ShantanuT01/DACTYL-Pretraining huggingface dataset:
Using multiwavelength observations of radio afterglows, we confirm the hypothesis that the flux density of gamma-ray bursts (GRBs) at a fixed observing frequency is invariable when the distance of the GRBs increases, which means the detection rate will be approximately independent of redshift. We study this behavior theoretically and find that it can be well explained by the standard forward shock model involving a thin shell expanding in either a homogeneous interstellar medium (ISM) or a wind environment. We also found that short GRBs and supernova-associated GRBs, which are at relatively smaller distances, marginally match the flux-redshift relationship and they could be outliers. We rule out the assumption that the medium density evolves with redshift as $n\propto(1+z)^4$ from the current measurements of $n$ and $z$ for short and long GRBs. In addition, the possible dependence of host flux on the redshift is also investigated. We find that a similar redshift independence of the flux exists for host galaxies as well, which implies that the detection rate of radio hosts might also be independent of the redshift. It is also hinted that most radio hosts have the spectral indices ranging from $\beta_h\simeq-1$ to 2.5 in statistics. Finally, we predict the detection rates of radio afterglows by the next-generation radio telescopes such as the Five-hundred meter Aperture Spherical Telescope (FAST) and the Square Kilometer Array (SKA).
We construct an evidently positive multiple series as a generating function for partitions satisfying the multiplicity condition in Schur's partition theorem.   Refinements of the series when parts in the said partitions are classified according to their parities or values mod 3 are also considered.   Direct combinatorial interpretations of the series are provided.
We compute the E-polynomial of the character variety of representations of a rank r free group in SL(3, C). Expanding upon existing techniques, we stratify the space of representations and compute the E-polynomial of each geometrically described stratum using fibrations. Consequently, we also determine the E-polynomial of its smooth, singular, and abelian loci and the corresponding Euler characteristic in each case. Along the way, we give new proofs of the SL(2,C), PGL(2,C), and PGL(3,C) cases.
We revisit AdS$_2$ holography with the Sachdev-Ye-Kitaev models in mind. Our main result is to rewrite a generic theory of gravity near an AdS$_2$ throat as a novel hydrodynamics coupled to the correlation functions of a conformal quantum mechanics. This gives a prescription for the computation of $n$-point functions in the dual quantum mechanics. We thereby find that the dual is maximally chaotic.
The van der Waals heterostructures of allotropes of phosphorene (${\alpha}$- and $\beta-P$) with MoSe2 (H-, T-, ZT- and SO-MoSe2) are investigated in the framework of state-of-the-art density functional theory. The semiconducting heterostructures, $\beta$-P /H-MoSe2 and ${\alpha}$-P / H-MoSe2, forms anti-type structures with type I and type II band alignments, respectively, whose bands are tunable with external electric field. ${\alpha}$-P / ZT-MoSe2 and ${\alpha}$-P / SO-MoSe2 form ohmic semiconductor-metal contacts while Schottky barrier in $\beta$-P / T-MoSe2 can be reduced to zero by external electric field to form ohmic contact which is useful to realize high-performance devices. Simulated STM images of given heterostructures reveal that ${\alpha}$-P can be used as a capping layer to differentiate between various allotropes of underlying MoSe2. The dielectric response of considered heterostructures is highly anisotropic in terms of lateral and vertical polarization. The tunable electronic and dielectric response of van der Waals phosphorene/MoSe2 heterostructure may find potentials applications in the fabrication of optoelectronic devices.
We describe the worldvolume for the bosonic sector of the lower-dimensional F-theory that embeds 4D, N=1 M-theory and the 3D Type II superstring. The worldvolume (5-brane) theory is that of a single 6D gauge 2-form $X_{MN}(\sigma^P)$ whose field strength is selfdual. Thus unlike string theory, the spacetime indices are tied to the worldsheet ones: In the Hamiltonian formalism, the spacetime coordinates are a $\mathbf{10}$ of the GL(5) of the 5 $\sigma$'s (neglecting $\tau$). The current algebra gives a rederivation of the F-bracket. The background-independent subalgebra of the Virasoro algebra gives the usual section condition, while a new type of section condition follows from Gau\ss{}'s law, tying the worldvolume to spacetime: Solving just the old condition yields M-theory, while solving only the new one gives the manifestly T-dual version of the string, and the combination produces the usual string. We also find a covariant form of the condition that dimensionally reduces the string coordinates.
By means of first-principles methods we analyze the optical response of transparent dense sodium as a function of applied pressure. We discover an unusual kind of charge-transfer exciton that proceeds from the interstitial distribution of valence electrons repelled away from the ionic cores by the Coulomb interaction and the Pauli repulsion. The predicted absorption spectrum shows a strong anisotropy with light polarization that just at pressures above the metal-insulator transition manifests as sodium being optically transparent in one direction but reflective in the other. This result provides a key information about the crystal structure of transparent sodium, a new unconventional inorganic electride.
We completely decide which minimal algebraic surfaces in positive characteristics allow a lifting of their Frobenius over the trucated witt rings of lengh 2.
The discovery of the Higgs boson with a mass of around 125 GeV gives a strong motivation for further study of a high-scale supersymmetry (SUSY) breaking model. In this framework, the minimal SUSY SU(5) grand unification model may be viable since heavy sfermions suppress the proton decay via color-triplet Higgs exchanges. At the same time, sizable flavor violation in sfermion masses is still allowed by low-energy precision experiments when the mass scale is as high as O(100) TeV, which naturally explains the 125 GeV Higgs mass. In the presence of the sfermon flavor violation, however, the rates and branching fractions of proton decay can be drastically changed. In this paper, we study the effects of sfermion flavor structure on proton decay and discuss the experimental constraints on sfermion flavor violation. We find that proton-decay experiments may give us a valuable knowledge on sfermon flavor violation, and by combining it with the results from other low-energy precision experiments, we can extract insights to the structure of sfermion sector as well as the underlying grand unification model.
Parameterized optimization and parameter estimation is of great importance in almost every branch of modern science, technology and engineering. A practical issue in the problem is that when the parameter space is large and the available data is noisy, the geometry of the likelihood surface in the parameter space will be complicated. This makes searching and optimization algorithms computationally expensive, sometimes even beyond reach. In this paper, we define a likelihood transform which can make the structure of the likelihood surface much simpler, hence reducing the intrinsic complexity and easing optimization significantly. We demonstrate the properties of likelihood transform by apply it to a simplified gravitational wave chirp signal search. For the signal with an signal-to-noise ratio 20, likelihood transform has made a deterministic template-based search possible for the first time, which turns out to be 1000 times more efficient than an exhaustive grid- based search. The method in principle can be applied to other problems in other fields as the spirit of parameterized optimization and parameter estimation problem is the same.
We have studied spin excitations in a single-domain crystal of antiferromagnetic LiCoPO4 by THz absorption spectroscopy. By analyzing the selection rules and comparing the strengths of the absorption peaks in the different antiferromagnetic domains, we found electromagnons and magnetoelectric spin resonances besides conventional magnetic-dipole active spin-wave excitations. Using the sum rule for the magnetoelectric susceptibility we determined the contribution of the spin excitations to all the different off-diagonal elements of the static magnetoelectric susceptibility tensor in zero as well as in finite magnetic fields. We conclude that the magnetoelectric spin resonances are responsible for the static magnetoelectric response of the bulk when the magnetic field is along the x-axis, and the symmetric part of the magnetoelectric tensor with zero diagonal elements dominates over the antisymmetric components.
We show that any of a large class of schemes receives a universal homeomorphism from a reduced scheme that in turn receives no nontrivial universal homeomorphism from any other reduced scheme. This construction serves as a categorical input for the formal inversion of universal homeomorphisms; the result is an infinity-category that embeds as a full subcategory of the h infinity-topos of Voevodsky.
A brief review of the Hadron Gas model with reference to high energy heavy ion collisions is presented. The entropy dependence on temperature and baryonic chemical potential is numerically calculated, together with the entropy distribution between baryons and mesons. The theoretical entropy for a QGP with equivalent parameters is also calculated. It is shown that at low temperatures the dominant entropy contribution comes from baryons, while at high energies the dominant contribution comes from mesons. The turnover from baryon to meson domination occurs at T approx 140 MeV, which corresponds to an energy domain of the AGS at Brookhaven National Laboratory.
We study the nonlinear operator of mapping the terminal value $\xi$ to the corresponding minimal supersolution of a backward stochastic differential equation with the generator being monotone in $y$, convex in $z$, jointly lower semicontinuous and bounded below by an affine function of the control variable $z$. We show existence, uniqueness, monotone convergence, Fatou's lemma and lower semicontinuity of this operator. We provide a comparison principle for minimal supersolutions of BSDEs.
The equivalent photon content of polarized and unpolarized nucleons (protons, neutrons), utilized in Weizs\"acker--Williams approximations, are presented. For this purpose a new expression for the elastic photon component of a polarized nucleon is derived. The inelastic photon components are obtained from the corresponding momentum evolution equations subject to the boundary conditions of their vanishing at some low momentum scale. The resulting photon asymmetries, important for estimating cross section asymmetries in photon induced subprocesses are also presented for some typical relevant momentum scales.
In this article we review the quantum Hall physics of graphene based two-dimensional electron systems, with a special focus on recent experimental and theoretical developments. We explain why graphene and bilayer graphene can be viewed respectively as J=1 and J=2 chiral two-dimensional electron gases (C2DEGs), and why this property frames their quantum Hall physics. The current status of experimental and theoretical work on the role of electron-electron interactions is reviewed at length with an emphasis on unresolved issues in the field, including assessing the role of disorder in current experimental results. Special attention is given to the interesting low magnetic field limit and to the relationship between quantum Hall effects and the spontaneous anomalous Hall effects that might occur in bilayer graphene systems in the absence of a magnetic field.
We develop explicit formulas for Hecke operators of higher genus in terms of spherical coordinates. Applications are given to summation of various generating series with coefficients in local Hecke algebra and in a tensor product of such algebras. In particular, we formulate and prove Rankin's lemma in genus two. An application to a lifting from (GSp2 \times GSp2) to GSp4 is given using Ikeda-Miyawaki constructions.
Machine learning (ML) has become an attractive tool in information processing, however few ML algorithms have been successfully applied in the quantum domain. We show here how classical reinforcement learning (RL) could be used as a tool for quantum state engineering (QSE). We employ a measurement based control for QSE where the action sequences are determined by the choice of the measurement basis and the reward through the fidelity of obtaining the target state. Our analysis clearly displays a learning feature in QSE, for example in preparing arbitrary two-qubit entangled states. It delivers successful action sequences, that generalise previously found human solutions from exact quantum dynamics. We provide a systematic algorithmic approach for using RL algorithms for quantum protocols that deal with non-trivial continuous state (parameter) space, and discuss on scaling of these approaches for preparation of arbitrarily large entangled (cluster) states.
We discuss the orbital angular momentum of partons inside a longitudinally polarized proton in the recently proposed framework of spin decomposition. The quark orbital angular momentum defined by Ji can be decomposed into the `canonical' and the `potential' angular momentum parts, both of which are represented as the matrix element of a manifestly gauge invariant operator.
We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.
Let K be a field of characteristic 0 and let n be a natural number. Let Gamma be a subgroup of the multiplicative group $(K^\ast)^n$ of finite rank r. Given $A_2,...,a_n\in K^\ast$ write $A(a_1,...,a_n,\Gamma)$ for the number of solutions x=(x_1,...,x_n)\in \Gamma$ of the equation a_1x_1+...+a_nx_n=1$, such that no proper subsum of $a_1x_1+...+a_nx_n$ vanishes. We derive an explicit upper bound for $A(a_1,...,a_n,\Gamma)$ which depends only on the dimension n and on the rank r.
In Yang-Mills theories, variational calculations of the Rayleigh-Ritz type face the problem that on the one hand, calculability puts severe constraints on the space of test wave functionals; on the other hand, the test wave functionals have to be gauge invariant. The conflict between the two requirements can be resolved by introducing a projector. In this paper we present an approach to approximating the projector in a way known and successfully employed in nuclear physics: the Kamlah expansion. We discuss it both for electrodynamics and for Yang-Mills theories to leading order in a perturbative expansion, and demonstrate that the results are compatible with what one would expect from perturbation theory.
Neutron inelastic scattering measurements of the polar TO phonon mode in the cubic relaxor Pb(Mg1/3Nb2/3)O3, at room temperature, reveal anomalous behavior similar to that recently observed in the Pb(Zn1/3Nb2/3)_{0.92}Ti_{0.08}O3 system in which the optic branch appears to drop precipitously into the acoustic branch at a finite value of the momentum transfer q = 0.20 1/Angstroms, measured from the zone center. By contrast, a recent neutron study showed that PMN exhibits a normal TO phonon dispersion at 800 K. We speculate this behavior is common to all relaxor materials and is the result of the presence of nanometer-scale polarized domains in the crystal that form below a temperature Td, which effectively prevent the propagation of long wavelength (q = 0) phonons.
In this paper we first show that, under certain conditions, the solution of a single quadratic diophantine equation in four variables $Q(x_1,\,x_2,\,x_3,\,x_4)=0$ can be expressed in terms of bilinear forms in four parameters. We use this result to establish a necessary, though not sufficient, condition for the solvability of the simultaneous quadratic diophantine equations $Q_j(x_1,\,x_2,\,x_3,\,x_4)=0,\;j=1,\,2,$ and give a method of obtaining their complete solution. In general, when these two equations have a rational solution, they represent an elliptic curve but we show that there are several cases in which their complete solution may be expressed by a finite number of parametric solutions and/ or a finite number of primitive integer solutions. Finally we relate the solutions of the quartic equation $y^2=t^4+a_1t^3+a_2t^2+a_3t+a_4$ to the solutions of a pair of quadratic diophantine equations, and thereby obtain new formulae for deriving rational solutions of the aforementioned quartic equation starting from one or two known solutions.
The present calculations in perturbative QCD reach the order $\alpha_s^4$ for several correlators calculated to five loops, and the huge computational difficulties make unlikely the full six-loop calculation in the near future. This situation has practical consequences, in particular the treatment of the higher orders of the perturbation series for the current-current correlator of light quarks is one of the main sources of errors in the extraction of the strong coupling from hadronic $\tau$ decays. Several approximate estimates of the next coefficients of the corresponding Adler function have been proposed, using various arguments. In the present paper we exploit the analytic structure of the Adler function in the Borel plane, which allows the definition of an improved perturbative expansion in powers of a conformal variable which maps the cut Borel plane onto the unit disk. The new expansions converge in a larger domain of the Borel plane and, when reexpanded in powers of the strong coupling, yield definite values for the higher perturbative coefficients. We apply the method to the Adler function in the $\bar{\rm MS}$ scheme and to a suitable weighted integral of this function in the complex $s$ plane, chosen such as to avoid model-dependent assumptions on analyticity. Our results $c_{5,1}=287 \pm 40$, $c_{6,1}=2948 \pm 208$ and $c_{7,1}=(1.89 \pm 0.75)\times 10^4$, for the six, seven and eigth-loop coefficients, respectively, agree with a recent determination from Pad\'e approximants applied to the perturbative expansion of the hadronic $\tau$ decay rate.
We review the Majumdar-Dhar bijection between recurrent states of the Abelian sandpile model and spanning trees. We generalize earlier results of Athreya and Jarai on the infinite volume limit of the stationary distribution of the sandpile model on Z^d, d >= 2, to a large class of graphs. This includes: (i) graphs on which the wired spanning forest is connected and has one end; (ii) transitive graphs with volume growth at least c n^5 on which all bounded harmonic functions are constant. We also extend a result of Maes, Redig and Saada on the stationary distribution of sandpiles on infinite regular trees, to arbitrary exhaustions.
We have studied $A+A \rightarrow \emptyset$ reaction-diffusion model on a ring, with a bias $\epsilon$ $(0 \leq \epsilon \leq 0.5)$ of the random walkers $A$ to hop towards their nearest neighbor. Though the bias is local in space and time, we show that it alters the universality class of the problem. The $z$ exponent, which describes the growth of average spacings between the walkers with time, changes from the value 2 at $\epsilon=0$ to the mean-field value of unity for any non-zero $\epsilon$. We study the problem analytically using independent interval approximation and compare the scaling results with that obtained from simulation. The distribution $P(k,t)$ of the spacing $k$ between two walkers (per site) is given by $t^{-2/z} f(k/t^{1/z})$ as expected; however, the scaling function shows different behaviour in the two approaches.
1RXS J180408.9--342058 is a low mass X-ray binary hosting a neutron star, which shows X-ray activity at very different mass-accretion regimes, from very faint to almost the Eddington luminosity. In this work, we present a comprehensive X-ray study of this source using data from the Neil Gehrels Swift Observatory, NuSTAR and INTEGRAL/JEM-X. In order to follow the spectral evolution, we analysed the 2015 outburst using Swift data and three Nustar observations. Besides the canonical hard and soft spectral states, we identified the rarely observed intermediate state. This was witnessed by the appeareance of the accretion disk emission in the spectrum (at $kT_{\rm disk}$ $\sim$0.7 keV) and the simultaneous cooling of the hot corona. In addition, we also unveiled a hard tail above 30 keV in this state. In the hard state, a thermal Comptonization model with two seed photons populations ($kT_{\rm s,1}\sim 1.5$ keV and $kT_{\rm s,2}\sim 0.4$ keV, respectively) and a hot Comptonising plasma, represents the physically best motivated scenario to describe the data. We also estimated a reflection fraction below 20% in all states, while no constraints on the inclination and only lower limits on the inner disk radius could be inferred. Finally, we studied a number of type-I X-ray bursts displayed from the source, one of them at the Eddington limit (observed with JEM-X). Their characteristics, combined with the clocked behaviour observed during the intermediate state, point out H/He composition for the accreted material, which makes unlikely the helium dwarf nature for the companion.
Using Science Verification data from the Atacama Large Millimeter/Submillimeter Array (ALMA), we have identified and imaged five rotational transitions (J=5-4 and J=6-5) of the three silicon monoxide isotopologues 28SiO v=0, 1, 2 and 29SiO v=0 and 28Si18O v=0 in the frequency range from 214 to 246 GHz towards the Orion BN/KL region. The emission of the ground-state 28SiO, 29SiO and 28Si18O shows an extended bipolar shape in the northeast-southwest direction at the position of Radio Source I, indicating that these isotopologues trace an outflow (~18 km/s, P.A. ~50deg, ~5000 AU in diameter) that is driven by this embedded high-mass young stellar object (YSO). Whereas on small scales (10-1000 AU) the outflow from Source I has a well-ordered spatial and velocity structure, as probed by Very Long Baseline Interferometry (VLBI) imaging of SiO masers, the large scales (500-5000 AU) probed by thermal SiO with ALMA reveal a complex structure and velocity field, most likely related to the effects of the environment of the BN/KL region on the outflow emanating from Source I.   The emission of the vibrationally-excited species peaks at the position of Source I. This emission is compact and not resolved at an angular resolution of ~1.5" (~600 AU at a distance of 420 pc). 2-D Gaussian fitting to individual velocity channels locates emission peaks within radii of 100 AU, i.e. they trace the innermost part of the outflow. A narrow spectral profile and spatial distribution of the v=1 J=5-4 line similar to the masing v=1 J=1-0 transition, provide evidence for the most highly rotationally excited (frequency > 200 GHz) SiO maser emission associated with Source I known to date. The maser emission will enable studies of the Source I disk-outflow interface with future ALMA longest baselines.