ShantanuT01/DACTYL-Pretraining huggingface dataset:
We extend the variational approach to regularity for optimal transport maps initiated by Goldman and the first author to the case of general cost functions. Our main result is an $\epsilon$-regularity result for optimal transport maps between H\"older continuous densities slightly more quantitative than the result by De Philippis-Figalli. One of the new contributions is the use of almost-minimality: if the cost is quantitatively close to the Euclidean cost function, a minimizer for the optimal transport problem with general cost is an almost-minimizer for the one with quadratic cost. This further highlights the connection between our variational approach and De Giorgi's strategy for $\epsilon$-regularity of minimal surfaces.
We performed numerical simulations of stellar occultations by extra-solar cometary tails. We find that extra-solar comets can be detected by the apparent photometric variations of the central stars. In most cases, the light curve shows a very peculiar ``rounded triangular'' shape. However, in some other cases, the curve can mimic a planetary occultation. Photometric variations due to comet occultations are mainly achromatic. Nevertheless, if comets with small periastrons have smaller particles, these occultations could be chromatic with a larger extinction in the blue by few percents.   We also estimate the number of detections expected in a large photometric survey at high accuracy. By the observation of several tens of thousand of stars, it should be possible to detect several hundreds of occultation per year. We thus conclude that a spatial photometric survey would detect a large number of extra-solar comets. This would allow to explore the time evolution of cometary activity, and consequently would probe structure and evolution of extra-solar planetary systems.
We consider the next-to-leading order corrections, O(alpha_s), to forward-backward charge asymmetries for lepton-pair production in association with a large transverse momentum jet at large hadron colliders. We find that the leading order results are essentially confirmed. Although experimentally challenging and in practice with large backgrounds, these observables could provide a new determination of the weak mixing angle sin2 theta^lept_eff (M_Z^2) with a statistical precision for each lepton flavour of ~10^(-3) (7 x 10^{-3}) at LHC (Tevatron), and if b jets are identified, of the b quark Z asymmetry A^b_{FB} with a statistical precision of ~ 2x10^{-3} (4x10{-2}) at LHC (Tevatron).
We consider a Dirichlet problem for the Allen-Cahn equation in a smooth, bounded or unbounded, domain $\Omega\subset {\bf R}^n.$ Under suitable assumptions, we prove an existence result and a uniform exponential estimate for symmetric solutions. In dimension n=2 an additional asymptotic result is obtained. These results are based on a pointwise estimate obtained for local minimizers of the Allen-Cahn energy.
It has been shown recently (Phys. Rev. Lett. 106, 090504 (2011)) that entangled light with Einstein-Podolsky-Rosen (EPR) correlations retrieves information from digital memory better than any classical light. In identifying this, a model of digital memory with each cell consisting of reflecting medium with two reflectivities (each memory cell encoding the binary numbers 0 or 1) is employed. The readout of binary memory essentially corresponds to discrimination of two Bosonic attenuator channels characterized by different reflectivities. The model requires an entire mathematical paraphernalia of continuous variable Gaussian setting for its analysis, when arbitrary values of reflectivities are considered. Here we restrict to a basic quantum read-out mechanism with non-Gaussian entangled states of light, with the binary channels to be discriminated being ideal memory characterized by reflectivity one i.e., an identity channel and thermal noise channel, where the signal light illuminating the memory location gets completely lost (zero reflectivity) and only a white thermal noise hitting the upper side of the memory reaches the decoder. We compare the quantum reading efficiency of entangled light with any classical source of light in this model. We show that entangled transmitters offer better reading performance than any classical transmitters of light in the regime of low signal intensity.
Relativistic exchange current corrections to the impulse approximation in low and intermediate energy neutrino--nucleus scattering are presented assuming non--vanishing strange quark form factors for constituent nucleons. Two--body exchange current operators which treat {\em all} $SU(3)$ vector and axial currents on an equal footing are constructed by generalizing the soft--pion dominance method of Chemtob and Rho. For charged current reactions, exchange current corrections can reduce the impulse approximation results by 5 to 10 \% depending on the nuclear density. A finite strange quark form factor may change the total cross section for neutral current scattering by 20\% while exchange current corrections are found to be sensitive to the nuclear density. Implications on the current LSND experiment to extract the strange quark axial form factor of the nucleon are discussed.
We argue that robust dense SLAM systems can make valuable use of the layers of features coming from a standard CNN as a pyramid of `semantic texture' which is suitable for dense alignment while being much more robust to nuisance factors such as lighting than raw RGB values. We use a straightforward Lucas-Kanade formulation of image alignment, with a schedule of iterations over the coarse-to-fine levels of a pyramid, and simply replace the usual image pyramid by the hierarchy of convolutional feature maps from a pre-trained CNN. The resulting dense alignment performance is much more robust to lighting and other variations, as we show by camera rotation tracking experiments on time-lapse sequences captured over many hours. Looking towards the future of scene representation for real-time visual SLAM, we further demonstrate that a selection using simple criteria of a small number of the total set of features output by a CNN gives just as accurate but much more efficient tracking performance.
When complex mechanisms are involved, pinpointing high-performance materials within large databases is a major challenge in materials discovery. We focus here on phonon-limited conductivities, and study 2D semiconductors doped by field effects. Using state-of-the-art density-functional perturbation theory and Boltzmann transport equation, we discuss 11 monolayers with outstanding transport properties. These materials are selected from a computational database of exfoliable materials providing monolayers that are dynamically stable and that do not have more than 6 atoms per unit cell. We first analyse electron-phonon scattering in two well-known systems: electron-doped InSe and hole-doped phosphorene. Both are single-valley systems with weak electron-phonon interactions, but they represent two distinct pathways to fast transport: a steep and deep isotropic valley for the former and strongly anisotropic electron-phonon physics for the latter. We identify similar features in the database and compute the conductivities of the relevant monolayers. This process yields several high-conductivity materials, some of them only very recently emerging in the literature (GaSe, Bi$_2$SeTe$_2$, Bi$_2$Se$_3$, Sb$_2$SeTe$_2$), others never discussed in this context (AlLiTe$_2$, BiClTe, ClGaTe, AuI). Comparing these 11 monolayers in detail, we discuss how the strength and angular dependency of the electron-phonon scattering drives key differences in the transport performance of materials despite similar valley structure. We also discuss the high conductivity of hole-doped WSe$_2$, and how this case study shows the limitations of a selection process that would be based on band properties alone.
The formalism of rainbow gravity is studied in a cosmological setting. We consider the very early universe which is radiation dominated. A novel treatment in our paper is to look for an ``averaged'' cosmological metric probed by radiation particles themselves. Taking their cosmological evolution into account, we derive the modified Friedmann-Robertson-Walker(FRW) equations which is a generalization of the solution presented by Magueijo and Smolin. Based on this phenomenological cosmological model we argue that the spacetime curvature has an upper bound such that the cosmological singularity is absent. These modified $FRW$ equations can be treated as effective equations in the semi-classical framework of quantum gravity and its analogy with the one recently proposed in loop quantum cosmology is also discussed.
The rapidity densities in Au-Au collisions at center-of-mass energies 200 and 130 A GeV measured at Relativistic Heavy-Ion Collider by STAR and PHENIX collaborations are analyzed within the statistical hadronization model at chemical freeze-out. We find that the model can describe the experimental rapidity densities well. The corresponding chemical freeze-out parameters are determined and they are seen to be in agreement with what we expect from our previous analyzes at lower beam energies at AGS and SPS.
Local variables can't describe the quantum correlations observed in tests of Bell inequalities. Likewise, we show that nonlocal variables can't describe quantum correlations in a relativistic time-order invariant way.
We defined a sub-sample of twelve GPS sources which have not been observed with the VLBI before, from the Parkes half-Jansky sample, and carried out VLBI observations at 1.6 GHz and 5 GHz with the European VLBI Network (EVN) in 2006 and 2008, respectively, to classify the source structure and to find compact symmetric objects (CSOs). Additionally, we carried out the 4.85 GHz flux density observations for these sources with the Urumqi 25-m telescope between the years 2007 and 2009 to study whether there is any variability in the total flux density of the GPS sources. The results of the 5 GHz VLBI observations and total flux densities of these sources are presented in this paper. From the VLBI morphologies, the spectral indices of components and the total flux variability of the twelve targets, we firmly classify three sources J0210+0419, J1135$-$0021, and J2058+0540 as CSOs, and classify J1057+0012, J1203+0414, and J1600$-$0037 as core-jet sources. The others J0323+0534, J0433$-$0229, J0913+1454, J1109+1043, and J1352+0232 are labelled CSO candidates, and J1352+1107 is a complex feature. Apart from core-jet sources, the total flux densities of the CSOs and candidates are quite stable at 5 GHz both during a long-term of $\sim$20 years relative to the PKS90 data and in a period between 2007 and 2009. The total flux densities are resolved-out by more than 20\% in the 5 GHz VLBI images for 6 sources, probably because of diffuse emission. In addition, we estimated the jet viewing angles $\Theta$ for the confirmed CSOs by using the double-lobe flux ratio of the sources, the result being indicative of relatively large $\Theta$ for the CSOs.
An approximate Z_3 family symmetry is proposed for leptons which results in a neutrino mass matrix with sin^2 2 theta_atm = 1 and tan^2 theta_sol = 0.5, but the latter value could easily be smaller. A generic requirement of this approach is the appearance of three Higgs doublets at the electroweak scale, resulting in possibly observable flavor violating leptonic decays, such as mu -> eee and mu -> e gamma.
Back-reaction of the massless scalar field vacuum to the Universe expansion is considered. Automatic renormalization procedure based on the equations of motion instead of the Friedman equation is used to avoid the cosmological constant problem. It is found, that the vacuum tends to decelerate an expansion of Universe if the conformal acceleration of Universe is equal to zero. In contract, the vacuum acts as the true cosmological constant in Universe expanding with the present day acceleration. Estimation for third derivative of the Universe scale factor with respect to conformal time is presented.
Let $\pi$ be an irreducible unitary cuspidal representation for $GL_m({\Bbb A}_{\Bbb Q})$, and let $L(s, \pi)$ be the automorphic $L$-function attached to $\pi$, which has a Dirichlet series expression in the half-plane $\mbox{Re} s>1$. When $\pi$ is self-contragredient, all the coefficients in the Dirichlet series expression are real. In this paper we give non-trivial lower bounds for the number of positive and negative coefficients, respectively.
Let $d$ and $n$ be integers satisfying $C\leq d\leq \exp(c\sqrt{\ln n})$ for some universal constants $c, C>0$, and let $z\in \mathbb{C}$. Denote by $M$ the adjacency matrix of a random $d$-regular directed graph on $n$ vertices. In this paper, we study the structure of the kernel of submatrices of $M-z\,{\rm Id}$, formed by removing a subset of rows. We show that with large probability the kernel consists of two non-intersecting types of vectors, which we call very steep and gradual with many levels. As a corollary, we show, in particular, that every eigenvector of $M$, except for constant multiples of $(1,1,\dots,1)$, possesses a weak delocalization property: its level sets have cardinality less than $Cn\ln^2 d/\ln n$. For a large constant $d$ this provides a principally new structural information on eigenvectors, implying that the number of their level sets grows to infinity with $n$. As a key technical ingredient of our proofs we introduce a decomposition of $\mathbb{C}^n$ into vectors of different degrees of `structuredness', which is an alternative to the decomposition based on the least common denominator in the regime when the underlying random matrix is very sparse.
In this paper, which is the second in a series of papers, we analyse what parameters can determine the width of the radio pulsar 'death valley' in the $P$-${\dot P}$ diagram. Using exact expression for the maximum potential drop, which can be realised over magnetic polar caps and the corresponding threshold for the secondary plasma production determined in Paper I, we analyse in detail the observed distribution of pulsars taking into account all the possible parameters (radius $R$ and moment of inertia of a neutron star $I_{\rm r}$, high-energy tail in the $\gamma$-quanta energy distribution giving rise to secondary particles, etc.) which could broaden 'the death line'. We show that the consistent allowance for all these effects leads to a sufficiently wide of 'the death valley' containing all the observed pulsars even for dipole magnetic field of a neutron star.
We report the discovery of a radio transient in the spiral galaxy M81. The transient was detected in early 2015 as part of a two-year survey of M81 made up of 12 epochs using the Karl G. Jansky Very Large Array. While undetected on 2014 September 12, the source was first detected on 2015 January 2, from which point it remained visible at an approximately constant luminosity of $L_{R} = 1.5 \pm 0.1 \times 10^{24}$erg s$^{-1}$ Hz$^{-1}$ at the observing frequency of 6 GHz for at least 2 months. Assuming this is a synchrotron event with a rise-time between 2.6 and 112 days, the peak luminosity (at equipartition) corresponds to a minimum energy of $10^{44} \lesssim E_{min} \lesssim 10^{46}$erg and jet power of $P_{min} \sim 10^{39}$erg s$^{-1}$, which are higher than most known X-ray binaries. Given its longevity, lack of short-term radio variability, and the absence of any multi-wavelength counterpart (X-ray luminosity $L_{X} \lesssim 10^{36}$erg s$^{-1}$), it does not behave like known Galactic or extragalactic X-ray binaries. The M81 transient radio properties more closely resemble the unidentified radio transient 43.78+59.3 discovered in M82, which has been suggested to be a radio nebula associated with an accreting source similar to SS 433. One possibility is that both the new M81 transient and the M82 transient may be the birth of a short-lived radio bubble associated with a discrete accretion event similar to those observed from the ULX Holmberg II X-1. However, it is not possible to rule out other identifications including long-term supernova shockwave interactions with the surrounding medium from a faint supernova or a background active galaxy.
Correlation between the variations of quasar absorption lines and the ionizing continuum have been recently confirmed in systematic studies. However, no convincing individual case is reported. We present a statistical analysis of the variable C iv broad absorption line (BAL) in the quasar SDSS J141007.74+541203.3, which have been observed with 44 epochs by the Sloan Digital Sky Survey Data Release 14. Grier et al. (2015) has recently concluded that the most likely cause of the variability of the BAL in SDSS J141007.74+541203.3 is a rapid response to changes in the incident ionizing continuum. In this paper, we confirm the anticorrelation between the equivalent width of BALs and the flux of the continuum based on the spectra of this quasar that show significant variations, which serve as another independent evidence for the view of Grier et al. (2015).
We determine all families of Markovian three-states lattice gases with pair interaction and a single local conservation law. One such family of models is an asymmetric exclusion process where particles exist in two different nonconserved states. We derive conditions on the transition rates between the two states such that the shock has a particularly simple structure with minimal intrinsic shock width and random walk dynamics. We calculate the drift velocity and diffusion coefficient of the shock.
If a fermion is travelling through a medium, it can have matter-induced magnetic and electric dipole moments. These contributions conserve chirality, and can be non-vanishing even for a Majorana neutrino. Several implications for neutrino physics are discussed.
Given a graph $G$, the exact distance-$p$ graph $G^{[\natural p]}$ has $V(G)$ as its vertex set, and two vertices are adjacent whenever the distance between them in $G$ equals $p$. We present formulas describing the structure of exact distance-$p$ graphs of the Cartesian, the strong, and the lexicographic product. We prove such formulas for the exact distance-$2$ graphs of direct products of graphs. We also consider infinite grids and some other product structures. We characterize the products of graphs of which exact distance graphs are connected. The exact distance-$p$ graphs of hypercubes $Q_n$ are also studied. As these graphs contain generalized Johnson graphs as induced subgraphs, we use some known and find some new constructions of their colorings. These constructions are applied for colorings of the exact distance-$p$ graphs of hypercubes with the focus on the chromatic number of $Q_{n}^{[\natural p]}$ for $p\in \{n-2,n-3,n-4\}$.
This paper presents PANIC, a 3D discrete mesoscale dislocation dynamics model which includes a fully quantitative treatment of both dislocation climb and dislocation glide, including climb driven by both osmotic and mechanical stresses and climb enabled by both bulk and pipe diffusion, including full elastic anisotropy for materials with hexagonal symmetry. Efficient calculations can be performed for epitaxial thin films, multilayers and device structures with free surfaces, including those with irregular geometries (e.g. islands). The model also includes the capability to simulate dislocation dynamics during the growth of the thin films or heterostructures. The model has been validated against experiment for thin films of GaN, AlN and AlGaN but is widely applicable to other material systems, both hexagonal and cubic.
We study non-linear phenomena in quantum dots. Non linearities are reflected in the I-V characteristic curve as bistabilities, instabilities and time dependent oscillations of the currents. The nature of the non-linear behavior depends upon the parameters that define the system.
We have studied the spin dynamics of a dense two-dimensional electron gas confined in a GaAs/AlGaAs triple quantum well by using time-resolved Kerr rotation and resonant spin amplification. Strong anisotropy of the spin relaxation time up to a factor of 10 was found between the electron spins oriented in-plane and out-of-plane when the excitation energy is tuned to an exciton bound to neutral donor transition. We model this anisotropy using an internal magnetic field and the inhomogeneity of the electron g-factor. The data analysis allows us to determine the direction and magnitude of this internal field in the range of a few mT for our studied structure, which decreases with the sample temperature and optical power. The dependence of the anisotropic spin relaxation was directly measured as a function of several experimental parameters: excitation wavelength, sample temperature, pump-probe time delay, and pump power.
We performed deep photometry of the central region of Galactic globular cluster M15 from archival Hubble Space Telescope data taken on the High Resolution Channel and Solar Blind Channel of the Advanced Camera for Surveys. Our data set consists of images in far-UV (FUV$_{140}$; F140LP), near-UV (NUV$_{220}$; F220W), and blue (B$_{435}$; F435W) filters. The addition of an optical filter complements previous UV work on M15 by providing an additional constraint on the UV-bright stellar populations. Using color-magnitude diagrams (CMDs) we identified several populations that arise from non-canonical evolution including candidate blue stragglers, extreme horizontal branch stars, blue hook stars (BHks), cataclysmic variables (CVs), and helium-core white dwarfs (He WDs). Due to preliminary identification of several He WD and BHk candidates, we add M15 as a cluster containing a He WD sequence and suggest it be included among clusters with a BHk population.   We also investigated a subset of CV candidates that appear in the gap between the main sequence (MS) and WDs in FUV$_{140}-$NUV$_{220}$ but lie securely on the MS in NUV$_{220}-$B$_{435}$. These stars may represent a magnetic CV or detached WD-MS binary population. Additionally, we analyze our candidate He WDs using model cooling sequences to estimate their masses and ages and investigate the plausibility of thin vs. thick hydrogen envelopes. Finally, we identify a class of UV-bright stars that lie between the horizontal branch and WD cooling sequences, a location not usually populated on cluster CMDs. We conclude these stars may be young, low-mass He WDs.
Representation learning from 3D point clouds is challenging due to their inherent nature of permutation invariance and irregular distribution in space. Existing deep learning methods follow a hierarchical feature extraction paradigm in which high-level abstract features are derived from low-level features. However, they fail to exploit different granularity of information due to the limited interaction between these features. To this end, we propose Multi-Abstraction Refinement Network (MARNet) that ensures an effective exchange of information between multi-level features to gain local and global contextual cues while effectively preserving them till the final layer. We empirically show the effectiveness of MARNet in terms of state-of-the-art results on two challenging tasks: Shape classification and Coarse-to-fine grained semantic segmentation. MARNet significantly improves the classification performance by 2% over the baseline and outperforms the state-of-the-art methods on semantic segmentation task.