ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study transport across a point contact separating two line junctions in a \nu = 5/2 quantum Hall system. We analyze the effect of inter-edge Coulomb interactions between the chiral bosonic edge modes of the half-filled Landau level (assuming a Pfaffian wave function for the half-filled state) and of the two fully filled Landau levels. In the presence of inter-edge Coulomb interactions between all the six edges participating in the line junction, the stable fixed point corresponds to a point contact which is neither fully opaque nor fully transparent. Remarkably, this fixed point represents a situation where the half-filled level is fully transmitting, while the two filled levels are completely backscattered; hence the fixed point Hall conductance is given by G_H = {1/2} e^2/h. We predict the non-universal temperature power laws by which the system approaches the stable fixed point from the two unstable fixed points corresponding to the fully connected case (G_H = {5/2} e^2/h) and the fully disconnected case (G_H = 0).
We find a different method to compute the generating series in Shimura's conjecture for Sp3, proved by Andrianov in 1967. Formulas for the Satake spherical map for Sp3 are used.
The aim of this paper is to propose a new method for numerical approximations of the solution of the linear stochastic partial differential equation arising in non-linear filtering problems: the Zaka\"i equation. The approximation scheme is based on a representation of the solution of the Zaka\"i equation involving a stochastic part arising from the observation process and a deterministic partial differential equation in which are involved only the parameters of the signal process. We may then employ a dynamic programming principle in order to write down an approximation of this partial differential equation. A quantization method based on the underlying diffusion process (which is a not the signal itself) is used.
A sequence $S$ is potentially $K_{m}-H$-graphical if it has a realization containing a $K_{m}-H$ as a subgraph. Let $\sigma(K_{m}-H, n)$ denote the smallest degree sum such that every $n$-term graphical sequence $S$ with $\sigma(S)\geq \sigma(K_{m}-H, n)$ is potentially $K_{m}-H$-graphical. In this paper, we determine $\sigma (K_{r+1}-(kP_2\bigcup tK_2), n)$ for $n\geq 4r+10, r+1 \geq 3k+2t, k+t \geq 2,k \geq 1, t \geq 0$ .
Two-dimensional (2D) semiconductors are promising channel materials for next-generation field-effect transistors (FETs) thanks to their unique mechanical properties and enhanced electrostatic control. However, the performance of these devices can be strongly limited by the scattering processes between carriers and phonons, usually occurring at high rates in 2D materials. Here, we use quantum transport simulations calibrated on first-principle computations to report on dissipative transport in antimonene and arsenene $n$-type FETs at the scaling limit. We show that the widely-used approximations of either ballistic transport or simple acoustic deformation potential scattering result in large overestimation of the ON current, due to neglecting the dominant intervalley and optical phonon scattering processes. We additionally investigate valley engineering strategy [Nano Lett. \textbf{19}, 3723 (2019)] to improve the device performance by removing the valley degeneracy and suppressing most of the intervalley scattering channels via an uniaxial strain along the zigzag direction. The method is applicable to other similar 2D semiconductors characterized by multivalley transport.
Transformers are built upon multi-head scaled dot-product attention and positional encoding, which aim to learn the feature representations and token dependencies. In this work, we focus on enhancing the distinctive representation by learning to augment the feature maps with the self-attention mechanism in Transformers. Specifically, we propose the horizontal attention to re-weight the multi-head output of the scaled dot-product attention before dimensionality reduction, and propose the vertical attention to adaptively re-calibrate channel-wise feature responses by explicitly modelling inter-dependencies among different channels. We demonstrate the Transformer models equipped with the two attentions have a high generalization capability across different supervised learning tasks, with a very minor additional computational cost overhead. The proposed horizontal and vertical attentions are highly modular, which can be inserted into various Transformer models to further improve the performance. Our code is available in the supplementary material.
We consider a generalized version of the Random Energy Model in which the energy of each configuration is given by the sum of $N$ independent contributions ("local energies") with finite variances but otherwise arbitrary statistics. Using the large deviation formalism, we find that the glass transition generically exists when local energies have a smooth distribution. In contrast, if the distribution of the local energies has a {Dirac mass} at the minimal energy (e.g., if local energies take discrete values), the glass transition ceases to exist if the number of energy levels grows sufficiently fast with system size. This shows that statistical independence of energy levels does not imply the existence of a glass transition.
This paper is part of a series in which we perform a systematic comparison of the galaxy properties inhabiting compact groups, loose groups and the field. In this paper we focus our study to the age and the star formation in galaxies. For galaxies in selected samples of compact groups, loose groups and field, we compare the distributions of the following parameters: D$_n(4000)$ as an age indicator, and the specific star formation rate as indicator of ongoing star formation. We analyse the dependence of these parameters on galaxy type, stellar mass and, for group galaxies, their dependence on the dynamic state of the system. We also analyse the fraction of old, and of high star forming galaxies as a function of galaxy stellar mass in the environments we probe. Galaxies in compact groups have, on average, older stellar populations than their loose group or field counterparts. Early-type galaxies in compact groups formed their stars and depleted their gas content more rapidly than in the other environments. We have found evidence of two populations of late-type galaxies in dynamically old compact groups: one with normal specific star formation rates and another with markedly reduced star formation. Processes that transform galaxies from star forming to quiescent act upon galaxies faster and more effectively in compact groups. The unique characteristics of compact groups make them an extreme environment for galaxies, where the transition to quiescence occurs rapidly.
This thesis presents an overview of the flow equations recently introduced by Wegner. The little known mathematical framework of the flow in the manifold of unitarily equivalent matrices, as discovered in the mathematical literature before Wegner's paper, is established in the initial chapter and used as a background for the entire presentation. The application of flow equations to the Foldy-Wouthuysen transformation and to the elimination of the electron-phonon coupling in a solid is reviewed. Recent flow equations approaches to the Lipkin model are examined thoroughly, paying special attention to their utility near the phase change boundary. We present more robust schemes by requiring that expectation values be flow dependent; either through a variational or self-consistent calculation. The similarity renormalization group equations recently developed by Glazek and Wilson are also reviewed. Their relationship to Wegner's flow equations is investigated through the aid of an instructive model.
We introduce the transition-density formalism, an efficient and general method for calculating the interaction of external probes with light nuclei. One- and two-body transition densities that encode the nuclear structure of the target are evaluated once and stored. They are then convoluted with an interaction kernel to produce amplitudes, and hence observables. By choosing different kernels, the same densities can be used for any reaction in which a probe interacts perturbatively with the target. The method therefore exploits the factorisation between nuclear structure and interaction kernel that occurs in such processes. We study in detail the convergence in the number of partial waves for matrix elements relevant in elastic Compton scattering on $^3$He. The results are fully consistent with our previous calculations in Chiral Effective Field Theory. But the new approach is markedly more computationally efficient, which facilitates the inclusion of more partial-wave channels in the calculation. We also discuss the usefulness of the transition-density method for other nuclei and reactions. Calculations of elastic Compton scattering on heavier targets like $^4$He are straightforward extensions of this study, since the same interaction kernels are used. And the generality of the formalism means that our $^3$He densities can be used to evaluate any $^3$He elastic-scattering observable with contributions from one- and two-body operators. They are available at https://datapub.fz-juelich.de/anogga.
Given a compact and connected four dimensional smooth Riemannian manifold $(M,g_0)$ with $k_P := \int_M Q_{g_0} dV_{g_0} <0$ and a smooth non-constant function $f_0$ with $\max_{p\in M}f_0(p)=0$, all of whose maximum points are non-degenerate, we assume that the Paneitz operator is nonnegative and with kernel consisting of constants. Then, we are able to prove that for sufficiently small $\lambda>0$ there are at least two distinct conformal metrics $g_\lambda=e^{2u_\lambda}g_0$ and $g^\lambda=e^{2u^\lambda}g_0$ of $Q$-curvature $Q_{g_\lambda}=Q_{g^\lambda}=f_0+\lambda$. Moreover, by means of the "monotonicity trick", we obtain crucial estimates for the "large" solutions $u^\lambda$ which enable us to study their "bubbling behavior" as $\lambda \downarrow 0$.
Face detection from low-light images is challenging due to limited photos and inevitable noise, which, to make the task even harder, are often spatially unevenly distributed. A natural solution is to borrow the idea from multi-exposure, which captures multiple shots to obtain well-exposed images under challenging conditions. High-quality implementation/approximation of multi-exposure from a single image is however nontrivial. Fortunately, as shown in this paper, neither is such high-quality necessary since our task is face detection rather than image enhancement. Specifically, we propose a novel Recurrent Exposure Generation (REG) module and couple it seamlessly with a Multi-Exposure Detection (MED) module, and thus significantly improve face detection performance by effectively inhibiting non-uniform illumination and noise issues. REG produces progressively and efficiently intermediate images corresponding to various exposure settings, and such pseudo-exposures are then fused by MED to detect faces across different lighting conditions. The proposed method, named REGDet, is the first `detection-with-enhancement' framework for low-light face detection. It not only encourages rich interaction and feature fusion across different illumination levels, but also enables effective end-to-end learning of the REG component to be better tailored for face detection. Moreover, as clearly shown in our experiments, REG can be flexibly coupled with different face detectors without extra low/normal-light image pairs for training. We tested REGDet on the DARK FACE low-light face benchmark with thorough ablation study, where REGDet outperforms previous state-of-the-arts by a significant margin, with only negligible extra parameters.
This paper consolidates noscalar hair theorem for a charged spherically symmetric black hole in four dimension in general relativity as well as in all scalar tensor theories, both minimally and nonminimally coupled, when the effective Newtonian constant of gravity is positive. However, there is an exception when the matter field itself is coupled to the scalar field, such as in dilaton gravity.
The algebra of constraints arising in the canonical quantization of N=1 supergravity in four dimensions is investigated. Using the holomorphic action, the structure functions of the algebra are given and it is shown that the algebra does not close formally for two chosen operator orderings.
A careful analysis of the gravitational geon solution found by Brill and Hartle is made. The gravitational wave expansion they used is shown to be consistent and to result in a gauge invariant wave equation. It also results in a gauge invariant effective stress-energy tensor for the gravitational waves provided that a generalized definition of a gauge transformation is used. To leading order this gauge transformation is the same as the usual one for gravitational waves. It is shown that the geon solution is a self-consistent solution to Einstein's equations and that, to leading order, the equations describing the geometry of the gravitational geon are identical to those derived by Wheeler for the electromagnetic geon. An appendix provides an existence proof for geon solutions to these equations.
In ABO3 perovskites, oxygen octahedron rotations are common structural distortions that can promote large ferroelectricity in BiFeO3 with an R3c structure [1], but suppress ferroelectricity in CaTiO3 with a Pbnm symmetry [2]. For many CaTiO3-like perovskites, the BiFeO3 structure is a metastable phase. Here, we report the stabilization of the highly-polar BiFeO3-like phase of CaTiO3 in a BaTiO3/CaTiO3 superlattice grown on a SrTiO3 substrate. The stabilization is realized by a reconstruction of oxygen octahedron rotations at the interface from the pattern of nonpolar bulk CaTiO3 to a different pattern that is characteristic of a BiFeO3 phase. The reconstruction is interpreted through a combination of amplitude-contrast sub 0.1nm high-resolution transmission electron microscopy and first-principles theories of the structure, energetics, and polarization of the superlattice and its constituents. We further predict a number of new artificial ferroelectric materials demonstrating that nonpolar perovskites can be turned into ferroelectrics via this interface mechanism. Therefore, a large number of perovskites with the CaTiO3 structure type, which include many magnetic representatives, are now good candidates as novel highly-polar multiferroic materials [3].
We study the underlying chemical, electronic and magnetic properties of a number of magnetite based thin films. The main focus is placed onto NiO/Fe$_3$O$_4$(001) bilayers grown on MgO(001) and Nb-SrTiO$_3$(001) substrates. We compare the results with those obtained on pure Fe$_3$O$_4$(001) thin films. It is found that the magnetite layers are oxidized and Fe$^{3+}$ dominates at the surfaces due to maghemite ($\gamma$-Fe$_2$O$_3$) formation, which decreases with increasing magnetite layer thickness. From a layer thickness of around 20 nm on the cationic distribution is close to that of stoichiometric Fe$_3$O$_4$. At the interface between NiO and Fe$_3$O$_4$ we find the Ni to be in a divalent valence state, with unambiguous spectral features in the Ni 2p core level x-ray photoelectron spectra typical for NiO. The formation of a significant NiFe$_2$O$_4$ interlayer can be excluded by means of XMCD. Magneto optical Kerr effect measurements reveal significant higher coercive fields compared to magnetite thin films grown on MgO(001), and a 45$^{\circ}$ rotated magnetic easy axis. We discuss the spin magnetic moments of the magnetite layers and find that the moment increases with increasing thin film thickness. At low thickness the NiO/Fe$_3$O$_4$ films grown on Nb-SrTiO$_3$ exhibits a significantly decreased spin magnetic moments. A thickness of 20 nm or above leads to spin magnetic moments close to that of bulk magnetite.
Transport properties of holes in InP nanowires were calculated considering electron-phonon interaction via deformation potentials, the effect of temperature and strain fields. Using molecular dynamics, we simulate nanowire structures, LO-phonon energy renormalization and lifetime. The valence band ground state changes between light- and heavy-hole character, as the strain fields and the nanowire size are changed. Drastic changes in the mobility arise with the onset of resonance between the LO-phonons and the separation between valence subbands.
In this paper, we consider a multi-layer tumor model with a periodic provision of external nutrients. The domain occupied by tumor has a different shape (flat shape) than spherical shape which has been studied widely. The important parameters are periodic external nutrients $\Phi(t)$ and threshold concentration for proliferation $\widetilde{\sigma}$. In this paper, we give a complete classification about $\Phi(t)$ and $\widetilde{\sigma}$ according to global stability of zero equilibrium solution or global stability of the positive periodic solution. Precisely, if $\frac{1}{T} \int_{0}^{T} \Phi(t)d t\leqslant\widetilde{\sigma}$, then the zero equilibrium solution is globally stable while if $\frac{1}{T} \int_{0}^{T} \Phi(t)d t>\widetilde{\sigma}$, then there exists a unique positive T-periodic solution and it is globally stable.
The electronic states in incommensurate (IC) helical magnets are studied theoretically from the viewpoint of the localization/delocalization. It is found that in the multi-band system with relativistic spin-orbit interaction, the electronic wavefunctions show both the extended and localized natures along the helical axis depending on the orbital, helical wavenumber, and the direction of the plane on which spins rotate. Possible realization of this localization is discussed.
Recent studies suggest that Swift gamma-ray bursts (GRBs) may not trace an ordinary star formation history. Here we show that the GRB rate turns out to be consistent with the star formation history with an evolving stellar initial mass function (IMF). We first show that the latest Swift sample of GRBs reveals an increasing evolution in the GRB rate relative to the ordinary star formation rate at high redshifts. We then assume only massive stars with masses greater than the critical value to produce GRBs, and use an evolving stellar IMF suggested by Dav\'{e} (2010) to fit the latest GRB redshift distribution. This evolving IMF would increase the relative number of massive stars, which could lead to more GRB explosions at high redshifts. We find that the evolving IMF can well reproduce the observed redshift distribution of Swift GRBs.
We explore the vicinity of the Milky Way through the use of spectro-photometric data from the Sloan Digital Sky Survey and high-quality proper motions derived from multi-epoch positions extracted from the Guide Star Catalogue II database. In order to identify and characterise streams as relics of the Milky Way formation, we start with classifying, select, and study $2417$ subdwarfs with $\rm{[Fe/H] < -1.5}$ up to $3$ kpc away from the Sun as tracers of the local halo system. Then, through phase-space analysis, we find statistical evidence of five discrete kinematic overdensities among $67$ of the fastest-moving stars, and compare them to high-resolution N-body simulations of the interaction between a Milky-Way like galaxy and orbiting dwarf galaxies with four representative cases of merging histories. The observed overdensities can be interpreted as fossil substructures consisting of streamers torn from their progenitors, such progenitors appear to be satellites on prograde and retrograde orbits on different inclinations. In particular, of the five detected overdensities, two appear to be associated, yelding twenty-one additional main-sequence members, with the stream of Helmi et al. (1999) that our analysis confirms on a high inclination prograde orbit. The three newly identified kinematic groups could be associated with the retrograde streams detected by Dinescu (2002) and Kepley et al. (2007), whatever their origin, the progenitor(s) would be on retrograde orbit(s) and inclination(s) within the range $10^{\circ} \div 60^{\circ}$. Finally, we use our simulations to investigate the impact of observational errors and compare the current picture to the promising prospect of highly improved data expected from the Gaia mission.
We use ab-initio calculations to predict the thermal conductivity of cubic SiC with different types of defects. An excellent quantitative agreement with previous experimental measurements is found. The results unveil that B$_\mathrm{C}$ substitution has a much stronger effect than any of the other defect types in 3C-SiC, including vacancies. This finding contradicts the prediction of the classical mass-difference model of impurity scattering, according to which the effects of B$_\mathrm{C}$ and N$_\mathrm{C}$ would be similar and much smaller than that of the C vacancy. The strikingly different behavior of the B$_\mathrm{C}$ defect arises from a unique pattern of resonant phonon scattering caused by the broken structural symmetry around the B impurity.
Radiation fields emitted by O, B-type stars or young stellar populations (SPs) are generally considered as significant central ionizing sources (CISs) of classic H II regions. In our previous studies, we show that the inclusion of binary interactions in stellar population synthesis models can significantly increase the ultraviolet spectrum hardness and the number of ionizing photons of intermediate-age (IA, 7<~log(t/yr)<~8) SPs. In this work, we present photoionization models of H II regions ionized by radiation fields emitted by IA SPs, and show that radiation fields of IA SPs, including binary systems, are in theory possible candidates of significant CISs of classic H II regions. When radiation fields of IA SPs comprising binary systems are used as the CISs of classic H II regions, the theoretical strengths of a number of lines (such as [O III]4959', [S II]6716', etc.), weaker than observations, are raised; the border /selection-criterion lines, between star-forming galaxies and AGNs in the diagnostic diagrams (for example, [N II]6583/Ha~[O III]5007/Hb), move into the region occupied originally by AGNs; and He II 1640 line, observed in Lyman break and high-redshift gravitationally lensed galaxies, also can be produced.
We suggest a mechanism explaining the origin of three generations of the Standard Model fermions from one generation in a higher-dimensional theory. Four-dimensional fermions appear as zero modes trapped in the core of a topological defect with topological number three. We discuss hierarchical pattern of masses and mixings which arises in these models.
In this paper, we exhibit upper and lower bounds with explicit constants for some objects related to entire $L$-functions in the critical strip, under the generalized Riemann hypothesis. The examples include the entire Dirichlet $L$-functions $L(s,\chi)$ for primitive characters $\chi$.
We consider the Ising phase of the antiferromagnetic XXZ Heisenberg chain on a finite-size lattice with N sites.We compute the large $N$ behavior of the spin stiffness, obtaining the correlation length \xi. We use our results to discuss the scaling behavior of metal-insulator transitions in 1D systems, taking into account the mapping between the XXZ Heisenberg chain and the spinless fermion model and known results for the Hubbard model. We study the scaling properties of both the Hubbard model and the XXZ Heisenberg chain, by solving numerically the Bethe Ansatz equations. We find that for some range of values of \xi/N the scaling behavior may be observed for the Hubbard model but not for the XXZ Heisenserg chain. We show how \xi can be obtained from the scaling properties of the spin stiffness for small system sizes. This method can be applied to models having not an exact solution, illuminating their transport properties.