ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper we consider the extreme behavior of the extremal eigenvalues of white Wishart matrices, which plays an important role in multivariate analysis. In particular, we focus on the case when the dimension of the feature p is much larger than or comparable to the number of observations n, a common situation in modern data analysis. We provide asymptotic approximations and bounds for the tail probabilities of the extremal eigenvalues. Moreover, we construct efficient Monte Carlo simulation algorithms to compute the tail probabilities. Simulation results show that our method has the best performance amongst known approximation approaches, and furthermore provides an efficient and accurate way for evaluating the tail probabilities in practice.
We present a brief historical overview of the classical theory of a radiating point charge, described by the Lorentz-Dirac equation. A recent development is the discovery of tunnelling of a charge through a potential barrier, in a completely classical context. Also, a concrete example is discussed of the existence of several physically acceptable solutions for a range of initial data. We end by pointing out some open problems in connection with D-brane and monopole physics.
The effect of a generalized uncertainty principle on the structure of an ideal white dwarf star is investigated. The equation describing the equilibrium configuration of the star is a generalized form of the Lane-Emden equation. It is proved that the star always has a finite size. It is then argued that the maximum mass of such an ideal white dwarf tends to infinity, as opposed to the conventional case where it has a finite value.
A detailed description of the structure of two-ended arc-transitive digraphs is given. It is also shown that several sets of conditions, involving such concepts as Property Z, local quasi-primitivity and prime out-valency, imply that an arc-transitive digraph must be highly-arc-transitive. These are then applied to give a complete classification of two-ended highly-arc-transitive digraphs with prime in- and out-valencies.
We introduce the Unity Perception package which aims to simplify and accelerate the process of generating synthetic datasets for computer vision tasks by offering an easy-to-use and highly customizable toolset. This open-source package extends the Unity Editor and engine components to generate perfectly annotated examples for several common computer vision tasks. Additionally, it offers an extensible Randomization framework that lets the user quickly construct and configure randomized simulation parameters in order to introduce variation into the generated datasets. We provide an overview of the provided tools and how they work, and demonstrate the value of the generated synthetic datasets by training a 2D object detection model. The model trained with mostly synthetic data outperforms the model trained using only real data.
We study the phenomenology of singlet Dirac fermion dark matter in the simplified models where the dark matter interacts with the Standard Model particles at loop-level with the help of either colored or non-colored mediators. We especially focus on the implications of non-zero CP phases in the dark sector, which induce the electric dipole moments of the Dirac fermion dark matter as well as those of electron and nucleon. It is then found that the dark matter direct detection searches and the measurements of the electric dipole moments are able to test the singlet Dirac fermion dark matter scenario in the forthcoming experiments.
The increase in the resistivity with decreasing temperature followed by a drop by more than one order of magnitude is observed on the metallic side near the zero-magnetic-field metal-insulator transition in a strongly interacting two-dimensional electron system in ultra-clean SiGe/Si/SiGe quantum wells. We find that the temperature $T_{\text{max}}$, at which the resistivity exhibits a maximum, is close to the renormalized Fermi temperature. However, rather than increasing along with the Fermi temperature, the value $T_{\text{max}}$ decreases appreciably for spinless electrons in spin-polarizing (parallel) magnetic fields. The observed behaviour of $T_{\text{max}}$ cannot be described by existing theories. The results indicate the spin-related origin of the effect.
Based on the low-energy effective field theory of D-branes, the mass spectrum of an extended Standard Model with two-Higgs doublets used to generate all the mass terms is investigated. Besides the gauge bosons, the fermion mass spectrum is weighted by the Higgs VEVs with a partial hierarchy and the smallness of neutrino masses is exhibited. With reference to the known data, the involved scales of the model are approached.
Most realistic, off-lattice surface simulations are done canonically--- conserving particles. For some applications, however, such as studying the thermal behavior of rare gas solid surfaces, these constitute bad working conditions. Surface layer occupancies are believed to change with temperature, particularly at preroughening, and naturally call for a grand canonical approach, where particle number is controlled by a chemical potential. We report preliminary results of novel realistic grand canonical Monte Carlo simulations of the Lennard-Jones (LJ) fcc(111) surface, believed to represent a quantitative model of e.g. Ar(111). The results are successful and highly informative for temperatures up to roughly 0.8 T_m, where clear precursor signals of preroughening are found. At higher temperatures, convergence to equilibrium is hampered by large fluctuations.
We present two new solutions of Romans' massive type IIA supergravity characterized by the two non-trivial massive potentials of Romans' theory: the NSNS 2-form and the RR 7-form. They can be interpreted respectively as the intersection of a fundamental string and a D8-brane over a D0-brane and the intersection of a D6-brane with a D8-brane over a NSNS5-brane. The D8-brane manifests itself through the mass parameter and in the massless limit one recovers the standard fundamental string and D6-brane solutions. Although these solutions do not have the usual form for BPS bound states at threshold and each of them involves 3 objects, both of them preserve 1/4 of the supersymmetries.
We use multiple scattering theory to evaluate the $Q^{2}$ dependence   of the forward-backward asymmetry, $A_{z}$, of the missing momentum distribution in quasielstic $A(e,e'p)$ scattering, which is expected to be affected by color transparency. The novel features of our analysis are a consistent treatment of the structure of the ejectile state formed after absorption of the virtual photon by the struck proton and a careful evaluation of the background asymmetry induced by the nonvanishing real part of the proton-nucleon scattering amplitude. We find that the absolute magnitude of $A_{z}$ is dominated by this background at the $Q^{2}$'s attainable at the Continuous Electron Beam Accelerator Facility. However, the $Q^{2}$ dependence of the asymmetry is sensitive to the onset of color transparency, whose observation in high statistics experiments appears to be feasible, particularly using light targets such as $^{12}C$ or $^{16}O$.
We reexamine physical causal propagators for scalar and pseudoscalar bound states at finite temperature in a chiral $U_L(1)\times U_R(1)$ NJL model, defined by four-point amputated functions subtracted through the gap equation, and prove that they are completely equivalent in the imaginary-time and real-time formalism by separating carefully the imaginary part of the zero-temperature loop integral. It is shown that the thermal transformation matrix of the matrix propagators for these bound states in the real-time formalism is precisely the one of the matrix propagator for an elementary scalar particle and this fact shows similarity of thermodynamic property between a composite and an elementary scalar particle. The retarded and advanced propagators for these bound states are also given explicitly from the imaginary-time formalism.
We present a study of the properties of the star-cluster systems around pseudo-bulges of late-type spiral galaxies using a sample of 11 galaxies with distances from 17 to 37 Mpc. Star clusters are identified from multiband HST ACS and WFPC2 imaging data by combining detections in 3 bands (F435W and F814W with ACS and F606W with WFPC2). The photometric data are then compared to population synthesis models to infer the masses and ages of the star clusters. Photometric errors and completeness are estimated by means of artificial source Monte Carlo simulations. Dust extinction is estimated by considering F160W NICMOS observations of the central regions of the galaxies, augmenting our wavelength coverage. In all galaxies we identify star clusters with a wide range of ages, from young (age < 8 Myr) blue clusters, with typical mass of 10^3 Msun to older (age > 100-250 Myr), more massive, red clusters. Some of the latter might likely evolve into objects similar to the Milky Way's globular clusters. We compute the specific frequencies for the older clusters with respect to the galaxy and bulge luminosities. Specific frequencies relative to the galaxy light appear consistent with the globular cluster specific frequencies of early-type spirals. We compare the specific frequencies relative to the bulge light with the globular cluster specific frequencies of dwarf galaxies, which have a surface-brightness profile that is similar to that of the pseudo-bulges in our sample. The specific frequencies we derive for our sample galaxies are higher than those of the dwarf galaxies, supporting an evolutionary scenario in which some of the dwarf galaxies might be the remnants of harassed late-type spiral galaxies which hosted a pseudo-bulge.
This survey is based on a graduate short course given by the author at the Universit\`a degli Studi dell'Aquila, as a part of the Intensive Programme of the European Union "Mathematical Models in Life and Social Sciences", in July 2008. It covers the basics of probability and some examples of modelling of random phenomena in daily life, industry, biology and economy.   The year after the course, on April 6th 2009, the building where the programme took place was destroyed by a strong earthquake that caused more than 300 deaths in the region. This work is dedicated to the people that died, lost a beloved one, or lost their homes that day.
The quantum dynamics of an electron in a uniform magnetic field is studied for geometries corresponding to integrable cases. We obtain the uniform asymptotic approximation of the WKB energies and wavefunctions for the semi-infinite plane and the disc. These analytical solutions are shown to be in excellent agreement with the numerical results obtained from the Schrodinger equations even for the lowest energy states. The classically exact notions of bulk and edge states are followed to their semi-classical limit, when the uniform approximation provides the connection between bulk and edge.
The conformal Skorokhod embedding problem (CSEP) is a planar variant of the classical problem where the solution is now a simply connected domain $D\subset\mathbb{C}$ whose exit time embeds a given probability distribution $\mu$ by projecting the stopped Brownian motion onto the real axis. In this paper we explore two new research directions for the CSEP by proving general bounds on the principal Dirichlet eigenvalue of a solution domain in terms of the corresponding $\mu$ and by proposing related extremal problems. Moreover, we give a new and nontrivial example of an extremal domain $\mathbb{U}$ that attains the lowest possible principal Dirichlet eigenvalue over all domains solving the CSEP for the uniform distribution on $[-1,1]$. Remarkably, the boundary of $\mathbb{U}$ is related to the Grim Reaper translating solution to the curve shortening flow in the plane. The novel tool used in the proof of the sharp lower bound is a precise relationship between the widths of the orthogonal projections of a simply connected planar domain and the support of its harmonic measure that we develop in the paper. The upper bound relies on spectral bounds for the torsion function which have recently appeared in the literature.
In a recent paper, Bruns and von Thaden established a bound for the length of vectors involved in a unimodular triangulation of simplicial cones. The bound is exponential in the square of the logarithm of the multiplicity, and improves previous bounds significantly. The authors mentioned that the next goal would be a bound that is polynomial in the multiplicity but not knowing if such a bound exists. In this paper we will prove that such a bound, which is polynomial in the multiplicity $\mu$, indeed exists. In detail, the bound is of the type $\mu^{f(d)}$ with $f(d) \in \mathcal{O}(d)$.
The excitation spectrum of the frustrated spin-$1/2$ Heisenberg chain is reexamined using variational and exact diagonalization calculations. We show that the overlap matrix of the short-range resonating valence bond states basis can be inverted which yields tractable equations for single and two spinons excitations. Older results are recovered and new ones, such as the bond-state dispersion relation and its size with momentum at the Majumdar-Ghosh point are found. In particular, this approach yields a gap opening at $J_2=0.25J_1$ and an onset of incommensurability in the dispersion relation at $J_2=9/17J_1$ [as in S. Brehmer \emph{et al.}, J. Phys.: Condens. Matter \textbf{10}, 1103 (1998)]. These analytical results provide a good support for the understanding of exact diagonalization spectra, assuming an independent spinons picture.
The neutrino-cooled accretion disk, which was proposed to work as the central engine of gamma-ray bursts, encounters difficulty in interpreting the X-ray flares after the prompt gamma-ray emission. In this paper, the magnetic coupling between the inner disk and the central black hole is taken into consideration. For mass accretion rates around $0.001 \sim 0.1 M_{\sun} s^{-1}$, our results show that the luminosity of neutrino annihilation can be significantly enhanced due to the coupling effects. As a consequence, after the gamma-ray emission, a remnant disk with mass $M_{disk} \la 0.5 M_{\sun}$ may power most of the observed X-ray flares with the rest frame duration less than 100 seconds. In addition, a comparison between the magnetic coupling process and the Blandford-Znajek mechanism is shown on the extraction of black hole rotational energy.
Recent single image unsupervised representation learning techniques show remarkable success on a variety of tasks. The basic principle in these works is instance discrimination: learning to differentiate between two augmented versions of the same image and a large batch of unrelated images. Networks learn to ignore the augmentation noise and extract semantically meaningful representations. Prior work uses artificial data augmentation techniques such as cropping, and color jitter which can only affect the image in superficial ways and are not aligned with how objects actually change e.g. occlusion, deformation, viewpoint change. In this paper, we argue that videos offer this natural augmentation for free. Videos can provide entirely new views of objects, show deformation, and even connect semantically similar but visually distinct concepts. We propose Video Noise Contrastive Estimation, a method for using unlabeled video to learn strong, transferable single image representations. We demonstrate improvements over recent unsupervised single image techniques, as well as over fully supervised ImageNet pretraining, across a variety of temporal and non-temporal tasks. Code and the Random Related Video Views dataset are available at https://www.github.com/danielgordon10/vince
The Ising spin - S model on recursive p - polygonal structures in the external magnetic field is considered and the general form of the free energy and magnetization for arbitrary spin is derived. The exact relation between the free energies on infinite entire tree and on its infinite "interior" is obtained.
This paper investigates the shadow of a charged rotating non-commutative black hole. For this purpose, we first formulate the null geodesics and study the effects of non-commutative charge on the photon orbit. We then explore the effect of spin, angle of inclination as well as non-commutative charge on the silhouette of the shadow. It is found that shape of the shadow deviates from the circle with the decrease in the non-commutative charge. We also discuss observable quantities to study the deformation and distortion in the shadow cast by the black hole which decreases for small values of non-commutative charge. Finally, we study the shadows in the presence of plasma. We conclude that the non-commutativity has a great impact on the black hole shadow.
Dilepton production in proton- and nucleus-induced reactions is studied in relativistic transport model using initial conditions determined by the string dynamics from RQMD. It is found that both the CERES and HELIOS-3 data for dilepton spectra in proton-nucleus reactions can be well described by the `conventional' mechanism of Dalitz decay and direct vector meson decay. However, to provide a quantitative explanation of the observed dilepton spectra in central S+Au and S+W collisions requires contributions other than these direct decays. Introducing a decrease of vector meson masses in hot and dense medium, we find that these heavy-ion data can also be satisfactorily explained. This agrees with our earlier conclusions based on a fire cylinder model. We also give predictions for Pb+Au collisions at 160 GeV/nucleon using current CERES mass resolution and acceptance.
We describe some antiferromagnetic systems which exhibit spin gaps. We also discuss the effect of doping one such system, namely, the spin-ladders, with holes. Some model antiferromagnetic systems with spin gap are reviewed for which exact results are available. Exact results for a doped spin-ladder model are also mentioned.
Artificial honeycomb lattices with Dirac cone dispersion provide a macroscopic platform to study the massless Dirac quasiparticles and their novel geometric phases. In this paper, a quadruple-degenerate state is achieved at the center of Brillouin zone (BZ) in a two-dimensional honeycomb lattice phononic crystal, which is a result of accidental degeneracy of two double-degenerate states. In the vicinity of the quadruple-degenerate state, the dispersion relation is linear. Such quadruple degeneracy is analyzed by rigorous representation theory of groups. Using method, a reduced Hamiltonian is obtained to describe the linear Dirac dispersion relations of such quadruple-degenerate state, which is well consistent with the simulation results. Near such accidental degeneracy, we observe some unique wave propagating properties, such as defect insensitive propagating character and Talbot effect.
We study the cones of q-ample divisors on smooth complex varieties. In favourable cases, we identify a part where the closure of this cone and the nef cone have the same boundary. This is especially interesting for Fano (or almost Fano) varieties.
We extend the concept of the law of a finite graph to graphings, which are, in general, infinite graphs whose vertices are equipped with the structure of a probability space. By doing this, we obtain a vast array of new unimodular measures. Furthermore, we work out in full detail a proof of a known result, which states that weak limits preserve unimodularity.
We investigate the efficiency of an isothermal Brownian work-to-work converter engine, composed of a Brownian particle coupled to a heat bath at a constant temperature. The system is maintained out of equilibrium by using two external time-dependent stochastic Gaussian forces, where one is called load force and the other is called drive force. Work done by these two forces are stochastic quantities. The efficiency of this small engine is defined as the ratio of stochastic work done against load force to stochastic work done by the drive force. The probability density function as well as large deviation function of the stochastic efficiency are studied analytically and verified by numerical simulations.
Using high spatial and temporal data from the New Vacuum Solar Telescope (NVST) and the Solar Dynamics Observatory (SDO), we present unambiguous observations of recurrent two-sided loop jets caused by magnetic reconnection between erupting minifilaments and nearby large filament. The observations demonstrate that three two-sided loop jets, which ejected along the large filament in opposite directions, had similar appearance and originated from the same region. We find that a minifilament erupted and drove the first jet. It reformed at the same neutral line later, and then underwent partial and total eruptions, drove the second and third jets, respectively. In the course of the jets, cool plasma was injected into the large filament. Furthermore, persistent magnetic flux cancelation occurred at the neutral line under the minifilament before its eruption and continued until the end of the observation. We infer that magnetic flux cancellation may account for building and then triggering the minifilament to erupt to produce the two-sided loop jets. This observation not only indicates that two-sided loop jets can be driven by minifilament eruptions, but also sheds new light on our understanding of the recurrent mechanism of two-sided loop jets.
We study the exactness of certain combinatorially defined complexes which generalize the Orlik-Solomon algebra of a geometric lattice. The main results pertain to complex reflection arrangements and their restrictions. In particular, we consider the corresponding relation complexes and give a simple proof of the $n$-formality of these hyperplane arrangements. As an application, we are able to bound the Castelnouvo-Mumford regularity of certain modules over polynomial rings associated to Coxeter arrangements (real reflection arrangements) and their restrictions. The modules in question are defined using the relation complex of the Coxeter arrangement and fiber polytopes of the dual Coxeter zonotope. They generalize the algebra of piecewise polynomial functions on the original arrangement.
Koide's mass formula is an empirical relation among the charged lepton masses which holds with a striking precision. We propose a mechanism for cancelling the QED correction to Koide's formula. This is discussed in an effective theory with U(3) family gauge symmetry and a scenario in which this symmetry is unified with SU(2)_L symmetry at 10^2-10^3 TeV scale.
It is shown that the two-loop four-point functions are similar in structure to the three-point two-loop functions for all mass cases and topologies. The result is derived by using a rotation to a (+,-,-,+) signature without spoiling analyticity properties.
We introduce an approach that enhances images using a color filter in order to create adversarial effects, which fool neural networks into misclassification. Our approach, Adversarial Color Enhancement (ACE), generates unrestricted adversarial images by optimizing the color filter via gradient descent. The novelty of ACE is its incorporation of established practice for image enhancement in a transparent manner. Experimental results validate the white-box adversarial strength and black-box transferability of ACE. A range of examples demonstrates the perceptual quality of images that ACE produces. ACE makes an important contribution to recent work that moves beyond $L_p$ imperceptibility and focuses on unrestricted adversarial modifications that yield large perceptible perturbations, but remain non-suspicious, to the human eye. The future potential of filter-based adversaries is also explored in two directions: guiding ACE with common enhancement practices (e.g., Instagram filters) towards specific attractive image styles and adapting ACE to image semantics. Code is available at https://github.com/ZhengyuZhao/ACE.