ShantanuT01/DACTYL-Pretraining huggingface dataset:
A graph $\Gamma$ is said to be symmetric if its automorphism group $\rm Aut(\Gamma)$ acts transitively on the arc set of $\Gamma$. In this paper, we show that if $\Gamma$ is a finite connected heptavalent symmetric graph with solvable stabilizer admitting a vertex-transitive non-abelian simple group $G$ of automorphisms, then either $G$ is normal in $\rm Aut(\Gamma)$, or $\rm Aut(\Gamma)$ contains a non-abelian simple normal subgroup $T$ such that $G\leq T$ and $(G,T)$ is explicitly given as one of $11$ possible exception pairs of non-abelian simple groups. Furthermore, if $G$ is regular on the vertex set of $\Gamma$ then the exception pair $(G,T)$ is one of $7$ possible pairs, and if $G$ is arc-transitive then the exception pair $(G,T)=(A_{17},A_{18})$ or $(A_{35},A_{36})$.
Using first-principle plane wave method we investigate the effects of static charging on structural, elastic, electronic and magnetic properties of suspended, single layer graphene, graphane, fluorographene, BN and MoS2 in honeycomb structures. The limitations of periodic boundary conditions in the treatment of charged layers are clarified. Upon positive charging the band gaps between the conduction and valence bands increase, but the single layer materials become metallic owing to the Fermi level dipping below the maximum of valence band. Moreover, their bond lengths increase and their in-plane stiffness decreases. As a result, phonons are softened and frequencies of Raman active modes are lowered. High level of charging leads to instability. We showed that wide band gap BN and MoS2 slabs are metallized as a result of electron removal and their outermost layers are exfoliated once the charging exceeds a threshold value.
We demonstrate quantitative magnetic field mapping with nanoscale resolution, by applying a lock-in technique on the electron spin resonance frequency of a single nitrogen-vacancy defect placed at the apex of an atomic force microscope tip. In addition, we report an all-optical magnetic imaging technique which is sensitive to large off-axis magnetic fields, thus extending the operation range of diamond-based magnetometry. Both techniques are illustrated by using a magnetic hard disk as a test sample. Owing to the non-perturbing and quantitative nature of the magnetic probe, this work should open up numerous perspectives in nanomagnetism and spintronics.
We consider the Hamiltonian theory for the multi-component KP hierarchy. We show that the second Hamiltonian structures constructed by Sidorenko and Strampp[J. Math. Phys. {\bf 34}, 1429(1993)] are not Hamiltonian. A candidate for the second Hamiltonian Structures is proposed and is proved to lead to hereditary operators.
StyleGAN family is one of the most popular Generative Adversarial Networks (GANs) for unconditional generation. Despite its impressive performance, its high demand on storage and computation impedes their deployment on resource-constrained devices. This paper provides a comprehensive study of distilling from the popular StyleGAN-like architecture. Our key insight is that the main challenge of StyleGAN distillation lies in the output discrepancy issue, where the teacher and student model yield different outputs given the same input latent code. Standard knowledge distillation losses typically fail under this heterogeneous distillation scenario. We conduct thorough analysis about the reasons and effects of this discrepancy issue, and identify that the mapping network plays a vital role in determining semantic information of generated images. Based on this finding, we propose a novel initialization strategy for the student model, which can ensure the output consistency to the maximum extent. To further enhance the semantic consistency between the teacher and student model, we present a latent-direction-based distillation loss that preserves the semantic relations in latent space. Extensive experiments demonstrate the effectiveness of our approach in distilling StyleGAN2 and StyleGAN3, outperforming existing GAN distillation methods by a large margin.
We construct a new counterexample confirming the sharpness of the Dini-type condition for the boundary of $\Omega$. In particular, we show that for convex domains the Dini-type assumption is the necessary and sufficient condition which guarantees the Hopf-Oleinik type estimates.
Topological insulators in three dimensions are nonmagnetic insulators that possess metallic surface states as a consequence of the nontrivial topology of electronic wavefunctions in the bulk of the material. They are the first known examples of topological order in bulk solids. We review the basic phenomena and experimental history, starting with the observation of topological insulator behavior in Bi$_x$Sb$_{1-x}$ by spin- and angle-resolved photoemission spectroscopy and continuing through measurements on other materials and by other probes. A self-contained introduction to the single-particle theory is then given, followed by the many-particle definition of a topological insulator as a material with quantized magnetoelectric polarizability. The last section reviews recent work on strongly correlated topological insulators and new effects that arise from the proximity effect between a topological insulator and a superconductor. While this article is not intended to be a comprehensive review of what is already a rather large field, we hope that it will serve as a useful introduction, summary of recent progress, and guideline to future directions.
This paper deals with the quadratic integers of small norms and asserts that in some sense R >> (log D)^2 is true for almost all real quadratic number fields. (A few errata is corrected.)
The increasing prevalence of diet-related chronic diseases coupled with the ineffectiveness of traditional diet management methods have resulted in a need for novel tools to accurately and automatically assess meals. Recently, computer vision based systems that use meal images to assess their content have been proposed. Food portion estimation is the most difficult task for individuals assessing their meals and it is also the least studied area. The present paper proposes a three-stage system to calculate portion sizes using two images of a dish acquired by mobile devices. The first stage consists in understanding the configuration of the different views, after which a dense 3D model is built from the two images; finally, this 3D model serves to extract the volume of the different items. The system was extensively tested on 77 real dishes of known volume, and achieved an average error of less than 10% in 5.5 seconds per dish. The proposed pipeline is computationally tractable and requires no user input, making it a viable option for fully automated dietary assessment.
Interpenetrating streams of solids and gas in a Keplerian disk produce a local, linear instability. The two components mutually interact via aerodynamic drag, which generates radial drift and triggers unstable modes. The secular instability does not require self-gravity, yet it generates growing particle density perturbations that could seed planetesimal formation. Growth rates are slower than dynamical, but faster than radial drift, timescales. Growth rates, like streaming velocities, are maximized for marginal coupling (stopping times comparable dynamical times). Fastest growth occurs when the solid to gas density ratio is order unity and feedback is strongest. Curiously, growth is strongly suppressed when the densities are too nearly equal. The relation between background drift and wave properties is explained by analogy with Howard's semicircle theorem. The three-dimensional, two-fluid equations describe a sixth order (in the complex frequency) dispersion relation. A terminal velocity approximation allows simplification to an approximate cubic dispersion relation. To describe the simplest manifestation of this instability, we ignore complicating (but possibly relevant) factors like vertical stratification, dispersion of particle sizes, turbulence, and self-gravity. We consider applications to planetesimal formation and compare our work to other studies of particle-gas dynamics.
We review important reactions in the big bang nucleosynthesis (BBN) model involving a long-lived negatively charged massive particle, $X^-$, which is much heavier than nucleons. This model can explain the observed $^7$Li abundances of metal-poor stars, and predicts a primordial $^9$Be abundance that is larger than the standard BBN prediction. In the BBN epoch, nuclei recombine with the $X^-$ particle. Because of the heavy $X^-$ mass, the atomic size of bound states $A_X$ is as small as the nuclear size. The nonresonant recombination rates are then dominated by the $d$-wave $\rightarrow$ 2P transition for $^7$Li and $^{7,9}$Be. The $^7$Be destruction occurs via a recombination with the $X^-$ followed by a proton capture, and the primordial $^7$Li abundance is reduced. Also, the $^9$Be production occurs via the recombination of $^7$Li and $X^-$ followed by deuteron capture. The initial abundance and the lifetime of the $X^-$ particles are constrained from a BBN reaction network calculation. We estimate that the derived parameter region for the $^7$Li reduction is allowed in supersymmetric or Kaluza-Klein (KK) models. We find that either the selectron, smuon, KK electron or KK muon could be candidates for the $X^-$ with $m_X\sim {\mathcal O}(1)$ TeV, while the stau and KK tau cannot.
The Large Yield Radiometer (LYRA) is a radiometer that has monitored the solar irradiance at high cadence and in four pass bands since January 2010. Both the instrument and its space- craft, PROBA2 (Project for On-Board Autonomy), have several innovative features for space instrumentation, which makes the data reduction necessary to retrieve the long term variations of solar irradiance more complex than for a fully optimized solar physics mission. In this paper, we describe how we compute the long term time series of the two extreme ultraviolet irradiance channels of LYRA, and compare the results with SDO/EVE. We find that the solar EUV irradi- ance has increased by a factor 2 since the last solar minimum (between solar cycles 23 and 24), which agrees reasonably well with the EVE observations.
The recent interferometric study of Achernar, leading to the conclusion that its geometrical oblateness cannot be explained in the Roche approximation, has stirred substantial interest in the community, in view of its potential impact in many fields of stellar astrophysics. It is the purpose of this paper to reinterpret the interferometric observations with a fast rotating, gravity darkened central star surrounded by a small equatorial disk, whose presence is consistent with contemporaneous spectroscopic data. We find that we can only fit the available data assuming a critically rotating central star. We identified two different disk models that simultaneously fit the spectroscopic, polarimetric, and interferometric observational constraints: a tenuous disk in hydrostatic equilibrium (i.e., with small scaleheight) and a smaller, scaleheight enhanced disk. We believe that these relatively small disks correspond to the transition region between the photosphere and the circumstellar environment, and that they are probably perturbed by some photospheric mechanism. The study of this interface between photosphere and circumstellar disk for near-critical rotators is crucial to our understanding of the Be phenomenon, and the mass and angular momentum loss of stars in general. This work shows that it is nowadays possible to directly study this transition region from simultaneous multi-technique observations.
In this note we obtain a unique continuation result for the differential inequality $|\bar{\partial}u|\leq|Vu|$, where $\bar{\partial}=(i\partial_y+\partial_x)/2$ denotes the Cauchy-Riemann operator and $V(x,y)$ is a function in $L^2(\mathbb{R}^2)$.
The impacts of radiative, electrical and thermal losses on the power output enhancement of nanoscale-gap thermophotovoltaic (nano-TPV) power generators consisting of a gallium antimonide cell paired with a broadband tungsten and a radiatively-optimized Drude radiator are analyzed. Results reveal that surface mode mediated nano-TPV power generation with the Drude radiator outperforms the tungsten emitter, dominated by frustrated modes, only for a vacuum gap thickness of 10 nm and if both electrical and thermal losses are neglected. The key limiting factors for the Drude and tungsten-based devices are respectively the recombination of electron-hole pairs at the cell surface and thermalization of radiation with energy larger than the absorption bandgap. In a nano-TPV power generator cooled by convection with a fluid at 293 K and a heat transfer coefficient of 10^4 Wm^-2K^-1, power output enhancements of 4.69 and 1.89 are obtained for the tungsten and Drude radiators, respectively, when a realistic vacuum gap thickness of 100 nm is considered. A design guideline is also proposed where a high energy cutoff above which radiation has a net negative effect on nano-TPV power output is determined. This work demonstrates that design and optimization of nano-TPV devices must account for radiative, electrical and thermal losses.
For Grassmann varieties, we explain how the duality between the Gelfand-Tsetlin polytopes and the Feigin-Fourier-Littelmann-Vinberg polytopes arises from different positive structures.
This paper investigates the Terwilliger algebra of some group association schemes related to codes. In addition, it also shows the generators of invariant rings appearing by E-polynomials.
The kinematics of a final state system with two invisible particles and two visible particles can develop cusped peak structures. This happens when the system has a fixed invariant mass (such as from a narrow resonant particle decay or with a fixed collision c.m. energy) and undergoes decays of two on-shell intermediate particles. Focusing on the "antler decay topology", we derive general analytic expressions for the invariant mass distribution and the kinematic cusp position. The sharp cusp peaks and the endpoint positions can help to determine the masses of the missing particles and the intermediate particles. We also consider transverse momentum variables and angular variables. In various distributions the kinematic cusp peaks are present and pronounced. We also study the effects on such kinematic cusp structures from realistic considerations including finite decay widths, the longitudinal boost of the system, and spin correlations.
A kinetic Ising model description of Liesegang phenomena is studied using Monte Carlo simulations. The model takes into account thermal fluctuations, contains noise in the chemical reactions, and its control parameters are experimentally accessible. We find that noisy, irregular precipitation takes place in dimension d=2 while, depending on the values of the control parameters, either irregular patterns or precipitation bands satisfying the regular spacing law emerge in d=3.
It is fairly well known that rotation in three dimensions can be expressed as a quadratic in a skew symmetric matrix via the Euler-Rodrigues formula. A generalized Euler-Rodrigues polynomial of degree 2n in a skew symmetric generating matrix is derived for the rotation matrix of tensors of order $n$. The Euler-Rodrigues formula for rigid body rotation is recovered by n=1. A Cayley form of the n-th order rotation tensor is also derived. The representations simplify if there exists some underlying symmetry, as is the case for elasticity tensors such as strain and the fourth order tensor of elastic moduli. A new formula is presented for the transformation of elastic moduli under rotation: as a 21-vector with a rotation matrix given by a polynomial of degree 8. Explicit spectral representations are constructed from three vectors: the axis of rotation and two orthogonal bivectors. The tensor rotation formulae are related to Cartan decomposition of elastic moduli and projection onto hexagonal symmetry.
We investigate quantum corrections to the conductivity due to the interference of electron-electron (electron-phonon) scattering and elastic electron scattering in weakly disordered conductors. The electron-electron interaction results in a negative $T^2 \ln T$-correction in a 3D conductor. In a quasi-two-dimensional conductor, $d < v_F/T$ ($d$ is the thickness, $v_F$ is the Fermi velocity), with 3D electron spectrum this correction is linear in temperature and differs from that for 2D electrons (G. Zala et. al., Phys. Rev.B {\bf 64}, 214204 (2001)) by a numerical factor. In a quasi-one-dimensional conductor, temperature-dependent correction is proportional to $T^2$. The electron interaction via exchange of virtual phonons also gives $T^2$-correction. The contribution of thermal phonons interacting with electrons via the screened deformation potential results in $T^4$-term and via unscreened deformation potential results in $T^2$-term. The interference contributions dominate over pure electron-phonon scattering in a wide temperature range, which extends with increasing disorder.
We study the dynamical properties of the ordered phases obtained in a coupled nonequilibrium system describing advection of two species of particles by a stochastically evolving landscape. The local dynamics of the landscape also gets affected by the particles. In a companion paper we have presented static properties of different phases that arise as the two-way coupling parameters are varied. In this paper we discuss the dynamics. We show that in the ordered phases macroscopic particle clusters move over an ergodic time-scale growing exponentially with system size but the ordered landscape shows dynamics over a faster time-scale growing as a power of system size. We present a scaling ansatz that describes several dynamical correlation functions of the landscape measured in steady state.
An alternative proof of factorization theorem for Drell-Yan process that works at operator level is given in the article. Final state interactions for such inclusive processes are proved to be cancel out at operator level according to the unitarity of time evolution operator. After this cancellation, one can always deform the integral path so that eikonal line approximation works while calculating the time evolution of electromagnetic currants. Decoupling of soft gluons from collinear jets is realized by defining new collinear fields that decouple from soft gluons. Cancelation of soft gluons is attribute to unitarity of time evolution operator and light-like Wilson lines of soft gluons.
It is shown that the conventional many-body techniques to calculate the Green's functions can be applied to the wide, compressible edge of a quantum Hall bar. The only ansatz we need is the existence of stable density modes that yields a simple equation of motion of the density operators. We derive the spectral density at a finite temperature and show how the tunneling characteristics of a sharp edge can be deduced as a limiting case.
The dwarf stars in the 26 year period binary Alpha Com are predicted to eclipse each other in early 2015. Simulations of randomly selected orbital parameters based on the most recently published orbital elements and uncertainties show the eclipse will happen within 3 days of MJD 57047 (January 25, 2015; 1 sigma; all simulations fall within 2 weeks of this) and will have a depth of several tenths of a magnitude. The eclipse will last between 28 and 45 hours, depending on the exact orbital parameters. Observers are encouraged to monitor this unique event.
We present a quantitative study of most prominent incompressible quantum Hall states in the partially filled first excited Landau level (LL1) which have been recently studied experimentally by Choi et al. The pseudopotential describing the electron - electron interaction in LL1 is harmonic at short range. It produces a series of incompressible states which is different from its LL0 counterpart. The numerical data indicate that the most prominent states $\nu={5/2}$, 7/3, and 8/3 are not produced by Laughlin correlated electrons, but result from a tendency of electrons to form pairs or larger clusters which eventually become Laughlin correlated. States with smaller gaps at filling factors 14/5, 16/7, 11/5, 19/7 are Laughlin correlated electron or hole states and fit Jain's sequence of filled $\rm{CF}^4$ levels.
Layers of twisted bilayer graphene exhibit varieties of exotic quantum phenomena1-5. Today, the twist angle {\Theta} has become an important degree of freedom for exploring novel states of matters, i.e. two-dimensional superconductivity ( {\Theta} = 1.1{\deg})6, 7 and a two-dimensional quasicrystal ({\Theta} = 30{\deg})8, 9. We report herein experimental observation on the photo-induced ultrafast dynamics of Dirac fermions in the quasicrystalline 30{\deg} twisted bilayer graphene (QCTBG). We discover that hot carriers are asymmetrically distributed between the two graphene layers, followed by the opposing femtosecond relaxations, by using time- and angle-resolved photoemission spectroscopy. The key mechanism involves the differing carrier transport between layers and the transient doping from the substrate interface. The ultrafast dynamics scheme continues after the Umklapp scattering, which is induced by the incommensurate interlayer stacking of the quasi-crystallinity. The dynamics in the atomic layer opens the possibility of new applications and creates interdisciplinary links in the optoelectronics of van der Waals crystals.
We develop a general framework for the discussion of detailed balance and analyse its microscopic background. We find that there should be two additions to the well-known $T$- or $PT$-invariance of the microscopic laws of motion:   1. Equilibrium should not spontaneously break the relevant $T$- or $PT$-symmetry.   2. The macroscopic processes should be microscopically distinguishable to guarantee persistence of detailed balance in the model reduction from micro- to macrokinetics.   We briefly discuss examples of the violation of these rules and the corresponding violation of detailed balance.
We consider multiparameter dynamics on the space of unimolular lattices. Along with quantitative nondivergence we prove that multiplicative Diophantine exponents of hyperplanes are inherited by their nondegenerate submanifolds.
Of the known microquasars, V4641 Sgr boasts the most severe lower limit (> 52{\deg}) on the misalignment angle between the relativistic jet axis and the binary orbital angular momentum. Assuming the jet and black hole spin axes coincide, we attempt to explain the origin of this extreme spin-orbit misalignment with a natal kick model, whereby an aligned binary system becomes misaligned by a supernova kick imparted to the newborn black hole. The model inputs are the kick velocity distribution, which we measure customized to V4641 Sgr, and the immediate pre/post-supernova binary system parameters. Using a grid of binary stellar evolution models, we determine post-supernova configurations that evolve to become consistent with V4641 Sgr today and obtain the corresponding pre-supernova configurations by using standard prescriptions for common envelope evolution. Using each of these potential progenitor system parameter sets as inputs, we find that a natal kick struggles to explain the origin of the V4641 Sgr spin-orbit misalignment. Consequently, we conclude that evolutionary pathways involving a standard common envelope phase followed by a supernova kick are highly unlikely for V4641 Sgr. An alternative interpretation is that the jet axis does not reliably trace the black hole spin axis. Our results raise concerns about compact object merger statistics gleaned from binary population synthesis models, which rely on unverified prescriptions for common envelope evolution and natal kicks. We also challenge the spin-orbit alignment assumption routinely invoked to measure black hole spin magnitudes.