ShantanuT01/DACTYL-Pretraining huggingface dataset:
We derive the self-consistent harmonic approximation for the $2D$ XY model with non-local interactions. The resulting equation for the variational couplings holds for any form of the spin-spin coupling as well as for any dimension. Our analysis is then specialized to power-law couplings decaying with the distance $r$ as $\propto 1/r^{2+\sigma}$ in order to investigate the robustness, at finite $\sigma$, of the Berezinskii-Kosterlitz-Thouless (BKT) transition, which occurs in the short-range limit $\sigma \to \infty$. We propose an ansatz for the functional form of the variational couplings and show that for any $\sigma>2$ the BKT mechanism occurs. The present investigation provides an upper bound for the lower critical threshold $\sigma^\ast=2$, above which the traditional BKT transition persists in spite of the LR couplings.
We construct plane models of the modular curve $X_H(\ell)$, and use their explicit equations to compute Galois representations associated to modular forms for values of $\ell$ that are significantly higher than in prior works.
We argue that eleven dimensional supergravity can be described by a non-linear realisation based on the group E_{11}. This requires a formulation of eleven dimensional supergravity in which the gravitational degrees of freedom are described by two fields which are related by duality. We show the existence of such a description of gravity.
We study the spreading of viscous drops on a solid substrate, taking into account the effects of thermal fluctuations in the fluid momentum. A nonlinear stochastic lubrication equation is derived, and studied using numerical simulations and scaling analysis. We show that asymptotically spreading drops admit self-similar shapes, whose average radii can increase at rates much faster than these predicted by Tanner's law. We discuss the physical realizability of our results for thin molecular and complex fluid films, and predict that such phenomenon can in principal be observed in various flow geometries.
We propose two efficient approximations to standard convolutional neural networks: Binary-Weight-Networks and XNOR-Networks. In Binary-Weight-Networks, the filters are approximated with binary values resulting in 32x memory saving. In XNOR-Networks, both the filters and the input to convolutional layers are binary. XNOR-Networks approximate convolutions using primarily binary operations. This results in 58x faster convolutional operations and 32x memory savings. XNOR-Nets offer the possibility of running state-of-the-art networks on CPUs (rather than GPUs) in real-time. Our binary networks are simple, accurate, efficient, and work on challenging visual tasks. We evaluate our approach on the ImageNet classification task. The classification accuracy with a Binary-Weight-Network version of AlexNet is only 2.9% less than the full-precision AlexNet (in top-1 measure). We compare our method with recent network binarization methods, BinaryConnect and BinaryNets, and outperform these methods by large margins on ImageNet, more than 16% in top-1 accuracy.
Gait recognition is a promising video-based biometric for identifying individual walking patterns from a long distance. At present, most gait recognition methods use silhouette images to represent a person in each frame. However, silhouette images can lose fine-grained spatial information, and most papers do not regard how to obtain these silhouettes in complex scenes. Furthermore, silhouette images contain not only gait features but also other visual clues that can be recognized. Hence these approaches can not be considered as strict gait recognition.   We leverage recent advances in human pose estimation to estimate robust skeleton poses directly from RGB images to bring back model-based gait recognition with a cleaner representation of gait. Thus, we propose GaitGraph that combines skeleton poses with Graph Convolutional Network (GCN) to obtain a modern model-based approach for gait recognition. The main advantages are a cleaner, more elegant extraction of the gait features and the ability to incorporate powerful spatio-temporal modeling using GCN. Experiments on the popular CASIA-B gait dataset show that our method archives state-of-the-art performance in model-based gait recognition.   The code and models are publicly available.
We report a systematic nuclear magnetic resonance investigation of the $^{23}$Na spin-lattice relaxation rate, $1/T_1$, in sodium loaded low-silica X (LSX) zeolite, Na$_n$/Na$_{12}$-LSX, for various loading levels of sodium atoms $n$ across the metal-to-insulator crossover. For high loading levels of $n \geq 14.2$, $1/T_1T$ shows nearly temperature-independent behavior between 10 K and 25 K consistent with the Korringa relaxation mechanism and metallic ground state. As the loading levels decrease below $n \leq 11.6$, the extracted density of states (DOS) at the Fermi level sharply decreases, although a residual DOS at Fermi level is still observed even in samples that lack the metallic Drude-peak in the optical reflectance. The observed crossover is a result of a complex loading-level dependence of electric potential felt by the electrons confined to zeolite cages, where the electronic correlations and disorder both play an important role.
We review the status of quantising (non-abelian) gauge theories using different versions of a Hamiltonian formulation corresponding to Dirac's instant and front form of dynamics, respectively. In order to control infrared divergences we work in a finite spatial volume, chosing a torus geometry for convenience. We focus on the determination of the physical configuration space of gauge invariant variables via gauge fixing. This naturally leads us to the issue of the Gribov problem. We discuss it for different gauge choices, in particular finite volume modifications of the axial gauge. Conventional and light-front quantisation are compared and the differences pointed out.
Motivated by an experimental report of iridate superlattices, we performed first-principle electronic structure calculations for SrIrO$_3$/SrTiO$_3$. Heterostructuring causes SrIrO$_3$ to become Sr$_2$IrO$_4$-like, and the system has the well-defined $j_{\rm eff}$=1/2 states near the Fermi level as well as canted antiferromagnetic order within the quasi-two-dimensional IrO$_2$ plane. In response to a larger tensile strain, the band gap is increased due to the resulting increase in bond length and the bandwidth reduction. The ground state magnetic properties are discussed in comparison to the metastable collinear antiferromagnetic state. Our work sheds new light for understanding the recent experimental results on the iridate heterostructures.
We consider the generalized parabolic Anderson equation (gPAM) in 2 dimensions with periodic boundary. This is an example of a singular semilinear stochastic partial differential equations, solutions of which require renormalization and have only be understood recently via Hairer's regularity structures and, in some cases equivalently, paracontrollled distributions due to Gubinelli, Imkeller and Perkowski. In the present paper we describe the law of gPAM, by establishing a Stroock{Varadhan type support theorem in suitable Holder{Besov spaces.
The Blanco Cosmology Survey (BCS) is a 60 night imaging survey of $\sim$80 deg$^2$ of the southern sky located in two fields: ($\alpha$,$\delta$)= (5 hr, $-55^{\circ}$) and (23 hr, $-55^{\circ}$). The survey was carried out between 2005 and 2008 in $griz$ bands with the Mosaic2 imager on the Blanco 4m telescope. The primary aim of the BCS survey is to provide the data required to optically confirm and measure photometric redshifts for Sunyaev-Zel'dovich effect selected galaxy clusters from the South Pole Telescope and the Atacama Cosmology Telescope. We process and calibrate the BCS data, carrying out PSF corrected model fitting photometry for all detected objects. The median 10$\sigma$ galaxy (point source) depths over the survey in $griz$ are approximately 23.3 (23.9), 23.4 (24.0), 23.0 (23.6) and 21.3 (22.1), respectively. The astrometric accuracy relative to the USNO-B survey is $\sim45$ milli-arcsec. We calibrate our absolute photometry using the stellar locus in $grizJ$ bands, and thus our absolute photometric scale derives from 2MASS which has $\sim2$% accuracy. The scatter of stars about the stellar locus indicates a systematics floor in the relative stellar photometric scatter in $griz$ that is $\sim$1.9%, $\sim$2.2%, $\sim$2.7% and$\sim$2.7%, respectively. A simple cut in the AstrOmatic star-galaxy classifier {\tt spread\_model} produces a star sample with good spatial uniformity. We use the resulting photometric catalogs to calibrate photometric redshifts for the survey and demonstrate scatter $\delta z/(1+z)=0.054$ with an outlier fraction $\eta<5$% to $z\sim1$. We highlight some selected science results to date and provide a full description of the released data products.
In this paper, we propose a generic neural-based hair rendering pipeline that can synthesize photo-realistic images from virtual 3D hair models. Unlike existing supervised translation methods that require model-level similarity to preserve consistent structure representation for both real images and fake renderings, our method adopts an unsupervised solution to work on arbitrary hair models. The key component of our method is a shared latent space to encode appearance-invariant structure information of both domains, which generates realistic renderings conditioned by extra appearance inputs. This is achieved by domain-specific pre-disentangled structure representation, partially shared domain encoder layers and a structure discriminator. We also propose a simple yet effective temporal conditioning method to enforce consistency for video sequence generation. We demonstrate the superiority of our method by testing it on a large number of portraits and comparing it with alternative baselines and state-of-the-art unsupervised image translation methods.
We show how two level atoms can be used to determine the local time dependent spectrum. The method is applied to a one dimensional cavity. The spectrum obtained is compared with the mode spectrum determined using spatially filtered second order correlation functions. The spectra obtained using two level atoms give identical results with the mode spectrum. One benefit of the method is that only one time averages are needed. It is also more closely related to a realistic measurement scheme than any other definition of a time dependent spectrum.
In previous galactic dynamo theories of the origin of the magnetic field in our galaxy, the subject of flux-freezing has been omitted. As a consequence, the equation of mass flow has generally also been omitted, particularly in the halo where the galactic gravitational field will operate on the mass flow. In this paper it has been shown that this neglect could have serious consequences for the results obtained from those galactic dynamo simulations that include the halo. A modification of these dynamo theories is proposed which involves the expulsion of very small bits of the magnetic field lines, rather than the wholesale expulsion of the complete magnetic lines encapsulated in the previous theories. This expulsion is accomplished by a spike instability that arises from superbubbles, when they break out of the galactic disc and their shell fragment. This leads to a {\it cut } in the lines of force that still remain in the disc. Subsequently, normal disc turbulence rotates the {\it cut} lines and thus dissipates their mean flux removing them from a role in the dynamo theory. This new process takes a length of time comparable, but a little longer than the previous growth time of the disc dynamo, but avoids the previous difficulties associated with flux-freezing and flux expulsion.
Let $\mathcal{H}$ be a hypergraph with $n$ vertices. Suppose that $d_1,d_2,\ldots,d_n$ are degrees of the vertices of $\mathcal{H}$. The $t$-th graph entropy based on degrees of $\mathcal{H}$ is defined as $$ I_d^t(\mathcal{H}) =-\sum_{i=1}^{n}\left(\frac{d_i^{t}}{\sum_{j=1}^{n}d_j^{t}}\log\frac{d_i^{t}}{\sum_{j=1}^{n}d_j^{t}}\right) =\log\left(\sum_{i=1}^{n}d_i^{t}\right)-\sum_{i=1}^{n}\left(\frac{d_i^{t}}{\sum_{j=1}^{n}d_j^{t}}\log d_i^{t}\right), $$ where $t$ is a real number and the logarithm is taken to the base two. In this paper we obtain upper and lower bounds of $I_d^t(\mathcal{H})$ for $t=1$, when $\mathcal{H}$ is among all uniform supertrees, unicyclic uniform hypergraphs and bicyclic uniform hypergraphs, respectively.
Two recent papers (Renou et al., arXiv:2101.10873, and Chen et al., arXiv:2103.08123) have indicated that complex numbers are necessary for quantum theory. This short note is a comment on their result.
The CoRoT satellite has announced its fourth transiting planet (Aigrain et al. 2008) with space photometry. We describe and analyse complementary observations of this system performed to establish the planetary nature of the transiting body and to estimate the fundamental parameters of the planet and its parent star. We have analysed high precision radial-velocity data, ground-based photometry, and high signal-to-noise ratio spectroscopy. The parent star CoRoT-Exo-4 (2MASS 06484671-0040219) is a late F-type star of mass of 1.16 Msun and radius of 1.17 Rsun. The planet has a circular orbit with a period of 9.20205d. The planet radius is 1.19 Rjup and the mass is 0.72 Mjup. It is a gas-giant planet with a ''normal'' internal structure of mainly H and He. CoRoT-Exo-4b has the second longest period of the known transiting planets. It is an important discovery since it occupies an empty area in the mass-period diagram of transiting exoplanets.
We propose a one-dimensional (1D) diffusion equation (heat equation) for systems in which the diffusion constant (thermal diffusivity) varies alternately with a spatial period $a$. We solve the time evolution of the field (temperature) profile from a given initial distribution, by diagonalising the Hamiltonian, i.e., the Laplacian with alternating diffusion constants, and expanding the temperature profile by its eigenstates. We show that there are basically phases with or without edge states. The edge states affect the heat conduction around heat baths. In particular, rapid heat transfer to heat baths would be observed in a short time regime, which is estimated to be $t<10^{-2}$s for $a\sim 10^{-3}$m system and $t< 1$s for $a\sim 10^{-2}$m system composed of two kinds of familiar metals such as titanium, zirconium and aluminium, gold, etc. We also discuss the effective lattice model which simplifies the calculation of edge states up to high energy. It is suggested that these high energy edge states also contribute to very rapid heat conduction in a very short time regime.
Let $\{X_i(t),t\ge0\}, 1\le i\le n$ be independent copies of a random process $\{X(t), t\ge0\}$. For a given positive constant $u$, define the set of $r$th conjunctions $C_r(u):=\{t\in[0,1]: X_{r:n}(t)>u\}$ with $ X_{r:n}$ the $r$th largest order statistics of $X_i, 1\le i\le n$. In numerical applications such as brain mapping and digital communication systems, of interest is the approximation of $p_r(u)=\mathbb P\{C_r(u)\neq\phi\}$. Instead of stationary processes dealt with by D\c{e}bicki et al. (2014), we consider in this paper $X$ a self-similar $\mathbb R$-valued process with $P$-continuous sample paths. By imposing the Albin's conditions directly on $X$, we establish an exact asymptotic expansion of $p_r(u)$ as $u$ tends to infinity. As a by-product we derive the asymptotic tail behaviour of the mean sojourn time of $X_{r:n}$ over an increasing threshold. Finally, our findings are illustrated for the case that $X$ is a bi-fractional Brownian motion, a sub-fractional Brownian motion, and a generalized self-similar skew-Gaussian process.
In this paper we investigate the quantum Brownian motion of a massive scalar point particle induced by the FRW spacetime in the presence of a linear topological defect named cosmic string. In addition, we also consider a flat boundary orthogonal to the defect to analyse its effect on the particle's motion. For both cases we found exact expressions for the renormalized mean square deviation of the particle velocity, the quantity that measures the induced Brownian motion, and obtain asymptotic expressions when the point particle is near and far away from the cosmic string and the boundary. Furthermore, in both cases, there appears divergencies in the mean square deviation of the particle velocity coming from a time interval that correspond to a round trip of the massive point particle between its position and the cosmic string/flat boundary. The number of divergencies depends upon the radial position of the particle and the parameter associated with the cosmic string in the case without boundary, and upon this parameter and the radial and $z$ positions of the particle in the case with boundary.
BiFeO3 thin films have been grown on Pt/Ti/SiO2/Si substrates with pulsed laser deposition using Au as the top electrode. The resistive switching property of the Au/BiFeO3/Pt stack has been significantly improved by carefully tuning the oxygen pressure during the growth, and a large switching ratio of ~4500 has been achieved. The deposition pressure modifies the concentration of oxygen vacancies and the rectifying behavior of the Au/BiFeO3 junction, and consequently influences the resistive switching behavior of the whole stack. The switching takes place homogeneously over the entire electrode, and shows a long-term retention.
Every word has a shape determined by its image under the Robinson-Schensted-Knuth correspondence. We show that when a word w contains a separable (i.e., 3142- and 2413-avoiding) permutation \sigma\ as a pattern, the shape of w contains the shape of \sigma. As an application, we exhibit lower bounds for the lengths of supersequences of sets containing separable permutations.
The problem of discontinuous functions and their representations in the form of Legendre polynomial series in quantum nuclear scattering theory is presented briefly. The problem is quite old yet not adequately explained in numerous Quantum Theory textbooks and sometimes not correctly understood by physicists. This problem might be quite important in interpretation and analyses of nuclear elastic scattering data and so requires to be stated in a more detailed and clear way.
Pinning and depinning of wavefronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators with nearest-neighbor coupling and controlled by constant external forces. A theory of the depinning transition for these systems, including scaling laws and asymptotics of wavefronts, is presented and confirmed by numerical calculations.
We study the interplay between the isoscalar (T=0) and isovector (T=1) pairing correlations in N=Z odd-odd nuclei from 14N to 58Cu by using three-body model calculations. The strong spin-triplet T=0 pairing correlation dominates in the ground state of 14N, 18F, 30P, and 58Cu with the spin-parity J^{\pi}=1+, which can be well reproduced by the present calculations. The magnetic dipole and Gamow-Teller transitions are found to be strong in 18F and 42Sc as a manifestation of SU(4) symmetry in the spin-isospin space. We also discuss the spin-quadrupole transitions in these nuclei.
Previous claims of significant evidence for mirror-parity in the large-scale cosmic microwave background (CMB) data from the Wilkinson Microwave Anisotropy Probe (WMAP) experiment have been recently echoed in the first study of isotropy and statistics of CMB data from Planck. We revisit these claims with a careful analysis of the latest data available. We construct statistical estimators in both harmonic and pixel space, test them on simulated data with and without mirror-parity symmetry, apply different Galactic masks, and study the dependence of the results on arbitrary choices of free parameters. We confirm that the data exhibit evidence for odd mirror-parity at a significance which reaches as high as ~ 99 per cent C.L., under some circumstances. However, given the inherent biases in the pixel-based statistic and the dependence of both pixel and harmonic space statistics on the particular form of Galactic masking and other a-posteriori choices, we conclude that these results are not in significant tension with the predictions of the concordance cosmological model.
We use Monte Carlo approach to study the energetics of electrons accelerated in a pulsar polar gap. As energy-loss mechanisms we consider magnetic Compton scattering of thermal X-ray photons and curvature radiation. The results are compared with previous calculations which assumed that changes of electron energy occurred smoothly according to approximations for the average energy loss rate due to the Compton scattering. We confirm a general dependence of efficiency of electron energy losses due to inverse Compton mechanism on the temperature and size of a thermal polar cap and on the pulsar magnetic field. However, we show that trajectories of electrons in energy-altitude space as calculated in the smooth way do not always coincide with averaged Monte Carlo behaviour. In particular, for pulsars with high magnetic field strength ($B_{pc} > 3\times 10^{12}$ G) and low thermal polar cap temperatures ($T < 5\times 10^6$ K) final electron Lorentz factors computed with the two methods may differ by a few orders of magnitude. We discuss consequences for particular objects with identified thermal X-ray spectral components like Geminga, Vela, and PSR B1055-52.
A novel broad-band measurement method of the MI in thin films and ribbons is presented. It is based on the automated measurement of the reflection coefficient of a cell loaded with the sample. Illustrative results obtained with a permalloy multilayer thin film are presented and discussed.
In this article, we study the possibility of producing a Calabi-Yau threefold in positive characteristic which is a counter-example to Kodaira vanishing. The only known method to construct the counter-example is so called inductive method such as the Raynaud-Mukai construction or Russel construction. We consider Mukai's method and its modification. Finally, as an application of Shepherd-Barron vanishing theorem of Fano threefolds, we compute $H^1(X, H^{-1})$ for any ample line bundle $H$ on a Calabi-Yau threefold $X$ on which Kodaira vanishing fails.
The ultimate goal of multiferroic research is the development of new-generation non-volatile memory devices, the so-called magnetoelectric (ME) memories, where magnetic bits are controlled via electric fields without the application of electrical currents subject to dissipation. This low-power operation exploits the entanglement of the magnetization and the electric polarization coexisting in multiferroic materials. Here we demonstrate the optical readout of ME memory states in the antiferromagnetic (AFM) and antiferroelectric (AFE) LiCoPO$_4$, based on the strong absorption difference of THz radiation between its two types of ME domains. This unusual contrast is attributed to the dynamic ME effect of the spin-wave excitations, as confirmed by our microscopic model, which also captures the characteristics of the observed static ME effect. Our proof-of-principle study, demonstrating the control and the optical readout of ME domains in LiCoPO$_4$, lays down the foundation for future ME memory devices based on antiferroelectric-antiferromagnetic insulators.