ShantanuT01/DACTYL-Pretraining huggingface dataset:
The Dirac-Moshinsky oscillator is an elegant example of an exactly solvable quantum relativistic model that under certain circumstances can be mapped onto the Jaynes-Cummings model in quantum optics. In this work we show, how to do this in detail. Then we extend it by considering its coupling with an external (isospin) field and find the conditions that maintain solvability. We use this extended system to explore entanglement in relativistic systems and then identify its quantum optical analog: two different atoms interacting with an electromagnetic mode. We show different aspects of entanglement which gain relevance in this last system, which can be used to emulate the former.
We consider some iterative methods for finding the best interpolation data in the images compression with noise. The interpolation data consists of the set of pixels and their grey/color values. The aim in the iterative approach is to allow the change of the data dynamically during the inpainting process for a reconstruction of the image that includes the enhancement and denoising effects. The governing PDE model of this approach is a fully parabolic problem where the set of stored pixels is time dependent. We consider the semi-discrete dynamical system associated to the model which gives rise to an iterative method where the stored data are modified during the iterations for best outcomes. Finding the compression sets follows from a shape-based analysis within the $\Gamma$-convergence tools, in particular well suited topological asymptotic and a ``fat pixels'' approach are considered to obtain an analytic characterization of the optimal sets in the sense of shape optimization theory. We perform the analysis and derive several iterative algorithms that we implement and compare to obtain the most efficient strategies of compression and inpainting for noisy images. Some numerical computations are presented to confirm the theoretical findings. Finally, we propose a modified model that allows the inpainting data to change with the iteration and compare the resulting new method to the ``probabilistic'' ones from the state-of-the-art.
We introduce a notion of `proChow group' of varieties, agreeing with the notion of Chow group for complete varieties and covariantly functorial with respect to arbitrary morphisms. We construct a natural transformation from the functor of constructible functions to the proChow functor, extending MacPherson's natural transformation. We illustrate the result by providing very short proofs of (a generalization of) two well-known facts on Chern-Schwartz-MacPherson classes: Kwiecinski's product formula, and the Ehlers-Barthel-Brasselet-Fieseler computation of Chern-Schwartz-MacPherson classes of toric varieties.
We study D-branes in SU(2) WZW model by means of the boundary state techniques. We realize the ``fuzzy sphere'' configuration of multiple D0-branes as the boundary state with the insertion of suitable Wilson line. By making use of the path-integral representation we show that this boundary state preserves the appropriate boundary conditions and leads to the Cardy state describing a spherical D2-brane under the semi-classical approximation. This result directly implies that the spherical D2-brane in SU(2) WZW model can be well described as the bound state of D0-branes.   After presenting the supersymmetric extension, we also investigate the BPS and the non-BPS configurations of D-branes in the NS5 background. We demonstrate that the non-BPS configurations are actually unstable, since they always possess the open string tachyons. We further notice that the stable BPS bound state constructed by the tachyon condensation is naturally interpreted as the brane configuration of fuzzy sphere.
In this paper, we present a characterization for the Hausdorff distance between two given algebraic curves in the $n$-dimensional space (parametrically or implicitly defined) to be finite. The characterization is related with the asymptotic behavior of the two curves and it can be easily checked. More precisely, the Hausdorff distance between two curves $\cal C$ and $\overline{\cal C}$ is finite if and only if for each infinity branch of $\cal C$ there exists an infinity branch of $\overline{\cal C}$ such that the terms with positive exponent in the corresponding series are the same, and reciprocally.
The reasonableness of the use of perturbative QCD notions in the region close to the scale of hadronization, i.e., below $\lesssim 1 \GeV$ is under study. First, the interplay between higher orders of pQCD expansion and higher twist contributions in the analysis of recent Jefferson Lab (JLab) data on the Generalized Bjorken Sum Rule function $\Gamma_1^{p-n} (Q^2)$ at $0.1<Q^2< 3 {\rm GeV}^2$ is studied. It is shown that the inclusion of the higher-order pQCD corrections could be absorbed, with good numerical accuracy, by change of the normalization of the higher-twist terms. Second, to avoid the issue of unphysical singularity (Landau pole at $Q=\Lambda\sim 400 \MeV $), we deal with the ghost-free Analytic Perturbation Theory (APT) that recently proved to be an intriguing candidate for a quantitative description of light quarkonia spectra within the Bethe-Salpeter approach. The values of the twist coefficients $\mu_{2k} $ extracted from the mentioned data by using the APT approach provide a better convergence of the higher-twist series than with the common pQCD. As the main result, a good quantitative description of the JLab data down to $Q\simeq$ 350 MeV is achieved.
Vision-based deep learning models can be promising for speech-and-hearing-impaired and secret communications. While such non-verbal communications are primarily investigated with hand-gestures and facial expressions, no research endeavour is tracked so far for the lips state (i.e., open/close)-based interpretation/translation system. In support of this development, this paper reports two new Convolutional Neural Network (CNN) models for lips state detection. Building upon two prominent lips landmark detectors, DLIB and MediaPipe, we simplify lips-state model with a set of six key landmarks, and use their distances for the lips state classification. Thereby, both the models are developed to count the opening and closing of lips and thus, they can classify a symbol with the total count. Varying frame-rates, lips-movements and face-angles are investigated to determine the effectiveness of the models. Our early experimental results demonstrate that the model with DLIB is relatively slower in terms of an average of 6 frames per second (FPS) and higher average detection accuracy of 95.25%. In contrast, the model with MediaPipe offers faster landmark detection capability with an average FPS of 20 and detection accuracy of 94.4%. Both models thus could effectively interpret the lips state for non-verbal semantics into a natural language.
We study the Ising antiferromagnet on the triangular lattice which are interacting along three different directions via two $J$-bonds and one anisotropic $J'$-bond with $J' \ge J$. Although its finite temperature state has long been considered as simply disordered, we find a systematic generation of a ferromagnetic $J'$-bonds named "good defects" each carrying the energy $2\delta_J\equiv 2(J'-J)$. They exhibit an eminent correlation which is regarded as a network or a soft lattice. The specific heat shows a universal peak at $T^* \sim \delta_J$ and the corresponding energy follows the activation type of temperature-dependence with an excitation gap $2\delta_J$. Energetics and the crossover between this particular two-dimensional state and the other disordered or one-dimensional states are discussed.
We classify all primitive embeddings of the lattice of numerical equivalence classes of divisors of an Enriques surface with the intersection form multiplied by 2 into an even unimodular hyperbolic lattice of rank 26. These embeddings have a property that facilitates the computation of the automorphism group of an Enriques surface by Borcherds' method.
Mixtures of Fe and Cu powders are cold-compacted and subsequently deformed with severe plastic deformation by high-pressure torsion, leading to bulk samples. The dilution of Fe in the Cu matrix is investigated with SQUID-magnetometry, whereas the magnetic properties change as a function of Fe-content from a frustrated regime to a thermal activated behaviour. The magnetic properties are correlated with the microstructure, investigated by synchrotron X-ray diffraction and atom probe tomography. Annealing of the as-deformed states leads to demixing and grain growth, with the coercivity as a function of annealing temperature obeying the random anisotropy model. The presented results show that high-pressure torsion is a technique capable to affect the microstructure even on atomic length scales.
We present full quantum mechanical calculations of the hybridized plasmon modes of two nanowires at small separation, providing real space visualization of the modes in the transition from the classical to the quantum tunneling regime. The plasmon modes are obtained as certain eigenfunctions of the dynamical dielectric function which is computed using time dependent density functional theory (TDDFT). For freestanding wires, the energy of both surface and bulk plasmon modes deviate from the classical result for low wire radii and high momentum transfer due to effects of electron spill-out, non-local response, and coupling to single-particle transitions. For the wire dimer the shape of the hybridized plasmon modes are continuously altered with decreasing separation, and below 6 {\AA} the energy dispersion of the modes deviate from classical results due to the onset of weak tunneling. Below 2-3 {\AA} separation this mode is replaced by a charge-transfer plasmon which blue shifts with decreasing separation in agreement with experiment, and marks the onset of the strong tunneling regime.
We investigate strange quark production in Au-Au collisions at RHIC in the framework of the Parton Cascade Model(PCM). The yields of (anti-) strange quarks for three production scenarios -- primary-primary scattering, full scattering, and full production -- are compared to a proton-proton baseline. Enhancement of strange quark yields in central Au-Au collisions compared to scaled p-p collisions increases with the number of secondary interactions. The centrality dependence of strangeness production for the three production scenarios is studied as well. For all production mechanisms, the strangeness yield increases with $(N_{\rm part})^{4/3}$. The perturbative QCD regime described by the PCM is able to account for up to 50% of the observed strangeness at RHIC.
In this paper we analyze Abelian-Higgs strings in a phenomenological model that takes quantum effects in curved space-time into account. This model, first introduced by Rastall, cannot be derived from an action principle. We formulate phenomenological equations of motion under the guiding principle of minimal possible deformation of the standard equations. We construct string solutions that asymptote to a flat space-time with a deficit angle by solving the set of coupled non-linear ordinary differential equations numerically. Decreasing the Rastall parameter from its Einstein gravity value we find that the deficit angle of the space-time increases and becomes equal to $2\pi$ at some critical value of this parameter that depends on the remaining couplings in the model. For smaller values the resulting solutions are supermassive string solutions possessing a singularity at a finite distance from the string core. Assuming the Higgs boson mass to be on the order of the gauge boson mass we find that also in Rastall gravity this happens only when the symmetry breaking scale is on the order of the Planck mass. We also observe that for specific values of the parameters in the model the energy per unit length becomes proportional to the winding number, i.e. the degree of the map $S^1 \rightarrow S^1$. Unlike in the BPS limit in Einstein gravity, this is, however, not connect to an underlying mathematical structure, but rather constitutes a would-be-BPS bound.
We examine the thermodynamics of a regular charged black hole (RCB) added with corrections due to massive gravity and thermal fluctuations at quantum level. We then derive the expressions for all the relevant thermodynamic quantities such as entropy, Hawkings temperature, internal energy, Gibbs free energy, corrected to first order. We also briefly discuss the stability of such a system with the help of quantities like specific heat and thermodynamic pressure, along with this we present their comparative study with the corresponding original values.
Collisionless damping of electrical waves in plasma is investigated in the frame of the classical formulation of the problem. The new principle of regularization of the singular integral is used. The exact solution of the corresponding dispersion equation is obtained. The results of calculations lead to existence of discrete spectrum of frequencies and discrete spectrum of dispersion curves. Analytical results are in good coincidence with results of direct mathematical experiments. Key words: Foundations of the theory of transport processes and statistical physics; Boltzmann physical kinetics; damping of plasma waves, linear theory of wave`s propagation PACS: 67.55.Fa, 67.55.Hc
Biometrics systems have significantly improved person identification and authentication, playing an important role in personal, national, and global security. However, these systems might be deceived (or "spoofed") and, despite the recent advances in spoofing detection, current solutions often rely on domain knowledge, specific biometric reading systems, and attack types. We assume a very limited knowledge about biometric spoofing at the sensor to derive outstanding spoofing detection systems for iris, face, and fingerprint modalities based on two deep learning approaches. The first approach consists of learning suitable convolutional network architectures for each domain, while the second approach focuses on learning the weights of the network via back-propagation. We consider nine biometric spoofing benchmarks --- each one containing real and fake samples of a given biometric modality and attack type --- and learn deep representations for each benchmark by combining and contrasting the two learning approaches. This strategy not only provides better comprehension of how these approaches interplay, but also creates systems that exceed the best known results in eight out of the nine benchmarks. The results strongly indicate that spoofing detection systems based on convolutional networks can be robust to attacks already known and possibly adapted, with little effort, to image-based attacks that are yet to come.
The low energy spin excitations of the Fe pnictide parent compounds have been determined by inelastic neutron scattering and interpreted within the local moment J_1a,b-J_2 Heisenberg model with orthorhombic symmetry. This has led to alternative exchange models that strongly differ in the size of anisotropy. Although the compounds are itinerant the localised spin model can explain basic features of the excitations. The inherent frustration of this model leads to quantum fluctuations and possible moment reduction. We investigate this question in detail using spin wave approximation and partly exact diagonalisation Lanczos calculations for finite clusters. We find that the orthorhombic anisotropy stabilizes the columnar AF phase and its moment. For the exchange models proposed from inelastic neutron scattering we can exclude a strong influcence of frustration on the moment size. We also investigate dependence of magnetisation and susceptibility on field and temperature.
A general method for implementing weakly entangling multipartite unitary operations using a small amount of entanglement and classical communication is presented. For the simple Hamiltonian \sigma_z\otimes\sigma_z this method requires less entanglement than previously known methods. In addition, compression of multiple operations is applied to reduce the average communication required.
We report on the computational characteristics of ab initio nuclear structure calculations in a symmetry-adapted no-core shell model (SA-NCSM) framework. We examine the computational complexity of the current implementation of the SA-NCSM approach, dubbed LSU3shell, by analyzing ab initio results for 6Li and 12C in large harmonic oscillator model spaces and SU(3)-selected subspaces. We demonstrate LSU3shell's strong-scaling properties achieved with highly-parallel methods for computing the many-body matrix elements. Results compare favorably with complete model space calculations and significant memory savings are achieved in physically important applications. In particular, a well-chosen symmetry-adapted basis affords memory savings in calculations of states with a fixed total angular momentum in large model spaces while exactly preserving translational invariance.
We present preliminary asteroseismic results from Kepler on three G-type stars. The observations, made at one-minute cadence during the first 33.5d of science operations, reveal high signal-to-noise solar-like oscillation spectra in all three stars: About 20 modes of oscillation may be clearly distinguished in each star. We discuss the appearance of the oscillation spectra, use the frequencies and frequency separations to provide first results on the radii, masses and ages of the stars, and comment in the light of these results on prospects for inference on other solar-type stars that Kepler will observe.
This paper presents a novel multi-attention driven system that jointly exploits Convolutional Neural Network (CNN) and Recurrent Neural Network (RNN) in the context of multi-label remote sensing (RS) image classification. The proposed system consists of four main modules. The first module aims to extract preliminary local descriptors of RS image bands that can be associated to different spatial resolutions. To this end, we introduce a K-Branch CNN, in which each branch extracts descriptors of image bands that have the same spatial resolution. The second module aims to model spatial relationship among local descriptors. This is achieved by a bidirectional RNN architecture, in which Long Short-Term Memory nodes enrich local descriptors by considering spatial relationships of local areas (image patches). The third module aims to define multiple attention scores for local descriptors. This is achieved by a novel patch-based multi-attention mechanism that takes into account the joint occurrence of multiple land-cover classes and provides the attention-based local descriptors. The last module exploits these descriptors for multi-label RS image classification. Experimental results obtained on the BigEarthNet that is a large-scale Sentinel-2 benchmark archive show the effectiveness of the proposed method compared to a state of the art method.
Using methods developed by Coons and Tyler, we give a new proof of a recent result of Defant, by determining the maximal order of the number of hyper-($b$-ary)-expansions of a nonnegative integer $n$ for general integral bases $b\geqslant 2$.
In recent years, the interaction between the local positivity of divisors and Okounkov bodies has attracted considerable attention, and there have been attempts to find a satisfactory theory of positivity of divisors in terms of convex geometry of Okounkov bodies. Many interesting results in this direction have been established by Choi--Hyun--Park--Won and K\"{u}ronya--Lozovanu separately. The first aim of this paper is to give uniform proofs of these results. Our approach provides not only a simple new outlook on the theory but also proofs for positive characteristic in the most important cases. Furthermore, we extend the theorems on Seshadri constants to graded linear series setting. Finally, we introduce the integrated volume function to investigate the relation between Seshadri constants and filtered Okounkov bodies introduced by Boucksom--Chen.
Let n points be chosen randomly and independently in the unit disk. "Sylvester's question" concerns the probability p_n that they are the vertices of a convex n-sided polygon. Here we establish the link with another problem. We show that for large n this polygon, when suitably parametrized by a function r(phi) of the polar angle phi, satisfies the equation of the random acceleration process (RAP), d^2 r/d phi^2 = f(phi), where f is Gaussian noise. On the basis of this relation we derive the asymptotic expansion log p_n = -2n log n + n log(2 pi^2 e^2) - c_0 n^{1/5} + ..., of which the first two terms agree with a rigorous result due to Barany. The nonanalyticity in n of the third term is a new result. The value 1/5 of the exponent follows from recent work on the RAP due to Gyorgyi et al. [Phys. Rev. E 75, 021123 (2007)]. We show that the n-sided polygon is effectively contained in an annulus of width \sim n^{-4/5} along the edge of the disk. The distance delta_n of closest approach to the edge is exponentially distributed with average 1/(2n).
When minimal length uncertainty emerging from generalized uncertainty principle (GUP) is thoughtfully implemented, it is of great interest to consider its impacts on {\it "gravitational} Einstein field equations (gEFE) and to try to find out whether consequential modifications in metric manifesting properties of quantum geometry due to quantum gravity. GUP takes into account the gravitational impacts on the noncommutation relations of length (distance) and momentum operators or time and energy operators, etc. On the other hand, gEFE relates {\it classical geometry or general relativity gravity} to the energy-momentum tensors, i.e. proposing quantum equations of state. Despite the technical difficulties, we confront GUP to the metric tensor so that the line element and the geodesic equation in flat and curved space are accordingly modified. The latter apparently encompasses acceleration, jerk, and snap (jounce) of a particle in the {\it "quasi-quantized"} gravitational field. Finite higher-orders of acceleration apparently manifest phenomena such as accelerating expansion and transitions between different radii of curvature, etc.
The determination of chemical abundances from stellar spectra is considered a mature field of astrophysics. Digital spectra of stars are recorded and processed with standard techniques, much like samples in the biological sciences. Nevertheless, uncertainties typically exceed 20%, and are dominated by systematic errors. The first part of this paper addresses what is being done to reduce measurement errors; and what is not being done, but should be. The second part focuses in some of the most exciting applications of stellar spectroscopy in the arenas of galactic structure and evolution, the origin of the chemical elements, and cosmology.
We present the phase diagram of the $S=1/2$ Heisenberg model on the two leg ladder with cyclic four spin exchange, determined by a combination of Exact Diagonalization and Density Matrix Renormalization Group techniques. We find six different phases and regimes: the rung singlet phase, a ferromagnetic phase, two symmetry broken phases with staggered dimers and staggered scalar chiralities, and a gapped region with dominant vector chirality or collinear spin correlations. We localize the phase transitions and investigate their nature.