ShantanuT01/DACTYL-Pretraining huggingface dataset:
We review the field theory approach to percolation processes. Specifically, we focus on the so-called simple and general epidemic processes that display continuous non-equilibrium active to absorbing state phase transitions whose asymptotic features are governed respectively by the directed (DP) and dynamic isotropic percolation (dIP) universality classes. We discuss the construction of a field theory representation for these Markovian stochastic processes based on fundamental phenomenological considerations, as well as from a specific microscopic reaction-diffusion model realization. Subsequently we explain how dynamic renormalization group (RG) methods can be applied to obtain the universal properties near the critical point in an expansion about the upper critical dimensions d_c = 4 (DP) and 6 (dIP). We provide a detailed overview of results for critical exponents, scaling functions, crossover phenomena, finite-size scaling, and also briefly comment on the influence of long-range spreading, the presence of a boundary, multispecies generalizations, coupling of the order parameter to other conserved modes, and quenched disorder.
We define a completely new space-time starting from the well known Schwarzschild Space time by defining a new polar angle $\phi '= \phi - \omega t$ and then redefining the periodicity: instead of demanding that the original angle be periodic, we demand that the new angle $\phi'$ be periodic, with period $2\pi$. This defines the "topologically rotating Schwarzchild space", which is physically different from the standard Schwarzschild space. For this space, we work out some properties of the geodesics and related properties.This method of generating solutions can be used also for the Reissner-Nordstrom case, both in the case of Reissner-Nordstrom Black hole as well as in the case where there are no horizons, the supercharged case. Horizon shall exist in this case, but with a real singularity, not removable one by a transformation in coordinate at the radius of the horizon of the original metric. This solution should be used as an external solution rather than the internal one. Another topic to notice is that the improper coordinate transformation that we consider introduces closed time like curves.The noticeable topic is that the improper coordinate transformation introduces closed time like curves which we can possibly find here too. This is a common effect in rotating spacetimes, noticeable the Godel universe and others.
An understanding of the phase diagram of elemental plutonium (Pu) must include both the effects of the strong directional bonding and the high density of states of the Pu 5f electrons, as well as how that bonding weakens under the influence of strong electronic correlations. We present for the first time electronic-structure calculations of the full 16-atom per unit cell alpha-phase structure within the framework of density functional theory (DFT) together with dynamical mean-field theory (DMFT). Our calculations demonstrate that Pu atoms sitting on different sites within the alpha-Pu crystal structure have a strongly varying site dependence of the localization-delocalization correlation effects of their 5f electrons and a corresponding effect on the bonding and electronic properties of this complicated metal. In short, alpha-Pu has the capacity to simultaneously have multiple degrees of electron localization/delocalization of Pu 5f electrons within a pure single-element material.
We consider a two-dimensional weakly dissipative dynamical system with time-periodic drift and diffusion coefficients. The average of the drift is governed by a degenerate Hamiltonian whose set of critical points has an interior. The dynamics of the system is studied in the presence of three time scales. Using the martingale problem approach and separating the time scales, we average the system to show convergence to a Markov process on a stratified space. The averaging combines the deterministic time averaging of periodic coefficients, and the stochastic averaging of the resulting system. The corresponding strata of the reduced space are a two-sphere, a point and a line segment. Special attention is given to the description of the domain of the limiting generator, including the analysis of the gluing conditions at the point where the strata meet. These gluing conditions, resulting from the effects of the hierarchy of time scales, are similar to the conditions on the domain of skew Brownian motion and are related to the description of spider martingales.
We discuss the possibility of having gravity ``localized'' in dimension d in a system where gauge bosons propagate in dimension d+1. In such a circumstance - depending on the rate of falloff of the field strengths in d dimensions - one might expect the gauge symmetry in d+1 dimensions to behave like a global symmetry in d dimensions, despite the presence of gravity. Naive extrapolation of warped long-wavelength solutions of general relativity coupled to scalars and gauge fields suggests that such an effect might be possible. However, in some basic realizations of such solutions in M theory, we find that this effect does not persist microscopically. It turns over either to screening or the Higgs mechanism at long distances in the d-dimensional description of the system. We briefly discuss the physics of charged objects in this type of system.
Extremely metal-poor (EMP) stars are an integral piece in the puzzle that is the early Universe, and although anomolous subclasses of EMP stars such as carbon-enhanced metal-poor (CEMP) stars are well-studied, they make up less than half of all EMP stars with [Fe/H] $\sim -3.0$. The amount of carbon depletion occurring on the red giant branch (carbon offset) is used to determine the evolutionary status of EMP stars, and this offset will differ between CEMP and normal EMP stars. The depletion mechanism employed in stellar models (from which carbon offfsets are derived) is very important, however the only widely available carbon offsets in the literature are derived from stellar models using a thermohaline mixing mechanism that cannot simultaneously match carbon and lithium abundances to observations for a single diffusion coeffcient. Our stellar evolution models utilise a modified thermohaline mixing model that can match carbon and lithium in the metal-poor globular cluster NGC 6397. We compare our models to the bulk of the EMP star sample at [Fe/H] $= -3$ and show that our modified models follow the trend of the observations and deplete less carbon compared to the standard thermohaline mixing theory. We conclude that stellar models that employ the standard thermohaline mixing formalism overestimate carbon offsets and hence CEMP star frequencies, particularly at metallicities where carbon-normal stars dominate the EMP star population.
While self-training has advanced semi-supervised semantic segmentation, it severely suffers from the long-tailed class distribution on real-world semantic segmentation datasets that make the pseudo-labeled data bias toward majority classes. In this paper, we present a simple and yet effective Distribution Alignment and Random Sampling (DARS) method to produce unbiased pseudo labels that match the true class distribution estimated from the labeled data. Besides, we also contribute a progressive data augmentation and labeling strategy to facilitate model training with pseudo-labeled data. Experiments on both Cityscapes and PASCAL VOC 2012 datasets demonstrate the effectiveness of our approach. Albeit simple, our method performs favorably in comparison with state-of-the-art approaches. Code will be available at https://github.com/CVMI-Lab/DARS.
This paper is the completion of an earlier work arXiv:1207.4867 which involves the derivation of oblique corrections in the MSSM at one loop. In terms of the two-component spinor formalism, which is new in compared with those used in the literature, the contributions arising from the fermion superpartners i.e, neutralino-chargino sector to self-energy of standard model electroweak gauge bosons are calculated. Corresponding descendants the $S$, $T$ and $U$ parameters are presented. The validity of our results is examined in two ways, which are then followed by detailed analysis on the results in the literature.
We study the perturbative response of a complex quantum system on time changes of an external parameter $X$. The driven dynamics is treated in adiabatic basis of the system's Hamiltonian $\hat{H}[X]$. Within a random matrix approach we obtained non--Markovian Fokker--Planck equation for the occupancy of given adiabatic state. We observed normal diffusion regime of the driven quantum dynamics at quite small values of the memory time defined by the time scales of the $X$--correlations and energy--distribution of the coupling matrix elements $(\partial \hat{H}/\partial X)_{nm}$. Here the normal energy diffusion was found to drop out with the width of the matrix elements' energy--distribution and the diffusion may be significantly suppressed with the decrease of the correlations between the matrix elements. In the opposite limit of relatively large memory times we obtained ballistic regime of the dynamics.
Deep CNN-based methods have so far achieved the state of the art results in multi-view 3D object reconstruction. Despite the considerable progress, the two core modules of these methods - multi-view feature extraction and fusion, are usually investigated separately, and the object relations in different views are rarely explored. In this paper, inspired by the recent great success in self-attention-based Transformer models, we reformulate the multi-view 3D reconstruction as a sequence-to-sequence prediction problem and propose a new framework named 3D Volume Transformer (VolT) for such a task. Unlike previous CNN-based methods using a separate design, we unify the feature extraction and view fusion in a single Transformer network. A natural advantage of our design lies in the exploration of view-to-view relationships using self-attention among multiple unordered inputs. On ShapeNet - a large-scale 3D reconstruction benchmark dataset, our method achieves a new state-of-the-art accuracy in multi-view reconstruction with fewer parameters ($70\%$ less) than other CNN-based methods. Experimental results also suggest the strong scaling capability of our method. Our code will be made publicly available.
Video deblurring models exploit information in the neighboring frames to remove blur caused by the motion of the camera and the objects. Recurrent Neural Networks~(RNNs) are often adopted to model the temporal dependency between frames via hidden states. When motion blur is strong, however, hidden states are hard to deliver proper information due to the displacement between different frames. While there have been attempts to update the hidden states, it is difficult to handle misaligned features beyond the receptive field of simple modules. Thus, we propose 2 modules to supplement the RNN architecture for video deblurring. First, we design Ping-Pong RNN~(PPRNN) that acts on updating the hidden states by referring to the features from the current and the previous time steps alternately. PPRNN gathers relevant information from the both features in an iterative and balanced manner by utilizing its recurrent architecture. Second, we use a Selective Non-Local Attention~(SNLA) module to additionally refine the hidden state by aligning it with the positional information from the input frame feature. The attention score is scaled by the relevance to the input feature to focus on the necessary information. By paying attention to hidden states with both modules, which have strong synergy, our PAHS framework improves the representation powers of RNN structures and achieves state-of-the-art deblurring performance on standard benchmarks and real-world videos.
The variation of the dimensionless fundamental physical constant mu = m_p/m_e (the proton to electron mass ratio) can be constrained via observation of Lyman and Werner lines of molecular hydrogen in the spectra of damped Lyman alpha systems (DLAs) in the line of sight to distant QSOs. Drawing on VLT-UVES high resolution data sets of QSO 0347-383 and its DLA obtained in 2009 our analysis yields dmu/mu = (4.3 +/- 7.2) * 10^-6 at z_abs =3.025. We apply corrections for the observed offsets between discrete spectra and for the first time we find indications for inter-order distortions. Current analyses tend to underestimate the impact of systematic errors. Based on the scatter of the measured redshifts and the corresponding low significance of the redshift-sensitivity correlation we estimate the limit of accuracy of line position measurements to about 220 m/s, consisting of roughly 150 m/s due to the uncertainty of the absorption line fit and about 150 m/s allocated to systematics related to instrumentation and calibration.
Interactions of quantum systems with their environment play a crucial role in resource-theoretic approaches to thermodynamics in the microscopic regime. Here, we analyze the possible state transitions in the presence of "small" heat baths of bounded dimension and energy. We show that for operations on quantum systems with fully degenerate Hamiltonian (noisy operations), all possible state transitions can be realized exactly with a bath that is of the same size as the system or smaller, which proves a quantum version of Horn's lemma as conjectured by Bengtsson and Zyczkowski. On the other hand, if the system's Hamiltonian is not fully degenerate (thermal operations), we show that some possible transitions can only be performed with a heat bath that is unbounded in size and energy, which is an instance of the third law of thermodynamics. In both cases, we prove that quantum operations yield an advantage over classical ones for any given finite heat bath, by allowing a larger and more physically realistic set of state transitions.
Time-dependent density functional theory, proposed recently in the context of atomic diffusion and non-equilibrium processes in solids, is tested against Monte Carlo simulation. In order to assess the basic approximation of that theory, the representation of non-equilibrium states by a local equilibrium distribution function, we focus on one-dimensional lattice models, where all equilibrium properties can be worked exactly from the known free energy as a functional of the density. This functional determines the thermodynamic driving forces away from equilibrium. In our studies of the interfacial kinetics of atomic hopping and spin relaxation, we find excellent agreement with simulations, suggesting that the method is useful also for treating more complex problems.
We examine numerically the post-merger regime of two Schwarzschild black holes in non head-on collision. Our treatment is made in the realm of non-axisymmetric Robinson-Trautman spacetimes which are appropriate for the description of the system. Characteristic initial data for the system are constructed and the Robinson-Trautman equation is integrated using a numerical code based on the Galerkin spectral method. The collision is planar, restricted to the plane determined by the directions of the two initial colliding black holes, with the net momentum fluxes of gravitational waves confined to this plane. We evaluate the efficiency of mass-energy extraction, the total energy and momentum carried out by gravitational waves and the momentum distribution of the remnant black hole. Our analysis is based on the Bondi-Sachs four momentum conservation laws. Head-on collisions and orthogonal collisions constitute, respectively, upper and lower bounds to the power emission and to the efficiency of mass-energy extraction by gravitational waves. The momentum extraction and the pattern of the momentum fluxes, as a function of the incidence angle, are examined. The momentum extraction characterizes a regime of strong deceleration of the system. The angular pattern of gravitational wave signals is also examined. They are typically bremsstrahlung for early times emission. Gravitational waves are also emitted outside the plane of collision but this component has a zero net momentum flux. The relation between the incidence angle of collision and the exit angle of the remnant closely approximates a relation for inelastic collisions of classical particles in Newtonian dynamics.
In this review paper, we illustrate a possible route to obtain a reliable solution of the 2D Hubbard model and an explanation for some of the unconventional behaviours of underdoped high-$T_\text{c}$ cuprate superconductors within the framework of the composite operator method. The latter is described exhaustively in its fundamental philosophy, various ingredients and robust machinery to clarify the reasons behind its successful applications to many diverse strongly correlated systems, controversial phenomenologies and puzzling materials.
Starting from chiral Lagrangians, possessing the SU(2)_L x SU(2)_R local chiral symmetry, we derive weak axial one-boson exchange currents in the leading order in the 1/M expansion (M is the nucleon mass). We apply these currents in calculations of the cross sections for the disintegration of the deuterons by the low energy neutrinos. The nuclear wave functions are derived from a variant of the OBEPQB potential and from the Nijmegen 93 and Nijmegen I nucleon-nucleon interactions. The comparison of our cross sections with those obtained within the pionless effective field theory and other potential model calculations shows that the solar neutrino-deuteron cross sections can be calculated within an accuracy of 3.3 %.
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently sample the invariant distribution of the diffusion process, thanks to the approximation of the associated free energy function (relative to a reaction coordinate). The bias which is introduced in the dynamics is computed adaptively; it depends on the past of the trajectory of the process through some time-averages.   We give a detailed and general construction of such methods. We prove the consistency of the approach (almost sure convergence of well-chosen weighted empirical probability distribution). We justify the efficiency thanks to several qualitative and quantitative additional arguments. To prove these results , we revisit and extend tools from stochastic approximation applied to self-interacting diffusions, in an original context.
Let $n\geq 3$ be a positive integer and let $\mathbb{F}_{q^k}$ be the splitting field of $x^n-1$. By $\gamma$ we denote a primitive element of $\mathbb{F}_{q^k}$. Let $C$ be a cyclic code of length $n$ whose check polynomial contains two zeros $\gamma^d$ and $\gamma^{d+D}$, where $de \mid (q-1)$, $e>1$ and $D=(q^k-1)/e$. This family of cyclic codes is not projective. Many authors have studied the weight distribution of these codes for certain parameters. In this paper, we prove that these codes are never two-weight codes. This result would strengthen a conjecture by Vega which states that all two-weight cyclic codes are the "known" ones.
We outline the methodology of simulating common envelope evolution (CEE) with the moving-mesh code MANGA. We extend MANGA to include multiple time-steps. This provides substantial speedups for problems with large dynamic range. We describe the implementation of realistic equations of state relevant in stellar structure and the generation of suitable initial conditions. We then carry out two example simulations of a 2 $\rm{M}_{\odot}$ red giant with a 0.36 $\rm{M}_{\odot}$ core and a 1 $\rm{M}_{\odot}$ companion undergoing CEE for 240 days. In one simulation the red giant is set into corotation with the orbital motion and in the other it is non-rotating. We find that the separation between the companion and red giant core shrinks from 52 $\rm{R}_{\odot}$ to 3.6 $\rm{R}_{\odot}$ and 3.2 $\rm{R}_{\odot}$ respectively, ending with an eccentricity of 0.1. We also find that 66 and 63 per cent of the envelope mass is ejected. This is higher than in many previous works. Several reasons for this are discussed. These include our inclusion of recombination energy. Our simulations show that putting giants in corotation increases the fraction of mass ejected from the system and results in a larger final orbital separation. We conclude that the entire envelope of the red giant might be ejected during the plunge phase of CEE in this region of parameter space.
Hand pose estimation from a single depth image is an essential topic in computer vision and human computer interaction. Despite recent advancements in this area promoted by convolutional neural network, accurate hand pose estimation is still a challenging problem. In this paper we propose a Pose guided structured Region Ensemble Network (Pose-REN) to boost the performance of hand pose estimation. The proposed method extracts regions from the feature maps of convolutional neural network under the guide of an initially estimated pose, generating more optimal and representative features for hand pose estimation. The extracted feature regions are then integrated hierarchically according to the topology of hand joints by employing tree-structured fully connections. A refined estimation of hand pose is directly regressed by the proposed network and the final hand pose is obtained by utilizing an iterative cascaded method. Comprehensive experiments on public hand pose datasets demonstrate that our proposed method outperforms state-of-the-art algorithms.
New models are presented for star-forming condensations in clusters. In each model, the condensation mass increases linearly with radius on small scales, and more rapidly on large scales, as in "thermal-nonthermal" models. Spherical condensations with this structure form protostars which match the IMF if their infall is subject to equally likely stopping. However such spherical models do not match the filamentary nature of cluster gas, and they are too extended to form protostars having high mass and short spacing. Two hybrid models are presented, which are spherical on small scales and filamentary on large scales. In and around clusters, cores embedded in linear filaments match the elongation of cluster gas, and the central concentration of low-mass stars. In cluster centers, condensations require a low volume filling factor to produce massive stars with short spacing. These may have stellate shape, where cores are nodes of filamentary networks, as seen in some simulations of colliding flows and of collapsing turbulent clumps. A dense configuration of such stellate condensations may be indistinguishable from a clump forming multiple protostars via filamentary flow paths.