ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we present several heavy-tailed distributions belonging to the new class J of distributions obeying the principle of a single big jump introduced by Beck et al. [1]. We describe the structure of this class from different angles. First, we show that heavy-tailed distributions in the class J are automatically strongly heavy-tailed and thus have tails which are not too irregular. Second, we show that such distributions are not necessarily weakly tail equivalent to a subexponential distribution. We also show that the class of heavy-tailed distributions in J which are neither long-tailed nor dominatedly-varying-tailed is not only non-empty but even quite rich in the sense that it has a nonempty intersection with several other well-established classes. In addition, the integrated tail distribution of some particular of these distributions shows that the Pakes-Veraverbeke-Embrechts Theorem for the class J in [1] does not hold trivially.
We present high-precision spectro-polarimetric data with high spatial resolution (0.4$''$) of the very quiet Sun at 1.56$\mu$m obtained with the GREGOR telescope to shed some light on this complex magnetism. Half of our observed quiet-Sun region is better explained by magnetic substructure within the resolution element. However, we cannot distinguish whether this substructure comes from gradients of the physical parameters along the line of sight or from horizontal gradients (across the surface). In these pixels, a model with two magnetic components is preferred, and we find two distinct magnetic field populations. The population with the larger filling factor has very weak ($\sim$150 G) horizontal fields similar to those obtained in previous works. We demonstrate that the field vector of this population is not constrained by the observations, given the spatial resolution and polarimetric accuracy of our data. The topology of the other component with the smaller filling factor is constrained by the observations for field strengths above 250 G: we infer hG fields with inclinations and azimuth values compatible with an isotropic distribution. The filling factors are typically below 30\%. We also find that the flux of the two polarities is not balanced. From the other half of the observed quiet-Sun area $\sim$50\% are two-lobed Stokes $V$ profiles, meaning that 23\% of the field of view can be adequately explained with a single constant magnetic field embedded in a non-magnetic atmosphere. The magnetic field vector and filling factor are reliable inferred in only 50\% based on the regular profiles. Therefore, 12\% of the field of view harbour hG fields with filling factors typically below 30\%. At our present spatial resolution, 70\% of the pixels apparently are non-magnetised.
We study the efficacy of a new ab initio framework that combines the symmetry-adapted (SA) no-core shell-model approach with the resonating group method (RGM) for unified descriptions of nuclear structure and reactions. We obtain ab initio neutron-nucleus interactions for $^4$He, $^{16}$O, and $^{20}$Ne targets, starting with realistic nucleon-nucleon potentials. We discuss the effect of increasing model space sizes and symmetry-based selections on the SA-RGM norm and direct potential kernels, as well as on phase shifts, which are the input to calculations of cross sections. We demonstrate the efficacy of the SA basis and its scalability with particle numbers and model space dimensions, with a view toward ab initio descriptions of nucleon scattering and capture reactions up through the medium-mass region.
The paper introduces a new way to construct dissipative solutions to a second order variational wave equation. By a variable transformation, from the nonlinear PDE one obtains a semilinear hyperbolic system with sources. In contrast with the conservative case, here the source terms are discontinuous and the discontinuities are not always crossed transversally. Solutions to the semilinear system are obtained by an approximation argument, relying on Kolmogorov's compactness theorem. Reverting to the original variables, one recovers a solution to the nonlinear wave equation where the total energy is a monotone decreasing function of time.
We present a renormalization group (RG) approach to explain universal features of extreme statistics, applied here to independent, identically distributed variables. The outlines of the theory have been described in a previous Letter, the main result being that finite-size shape corrections to the limit distribution can be obtained from a linearization of the RG transformation near a fixed point, leading to the computation of stable perturbations as eigenfunctions. Here we show details of the RG theory which exhibit remarkable similarities to the RG known in statistical physics. Besides the fixed points explaining universality, and the least stable eigendirections accounting for convergence rates and shape corrections, the similarities include marginally stable perturbations which turn out to be generic for the Fisher-Tippett-Gumbel class. Distribution functions containing unstable perturbations are also considered. We find that, after a transitory divergence, they return to the universal fixed line at the same or at a different point depending on the type of perturbation.
The work deals with the thermodynamics of the universe bounded by the event horizon. The matter in the universe has three constituents namely dark energy, dark matter and radiation in nature and interaction between then is assumed. The variation of entropy of the surface of the horizon is obtained from unified first law while matter entropy variation is calculated from the Gibbss' law. Finally, validity of the generalized second law of thermodynamics is examined and conclusions are written point wise.
We present optical, radio, and X-ray observations of SN2020bvc (=ASASSN20bs; ZTF20aalxlis), a nearby ($z=0.0252$; $d$=114 Mpc) broad-lined (BL) Type Ic supernova (SN). Our observations show that SN2020bvc shares several properties in common with the Ic-BL SN2006aj, which was associated with the low-luminosity gamma-ray burst (LLGRB) 060218. First, the 10 GHz radio light curve is on the faint end of LLGRB-SNe ($L_\mathrm{radio} \approx 10^{37}$erg/s): we model our VLA observations (spanning 13-43 d) as synchrotron emission from a mildly relativistic ($v \gtrsim 0.3c$) forward shock. Second, with Swift and Chandra we detect X-ray emission ($L_X \approx 10^{41}$erg/s) that is not naturally explained as inverse Compton emission or as part of the same synchrotron spectrum as the radio emission. Third, high-cadence ($6\times$/night) data from the Zwicky Transient Facility (ZTF) shows a double-peaked optical light curve, the first peak from shock-cooling emission from extended low-mass material (mass $M<10^{-2} M_\odot$ at radius $R>10^{12}$cm) and the second peak from the radioactive decay of Ni-56. SN2020bvc is the first confirmed double-peaked Ic-BL SN discovered without a GRB trigger, and shows X-ray and radio emission similar to LLGRB-SNe: this is consistent with models in which the same mechanism produces both the LLGRB and the shock-cooling emission. For four of the five other nearby ($z\lesssim0.05$) Ic-BL SNe with ZTF high-cadence data, we rule out a first peak like that seen in SN2006aj and SN2020bvc, i.e. that lasts $\approx 1$d and reaches a peak luminosity $M \approx -18$. X-ray and radio follow-up observations of future such events will establish whether double-peaked optical light curves are indeed predictive of LLGRB-like X-ray and radio emission.
We study the $A$-discriminant of toric varieties. We reduce its computation to the case of irreducible configurations and describe its behavior under specialization of some of the variables to zero. We prove a Gale dual characterization of dual defect toric varieties and deduce from it the classsification of such varieties in codimension less than or equal to four. This classification motivates a decomposition theorem which yields a sufficient condition for a toric variety to be dual defect. For codimension less than or equal to four, this condition is also necessary and we expect this to be the case in general.
The recent discovery of a millisecond radio burst from the Galactic magnetar SGR 1935+2154 has initiated an intense discussion about the connection between magnetars and fast radio bursts (FRBs). Although some properties of the radio burst from SGR 1935+2154 are not the same as cosmological FRBs, there are theoretical models which propose a connection between magnetars and FRBs (see review by Margalit et al. 2020). In particular, the role of a magnetar wind nebula is included in some models, and therefore it is worthwhile to investigate the X-ray environment of SGR 1935+2154 in more detail. Here, we report on the discovery of an X-ray transient feature near SGR 1935+2154 using archival Chandra data and discuss its possible origin.
The structure of ground states of generic FQH states on a torus is studied by using both effective theory and electron wave function. The relation between the effective theory and the wave function becomes transparent when one considers the ground state structure. We find that the non-abelian Berry's phases of the abelian Hall states generated by twisting the mass matrix are identical to the modular transformation matrix for the characters of a Gaussian conformal field theory. We also show that the Haldane-Rezayi spin singlet state has a ten fold degeneracy on a torus which indicates such a state is a non-abelian Hall state.
We investigate the random continuous trees called L\'evy trees, which are obtained as scaling limits of discrete Galton-Watson trees. We give a mathematically precise definition of these random trees as random variables taking values in the set of equivalence classes of compact rooted R-trees, which is equipped with the Gromov-Hausdorff distance. To construct L\'evy trees, we make use of the coding by the height process which was studied in detail in previous work. We then investigate various probabilistic properties of L\'evy trees. In particular we establish a branching property analogous to the well-known property for Galton-Watson trees: Conditionally given the tree below level a, the subtrees originating from that level are distributed as the atoms of a Poisson point measure whose intensity involves a local time measure supported on the vertices at distance a from the root. We study regularity properties of local times in the space variable, and prove that the support of local time is the full level set, except for certain exceptional values of a corresponding to local extinctions. We also compute several fractal dimensions of L\'evy trees, including Hausdorff and packing dimensions, in terms of lower and upper indices for the branching mechanism function $\psi$ which characterizes the distribution of the tree. We finally discuss some applications to super-Brownian motion with a general branching mechanism.
We study a generalized Anderson model that mixes two localized configurations --one formed by two degenerate doublets and the other by a triplet with single-ion anisotropy $DS_z^2$-- by means of two degenerate conduction channels. The model has been derived for a single Ni impurity embedded into an O-doped Au chain. Using the numerical renormalization group, we find a topological quantum phase transition, at a finite value $D_c,$ between two regular Fermi liquid phases of high (low) conductance and topological number $2 I_L/\pi = 0$ (-1) for $D < D_c$ ($D > D_c$), where $I_L$ is the well-known Luttinger integral. At finite temperature the two phases are separated by a non-Fermi liquid phase with fractional impurity entropy $\frac{1}{2}{\rm ln}2$ and other properties which remind those of the two-channel Kondo model.
We construct a family of compactifications of the affine cone of the Grassmannian variety of 2-planes. We show that both the tropical variety of the Pl\"ucker ideal and familiar valuations associated to the construction of Newton-Okounkov bodies for the Grassmannian variety can be recovered from these compactifications. In this way, we unite various perspectives for constructing toric degenerations of flag varieties.
In a recent Letter we proposed a means to realize a quasicrystal with eight-fold symmetry by trapping particles in an optical potential created by four lasers. The quasicrystals obtained in this way, which are closely related to the well-known octagonal tiling, offer unique possibilities to study the effects of quasiperiodicity on physical properties. This method allows to transform the structures, to inflate or deflate them, include interactions or disorder and thus realize a large variety of theoretical models, both classical and quantum. In this paper we derive a number of interesting geometrical properties of the optical quasicrystals, and present some results obtained by numerical calculations.
We shall give some results for an integer divisible by its unitary totient.
Let $a\in\mathbb{R}$ denote an unknown stationary target with a known distribution $\mu\in\mathcal{P(\mathbb{R}})$, the space of probability measures on $\mathbb{R}$. A diffusive searcher $X(\cdot)$ sets out from the origin to locate the target. The time to locate the target is $T_a=\inf\{t\ge0: X(t)=a\}$. The searcher has a given constant diffusion rate $D>0$, but its drift $b$ can be set by the search designer from a natural admissible class $\mathcal{D}_\mu$ of drifts. Thus, the diffusive searcher is a Markov process generated by the operator $L=\frac D2\frac{d^2}{dx^2}+b(x)\frac d{dx}$. % equivalently, $X(\cdot)$ satisfies the stochastic differential equation %$X(t)=W(t)+\int_0^tb(X(s))ds$, where $W(\cdot)$ is a standard Brownian motion. For a given drift $b$, the expected time of the search is \begin{equation} \int_{\mathbb{R}} (E^{(b)}_0T_a)\thinspace\mu(da). \end{equation} Our aim is to minimize this expected search time over all admissible drifts $b\in\mathcal{D}_\mu$. For measures $\mu$ that satisfy a certain balance condition between their restriction to the positive axis and their restriction to the negative axis, a condition satisfied, in particular, by all symmetric measures, we can give a complete answer to the problem. We calculate the above infimum explicitly, we classify the measures for which the infimum is attained, and in the case that it is attained, we calculate the minimizing drift explicitly. For measures that do not satisfy the balance condition, we obtain partial results.
We consider an Ising model confined in an $L \times \infty$ geometry with identical surface fields at the boundaries. According to the Kelvin equation the bulk coexistence field scales as 1/L for large L; thermodynamics and scaling arguments predict higher order corrections of the type $1/L^2$ and $1/L^{5/3}$ at partial and complete wetting respectively. Our numerical results, obtained by density-matrix renormalization techniques for systems of widths up to L = 144, are in agreement with a $1/L^2$ correction in the partial wet regime. However at complete wetting we find a large range of surface fields and temperatures with a correction to scaling of type $1/L^{4/3}$. We show that this term is generated by a {\it thin} wetting layer whose free energy is dominated by the contacts with the wall. For $L$ sufficiently large we expect a crossover to a $1/L^{5/3}$ correction as predicted by the theory for a {\it thick} wetting layer. This crossover is indeed found in a solid-on-solid model which provides a simplified description of the wetting layer and allows the study of much larger systems than those available in a density-matrix renormalization calculation.
The purpose of the classical Einstein and Landau-Lifshitz pseudotensors is for determining the gravitational energy. Neither of them can guarantee a positive energy in holonomic frames. In the small sphere approximation, it has been required that the quasilocal expression for the gravitational energy-momentum density should be proportional to the Bel-Robinson tensor $B_{\alpha\beta\mu\nu}$. However, we propose a new tensor $V_{\alpha\beta\mu\nu}$ which is the sum of certain tensors $S_{\alpha\beta\mu\nu}$ and $K_{\alpha\beta\mu\nu}$, it has certain properties so that it gives the same gravitational "energy-momentum" content as $B_{\alpha\beta\mu\nu}$ does. Moreover, we show that a modified Einstein pseudotensor turns out to be one of the Chen-Nester quasilocal expressions, while the modified Landau-Lifshitz pseudotensor becomes the Papapetrou pseudotensor; these two modified pseudotensors have positive gravitational energy in a small region.
Monolayer epitaxial graphene is an appropriate candidate for a wide variety of electronic and optical applications. One advantage of growing graphene on the Si face of SiC is that it develops as a single crystal, as does the layer underneath, commonly referred to as the interfacial buffer layer. The properties of this supporting layer include a band gap, making it of interest to groups seeking to build devices with on-off capabilities. In this work, using density functional theory, we have calculated the bonding characteristics of the buffer layer to the SiC substrate beneath. These calculations were used to determine a periodic length between the covalent bonds acting as anchor points in this interface. Additionally, it is evident that the formation of these anchor points depends on the lattice mismatch between the graphene layer and SiC.
We consider the Schr\"{o}dinger equation $-\Delta u +V(x)u=f(x, u)$, where $V$ is periodic and $f$ is non-periodic, 0 is a boundary point of the continuous spectrum of $A:=-\Delta +V(x)$. We use M. Willem and W. M. Zou's linking theorem and M. Schechter's method to establish an existence result for this problem in weak superlinear cases. In a sense, we enrich a recent result of M. Willem and W.M. Zou [M. Willem and W.M. Zou, On a Schr\"{o}dinger Equation with Periodic Potential and Spectrum Point Zero,Indiana Univ. Math. J. 2003].
The mechanical behavior in compression of [111] LiF micropillars with diameters in the range 0.5 $\mu$m to 2.0 $\mu$m was analyzed by means of discrete dislocation dynamics at ambient and elevated temperature. The dislocation velocity was obtained from the Peach-Koehler force acting on the dislocation segments from a thermally-activated model that accounted for the influence of temperature on the lattice resistance. A size effect of the type "smaller is stronger" was predicted by the simulations, which was in quantitative agreement with previous experimental results by the authors \cite{SWC14}. The contribution of the different physical deformation mechanisms to the size effect (namely, nucleation of dislocations, dislocation exhaustion and forest hardening) could be ascertained from the simulations and the dominant deformation mode could be assessed as a function of the specimen size and temperature. These results shed light into the complex interaction among size, lattice resistance and dislocation mobility in the mechanical behavior of $\mu$m-sized single crystals.
We present the results on period search and modeling of the cool DAV star KUV 02464+3239. Our observations resolved the multiperiodic pulsational behaviour of the star. In agreement with its position near the red edge of the DAV instability strip, it shows large amplitude, long period pulsation modes, and has a strongly non-sinusoidal light curve. We determined 6 frequencies as normal modes and revealed remarkable short-term amplitude variations. A rigorous test was performed for the possible source of amplitude variation: beating of modes, effect of noise, unresolved frequencies or rotational triplets. Among the best-fit models resulting from a grid search, we selected 3 that gave l=1 solutions for the largest amplitude modes. These models had masses of 0.645, 0.650 and 0.680 M_Sun. The 3 `favoured' models have M_H between 2.5x10^-5 - 6.3x10^-6 M_* and give 14.2 - 14.8 mas seismological parallax. The 0.645 M_Sun (11400 K) model also matches the spectroscopic log g and T_eff within 1 sigma. We investigated the possibility of mode trapping and concluded that while it can explain high amplitude modes, it is not required.
The deterministic single-photon emission by means of STIRAP through the atoms with degenerate levels is studied. The expression for the polarization matrix of the emitted photon is obtained and its dependence on the polarization of the driving laser field and on the initial atomic state is examined.
The goal of the present paper is to investigate the circumstellar material around the brightest dust-enshrouded sources in the central stellar cluster of the Milky Way. Observations have been carried out at the European Southern Observatory's Very Large Telescope on Paranal, Chile. We have used the long wavelength (LWS3) low resolution (LR) spectroscopic mode of the ISAAC camera at the VLT in the spectral range of the M filter from 4.4micron to 5.1micron. The use of a slit width of 0.6" implied a spectral resolution of R=l/Dl=800 (Dv=375 km/s). These observations resulted in M-band spectra of 15 bright sources in the central stellar cluster of the Milky Way. In addition to gaseous 12^CO (4.666 micron) and 13^CO (4.77 micron) vibration-rotational absorptions, we detect a strong absorption due to a mixture of polar and apolar CO ice (centered at 4.675 micron). In the shorter wavelength absorption wing there is an absorption feature due to XCN at 4.62 micron. The XCN absorption is strongest toward the M2 supergiant IRS7. We find that the extinctions due to material traced by the CO ice and the CO gas absorptions may be of comparable importance. Using the spectra of IRS2L and IRS16C we perform a first order correction of the line of sight absorption due to CO-ice and 13^CO gas. In combination with published hydrogen number density estimates from sub-mm CO(7-6) and FIR [OI] line data we obtain gas masses of the circumstellar shells of the order of 10^-3 and 10^-2 solar masses. This implies that in future spectra taken at high spectral and angular resolution the bright and dust embedded Galactic Center sources should show a substantial line absorption due to source intrinsic absorption.
We discuss the approximation of real numbers by Fourier coefficients of newforms, following recent work of Alkan, Ford and Zaharescu. The main tools used here, besides the (now proved) Sato-Tate Conjecture, come from metric number theory.
The mixed spin-(1/2, 1) Ising model on two fully frustrated triangles-in-triangles lattices is exactly solved with the help of the generalized star-triangle transformation, which establishes a rigorous mapping correspondence with the equivalent spin-1/2 Ising model on a triangular lattice. It is shown that the mutual interplay between the spin frustration and single-ion anisotropy gives rise to various spontaneously ordered and disordered ground states, which differ mainly in an occurrence probability of the non-magnetic spin state of the integer-valued decorating spins. We have convincingly evidenced a possible coexistence of the spontaneous long-range order with a partial disorder within the striking ordered-disordered ground state, which manifest itself through a non-trivial criticality at finite temperatures as well. A rather rich critical behaviour including the order-from-disorder effect and reentrant phase transitions with either two or three successive critical points is also found.
We reduce the Abundance Conjecture in dimension 4 to the following numerical statement: if the canonical divisor K is nef and has maximal nef dimension, then K is big. From this point of view, we ``classify'' in dimension 2 nef divisors which have maximal nef dimension, but which are not big.