ShantanuT01/DACTYL-Pretraining huggingface dataset:
We use N-body simulations to study the velocity bias of dark matter halos, the difference in the velocity fields of dark matter and halos, in a flat low- density LCDM model. The high force, 2kpc/h, and mass, 10^9Msun/h, resolution allows dark matter halos to survive in very dense environments of groups and clusters making it possible to use halos as galaxy tracers. We find that the velocity bias pvb measured as a ratio of pairwise velocities of the halos to that of the dark matter evolves with time and depends on scale. At high redshifts (z ~5) halos move generally faster than the dark matter almost on all scales: pvb(r)~1.2, r>0.5Mpc/h. At later moments the bias decreases and gets below unity on scales less than r=5Mpc/h: pvb(r)~(0.6-0.8) at z=0. We find that the evolution of the pairwise velocity bias follows and probably is defined by the spatial antibias of the dark matter halos at small scales. One-point velocity bias b_v, defined as the ratio of the rms velocities of halos and dark matter, provides a more direct measure of the difference in velocities because it is less sensitive to the spatial bias. We analyze b_v in clusters of galaxies and find that halos are ``hotter'' than the dark matter: b_v=(1.2-1.3) for r=(0.2-0.8)r_vir, where r_vir is the virial radius. At larger radii, b_v decreases and approaches unity at r=(1-2)r_vir. We argue that dynamical friction may be responsible for this small positive velocity bias b_v>1 found in the central parts of clusters. We do not find significant difference in the velocity anisotropy of halos and the dark matter. The dark matter the velocity anisotropy can be approximated as beta(x)=0.15 +2x/(x^2+4), where x is measured in units of the virial radius.
Recently, the design study `Einstein gravitational wave Telescope' (ET) has been funded within the European FP7 framework. The ambitious goal of this project is to provide a conceptual design of a detector with a hundred times better sensitivity than currently operating instruments. It is expected that this will require the development and implementation of new technologies, which go beyond the concepts employed for the first and second detector generations. However, it is a very interesting and educational exercise to imagine a Michelson interferometer in which conventional technologies have been pushed to - or maybe beyond - their limits to reach the envisaged sensitivity for the Einstein Telescope. In this document we present a first sketchy analysis of what modifications and improvements are necessary to go, step-by-step, from second generation gravitational wave detectors to the Einstein Telescope.
We show that Fay's trisecant identity follows from the A_{infinity}-constraint between certain triple Massey products in the derived category of coherent sheaves on a curve. We also deduce the matrix analogue of this identity that can be conveniently formulated using quasideterminants of matrices with non-commuting entries. On the other hand, looking at more special triple Massey products we derive a formula for the tangent line to a canonically embedded curve at a given point.
Radio loud Active Galactic Nuclei are episodic in nature, cycling through periods of activity and quiescence. In this work we investigate the duty cycle of the radio galaxy B2~0258+35, which was previously suggested to be a restarted radio galaxy based on its morphology. The radio source consists of a pair of kpc-scale jets embedded in two large-scale lobes (~240 kpc) with relaxed shape and very low surface brightness, which resemble remnants of a past AGN activity. We have combined new LOFAR data at 145 MHz and new SRT data at 6600 MHz with available WSRT data at 1400 MHz to investigate the spectral properties of the outer lobes and derive their age. Interestingly, the spectrum of both the outer Northern and Southern lobes is not ultra-steep as expected for an old ageing plasma with spectral index values equal to $\rm \alpha_{1400}^{145}=0.48\pm0.11$ and $\rm \alpha_{6600}^{1400}=0.69\pm0.20$ in the outer Northern lobe, and $\rm \alpha_{1400}^{145}=0.73\pm0.07$ in the outer Southern lobe. Moreover, despite the wide frequency coverage available for the outer Northern lobe (145-6600~MHz), we do not identify a significant spectral curvature (SPC$\simeq$0.2$\pm0.2$). While mechanisms such as in-situ particle reacceleration, mixing or compression can temporarily play a role in preventing the spectrum from steepening, in no case seem the outer lobes to be compatible with being very old remnants of past activity as previously suggested (with age $\gtrsim$ 80 Myr). We conclude that either the large-scale lobes are still fuelled by the nuclear engine or the jets have switched off no more than a few tens of Myr ago. Our study shows the importance of combining morphological and spectral properties to reliably classify the evolutionary stage of low surface brightness, diffuse emission that low frequency observations are revealing around a growing number of radio sources.
Pedestrian analysis plays a vital role in intelligent video surveillance and is a key component for security-centric computer vision systems. Despite that the convolutional neural networks are remarkable in learning discriminative features from images, the learning of comprehensive features of pedestrians for fine-grained tasks remains an open problem. In this study, we propose a new attention-based deep neural network, named as HydraPlus-Net (HP-net), that multi-directionally feeds the multi-level attention maps to different feature layers. The attentive deep features learned from the proposed HP-net bring unique advantages: (1) the model is capable of capturing multiple attentions from low-level to semantic-level, and (2) it explores the multi-scale selectiveness of attentive features to enrich the final feature representations for a pedestrian image. We demonstrate the effectiveness and generality of the proposed HP-net for pedestrian analysis on two tasks, i.e. pedestrian attribute recognition and person re-identification. Intensive experimental results have been provided to prove that the HP-net outperforms the state-of-the-art methods on various datasets.
We present an explicit numerical method to obtain the Cartan-Khaneja-Glaser decomposition of a general element G of SU(2^N) in terms of its `Cartan' and `non-Cartan' components. This effectively factors G in terms of group elements that belong in SU(2^n) with n<N, a procedure that can be iterated down to n=2. We show that every step reduces to solving the zeros of a matrix polynomial, obtained by truncation of the Baker-Campbell-Hausdorff formula, numerically. All computational tasks involved are straightforward and the overall truncation errors are well under control.
In this article we use a criterion for the integrability of paths of one-dimensional diffusion processes from which we derive new insights on allelic fixation in several situations. This well known criterion involves a simple necessary and sufficient condition based on scale function and speed measure. We provide a new simple proof for this result and also obtain explicit bounds for the moments of such integrals. We also extend this criterion to non-homogeneous processes by use of Girsanov's transform. We apply our results to multi-type population dynamics: using the criterion with appropriate time changes, we characterize the behavior of proportions of each type before population extinction in different situations.
Cosmological models with an inhomogeneous viscous dark fluid, coupled with dark matter in the Friedmann- Robertson-Walker (FRW) flat universe, are considered. The influence of thermal effects caused by Hawking radiation on the visible horizon is studied, in connection with the classified type I and type III singularities which are known to occur within a finite amount of time. Allowance of thermal effects implies that a transition to a type II singularity can take place, in a finite time. We take into account a bulk viscosity of the dark fluid, observing the equation of state in the case of radiation, and find that there is a qualitative change in the singular universe of type I: it may pass into a singularity of type III, or it may avoid the singularity at all.
The notion of black-hole entropy was introduced by Jacob Bekenstein in 1972. During past 45 years this subject was in the center of interests of the modern theoretical physics. In this paper we briefly discuss "puzzles" of the black-hole physics, connected with their entropy. We also demonstrate that when the standard energy conditions are violated entropy associated with the event horizon can have quite unexpected behavior.
Gravitation as a fundamental interaction that governs all phenomena at large and very small scales, but still not well understood at a quantum level, is a cardinal missing link in unification of all physical interactions. Discovery of the present acceleration of the Universe, the dark matter and dark energy problems are also a great challenge to modern physics, which may lead to a new revolution in it. Integrable multidimensional models of gravitation and cosmology make up one of the proper approaches to studying basic issues and strong field objects, the early and present Universe and black hole (BH) physics in particular. Our main results within this approach are described for both cosmology and BH physics. Problems of the absolute G measurements and its possible time and range variations are reflections of the unification problem. The choice, nature, classification and precision of determination of the fundamental physical constants as well as their role in a transition, expected in 2011, to new definitions of the main SI units, supposed to be based on fundamental physical constants and stable quantum phenomena, are described. The problem of temporal variations of constants is also discussed, temporal and spatial variations of G in particular. A need for further absolute measurements of G, its possible range and time variations is pointed out. The multipurpose space project SEE is briefly described, aimed at measuring G and its stability in space and time, with precision 3-4 orders better than at present. It may answer many important questions posed by gravitation, cosmology and unified theories. A project of a laboratory experiment for testing possible deviations from the Newton law is also presented.
We analyze and compute, within a number of standard model (SM) extensions, the cross sections $\sigma_{A\to VV'}$ for the production of a heavy neutral pseudoscalar Higgs boson/spin-zero resonance at the LHC and its subsequent decays into electroweak gauge bosons. For comparison we calculate also the corresponding cross sections for a heavy scalar. The SM extensions we consider include a type-II two-Higgs doublet model (2HDM), a 2HDM with 4 chiral fermion generations, the minimal supersymmetric extension of the SM (MSSM), and top-color assisted technicolour models. Presently available phenomenological constraints on the parameters of these models are taken into account. We find that, with the exception of the MSSM, these models permit the LHC cross sections $\sigma_{A\to VV'}$ to be of observable size. That is, a pseudoscalar resonance may be observable, if it exists, at the LHC in its decays into electroweak gauge bosons, in particular in $WW$ and $\gamma \gamma$ final states.
We analyze orbital solutions for 48 massive multiple-star systems in the Cygnus OB2 Association, 23 of which are newly presented here, to find that the observed distribution of orbital periods is approximately uniform in log P for P<45 d, but it is not scale-free. Inflections in the cumulative distribution near 6 d, 14, d, and 45 d, suggest key physical scales of ~0.2, ~0.4, and ~1 A.U. where yet-to-be-identified phenomena create distinct features. No single power law provides a statistically compelling prescription, but if features are ignored, a power law with exponent beta = -0.22 provides a crude approximation over P=1.4 -- 2000 d, as does a piece-wise linear function with a break near 45 d. The cumulative period distribution flattens at P > 45 d, even after correction for completeness, indicating either a lower binary fraction or a shift toward low-mass companions. A high degree of similarity (91% likelihood) between the Cyg OB2 period distribution and that of other surveys suggests that the binary properties at P<25 d are determined by local physics of disk/clump fragmentation and are relatively insensitive to environmental and evolutionary factors. Fully 30% of the unbiased parent sample is a binary with period P < 45 d. Completeness corrections imply a binary fraction near 55% for P < 5000 d. The observed distribution of mass ratios 0.2<q<1 is consistent with uniform, while the observed distribution of eccentricities 0.1<e<0.6 is consistent with uniform plus an excess of e ~ 0 systems. We identify six stars, all supergiants, that exhibit aperiodic velocity variations of ~30 km/s attributed to atmospheric fluctuations.
This is the second in a sequence of articles, in which we explore moduli stacks of global G-shtukas, the function field analogs for Shimura varieties. Here G is a flat affine group scheme of finite type over a smooth projective curve C over a finite field. Global G-shtukas are generalizations of Drinfeld shtukas and analogs of abelian varieties with additional structure. We prove that the moduli stacks of global G-shtukas are algebraic Deligne-Mumford stacks separated and locally of finite type. They generalize various moduli spaces used by different authors to prove instances of the Langlands program over function fields. In the first article we explained the relation between global G-shtukas and local P-shtukas, which are the function field analogs of p-divisible groups. Here P is the base change of G to the complete local ring at a point of C. When P is smooth with connected reductive generic fiber we proved the existence of Rapoport-Zink spaces for local P-shtukas. In the present article we use these spaces to (partly) uniformize the moduli stacks of global G-shtukas for smooth G with connected fibers and reductive generic fiber. This is our main result. It has applications to the analog of the Langlands-Rapoport conjecture for our moduli stacks.
The metal-insulator transition of the Magneli phase Ti4O7 is studied by means of augmented spherical wave (ASW) electronic structure calculations as based on density functional theory and the local density approximation. The results show that the metal-insulator transition arises from a complex interplay of charge order, orbital order, and singlet formation of those Ti 3d states which mediate metal-metal bonding inside the four-atom chains characteristic of the material. Ti4O7 thus combines important aspects of Fe3O4 and VO2. While the charge ordering closely resembles that observed at the Verwey transition, the orbital order and singlet formation appear to be identical to the mechanisms driving the metal-insulator transition of vanadium dioxide.
We review the definition by Perlick of standard clocks in a Weyl geometry and show how a congruence of clocks can be used to fix the conformal gauge in the EPS framework. Examples are discussed in details.
The degenerate de Gennes-Cahn-Hilliard (dGCH) equation is a model for phase separation which may more closely approximate surface diffusion than others in the limit when the thickness of the transition layer approaches zero. As a first step to understand the limiting behavior, in this paper we study the $\Gamma$--limit of the dGCH energy. We find that its $\Gamma$--limit is a constant multiple of the interface area, where the constant is determined by the de Gennes coefficient together with the double well potential. In contrast, the transition layer profile is solely determined by the double well potential.
In Brans Dicke theory of gravity, from the nature of the scalar field-potential considered, the dark energy, dark matter, radiation densities predicted by different observations and the closedness of the universe considered, we can fix our $\omega_{BD}$, the Brans Dicke parameter, keeping only the thing in mind that from different solar system constrains it must be greater than $5\times 10^{5}$. Once we have a value, satisfying the required lower boundary, in our hand we proceed for setting unknown parameters of the different dark energy models' EoS parameter. In this paper we work with three well known red shift parametrizations of dark energy EoS. To constrain their free parameters for Brans Dicke theory of gravity we take twelve point red shift vs Hubble's parameter data and perform $\chi^{2}$ test. We present the observational data analysis mechanism for Stern, Stern+BAO and Stern+BAO+CMB observations. Minimising $\chi^2$, we obtain the best fit values and draw different confidence contours. We analyze the contours physically. Also we examine the best fit of distance modulus for our theoretical models and the Supernovae Type Ia Union2 sample. For Brans Dicke theory of gravity the difference from the mainstream confidence contouring method of data analysis id that the confidence contours evolved are not at all closed contours like a circle or a ellipse. Rather they are found to be open contours allowing the free parameters to float inside a infinite region of parameter space. However, negative EoSs are likely to evolve from the best fit values.
The Ensemble Kalman filter and Ensemble square root filters are data assimilation methods used to combine high dimensional nonlinear models with observed data. These methods have proved to be indispensable tools in science and engineering as they allow computationally cheap, low dimensional ensemble state approximation for extremely high dimensional turbulent forecast models. From a theoretical perspective, these methods are poorly understood, with the exception of a recently established but still incomplete nonlinear stability theory. Moreover, recent numerical and theoretical studies of catastrophic filter divergence have indicated that stability is a genuine mathematical concern and can not be taken for granted in implementation. In this article we propose a simple modification of ensemble based methods which resolves these stability issues entirely. The method involves a new type of adaptive covariance inflation, which comes with minimal additional cost. We develop a complete nonlinear stability theory for the adaptive method, yielding Lyapunov functions and geometric ergodicity under weak assumptions. We present numerical evidence which suggests the adaptive methods have improved accuracy over standard methods and completely eliminate catastrophic filter divergence. This enhanced stability allows for the use of extremely cheap, unstable forecast integrators, which would otherwise lead to widespread filter malfunction.
We extend White's classification of empty tetrahedra to the complete classification of lattice $3$-polytopes with five lattice points, showing that, apart from infinitely many of width one, there are exactly nine equivalence classes of them with width two and none of larger width. We also prove that, for each $n\in \mathbb{N}$, there is only a finite number of (classes of) lattice $3$-polytopes with $n$ lattice points and of width larger than one. This implies that extending the present classification to larger sizes makes sense, which is the topic of subsequent papers of ours.
We apply the similarity renormalization group (SRG) approach to evolve a nucleon-nucleon ($NN$) interaction in leading-order (LO) chiral effective field theory (ChEFT), renormalized within the framework of the subtracted kernel method (SKM). We derive a fixed-point interaction and show the renormalization group (RG) invariance in the SKM approach. We also compare the evolution of $NN$ potentials with the subtraction scale through a SKM RG equation in the form of a non-relativistic Callan-Symanzik (NRCS) equation and the evolution with the similarity cutoff through the SRG transformation.
R. Doney identifies a striking factorization of the arc-sine law in terms of the suprema of two independent stable processes of the same index by an elegant random walks approximation. In this paper, we provide an alternative proof and a generalization of this factorization based on the theory recently developed for the exponential functional of L\'evy processes. As a by-product, we provide some interesting distributional properties for these variables and also some new examples of the factorization of the arc-sine law.
We first introduce and derive some basic properties of a two-parameters family of one-sided Levy processes. Their Laplace exponents are given in terms of the Pochhammer symbol. This family includes, in a limit case, the family of Brownian motion with drifts. Then, we proceed by computing the density of the law of the exponential functional associated to some elements of this family (and their dual) and some transformations of these elements. These densities are expressed in terms of the Wright hypergeometric functions. By means of probabilistic arguments, we derive some interesting properties enjoyed by these functions. On the way we also characterize explicitly the density of the semi-groups of the family of self-similar continuous state branching processes with immigration.
It has recently been observed that the normalization of a one-dimensional out-of-equilibrium model, the Asymmetric Exclusion Process (ASEP) with random sequential dynamics, is exactly equivalent to the partition function of a two-dimensional lattice path model of one-transit walks, or equivalently Dyck paths. This explains the applicability of the Lee-Yang theory of partition function zeros to the ASEP normalization.   In this paper we consider the exact solution of the parallel-update ASEP, a special case of the Nagel-Schreckenberg model for traffic flow, in which the ASEP phase transitions can be intepreted as jamming transitions, and find that Lee-Yang theory still applies. We show that the parallel-update ASEP normalization can be expressed as one of several equivalent two-dimensional lattice path problems involving weighted Dyck or Motzkin paths. We introduce the notion of thermodynamic equivalence for such paths and show that the robustness of the general form of the ASEP phase diagram under various update dynamics is a consequence of this thermodynamic equivalence.
We prove a result on linear forms related to Peres-Schlag's theorem on badly approximable numbers with respect to lacunary sequences.
During the last 50 years we have been witness of an extraordinary revolution in the knowledge and understanding of our star thanks to the development of Helioseismology, the study of solar oscillations. Similar to what happens on the Earth during earthquakes, the interior of the Sun is continuously pervaded by seismic waves which produce small oscillations on the photosphere. These oscillations bring the signature of several processes which happen in the interior of the solar structure and the seismic frequencies of the oscillation modes detected on the solar surface are directly related to physical parameters of the internal layers crossed by the seismic waves. The study of oscillations represents, then, the only method to infer directly the internal structure and dynamics of the Sun. This article will present the general characteristics of solar oscillations, the main important results and the advances obtained in stellar physics thanks to the methods of Helioseismology.
This survey is an invitation to recent developments in higher dimensional birational geometry.