ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider a multivariate non-linear Hawkes process in a multi-class setup where particles are organised within two populations of possibly different sizes, such that one of the populations acts excitatory on the system while the other population acts inhibitory on the system. The goal of this note is to present a class of Hawkes Processes with stable dynamics without assumptions on the spectral radius of the associated weight function matrix. This illustrates how inhibition in a Hawkes system significantly affects the stability properties of the system.
We consider a perturbed ordinary differential equation where the perturbation is only significant when a one-dimensional null recurrent diffusion is close to zero. We investigate the first order correction to the unperturbed system and prove a central limit theorem type result, i.e., that the normalized deviation process converges in law in the space of continuous functions to a limit process which we identify. We show that this limit process has a component which only moves when the limit of the null-recurrent fast motion equals zero. The set of these times forms a zero-measure Cantor set and therefore the limiting process cannot be described by a standard SDE. We characterize this process by its infinitesimal generator (with appropriate boundary conditions) and we also characterize the process as the weak solution of an SDE that depends on the local time of the fast motion process. We also investigate the long time behavior of such a system when the unperturbed motion is trivial. In this case, we show that the long-time limit is constant on a set of full Lebesgue measure with probability 1, but it has nontrivial drift and diffusion components that move only when the fast motion equals zero.
The paper is withdrawn by the author. This was an embryon of the book which has now been published with World Scientific under the title "Lectures on Quantum Chromodynamics". See http://www.wspc.com.sg/books/physics/4443.html, where the beginning of the book will soon be available in the pdf format.
Surprising asymmetry in the local electromechanical response across a single antiparallel ferroelectric domain wall is reported. Piezoelectric force microscopy is used to investigate both the in-plane and out-of- plane electromechanical signals around domain walls in congruent and near-stoichiometric lithium niobate. The observed asymmetry is shown to have a strong correlation to crystal stoichiometry, suggesting defect-domain wall interactions. A defect-dipole model is proposed. Finite element method is used to simulate the electromechanical processes at the wall and reconstruct the images. For the near-stoichiometric composition, good agreement is found in both form and magnitude. Some discrepancy remains between the experimental and modeling widths of the imaged effects across a wall. This is analyzed from the perspective of possible electrostatic contributions to the imaging process, as well as local changes in the material properties in the vicinity of the wall.
A Cattaneo equation for a comb structure is considered. We present a rigorous analysis of the obtained fractional diffusion equation, and corresponding solutions for the probability distribution function are obtained in the form of the Fox $H$-function and its infinite series. The mean square displacement along the backbone is obtained as well in terms of the infinite series of the Fox $H$-function. The obtained solutions describe the transition from normal diffusion to subdiffusion, which results from the comb geometry.
Weyl semimetals harbor topological Fermi-arc surface states which determine the nontrivial charge current response to external fields. We here study the quasiparticle decay rate of Fermi arc states arising from their coupling to acoustic phonons, as well as the phonon-limited conductivity tensor for a clean Weyl semimetal slab. Using the phonon modes for an isotropic elastic continuum with a deformation potential coupling to electrons, we determine the temperature dependence of the quasiparticle decay rate, both near and far away from the arc termination points. By solving the coupled Boltzmann equations for the bulk and arc state distribution functions in the slab geometry, we show how the linear response conductivity depends on key parameters such as the temperature, the chemical potential, the geometric shape of the Fermi arcs, or the slab width. The chiral nature of Fermi arc states causes an enhancement of the longitudinal conductivity along the chiral direction at low temperatures, together with a 1/T^2 scaling regime at intermediate temperatures without counterpart for the conductivity along the perpendicular direction.
We refute the widely held belief that the quantum weak value necessarily pertains to weak measurements. To accomplish this, we use the transverse position of a beam as the detector for the conditioned von Neumann measurement of a system observable. For any coupling strength, any initial states, and any choice of conditioning, the averages of the detector position and momentum are completely described by the real parts of three generalized weak values in the joint Hilbert space. Higher-order detector moments also have similar weak value expansions. Using the Wigner distribution of the initial detector state, we find compact expressions for these weak values within the reduced system Hilbert space. As an application of the approach, we show that for any Hermite-Gauss mode of a paraxial beam-like detector these expressions reduce to the real and imaginary parts of a single system weak value plus an additional weak-value-like contribution that only affects the momentum shift.
Quantum Geometrodynamics with intrinsic time development and momentric variables is presented. An underlying SU(3) group structure at each spatial point regulates the theory. The intrinsic time behavior of the theory is analyzed, together with its ground state and primordial quantum fluctuations. Cotton-York potential dominates at early times when the universe was small; the ground state naturally resolves Penrose's Weyl Curvature Hypothesis, and thermodynamic and gravitational `arrows of time' point in the same direction. Ricci scalar potential corresponding to Einstein's General Relativity emerges as a zero-point energy contribution. A new set of fundamental commutation relations without Planck's constant emerges from the unification of Gravitation and Quantum Mechanics.
In this paper we investigate functions that are harmonic with respect to the non-symmetric strictly $\alpha$-stable L\'evy processes on an open set $D \in \mathbb{R}^d$. We obtain the explicit formula for their boundary decay rate at parts of the boudary of $D$ outside of which they vanish.
We study $N=5$ gauged supergravity in three dimensions with compact, non-compact and non-semisimple gauge groups. The theory under consideration is of Chern-Simons type with $USp(4,k)/USp(4)\times USp(k)$ scalar manifold. We classify possible semisimple gauge groups of the $k=2,4$ cases and identify some of their critical points. A number of supersymmetric $AdS_3$ critical points are found, and holographic RG flows interpolating between these critical points are also investigated. As one of our main results, we consider a non-semisimple gauge group $SO(5)\ltimes \mathbf{T}^{10}$ for the theory with $USp(4,4)/USp(4)\times USp(4)$ scalar manifold. The resulting theory describes $N=5$ gauged supergravity in four dimensions reduced on $S^1/\mathbb{Z}_2$ and admits a maximally supersymmetric $AdS_3$ critical point with $Osp(5|2,\mathbb{R})\times Sp(2,\mathbb{R})$ superconformal symmetry. We end the paper with the construction of $SO(6)\ltimes \mathbf{T}^{15}$ gauged supergravity with $N=6$ supersymmetry. The theory admits a half-supersymmetric domain wall as a vacuum solution and may be obtained from an $S^1/\mathbb{Z}_2$ reduction of $N=6$ gauged supergravity in four dimensions.
This paper investigates M-brane quantum geometry (and its representation by equations involving the 3-bracket) by looking at the compactification of an M-brane system to a D-brane system. Particularly of interest is the system where coincident M2-branes end at an angle on an M5-brane, and its reduction to D1- or F1-branes ending on a D3-brane. Since equations for the quantum geometries of both of these systems are known, the paper will attempt to directly relate them via a compactification.
Let $X= \{X(t), t \in \R^N\}$ be a Gaussian random field with values in $\R^d$ defined by \[ X(t) = \big(X_1(t),..., X_d(t)\big),\qquad t \in \R^N, \] where $X_1, ..., X_d$ are independent copies of a real-valued, centered, anisotropic Gaussian random field $X_0$ which has stationary increments and the property of strong local nondeterminism. In this paper we determine the exact Hausdorff measure function for the range $X([0, 1]^N)$.   We also provide a sufficient condition for a Gaussian random field with stationary increments to be strongly locally nondeterministic. This condition is given in terms of the spectral measures of the Gaussian random fields which may contain either an absolutely continuous or discrete part. This result strengthens and extends significantly the related theorems of Berman (1973, 1988), Pitt (1978) and Xiao (2007, 2009), and will have wider applicability beyond the scope of the present paper.
This survey paper explains how one can attach geometric invariants to semialgebraic sets defined over non-archimedean fields, using the theory of motivic integration of Hrushovski and Kazhdan. It also discusses tropical methods to compute these invariants in concrete cases, as well as an application to refined curve counting, developed in collaboration with Sam Payne and Franziska Schroeter.
We show that each real-representable matroid is a minor of a complex-representable excluded minor for real-representability. More generally, for an infinite field $\mathbb{F}_1$ and a field extension $\mathbb{F}_2$, if $\mathbb{F}_1$-representability is not equivalent to $\mathbb{F}_2$-representability, then each $\mathbb{F}_1$-representable matroid is a minor of a $\mathbb{F}_2$-representable excluded minor for $\mathbb{F}_1$-representability.
We use the bulge Sersic index n and bulge-to-total ratio (B/T) to explore the fundamental question of how bulges form. We perform 2D bulge-disk-bar decomposition on H-band images of 143 bright, high stellar mass (>1.0e10 solar masses) low-to-moderately inclined (i<70 degrees) spirals. Our results are: (1) Our H-band bar fraction (~58%) is consistent with that from ellipse fits. (2) 70% of the stellar mass is in disks, 10% in bars, and 20% in bulges. (3) A large fraction (~69%) of bright spirals have B/T<0.2, and ~76% have low n<2 bulges. These bulges exist in barred and unbarred galaxies across a wide range of Hubble types. (4) About 65% (68%) of bright spirals with n<2 (B/T<0.2) bulges host bars, suggesting a possible link between bars and bulges. (5) We compare the results with predictions from a set of LCDM models. In the models, a high mass spiral can have a bulge with a present-day low B/T<0.2 only if it did not undergo a major merger since z<2. The predicted fraction (~1.6%) of high mass spirals, which have undergone a major merger since z<4 and host a bulge with a present-day low B/T<0.2, is a factor of over thirty smaller than the observed fraction (~66%) of high mass spirals with B/T<0.2. Thus, contrary to common perception, bulges built via major mergers since z<4 seriously fail to account for the bulges present in ~66% of high mass spirals. Most of these present-day low B/T<0.2 bulges are likely to have been built by a combination of minor mergers and/or secular processes since z<4.
We show how QKD on a multi-user, multi-path, network can be used to establish a key between any two end users in an asynchronous fashion using the technique of bit-transport. By a suitable adaptation of our previous secret-sharing scheme we show that an attacker has to compromise all of the intermediate relays on the network in order to obtain the key. Thus, two end users can establish a secret key provided they trust at least one of the network relays.
Local infrared (IR) luminosity functions (LFs) are necessary benchmarks for high-redshift IR galaxy evolution studies. Any accurate IR LF evolution studies require accordingly accurate local IR LFs. We present infrared galaxy LFs at redshifts redshifts of $z \leq 0.3$ from AKARI space telescope, which performed an all-sky survey in six IR bands (9, 18, 65, 90, 140 and 160 micron) with 10 times better sensitivity than its precursor IRAS. Availability of 160 micron filter is critically important in accurately measuring total IR luminosity of galaxies, covering across the peak of the dust emission. By combining data from Wide-field Infrared Survey Explorer (WISE), Sloan Digital Sky Survey (SDSS) Data Release 13 (DR13), 6-degree Field Galaxy Survey (6dFGS) and the 2MASS Redshift Survey (2MRS), we created a sample of 15,638 local IR galaxies with spectroscopic redshifts, factor of 7 larger compared to previously studied AKARI -SDSS sample. After carefully correcting for volume effects in both IR and optical, the obtained IR LFs agree well with previous studies, but comes with much smaller errors. Measured local IR luminosity density is $\Omega_{IR}=$ 1.19$\pm$0.05 $\times 10^{8}$ L$_{\odot}$ Mpc$^{-3}$. The contributions from luminous infrared galaxies and ultra luminous infrared galaxies to IR are very small, 9.3 per cent and 0.9 per cent, respectively. There exists no future all sky survey in far-infrared wavelengths in the foreseeable future. The IR LFs obtained in this work will therefore remain an important benchmark for high-redshift studies for decades.
Let $\mathcal{V}$ be a mixed characteristic complete discrete valuation ring, $k$ its residual field, $\mathcal{P}$ a proper smooth formal scheme over $\mathcal{V}$, $P$ its special fiber, $T$ a divisor of $P$, $U:=P\setminus T$, $Y$ a smooth closed subscheme of $U$. We prove that the category of overconvergent $F$-isocrystals on $Y$ is equivalent to the category of overcoherent $F$-isocrystals on $Y$. More generally, we prove such an equivalence by gluing for any smooth variety $Y$ over $k$. Moreover, we check that overcoherent $F$-complexes of arithmetic $\mathcal{D}$-modules split in overconvergent $F$-isocrystals.
We calculate the standard model effective potential to two loops using minimal subtraction, and use the result to deduce the two-loop beta-functions for the scalar mass and quartic self-interaction.
In view of the integration of membrane resonators with more complex MEMS structures, we developed a general fabrication procedure for circular shape SiN$_x$ membranes using Deep Reactive Ion Etching (DRIE). Large area and high-stress SiN$_x$ membranes were fabricated and used as optomechanical resonators in a Michelson interferometer and in a Fabry-P\'erot cavity. The measurements show that the fabrication process preserves both the optical quality and the mechanical quality factor of the membrane.
The observed value of the muon magnetic dipole moment, which deviates from the Standard Model prediction by $4.2\sigma$, can be explained in models with weakly-interacting massive particles (WIMPs) coupled to muons. However, a considerable range of parameter space of such models will remain unexplored in the future LHC experiments and dark matter (DM) direct searches. In this work we discuss the temperature observation of neutron stars (NSs) as a promising way to probe such models given that WIMPs are efficiently captured by NSs through DM-muon or spin-dependent DM-nucleon scattering. The captured WIMPs eventually annihilate in the star core and heat the NS. This effect can be observed in old NSs as it keeps the NS surface temperature at a few thousand K at most, which is much higher than the predicted values of the standard NS cooling theory for NSs older than $\sim 10^7$ years. We consider two classes of representative models, where the DM couples or does not couple to the Higgs field at tree level, and show that the maximal DM heating is realized in both scenarios.
We study a class of non-unitary so(2,d) representations (for even values of d), describing mixed-symmetry partially massless fields which constitute natural candidates for defining higher-spin singletons of higher order. It is shown that this class of so(2,d) modules obeys of natural generalisation of a couple of defining properties of unitary higher-spin singletons. In particular, we find out that upon restriction to the subalgebra so(2,d-1), these representations branch onto a sum of modules describing partially massless fields of various depths. Finally, their tensor product is worked out in the particular case of d=4, where the appearance of a variety of mixed-symmetry partially massless fields in this decomposition is observed.
In this work, we have studied the structural, elastic, mechanical, electronic, bonding, acoustic, thermal and optical properties of TaX (X = P, As) in detail via first-principles method using the density functional theory. A comprehensive study of elastic constants and moduli shows that both TaP and TaAs possesses low to medium level of elastic anisotropy (depending on the measure), reasonably good machinability, mixed bonding characteristics with ionic and covalent contributions, brittle nature and relatively high Vickers hardness with a low Debye temperature and melting temperature. The minimum thermal conductivities and anisotropies of TaX (X = P, As) are calculated. Bond population analysis supports the bonding nature as predicted by the elastic parameters. The bulk electronic band structure calculations reveal clear semi-metallic features with signature Dirac cone-like dispersions near the Fermi level. A pseudogap in the electronic energy density of states at the Fermi level separating the bonding and the antibonding states indicates significant electronic stability of tetragonal TaX (X = P, As). The reflectivity spectra show almost non-selective behavior over a wide range of photon energy encompassing visible to mid-ultraviolet regions. High reflectivity over wide spectral range makes TaX suitable as reflecting coating. TaX (X = P, As) are very efficient absorber of ultraviolet radiation. Both the compounds are moderately optically anisotropic owing to the anisotropic nature of the electronic band structure. The refractive indices are very high in the infrared to visible range. All the energy dependent optical parameters show metallic features and are in complete accord with the underlying bulk electronic density of states calculations.
In this paper, we use the cell dynamics method to study the dynamics of phase transformation when three phases exist. The system we study is a two-dimensional system. The system is able to achieve three phases coexistence, which for simplicity we call crystal, liquid and vapor phases. We focus our study on the case when the vapor and crystal phases are stable and can coexist while the other intermediate liquid phase is metastable. In this study we examine the most fundamental process of the growth of a composite nucleus which consists of a circular core of one phase surrounded by a circular layer of second phase embedded in a third phase. We found that there is one special configuration that consists of a core stable phase surrounded by another stable phase in a metastable liquid environment which becomes stationary and stable. Then, the nucleus does not grow and the metastable liquid survives. The macroscopic liquid phase does not disappear even though it is thermodynamically metastable. This result seems compatible to the argument of kinetics of phase transition developed by Cahn [J. Am. Ceram. Soc. {\bf 52}, 118 (1969)] based on the construction of a common tangent of the free energy curve.
In this paper we introduce a refined multiplicity for rational tropical curves in arbitrary dimension, which generalizes the refined multiplicity introduced by F. Block and L. G\"ottsche in arXiv:1407.2901 . We then prove an invariance statement for the count of rational tropical curves in several enumerative problems using this new refined multiplicity. This leads to the definition of Block-G\"ottsche polynomials in any dimension.
Let S $\subseteq$ N be a numerical semigroup with multiplicity m = min(S \ {0}), conductor c = max(N \ S) + 1 and minimally generated by e elements. Let L be the set of elements of S which are smaller than c. Wilf conjectured in 1978 that |L| is bounded below by c/e. We show here that if c $\le$ 3m, then S satisfies Wilf's conjecture. Combined with a recent result of Zhai, this implies that the conjecture is asymptotically true as the genus g(S) = |N \ S| goes to infinity. One main tool in this paper is a classical theorem of Macaulay on the growth of Hilbert functions of standard graded algebras.
We look at random walks in Dirichlet environment. It was known that in dimension $d\geq 3$, if the walk is sub-ballistic, the displacement of the walk is polynomial of order $\kappa$ for some explicit $\kappa$. We show that the walk, after renormalization, actually converges to a $\kappa$-stable completely asymmetric Levy Process.
Necessary and sufficient conditions are exhibited for a Korn type inequality to hold between (possibly different) Orlicz norms of the gradient of vector-valued functions and of the deviatoric part of their symmetric gradients. As a byproduct of our approach, a positive answer is given to the question of the necessity of the same sufficient conditions in related Korn type inequalities for the full symmetric gradient, for negative Orlicz-Sobolev norms, and for the gradient of the Bogovskii operator.
We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we caracterize the maps corresponding to stochastic chains with memory of variable length. The problem treated here is the converse of the classical construction of the Gibbs formalism for Markov expanding maps of the interval.
If the face\mbox{-}cycles at all the vertices in a map are of same type then the map is called semi\mbox{-}equivelar. In particular, it is called equivelar if the face-cycles contain same type of faces. A map is semiregular (or almost regular) if it has as few flag orbits as possible for its type. A map is $k$-regular if it is equivelar and the number of flag orbits of the map $k$ under the automorphism group. In particular, if $k =1$, its called regular. A map is $k$-semiregular if it contains more number of flags as compared to its type with the number of flags orbits $k$. Drach et al. \cite{drach:2019} have proved that every semi-equivelar toroidal map has a finite unique minimal semiregular cover. In this article, we show the bounds of flag orbits of semi-equivelar toroidal maps, i.e., there exists $k$ for each type such that every semi-equivelar map is $\ell$-uniform for some $\ell \le k$. We show that none of the Archimedean types on the torus is semiregular, i.e., for each type, there exists a map whose number of flag orbits is more than its type. We also prove that if a semi-equivelar map is $m$-semiregular then it has a finite index $t$-semiregular minimal cover for $t \le m$. We also show the existence and classification of $n$ sheeted $k$-semiregular maps for some $k$ of semi-equivelar toroidal maps for each $n \in \mathbb{N}$.
We consider a scenario in which the global geometry of the universe is driven by non-linear fermions obeying Heisenberg dynamics.