ShantanuT01/DACTYL-Pretraining huggingface dataset:
We establish sharp higher-order H\"older regularity estimates up to the boundary for solutions to equations of the form $\partial_t u-Lu=f(t,x)$ in $I\times\Omega$ where $I\subset\mathbb{R}$, $\Omega\subset\mathbb{R}^n$ and $f$ is H\"older continuous. The nonlocal operators $L$ considered are those arising in stochastic processes with jumps such as the fractional Laplacian $(-\Delta)^s$, $s\in(0,1)$.   Our main result establishes that, if $f$ is $C^\gamma$ is space and $C^{\gamma/2s}$ in time, and $\Omega$ is a $C^{2,\gamma}$ domain, then $u/d^s$ is $C^{s+\gamma}$ up to the boundary in space and $u$ is $C^{1+\gamma/2s}$ up the boundary in time, where $d$ is the distance to $\partial\Omega$. This is the first higher order boundary regularity estimate for nonlocal parabolic equations, and is new even for the fractional Laplacian in $C^\infty$ domains.
Regime-switching processes contain two components: continuous component and discrete component, which can be used to describe a continuous dynamical system in a random environment. Such processes have many different properties than general diffusion processes, and much more difficulties are needed to be overcome due to the intensive interaction between continuous and discrete component. We give conditions for the existence and uniqueness of invariant measures for state-dependent regime-switching diffusion processes by constructing a new Markov chain to control the evolution of the state-dependent switching process. We also establish the strong convergence in the $L^1$-norm of the Euler-Maruyama's approximation and estimate the order of error. A refined application of Skorokhod's representation of jumping processes plays a substantial role in this work.
The energy of a compact binary system at the fifth post-Newtonian order is explicitly computed in the post-Minkowskian approximation by means of the Effective Field Theory approach. This result allows to determine, for the first time beyond the test particle limit, one coefficient of the energy expression for binary point masses on circular orbit as a function of the orbital angular frequency.
Neutron inelastic scattering has been used to probe the spin dynamics of the quantum (S=1/2) ferromagnet on the pyrochlore lattice Lu2V2O7. Well-defined spin waves are observed at all energies and wavevectors, allowing us to determine the parameters of the Hamiltonian of the system. The data are found to be in excellent overall agreement with a minimal model that includes a nearest- neighbour Heisenberg exchange J = 8:22(2) meV and a Dzyaloshinskii-Moriya interaction (DMI) D =1:5(1) meV. The large DMI term revealed by our study is broadly consistent with the model developed by Onose et al. to explain the magnon Hall effect they observed in Lu2V2O7 [1], although our ratio of D=J = 0:18(1) is roughly half of their value and three times larger than calculated by ab initio methods [2].
Yttrium (Y) substituted Mg Zn ferrites with the compositions of Mg0.5Zn0.5YxFe2 xO4 have been synthesized by conventional standard ceramic technique. The effect of Y3+ substitution on the structural, electrical, dielectric and magnetic properties of Mg Zn ferrites has been studied.
Large spin Hall angles have been observed in 3d ferromagnets, but their origin, and especially their link with the ferromagnetic order, remain unclear. Here, we investigate the inverse spin Hall effect of Ni60Cu40 and Ni50Cu50 across their Curie temperature using spin pumping experiments. We evidence that the inverse spin Hall effect in these samples is comparable to that of platinum, and that it is insensitive to the magnetic order. These results points towards a Heisenberg localized model of the transition, and suggest that the large spin Hall effects in 3d ferromagnets can be independent of the magnetic phase.
We examine the phenomenon of enhanced dissipation from the perspective of H\"ormander's classical theory of second order hypoelliptic operators [31]. Consider a passive scalar in a shear flow, whose evolution is described by the advection-diffusion equation \[ \partial_t f + b(y) \partial_x f - \nu \Delta f = 0 \text{ on } \mathbb{T} \times (0,1) \times \mathbb{R}_+ \] with periodic, Dirichlet, or Neumann conditions in $y$. We demonstrate that decay is enhanced on the timescale $T \sim \nu^{-(N+1)/(N+3)}$, where $N-1$ is the maximal order of vanishing of the derivative $b'(y)$ of the shear profile and $N=0$ for monotone shear flows. In the periodic setting, we recover the known timescale of Bedrossian and Coti Zelati [8]. Our results are new in the presence of boundaries.
In this paper we apply the differential inequality technique of Payne {\it et. al} \cite{Payne&SchaeferRobin08} to show that a reaction-diffusion system admits blow-up solutions, and to determine an upper bound for the blow-up time. For a particular nonlinearity, a lower bound on the blow-up time, when blow-up does occur, is also given.
The Telescope Array (TA) experiment is the largest detector to observe ultra-high-energy cosmic rays in the northern hemisphere. The fluorescence detectors at southern two stations of TA are newly constructed and have now completed seven years of steady operation. One advantage of monocular analysis of the fluorescence detectors is a lower energy threshold for cosmic rays than that of other techniques like stereoscopic observations or coincidences with the surface detector array, allowing the measurement of an energy spectrum covering three orders of magnitude in energy. Analyzing data collected during those seven years, we report the energy spectrum of cosmic rays covering a broad range of energies above 10$^{17.2}$ eV measured by the fluorescence detectors and a comparison with previously published results.
Face recognition (FR) has recently made substantial progress and achieved high accuracy on standard benchmarks. However, it has raised security concerns in enormous FR applications because deep CNNs are unusually vulnerable to adversarial examples, and it is still lack of a comprehensive robustness evaluation before a FR model is deployed in safety-critical scenarios. To facilitate a better understanding of the adversarial vulnerability on FR, we develop an adversarial robustness evaluation library on FR named \textbf{RobFR}, which serves as a reference for evaluating the robustness of downstream tasks. Specifically, RobFR involves 15 popular naturally trained FR models, 9 models with representative defense mechanisms and 2 commercial FR API services, to perform the robustness evaluation by using various adversarial attacks as an important surrogate. The evaluations are conducted under diverse adversarial settings in terms of dodging and impersonation, $\ell_2$ and $\ell_\infty$, as well as white-box and black-box attacks. We further propose a landmark-guided cutout (LGC) attack method to improve the transferability of adversarial examples for black-box attacks by considering the special characteristics of FR. Based on large-scale evaluations, the commercial FR API services fail to exhibit acceptable performance on robustness evaluation, and we also draw several important conclusions for understanding the adversarial robustness of FR models and providing insights for the design of robust FR models. RobFR is open-source and maintains all extendable modules, i.e., \emph{Datasets}, \emph{FR Models}, \emph{Attacks\&Defenses}, and \emph{Evaluations} at \url{https://github.com/ShawnXYang/Face-Robustness-Benchmark}, which will be continuously updated to promote future research on robust FR.
The viscous motion of an interface driven by an ac external field of frequency omega_0 in a random medium is considered here for the first time. The velocity exhibits a smeared depinning transition showing a double hysteresis which is absent in the adiabatic case omega_0 --> 0. Using scaling arguments and an approximate renormalization group calculation we explain the main characteristics of the hysteresis loop. In the low frequency limit these can be expressed in terms of the depinning threshold and the critical exponents of the adiabatic case.
Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological, and social processes. The concept of entropy originated in thermodynamics and statistical physics during the 19th century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the theme issue is intended to provide an introduction to entropy, convexity, and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this theme issue.
Using Wannier functions to represent the density functional results we calculate the hybridization corrections to the orbital momentum operator in the Os 5d shell of Mott insulators Ba2NaOsO6 and Ba2YOsO6. The g-factors are obtained by evaluating the spin and orbital momentum operators in the atomic ground states of the Os ion. While the hybridization corrections play minor role in d3 ion of Ba2YOsO6 with dominant spin moment, they are instrumental for observation of non- zero g-factor of the d1 ions of Ba2NaOsO6. In addition we analyze the exchange interactions in Ba2YOsO6 and find them consistent with the reported magnetic structure.
Good quantum codes, such as quantum MDS codes, are typically nondegenerate, meaning that errors of small weight require active error-correction, which is--paradoxically--itself prone to errors. Decoherence free subspaces, on the other hand, do not require active error correction, but perform poorly in terms of minimum distance. In this paper, examples of degenerate quantum codes are constructed that have better minimum distance than decoherence free subspaces and allow some errors of small weight that do not require active error correction. In particular, two new families of [[n,1,>= sqrt(n)]]_q degenerate quantum codes are derived from classical duadic codes.
In this paper, we show that for a fixed rank $n$, there are only finitely many $m$ for which there is a regular $m$-gonal form of rank $n$ and determine every type of the (generalized) regular $m$-gonal form for every sufficiently large $m$.
It has been found that, for the Supernova Legacy Survey three-year (SNLS3) data, there is strong evidence for the redshift-evolution of color-luminosity parameter $\beta$. In this paper, adopting the $w$-cold-dark-matter ($w$CDM) model and considering its interacting extensions (with three kinds of interaction between dark sectors), we explore the evolution of $\beta$ and its effects on parameter estimation. In addition to the SNLS3 data, we also take into account the Planck distance priors data of the cosmic microwave background (CMB), the galaxy clustering (GC) data extracted from SDSS DR7 and BOSS, as well as the direct measurement of Hubble constant from the Hubble Space Telescope (HST) observation. We find that, for all the interacting dark energy (IDE) models, adding a parameter of $\beta$ can reduce $\chi^2$ by $\sim$ 34, indicating that $\beta_1 = 0$ is ruled out at 5.8$\sigma$ confidence level (CL). Furthermore, it is found that varying $\beta$ can significantly change the fitting results of various cosmological parameters: for all the dark energy models considered in this paper, varying $\beta$ yields a larger $\Omega_{c0}$ and a larger $w$; on the other side, varying $\beta$ yields a smaller $h$ for the $w$CDM model, but has no impact on $h$ for the three IDE models. This implies that there is a degeneracy between $h$ and $\gamma$. Our work shows that the evolution of $\beta$ is insensitive to the interaction between dark sectors, and then highlights the importance of considering $\beta$'s evolution in the cosmology fits.
Fast radio bursts (FRBs) are mysterious millisecond-duration radio transients of unknown origin observed at extragalactic distances. It has been long speculated that magnetars are the engine powering repeating bursts from FRB sources, but no convincing evidence has been collected so far\cite{sun19}. Recently, the Galactic magnetar SGR J1935+2154 entered an active phase by emitting intense soft Gamma-ray bursts. One FRB-like event with two peaks (FRB 200428) and a luminosity slightly lower than the faintest extragalactic FRBs was detected from the source, in association with a soft Gamma-ray / hard X-ray flare. Here we report an eight-hour targeted radio observational campaign comprising four sessions and assisted by multi-wavelength (optical and hard X-rays) data. During the third session, 29 soft Gamma-ray repeater (SGR) bursts were detected in Gamma-ray energies. Throughout the observing period, we detected no single dispersed pulsed emission coincident with the arrivals of SGR bursts, but unfortunately we were not observing when the FRB was detected. The non-detection places a fluence upper limit that is eight orders of magnitude lower than the fluence of FRB 200428. Our results suggest that FRB -- SGR burst associations are rare. FRBs may be highly relativistic and geometrically beamed, or FRB-like events associated with SGR bursts may have narrow spectra and characteristic frequencies outside the observed band. It is also possible that the physical conditions required to achieve coherent radiation in SGR bursts are difficult to satisfy, and that only under extreme conditions could an FRB be associated with an SGR burst.
The formulation of the eigenvalue problem for the Schr\"odinger equation is studied, for the numerical solution a new approach is applied. With the usual exponentially rising free-state asymptotical behavior, and also with a first order correction to it, the lower half of the $k$ plane is systematically explored. Note that no other method, including the complex rotation one, is suitable for calculating virtual bound states far from the origin. Various phenomena are studied about how the bound and the virtual bound states are organized into a system. Even for short range potentials, the free state asymptotical condition proves to be inadequate at some distance from the real $k$ axis; the first order correction doesn't solve this problem.   Therefore, the structure of the space spanned by the mathematically possible solutions is studied and the notion of minimal solutions is introduced. Such solutions provide the natural boundary condition for bound states, their analytical continuation to the lower half plane does the same for resonances and virtual bound states. The eigenvalues coincide with the poles of the S-matrix. The possibility of continuation based on numerical data is also demonstrated. The proposed scheme is suitable for the definition of the in- and outgoing solutions for positive energies; therefore, also for the calculation of the so called distorted S-matrix in case of long range interactions.
We experimentally investigate charge transport through the interface between a niobium superconductor and a three-dimensional WTe$_2$ Weyl semimetal. In addition to classical Andreev reflection, we observe sharp non-periodic subgap resistance resonances. From an analysis of their positions, magnetic field and temperature dependencies, we can interpret them as an analog of Tomasch oscillations for transport along the topological surface state across the region of proximity-induced superconductivity at the Nb-WTe$_2$ interface. Observation of distinct geometrical resonances implies a specific transmission direction for carriers, which is a hallmark of the Fermi arc surface states.
Clustering of dark matter halos has been shown to depend on halo properties beyond mass such as halo concentration, a phenomenon referred to as halo assembly bias. Standard halo occupation models (HOD) in large scale structure studies assume that halo mass alone is sufficient in characterizing the connection between galaxies and halos. Modeling of galaxy clustering can face systematic effects if the number of galaxies within a halo is correlated with other halo properties. Using the Small MultiDark-Planck high resolution $N$-body simulation and the clustering measurements of the Sloan Digital Sky Survey (SDSS) DR7 main galaxy sample, we investigate the extent to which the concentration-dependence of halo occupation can be constrained. Furthermore, we study how allowing for the concentration dependence can improve our modeling of galaxy clustering.   Our constraints on HOD with assembly bias suggest that satellite population is not correlated with halo concentration at fixed halo mass. At fixed halo mass, our constraints favor lack of correlation between the occupation of centrals and halo concentration in the most luminous samples ($M_{\rm r}<-21.5,-21$), and modest correlation in the $M_{\rm r}<-20.5,-20, -19.5$ samples. We show that in comparison with abundance-matching mock catalogs, our findings suggest qualitatively similar but modest levels of the impact of halo assembly bias on galaxy clustering. The effect is only present in the central occupation and becomes less significant in brighter galaxy samples. Furthermore, by performing model comparison based on information criteria, we find that in most cases, the standard mass-only HOD model is still favored by the observations.
As Pr. Th. Henning said at the conference, cold precursors of high-mass stars are now "hot topics". We here propose some observational criteria to identify massive infrared-quiet dense cores which can host the high-mass analogs of Class 0 protostars and pre-stellar condensations. We also show how far-infrared to millimeter imaging surveys of entire complexes forming OB stars are starting to unveil the initial conditions of high-mass star formation.
We consider inverse boundary value problems for polyharmonic operators and in particular, the problem of recovering the coefficients of terms up to order one. The main interest of our result is that it further relaxes the regularity required to establish uniqueness. The proof relies on an averaging technique introduced by Haberman and Tataru for the study of an inverse boundary value problem for a second order operator.
We prove that the cohomology groups with rational coefficients of the Voronoi compactification of the moduli space of abelian threefolds coincide with the Chow groups of that space, as determined by Van der Geer.
We investigate six supernova remnant (SNR) candidates --- G51.21+0.11, G52.37-0.70, G53.07+0.49, G53.41+0.03, G53.84-0.75, and the possible shell around G54.1-0.3 --- in the Galactic Plane using newly acquired LOw-Frequency ARray (LOFAR) High-Band Antenna (HBA) observations, as well as archival Westerbork Synthesis Radio Telescope (WSRT) and Very Large Array Galactic Plane Survey (VGPS) mosaics. We find that G52.37-0.70, G53.84-0.75, and the possible shell around pulsar wind nebula G54.1+0.3 are unlikely to be SNRs, while G53.07+0.49 remains a candidate SNR. G51.21+0.11 has a spectral index of $\alpha=-0.7\pm0.21$, but lacks X-ray observations and as such requires further investigation to confirm its nature. We confirm one candidate, G53.41+0.03, as a new SNR because it has a shell-like morphology, a radio spectral index of $\alpha=-0.6\pm0.2$ and it has the X-ray spectral characteristics of a 1000-8000 year old SNR. The X-ray analysis was performed using archival XMM-Newton observations, which show that G53.41+0.03 has strong emission lines and is best characterized by a non-equilibrium ionization model, consistent with an SNR interpretation. Deep Arecibo radio telescope searches for a pulsar associated with G53.41+0.03 resulted in no detection, but place stringent upper limits on the flux density of such a source if it is beamed towards Earth.
We present an analytic study, based on the tight-binding approximation, of strain effects on the electronic bandgap in single-layer black phosphorus. We obtain an expression for the variation of the bandgap induced by a general strain type that includes both tension in and out of the plane and shear, and use this to determine the most efficient strain direction for different strain types, along which the strongest bandgap manipulation can be achieved. We find that the strain direction that enables the maximum manipulation of the bandgap is not necessarily in the armchair or zigzag direction. Instead, to achieve the strongest bandgap modulation, the direction of the applied mechanical strain is dependent on the type of applied strain.
We explore the feasibility of applying the Christensen-Dalsgaard diagram to real asteroseismic data and provide quantitative measures of the uncertainty associated with the results. We also propose a new kind of seismic diagram, based on the determination of the locations of sharp acoustic features inside a star. We show that by combining the information about the position of the base of the convective envelope or the HeII ionisation zone with a measure of the average large separation, it is possible to constrain the unknown chemical composition or the various parameters characterising the physical processes in the stellar interior. We demonstrate the application of this technique to the analysis of mock data for a CoRoT target star.
We present an IGM HI tomography map in a survey volume of $16 \times 19 \times 131 \ h^{-3} {\rm comoving \ Mpc}^{3}$ (cMpc$^3$) centered at MAMMOTH-1 nebula and three neighbouring quasars at $z=2.3$. MAMMOTH-1 nebula is an enormous Ly$\alpha$ nebula (ELAN), hosted by a type-II quasar dubbed MAMMOTH1-QSO, that extends over $1\ h^{-1}$ cMpc with not fully clear physical origin. Here we investigate the HI-gas distribution around MAMMOTH1-QSO with the ELAN and three neighbouring type-I quasars, making the IGM HI tomography map with a spatial resolution of $2.6\ h^{-1}$ cMpc. Our HI tomography map is reconstructed with HI Ly$\alpha$ forest absorption of bright background objects at $z=2.4-2.9$: one eBOSS quasar and 16 Keck/LRIS galaxy spectra. We estimate the radial profile of HI flux overdensity for MAMMOTH1-QSO, and find that MAMMOTH1-QSO resides in a volume with significantly weak HI absorption. This suggests that MAMMOTH1-QSO has a proximity zone where quasar illuminates and photo-ionizes the surrounding HI gas and suppresses HI absorption, and that the ELAN is probably a photo-ionized cloud embedded in the cosmic web. The HI radial profile of MAMMOTH1-QSO is very similar to those of three neighbouring type-I quasars at $z=2.3$, which is compatible with the AGN unification model. We compare the distributions of the HI absorption and star-forming galaxies in our survey volume, and identify a spatial offset between density peaks of star-forming galaxies and HI gas. This segregation may suggest anisotropic UV background radiation created by star-forming galaxy density fluctuations.