ShantanuT01/DACTYL-Pretraining huggingface dataset:
We prove that given any fixed asymptotic velocity, the finite length O'Connell-Yor polymer has an infinite length limit satisfying the law of large numbers with this velocity. By a Markovian property of the quenched polymer this reduces to showing the existence of Busemann functions: almost sure limits of ratios of random point-to-point partition functions. The key ingredients are the Burke property of the O'Connell-Yor polymer and a comparison lemma for the ratios of partition functions. We also show the existence of infinite length limits in the Brownian last passage percolation model.
We study the fluctuations of the autocorrelation and autoresponse functions and, in particular, their variances and co-variance. In a first general part of the Article, we show the equivalence of the variance of the response function with the second-order susceptibility of a composite operator, and we derive an equilibrium fluctuation-dissipation theorem beyond-linear order relating it to the other variances. In a second part of the paper we apply the formalism to the study to non-disordered ferromagnets, in equilibrium or in the coarsening kinetics following a critical or sub-critical quench. We show numerically that the variances and the non-linear susceptibility obey scaling with respect to the coherence length $\xi$ in equilibrium, and with respect to the growing length $L(t)$ after a quench, similarly to what is known for the autocorrelation and the autoresponse functions.
We investigate the possibility that multiple populations in globular clusters arise as a natural by-product of massive star-cluster formation. We use 3D radiative hydrodynamics simulations for the formation of young massive clusters to track their chemical self-enrichment during their first 5 Myr. These clusters form embedded within filamentary Giant Molecular Clouds by a combination of gas accretion and rapid merging of protoclusters. Chemical enrichment is a dynamic process happening as the young cluster assembles, so that the original (1P) and enriched (2P) subpopulations of stars form almost simultaneously. Here we test two simple and opposite extremes for the injection of enriched material into the intracluster gas: we assume either continuous injection in a way that tracks the star formation rate; or sudden injection by a single instantaneous event. Using helium abundance as a proxy for the enrichment, we find that realistic multiple population features can be reproduced by injecting a total helium mass amounting to a few percent of the cluster's total mass. The differences in individual growth histories can lead to widely differing 1P/2P outcomes. These models suggest that dual or multiple populations can emerge rapidly in massive star clusters undergoing the typical mode of star cluster formation.
Orofacial deficits are common in people with Parkinson's disease (PD) and their evolution might represent an important biomarker of disease progression. We are developing an automated system for assessment of orofacial function in PD that can be used in-home or in-clinic and can provide useful and objective clinical information that informs disease management. Our current approach relies on color and depth cameras for the estimation of 3D facial movements. However, depth cameras are not commonly available, might be expensive, and require specialized software for control and data processing. The objective of this paper was to evaluate if depth cameras are needed to differentiate between healthy controls and PD patients based on features extracted from orofacial kinematics. Results indicate that 2D features, extracted from color cameras only, are as informative as 3D features, extracted from color and depth cameras, differentiating healthy controls from PD patients. These results pave the way for the development of a universal system for automatic and objective assessment of orofacial function in PD.
We introduce the concept of an extremely negatively dependent (END) sequence of random variables with a given common marginal distribution. The END structure, as a new benchmark for negative dependence, is comparable to comonotonicity and independence. We show that an END sequence always exists for any given marginal distributions with a finite mean and we provide a probabilistic construction. Through such a construction, the partial sum of identically distributed but dependent random variables is controlled by a random variable that depends only on the marginal distribution of the sequence. The new concept and derived results are used to obtain asymptotic bounds for risk aggregation with dependence uncertainty.
Magnetic fields created in the noncentral heavy-ion collision are studied within a microscopic transport model, namely the Ultrarelativistic Quantum Molecular Dynamics model (UrQMD). Simulations were carried out for different impact parameters within the SPS energy range ($E_{lab} = 10 - 158 A$ GeV) and for highest energies accessible for RHIC. We show that the magnetic field emerging in heavy-ion collisions has the magnitude of the order of $eB_y \sim 10^{-1} m_\pi^2$ for the SPS energy range and $eB_y \sim m_\pi^2$ for the RHIC energies. The estimated value of the magnetic field strength for the LHC energy amounts to $eB_y \sim 15 m_\pi^2$.
Reliable experimental demonstrations of violations of local realism are highly desirable for fundamental tests of quantum mechanics. One can quantify the violation witnessed by an experiment in terms of a statistical p-value, which can be defined as the maximum probability according to local realism of a violation at least as high as that witnessed. Thus, high violation corresponds to small p-value. We propose a prediction-based-ratio (PBR) analysis protocol whose p-values are valid even if the prepared quantum state varies arbitrarily and local realistic models can depend on previous measurement settings and outcomes. It is therefore not subject to the memory loophole [J. Barrett et al., Phys. Rev. A 66, 042111 (2002)]. If the prepared state does not vary in time, the p-values are asymptotically optimal. For comparison, we consider protocols derived from the number of standard deviations of violation of a Bell inequality and from martingale theory [R. Gill, arXiv:quant-ph/0110137]. We find that the p-values of the former can be too small and are therefore not statistically valid, while those derived from the latter are sub-optimal. PBR p-values do not require a predetermined Bell inequality and can be used to compare results from different tests of local realism independent of experimental details.
The problem of asymptotic density of quantum states of fundamental extended objects is revised in detail. We argue that in the near-extremal regime the fundamental $p$-brane approach can yield a microscopic interpretation of the black hole entropy. The asymptotic behavior of partition functions, associated with the $p$-branes, and the near-extremal entropy of five-dimensional black holes are explicitly calculated.
Several aspects of the analysis of the data obtained with the cryogenic heat-and-ionisation Ge detectors used by the EDELWEISS dark matter search experiment are presented. Their calibration, the determination of their energy threshold, fiducial volume and nuclear recoil acceptance are detailed.
The perturbations of string-theoretic black holes are analyzed by generalizing the method of Chandrasekhar. Attention is focussed on the case of the recently considered charged string-theoretic black hole solutions as a representative example. It is shown that string-intrinsic effects greatly alter the perturbed motions of the string-theoretic black holes as compared to the perturbed motions of black hole solutions of the field equations of general relativity, the consequences of which bear on the questions of the scattering behavior and the stability of string-theoretic black holes. The explicit forms of the axial potential barriers surrounding the string-theoretic black hole are derived. It is demonstrated that one of these, for sufficiently negative values of the asymptotic value of the dilaton field, will inevitably become negative in turn, in marked contrast to the potentials surrounding the static black holes of general relativity. Such potentials may in principle be used in some cases to obtain approximate constraints on the value of the string coupling constant. The application of the perturbation analysis to the case of two-dimensional string-theoretic black holes is discussed.
We present a study of the rotation measure (RM) obtained from a sample of extra-galactic radio sources either embedded in or seen in projection through a sample of seven southern galaxy clusters (declination less than 30 degrees). We compare our results with those obtained previously through similar statistical studies and conclude there is a statistically significant broadening of the RM signal in galaxy clusters when compared to a control sample. Further, we concur with the findings of Clarke (2000) that the typical influence of the cluster on the RM extends to around 800 kpc from the cluster core and that the RMs determined are on average consistent with a 1-2 micro G field.
We have investigated Rb adsorption on the Si(100) surface for 0.5 and 1 monolayer coverages using the total energy method with norm-conserving pseudopotentials. For 2$\times$1 reconstruction at 1 ML coverage symmetrized dimers are found to be energetically more favorable. On the other hand, half a ML coverage is found to have symmetrical dimers only for the most stable adsorption model. All possible surface-adatom configurations have been considered in the calculations to find which adsorption sites are energetically favored. In addition to the structural properties, the interface is investigated electronically for the work function and surface states. The results are discussed and compared with the existing experimental findings.
We present the detection of hydrogen fluoride, HF, in two luminous nearby galaxies NGC 253 and NGC 4945 using the Heterodyne Instrument for the Far-Infrared (HIFI) on board the Herschel Space Observatory. The HF line toward NGC 253 has a P-Cygni profile, while an asymmetric absorption profile is seen toward NGC 4945. The P-Cygni profile in NGC 253 suggests an outflow of molecular gas with a mass of M(H$_2$)$_{out}$ $\sim$ 1 $\times$ 10$^7$ M$_\odot$ and an outflow rate as large as \.{M} $\sim$ 6.4 M$_\odot$ yr$^{-1}$. In the case of NGC 4945, the axisymmetric velocity components in the HF line profile is compatible with the interpretation of a fast-rotating nuclear ring surrounding the nucleus and the presence of inflowing gas. The gas falls into the nucleus with an inflow rate of $\le$ 1.2 M$_\odot$ yr$^{-1}$, inside a inner radius of $\le$ 200 pc. The gas accretion rate to the central AGN is much smaller, suggesting that the inflow can be triggering a nuclear starburst. From these results, the HF $J = 1-0$ line is seen to provide an important probe of the kinematics of absorbing material along the sight-line to nearby galaxies with bright dust continuum and a promising new tracer of molecular gas in high-redshift galaxies.
It is well known that for every even integer $n$, the complete graph $K_{n}$ has a one-factorization, namely a proper edge coloring with $n-1$ colors. Unfortunately, not much is known about the possible structure of large one-factorizations. Also, at present we have only woefully few explicit constructions of one-factorizations. Specifically, we know essentially nothing about the {\em typical} properties of one-factorizations for large $n$.   Suppose that $\cal C_{\rm n}$ is a graph whose vertex set includes the set of all order-$n$ one-factorizations and that $\Psi: V(\cal C_{\rm n})\to \mathbb R$ takes its minimum precisely at the one-factorizations. Given $\cal C_{\rm n}$ and $\Psi$, we can generate one-factorizations via hill climbing. Namely, by taking a walk on $\cal C_{\rm n}$ that tends to go from a vertex to a neighbor of smaller $\Psi$. For over 30 years, hill-climbing has been essentially the only method for generating many large one-factorizations. However, the validity of such methods was supported so far only by numerical evidence. Here, we present for the first time hill-climbing algorithms that provably generate an order-$n$ one-factorization in $\text{polynomial}(n)$ steps regardless of the starting state, while all vertex degrees in the underlying graph are appropriately bounded.   We also raise many questions and conjectures regarding hill-climbing methods and concerning the possible and typical structure of one-factorizations.
In this paper we improve the estimate for the remainder term in the asymptotic formula concerning the circle problem in an arithmetic progression.
We assess the effectiveness of the Jeans-Anisotropic-MGE (JAM) technique with a state-of-the-art cosmological hydrodynamic simulation, the Illustris project. We perform JAM modelling on 1413 simulated galaxies with stellar mass M^* > 10^{10}M_{sun}, and construct an axisymmetric dynamical model for each galaxy. Combined with a Markov Chain Monte Carlo (MCMC) simulation, we recover the projected root-mean-square velocity (V_rms) field of the stellar component, and investigate constraints on the stellar mass-to-light ratio, M^*/L, and the fraction of dark matter f_{DM} within 2.5 effective radii (R_e). We find that the enclosed total mass within 2.5 R_e is well constrained to within 10%. However, there is a degeneracy between the dark matter and stellar components with correspondingly larger individual errors. The 1 sigma scatter in the recovered M^*/L is 30-40% of the true value. The accuracy of the recovery of M^*/L depends on the triaxial shape of a galaxy. There is no significant bias for oblate galaxies, while for prolate galaxies the JAM-recovered stellar mass is on average 18% higher than the input values. We also find that higher image resolutions alleviate the dark matter and stellar mass degeneracy and yield systematically better parameter recovery.
In a delightful article, Richard Stanley derived, algebraically, the surprisingly simple formula, 3 times 7 to the power n-1, for the sum of the cubes of the n-th row of Stern's diatomic array. In this note, we find an elegant bijective proof of this surprising fact, that explains it and gives insight. The novelty is that this gorgeous bijection was discovered by a computer (SBE), with minimal guidance by a human (DZ). This debunks the conventional wisdom, held by some human supremacists, that computers can only compute, but they can't give insight
We obtain precise temperature dependence of three transport coefficients that resembles strange metal: (a) longitudinal electrical conductivity (b) longitudinal thermoelectric conductivity (c) longitudinal thermal conductivity in the absence of magnetic field. This is achieved through one parameter, namely, when the dynamical exponent, $z=4$. Moreover, in the presence of magnetic field, we have cooked up a model where it exhibits the desired temperature dependence of the four transport quantities that resembles strange metal.
The J_1-J_2 model with the biquadratic (plaquette-four-spin) interaction was simulated with the numerical-diagonalization method. Some limiting cases of this model have been investigated thoroughly. Taking the advantage of the extended parameter space, we survey the phase boundary separating the N'eel and valence-bond-solid phases. According to the deconfined-criticality scenario, the singularity of this phase boundary is continuous, accompanied with unconventional critical indices. Diagonalizing the finite-size cluster with N \le 36 spins, we observe a signature of continuous phase transition. Our tentative estimate for the correlation-length critical exponent is \nu=1.1(3). In order to elucidate a non-local character of criticality, we evaluated the Roomany-Wyld \beta function around the critical point.
Self-supervised pretraining has been shown to yield powerful representations for transfer learning. These performance gains come at a large computational cost however, with state-of-the-art methods requiring an order of magnitude more computation than supervised pretraining. We tackle this computational bottleneck by introducing a new self-supervised objective, contrastive detection, which tasks representations with identifying object-level features across augmentations. This objective extracts a rich learning signal per image, leading to state-of-the-art transfer accuracy on a variety of downstream tasks, while requiring up to 10x less pretraining. In particular, our strongest ImageNet-pretrained model performs on par with SEER, one of the largest self-supervised systems to date, which uses 1000x more pretraining data. Finally, our objective seamlessly handles pretraining on more complex images such as those in COCO, closing the gap with supervised transfer learning from COCO to PASCAL.
In a recent paper, we applied Riemann--Hilbert techniques to analyze the Goursat problem for the hyperbolic Ernst equation, which describes the interaction of two colliding gravitational plane waves. Here we generalize this approach to colliding electromagnetic plane waves in Einstein--Maxwell theory.
Using a large flavor number expansion and a gap equation for the pion mass the chiral quark-meson model is solved at the lowest order in the fermion contributions. In the chiral limit the tricritical point (TCP) is determined analytically. The softening of the sigma particle is verified at this point and is further investigated for a physical pion mass in the neighbourhood of the critical endpoint (CEP).
In this paper, we propose a 3-parameter family of coupled Painlev\'e III systems in dimension four with affine Weyl group symmetry of type $A_5^{(2)}$. We also propose its symmetric form in which the $A_5^{(2)}$-symmetries become clearly visible.
The phenomena customly described with the standard $\Lambda$CDM model are broadly reproduced by an extremely simple model in TeVeS, Bekenstein's (2004) modification of General Relativity motivated by galaxy phenomenology. Our model can account for the acceleration of the universe seen in SNeIa distances without a cosmological constant, and the accelerations seen rotation curves of nearby spiral galaxies and gravitational lensing of high-redshift elliptical galaxies without cold dark matter. The model is consistent with BBN and the neutrino mass. The TeVeS scalar field is shown to play the effective dural roles of Dark Matter and Dark Energy with the amplitudes of the effects controled by a $\mu$-function of the scalar field, called the $\mu-$essence here. We also discuss outliers to the theory's predictions on multi-imaged galaxy lenses and outliers on sub-galaxy scale.
The spectrum and light curve of the bright X-ray source CG X-1 in the field of the Circinus galaxy are re-examined. Previous analyses have concluded that the source is an accreting black hole of about 50 solar masses although it was noted that the light curve resembles that of an AM Her system. Here we show that the short period and an assumed main sequence companion constrain the mass of the companion to less than one solar mass. Further a possible eclipse seen during one of the Chandra observations and a subsequent XMM-Newton observation constrains the mass of the compact object to less than about 60 solar masses. If such a system lies in the Circinus galaxy, then the accreting object must either radiate anisotropically or strongly violate the Eddington limit. Even if the emission is beamed, then the companion star which intercepts this flux during eclipse will be driven out of thermal equilibrium and evaporate within about 1000 years. We find that the observations cannot rule out an AM Her system in the Milky Way and that such a system can account for the variations seen in the light curve.
The stability and other properties of a staggered flux (SF) state or a correlated d-density wave state are studied for the Hubbard (t-t'-U) model on extended square lattices, as a low-lying state that competes with the d(x2-y2)-wave superconductivity (d-SC) and possibly causes the pseudogap phenomena in underdoped high-Tc cuprates and organic kappa-BEDT-TTF salts. In calculations, a variational Monte Carlo method is used. In the trial wave function, a configuration-dependent phase factor, which is vital to treat a current-carrying state for a large U/t, is introduced in addition to ordinary correlation factors. Varying U/t, t'/t, and the doping rate (delta) systematically, we show that the SF state becomes more stable than the normal state (projected Fermi sea) for a strongly correlated (U/t\gtrsim 5) and underdoped (delta\lesssim 0.16) area. The decrease in energy is sizable, particularly in the area where Mott physics prevails and the circular current (order parameter) is strongly suppressed. These features are consistent with those for the t-J model. The effect of the frustration t'/t plays a crucial role in preserving charge homogeneity and appropriately describing the behavior of hole- and electron-doped cuprates and kappa-BEDT-TTF salts. We argue that the SF state does not coexist with d-SC and is not a `normal state' from which d-SC arises. We also show that a spin current (flux or nematic) state is never stabilized in the same regime.
Spin-momentum locking in Weyl semimetals correlates the orbital motion of electrons with background magnetic textures. We show here that the dynamics of a magnetic texture in a magnetic Weyl semimetal induces a pumped electric current that is free from Joule heating. This pumped current can be regarded as a Hall current induced by axial electromagnetic fields equivalent to the magnetic texture. Taking a magnetic domain wall as a test case, we demonstrate that a moving domain wall generates a pumping current corresponding to the localized charge.
We present a classification of the unitarity quadrangles in the four-neutrino mixing scheme. We find that there are totally thirty-six distinct topologies among twelve different unitarity quadrangles. Concise relations are established between the areas of those unitarity quadrangles and the rephasing invariants of CP and $T$ violation.
We study positive entropy birational automorphisms of threefolds. We identify some conditions which imply that such an automorphism is non-regularizable. We show that this criterion applies in the example of a positive entropy birational automorphism of $\mathbb{P}^3$ constructed by J. Blanc, thus showing that for a general choice of parameters it is non-regularizable. Additionally, we establish a criterion which proves that the automorphism in this example does not preserve a structure of a fibration over a surface.
Video frame interpolation (VFI) aims to synthesize an intermediate frame between two consecutive frames. State-of-the-art approaches usually adopt a two-step solution, which includes 1) generating locally-warped pixels by flow-based motion estimations, 2) blending the warped pixels to form a full frame through deep neural synthesis networks. However, due to the inconsistent warping from the two consecutive frames, the warped features for new frames are usually not aligned, which leads to distorted and blurred frames, especially when large and complex motions occur. To solve this issue, in this paper we propose a novel Trajectory-aware Transformer for Video Frame Interpolation (TTVFI). In particular, we formulate the warped features with inconsistent motions as query tokens, and formulate relevant regions in a motion trajectory from two original consecutive frames into keys and values. Self-attention is learned on relevant tokens along the trajectory to blend the pristine features into intermediate frames through end-to-end training. Experimental results demonstrate that our method outperforms other state-of-the-art methods in four widely-used VFI benchmarks. Both code and pre-trained models will be released soon.