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In this paper, we continue with the results in \cite{Pg} and compute the group of quasi-isometries for a subclass of split solvable unimodular Lie groups. Consequently, we show that any finitely generated group quasi-isometric to a member of the subclass has to be polycyclic, and is virtually a lattice in an abelian-by-abelian solvable Lie group. We also give an example of a unimodular solvable Lie group that is not quasi-isometric to any finitely generated group, as well deduce some quasi-isometric rigidity results.
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arxiv:1002.4451
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This paper has been withdrawn by the author, since some results of the paper have been already obtained in [J.~Lewandowski, Class. Quantum Grav. 9 (1992), no. 10, L147--L151.]
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arxiv:1002.4540
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We investigate the properties of finite gold nanocones as optical antennas for enhancing molecular fluorescence. We compute the modification of the excitation rate, spontaneous emission rate, and quantum efficiency as a function of the nanocone base and length, showing that the maximum field and fluorescence enhancements do not occur for the same nanocone parameters. We compare the results with those for nanorods and nanospheroids and find that nanocones perform better.
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arxiv:1002.4643
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Circadian clocks are oscillatory genetic networks that help organisms adapt to the 24-hour day/night cycle. The clock of the green alga Ostreococcus tauri is the simplest plant clock discovered so far. Its many advantages as an experimental system facilitate the testing of computational predictions. We present a model of the Ostreococcus clock in the stochastic process algebra Bio-PEPA and exploit its mapping to different analysis techniques, such as ordinary differential equations, stochastic simulation algorithms and model-checking. The small number of molecules reported for this system tests the limits of the continuous approximation underlying differential equations. We investigate the difference between continuous-deterministic and discrete-stochastic approaches. Stochastic simulation and model-checking allow us to formulate new hypotheses on the system behaviour, such as the presence of self-sustained oscillations in single cells under constant light conditions. We investigate how to model the timing of dawn and dusk in the context of model-checking, which we use to compute how the probability distributions of key biochemical species change over time. These show that the relative variation in expression level is smallest at the time of peak expression, making peak time an optimal experimental phase marker. Building on these analyses, we use approaches from evolutionary systems biology to investigate how changes in the rate of mRNA degradation impacts the phase of a key protein likely to affect fitness. We explore how robust this circadian clock is towards such potential mutational changes in its underlying biochemistry. Our work shows that multiple approaches lead to a more complete understanding of the clock.
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arxiv:1002.4661
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In this Letter, the Evans and Koratkar Atlas of Hubble Space Telescope Faint Object Spectrograph Spectra of Active Galactic Nuclei and Quasars is used to study the redward asymmetry in CIV broad emission lines (BELs). It is concluded that there is a highly significant correlation between the spectral index from 10 GHz to 1350 $\AA$ and the amount of excess luminosity in the red wing of the CIV BEL ($>99.9999%$ significance level for the full sample and the radio loud subsample independently, but no correlation is found for the radio quiet subsample). This is interpreted as a correlation between radio core dominance and the strength of the CIV redward asymmetry. The data implies that within the quasar environment there is BEL gas with moderately blueshifted emission associated with the purely radio quiet quasar phenomenon (the accretion disk) and the radio jet emission mechanism is associated with a redward BEL component that is most prominent for lines of sight along the jet axis. Thus, radio quiet quasars have CIV BELs that tend to show blueshifted excess and radio loud quasars show either a red or blue excess with the tendency for a dominant red excess increasing as the line of sight approaches the jet axis.
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arxiv:1002.4681
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CDMA is a multiple access method in which the user's uses spread spectrum techniques and occupy the entire spectrum whenever they transmit. In wireless communication signal-to-noise ratio (SNR) is the very important parameter that influences the system performance. Any mode of mobile transmission is not free from channel impairment such as noise, interference and fading. This channel impairment caused signal distortion and degradation in SNR.Also there are differences between uplink (forward channel) and downlink (reverse channel).Along with these differences, both the links use different codes for chanellizing the individual users. This paper simulates the expressions for the pdfs of the SNR for both uplink and downlink transmission assuming that the system is operating at an average signal-to-noise ratio is 6dB per information bit.
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arxiv:1002.4727
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We develop a new Gibbs sampler for a linear mixed model with a Dirichlet process random effect term, which is easily extended to a generalized linear mixed model with a probit link function. Our Gibbs sampler exploits the properties of the multinomial and Dirichlet distributions, and is shown to be an improvement, in terms of operator norm and efficiency, over other commonly used MCMC algorithms. We also investigate methods for the estimation of the precision parameter of the Dirichlet process, finding that maximum likelihood may not be desirable, but a posterior mode is a reasonable approach. Examples are given to show how these models perform on real data. Our results complement both the theoretical basis of the Dirichlet process nonparametric prior and the computational work that has been done to date.
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arxiv:1002.4756
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We provide an unifying polynomial expression giving moments in terms of cumulants, and viceversa, holding in the classical, boolean and free setting. This is done by using a symbolic treatment of Abel polynomials. As a by-product, we show that in the free cumulant theory the volume polynomial of Pitman and Stanley plays the role of the complete Bell exponential polynomial in the classical theory. Moreover via generalized Abel polynomials we construct a new class of cumulants, including the classical, boolean and free ones, and the convolutions linearized by them. Finally, via an umbral Fourier transform, we state a explicit connection between boolean and free convolution.
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arxiv:1002.4803
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The effect of the site potential in an imperfect layer is studied in a d-wave layer superconductor on the basis of the electron correlation. The site potential binds electrons to the imperfect layer, and then, the superconductivity of the imperfect layer is independent of that of the bulk. We found that the superconducting transition temperature of the imperfect layer becomes higher than that of the bulk owing to the effect of the site potential. In this situation, the Fermi surface of the imperfect layer has a strong nesting feature leading to increases in both the antiferromagnetic spin fluctuation and the density of states near the Fermi level, which are in favor of d-wave pairing.
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arxiv:1002.4822
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The main implications of noncommutativity over astrophysical objects are examined. Noncommutativity is introduced through a deformed dispersion relation $E^{2}=p^{2}c^{2}(1+\lambda E)^{2} + m^{2}c^{4}$ and the relevant thermodynamical quantities are calculated using the grand canonical ensemble formalism. These results are applied to simple physical models describing main-sequence stars, white-dwarfs and neutron stars. The stability of main-sequence stars and white dwarfs is discussed.
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arxiv:1002.4861
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We investigate the holographic superconductors immersed in an external magnetic field by using the analytical approach. We obtain the spatially dependent condensate solutions in the presence of the magnetism and find analytically that the upper critical magnetic field satisfies the relation given in the Ginzburg-Landau theory. We observe analytically the reminiscent of the Meissner effect where the magnetic field expels the condensate. Extending to the D-dimensional Gauss-Bonnet AdS black holes, we examine the influence given by the Gauss-Bonnet coupling on the condensation. Different from the positive coupling, we find that the negative Gauss-Bonnet coupling enhances the condensation when the external magnetism is not strong enough.
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arxiv:1002.4901
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We present an analysis of interstellar H2 toward HD 37903, which is a hot, B 1.5 V star located in the NGC 2023 reflection nebula. Meyer et al. (2001) have used a rich spectrum of vibrationally excited H2 observed by the HST to calculate a model of the interstellar cloud toward HD 37903. We extend Mayer's analysis by including the v"=0 vibrational level observed by the FUSE satellite. The T01 temperature should not be interpreted as a rotational temperature, but rather as a temperature of thermal equilibrium between the ortho and para H2. The ortho to para H2 ratio is lower for collisionally populated levels than for the levels populated by fluorescence. The PDR model of the cloud located in front of HD 37903 points to a gas temperature Tkin=110-377 K, hydrogen density nH=1874-544 cm^-3 and the star-cloud distance of 0.45 pc.
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arxiv:1002.4940
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Here we present the development of a simplified version of double astronomical quadrant, designed for educational aims and realized on the occasion of the observational round of the XIII International Astronomy Olympiad, held in Trieste (Italy) October 13-21, 2008. (Italia: In questo contributo illustriamo il progetto di una versione semplificata di doppio quadrante astronomico, progettato per fini didattici e realizzato in occasione dello svolgimento della gara osservativa delle XIII Olimpiadi Internazionali di Astronomia (XIII International Astronomy Olympiad, XIII IAO), Trieste (I), 13-21 ottobre 2008))
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arxiv:1002.5009
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Aims: We aim at measuring mass-loss rates and the luminosities of a statistically large sample of Galactic bulge stars at several galactocentric radii. The sensitivity of previous infrared surveys of the bulge has been rather limited, thus fundamental questions for late stellar evolution, such as the stage at which substantial mass-loss begins on the red giant branch and its dependence on fundamental stellar properties, remain unanswered. We aim at providing evidence and answers to these questions. Methods: To this end, we observed seven 15 times 15 arcmin^2 fields in the nuclear bulge and its vicinity with unprecedented sensitivity using the IRAC and MIPS imaging instruments on-board the Spitzer Space Telescope. In each of the fields, tens of thousands of point sources were detected. Results: In the first paper based on this data set, we present the observations, data reduction, the final catalogue of sources, and a detailed comparison to previous mid-IR surveys of the Galactic bulge, as well as to theoretical isochrones. We find in general good agreement with other surveys and the isochrones, supporting the high quality of our catalogue.
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arxiv:1002.5015
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There is vast empirical evidence that given a set of assumptions on the real-world dynamics of an asset, the European options on this asset are not efficiently priced in options markets, giving rise to arbitrage opportunities. We study these opportunities in a generic stochastic volatility model and exhibit the strategies which maximize the arbitrage profit. In the case when the misspecified dynamics is a classical Black-Scholes one, we give a new interpretation of the classical butterfly and risk reversal contracts in terms of their (near) optimality for arbitrage strategies. Our results are illustrated by a numerical example including transaction costs.
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arxiv:1002.5041
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For any root system corresponding to a semisimple simply-laced Lie algebra a logarithmic CFT is constructed. Characters of irreducible representations were calculated in terms of theta functions.
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arxiv:1002.5047
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Previous surveys in a few metal-poor globular clusters (GCs) showed that the determination of abundances for Li and proton-capture elements offers a key tool to address the intracluster pollution scenario. In this Letter, we present Na, O, and Li abundances in a large sample of dwarf stars in the metal-rich GC 47 Tucanae. We found a clear Na-O anticorrelation, in good agreement with what obtained for giant members by Carretta et al. While lithium and oxygen abundances appear to be positively correlated with each other, there is a large scatter, well exceeding observational errors, and no anticorrelation with sodium. These findings suggest that Li depletion, due to mechanisms internal to the stars (which are cooler and more metal-rich than those on the Spite plateau), combines with the usual pollution scenario responsible for the Na-O anticorrelation.
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arxiv:1003.0013
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We construct link invariants using the $D_{2n}$ subfactor planar algebras, and use these to prove new identities relating certain specializations of colored Jones polynomials to specializations of other quantum knot polynomials. These identities can also be explained by coincidences between small modular categories involving the even parts of the $D_{2n}$ planar algebras. We discuss the origins of these coincidences, explaining the role of $SO$ level-rank duality, Kirby-Melvin symmetry, and properties of small Dynkin diagrams. One of these coincidences involves $G_2$ and does not appear to be related to level-rank duality.
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arxiv:1003.0022
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We present factorization theorems for two exclusive heavy-quarkonium production processes: production of two quarkonia in e^+e^- annihilation and production of a quarkonium and a light meson in B-meson decays. We describe the general proofs of factorization and supplement them with explicit one-loop analyses, which illustrate some of the features of the soft-gluon cancellations. We find that violations of factorization are generally suppressed relative to the factorized contributions by a factor v^2m_c/Q for each S-wave charmonium and a factor m_c/Q for each L-wave charmonium with L>0. Here, v is the velocity of the heavy quark or antiquark in the quarkonium rest frame, Q=sqrt{s} for e^+e^- annihilation, Q=m_B for B-meson decays, sqrt{s} is the e^+e^- center-of-momentum energy, m_c is the charm-quark mass, and m_B is the B-meson mass. There are modifications to the suppression factors if quantum-number restrictions apply for the specific process.
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arxiv:1003.0061
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The concept of "self-organized criticality" (SOC) has been introduced by Bak, Tang, and Wiesenfeld (1987) to describe the statistics of avalanches on the surface of a sandpile with a critical slope, which produces a scale-free powerlaw size distribution of avalanches. In the meantime, SOC behavior has been identified in many nonlinear dissipative systems that are driven to a critical state. On a most general level, SOC is the statistics of coherent nonlinear processes, in contrast to the Poisson statistics of incoherent random processes. The SOC concept has been applied to laboratory experiments (of rice or sand piles), to human activities (population growth, language, economy, traffic jams, wars), to biophysics, geophysics (earthquakes, landslides, forest fires), magnetospheric physics, solar physics (flares), stellar physics (flares, cataclysmic variables, accretion disks, black holes, pulsar glitches, gamma ray bursts), and to galactic physics and cosmology.
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arxiv:1003.0122
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In this paper, we discuss the Cram\'er-Lundberg model with investments, where the price of the invested risk asset follows a geometric Brownian motion with drift $a$ and volatility $\sigma> 0.$ By assuming there is a cap on the claim sizes, we prove that the probability of ruin has at least an algebraic decay rate if $2a/\sigma^2 > 1$. More importantly, without this assumption, we show that the probability of ruin is certain for all initial capital $u$, if $2a/\sigma^2 \le 1$.
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arxiv:1003.0135
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Deep Very Large Array imaging of the binary X-ray source SS 433, sometimes classified as a microquasar, has been used to study the intrinsic brightness distribution and evolution of its radio jets. The intrinsic brightness of the jets as a function of age at emission of the jet material tau is recovered by removal of the Doppler boosting and projection effects. We find that intrinsically the two jets are remarkably similar when compared for equal tau, and that they are best described by Doppler boosting of the form D^{2+alpha}, as expected for continuous jets. The intrinsic brightnesses of the jets as functions of age behave in complex ways. In the age range 60 < tau < 150 days, the jet decays are best represented by exponential functions of tau, but linear or power law functions are not statistically excluded. This is followed by a region out to tau ~ 250 days during which the intrinsic brightness is essentially constant. At later times the jet decay can be fit roughly as exponential or power law functions of tau.
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arxiv:1003.0145
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The possibility to explain basic physical properties of relaxors within the concept of the dipole-glass transition is discussed. We argue that this concept provides the only consistent picture accounting of all known anomalous features of relaxors. The origin of their history-dependent properties can be naturally traced to the main paradigm of glass-state theory - the existence of numerous metastable states. Based on this paradigm phenomenological description of known history-dependent phenomena in relaxors agrees qualitatively with experiments.
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arxiv:1003.0147
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In this note we prove that the Heisenberg group with a left-invariant pseudo-Riemannian metric admits a completely integrable totally geodesic distribution of codimension 1. This is on the contrary to the Riemannian case, as it was proved by T. Hangan.
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arxiv:1003.0189
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For the first time, a systematic analysis of the high energy behavior of total and diffractive proton-proton cross sections is performed within the Reggeon Field Theory framework, based on the resummation of all significant contributions of enhanced Pomeron diagrams to all orders with respect to the triple-Pomeron coupling. The importance of different classes of enhanced graphs is investigated and it is demonstrated that absorptive corrections due to "net"-like enhanced diagrams and due to Pomeron "loops" are both significant and none of those classes can be neglected at high energies. A comparison with other approaches based on partial resummations of enhanced diagrams is performed. In particular, important differences are found concerning the predicted high energy behavior of total and single high mass diffraction proton-proton cross sections, with our values of $\sigma_{pp}^{{\rm tot}}$ at $\sqrt{s}=14$ TeV being some $25\div40$% higher and with the energy rise of $\sigma_{{\rm HM}}^{{\rm SD}}$ saturating well below the LHC energy. The main causes for those differences are analyzed and explained.
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arxiv:1003.0196
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Recent experiments on imbalanced Fermi gases have raised interest in the physics of an impurity immersed in a Fermi sea, the so-called Fermi polaron. In this letter, a simple theory is devised to describe dilute Fermi-polaron ensembles corresponding to the normal phase of an imbalanced Fermi gas. An exact formula is obtained for the dominant interaction between polarons, expressed solely in terms of a single polaron parameter. The physics of this interaction is identified as a signature of the Pauli exclusion principle.
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arxiv:1003.0213
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A Borel resummation scheme of subtracting the perturbative contribution from the average plaquette is proposed using the bilocal expansion of Borel transform. It is shown that the remnant of the average plaquette, after subtraction of the perturbative contribution, scales as a dim-4 condensate. A critical review of the existing procedure of renormalon subtraction is presented.
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arxiv:1003.0231
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The relativistic six-quark equations are found in the framework of the dispersion relation technique. The approximate solutions of these equations using the method based on the extraction of leading singularities of the amplitudes are obtained. The relativistic six-quark amplitudes of hexaquarks including the quarks of three flavors ($u$, $d$, $s$) are calculated. The poles of these amplitudes determine the masses of six-quark systems.
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arxiv:1003.0257
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A new two-parametric family of mass distribution for spherical stellar systems is considered. It generalizes families by Kuzmin, Veltmann (1972) and by An, Evans (2006). Steady velocity dispersions are found for these models by solving an equation of hydrostatic equilibrium. Axisymmetric generalizations of the model are discussed.
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arxiv:1003.0259
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Studying the radial variation of the stellar mass function in globular clusters (GCs) has proved a valuable tool to explore the collisional dynamics leading to mass segregation and core collapse. In order to study the radial dependence of the luminosity and mass function of M 10, we used ACS/HST deep high resolution archival images, reaching out to approximately the cluster's half-mass radius (rhm), combined with deep WFPC2 images that extend our radial coverage to more than 2 rhm. From our photometry, we derived a radial mass segregation profile and a global mass function that we compared with those of simulated clusters containing different energy sources (namely hard binaries and/or an IMBH) able to halt core collapse and to quench mass segregation. A set of direct N-body simulations of GCs, with and without an IMBH of mass 1% of the total cluster mass, comprising different initial mass functions (IMFs) and primordial binary fractions, was used to predict the observed mass segregation profile and mass function. The mass segregation profile of M 10 is not compatible with cluster models without either an IMBH or primordial binaries, as a source of energy appears to be moderately quenching mass segregation in the cluster. Unfortunately, the present observational uncertainty on the binary fraction in M10 does not allow us to confirm the presence of an IMBH in the cluster, since an IMBH, a dynamically non-negligible binary fraction (~ 5%), or both can equally well explain the radial dependence of the cluster mass function.
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arxiv:1003.0280
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In two recent papers (arXiv:1002.1971 [hep-ph] and arXiv:0911.2460 [hep-ph]) Dermisek and Gunion provide new constraints on a light CP-odd Higgs boson in the framework of the NMSSM (or similar models) based on experimental data from LEP, CLEO, BaBar and CDF experiments. In this brief comment we argue that special care is still needed inside a narrow mass window where mixing with $\eta_b$ resonances below $B\bar{B}$ can occur. We also stress that observables testing lepton universality and a possible distorsion of the bottomonium mass spectrum can provide an alternative analysis at (Super) B-factories in the search of such an elusive light pseudoscalar Higgs-like object.
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arxiv:1003.0312
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We consider a multi-cell, frequency-selective fading, uplink channel (network MIMO) where K user terminals (UTs) communicate simultaneously with B cooperative base stations (BSs). Although the potential benefit of multi-cell cooperation grows with B, the overhead related to the acquisition of channel state information (CSI) will rapidly dominate the uplink resource. Thus, there exists a non-trivial tradeoff between the performance gains of network MIMO and the related overhead in channel estimation for a finite coherence time. Using a close approximation of the net ergodic achievable rate based on recent results from random matrix theory, we study this tradeoff by taking some realistic aspects into account such as unreliable backhaul links and different path losses between the UTs and BSs. We determine the optimal training length, the optimal number of cooperative BSs and the optimal number of sub-carriers to be used for an extended version of the circular Wyner model where each UT can communicate with B BSs. Our results provide some insight into practical limitations as well as realistic dimensions of network MIMO systems.
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arxiv:1003.0332
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Aims: The detached shells carry information on their formation process, as well as on the small-scale structure of the circumstellar medium around AGB stars due to the absence of significant line-of-sight confusion. Methods: The youngest detached shells, those around the carbon stars R Scl and U Cam, are studied here in great detail in scattered stellar light with the Advanced Survey Camera on the Hubble Space Telescope. Quantitative results are derived assuming optically thin dust scattering. Results: The detached dust shells around R Scl and U Cam are found to be consistent with an overall spherical symmetry. They have radii of 19.2" (corresponding to a linear size of 8x10^16 cm) and 7.7" (5x10^16 cm), widths of 1.2" (5x10^15 cm) and 0.6" (4x10^15 cm), and dust masses of 3x10^-6 and 3x10^-7 M(Sun), respectively. The dynamical ages of the R Scl and U Cam shells are estimated to be 1700 and 700 yr, respectively, and the shell widths correspond to time scales of 100 and 50 yr, respectively. Small-scale structure in the form of less than arcsec-sized clumps is clearly seen in the images of the R Scl shell. Average clump dust masses are estimated to be about 2x10^-9 M(Sun). Comparisons with CO line interferometer data show that the dust and gas shells coincide spatially, within the errors (<=1" for U Cam and approx. 2" for R Scl). Conclusions: The results are consistent with the interpretation of geometrically thin gas and dust shells formed by a mass-loss eruption during a He-shell flash, and where interaction with a previous wind plays a role as well. Clumpy structure is present in the R Scl shell, possibly as a consequence of the mass loss itself, but more likely as a consequence of instabilities in the expanding shell.
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arxiv:1003.0362
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The parametrization theorem is derived in a flat nD pseudo-complex affine space. The pseudo-complex hyperbolic space accomodates n-number of uncompactified time-like extra dimensions with sugnature (s,r), where s and r are the numbers of minus and plus signs associated with the diagonalized metric matrix. The main result of the theorem suggests a uniform parametrization for both time-like and space-like dimensions. The uniformization requirement preserves complex-hyperbolic inner product associated with the space. As application, the elements of the space is shown to be invariant under linear transformation.
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arxiv:1003.0422
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We describe two-photon absorption processes excited by entangled pairs, but not by non-entangled pairs of the same energy and polarization. Photon states are selected for destructive interference in the non-entangled process between different sequences of absorption via multiple intermediate states. A non-zero entangled absorption cross section is obtained by varying the entanglement time and pair delay parameters. Detailed energy and polarization requirements are derived for Rb 5S1/2 --> 5D3/2 transitions. Applications to Quantum Steganography and Quantum Key Distribution are discussed.
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arxiv:1003.0423
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The timed automata formalism is an important model for specifying and analysing real-time systems. Robustness is the correctness of the model in the presence of small drifts on clocks or imprecision in testing guards. A symbolic algorithm for the analysis of the robustness of timed automata has been implemented. In this paper, we re-analyse an industrial case lip synchronization protocol using the new robust reachability algorithm. This lip synchronization protocol is an interesting case because timing aspects are crucial for the correctness of the protocol. Several versions of the model are considered: with an ideal video stream, with anchored jitter, and with non-anchored jitter.
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arxiv:1003.0431
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We study the impact of the cosmological parameters uncertainties on the measurements of primordial non-Gaussianity through the large-scale non-Gaussian halo bias effect. While this is not expected to be an issue for the standard LCDM model, it may not be the case for more general models that modify the large-scale shape of the power spectrum. We consider the so-called local non-Gaussianity model and forecasts from planned surveys, alone and combined with a Planck CMB prior. In particular, we consider EUCLID- and LSST-like surveys and forecast the correlations among $f_{\rm NL}$ and the running of the spectral index $\alpha_s$, the dark energy equation of state $w$, the effective sound speed of dark energy perturbations $c^2_s$, the total mass of massive neutrinos $M_\nu=\sum m_\nu$, and the number of extra relativistic degrees of freedom $N_\nu^{rel}$. Neglecting CMB information on $f_{\rm NL}$ and scales $k > 0.03 h$/Mpc, we find that, if $N_\nu^{\rm rel}$ is assumed to be known, the uncertainty on cosmological parameters increases the error on $f_{\rm NL}$ by 10 to 30% depending on the survey. Thus the $f_{\rm NL}$ constraint is remarkable robust to cosmological model uncertainties. On the other hand, if $N_\nu^{\rm rel}$ is simultaneously constrained from the data, the $f_{\rm NL}$ error increases by $\sim 80%$. Finally, future surveys which provide a large sample of galaxies or galaxy clusters over a volume comparable to the Hubble volume can measure primordial non-Gaussianity of the local form with a marginalized 1--$\sigma$ error of the order $\Delta f_{\rm NL} \sim 2-5$, after combination with CMB priors for the remaining cosmological parameters. These results are competitive with CMB bispectrum constraints achievable with an ideal CMB experiment.
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arxiv:1003.0456
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There are ongoing divisions in the learning sciences between perspectives that treat cognition as occurring within individual minds and those that treat it as irreducibly distributed or situated in material and social contexts. We contend that accounts of individual minds as complex systems are theoretically continuous with distributed and situated cognition. On this view, the difference is a matter of the scale of the dynamics of interest, and the choice of scale can be informed by data. In this paper, we propose heuristics for empirically determining the scale of the relevant cognitive dynamics. We illustrate these heuristics in two contrasting cases, one in which the evidence supports attributing cognition to a group of students and one in which the evidence supports attributing cognition to an individual.
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arxiv:1003.0491
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We show efficient electro-optic modulation in a subwavelength gap-plasmon waveguide (GPW) formed by an electro-optic polymer with metal coatings. The proposed device is studied in the attenuated total reflection and end-fire configurations. In dealing with the end-fire configuration we used a taper from a micron sized guide to the GPW. The structure is shown to exhibit large phase accumulation over short distances, controllable by the applied modulating voltage.
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arxiv:1003.0497
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Polarization measurements in X-rays can provide unique opportunity to study the behavior of matter and radiation under extreme magnetic fields and extreme gravitational fields. Unfortunately, over past two decades, when X-ray astronomy witnessed multiple order of magnitude improvement in temporal, spatial and spectral sensitivities, there is no (or very little) progress in the field of polarization measurements of astrophysical X-rays. Recently, a proposal has been submitted to ISRO for a dedicated small satellite based experiment to carry out X-ray polarization measurement, which aims to provide the first X-ray polarization measurements since 1976. This experiment will be based on the well known principle of polarization measurement by Thomson scattering and employs the baseline design of a central low Z scatterer surrounded by X-ray detectors to measure the angular intensity distribution of the scattered X-rays. The sensitivity of such experiment is determined by the collecting area, scattering and detection efficiency, X-ray detector background, and the modulation factor. Therefore, it is necessary to carefully select the scattering geometry which can provide the highest modulation factor and thus highest sensitivity within the specified experimental constraints. The effective way to determine optimum scattering geometry is by studying various possible scattering geometries by means of Monte Carlo simulations. Here we present results of our detailed comparative study based on Geant4 simulations of five different scattering geometries which can be considered within the weight and size constraints of the proposed small satellite based X-ray polarization measurement experiment.
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arxiv:1003.0519
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We present an efficient implementation of the PBE0 hybrid functional within the full-potential linearized augmented-plane-wave (FLAPW) method. The Hartree-Fock exchange term, which is a central ingredient of hybrid functionals, gives rise to a computationally expensive nonlocal potential in the one-particle Schroedinger equation. The matrix elements of this exchange potential are calculated with the help of an auxiliary basis that is constructed from products of FLAPW basis functions. By representing the Coulomb interaction in this basis the nonlocal exchange term becomes a Brillouin-zone (BZ) sum over vector-matrix-vector products. We show that the Coulomb matrix can be made sparse by a suitable unitary transformation of the auxiliary basis, which accelerates the computation of the vector-matrix-vector products considerably. Additionally, we exploit spatial and time-reversal symmetry to identify the nonvanishing exchange matrix elements in advance and to restrict the k summations for the nonlocal potential to an irreducible set of k points. Favorable convergence of the self-consistent-field cycle is achieved by a nested density-only and density-matrix iteration scheme. We discuss the convergence with respect to the parameters of our numerical scheme and show results for a variety of semiconductors and insulators, including oxide materials, where the PBE0 hybrid functional improves the band gaps and the description of localized states in comparison with the PBE functional. Furthermore, we find that in contrast to conventional local exchange-correlation functionals ferromagnetic EuO is correctly predicted to be a semiconductor.
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arxiv:1003.0524
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We consider complex Fermi curves of electric and magnetic periodic fields. These are analytic curves in C^2 that arise from the study of the eigenvalue problem for periodic Schroedinger operators. We characterize a certain class of these curves in the region of C^2 where at least one of the coordinates has "large" imaginary part. The new results in this work extend previous results in the absence of magnetic field to the case of "small" magnetic field. Our theorems can be used to show that generically these Fermi curves belong to a class of Riemann surfaces of infinite genus.
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arxiv:1003.0586
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A new estimation of the orbital period of YY Her on the base of our and published observations is presented. Phased light curves in RI bands show evidently ellipsoidal effect connected with the tidal distortion of the giant surface.
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arxiv:1003.0595
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In a recent paper [arXiv:0904.2904] using a conjecture it is shown how one can calculate the effect of a weak stationary gravitational field on vacuum energy in the context of Casimir effect in an external gravitational field treated in 1+3 formulation of spacetime decomposition.. In this article, employing quntum field theory in curved spacetime, we explicitly calculate the effect of a weak static gravitational field on virtual massless scalar particles in a Casimir apparatus. It is shown that, as expected from the proposed conjecture, both the frequency and renormalized energy of the virtual scalar field are affected by the gravitational field through its index of refraction. This could be taken as a strong evidence in favour of the proposed conjecture. Generalizations to weak {\it stationary} spacetimes and virtual photons are also discussed.
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arxiv:1003.0614
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This paper deals with the dynamics of time-reversible Hamiltonian vector fields with 2 and 3 degrees of freedom around an elliptic equilibrium point in presence of symplectic involutions. The main results discuss the existence of one-parameter families of reversible periodic solutions terminating at the equilibrium. The main techniques used are Birkhoff and Belitskii normal forms combined with the Liapunov-Schmidt reduction.
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arxiv:1003.0656
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We prove Strichartz estimates with a loss of derivatives for the Schr\"odinger equation on polygonal domains with either Dirichlet or Neumann homogeneous boundary conditions. Using a standard doubling procedure, estimates the on polygon follow from those on Euclidean surfaces with conical singularities. We develop a Littlewood-Paley squarefunction estimate with respect to the spectrum of the Laplacian on these spaces. This allows us to reduce matters to proving estimates at each frequency scale. The problem can be localized in space provided the time intervals are sufficiently small. Strichartz estimates then follow from a result of the second author regarding the Schr\"odinger equation on the Euclidean cone.
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arxiv:1003.0666
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We reply to a recent comment [arXiv:1002.2445] and describe why the chemical potential conjugate to the mass of linear aggregates is not an independent parameter in the ensemble that the total length is free to adjust. It is only in the (unphysical) ensemble of fixed total polymer length that such a chemical potential can act as an independent control parameter for the aggregate radius.
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arxiv:1003.0830
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We employ a bias-corrected abundance matching technique to investigate the coevolution of the LCDM dark halo mass function (HMF), the observationally derived velocity dispersion and stellar mass functions (VDF, SMF) of galaxies between z=1 and 0. We use for the first time the evolution of the VDF constrained through strong lensing statistics by Chae (2010) for galaxy-halo abundance matching studies. As a local benchmark we use a couple of z ~ 0 VDFs (a Monte-Carlo realised VDF based on SDSS DR5 and a directly measured VDF based on SDSS DR6). We then focus on connecting the VDF evolution to the HMF evolution predicted by N-body simulations and the SMF evolution constrained by galaxy surveys. On the VDF-HMF connection, we find that the local dark halo virial mass-central stellar velocity dispersion (Mvir-sigma) relation is in good agreement with the individual properties of well-studied low-redshift dark haloes, and the VDF evolution closely parallels the HMF evolution meaning little evolution in the Mvir-sigma relation. On the VDF-SMF connection, it is also likely that the stellar mass-stellar velocity dispersion (Mstar-sigma) relation evolves little taking the abundance matching results together with other independent observational results and hydrodynamic simulation results. Our results support the simple picture that as the halo grows hierarchically, the stellar mass and the central stellar velocity dispersion grow in parallel. We discuss possible implications of this parallel coevolution for galaxy formation and evolution under the LCDM paradigm.
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arxiv:1003.0835
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In the study of Planck-scale ("quantum-gravity induced") violations of Lorentz symmetry, an important role was played by the deformed-electrodynamics model introduced by Myers and Pospelov. Its reliance on conventional effective quantum field theory, and its description of symmetry-violation effects simply in terms of a four-vector with nonzero component only in the time-direction, rendered it an ideal target for experimentalists and a natural concept-testing ground for many theorists. At this point however the experimental limits on the single Myers-Pospelov parameter, after improving steadily over these past few years, are "super-Planckian", {\it i.e.} they take the model out of actual interest from a conventional quantum-gravity perspective. In light of this we here argue that it may be appropriate to move on to the next level of complexity, still with vectorial symmetry violation but adopting a generic four-vector. We also offer a preliminary characterization of the phenomenology of this more general framework, sufficient to expose a rather significant increase in complexity with respect to the original Myers-Pospelov setup. Most of these novel features are linked to the presence of spatial anisotropy, which is particularly pronounced when the symmetry-breaking vector is space-like, and they are such that they reduce the bound-setting power of certain types of observations in astrophysics.
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arxiv:1003.0878
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Complex, non-additive genetic interactions are common and can be critical in determining phenotypes. Genome-wide association studies (GWAS) and similar statistical studies of linkage data, however, assume additive models of gene interactions in looking for genotype-phenotype associations. These statistical methods view the compound effects of multiple genes on a phenotype as a sum of partial influences of each individual gene and can often miss a substantial part of the heritable effect. Such methods do not use any biological knowledge about underlying genotype-phenotype mechanisms. Modeling approaches from the AI field that incorporate deterministic knowledge into models to perform statistical analysis can be applied to include prior knowledge in genetic analysis. We chose to use the most general such approach, Markov Logic Networks (MLNs), as a framework for combining deterministic knowledge with statistical analysis. Using simple, logistic regression-type MLNs we have been able to replicate the results of traditional statistical methods. Moreover, we show that even with simple models we are able to go beyond finding independent markers linked to a phenotype by using joint inference that avoids an independence assumption. The method is applied to genetic data on yeast sporulation, a phenotype governed by non-linear gene interactions. In addition to detecting all of the previously identified loci associated with sporulation, our method is able to identify four loci with small effects. Since their effect on sporulation is small, these four loci were not detected with methods that do not account for dependence between markers due to gene interactions. We show how gene interactions can be detected using more complex models, which can be used as a general framework for incorporating systems biology with genetics.
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arxiv:1003.0902
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A numerical study of an algorithm proposed by Gusein Guseinov, which determines approximations to the optimal solution of problems of calculus of variations using two discretizations and correspondent Euler-Lagrange equations, is investigated. The results we obtain to discretizations of the brachistochrone problem and Mania example with Lavrentiev's phenomenon are compared with the solutions found by other methods and solvers. We conclude that Guseinov's method presents better solutions in most of the cases studied.
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arxiv:1003.0934
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Polycrystalline NdFeAsO0.88F0.12 superconductors prepared by high pressure (HP) and ambient pressure (AP) method were comparatively studied by magnetization and transport measurements. Upper critical field (Hc2), irreversibility field (Hirr) and the anisotropy parameter were estimated from resistance transition curves. The broadening of transition width was observed, and ascribed to both Hc2 anisotropy and superconductivity inhomogeneity of samples. Magnetic hysteresis loops (MHLs) in low fields were measured to detect the trace of weak-link behavior. The reclosed hysteresis loops in low fields manifest that there are weak-links in both samples. Magnetization critical current density Jcm were derived from MHLs. High-pressure synthesized sample shows higher Jcm. However, by means of direct transport I-V measurements, transport critical current density Jct was very low. The Jct values for two samples are comparable. Large discrepancies between Jcm and Jct also indicate that there are weak-links in both samples. The relative mechanism is discussed in detail.
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arxiv:1003.0946
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We study the implications of the simultaneous existence of a texture zero and a vanishing minor in the neutrino mass matrix. There are thirty six possible texture structures of this type, twenty one of which reduce to two texture zero cases which have, already, been extensively studied. Of the remaining fifteen textures only six are allowed by the current data. We examine the phenomenological implications of the allowed texture structures for Majorana type CP-violating phases, 1-3 mixing angle and Dirac type CP-violating phase. All these possible textures can be generated through the seesaw mechanism and realized in the framework of discrete abelian flavor symmetry. We present the symmetry realization of these texture structures.
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arxiv:1003.1006
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We offer some, hopefully clarifying, comments on Verlinde's recent claim that gravity is an entropic force. A suitable identification of quantities shows that both formulations of Newtonian gravity, the classical and the thermodynamical one, are actually equivalent. It turns out that some additional assumptions made by Verlinde are unnecessary. However, when it comes to General Relativity there remain some gaps in the argument. We comment on whether this identification can be done also for electrostatics. Finally, some thoughts on the use of this reinterpretation are offered.
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arxiv:1003.1015
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In 1966, Shanks and Schmid investigated the asymptotic behavior of the number of positive integers less than or equal to x which are represented by the quadratic form X^2+nY^2. Based on some numerical computations, they observed that the constant occurring in the main term appears to be the largest for n=2. In this paper, we prove that in fact this constant is unbounded as n runs through positive integers with a fixed number of prime divisors.
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arxiv:1003.1094
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Let $G$ be a compact group of linear transformations of an Euclidean space $V$. The $G$-invariant $C^\infty$ functions can be expressed as $C^\infty$ functions of a finite basic set of $G$-invariant homogeneous polynomials, called an integrity basis. The mathematical description of the orbit space $V/G$ depends on the integrity basis too: it is realized through polynomial equations and inequalities expressing rank and positive semi-definiteness conditions of the $P$-matrix, a real symmetric matrix determined by the integrity basis. The choice of the basic set of $G$-invariant homogeneous polynomials forming an integrity basis is not unique, so it is not unique the mathematical description of the orbit space too. If $G$ is an irreducible finite reflection group, Saito et al. in 1980 characterized some special basic sets of $G$-invariant homogeneous polynomials that they called {\em flat}. They also found explicitly the flat basic sets of invariant homogeneous polynomials of all the irreducible finite reflection groups except of the two largest groups $E_7$ and $E_8$. In this paper the flat basic sets of invariant homogeneous polynomials of $E_7$ and $E_8$ and the corresponding $P$-matrices are determined explicitly. Using the results here reported one is able to determine easily the $P$-matrices corresponding to any other integrity basis of $E_7$ or $E_8$. From the $P$-matrices one may then write down the equations and inequalities defining the orbit spaces of $E_7$ and $E_8$ relatively to a flat basis or to any other integrity basis. The results here obtained may be employed concretely to study analytically the symmetry breaking in all theories where the symmetry group is one of the finite reflection groups $E_7$ and $E_8$ or one of the Lie groups $E_7$ and $E_8$ in their adjoint representations.
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arxiv:1003.1095
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An intertwine of a pair of matroids is a matroid such that it, but none of its proper minors, has minors that are isomorphic to each matroid in the pair. For pairs for which neither matroid can be obtained, up to isomorphism, from the other by taking free extensions, free coextensions, and minors, we construct a family of rank-k intertwines for each sufficiently large integer k. We also treat some properties of these intertwines.
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arxiv:1003.1120
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We present general, analytic methods for Cosmological likelihood analysis and solve the "many-parameters" problem in Cosmology. Maxima are found by Newton's Method, while marginalization over nuisance parameters, and parameter errors and covariances are estimated by analytic marginalization of an arbitrary likelihood function with flat or Gaussian priors. We show that information about remaining parameters is preserved by marginalization. Marginalizing over all parameters, we find an analytic expression for the Bayesian evidence for model selection. We apply these methods to data described by Gaussian likelihoods with parameters in the mean and covariance. This method can speed up conventional likelihood analysis by orders of magnitude when combined with Monte-Carlo Markov Chain methods, while Bayesian model selection becomes effectively instantaneous.
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arxiv:1003.1136
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The partition function of a family of four dimensional N=2 gauge theories has been recently related to correlation functions of two dimensional conformal Toda field theories. For SU(2) gauge theories, the associated two dimensional theory is A_1 conformal Toda field theory, i.e. Liouville theory. For this case the relation has been extended showing that the expectation value of gauge theory loop operators can be reproduced in Liouville theory inserting in the correlators the monodromy of chiral degenerate fields. In this paper we study Wilson loops in SU(N) gauge theories in the fundamental and anti-fundamental representation of the gauge group and show that they are associated to monodromies of a certain chiral degenerate operator of A_{N-1} Toda field theory. The orientation of the curve along which the monodromy is evaluated selects between fundamental and anti-fundamental representation. The analysis is performed using properties of the monodromy group of the generalized hypergeometric equation, the differential equation satisfied by a class of four point functions relevant for our computation.
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arxiv:1003.1151
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In an exact conformal theory there is no particle. The excitations have continuum spectra and are called "unparticles" by Georgi. We consider supersymmetric extensions of the Standard Model with approximate conformal sectors. The conformal symmetry is softly broken in the infrared which generates a gap. However, the spectrum can still have a continuum above the gap if there is no confinement. Using the AdS/CFT correspondence this can be achieved with a soft wall in the warped extra dimension. When supersymmetry is broken the superpartners of the Standard Model particles may simply be a continuum above gap. The collider signals can be quite different from the standard supersymmetric scenarios and the experimental searches for the continuum superpartners can be very challenging.
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arxiv:1003.1163
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This paper is a step in our program for proving the Piece-Birkhoff Conjecture for regular rings of any dimension (this would contain, in particular, the classical Pierce-Birkhoff conjecture which deals with polynomial rings over a real closed field). We first recall the Connectedness and the Definable Connectedness conjectures, both of which imply the Pierce - Birkhoff conjecture. Then we introduce the notion of a system of approximate roots of a valuation v on a ring A (that is, a collection Q of elements of A such that every v-ideal is generated by products of elements of Q). We use approximate roots to give explicit formulae for sets in the real spectrum of A which we strongly believe to satisfy the conclusion of the Definable Connectedness conjecture. We prove this claim in the special case of dimension 2. This proves the Pierce-Birkhoff conjecture for arbitrary regular 2-dimensional rings.
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arxiv:1003.1188
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We propose a simple method to detect the relative strength of Rashba and Dresselhaus spin-obit interactions in quantum wells (QWs) without relying on the directional-dependent physical quantities. This method utilize the asymmetry of critical gate voltages that leading to the remarkable signals of SU(2) symmetry, which happens to reflect the intrinsic structure inversion asymmetry of the QW. We support our proposal by the numerical calculation of in-plane relaxation times based on the self-consistent eight-band Kane model. We find that the two different critical gate voltages leading to the maximum spin relaxation times [one effect of the SU(2) symmetry] can simply determine the ratio of the coefficients of Rashba and Dresselhaus terms. Our proposal can also be generalized to extract the relative strengths of the spin-orbit interactions in quantum wire and quantum dot structures.
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arxiv:1003.1198
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It is known how to construct, in a bipartite quantum system, a unique low rank entangled mixed state with positive partial transpose (a PPT state) from an unextendible product basis (a UPB), defined as an unextendible set of orthogonal product vectors. We point out that a state constructed in this way belongs to a continuous family of entangled PPT states of the same rank, all related by non-singular product transformations, unitary or non-unitary. The characteristic property of a state $\rho$ in such a family is that its kernel $\Ker\rho$ has a generalized UPB, a basis of product vectors, not necessarily orthogonal, with no product vector in $\Im\rho$, the orthogonal complement of $\Ker\rho$. The generalized UPB in $\Ker\rho$ has the special property that it can be transformed to orthogonal form by a product transformation. In the case of a system of dimension $3\times 3$, we give a complete parametrization of orthogonal UPBs. This is then a parametrization of families of rank 4 entangled (and extremal) PPT states, and we present strong numerical evidence that it is a complete classification of such states. We speculate that the lowest rank entangled and extremal PPT states also in higher dimensions are related to generalized, non-orthogonal UPBs in similar ways.
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arxiv:1003.1221
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Several binary systems consisting of a massive star and a compact object have been detected above 100 GeV in the Galaxy. In most of these sources, gamma-rays show a modulation associated to the orbital motion, which means that the emitter should not be too far from the bright primary star. This implies that gamma-ray absorption will be non negligible, and large amounts of secondary electron-positron pairs will be created in the stellar surroundings. In this work, we show that the radio emission from these pairs should be accounted for when interpreting the radio spectrum, variability, and morphology found in gamma-ray binaries. Relevant features of the secondary radio emission are the relatively hard spectrum, the orbital motion of the radio peak center, and the extended radio structure following a spiral-like trajectory. The impact of the stellar wind free-free absorption should not be neglected.
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arxiv:1003.1227
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To every finitely generated group one can assign the conjugacy growth function that counts the number of conjugacy classes intersecting a ball of radius $n$. Results of Ivanov and Osin show that the conjugacy growth function may be constant even if the (ordinary) growth function is exponential. The aim of this paper is to provide conjectures, examples and statements that show that in "normal" cases, groups with exponential growth functions also have exponential conjugacy growth functions.
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arxiv:1003.1293
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The measurement of hadronic Higgs Boson branching ratios H -> bb, H -> gg for a light Standard Model-like Higgs boson produced at 250 GeV centre of mass energy at the International Linear Collider (ILC) is presented. The tools and techniques used for the analysis are briefly discussed.
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arxiv:1003.1333
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Photoproduction of neutral pions has been studied with the CBELSA/TAPS detector for photon energies between 0.92 and 1.68~GeV at the electron accelerator ELSA. The beam asymmetry~$\Sigma$ has been extracted for $115^\circ < \theta_{\rm c.m.} < 155^\circ$ of the $\pi^0$~meson and for $\theta_{\rm c.m.} < 60^\circ$. The new beam asymmetry data improve the world database for photon energies above 1.5~GeV and, by covering the very forward region, extend previously published data for the same reaction by our collaboration. The angular dependence of $\Sigma$ shows overall good agreement with the SAID parameterization.
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arxiv:1003.1346
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Results: We found that the (B-V) v.s. (V-S9W) color-color diagram is useful to identify the stars with infrared excess emerged from circumstellar envelopes/disks. Be stars with infrared excess are well separated from other types of stars in this diagram. Whereas (J-L18W) v.s. (S9W-L18W) diagram is a powerful tool to classify several object-types. Carbon-rich asymptotic giant branch (AGB) stars and OH/IR stars form distinct sequences in this color-color diagram. Young stellar objects (YSOs), pre-main sequence (PMS) stars, post-AGB stars and planetary nebulae (PNe) have largest mid-infrared color-excess, and can be identified in infrared catalog. Finally, we plot L18W v.s. (S9W-L18W) color-magnitude diagram, using the AKARI data together with Hipparcos parallaxes. This diagram can be used to identify low-mass YSOs, as well as AGB stars. We found that this diagram is comparable to the [24] vs ([8.0]-[24]) diagram of Large Magellanic Cloud sources using the Spitzer Space Telescope data. Our understanding of Galactic objects will be used to interpret color-magnitude diagram of stellar populations in nearby galaxies which Spitzer Space Telescope has observed. Conclusions: Our study of the AKARI color-color and color-magnitude will be used to explore properties of unknown objects in future. In addition, our analysis highlights a future key project to understand stellar evolution with circumstellar envelope, once the forthcoming astronometrical data with GAIA are available.
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arxiv:1003.1370
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Unlike static documents, version controlled documents are continuously edited by one or more authors. Such collaborative revision process makes traditional modeling and visualization techniques inappropriate. In this paper we propose a new representation based on local space-time smoothing that captures important revision patterns. We demonstrate the applicability of our framework using experiments on synthetic and real-world data.
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arxiv:1003.1410
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We study almost bi-paracontact structures on contact manifolds. We prove that if an almost bi-paracontact structure is defined on a contact manifold $(M,\eta)$, then under some natural assumptions of integrability, $M$ carries two transverse bi-Legendrian structures. Conversely, if two transverse bi-Legendrian structures are defined on a contact manifold, then $M$ admits an almost bi-paracontact structure. We define a canonical connection on an almost bi-paracontact manifold and we study its curvature properties, which resemble those of the Obata connection of an anti-hypercomplex (or complex-product) manifold. Further, we prove that any contact metric manifold whose Reeb vector field belongs to the $(\kappa,\mu)$-nullity distribution canonically carries an almost bi-paracontact structure and we apply the previous results to the theory of contact metric $(\kappa,\mu)$-spaces.
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arxiv:1003.1417
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The reduced properties and applications of Yangian Y(sl(2)) and Y(su(3)) algebras are discussed. By taking a special constraint, the representation of Y(su(3)) can be divided into three 3 * 3 blocks diagonal based on Gell-mann matrices. The reduced Yangian Y(sl(2)) and Y(su(3)) are applied to the bi-qubit system and the mixed light pseudoscalar meson state respectively, and are both able to make the final states disentangled after acting on the initial state by the transition operator, composed of the generators of Yangian.
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arxiv:1003.1461
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In this article it is shown that there is no continuous bijection from $\mathbb{R}^n$ onto $\mathbb{R}^2$ for $n\neq 2$ by an elementary method. This proof is based on showing that for any cardinal number $\beta\leq 2^{\aleph_0}$, there is a partition of $R^n$ ($n\geq 3$) into $\beta$ arcwise connected dense subsets.
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arxiv:1003.1467
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In this paper, we prove that every binomial ideal in a polynomial ring over an algebraically closed field of characteristic zero admits a canonical primary decomposition into binomial ideals. Moreover, we prove that this special decomposition is obtained from a cellular decomposition which is also defined in a canonical way and does not depend on the field.
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arxiv:1003.1701
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We present a new signature by which to one could potentially discriminate between a spectrum of gravitational radiation generated by a self-ordering scalar field vs that of inflation, specifically a comparison of the magnitude of a flat spectrum at frequencies probed by future direct detection experiments to the magnitude of a possible polarization signal in the Cosmic Microwave Background (CMB) radiation. In the process we clarify several issues related to the proper calculation of such modes, focusing on the effect of post-horizon-crossing evolution.
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arxiv:1003.1735
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We describe breakdown in 805 MHz rf accelerator cavities in terms of a number of self consistent mechanisms. We divide the breakdown process into three stages: 1) we model surface failure using molecular dynamics of fracture caused by electrostatic tensile stress, 2) we model the ionization of neutrals responsible for plasma initiation and plasma growth using a particle in cell code, and 3) we model surface damage by assuming a process similar to unipolar arcing. We find that the cold, dense plasma in contact with the surface produces very small Debye lengths and very high electric fields over a large area, consistent with unipolar arc behavior, although unipolar arcs are strictly defined with equipotential boundaries. These high fields produce strong erosion mechanisms, primarily self sputtering, compatible with the crater formation that we see. We use OOPIC modeling to estimate very high surface electric fields in the dense plasma and measure these field using electrohydrodynamic arguments to relate the dimensions of surface damage with the applied electric field. We also present a geometrical explanation of the large enhancement factors of field emitters.This is consistent with the apparent absence of whiskers on surfaces exposed to high fields. The enhancement factors we derive, when combined with the Fowler-Nordheim analysis produce a consistent picture of breakdown and field emission from surfaces at local fields of 7 - 10 GV/m. We show that the plasma growth rates we obtain from OOPIC are consistent with growth rates of the cavity shorting currents using x ray measurements. We believe the general picture presented here for rf breakdown arcs should be directly applicable to a larger class of vacuum arcs. Results from the plasma simulation are included as a guide to experimental verification of this model.
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arxiv:1003.1736
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In a family of curves, the Chern numbers of a singular fiber are the local contributions to the Chern numbers of the total space. We will give some inequalities between the Chern numbers of a singular fiber as well as their lower and upper bounds. We introduce the dual fiber of a singular fiber, and prove a duality theorem. As an application, we will classify singular fibers with large or small Chern numbers.
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arxiv:1003.1767
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We extend the study of the core of the Fe K$\alpha$ emission line at \sim 6.4 keV in Seyfert galaxies reported in Yaqoob & Padmanabhan (2004) using a larger sample observed by the Chandra High Energy Grating (HEG). Whilst heavily obscured active galactic nuclei (AGNs) are excluded from the sample, these data offer some of the highest precision measurements of the peak energy of the Fe K$\alpha$ line, and the highest spectral resolution measurements of the width of the core of the line in unobscured and moderately obscured ($N_{H}<10^{23} \ \rm cm^{-2}$) Seyfert galaxies to date. The Fe K$\alpha$ line is detected in 33 sources, and its centroid energy is constrained in 32 sources. In 27 sources the statistical quality of the data is good enough to yield measurements of the FWHM. We find that the distribution in the line centroid energy is strongly peaked around the value for neutral Fe, with over 80% of the observations giving values in the range 6.38--6.43 keV. Including statistical errors, 30 out of 32 sources ($\sim 94%$) have a line centroid energy in the range 6.35--6.47 keV. The mean equivalent width, amongst the observations in which a non-zero lower limit could be measured, was $53 \pm 3eV. The mean FWHM from the subsample of 27 sources was $2060 \pm 230 \ \rm km \ s^{-1}$. The mean EW and FWHM are somewhat higher when multiple observations for a given source are averaged. From a comparison with the H$\beta$ optical emission-line widths (or, for one source, Br$\alpha$), we find that there is no universal location of the Fe K$\alpha$ line-emitting region relative to the optical BLR. We confirm the presence of the X-ray Baldwin effect, an anti-correlation between the Fe K$\alpha$ line EW and X-ray continuum luminosity. The HEG data have enabled isolation of this effect to the narrow core of the Fe K$\alpha$ line.
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arxiv:1003.1790
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Double Hurwitz numbers count covers of the projective line by genus g curves with assigned ramification profiles over 0 and infinity, and simple ramification over a fixed branch divisor. Goulden, Jackson and Vakil have shown double Hurwitz numbers are piecewise polynomial in the orders of ramification, and Shadrin, Shapiro and Vainshtein have determined the chamber structure and wall crossing formulas for g=0. This paper gives a unified approach to these results and strengthens them in several ways -- the most important being the extension of the results of Shapiro, Shadrin and Vainshtein to arbitrary genus. The main tool is the authors' previous work expressing double Hurwitz number as a sum over certain labeled graphs. We identify the labels of the graphs with lattice points in the chambers of certain hyperplane arrangements, which are well known to give rise to piecewise polynomial functions. Our understanding of the wall crossing for these functions builds on the work of Varchenko, and could have broader applications.
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arxiv:1003.1805
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Suppose $E$ is fully symmetric Banach function space on $(0,1)$ or $(0,\infty)$ or a fully symmetric Banach sequence space. We give necessary and sufficient conditions on $f\in E$ so that its orbit $\Omega(f)$ is the closed convex hull of its extreme points. We also give an application to symmetrically normed ideals of compact operators on a Hilbert space.
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arxiv:1003.1817
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We study the universal characteristics of the shape of a polymer chain in an environment with correlated structural obstacles, applying the field-theoretical renormalization group approach. Our results qualitatively indicate an increase of the asymmetry of the polymer shape in crowded environment comparing with the pure solution case.
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arxiv:1003.1856
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The dynamics of a tachyon field plus a barotropic fluid is investigated in spatially curved FRW universe. We perform a phase-plane analysis and obtain scaling solutions accompanying with a discussion on their stability. Furthermore, we construct the form of scalar potential which may give rise to stable solutions for spatially open and closed universe separately.
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arxiv:1003.1870
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Basic uniform pseudo-random number generators are implemented on ATI Graphics Processing Units (GPU). The performance results of the realized generators (multiplicative linear congruential (GGL), XOR-shift (XOR128), RANECU, RANMAR, RANLUX and Mersenne Twister (MT19937)) on CPU and GPU are discussed. The obtained speed-up factor is hundreds of times in comparison with CPU. RANLUX generator is found to be the most appropriate for using on GPU in Monte Carlo simulations. The brief review of the pseudo-random number generators used in modern software packages for Monte Carlo simulations in high-energy physics is present.
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arxiv:1003.1898
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We present simple and computationally efficient nonparametric estimators of R\'enyi entropy and mutual information based on an i.i.d. sample drawn from an unknown, absolutely continuous distribution over $\R^d$. The estimators are calculated as the sum of $p$-th powers of the Euclidean lengths of the edges of the `generalized nearest-neighbor' graph of the sample and the empirical copula of the sample respectively. For the first time, we prove the almost sure consistency of these estimators and upper bounds on their rates of convergence, the latter of which under the assumption that the density underlying the sample is Lipschitz continuous. Experiments demonstrate their usefulness in independent subspace analysis.
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arxiv:1003.1954
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We prove a result on the representation of squares by second degree polynomials in the field of $p$-adic meromorphic functions in order to solve positively B\"uchi's $n$ squares problem in this field (that is, the problem of the existence of a constant $M$ such that any sequence $(x_n^2)$ of $M$ - not all constant - squares whose second difference is the constant sequence $(2)$ satisfies $x_n^2=(x+n)^2$ for some $x$). We prove (based on works by Vojta) an analogous result for function fields of characteristic zero, and under a Conjecture by Bombieri, an analogous result for number fields. Using an argument by B\"uchi, we show how the obtained results improve some theorems about undecidability for the field of $p$-adic meromorphic functions and the ring of $p$-adic entire functions.
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arxiv:1003.1969
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The short range ordered magnetic correlations have been studied in half doped La0.5Ca0.5-xSrxMnO3 (x = 0.1, 0.3 and 0.4) compounds by polarized neutron scattering technique. On doping Sr2+ for Ca2+ ion, these compounds with x = 0.1, 0.3, and 0.4 exhibit CE-type, mixture of CE-type and A-type, and A-type antiferromagnetic ordering, respectively. Magnetic diffuse scattering is observed in all the compounds above and below their respective magnetic ordering temperatures and is attributed to magnetic polarons. The correlations are primarily ferromagnetic in nature above T\_N, although a small antiferromagnetic contribution is also evident. Additionally, in samples x = 0.1 and 0.3 with CE-type antiferromagnetic ordering, superlattice diffuse reflections are observed indicating correlations between magnetic polarons. On lowering temperature below T\_N the diffuse scattering corresponding to ferromagnetic correlations is suppressed and the long range ordered antiferromagnetic state is established. However, the short range ordered correlations indicated by enhanced spin flip scattering at low Q coexist with long range ordered state down to 3K. In x = 0.4 sample with A-type antiferromagnetic ordering, superlattice diffuse reflections are absent. Additionally, in comparison to x = 0.1 and 0.3 sample, the enhanced spin flip scattering at low Q is reduced at 310K, and as temperature is reduced below 200K, it becomes negligibly low. The variation of radial correlation function, g(r) with temperature indicates rapid suppression of ferromagnetic correlations at the first nearest neighbor on approaching TN. Sample x = 0.4 exhibits growth of ferromagnetic phase at intermediate temperatures (~ 200K). This has been further explored using SANS and neutron depolarization techniques.
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arxiv:1003.2026
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Folding of the triangular lattice in a discrete three-dimensional space is investigated by means of the transfer-matrix method. This model was introduced by Bowick and co-workers as a discretized version of the polymerized membrane in thermal equilibrium. The folding rule (constraint) is incompatible with the periodic-boundary condition, and the simulation has been made under the open-boundary condition. In this paper, we propose a modified constraint, which is compatible with the periodic-boundary condition; technically, the restoration of translational invariance leads to a substantial reduction of the transfer-matrix size. Treating the cluster sizes L \le 7, we analyze the singularities of the crumpling transitions for a wide range of the bending rigidity K. We observe a series of the crumpling transitions at K=0.206(2), -0.32(1), and -0.76(10). At each transition point, we estimate the latent heat as Q=0.356(30), 0.08(3), and 0.05(5), respectively.
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arxiv:1003.2034
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A recent paper by V.V. Demjanov in Physics Letters A reported a formula that relates the magnitude of Michelson interferometer fringe shifts to refractive index and absolute velocity. We show here that relativistic corrections to the Sellmeier equation allow an alternative derivation of the formula.
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arxiv:1003.2035
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In this paper, we give the definition, different types and characterizations of Mannheim partner D-curves in Minkowski 3-space. We find the relations between the geodesic curvatures, the normal curvatures and the geodesic torsions of these associated curves. Furthermore, we show that the definition and the characterizations of Mannheim partner D-curves include those of Mannheim partner curves in some special cases in Minkowski 3-space.
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arxiv:1003.2043
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The mass matrix for $\eta-\eta^\prime$ is derived in the flavor basis at ${\cal O}(p^4)$ of the chiral Lagrangian using the large $N$ approximation. Under certain assumptions, the mixing angle $\phi=41.4^\circ$ and the decay constants ratio $f_K/f_\pi=1.15$ are calculated in agreement with the data. It appears that the FKS scheme arises as a special limit of the chiral Lagrangian. Their mass matrix is obtained without the hypothesis on the mixing pattern of the decay constants.
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arxiv:1003.2119
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Let $X_1,X_2$ be independent random walks on $\mathbf{Z}_n^d$, $d\geq3$, each starting from the uniform distribution. Initially, each site of $\mathbf{Z}_n^d$ is unmarked, and, whenever $X_i$ visits such a site, it is set irreversibly to $i$. The mean of $|\mathcal{A}_i|$, the cardinality of the set $\mathcal{A}_i$ of sites painted by $i$, once all of $\mathbf{Z}_n^d$ has been visited, is $\frac{1}{2}n^d$ by symmetry. We prove the following conjecture due to Pemantle and Peres: for each $d\geq3$ there exists a constant $\alpha_d$ such that $\lim_{n\to\infty}\operatorname{Var}(|\mathcal {A}_i|)/h_d(n)=\frac{1}{4}\alpha_d$ where $h_3(n)=n^4$, $h_4(n)=n^4(\log n)$ and $h_d(n)=n^d$ for $d\geq5$. We will also identify $\alpha_d$ explicitly and show that $\alpha_d\to1$ as $d\to\infty$. This is a special case of a more general theorem which gives the asymptotics of $\operatorname{Var}(|\mathcal{A}_i|)$ for a large class of transient, vertex transitive graphs; other examples include the hypercube and the Caley graph of the symmetric group generated by transpositions.
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arxiv:1003.2168
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We experimentally study the influence of 1-40 GHz radiation on the resistance of normal (N) mesoscopic conductors coupled to superconducting (S) loops (Andreev interferometers). At low RF amplitudes we observe the usual h/2e superconducting-phase-periodic resistance oscillations as a function of applied magnetic flux. We find that the oscillations acquire a pi-shift with increasing RF amplitude, and consistent with this result the resistance at fixed phase is an oscillating function of the RF amplitude. The results are explained qualitatively as a consequence of two processes. The first is the modulation of the phase difference between the N/S interfaces by the RF field, with the resistance adiabatically following the phase. The second process is the change in the electron temperature caused by the RF field. From the data the response time of the Andreev interferometer is estimated to be <40ps. However there are a number of experimental features which remain unexplained; these include the drastic difference in the behaviour of the resistance at different phases as a function of RF frequency and amplitude, and the existence of a "window of transparency" where heating effects are weak enough to allow for the pi-shift. A microscopic theory describing the influence of RF radiation on Andreev interferometers is required.
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arxiv:1003.2176
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The aim of this paper is to classify order-preserving functions according to their arity gap. Noteworthy examples of order-preserving functions are so-called aggregation functions. We first explicitly classify the Lov\'asz extensions of pseudo-Boolean functions according to their arity gap. Then we consider the class of order-preserving functions between partially ordered sets, and establish a similar explicit classification for this function class.
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arxiv:1003.2192
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We consider the AdS_4 x CP^3 IIA superstring sigma-model in the background of the "spinning string" classical solution, which possesses two Noether spins. In the limit when one of the spins is infinite there are massless excitations, which govern the infrared worldsheet properties of the model. We obtain a sigma-model of CP^3 with fermions, which describes the dynamics of these massless modes.
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arxiv:1003.2199
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Neutral hydrogen is ubiquitous, absorbing and emitting 21 cm radiation throughout much of the Universe's history. Active sources of perturbations, such as cosmic strings, would generate simultaneous perturbations in the distribution of neutral hydrogen and in the Cosmic Microwave Background (CMB) radiation from recombination. Moving strings would create wakes leading to 21 cm brightness fluctuations, while also perturbing CMB light via the Gott-Kaiser-Stebbins effect. This would lead to spatial correlations between the 21 cm and CMB anisotropies. Passive sources, like inflationary perturbations, predict no cross correlations prior to the onset of reionization. Thus, observation of any cross correlation between CMB and 21 cm radiation from dark ages would constitute evidence for new physics. We calculate the cosmic string induced correlations between CMB and 21 cm and evaluate their observability.
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arxiv:1003.2214
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In this paper, we present smooth examples of degenerate hyperbolic and mixed type Monge-Ampere equations in the plane, which do not admit a local C^3 solution.
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arxiv:1003.2241
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In this article we evaluate the statistical evidence that a population of students learn about the sub-game perfect Nash equilibrium of the centipede game via repeated play of the game. This is done by formulating a model in which a player's error in assessing the utility of decisions changes as they gain experience with the game. We first estimate parameters in a statistical model where the probabilities of choices of the players are given by a Quantal Response Equilibrium (QRE) (McKelvey and Palfrey, 1995, 1996, 1998), but are allowed to change with repeated play. This model gives a better fit to the data than similar models previously considered. However, substantial correlation of outcomes of games having a common player suggests that a statistical model that captures within-subject correlation is more appropriate. Thus we then estimate parameters in a model which allows for within-player correlation of decisions and rates of learning. Through out the paper we also consider and compare the use of randomization tests and posterior predictive tests in the context of exploratory and confirmatory data analyses.
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arxiv:1003.2253
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We show that the carrier-mediated exchange interaction, the so-called RKKY coupling, between two magnetic impurity moments in graphene is significantly modified in the presence of electron-electron interactions. Using the mean-field approximation of the Hubbard-$U$ model we show that the $(1+\cos(2{\bf k}_D\cdot {\bf R})$-oscillations present in the bulk for non-interacting electrons disappear and the power-law decay becomes more long ranged with increasing electron interactions. In zigzag graphene nanoribbons the effects are even larger with any finite $U$ rendering the long-distance RKKY coupling distance independent. Comparing our mean-field results with first-principles results we also extract a surprisingly large value of $U$ indicating that graphene is very close to an antiferromagnetic instability.
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arxiv:1003.2271
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We investigate the equilibrium of a fluid in contact with a solid boundary through a density-functional theory. Depending on the conditions, the fluid can be in one phase, gas or liquid, or two phases, while the wall induces an external field acting on the fluid particles. We first examine the case of a liquid film in contact with the wall. We construct bifurcation diagrams for the film thickness as a function of the chemical potential. At a specific value of the chemical potential, two equally stable films, a thin one and a thick one, can coexist. As saturation is approached, the thickness of the thick film tends to infinity. This allows the construction of a liquid-gas interface that forms a well defined contact angle with the wall.
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arxiv:1003.2302
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We construct a generalized Witten genus for spin$^c$ manifolds, which takes values in level 1 modular forms with integral Fourier expansion on a class of spin$^c$ manifolds called string$^c$ manifolds. We also construct a mod 2 analogue of the Witten genus for $8k+2$ dimensional spin manifolds. The Landweber-Stong type vanishing theorems are proven for the generalized Witten genus and the mod 2 Witten genus on string$^c$ and string (generalized) complete intersections in (product of) complex projective spaces respectively.
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arxiv:1003.2325
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Star clusters are studied widely both as benchmarks for stellar evolution models and in their own right. Cluster age and mass distributions within galaxies are probes of star formation histories, and of cluster formation and disruption processes. The vast majority of clusters in the Universe is small, and it is well known that the integrated fluxes and colors have broad probability distributions, due to small numbers of bright stars. This paper goes beyond the description of predicted probability distributions, and presents results of the analysis of cluster energy distributions in an explicitly stochastic context. The method developed is Bayesian. It provides posterior probability distributions in the age-mass-extinction space, using multi-wavelength photometric observations and a large collection of Monte-Carlo simulations of clusters of finite stellar masses. Both UBVI and UBVIK datasets are considered, and the study conducted in this paper is restricted to the solar metallicity. We first reassess and explain errors arising from the use of standard analysis methods, which are based on continuous population synthesis models: systematic errors on ages and random errors on masses are large, while systematic errors on masses tend to be smaller. The age-mass distributions obtained after analysis of a synthetic sample are very similar to those found for real galaxies in the literature. The Bayesian approach on the other hand, is very successful in recovering the input ages and masses. Taking stochastic effects into account is important, more important for instance than the choice of adding or removing near-IR data in many cases. We found no immediately obvious reason to reject priors inspired by previous (standard) analyses of cluster populations in galaxies, i.e. cluster distributions that scale with mass as M^-2 and are uniform on a logarithmic age scale.
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arxiv:1003.2334
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