ShantanuT01/DACTYL-Pretraining huggingface dataset:
Extrapolations of soft scalar mass parameters in supersymmetric theories can be used to explore elements of the physics scenario near the grand unification scale. We investigate the potential of this method in the lepton sector of SO(10) which incorporates right-handed neutrino superfields. The method is exemplified in two models by exploring limits on the precision that can be expected from coherent LHC and e+e- collider analyses in the reconstruction of the fundamental scalar mass parameters at the unification scale and of the D-terms related to the breaking of grand unification symmetries. In addition, the mass of the third-generation right-handed neutrino can be estimated in seesaw scenarios. Even though the models are simplified and not intended to account for all aspects of a final comprehensive SO(10) theory, they provide nevertheless a valid base for identifying essential elements that can be inferred on the fundamental high-scale theory from high-energy experiments.
Let $L= -\Delta_{\mathbb{H}^n}+V$ be a Schr\"odinger operator on the Heisenberg group $\mathbb{H}^n$, where $\Delta_{\mathbb{H}^n}$ is the sub-Laplacian and the nonnegative potential $V$ belongs to the reverse H\"older class $B_{\frac{Q}{2}}$ and $Q$ is the homogeneous dimension of $\mathbb{H}^n$. The Riesz transforms associated with the Schr\"odinger operator $L$ are bounded from $L^1(\mathbb{H}^n)$ to $L^{1,\infty}(\mathbb{H}^n)$. The $L^1$ integrability of the Riesz transforms associated with $L$ characterizes a certain Hardy type space denoted by $H^1_L(\mathbb{H}^n)$ which is larger than the usual Hardy space $H^1(\mathbb{H}^n)$. We define $H^1_L(\mathbb{H}^n)$ in terms of the maximal function with respect to the semigroup $\big \{e^{-s L}:\; s>0 \big\}$, and give the atomic decomposition of $H^1_L(\mathbb{H}^n)$. As an application of the atomic decomposition theorem, we prove that $H^1_L(\mathbb{H}^n)$ can be characterized by the Riesz transforms associated with $L$. All results hold for stratified groups as well.
Using ASAS-SN data, we find that the bright ($V{\sim}13.5$ mag) variable star MACHO 80.7443.1718 (ASASSN-V J052624.38-684705.6) is the most extreme heartbeat star yet discovered. This massive binary, consisting of at least one early B-type star, has an orbital period of $P_{\rm ASAS-SN}=32.83627\pm0.00846\,{\rm d},$ and is located towards the LH58 OB complex in the LMC. Both the ASAS-SN and TESS light curves show extreme brightness variations of ${\sim}40\%$ at periastron and variations of ${\sim}10\%$ due to tidally excited oscillations outside periastron. We fit an analytical model of the variability caused by the tidal distortions at pericenter to find orbital parameters of $\omega=-61.4$ deg, $i=44.8$ deg and $e=0.566$. We also present a frequency analysis to identify the pulsation frequencies corresponding to the tidally excited oscillations.
We present APEX, infrared and radio continuum observations of the G345.88-1.10 hub filament system which is a newly discovered star-forming cloud that hosts an unusually bright bipolar infrared nebulosity at its centre. At a distance of 2.26$^{+0.30}_{-0.21}$ kpc, G345.88-1.10 exhibits a network of parsec-long converging filaments. At the junction of these filaments lie four infrared-quiet fragments. The densest fragment (with M=210 M$_{\odot}$, R$_{\rm{eff}}=0.14$ pc) sits at the centre of a wide (opening angle of $\sim$ 90$\pm$15$^{o}$) bipolar nebulosity. $^{12}$CO(2-1) observations show that these infrared-bright nebulosities are spatially associated with a powerful molecular outflow from the central fragment. Negligible radio continuum and no H30$\alpha$ emission is detected towards the cavities, seemingly excluding that ionising radiation drives the evolution of the cavities. Furthermore, radiative transfer simulations are unable to reproduce the observed combination of a low-luminosity ($\lesssim$ 500 L$_{\odot}$) central source and a surrounding high-luminosity ($\sim 4000$ L$_{\odot}$) mid-infrared-bright bipolar cavity. This suggests that radiative heating from a central protostar cannot be responsible for the illumination of the outflow cavities. To our knowledge, this is the first reported object of this type. The rarity of objects like G345.88-1.10 is likely related to a very short phase in the massive star and/or cluster formation process that was so far unidentified. We discuss whether mechanical energy deposition by one episode or successive episodes of powerful mass accretion in a collapsing hub might explain the observations. While promising in some aspects, a fully coherent scenario that explains the presence of a luminous bipolar cavity centred on an infrared-dark fragment remains elusive at this point.
A 5-dimensional gravity theory, motivated by the brane world picture, with factorisable metric and with Kaluza scalar $G_{55}(r)$, is shown to give rise to a positive contribution to the Raychaudhuri equation. This inhibits the focusing of geodesics and possibly cause non-focusing of the geodesics. This feature is translated into the situation in which the universe has an infinite age and hence no beginning avoiding the big bang singularity.
Using the natural extension of the notion of the generalized coherent states the scalar and spinor ones for the de Sitter group SO(4,1) are constructed. These systems of coherent states obey the de Sitter--invariant Klein-Gordon and Dirac equations and correspond to the massive spin~0 and~1/2 particles over de Sitter space. These coherent states are used for the construction of the invariant scalar and spinor propagators over de Sitter space.
We introduce the notion of an instanton bundle on a Fano threefold of index 2. For such bundles we give an analogue of a monadic description and discuss the curve of jumping lines. The cases of threefolds of degree 5 and 4 are considered in a greater detail.
It has been shown that resonant absorption is a robust physical mechanism to explain the observed damping of magnetohydrodynamic (MHD) kink waves in the solar atmosphere due to naturally occurring plasma inhomogeneity in the direction transverse to the direction of the magnetic field. Theoretical studies of this damping mechanism were greatly inspired by the first observations of post-flare standing kink modes in coronal loops using the Transition Region And Coronal Explorer (TRACE). More recently, these studies have been extended to explain the attenuation of propagating coronal kink waves observed by the Coronal Multi-Channel Polarimeter (CoMP). In the present study, for the first time we investigate the properties of propagating kink waves in solar waveguides including the effects of both longitudinal and transverse plasma inhomogeneity. Importantly, it is found that the wavelength is only dependent on the longitudinal stratification and the amplitude is simply a product of the two effects. In light of these results the advancement of solar atmospheric magnetoseismology by exploiting high spatial/temporal resolution observations of propagating kink waves in magnetic waveguides to determine the length scales of the plasma inhomogeneity along and transverse to the direction of the magnetic field is discussed.
We show that two distinct singular moduli $j(\tau),j(\tau')$, such that for some positive integers $m, n$ the numbers $1,j(\tau)^m$ and $j(\tau')^n$ are linearly dependent over $\mathbb{Q}$ generate the same number field of degree at most $2$. This completes a result of Riffaut, who proved the above theorem except for two explicit pair of exceptions consisting of numbers of degree $3$. The purpose of this article is to treat these two remaining cases.
Local and global patterns of an object are closely related. Although each part of an object is incomplete, the underlying attributes about the object are shared among all parts, which makes reasoning the whole object from a single part possible. We hypothesize that a powerful representation of a 3D object should model the attributes that are shared between parts and the whole object, and distinguishable from other objects. Based on this hypothesis, we propose to learn point cloud representation by bidirectional reasoning between the local structures at different abstraction hierarchies and the global shape without human supervision. Experimental results on various benchmark datasets demonstrate the unsupervisedly learned representation is even better than supervised representation in discriminative power, generalization ability, and robustness. We show that unsupervisedly trained point cloud models can outperform their supervised counterparts on downstream classification tasks. Most notably, by simply increasing the channel width of an SSG PointNet++, our unsupervised model surpasses the state-of-the-art supervised methods on both synthetic and real-world 3D object classification datasets. We expect our observations to offer a new perspective on learning better representation from data structures instead of human annotations for point cloud understanding.
In this paper we obtain the energy distribution associated with the Ernst space-time (geometry describing Schwarzschild black hole in Melvin's magnetic universe) in Einstein's prescription. The first term is the rest-mass energy of the Schwarzschild black hole, the second term is the classical value for the energy of the uniform magnetic field and the remaining terms in the expression are due to the general relativistic effect. The presence of the magnetic field is found to increase the energy of the system.
The reverse shock (RS) model is generally introduced to interpret the optical afterglows with the rapid rising and decaying, such as the early optical afterglow of GRB 990123 (which is also called optical flash). In this paper, we collected 11 gamma-ray bursts (GRBs) early optical afterglows, which have such signatures of dominant RS emission. Since the temporal slopes of the optical flashes are determined by both the medium density distribution index $k$ and the electron spectral index $p$, we apply the RS model of the thin shell case to the optical flashes and determine the ambient medium of the progenitors. We find that the $k$ value is in the range of 0 - 1.5. The $k$ value in this paper is consistent with the result in Yi et al. (2013), where the forward shock (FS) model was applied to some onset bumps. However, the method adopted in this paper is only applicable to GRB afterglows with significant sharp rising and decaying RS emission. Our results indicate that the RS model can also be applied to confirm the circumburst medium, further implying that GRBs may have diverse circumburst media.
The aim of the paper is to study the limit distributions and the asymptotic behavior of summation arithmetic functions. A probabilistic approach based on the use of the axioms of probability theory is used for these purposes. Sufficient conditions are proved under which these functions have a limiting normal distribution. Arithmetic functions having a limiting normal distribution are found in the paper. The author investigates summation functions of a general form and finds sufficient conditions under which they have a limiting normal distribution. Examples of arithmetic functions that satisfy these requirements are considered. We prove an ergodic theorem for summation arithmetic functions, for which the sequence of random variables has the stationarity property in the broad sense. The asymptotics of the growth of the deviation of the values of the arithmetic function from its mean value are investigated. It is shown that an equivalent formulation of the Riemann hypothesis for the Mertens function is satisfied almost everywhere.
We study the optimal stopping problem of maximizing the variance of an unkilled linear diffusion. Especially, we demonstrate how the problem can be solved as a convex two-player zero-sum game, and reveal quite surprising application of game theory by doing so. Our main result shows that an optimal solution can, in general case, be found among stopping times that are mixtures of two hitting times. This and other revealed phenomena together with suggested solution methods could be helpful when facing more complex non-linear optimal stopping problems. The results are illustrated by a few examples.
A model of the Galaxy with the outer ring R1R2 can explain the observed distribution of the radial, VR, and azimuthal, VT, velocity components along the Galactocentric distance, R, derived from the Gaia EDR3 data. We selected stars from the Gaia EDR3 catalogue with reliable parallaxes, proper motions and line-of-sight velocities lying near the Galactic plane, |z|<200 pc, and in the sector of the Galactocentic angles |theta|<15 degrees and calculated the median velocities VR and VT in small bins along the distance R. The distribution of observed velocities appears to have some specific features: the radial velocity VR demonstrates a smooth fall from +5 km s-1 at the distance of R=R0-1.5 kpc to -3 km s-1 at R=R0+1.0 kpc while the azimuthal velocity VT shows a sharp drop by 7 km s-1 in the distance interval R0<R<R0+1.0 kpc, where R0 is the solar Galactocentric distance. We build a model of the Galaxy including bulge, bar, disc and halo components, which reproduces the observed specific features of the velocity distribution in the Galactocentric distance interval |R-R0|< 1.5 kpc. The best agreement corresponds to the time 1.8+/-0.5 Gyr after the start of the simulation. A model of the Galaxy with the bar rotating at the angular velocity of Omega_b=55+/-3 km s-1 kpc-1, which sets the OLR of the bar at the distance of R0-0.5+/-0.4 kpc, provides the best agreement between the model and observed velocities. The position angle of the bar, theta_b, corresponding to the best agreement between the model and observed velocities is theta_b=45+/-15 degrees.
We propose a method to refine geometry of 3D meshes from a consumer level depth camera, e.g. Kinect, by exploiting shading cues captured from an infrared (IR) camera. A major benefit to using an IR camera instead of an RGB camera is that the IR images captured are narrow band images that filter out most undesired ambient light, which makes our system robust against natural indoor illumination. Moreover, for many natural objects with colorful textures in the visible spectrum, the subjects appear to have a uniform albedo in the IR spectrum. Based on our analyses on the IR projector light of the Kinect, we define a near light source IR shading model that describes the captured intensity as a function of surface normals, albedo, lighting direction, and distance between light source and surface points. To resolve the ambiguity in our model between the normals and distances, we utilize an initial 3D mesh from the Kinect fusion and multi-view information to reliably estimate surface details that were not captured and reconstructed by the Kinect fusion. Our approach directly operates on the mesh model for geometry refinement. We ran experiments on our algorithm for geometries captured by both the Kinect I and Kinect II, as the depth acquisition in Kinect I is based on a structured-light technique and that of the Kinect II is based on a time-of-flight (ToF) technology. The effectiveness of our approach is demonstrated through several challenging real-world examples. We have also performed a user study to evaluate the quality of the mesh models before and after our refinements.
The diffusion of a fractional Brownian particle passing over the saddle point is studied in the field of the metastable potential. The barrier escaping probability is found to be greatly related to the fractional exponent $\alpha$. Properties are revealed to move reversely in the opposite direction of diffusion when $\alpha$ is relatively large despite of the zero-approximating effective friction of the system. This is very anomalous to the standard Brownian motion.
By using evolutionary algorithm USPEX, we have predicted a number of stable zirconium carbides. In addition to the well-known rocksalt-type stoichiometric ZrC (Fm-3m), present prediction also identifies five stable substoichiometric zirconium carbides adopting rocksalt-type structures with ordered carbon vacancies, Zr8C7 (P-1), Zr6C5 (C2/m), Zr5C4 (P-1), Zr3C2 (C2/m), and Zr2C (Fd-3m). The effects of carbon vacancies on structural and mechanical properties are investigated. We highlight that the distribution of carbon vacancies has significant influence on volume, Pugh's ratio, and hardness. We further propose that hardness can be enhanced by replacing carbon vacancies with suitable elements, in particular nitrogen and oxygen.
Using density-functional perturbation theory and the Gr\"uneisen formalism, we directly calculate the linear thermal expansion coefficients (TECs) of a hexagonal bulk system MoS$_2$ in the crystallographic $a$ and $c$ directions. The TEC calculation depends critically on the evaluation of a temperature-dependent quantity $I_i(T)$, which is the integral of the product of heat capacity and $\Gamma_i(\nu)$, of frequency $\nu$ and strain type $i$, where $\Gamma_i(\nu)$ is the phonon density of states weighted by the Gr\"uneisen parameters. We show that to determine the linear TECs we may use minimally two uniaxial strains in the $z$ direction, and either the $x$ or $y$ direction. However, a uniaxial strain in either the $x$ or $y$ direction drastically reduces the symmetry of the crystal from a hexagonal one to a base-centered orthorhombic one. We propose to use an efficient and accurate symmetry-preserving biaxial strain in the $xy$ plane to derive the same result for $\Gamma(\nu)$. We highlight that the Gr\"uneisen parameter associated with a biaxial strain may not be the same as the average of Gr\"uneisen parameters associated with two separate uniaxial strains in the $x$ and $y$ directions due to possible preservation of degeneracies of the phonon modes under a biaxial deformation. Large anisotropy of TECs is observed where the linear TEC in the $c$ direction is about $1.8$ times larger than that in the $a$ or $b$ direction at high temperatures. Our theoretical TEC results are compared with experiment. The symmetry-preserving approach adopted here may be applied to a broad class of two lattice-parameter systems such as hexagonal, trigonal, and tetragonal systems, which allows many complicated systems to be treated on a first-principles level.
We consider a fluid-structure interaction model for an incompressible fluid where the elastic response of the free boundary is given by a damped Kirchhoff plate model. Utilizing the Newton polygon approach, we first prove maximal regularity in $L^p$-Sobolev spaces for a linearized version. Based on this, we show existence and uniqueness of the strong solution of the nonlinear system for small data.
We revisit the short-time dynamics of 2D Ising model with three spin interactions in one direction and estimate the critical exponents $z,$ $\theta,$ $\beta$ and $\nu$. Taking properly into account the symmetry of the Hamiltonian we obtain results completely different from those obtained by Wang et al.. For the dynamic exponent $z$ our result coincides with that of the 4-state Potts model in two dimensions. In addition, results for the static exponents $\nu$ and $\beta$ agree with previous estimates obtained from finite size scaling combined with conformal invariance. Finally, for the new dynamic exponent $\theta$ we find a negative and close to zero value, a result also expected for the 4-state Potts model according to Okano et al.
We show that the quantum Hamilton Jacobi approach to a class of quantum mechanical bound state problems and the Gaussian orthogonal ensemble of random matrix theory are equivalent. The Berry connection for both problems is identical to their quantum momentum function.The potential that appears in the joint probability distribution function in the random matrix theory is a super potential allowing us to apply it to exceptional polynomials.
We show that entanglement can always arise in the interaction of an arbitrarily large system in any mixed state with a single qubit in a pure state. This small initial purity is enough to enforce entanglement even when the total entropy is close to maximum. We demonstrate this feature using the Jaynes-Cummings interaction of a two level atom in a pure state with a field in a thermal state at an arbitrarily high temperature. We find the time and temperature variation of a lower bound on the amount of entanglement produced and study the classical correlations quantified by the mutual information.
Quantum teleportation, the process by which Alice can transfer an unknown quantum state to Bob by using pre-shared entanglement and classical communication, is one of the cornerstones of quantum information. The standard benchmark for certifying quantum teleportation consists in surpassing the maximum average fidelity between the teleported and the target states that can be achieved classically. According to this figure of merit, not all entangled states are useful for teleportation. Here we propose a new benchmark that uses the full information available in a teleportation experiment and prove that all entangled states can implement a quantum channel which can not be reproduced classically. We introduce the idea of non-classical teleportation witness to certify if a teleportation experiment is genuinely quantum and discuss how to quantify this phenomenon. Our work provides new techniques for studying teleportation that can be immediately applied to certify the quality of quantum technologies.
We numerically investigate nucleation processes in the transient dynamics of the two-dimensional complex Ginzburg-Landau equation towards its "frozen" state with quasi-stationary spiral structures. We study the transition kinetics from either the defect turbulence regime or random initial configurations to the frozen state with a well-defined low density of quasi-stationary topological defects. Nucleation events of spiral structures are monitored using the characteristic length between the emerging shock fronts. We study two distinct situations, namely either when the system is quenched far away from the transition limit or near it. In the former deeply quenched case, the average nucleation time for different system sizes is measured over many independent realizations. We employ an extrapolation method as well as a phenomenological formula to account for and eliminate finite-size effects. The non-zero (dimensionless) barrier for the nucleation of single spiral droplets in the extrapolated infinite system size limit suggests that the transition to the frozen state is discontinuous. We also investigate the nucleation of spirals for systems that are quenched close to but beyond the crossover limit, and of target waves which emerge if a specific spatial inhomogeneity is introduced. In either of these cases, we observe long, "fat" tails in the distribution of nucleation times, which also supports a discontinuous transition scenario.
We report results from a Spitzer GO-1 program of IRS spectroscopy of a large sample of Luminous Infrared Galaxies and quasars selected from the European Large Area ISO Survey (ELAIS) which have a wide multiwavelength coverage, including ISOCAM, ISOPHOT, IRAC and MIPS (from SWIRE), and optical photometry. We present the sample selection and results from the IRS spectroscopy.
An important objective of the classical processing of stationary random sequences under nonparametric uncertainty is the problem of filtering in case when the distribution of the underlying signal is unknown. In this paper it is assumed that an unknown useful signal $(S_n)_{n\ge1}$ is Markov. This allows us to construct an estimate of the useful signal, expressed in terms of the distribution density function of an observable random sequence $(X_n)_{n\ge1}$. The equation of the optimal Bayesian estimation (so called equation of optimal filtering) of such signal has been received by A.V. Dobrovidov. Our main result is the following. It is proved that when the unobservable Markov sequence is defined by a linear equation with the Gaussian noise, the equation of optimal filtering coincides with the classical Kalman's filter and the conditional expectation defined by the theorem on normal correlation.