ShantanuT01/DACTYL-Pretraining huggingface dataset:
This paper proposes a novel framework for multi-group shape analysis relying on a hierarchical graphical statistical model on shapes within a population.The framework represents individual shapes as point setsmodulo translation, rotation, and scale, following the notion in Kendall shape space.While individual shapes are derived from their group shape model, each group shape model is derived from a single population shape model. The hierarchical model follows the natural organization of population data and the top level in the hierarchy provides a common frame of reference for multigroup shape analysis, e.g. classification and hypothesis testing. Unlike typical shape-modeling approaches, the proposed model is a generative model that defines a joint distribution of object-boundary data and the shape-model variables. Furthermore, it naturally enforces optimal correspondences during the process of model fitting and thereby subsumes the so-called correspondence problem. The proposed inference scheme employs an expectation maximization (EM) algorithm that treats the individual and group shape variables as hidden random variables and integrates them out before estimating the parameters (population mean and variance and the group variances). The underpinning of the EM algorithm is the sampling of pointsets, in Kendall shape space, from their posterior distribution, for which we exploit a highly-efficient scheme based on Hamiltonian Monte Carlo simulation. Experiments in this paper use the fitted hierarchical model to perform (1) hypothesis testing for comparison between pairs of groups using permutation testing and (2) classification for image retrieval. The paper validates the proposed framework on simulated data and demonstrates results on real data.
We report a robust anomalous Nernst effect in Co2MnGa thin films in the thickness regime between 20 and 50 nm. The anomalous Nernst coefficient varied in the range of -2.0 to -3.0 uV/K at 300 K. We demonstrate that the anomalous Hall and Nernst coefficients exhibit similar behavior and fulfill the Mott relation. We simultaneously measure all four transport coefficients of the longitudinal resistivity, transversal resistivity, Seebeck coefficient, and anomalous Nernst coefficient. We connect the values of the measured and calculated Nernst conductivity by using the remaining three magneto-thermal transport coefficients, where the Mott relation is still valid. The intrinsic Berry curvature dominates the transport due to the relation between the longitudinal and transversal transport. Therefore, we conclude that the Mott relationship is applicable to describe the magneto-thermoelectric transport in Weyl semimetal Co2MnGa as a function of film thickness.
We investigate global strong solutions for the incompressible viscoelastic system of Oldroyd--B type with the initial data close to a stable equilibrium. We obtain the existence and uniqueness of the global solution in a functional setting invariant by the scaling of the associated equations, where the initial velocity has the same critical regularity index as for the incompressible Navier--Stokes equations, and one more derivative is needed for the deformation tensor. Like the classical incompressible Navier-Stokes, one may construct the unique global solution for a class of large highly oscillating initial velocity. Our result also implies that the deformation tensor $F$ has the same regularity as the density of the compressible Navier--Stokes equations.
A class of energy-transport equations without electric field under mixed Dirichlet-Neumann boundary conditions is analyzed. The system of degenerate and strongly coupled parabolic equations for the particle density and temperature arises in semiconductor device theory. The global-in-time existence of weak nonnegative solutions is shown. The proof consists of a variable transformation and a semi-discretization in time such that the discretized system becomes elliptic and semilinear. Positive approximate solutions are obtained by Stampacchia truncation arguments and a new cut-off test function. Nonlogarithmic entropy inequalities yield gradient estimates which allow for the limit of vanishing time step sizes. Exploiting the entropy inequality, the long-time convergence of the weak solutions to the constant steady state is proved. Because of the lack of appropriate convex Sobolev inequalities to estimate the entropy dissipation, only an algebraic decay rate is obtained. Numerical experiments indicate that the decay rate is typically exponential.
Studying crystal structures of superprotonic phases of alkali metal hydrogen sulfates and selenates, a very unusual phenomenon has been revealed. Dynamically disordered hydrogen atoms with low position occupancies are clearly seen in corresponding electron density maps. To explain this effect, an idea about a new type of twinning, dynamic twinning, was proposed and discussed.
We consider a singular limit problem from the damped wave equation with a power type nonlinearity to the corresponding heat equation. We call our singular limit problem non-delay limit. Our proofs are based on the argument for non-relativistic limit from the nonlinear Klein-Gordon equation to the nonlinear Schr\"{o}dinger equation by the second author, Nakanishi, and Ozawa (2002), Nakanishi (2002), and Masmoudi and Nakanishi (2002). We can obtain better results for the non-delay limit problem than that for the non-relativistic limit problem due to the dissipation property. More precisely, we get the better convergence rate of the $L^2$-norm and we also obtain the global-in-time uniform convergence of the non-delay limit in the $L^2$-supercritical case.
We show that "The product of consecutive integers is never a power" and several results by Schinzel and Tijdeman on the solutions of the equation $y^m=P(x)$, for $m>1$, $y>1$, and $P(x)$ a polynomial with rational coefficients and with at least two distinct zeros, hold in a weak fragment of Peano Arithmetic, $PA^-$, which lacks any kind of induction, and whose models are the positive cones of discretely ordered rings.
Conical defects, or point particles, in AdS_3 are one of the simplest non-trivial gravitating systems, and are particularly interesting because black holes can form from their collision. We embed the BPS conical defects of three dimensions into the N=4b supergravity in six dimensions, which arises from IIB string theory compactified on K3. The required Kaluza-Klein reduction of the six dimensional theory on a sphere is analyzed in detail, including the relation to the Chern-Simons supergravities in three dimensions. We show that the six dimensional spaces obtained by embedding the 3d conical defects arise in the near-horizon limit of rotating black strings. Various properties of these solutions are analyzed and we propose a representation of our defects in the CFT dual to asymptotically AdS_3 x S^3 spaces. Our work is intended as a first step towards analyzing colliding defects that form black holes.
We consider generating functionals of Green's functions with external fields in the framework of BV and BLT quantization schemes for general gauge theories. The corresponding Ward identities are obtained, and the gauge dependence is studied.
The moduli space $\bar{M}_{0,n}$ of Deligne-Mumford stable n-pointed rational curves admits morphisms to spaces recently constructed by Giansiracusa, Jensen, and Moon that we call Veronese quotients. We study divisors on $\bar{M}_{0,n}$ associated to these maps and show that these divisors arise as first Chern classes of vector bundles of conformal blocks.
We use ultrafast electron diffraction to detect the temporal evolution of phonon populations in femtosecond laser-excited ultrathin single-crystalline gold films. From the time-dependence of the Debye-Waller factor we extract a 4.7 ps time-constant for the increase in mean-square atomic displacements. We show from the increase of the diffuse scattering intensity that the population of phonon modes near the X and K points in the Au fcc Brillouin zone grows with timescales of 2.3 and 2.9 ps, respectively, faster than the Debye-Waller average. We find that thermalization continues within the initially non-equilibrium phonon distribution after 10 ps. The observed momentum dependent timescale of phonon populations is in contrast to what is usually predicted in a two-temperature model.
Bow shock pulsar wind nebulae are observed with a variety of complex morphologies at different wavelengths, most likely due to differences in the magnetic field strength and pulsar wind geometry. Here we present a detailed analysis, showing how these differences affect the observational properties in these systems, focusing on non-thermal synchrotron emission. By adopting different prescriptions for the local emissivity, on top of the magnetic and flow patterns taken from 3D high-resolution numerical simulations in relativistic MHD, and considering various viewing angles, we try to characterize the main features of the emission and polarization, to verify if and how these can be used to get information, or to put constraints, on known objects. We found for example that conditions leading to a strong development of the turbulence in the bow shock tail produce substantial differences in the emission pattern, especially in polarized light.
NGC1566 is a changing-look active galaxy that exhibited an outburst during 2017-2018 with a peak in June 2018. We triggered AstroSat observations of NGC 1566 twice in August and October 2018 during its declining phase. Using the AstroSat observations along-with two XMM-Newton observations in 2015 (pre-outburst) and June 2018 (peak-outburst), we found that the X-ray power-law, the soft X-ray excess, and the disk components showed extreme variability during the outburst. Especially, the soft excess was negligible in 2015 before the outburst, it increased to a maximum level by a factor of $>200$ in June 2018, and reduced dramatically by a factor of $\sim7.4$ in August 2018 and become undetectable in October 2018. The Eddington fraction ($L/L_{Edd})$ increased from $\sim0.1\%$ (2015) to $\sim 5\%$ (June 2018), then decreased to $\sim 1.5\%$ (August 2018) and $0.3\%$ (October 2018). Thus, NGC 1566 made a spectral transition from a high soft-excess state to a negligible soft-excess state at a few $\%$ of the Eddington rate. The soft-excess is consistent with warm Comptonization in the inner disk that appears to have developed during the outburst and disappeared towards the end of the outburst over a timescale comparable to the sound crossing time. The multi-wavelength spectral evolution of NGC 1566 during the outburst is most likely caused by the radiation pressure instability in the inner regions of the accretion disk in NGC 1566.
The degree of irrationality of a smooth projective variety $X$ is the minimal degree of a dominant rational map $X\dashrightarrow \mathbb{P}^{\dim X}$. We show that if an abelian surface $A$ over $\mathbb{C}$ is such that the image of the intersection pairing $\text{Sym}^2NS(A)\to \mathbb{Z}$ does not contain $12$, then it has degree of irrationality $4$. In particular, a very general $(1,d)$-polarized abelian surface has degree of irrationality $4$ provided that $d\nmid 6$. This answers two questions of Yoshihara by providing the first examples of abelian surfaces with degree of irrationality greater than $3$ and showing that the degree of irrationality is not isogeny-invariant for abelian surfaces.
We report the results of mean field and the Monte Carlo study of the dynamic magnetization-reversal transition in the Ising model, brought about by the application of an external field pulse applied in opposition to the existing order before the application of the pulse. The transition occurs at a temperature T below the static critical temperature T_c without any external field. The transition occurs when the system, perturbed by the external field pulse competing with the existing order, jumps from one minimum of free energy to the other after the withdrawal of the pulse. The parameters controlling the transition are the strength h_p and the duration Delta t of the pulse. In the mean field case, approximate analytical expression is obtained for the phase boundary which agrees well with that obtained numerically in the small Delta t and large T limit. The order parameter of the transition has been identified and is observed to vary continuously near the transition. The order parameter exponent beta was estimated both for the mean field (beta =1) and the Monte Carlo beta = 0.90 \pm 0.02 in two dimension) cases. The transition shows a "critical slowing-down" type behaviour near the phase boundary with diverging relaxation time. The divergence was found to be logarithmic in the mean field case and exponential in the Monte Carlo case. The finite size scaling technique was employed to estimate the correlation length exponent nu (= 1.5 \pm 0.3 in two dimension) in the Monte Carlo case.
We derive expressions for the survey-window convolved galaxy power spectrum in real space for a full sky and deep redshift survey, but taking into account the geometrical lightcone effect. We investigate the impact of using the standard mean redshift approximation as a function of survey depth, and show that this assumption can lead to both an overall amplitude suppression and scale-dependent error when compared to the `true' spectrum. However, we also show that by using a carefully chosen `effective fixed-time', one can find a range of scales where the approximation to the full model is highly accurate, but only on a more restricted set of scales. We validate the theory by constructing dark matter and galaxy lightcone mock surveys from a large $N$-body simulation with a high cadence of snapshots. We do this by solving the light cone equation exactly for every particle, where the particle worldlines are obtained in a piecewise fashion with cubic interpolation between neighbouring snapshots. We find excellent agreement between our measurements and the theory ($\sim \pm 5\%$) over scales $(0.004 h{\rm Mpc}^{-1} \leq k \leq 0.54 h {\rm Mpc}^{-1})$ and for a variety of magnitude limits. Finally, we look to see how accurately we can measure the turnover scale of the galaxy power spectrum $k_0$. Using the lightcone mocks we show that one can detect the turnover scale with a probability $P \geq 95\%$ in an all-sky catalogue limited to an apparent magnitude $m_{\rm lim}\sim 21$. We also show that the detection significance would remain high for surveys with $m_{\rm lim}\sim22$ and $20\%$ sky coverage.
We consider equations of nonlinear Schrodinger type augmented by nonlinear damping terms. We show that nonlinear damping prevents finite time blow-up in several situations, which we describe. We also prove that the presence of a quadratic confinement in all spatial directions drives the solution of our model to zero for large time. In the case without external potential we prove that the solution may not go to zero for large time due to (non-trivial) scattering.
We consider the late-time evolution of {\it gravitational} and electromagnetic perturbations in realistic {\it rotating} Kerr spacetimes. We give a detailed analysis of the mode-coupling phenomena in rotating gravitational collapse. A consequence of this phenomena is that the late-time tail is dominated by modes which, in general, may have an angular distribution different from the original one. In addition, we show that different types of fields have {\it different} decaying rates. This result turns over the traditional belief (which has been widely accepted during the last three decades) that the late-time tail of gravitational collapse is universal.
Massive scalar particle production, due to the anisotropic evolution of a five-dimensional spacetime, is considered in the context of a quadratic Lagrangian theory of gravity. Those particles, corresponding to field modes with non-vanishing momentum component along the fifth dimension, are created mostly in the neighbourhood of a singular epoch where only their high-frequency behaviour is of considerable importance. At the 1-loop approximation level, general renormalizability conditions on the physical quantities relevant to particle production are derived and discussed. Exact solutions of the resulting Klein-Gordon field equation are obtained and the mass-energy spectrum attributed to the scalar field due to the cosmological evolution is being investigated further. Finally, analytic expressions regarding the number and the energy density of the created particles at late times, are also derived and discussed.
Suppose that $F$ is a non-Archimedean local field and $D$ is a central division algebra over $F$. Let $n$ be a positive integer. We show a classification modulo essentially square-integrable representations of standard modules of $\mathrm{GL}_n(D)$ which have non-zero linear periods. By this classification, the conjecture of Prasad and Takloo-Bighash is reduced to the case of essentially square integrable representations.
Recent observations and hydrodynamical simulations of star formation inside a giant molecular cloud have revealed that, within a star forming region, stars do not form evenly distributed throughout this region, but rather in small sub-clumps. It is generally believed that these sub-clumps merge and form a young star cluster. The time-scale of this merging process is crucial for the evolution and the possible survival of the final star cluster. The key issue is whether this merging process happens faster than the time needed to remove the residual gas of the cloud. A merging time-scale shorter than the gas-removal time would enhance the survival chances of the resulting star cluster. In this paper we show by means of numerical simulations that the time-scale of the merging is indeed very fast. Depending on the details of the initial sub-clump distribution, the merging may occur before the gas is expelled from the newly-formed cluster either via supernovae or the winds from massive stars. Our simulations further show that the resulting merger-objects have a higher effective star formation efficiency than the overall star forming region and confirm the results that mass-segregated sub-clumps form mass-segregated merger-objects.
Si$_x$Ge$_{1-x-y}$Sn$_y$ ternary alloys are a candidate material system for use in solar cells and other optoelectronic devices. We report on the direct transition energies and structural properties of Ge-rich Si$_x$Ge$_{1-x-y}$Sn$_y$ alloys with six different compositions up to 10 % Si and 3 % Sn, lattice-matched to Ge or GaAs substrates. The direct transitions occurring between 0.9 and 5.0 eV were investigated using spectroscopic ellipsometry (SE), and the resulting data was used to obtain the dielectric functions of the Si$_x$Ge$_{1-x-y}$Sn$_y$n layer by fitting a multi-layer model. Values for the $E_0$, $E_1$, $\Delta_1$, $E_0'$ and $E_2$ transition energies were then found by differentiating these dielectric functions to extract the locations of critical points. Structurally, the composition of the samples was measured using energy-dispersive X-ray measurements (EDX). The lattice constants predicted from these compositions are in good agreement with reciprocal space maps obtained through X-ray diffraction (XRD). The results confirm that a 1 eV direct absorption edge can be achieved using relatively low Si and Sn fractions ($<$ 10 % and $<$ 3 % respectively), while the higher-energy critical points show smaller shifts relative to Ge and match results previously observed or predicted in the literature.
I investigate viable textures with two texture zeros for the inverted neutrino mass matrix, and present the predictions of those textures for the neutrino masses and for lepton mixing. By using an Abelian symmetry and one or two heavy scalar singlets, I construct realizations of those textures in the context of seesaw models.
We discuss the implications of a gauged Abelian hidden-sector communicating with the Standard Model (SM) fields via kinetic mixing with the SM hypercharge gauge field, or via the Higgs quartic interaction. We discuss signatures of the hidden-sector gauge boson at the LHC in the four-lepton channel. We show that a hidden-sector fermion can be a natural dark-matter candidate with the correct relic-density, discuss direct-detection prospects, and show how Higgs signatures may be altered at the LHC.
We give a proof of the analiticity in time for the particle trajectories associated with the solutions of some transport equations when the initial datum is a patch. These results are obtained from a precise study of the Beurling transform, which provides estimates for the solutions of some new equations satisfied by the lagrangian flow.
Coupling between sub- and super-Hubble modes can affect the locally observed statistics of our universe. In the context of Quasi-Single Field Inflation, we can compute correlation functions and derive the influence of those unobservable modes on observed correlation functions as well as on the inferred cosmological parameters. We study how different classes of diagrams affect the bispectrum in the squeezed limit; in particular, while contact-like diagrams leave the scaling between the long and short modes unchanged, exchange-like diagrams do modify the shape of the bispectrum. We show that the mass of the hidden sector field can hence be biased by an unavoidable cosmic variance that can reach a 1-$\sigma$ uncertainty of $\mathcal{O}(10\%)$ for a weakly non-Gaussian universe. Finally, we go beyond the bispectrum and show how couplings between unobservable and observable modes can affect generic correlation functions with arbitrary order non-derivative self-interactions.
We present a novel calculation of the spectrum of electrons and positrons from random sources, supernova remnants and pulsars, distributed within the spiral arms of the Galaxy. The pulsar emissivity in terms of electron-positron pairs is considered as time dependent, following the magnetic dipole spin-down luminosity, and the temporal evolution of the potential drop is accounted for. Moreover each pulsar, with the magnetic field and initial spin period selected at random from the observed distribution, is considered as a source of pairs only after it leaves the parent supernova due to its birth kick velocity (also selected at random from the observed distribution). We show that (i) the spectrum of electrons is characterized by a feature at $\gtrsim 50$ GeV that proves that their transport is dominated by radiative losses. The flux reduction at $E\gtrsim 1$ TeV is explained as a result of lepton transport from sources in the spiral arms. (ii) The spectrum of positrons is very well described by the contribution of pulsars and the rising positron fraction originates naturally. The implications of pulsars as positron sources in terms of positron fraction at very high energies are also discussed. (iii) The role of fluctuations in the high-energy regime is thoroughly discussed and used to draw conclusions on the possibility to single out the contribution of local sources to the lepton spectrum with current and upcoming experiments.
The epitaxial growth of germanene on semiconducting GaAs(0001) substrate is studied using $ab$-$initio$ calculations. The interaction of the germanene is found to be minimum with the substrate. Our obtained results strongly indicate that it is possible to take off germanene from the substrate to make it free standing. We demonstrate a methods to achieve this aim. We also address the electronic structure of germanene on GaAs(0001) substrate and found to be the Dirac cone shift above the Fermi level with the spltting of 160 meV. Forthermore, we calculate the band structure of the free standing germanene with and without substrate and found band gap of 24 meV due to the intrinsic spin orbit coupling.
This document describes the strategies for the development of the Pythia7 program. Both the internal and external structure of the program is discussed. Some comments on relationship to other software is given as well as some comments on coding conventions and other technical details.