ShantanuT01/DACTYL-Pretraining huggingface dataset:
It is a fact simple to establish that the mixing time of the simple random walk on a d-regular graph $G_n$ with n vertices is asymptotically bounded from below by $d/ ((d-2)\log (d-1))\log n$. Such a bound is obtained by comparing the walk on $G_n$ to the walk on the infinite $d$-regular tree. If one can map another infinite transitive graph onto $G_n$, then we can improve the strategy by using a comparison with the random walk on this transitive graph (instead of that of the regular tree), and we obtain a lower bound of the form $1/h \log n$, where $h$ is the entropy rate associated with the walk on the transitive graph. We call this the entropic lower bound. It was recently proved that in the case of the tree, this entropic lower bound is sharp when graphs have minimal spectral radius and thus that in that case the random walk exhibit cutoff at the entropic time. In this paper, we provide a generalization of the result by providing a sufficient condition on the spectra the random walks on $G_n$ under which the random walk exhibit cutoff at the entropic time. It applies notably to anisotropic random walks on random $d$-regular graphs and to random walks on random $n$-lifts of a base graph (including non-reversible walks).
Molecular dynamics (MD) simulations are employed to investigate the capillary fluctuations of steps on the surface of a model metal system. The fluctuation spectrum, characterized by the wave number ($k$) dependence of the mean squared capillary-wave amplitudes and associated relaxation times, is calculated for $\left<110\right>$ and $\left<112\right>$ steps on the $\{111\}$ surface of elemental copper near the melting temperature of the classical potential model considered. Step stiffnesses are derived from the MD results, yielding values from the largest system sizes of $(37\pm1) \, \mathrm{meV}/\mathring{\mathrm{A}}$ for the different line orientations, implying that the stiffness is isotropic within the statistical precision of the calculations. The fluctuation lifetimes are found to vary by approximately four orders of magnitude over the range of wave numbers investigated, displaying a $k$ dependence consistent with kinetics governed by step-edge mediated diffusion. The values for step stiffness derived from these simulations are compared to step free energies for the same system and temperature obtained in a recent MD-based thermodynamic-integration (TI) study [Freitas, Frolov, and Asta, Phys. Rev. B 95, 155444 (2017)]. Results from the capillary-fluctuation analysis and TI calculations yield statistically significant differences that are discussed within the framework of statistical-mechanical theories for configurational contributions to step free energies.
In 1984, Kelly and Oxley introduced the model of a random representable matroid $M[A_n]$ corresponding to a random matrix $A_n \in \mathbb{F}_q^{m(n) \times n}$, whose entries are drawn independently and uniformly from $\mathbb{F}_q$. Whereas properties such as rank, connectivity, and circuit size have been well-studied, forbidden minors have not yet been analyzed. Here, we investigate the asymptotic probability as $n \to \infty$ that a fixed $\mathbb{F}_q$-representable matroid $M$ is a minor of $M[A_n]$. (We always assume $m(n) \geq \text{rank}(M)$ for all sufficiently large $n$, otherwise $M$ can never be a minor of the corresponding $M[A_n]$.) When $M$ is free, we show that $M$ is asymptotically almost surely (a.a.s.) a minor of $M[A_n]$. When $M$ is not free, we show a phase transition: $M$ is a.a.s. a minor if $n - m(n) \to \infty$, but is a.a.s. not if $m(n) - n \to \infty$. In the more general settings of $m \leq n$ and $m > n$, we give lower and upper bounds, respectively, on both the asymptotic and non-asymptotic probability that $M$ is a minor of $M[A_n]$. The tools we develop to analyze matroid operations and minors of random matroids may be of independent interest.   Our results directly imply that $M[A_n]$ is a.a.s. not contained in any proper, minor-closed class $\mathcal{M}$ of $\mathbb{F}_q$-representable matroids, provided: (i) $n - m(n) \to \infty$, and (ii) $m(n)$ is at least the minimum rank of any $\mathbb{F}_q$-representable forbidden minor of $\mathcal{M}$, for all sufficiently large $n$. As an application, this shows that graphic matroids are a vanishing subset of linear matroids, in a sense made precise in the paper. Our results provide an approach for applying the rich theory around matroid minors to the less-studied field of random matroids.
We construct a theory for long-distance quantum communication based on sharing entanglement through a linear chain of $N$ elementary swapping segments of length~$L=Nl$ where $l$ is the length of each elementary swap setup. Entanglement swapping is achieved by linear optics, photon counting and post-selection, and we include effects due to multi-photon sources, transmission loss and detector inefficiencies and dark counts. Specifically we calculate the resultant four-mode state shared by the two parties at the two ends of the chain, and we derive the two-photon coincidence rate expected for this state and thereby the visibility of this long-range entangled state. The expression is a nested sum with each sum extending from zero to infinite photons, and we solve the case $N=2$ exactly for the ideal case (zero dark counts, unit-efficiency detectors and no transmission loss) and numerically for $N=2$ in the non-ideal case with truncation at $n_\text{max}=3$ photons in each mode. For the general case, we show that the computational complexity for the numerical solution is $n_\text{max}^{12N}$.
A fundamental challenge to our current understanding of metals is the frequent observation of qualitative departures from Fermi liquid behavior. The standard view attributes such non-Fermi liquid phenomena to the scattering of electrons off quantum critical fluctuations of an underlying order parameter. While the possibility of non-Fermi liquid behavior isolated from the border of magnetism has long been speculated, no experimental confirmation has been made. Here we report on the observation of a strange metal region in the absence of a magnetic instability in an ultrapure single crystal. In particular, we show that the heavy fermion superconductor $\beta$-YbAlB$_4$ forms a possible phase with strange metallic behavior across an extensive pressure regime, distinctly separated from a high-pressure magnetic quantum phase transition by a Fermi liquid phase.
Previous approaches for scene text detection have already achieved promising performances across various benchmarks. However, they usually fall short when dealing with challenging scenarios, even when equipped with deep neural network models, because the overall performance is determined by the interplay of multiple stages and components in the pipelines. In this work, we propose a simple yet powerful pipeline that yields fast and accurate text detection in natural scenes. The pipeline directly predicts words or text lines of arbitrary orientations and quadrilateral shapes in full images, eliminating unnecessary intermediate steps (e.g., candidate aggregation and word partitioning), with a single neural network. The simplicity of our pipeline allows concentrating efforts on designing loss functions and neural network architecture. Experiments on standard datasets including ICDAR 2015, COCO-Text and MSRA-TD500 demonstrate that the proposed algorithm significantly outperforms state-of-the-art methods in terms of both accuracy and efficiency. On the ICDAR 2015 dataset, the proposed algorithm achieves an F-score of 0.7820 at 13.2fps at 720p resolution.
The linear response theory is used to describe magnetoresistance oscillations of short-period unilateral superlattices with strong modulation (or alternatively arrays of coupled quantum wires). The semiclassical description of this system fails for strong magnetic fields (magnetic breakdown) and we employ a simple fully-quantum-mechanical tight-binding model in conjunction with Kubo's formula instead. The resulting magnetoresistance data nicely compare to the experiments while the model opens good intuitive insight into the effects taking place in the system.
Data of $^{12}$CO/$^{13}$CO/C$^{18}$O $J=1\to0$ emission toward the Galactic plane region of $l=35^\circ$ to $45^\circ$ and $b= -5^\circ$ to $+5^\circ$ are available with the Milky Way Imaging Scroll Painting (MWISP) project. Using the data, we found a giant molecular filament (GMF) around $l\approx38\sim42^\circ$, $b\approx-3.5\sim0^\circ$, $V_{LSR} \approx 27 \sim 40$ km~s$^{-1}$, named the GMF MWISP G041-01. At a distance of 1.7 kpc, the GMF is about 160 pc long. With a median excitation temperature about 7.5 K and a median column density about $10^{21}$ cm$^{-2}$, this GMF is very cold and very diffuse compared to known GMFs. Using the morphology in the data cube, the GMF is divided into four components among which three show filamentary structure. Masses of the components are $ 10^3 \sim 10^4 M_\odot$, with a total mass for the whole filament being about $7\times10^4 M_\odot$ from the LTE method. $^{13}$CO cores inside each component are searched. Virial parameters are about 2.5 for these cores and have a power-law index of -0.34 against the mass. The mass fraction of dense cores traced by $^{13}$CO to the diffuse clouds traced by $^{12}$CO are about 7% for all components of the GMF. We found signatures of possible large scale filament-filament collision in the GMF.
The growing use of convolutional neural networks (CNN) for a broad range of visual tasks, including tasks involving fine details, raises the problem of applying such networks to a large field of view, since the amount of computations increases significantly with the number of pixels. To deal effectively with this difficulty, we develop and compare methods of using CNNs for the task of small target localization in natural images, given a limited "budget" of samples to form an image. Inspired in part by human vision, we develop and compare variable sampling schemes, with peak resolution at the center and decreasing resolution with eccentricity, applied iteratively by re-centering the image at the previous predicted target location. The results indicate that variable resolution models significantly outperform constant resolution models. Surprisingly, variable resolution models and in particular multi-channel models, outperform the optimal, "budget-free" full-resolution model, using only 5\% of the samples.
We characterize $p-$harmonic functions in the Heisenberg group in terms of an asymptotic mean value property, where $1<p<\infty$, following the scheme described in Manfredi et al. (2009) for the Euclidean case. The new tool that allows us to consider the subelliptic case is a geometric lemma, Lemma 3.2 below, that relates the directions of the points of maxima and minima of a function on a small subelliptic ball with the unit horizontal gradient of that function.
We present Keck II laser guide star adaptive optics observations of the brown dwarf WISEP J061135.13-041024.0 showing it is a binary with a component separation of 0.4". This system is one of the six known resolved binaries in which the magnitude differences between the components show a reversal in sign between the Y/J band and the H/K bands. Deconvolution of the composite spectrum results in a best fit binary solution with L9 and T1.5 components. We also present a preliminary parallax placing the system at a distance of 21.2+/-1.3 pc. Using the distance and resolved magnitudes we are able to place WISEP J061135.13-041024.0AB on a color-absolute magnitude diagram, showing that this system contributes to the well-known "J-band bump" and the components' properties appear similar to other late-type L and early-type T dwarfs. Fitting our data to a set of cloudy atmosphere models suggests the system has an age >1 Gyr with WISEP J061135.13-041024.0A having an effective temperature (Teff) of 1275-1325 K and mass of 64-65 M_Jup, and WISEP J061135.13-041024.0B having Teff = 1075-1115 K and mass 40-65 M_Jup.
In this paper we prove convergence results for the homogenization of the Dirichlet problem with rapidly oscillating boundary data in convex polygonal domains. Our analysis is based on integral representation of solutions. Under a certain Diophantine condition on the boundary of the domain and smooth coefficients we prove pointwise, as well as $L^p$ convergence results. For larger exponents $p$ we prove that the $L^p$ convergence rate is close to optimal. We shall also suggest several directions of possible generalization of the result in this paper.
Magnetite, Fe$_3$O$_4$, displays a highly complex low temperature crystal structure that may be charge and orbitally ordered. Many of the recent experimental claims of such ordering rely on resonant soft x-ray diffraction at the oxygen K and iron L edges. We have re-examined this system and undertaken soft x-ray diffraction experiments on a high-quality single crystal. Contrary to previous claims in the literature, we show that the intensity observed at the Bragg forbidden (001/2)$_c$ reflection can be explained purely in terms of the low-temperature structural displacements around the resonant atoms. This does not necessarily mean that magnetite is not charge or orbitally ordered, but rather that the present sensitivity of resonant soft x-ray experiments does not allow conclusive demonstration of such ordering.
We have begun a programme to obtain high-precision photometry of bright detached eclipsing binary (dEB) stars with the Wide field InfraRed Explorer (WIRE) satellite. Due to the small aperture of WIRE only stars brighter than V=6 can be observed. We are collecting data for about a dozen dEB targets and here we present preliminary results for three of them. We have chosen dEBs with primary components of B and early A type. One of our aims is to combine the information from the light curve analyses of the eclipses with asteroseismic information from the analysis of the pulsation of the primary component.
A wide range of multifield inflationary models generate non-Gaussian initial conditions in which the initial adiabatic fluctuation is of the form (zeta_G + g_{NL} zeta_G^3). We study halo clustering in these models using two different analytic methods: the peak-background split framework, and brute force calculation in a barrier crossing model, obtaining agreement between the two. We find a simple, theoretically motivated expression for halo bias which agrees with N-body simulations and can be used to constrain g_{NL} from observations. We discuss practical caveats to constraining g_{NL} using only observable properties of a tracer population, and argue that constraints obtained from populations whose observed bias is <~ 2.5 are generally not robust to uncertainties in modeling the halo occupation distribution of the population.
Fast Radio Bursts (FRBs) are extreme astrophysical phenomena entering the realm of non-linear optics, a field developed in laser physics. A classical non-linear effect is self-modulation. We examine the propagation of FRBs through the circumburst environment using the idealised setup of a monochromatic linearly-polarised GHz wave propagating through a uniform plasma slab of density $N$ at distance $R$ from the source. We find that self-modulation occurs if the slab is located within a critical radius $R_{\rm crit}\sim 10^{17}(N/10^2{\rm\; cm}^{-3})(L/10^{42}{\rm\; erg\; s}^{-1}){\rm\; cm}$, where $L$ is the isotropic equivalent of the FRB luminosity. Self-modulation breaks the burst into pancakes transverse to the radial direction. When $R\lesssim R_{\rm crit}$, the transverse size of the pancakes is smaller than the Fresnel scale. The pancakes are strongly diffracted as the burst exits the slab, and interference between the pancakes produces a frequency modulation of the observed intensity with a sub-GHz bandwidth. When $R\sim R_{\rm crit}$, the transverse size of the pancakes becomes comparable with the Fresnel scale, and the effect of diffraction is weaker. The observed intensity is modulated on a timescale of ten microseconds, which corresponds to the radial width of the pancakes. Our results suggest that self-modulation may cause the temporal and frequency structure observed in FRBs.
We study the universality of the eigenvalue statistics of the covariance matrices $\frac{1}{n}M^* M$ where $M$ is a large $p\times n$ matrix obeying condition $\bf{C1}$. In particular, as an application, we prove a variant of universality results regarding the smallest singular value of $M_{p,n}$. This paper is an extension of the results in \cite{tvcovariance} from the bulk of the spectrum up to the edge.
We study various supersymmetric RG flows of $N=3$ Chern-Simons-Matter theory in three dimensions by using four-dimensional $N=3$ gauged supergravity coupled to eight vector multiplets with $SO(3)\times SU(3)$ gauge group. The $AdS_4$ critical point preserving the full $SO(3)\times SU(3)$ provides a gravity dual of $N=3$ superconformal field theory with flavor symmetry $SU(3)$. We study the scalar potential and identify a new supersymmetric $AdS_4$ critical point preserving the full $N=3$ supersymmetry and unbroken $SO(3)\times U(1)$ symmetry. An analytic RG flow solution interpolating between $SO(3)\times SU(3)$ and $SO(3)\times U(1)$ critical points is explicitly given. We then investigate possible RG flows from these $AdS_4$ critical points to non-conformal field theories in the IR. All of the singularities appearing in the IR turn out to be physically acceptable. Furthermore, we look for supersymmetric solutions of the form $AdS_2\times \Sigma_2$ with $\Sigma_2$ being a two-sphere or a two-dimensional hyperbolic space and find a number of $AdS_2$ geometries preserving four supercharges with $SO(2)\times SO(2)\times SO(2)$ and $SO(2)\times SO(2)$ symmetries.
Anyon gas with interparticle (retarded) Coulomb interaction has been studied. The resulting system is shown to be a collection of dressed anyons, with a screening factor introduced in their spin. Close structural similarity with the Chern-Simons construction of anyons has helped considerably in computing the screening effect. Finally the present model is compared with the conventional Chern-Simons construction.
An exactly solvable model describing the low density limit of the spin-1 bosons in a one-dimensional optical lattice is proposed. The exact Bethe ansatz solution shows that the low energy physics of this system is described by a quantum liquid of spin singlet bound pairs. Motivated by the exact results, a mean-field approach to the corresponding three-dimensional system is carried out. Condensation of singlet pairs and coexistence with ordinary Bose-Einstein condensation are predicted.
We examine the nature of the transition to the antiferromagnetically ordered state in the half-filled three-dimensional Hubbard model using the dual-fermion multiscale approach. Consistent with analytics, in the weak-coupling regime we find that spin-flip excitations across the Fermi surface are important, and that the strong coupling regime is described by Heisenberg physics. In the intermediate interaction, strong correlation regime we find aspects of both local and non-local correlations. We analyze the critical exponents of the transition in the strong coupling regime and find them to be consistent with Heisenberg physics down to an interaction of $U/t=10$.
Indoor scene understanding is central to applications such as robot navigation and human companion assistance. Over the last years, data-driven deep neural networks have outperformed many traditional approaches thanks to their representation learning capabilities. One of the bottlenecks in training for better representations is the amount of available per-pixel ground truth data that is required for core scene understanding tasks such as semantic segmentation, normal prediction, and object edge detection. To address this problem, a number of works proposed using synthetic data. However, a systematic study of how such synthetic data is generated is missing. In this work, we introduce a large-scale synthetic dataset with 400K physically-based rendered images from 45K realistic 3D indoor scenes. We study the effects of rendering methods and scene lighting on training for three computer vision tasks: surface normal prediction, semantic segmentation, and object boundary detection. This study provides insights into the best practices for training with synthetic data (more realistic rendering is worth it) and shows that pretraining with our new synthetic dataset can improve results beyond the current state of the art on all three tasks.
Recent advances in Deep Learning show the existence of image-agnostic quasi-imperceptible perturbations that when applied to `any' image can fool a state-of-the-art network classifier to change its prediction about the image label. These `Universal Adversarial Perturbations' pose a serious threat to the success of Deep Learning in practice. We present the first dedicated framework to effectively defend the networks against such perturbations. Our approach learns a Perturbation Rectifying Network (PRN) as `pre-input' layers to a targeted model, such that the targeted model needs no modification. The PRN is learned from real and synthetic image-agnostic perturbations, where an efficient method to compute the latter is also proposed. A perturbation detector is separately trained on the Discrete Cosine Transform of the input-output difference of the PRN. A query image is first passed through the PRN and verified by the detector. If a perturbation is detected, the output of the PRN is used for label prediction instead of the actual image. A rigorous evaluation shows that our framework can defend the network classifiers against unseen adversarial perturbations in the real-world scenarios with up to 97.5% success rate. The PRN also generalizes well in the sense that training for one targeted network defends another network with a comparable success rate.
We present adaptive optics-assisted integral field spectroscopy around the Ha or Hb lines of 12 gravitationally lensed galaxies obtained with VLT/SINFONI, Keck/OSIRIS and Gemini/NIFS. We combine these data with previous observations and investigate the dynamics and star formation properties of 17 lensed galaxies at z = 1-4. Thanks to gravitational magnification of 1.4 - 90x by foreground clusters, effective spatial resolutions of 40 - 700 pc are achieved. The magnification also allows us to probe lower star formation rates and stellar masses than unlensed samples; our target galaxies feature dust-corrected SFRs derived from Ha or Hb emission of 0.8 - 40Msol/yr, and stellar masses M* ~ 4e8 - 6e10 Msol. All of the galaxies have velocity gradients, with 59% consistent with being rotating discs and a likely merger fraction of 29%, with the remaining 12% classed as 'undetermined.' We extract 50 star-forming clumps with sizes in the range 60pc - 1kpc from the Ha (or Hb) maps, and find that their surface brightnesses and their characteristic luminosities evolve to higher luminosities with redshift. We show that this evolution can be described by fragmentation on larger scales in gas-rich discs, and is likely to be driven by evolving gas fractions.