trigonometry:
Trigonometry – branch of mathematics that studies the relationships between the sides and the angles in triangles. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves.
Basics
Geometry – mathematics concerned with questions of shape, size, the relative position of figures, and the properties of space. Geometry is used extensively in trigonometry.
Angle – the angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane.
Ratio – a ratio indicates how many times one number contains another
Content of trigonometry
Trigonometry
Trigonometric functions
Trigonometric identities
Euler's formula
Scholars
Archimedes
Aristarchus
Aryabhata
Bhaskara I
Claudius Ptolemy
Euclid
Hipparchus
Madhava of Sangamagrama
Ptolemy
Pythagoras
Regiomontanus
History
Aristarchus's inequality
Bhaskara I's sine approximation formula
Greek astronomy
Indian astronomy
Jyā, koti-jyā and utkrama-jyā
Madhava's sine table
Ptolemy's table of chords
Rule of marteloio
Āryabhaṭa's sine table
Fields
Uses of trigonometry
Acoustics
Architecture
Astronomy
Biology
Cartography
Chemistry
Civil engineering
Computer graphics
Cryptography
Crystallography
Economics
Electrical engineering
Electronics
Game development
Geodesy
Mechanical engineering
Medical imaging
Meteorology
Music theory
Number theory
Oceanography
Optics
Pharmacy
Phonetics
Physical science
Probability theory
Seismology
Statistics
Surveying
Physics
Abbe sine condition
Greninger chart
Phasor
Snell's law
Astronomy
Equant
Parallax
Dialing scales
Chemistry
Greninger chart
Geography, geodesy, and land surveying
Hansen's problem
Sn
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https://en.wikipedia.org/wiki/4x4%20Off-Road%20Racing
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4x4 Off-Road Racing is a video game of the racing genre released in 1988 by Epyx and developed by Ogdan Micro Design Inc. The four maps consist of Mud, Ice, Desert and Mountains.
Reception
Compute! called the game "an enjoyable drive".
The Spanish magazine Microhobby valued the game with the following scores: Originality: 50% Graphics: 50% Motion: 60% Sound: 50% Difficulty: 70% Addiction: 40%
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https://en.wikipedia.org/wiki/Partial%20specific%20volume
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The partial specific volume express the variation of the extensive volume of a mixture in respect to composition of the masses. It is the partial derivative of volume with respect to the mass of the component of interest.
where is the partial specific volume of a component defined as:
The PSV is usually measured in milliLiters (mL) per gram (g), proteins > 30 kDa can be assumed to have a partial specific volume of 0.708 mL/g. Experimental determination is possible by measuring the natural frequency of a U-shaped tube filled successively with air, buffer and protein solution.
Properties
The weighted sum of partial specific volumes of a mixture or solution is an inverse of density of the mixture namely the specific volume of the mixture.
See also
Partial molar property
Apparent molar property
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https://en.wikipedia.org/wiki/Employee%20scheduling%20software
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Employee scheduling software automates the process of creating and maintaining a schedule. Automating the scheduling of employees increases productivity and allows organizations with hourly workforces to re-allocate resources to non-scheduling activities. Such software will usually track vacation time, sick time, compensation time, and alert when there are conflicts. As scheduling data is accumulated over time, it may be extracted for payroll or to analyze past activity. Although employee scheduling software may or may not make optimization decisions, it does manage and coordinate the tasks. Today's employee scheduling software often includes mobile applications. Mobile scheduling further increased scheduling productivity and eliminated inefficient scheduling steps. It may also include functionality including applicant tracking and on-boarding, time and attendance, and automatic limits on overtime. Such functionality can help organizations with issues like employee retention, compliance with labor laws, and other workforce management challenges.
Purpose
A theoretical underpinning of an employee scheduling problem can be represented as the Nurse scheduling problem, which is NP-hard. The theoretical complexity of the problem is a significant factor in the development of various software solutions. This is because systems must take into account many different forms of schedules that could be worked, and allocate employees to the correct schedule. Ultimately, optimization of scheduling is to minimize costs, but also often requires a reciprocal approach from management instead of complete reliance on software.
Transitioning to employee scheduling software
Prior to employee scheduling software companies would use physical mediums for tracking employee hours and work schedule. This then gave rise to data storage forms that later by the 80s were compatible with computer programs and software. These forms however never actually scheduled the employees, it just kept track
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https://en.wikipedia.org/wiki/Fiber%20%28mathematics%29
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In mathematics, the term fiber (US English) or fibre (British English) can have two meanings, depending on the context:
In naive set theory, the fiber of the element in the set under a map is the inverse image of the singleton under
In algebraic geometry, the notion of a fiber of a morphism of schemes must be defined more carefully because, in general, not every point is closed.
Definitions
Fiber in naive set theory
Let be a function between sets.
The fiber of an element (or fiber over ) under the map is the set that is, the set of elements that get mapped to by the function. It is the preimage of the singleton (One usually takes in the image of to avoid being the empty set.)
The collection of all fibers for the function forms a partition of the domain The fiber containing an element is the set For example, the fibers of the projection map that sends to are the vertical lines, which form a partition of the plane.
If is a real-valued function of several real variables, the fibers of the function are the level sets of . If is also a continuous function and is in the image of the level set will typically be a curve in 2D, a surface in 3D, and, more generally, a hypersurface in the domain of
Fiber in algebraic geometry
In algebraic geometry, if is a morphism of schemes, the fiber of a point in is the fiber product of schemes
where is the residue field at
Fibers in topology
Every fiber of a local homeomorphism is a discrete subspace of its domain.
If is a continuous function and if (or more generally, if ) is a T1 space then every fiber is a closed subset of
A function between topological spaces is called if every fiber is a connected subspace of its domain. A function is monotone in this topological sense if and only if it is non-increasing or non-decreasing, which is the usual meaning of "monotone function" in real analysis.
A function between topological spaces is (sometimes) called a if every fiber is a c
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https://en.wikipedia.org/wiki/Project%20Muse
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Project MUSE, a non-profit collaboration between libraries and publishers, is an online database of peer-reviewed academic journals and electronic books. Project MUSE contains digital humanities and social science content from over 250 university presses and scholarly societies around the world. It is an aggregator of digital versions of academic journals, all of which are free of digital rights management (DRM). It operates as a third-party acquisition service like EBSCO, JSTOR, OverDrive, and ProQuest.
MUSE's online journal collections are available on a subscription basis to academic, public, special, and school libraries. Currently, more than 2,500 libraries worldwide subscribe. Electronic book collections became available for institutional purchase in January 2012. Thousands of scholarly books are available on the platform.
History
Project MUSE was founded in 1993 as a joint project between the Johns Hopkins University Press and the Milton S. Eisenhower Library at the Johns Hopkins University. With grants from the Andrew W. Mellon Foundation and the National Endowment for the Humanities, Project MUSE was launched online alongside the JHU Press Journals in 1995. Beginning in 2000, journals from other scholarly publishers were integrated into MUSE's online collections. Additional publishers have added journals each subsequent year. In January 2012, a new interface was launched which incorporated its current journal collection with electronic books published by members of the University Press Content Consortium (UPCC).
The platform is powered by the WAIS searching utility called SWISH (Simple Web Indexing System for Humans), which allows Boolean searching in single issues, volumes, or across all 40+ titles. In cases where footnotes exist in articles, the footnote number is presented as a hyperlink to the article's bibliography or notes section.
Journals
Project MUSE offers tiered-pricing structures to meet budgetary and research needs of subscribing institu
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https://en.wikipedia.org/wiki/Infinite-dimensional%20Lebesgue%20measure
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In functional analysis and measure theory, there is a folklore claim that there is no analogue of the Lebesgue measure on an infinite-dimensional Banach space. The claim states that there is no translation invariant measure on a separable Banach spacebecause if any ball has a nonzero non-infinite volume, a slightly smaller ball has zero volume, and countable many such smaller balls cover the space. The folklore statement, however, is entirely false. The countable product of Lebesgue measures is translation invariant and gives the notion of volume as the infinite product of lengths. Only the domain on which this product measure is defined must necessarily be non-separable, but the measure itself is not sigma finite.
There are other kinds of measures with support entirely on separable Banach spaces such as the abstract Wiener space construction, which gives the analog of products of Gaussian measures. Alternatively, one may consider a Lebesgue measure on finite-dimensional subspaces of the larger space and consider the so-called prevalent and shy sets.
The Hilbert cube carries the product Lebesgue measure, and the compact topological group given by the Tychonoff product of infinitely many copies of the circle group is infinite-dimensional and carries a Haar measure that is translation-invariant. These two spaces can be mapped onto each other in a measure-preserving way by unwrapping the circles into intervals. The infinite product of the additive real numbers has the analogous product Haar measure, which is precisely the infinite-dimensional analog of the Lebesgue measure.
Motivation
It can be shown that the Lebesgue measure on Euclidean space is locally finite, strictly positive and translation-invariant, explicitly:
every point in has an open neighbourhood with finite measure
every non-empty open subset of has positive measure and
if is any Lebesgue-measurable subset of denotes the translation map, and denotes the push forward, then
Geometrica
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https://en.wikipedia.org/wiki/Wendelin%20Werner
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Wendelin Werner (born 23 September 1968) is a German-born French mathematician working on random processes such as self-avoiding random walks, Brownian motion, Schramm–Loewner evolution, and related theories in probability theory and mathematical physics. In 2006, at the 25th International Congress of Mathematicians in Madrid, Spain he received the Fields Medal "for his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory". He is currently Rouse Ball professor of Mathematics at the University of Cambridge.
Biography
Werner was born on 23 September 1968 in Cologne, West Germany. His parents moved to France when he was nine months old and he became a French citizen in 1977. After a classe préparatoire at Lycée Hoche in Versailles, he studied at École Normale Supérieure from 1987 to 1991. His 1993 doctorate was written at the Université Pierre-et-Marie-Curie and supervised by Jean-François Le Gall. Werner was a researcher at the CNRS (National Center of Scientific Research, Centre national de la recherche scientifique) from 1991 to 1997, during which he also held a two-year Leibniz Fellowship, at the University of Cambridge. He was Professor at
the University of Paris-Sud from 1997 to 2013 and also taught at the École Normale Supérieure from 2005 to 2013. He was then Professor at the ETH Zürich from 2013 to 2023.
Awards and honors
Werner has received several awards besides the Fields Medal, including the Rollo Davidson Prize in 1998, the Prix Paul Doistau–Émile Blutet in 1999, the Fermat Prize in 2001, the Grand Prix Jacques Herbrand of the French Academy of Sciences in 2003, the Loève Prize in 2005, the 2006 SIAM George Pólya Prize with his collaborators Gregory Lawler and Oded Schramm, and the Heinz Gumin Prize (de) in 2016.
He became a member of the French Academy of Sciences in 2008. He is also a member of other academies of sciences, including the Academy of Sciences L
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https://en.wikipedia.org/wiki/Max%20Planck%20Institute%20for%20Solid%20State%20Research
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The Max Planck Institute for Solid State Research (German: Max-Planck-Institut für Festkörperforschung) was founded in 1969 and is one of the 82 Max Planck Institutes of the Max Planck Society. It is located on a campus in Stuttgart, together with the Max Planck Institute for Intelligent Systems.
Research focus
Research at the Max Planck Institute for Solid State Research is focused on the physics and chemistry of condensed matter, including especially complex materials and nanoscale science. In both of these fields, electronic and ionic transport phenomena are of particular interest.
Organization
The institute currently has eight departments.
Electronic Structure Theory
Led by Ali Alavi, the Department of Electronic Structure Theory is concerned with the development of ab initio methods for treating correlated electronic systems, using Quantum Monte Carlo, quantum chemical and many-body methodologies. Ab initio methods (including density functional theory) will be applied to problems of interest in heterogeneous catalysis, surface chemistry, electrochemistry, and photochemistry.
Solid State Spectroscopy
The Department of Solid State Spectroscopy is headed by Bernhard Keimer. Collective quantum phenomena in highly correlated electronic materials are studied by spectroscopic and scattering techniques. Topics of particular current interest include the interplay between charge, orbital, and spin degrees of freedom in transition metal oxides, the mechanism of high-temperature superconductivity, and the control of electronic phase behavior in metal-oxide superlattices. The department also develops new spectroscopic methods such as high-resolution neutron spectroscopy and spectral ellipsometry.
Nanoscale Science
Research efforts in the Department of Nanoscale Science, directed by Klaus Kern, are centered on nanometer-scale science and technology with a focus on the bottom-up paradigm. The aim of the interdisciplinary research at the interface between physics, chemi
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https://en.wikipedia.org/wiki/Fish%20tape
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A fish tape (also called a draw wire, draw tape, or an electricians snake) is a tool used by electricians to route new wiring through walls and electrical conduit.
Made of a narrow band of spring steel, by careful manipulation, the tape can be guided through confined spaces such as wall cavities or conduits in many countries. The goal is to push toward an area where guide string has been dropped inside the confined space and to pull it through, so the guide string can then be used to pull through various types of wiring, such as phone wire, network cables or speaker wire. Fish tape is designed to pull through guide string only. Using it to directly pull the target wire can damage or warp the fish tape.
Design
Fish tapes are usually stored coiled on a plastic reel. Because of this, they have a natural curvature and it is this curvature that allows them to be guided. By manipulating the reel, the end of the tape can be directed slightly. The tape is rigid enough that it can then be pushed in the direction in which it is pointing. In this way it can be easily guided through an empty wall cavity. Thermal insulation, firestops, pipes, HVAC ducts, electrical conduits, and other obstructions make use of a fish tape more challenging.
The "tape" can be made from many different materials including steel, fiberglass, and nylon. The tape usually has a special end ranging from a hook or loop to a specialized fastener device to allow the user to attach the tape to the guide string (or a very light cable) before pulling.
Invention and patent
Keith Leroy Wilson of Colorado Springs, Colorado, owner of the Electrical Construction Co, founded in 1947; invented the Fish Tape Snagger. Wilson filed the original patent on 29 Mar 1960 and Patent # 3,035,817 was awarded on 22 May 1962 by the US Patent Office.
Double use
Occasionally, two fish tapes are used from opposite ends of the wall. Because they each have a hooked end, one fish tape is capable of catching the other, and the
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https://en.wikipedia.org/wiki/Chi-square%20automatic%20interaction%20detection
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Chi-square automatic interaction detection (CHAID) is a decision tree technique based on adjusted significance testing (Bonferroni correction, Holm-Bonferroni testing). The technique was developed in South Africa and was published in 1980 by Gordon V. Kass, who had completed a PhD thesis on this topic. CHAID can be used for prediction (in a similar fashion to regression analysis, this version of CHAID being originally known as XAID) as well as classification, and for detection of interaction between variables. CHAID is based on a formal extension of AID (Automatic Interaction Detection) and THAID (THeta Automatic Interaction Detection) procedures of the 1960s and 1970s, which in turn were extensions of earlier research, including that performed by Belson in the UK in the 1950s. A history of earlier supervised tree methods together with a detailed description of the original CHAID algorithm and the exhaustive CHAID extension by Biggs, De Ville, and Suen, can be found in Ritschard.
In practice, CHAID is often used in the context of direct marketing to select groups of consumers to predict how their responses to some variables affect other variables, although other early applications were in the fields of medical and psychiatric research.
Like other decision trees, CHAID's advantages are that its output is highly visual and easy to interpret. Because it uses multiway splits by default, it needs rather large sample sizes to work effectively, since with small sample sizes the respondent groups can quickly become too small for reliable analysis.
One important advantage of CHAID over alternatives such as multiple regression is that it is non-parametric.
See also
Chi-squared distribution
Bonferroni correction
Latent class model
Structural equation modeling
Market segment
Decision tree learning
Multiple comparisons
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https://en.wikipedia.org/wiki/Spectral%20slope
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In astrophysics and planetary science, spectral slope, also called spectral gradient, is a measure of dependence of the reflectance on the wavelength.
In digital signal processing, it is a measure of how quickly the spectrum of an audio sound tails off towards the high frequencies, calculated using a linear regression.
Spectral slope in astrophysics and planetary science
The visible and infrared spectrum of the reflected sunlight is used to infer physical and chemical properties of the surface of a body. Some objects are brighter (reflect more) in longer wavelengths (red). Consequently, in visible light they will appear redder than objects showing no dependence of reflectance on the wavelength.
The diagram illustrates three slopes:
a red slope, the reflectance is increasing with the wavelengths
flat spectrum (in black)
And a blue slope, the reflectance actually diminishing with the wavelengths
The slope (spectral gradient) is defined as:
where is the reflectance measured with filters F0, F1 having the central wavelengths λ0 and λ1, respectively.
The slope is typically expressed in percentage increase of reflectance (i.e. reflexivity) per unit of wavelength: %/100 nm (or % /1000 Å)
The slope is mostly used in near infrared part of the spectrum while colour indices are commonly used in the visible part of the spectrum.
The trans-Neptunian object Sedna is a typical example of a body showing a steep red slope (20%/100 nm) while Orcus' spectrum appears flat in near infra-red.
Spectral slope in audio
The spectral "slope" of many natural audio signals (their tendency to have less energy at high frequencies) has been known for many years, and the fact that this slope is related to the nature of the sound source. One way to quantify this is by applying linear regression to the Fourier magnitude spectrum of the signal, which produces a single number indicating the slope of the line-of-best-fit through the spectral data.
Alternative ways to characterise a sound sign
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https://en.wikipedia.org/wiki/Palivizumab
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Palivizumab, sold under the brand name Synagis, is a monoclonal antibody produced by recombinant DNA technology used to prevent severe disease caused by respiratory syncytial virus (RSV) infections. It is recommended for infants at high-risk for RSV due to conditions such as prematurity or other medical problems including heart or lung diseases.
The most common side effects include fever and rash.
Palivizumab is a humanized monoclonal antibody (IgG) directed against an epitope in the A antigenic site of the F protein of RSV. In two phase III clinical trials in the pediatric population, palivizumab reduced the risk of hospitalization due to RSV infection by 55% and 45%. Palivizumab is dosed once a month via intramuscular (IM) injection, to be administered throughout the duration of the RSV season, which in based on past trends has started in Mid-September to Mid-November.
Palivizumab targets the fusion protein of RSV, inhibiting its entry into the cell and thereby preventing infection. Palivizumab was approved for medical use in 1998.
Medical use
Palivizumab is indicated for the prevention of serious lower respiratory tract disease requiring hospitalization caused by the respiratory syncytial virus (RSV) in children at high risk for RSV disease:
children born at 35 weeks of gestation or less and less than six months of age at the onset of the RSV season;
children less than two years of age and requiring treatment for bronchopulmonary dysplasia within the last six months;
children less than two years of age and with hemodynamically significant congenital heart disease.
The American Academy of Pediatrics has published guidelines for the use of palivizumab. The most recent updates to these recommendations are based on new information regarding RSV seasonality, palivizumab pharmacokinetics, the incidence of bronchiolitis hospitalizations, the effect of gestational age and other risk factors on RSV hospitalization rates, the mortality of children hospitalized w
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https://en.wikipedia.org/wiki/Mitochondrial%20trifunctional%20protein
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Mitochondrial trifunctional protein (MTP) is a protein attached to the inner mitochondrial membrane which catalyzes three out of the four steps in beta oxidation. MTP is a hetero-octamer composed of four alpha and four beta subunits:
HADHA
HADHB
The three functions are 2-enoyl coenzyme A (CoA) hydratase, long-chain 3-hydroxy acyl-coenzyme A dehydrogenase and long-chain 3-ketoacyl CoA thiolase.
Association with the electron transport chain
Fatty acid beta-oxidation (FAO) and oxidative phosphorylation (OXPHOS) are two major metabolism pathways in the mitochondria. Reducing equivalents from FAO enter OXPHOS at the level of Complexes I and III. In 2010, Wang et al. discovered a functional and physical association between MTP and ETC respirasomes. Not only does MTP appear to be bound to Complex I, but it also appears to channel substrates between the two enzymes. This is especially interesting, because up until then it was unknown exactly how MTP was associated with the inner mitochondrial membrane, and this discovery may provide the explanation.
Hormonal influences
Recent research has revealed that MTP can be affected by various hormones, via hormone receptors located in the mitochondria. Chochron et al. (2012) demonstrated that thyroid hormone stimulates mitochondrial metabolism in a pathway mediated by MTP. Zhou et al. (2012) used 2D gel electrophoresis and mass spectrometry to identify MTP as one of the proteins that interacts with ER alpha, a receptor triggered by estrogen.
Cardiolipin remodeling
In 2009, Taylor et al. identified a human mitochondrial protein, monolysocardiolipin acyltransferase (MLCL AT-1), that is identical in amino acid sequence to the 59-kDa C-terminal end of MTP, linking MTP to the remodeling of cardiolipin from monolysocardiolipin. Although MLCL AT-1 and MTP are different proteins, in 2012 the same lab discovered that MTP did indeed have cardiolipin remodeling capabilities. This suggests a possible link between mitochondrial membrane c
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https://en.wikipedia.org/wiki/Creditcall
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Creditcall (now NMI) is a payment service provider and payment gateway with offices in the United States and UK, providing credit card authorisation and settlement services to banks and processors in the United Kingdom, United States and Canada.
History
Creditcall Limited, originally Creditcall Communications Limited, was founded in 1996. Later, a North American subsidiary, Creditcall Corporation, was incorporated in 2005. The name Creditcall is derived from the name of Creditcall's first product, a telecommunications service that enabled callers to bill telephone calls to their credit or debit card. Creditcall won 3i's Business Catapult Award in 1998 along with an initial investment in the company.
In 2012 the management team completed a management buyout of the company backed by FF&P Private Equity and Bestport Ventures.
On 21 April 2014 Creditcall was awarded the Queen's Award for Enterprise.
Acquisition
In March 2018, Creditcall was acquired by US-based payments' technology company NMI. NMI is headquartered in Schaumburg, Illinois, with offices in Utah, New York, and Bristol, UK. NMI is backed by US private equity firms Insight Partners, Great Hill Partners and Francisco Partners.
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https://en.wikipedia.org/wiki/Buffer%20P2
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Buffer P2 is a lysis buffer solution produced by Qiagen. It contains 1% sodium dodecyl sulfate (SDS) (w/v) to puncture holes in cellular membranes, and 200mM NaOH. It is used in conjunction with other resuspension buffers and lysis buffers to release DNA from cells, often as part of the alkaline lysis method of purifying plasmid DNA from bacterial cell culture.
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https://en.wikipedia.org/wiki/Lindel%C3%B6f%27s%20lemma
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In mathematics, Lindelöf's lemma is a simple but useful lemma in topology on the real line, named for the Finnish mathematician Ernst Leonard Lindelöf.
Statement of the lemma
Let the real line have its standard topology. Then every open subset of the real line is a countable union of open intervals.
Generalized Statement
Lindelöf's lemma is also known as the statement that every open cover in a second-countable space has a countable subcover (Kelley 1955:49). This means that every second-countable space is also a Lindelöf space.
Proof of the generalized statement
Let be a countable basis of . Consider an open cover, . To get prepared for the following deduction, we define two sets for convenience, , .
A straight-forward but essential observation is that, which is from the definition of base. Therefore, we can get that,
where , and is therefore at most countable. Next, by construction, for each there is some such that . We can therefore write
completing the proof.
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https://en.wikipedia.org/wiki/Hilbert%20scheme
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In algebraic geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some projective space (or a more general projective scheme), refining the Chow variety. The Hilbert scheme is a disjoint union of projective subschemes corresponding to Hilbert polynomials. The basic theory of Hilbert schemes was developed by . Hironaka's example shows that non-projective varieties need not have Hilbert schemes.
Hilbert scheme of projective space
The Hilbert scheme of classifies closed subschemes of projective space in the following sense: For any locally Noetherian scheme , the set of -valued points
of the Hilbert scheme is naturally isomorphic to the set of closed subschemes of that are flat over . The closed subschemes of that are flat over can informally be thought of as the families of subschemes of projective space parameterized by . The Hilbert scheme breaks up as a disjoint union of pieces corresponding to the Hilbert polynomial of the subschemes of projective space with Hilbert polynomial . Each of these pieces is projective over .
Construction as a determinantal variety
Grothendieck constructed the Hilbert scheme of -dimensional projective space as a subscheme of a Grassmannian defined by the vanishing of various determinants. Its fundamental property is that for a scheme , it represents the functor whose -valued points are the closed subschemes of that are flat over .
If is a subscheme of -dimensional projective space, then corresponds to a graded ideal of the polynomial ring in variables, with graded pieces . For sufficiently large all higher cohomology groups of with coefficients in vanish. Using the exact sequencewe have has dimension , where is the Hilbert polynomial of projective space. This can be shown by tensoring the exact sequence above by the locally flat sheaves , giving an exact sequence where the latter two terms have trivial cohomology, implying the triviality of the
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https://en.wikipedia.org/wiki/Hilbert%20series%20and%20Hilbert%20polynomial
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In commutative algebra, the Hilbert function, the Hilbert polynomial, and the Hilbert series of a graded commutative algebra finitely generated over a field are three strongly related notions which measure the growth of the dimension of the homogeneous components of the algebra.
These notions have been extended to filtered algebras, and graded or filtered modules over these algebras, as well as to coherent sheaves over projective schemes.
The typical situations where these notions are used are the following:
The quotient by a homogeneous ideal of a multivariate polynomial ring, graded by the total degree.
The quotient by an ideal of a multivariate polynomial ring, filtered by the total degree.
The filtration of a local ring by the powers of its maximal ideal. In this case the Hilbert polynomial is called the Hilbert–Samuel polynomial.
The Hilbert series of an algebra or a module is a special case of the Hilbert–Poincaré series of a graded vector space.
The Hilbert polynomial and Hilbert series are important in computational algebraic geometry, as they are the easiest known way for computing the dimension and the degree of an algebraic variety defined by explicit polynomial equations. In addition, they provide useful invariants for families of algebraic varieties because a flat family has the same Hilbert polynomial over any closed point . This is used in the construction of the Hilbert scheme and Quot scheme.
Definitions and main properties
Consider a finitely generated graded commutative algebra over a field , which is finitely generated by elements of positive degree. This means that
and that .
The Hilbert function
maps the integer to the dimension of the -vector space . The Hilbert series, which is called Hilbert–Poincaré series in the more general setting of graded vector spaces, is the formal series
If is generated by homogeneous elements of positive degrees , then the sum of the Hilbert series is a rational fraction
where is a polynomial
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https://en.wikipedia.org/wiki/Equivalence%20%28measure%20theory%29
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In mathematics, and specifically in measure theory, equivalence is a notion of two measures being qualitatively similar. Specifically, the two measures agree on which events have measure zero.
Definition
Let and be two measures on the measurable space and let
and
be the sets of -null sets and -null sets, respectively. Then the measure is said to be absolutely continuous in reference to if and only if This is denoted as
The two measures are called equivalent if and only if and which is denoted as That is, two measures are equivalent if they satisfy
Examples
On the real line
Define the two measures on the real line as
for all Borel sets Then and are equivalent, since all sets outside of have and measure zero, and a set inside is a -null set or a -null set exactly when it is a null set with respect to Lebesgue measure.
Abstract measure space
Look at some measurable space and let be the counting measure, so
where is the cardinality of the set a. So the counting measure has only one null set, which is the empty set. That is, So by the second definition, any other measure is equivalent to the counting measure if and only if it also has just the empty set as the only -null set.
Supporting measures
A measure is called a of a measure if is -finite and is equivalent to
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