ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigate the onset of the discontinuous percolation transition in small-world hyperbolic networks by studying the systems-size scaling of the typical largest cluster approaching the transition, $p\nearrow p_{c}$. To this end, we determine the average size of the largest cluster $\left\langle s_{{\rm max}}\right\rangle \sim N^{\Psi\left(p\right)}$ in the thermodynamic limit using real-space renormalization of cluster generating functions for bond and site percolation in several models of hyperbolic networks that provide exact results. We determine that all our models conform to the recently predicted behavior regarding the growth of the largest cluster, which found diverging, albeit sub-extensive, clusters spanning the system with finite probability well below $p_{c}$ and at most quadratic corrections to unity in $\Psi\left(p\right)$ for $p\nearrow p_{c}$. Our study suggest a large universality in the cluster formation on small-world hyperbolic networks and the potential for an alternative mechanism in the cluster formation dynamics at the onset of discontinuous percolation transitions.
A generalization of Serre's $p$-adic Eisenstein series in the case of Siegel modular forms is studied and a coincidence between a $p$-adic Siegel Eisenstein series and a genus theta series associated with a quaternary quadratic form is proved.
We present results of systematic calculations of the isospin-symmetry-breaking corrections to the superallowed I=$0+,T=1 --> I=0+,T=1 beta-decays, based on the self-consistent isospin- and angular-momentum-projected nuclear density functional theory (DFT). We discuss theoretical uncertainties of the formalism related to the basis truncation, parametrization of the underlying energy density functional, and ambiguities related to determination of Slater determinants in odd-odd nuclei. A generalization of the double-projected DFT model towards a no core shell-model-like configuration-mixing approach is formulated and implemented. We also discuss new opportunities in charge-symmetry- and charge-independence-breaking studies offered by the newly developed DFT formalism involving proton-neutron mixing in the particle-hole channel.
The aim of this paper is to give a short overview for the set of publications considering recently found effect of non-equivalence of multiplicity fluctuations in relativistic gases with globally conserved charge and energy.
We report a technique for transferring large areas of the CVD-grown, few-layer MoS2 from the original substrate to another arbitrary substrate and onto holey substrates, in order to obtain free-standing structures. The method consists of a polymer- and residue-free, surface-tension-assisted wet transfer, in which we take advantage of the hydrophobic properties of the MoS2. The methods yields better quality transferred layers, with fewer cracks and defects, and less contamination than the widely used PMMA-mediated transfer and allows fabrication of few-layer, fee-standing structures with diameters up to 100 micro-m. We report thermal conductivity measurements by means of contactless Raman thermometry on the so-fabricated samples. The measurements revealed a strong reduction in the in-plane thermal conductivity down to 0.5 W/mK. The results are explained using finite elements method simulations for a polycrystalline film.
We present the 2019 DAVIS Challenge on Video Object Segmentation, the third edition of the DAVIS Challenge series, a public competition designed for the task of Video Object Segmentation (VOS). In addition to the original semi-supervised track and the interactive track introduced in the previous edition, a new unsupervised multi-object track will be featured this year. In the newly introduced track, participants are asked to provide non-overlapping object proposals on each image, along with an identifier linking them between frames (i.e. video object proposals), without any test-time human supervision (no scribbles or masks provided on the test video). In order to do so, we have re-annotated the train and val sets of DAVIS 2017 in a concise way that facilitates the unsupervised track, and created new test-dev and test-challenge sets for the competition. Definitions, rules, and evaluation metrics for the unsupervised track are described in detail in this paper.
We present a calculation of the angle-averaged squeezed matter bispectrum covariance ${\rm Cov}\left(B_{m}(k_1, k_1', s_1), B_{m}(k_2, k_2', s_2)\right)$, $s_i \ll k_i,k_i'$ ($i=1,2$), that uses matter power spectrum responses to describe the coupling of large- to short-scale modes in the nonlinear regime. The covariance is given by a certain configuration of the 6-point function, which we show is dominated by response-type mode-coupling terms in the squeezed bispectrum limit. The terms that are not captured by responses are small, effectively rendering our calculation complete and predictive for linear $s_1,s_2$ values and any nonlinear values of $k_1,k_1',k_2,k_2'$. Our numerical results show that the squeezed bispectrum super-sample covariance is only a negligible contribution. We also compute the power spectrum-bispectrum cross-covariance using responses. Our derivation for the squeezed matter bispectrum is the starting point to calculate analytical covariances for more realistic galaxy clustering and weak-lensing applications. It can also be used in cross-checks of numerical ensemble estimates of the general bispectrum covariance, given that it is effectively noise-free and complete in the squeezed limit.
An oriented cycle is an orientation of a undirected cycle. We first show that for any oriented cycle $C$, there are digraphs containing no subdivision of $C$ (as a subdigraph) and arbitrarily large chromatic number. In contrast, we show that for any $C$ a cycle with two blocks, every strongly connected digraph with sufficiently large chromatic number contains a subdivision of $C$. We prove a similar result for the antidirected cycle on four vertices (in which two vertices have out-degree $2$ and two vertices have in-degree $2$).
We present an analysis of the intracluster light in the Frontier Field Cluster MACS J1149.5+2223 (z=0.544), which combines new and archival Hubble WFC3/IR imaging to provide continuous radial coverage out to 2.8 Mpc from the brightest cluster galaxy. Employing careful treatment of potential systematic biases and using data at the largest radii to determine the background sky level, we reconstruct the surface brightness profile out to a radius of 2 Mpc. This radius is the largest to which the intracluster light (ICL) has been measured for an individual cluster. Within this radius, we measure a total luminosity of 1.5e13 Lsun for the brightest cluster galaxy plus ICL light. From the profile and its logarithmic slope, we identify the transition from the brightest cluster galaxy to ICL at r~70 kpc. Remarkably, we also detect an inflection in the profile centered in the 1.2-1.7 Mpc (0.37-0.52 r200m) radial bin, a signature of an infall caustic in the stellar distribution. Based upon the shape and strength of the feature, we interpret it as potentially being at the splashback radius, although the radius is smaller than theoretical predictions. If this is the splashback radius, then it is the first such detection in the ICL and the first detection of the splashback radius for an individual cluster. Similar analyses should be possible with the other Frontier Field clusters, and eventually with clusters from the Euclid and Roman missions.
We construct a smooth symmetric compactification of the space of all labeled tetrahedra in P^3.
We describe a simple model which explains the qualitative and (approximate) quantitative features of the distribution of orbital velocities of merging pairs of dark matter halos. Our model considers a primary dark matter halo as a perturber in a background of secondary halos with velocities described by linear theory. By evaluating the ensemble of secondary halos on orbits within the perturbing halo's "loss cone" we derive the distribution of orbital parameters of these captured halos. This model is able provide qualitative explanations for the features of this distribution as measured from N-body simulations, and is in approximate quantitative agreement with those measurements. As the velocity dispersion of the background halos is larger on smaller scales our model predicts an overall increase in the characteristic velocities of merging halos, relative to the virial velocities of those halos, in lower mass systems. Our model also provides a simple explanation for the measured independence of the orbital velocity distribution function on redshift when considered at fixed peak height. By connecting the orbital parameter distribution to the underlying power spectrum our model also allows for estimates to be made of the effect of modifying that power spectrum, for example by including a truncation at large wavenumber. For plausible warm dark matter models we find that this truncation has only a small effect on the predicted distributions.
In this paper we study the existence of densities for strongly degenerate stochastic differential equations (SDEs) whose coefficients depend on time and are not globally Lipschitz. In these models neither local ellipticity nor the strong H\"ormander condition is satisfied. In this general setting we show that continuous transition densities indeed exist in all neighborhoods of points where the weak H\"ormander condition is satisfied. We also exhibit regions where these densities remain positive. We then apply these results to stochastic Hodgkin-Huxley models with periodic input as a first step towards the study of ergodicity properties of such systems in the sense of [27]-[28].
The effect of a lateral electric current on the photoluminescence H-band of an AlGaAs/GaAs heterostructure is investigated. The photoluminescence intensity and optical orientation of electrons contributing to the H-band are studied by means of continuous wave and time-resolved photoluminescence spectroscopy and time-resolved Kerr rotation. It is shown that the H-band is due to recombination of the heavy holes localized at the heterointerface with photoexcited electrons attracted to the heterointerface from the GaAs layer. Two lines with significantly different decay times constitute the H-band: a short-lived high-energy one and a long-lived low-energy one. The high-energy line originates from recombination of electrons freely moving along the structure plane, while the low-energy one is due to recombination of donor-bound electrons near the interface. Application of the lateral electric field of ~ 100-200 V/cm results in a quenching of both lines. This quenching is due to a decrease of electron concentration near the heterointerface as a result of a photocurrent-induced heating of electrons in the GaAs layer. On the contrary, electrons near the heterointerface are effectively cooled, so the donors near the interface are not completely empty up to ~ 100 V/cm, which is in stark contrast with the case of bulk materials. The optical spin polarization of the donor-bound electrons near the heterointerface weakly depends on the electric field. Their polarization kinetics is determined by the spin dephasing in the hyperfine fields of the lattice nuclei. The long spin memory time (> 40 ns) can be associated with suppression of the Bir-Aronov-Pikus mechanism of spin relaxation for electrons.
In constrast to discretized space-time approximations to continuum quantum field theories, discretized velocity space approximations to continuum quantum field theories are investigated. A four-momentum operator is given in terms of bare fermion-antifermion-boson creation and annihilation operators with discrete indices. In continuum quantum field theories the fermion-antifermion creation and annihilation operators appear as bilinears in the four-momentum operator and generate a unitary algebra. When the number of modes range over only a finite number of values, the algebra is that associated with the Lie algebra of U(2N). By keeping N finite (but arbitrary) problems due to an infinite Lorentz volume and to the creation of infinite numbers of bare fermion-antifermion pairs are avoided. But even with a finite number of modes, it is still possible to create an infinite number of bare bosons. We show how the full boson algebra arises as the contraction limit of another unitary algebra that restricts the number of bare bosons in any mode to be finite. Generic properties of finite mode Hamiltonians are investigated, as are several simple models to see the rate of convergence of the boson contraction; the possibility of fine tuning the bare strong coupling constant is also briefly discussed.
We give two characterizations, one for the class of generalized Young measures generated by $\mathcal A$-free measures, and one for the class generated by $\mathcal B$-gradient measures $\mathcal Bu$. Here, $\mathcal A$ and $\mathcal B$ are linear homogeneous operators of arbitrary order, which we assume satisfy the constant rank property. The characterization places the class of generalized $\mathcal A$-free Young measures in duality with the class of $\mathcal A$-quasiconvex integrands by means of a well-known Hahn--Banach separation property. A similar statement holds for generalized $\mathcal B$-gradient Young measures. Concerning applications, we discuss several examples that showcase the rigidity or the failure of $\mathrm{L}^1$-compensated compactness when concentration of mass is allowed. These include the failure of $\mathrm{L}^1$-estimates for elliptic systems and the failure of $\mathrm{L}^1$-rigidity for the two-state problem. As a byproduct of our techniques we also show that, for any bounded open set $\Omega$, the inclusions \[ \mathrm{L}^1(\Omega) \cap \ker \mathcal A \hookrightarrow \mathcal M(\Omega) \cap \ker \mathcal A, \] \[ \{\mathcal B u\in \mathrm{C}^\infty(\Omega)\} \hookrightarrow \{\mathcal B u\in \mathcal M(\Omega)\}, \] are dense with respect to area-functional convergence of measures
A minimal model is proposed for the perovskite manganese oxides showing the strongly incoherent charge dynamics with a suppressed Drude weight in the ferromagnetic and metallic phase near the insulator. We investigate a generalized double-exchange model including three elements; the orbital degeneracy of $e_g$ conduction bands, the Coulomb interaction and fluctuating Jahn-Teller distortions. We demonstrate that Lancz$\ddot{\rm o}$s diagonalization calculations combined with Monte Carlo sampling of the largely fluctuating lattice distortions result in the optical conductivity which quantitatively accounts for the experimental indications. It is found that all the three elements are indispensable to understand the charge dynamics in these compounds.
We consider the evolution of white dwarfs with compact object companions (specifically black holes with masses up to 10^6 solar masses, neutron stars, and other white dwarfs). We suppose that the orbits are initially quite elliptical and then shrink and circularise under the action of gravitational radiation. During this evolution, the white dwarfs will pass through resonances when harmonics of the orbital frequency match the stellar oscillation eigenfrequencies. As a star passes through these resonances, the associated modes will be excited and can be driven to amplitudes that are so large that there is a back reaction on the orbit which, in turn, limits the growth of the modes. A formalism is presented for describing this dynamical interaction for a non-rotating star in the linear approximation when the orbit can be treated as non-relativistic. A semi-analytical expression is found for computing the resonant energy transfer as a function of stellar and orbital parameters for the regime where back reaction may be neglected. This is used to calculate the results of passage through a sequence of resonances for several hypothetical systems. It is found that the amplitude of the l=m=2 f-mode can be driven into the non-linear regime for appropriate initial conditions. We also discuss where the no back reaction approximation is expected to fail, and the qualitative effects of back reaction.
Magnetically-driven non-stationary acceleration of jets in AGNs results in the leading parts of the flow been accelerated to much higher Lorentz factors than in the case of steady state acceleration with the same parameters. The higher Doppler-boosted parts of the flow may dominate the high energy emission of blazar jets. We suggest that highly variable GeV and TeV emission in blazars is produced by the faster moving leading edges of highly magnetized non-stationary ejection blobs, while the radio data trace the slower-moving bulk flow. Model predictions compare favorably with the latest Fermi gamma-ray and MOJAVE radio VLBI results.
From in-situ ellipsometric measurements during condensation of As4 molecular beam on GaAs(001) substrate the arsenic sticking coefficient was determined. For the substrate with Ga-rich surface reconstruction at 60C the sticking coefficient was found to be 7x10-3, whereas for the surface of amorphous arsenic this coefficient was only 8x10-4. Kinetic studies of As sublimation were also performed and activation energy for the process was obtained. For amorphous As films grown from As2 beam the activation energy was found to be DeltaE=1.84+-0.03eV, which is 0.39eV higher than the enthalpy of solid-vapor phase transition. Temperature dependence of evaporation coefficient for amorphous As was determined in the 230-290C range.
This paper tackles face recognition in videos employing metric learning methods and similarity ranking models. The paper compares the use of the Siamese network with contrastive loss and Triplet Network with triplet loss implementing the following architectures: Google/Inception architecture, 3D Convolutional Network (C3D), and a 2-D Long short-term memory (LSTM) Recurrent Neural Network. We make use of still images and sequences from videos for training the networks and compare the performances implementing the above architectures. The dataset used was the YouTube Face Database designed for investigating the problem of face recognition in videos. The contribution of this paper is two-fold: to begin, the experiments have established 3-D Convolutional networks and 2-D LSTMs with the contrastive loss on image sequences do not outperform Google/Inception architecture with contrastive loss in top $n$ rank face retrievals with still images. However, the 3-D Convolution networks and 2-D LSTM with triplet Loss outperform the Google/Inception with triplet loss in top $n$ rank face retrievals on the dataset; second, a Support Vector Machine (SVM) was used in conjunction with the CNNs' learned feature representations for facial identification. The results show that feature representation learned with triplet loss is significantly better for n-shot facial identification compared to contrastive loss. The most useful feature representations for facial identification are from the 2-D LSTM with triplet loss. The experiments show that learning spatio-temporal features from video sequences is beneficial for facial recognition in videos.
Cactus varieties are a generalization of secant varieties. They are defined using linear spans of arbitrary finite schemes of bounded length, while secant varieties use only isolated reduced points. In particular, any secant variety is always contained in the respective cactus variety, and, except in a few initial cases, the inclusion is strict. It is known that lots of natural criteria that test membership in secant varieties are actually only tests for membership in cactus varieties. In this article, we propose the first techniques to distinguish actual secant variety from the cactus variety in the case of the Veronese variety. We focus on two initial cases, $\kappa_{14}(\nu_d(\mathbb{P}^n))$ and $\kappa_{8,3}(\nu_d(\mathbb{P}^n))$, the simplest that exhibit the difference between cactus and secant varieties. We show that for $d\geq 5$, the component of the cactus variety $\kappa_{14}(\nu_d(\mathbb{P}^6))$ other than the secant variety $\sigma_{14}(\nu_d(\mathbb{P}^6))$ consists of degree $d$ polynomials divisible by a $(d-3)$-rd power of a linear form. We generalize this description to an arbitrary number of variables. We present an algorithm for deciding whether a point in the cactus variety $\kappa_{14}(\nu_d(\mathbb{P}^n))$ belongs to the secant variety $\sigma_{14}(\nu_d(\mathbb{P}^n))$ for $d\geq 6,$ $n \geq 6$. We obtain similar results for the Grassmann cactus variety $\kappa_{8,3}(\nu_d(\mathbb{P}^n))$. Our intermediate results give also a partial answer to analogous problems for other cactus varieties and Grassmann cactus varieties to any Veronese variety.
An edge labeling of a connected graph $G = (V, E)$ is said to be local antimagic if it is a bijection $f:E \to\{1,\ldots ,|E|\}$ such that for any pair of adjacent vertices $x$ and $y$, $f^+(x)\not= f^+(y)$, where the induced vertex label $f^+(x)= \sum f(e)$, with $e$ ranging over all the edges incident to $x$. The local antimagic chromatic number of $G$, denoted by $\chi_{la}(G)$, is the minimum number of distinct induced vertex labels over all local antimagic labelings of $G$. In this paper, several sufficient conditions for $\chi_{la}(H)\le \chi_{la}(G)$ are obtained, where $H$ is obtained from $G$ with a certain edge deleted or added. We then determined the exact value of the local antimagic chromatic number of many cycle related join graphs.
Image super-resolution (SR) is a representative low-level vision problem. Although deep SR networks have achieved extraordinary success, we are still unaware of their working mechanisms. Specifically, whether SR networks can learn semantic information, or just perform complex mapping function? What hinders SR networks from generalizing to real-world data? These questions not only raise our curiosity, but also influence SR network development. In this paper, we make the primary attempt to answer the above fundamental questions. After comprehensively analyzing the feature representations (via dimensionality reduction and visualization), we successfully discover the distinctive "semantics" in SR networks, i.e., deep degradation representations (DDR), which relate to image degradation instead of image content. We show that a well-trained deep SR network is naturally a good descriptor of degradation information. Our experiments also reveal two key factors (adversarial learning and global residual) that influence the extraction of such semantics. We further apply DDR in several interesting applications (such as distortion identification, blind SR and generalization evaluation) and achieve promising results, demonstrating the correctness and effectiveness of our findings.
The electromagnetic field is studied in a family of exact solutions of the Einstein equations whose material content is a perfect fluid with stiff equation of state (p = $\epsilon $ ). The field equations are solved exactly for several members of the family.
The possibility of having a gauge fixing term in the effective Lagrangian that is not a quadratic expression has been explored in spin-two theories so as to have a propagator that is both traceless and transverse. We first show how this same approach can be used in spontaneously broken gauge theories as an alternate to the 't Hooft gauge fixing which avoids terms quadratic in the scalar fields. This "non-quadratic" gauge fixing in the effective action results in there being two complex Fermionic and one real Bosonic ghost fields. A global gauge invariance involving a Fermionic gauge parameter, analogous to the usual BRST invariance, is present in this effective action.