ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study a totally asymmetric simple exclusion process (TASEP) with one defect site, hopping rate $q<1$, near the system boundary. Regarding our system as a pair of uniform TASEP's coupled through the defect, we study various methods to match a \emph{finite} TASEP and an \emph{infinite} one across a common boundary. Several approximation schemes are investigated. Utilizing the finite segment mean-field (FSMF) method, we set up a framework for computing the steady state current $J$ as a function of the entry rate $% \alpha $ and $q$. For the case where the defect is located at the entry site, we obtain an analytical expression for $J(\alpha, q) $ which is in good agreement with Monte Carlo simulation results. When the defect is located deeper in the bulk, we refined the scheme of MacDonald, et.al. [Biopolymers, \textbf{6}, 1 (1968)] and find reasonably good fits to the density profiles before the defect site. We discuss the strengths and limitations of each method, as well as possible avenues for further studies.
In this paper, we prove a Kawamata--Viehweg type vanishing theorem for smooth Fano threefolds, canonical del Pezzo surfaces and del Pezzo fibrations in positive characteristic.
The purpose of this brief paper is to prove De Giorgi type results for stable solutions of the following nonlocal system of integral equations in two dimensions $$ L(u_i) = H_i(u) \quad \text{in} \ \ \mathbb R^2 , $$ where $u=(u_i)_{i=1}^m$ for $u_i: \mathbb R^n\to \mathbb R$, $H=(H_i)_{i=1}^m$ is a general nonlinearity. The operator $L$ is given by $$L(u_i (x)):= \int_{\mathbb R^2} [u_i(x) - u_i(z)] K(z-x) dz,$$ for some kernel $K$. The idea is to apply a linear Liouville theorem for the quotient of partial derivatives, just like in the proof of the classical De Giorgi's conjecture in lower dimensions. Since there is no Caffarelli-Silvestre local extension problem associated to the above operator, we deal with this problem directly via certain integral estimates.
Born's rule, one of the cornerstones of quantum mechanics, relates detection probabilities to the modulus square of the wave function. Single-particle interference is accordingly limited to pairs of quantum paths and higher-order interferences are prohibited. Deviations from Born's law have been quantified via the Sorkin parameter which is proportional to the third-order term. We here extend this formalism to many-particle interferences and find that they exhibit a much richer structure. We demonstrate, in particular, that all interference terms of order $(2M+1)$ and greater vanish for $M$ particles. We further introduce a family of many-particle Sorkin parameters and show that they are exponentially more sensitive to deviations from Born's rule than their single-particle counterpart.
In this paper we consider quintessence reconstruction of interacting holographic dark energy in a non-flat background. As system's IR cutoff we choose the radius of the event horizon measured on the sphere of the horizon, defined as $L=ar(t)$. To this end we construct a quintessence model by a real, single scalar field. Evolution of the potential, $V(\phi)$, as well as the dynamics of the scalar field, $\phi$, are obtained according to the respective holographic dark energy. The reconstructed potentials show a cosmological constant behavior for the present time. We constrain the model parameters in a flat universe by using the observational data, and applying the Monte Carlo Markov chain simulation. We obtain the best fit values of the holographic dark energy model and the interacting parameters as $c=1.0576^{+0.3010+0.3052}_{-0.6632-0.6632}$ and $\zeta=0.2433^{+0.6373+0.6373}_{-0.2251-0.2251}$, respectively. From the data fitting results we also find that the model can cross the phantom line in the present universe where the best fit value of of the dark energy equation of state is $w_D=-1.2429$.
The junction conditions for the infinite derivative gravity theory ${R{+}RF(\Box)R}$ are derived under the assumption that the conditions can be imposed by avoiding the `ill-defined expressions' in the theory of distributions term by term in infinite summations. We find that the junction conditions of such non-local theories are much more restrictive than in local theories, since the conditions comprise an infinite number of equations for the Ricci scalar. These conditions can constrain the geometry far beyond the matching hypersurface. Furthermore, we derive the junction field equations which are satisfied by the energy-momentum on the hypersurface. It turns out that the theory still allows some matter content on the hypersurface (without external flux and external tension), but with a traceless energy-momentum tensor. We also discuss the proper matching condition where no matter is concentrated on the hypersurface. Finally, we explore the possible applications and consequences of our results to the braneworld scenarios and star models. Particularly, we find that the internal tension is given purely by the trace of the energy-momentum tensor of the matter confined to the brane. Consequences of the junction conditions are illustrated on two simple examples of static and collapsing stars. It is demonstrated that even without solving the field equations the geometry on one side of the hypersurface can be determined to a great extent by the geometry on the other side if the Ricci scalar is analytic. We further show that some usual star models in the general relativity are no longer solutions of the infinite derivative gravity.
We have grown a single crystal of the equiatomic FeCoCrMnAl high-entropy alloy. The crystal was grown by means of the Bridgman technique and is about 1 cm in diameter and 6.6 cm in length. X-ray Laue images taken at various positions on the surface are sharp and mutually consistent, reflecting its single-crystal nature. We thus report on the first successful growth of a single crystal of a high-entropy alloy with a volume of the order of cubic centimeters. The material has a microstructure consisting of B2 inclusions in a body-centered cubic matrix on the 10 nm length scale.
We present a model for the distribution of void sizes and its evolution in the context of hierarchical scenarios of gravitational structure formation. We find that at any cosmic epoch the voids have a size distribution which is well-peaked about a characteristic void size which evolves self-similarly in time. This is in distinct contrast to the distribution of virialized halo masses which does not have a small-scale cut-off.   In our model, the fate of voids is ruled by two processes. The first process affects those voids which are embedded in larger underdense regions: the evolution is effectively one in which a larger void is made up by the mergers of smaller voids, and is analogous to how massive clusters form from the mergers of less massive progenitors. The second process is unique to voids, and occurs to voids which happen to be embedded within a larger scale overdensity: these voids get squeezed out of existence as the overdensity collapses around them. It is this second process which produces the cut-off at small scales.   In the excursion set formulation of cluster abundance and evolution, solution of the cloud-in-cloud problem, i.e., counting as clusters only those objects which are not embedded in larger clusters, requires study of random walks crossing one barrier. We show that a similar formulation of void evolution requires study of a two-barrier problem: one barrier is required to account for voids-in-voids, and the other for voids-in-clouds. Thus, in our model, the void size distribution is a function of two parameters, one of which reflects the dynamics of void formation, and the other the formation of collapsed objects.
Planets less massive than about 10 MEarth are expected to have no massive H-He atmosphere and a cometary composition (50% rocks, 50% water, by mass) provided they formed beyond the snowline of protoplanetary disks. Due to inward migration, such planets could be found at any distance between their formation site and the star. If migration stops within the habitable zone, this will produce a new kind of planets, called Ocean-Planets. Ocean-planets typically consist in a silicate core, surrounded by a thick ice mantle, itself covered by a 100 km deep ocean. The existence of ocean-planets raises important astrobiological questions: Can life originate on such body, in the absence of continent and ocean-silicate interfaces? What would be the nature of the atmosphere and the geochemical cycles ?   In this work, we address the fate of Hot Ocean-Planets produced when migration ends at a closer distance. In this case the liquid/gas interface can disappear, and the hot H2O envelope is made of a supercritical fluid. Although we do not expect these bodies to harbor life, their detection and identification as water-rich planets would give us insight as to the abundance of hot and, by extrapolation, cool Ocean-Planets.
Massive stars are of interest as progenitors of super novae, i.e. neutron stars and black holes, which can be sources of gravitational waves. Recent population synthesis models can predict neutron star and gravitational wave observations but deal with a fixed super nova rate or an assumed initial mass function for the population of massive stars. Here we investigate those massive stars, which are supernova progenitors, i.e. with O and early B type stars, and also all super giants within 3kpc. We restrict our sample to those massive stars detected both in 2MASS and observed by Hipparcos, i.e. only those stars with parallax and precise photometry. To determine the luminosities we calculated the extinctions from published multi-colour photometry, spectral types, luminosity class, all corrected for multiplicity and recently revised Hipparcos distances. We use luminosities and temperatures to estimate the masses and ages of these stars using different models from different authors. Having estimated the luminosities of all our stars within 3kpc, in particular for all O- and early B-type stars, we have determined the median and mean luminosities for all spectral types for luminosity classes I, III, and V. Our luminosity values for super giants deviate from earlier results: Previous work generally overestimates distances and luminosities compared to our data, this is likely due to Hipparcos parallaxes (generally more accurate and larger than previous ground-based data) and the fact that many massive stars have recently been resolved into multiples of lower masses and luminosities. From luminosities and effective temperatures we derived masses and ages using mass tracks and isochrones from different authors. From masses and ages we estimated lifetimes and derived a lower limit for the supernova rate of ~20 events/Myr averaged over the next 10 Myrs within 600 pc from the sun. These data are then used to search for areas in the sky with higher likelihood for a supernova or gravitational wave event (like OB associations).
We consider the momentum distribution and the polarization of an inclusive heavy fermion in a process assumed to arise from standard-model (SM) $s$-channel exchange of a virtual $\gamma$ or $Z$ with a further contribution from physics beyond the standard model involving $s$-channel exchanges. The interference of the new physics amplitude with the SM $\gamma$ or $Z$ exchange amplitude is expressed entirely in terms of the space-time signature of such new physics. Transverse as well as longitudinal polarizations of the electron and positron beams are taken into account. Similarly, we consider the cases of the polarization of the observed final-state fermion along longitudinal and two transverse spin-quantization axes which are required for a full reconstruction of the spin dependence of the process. We show how these model-independent distributions can be used to deduce some general properties of the nature of the interaction and some of their properties in prior work which made use of spin-momentum correlations.
An adaptive method for quantum state fidelity estimation in bipartite higher dimensional systems is established. This method employs state verifier operators which are constructed by local POVM operators and adapted to the measurement statistics in the computational basis. Employing this method, the state verifier operators that stabilize Bell-type entangled states are constructed explicitly. Together with an error operator in the computational basis, one can estimate the lower and upper bounds on the state fidelity for Bell-type entangled states in few measurement configurations. These bounds can be tighter than the fidelity bounds derived in [Bavaresco et.al., Nature Physics (2018), 14, 1032~1037], if one constructs more than one local POVM measurements additional to the measurement in the computational basis.
A stochastic calculus is given for processes described by stochastic integrals with respect to fractional Brownian motions and Rosenblatt processes somewhat analogous to the stochastic calculus for It\^{o} processes. These processes for this stochastic calculus arise naturally from a stochastic chain rule for functionals of Rosenblatt processes; and some It\^{o}-type expressions are given here. Furthermore, there is some analysis of these results for their applications to problems using Rosenblatt noise.
Balogh, Csaba, Jing and Pluh\'ar recently determined the minimum degree threshold that ensures a $2$-coloured graph $G$ contains a Hamilton cycle of significant colour bias (i.e., a Hamilton cycle that contains significantly more than half of its edges in one colour). In this short note we extend this result, determining the corresponding threshold for $r$-colourings.
Magnetic and dielectric properties of the hexagonal triangular lattice antiferromagnet 2H-AgFeO2 have been studied by neutron diffraction, magnetic susceptibility, specific heat, pyroelectric current, and dielectric constant measurements. The ferroelectric polarization, P ~ 5 {\mu}C/m2, has been found to appear below 11 K due to a polar nature of the magnetic ground state of the system. In the temperature range of 11 K < T < 18 K, an incommensurate spin density wave (ICM1) with the nonpolar magnetic point group mmm1' and the k1 = (0,q1_b,0; q1_b = 0.390-0.405)propagation vector takes place. Below 14 K, a proper screw ordering (ICM2) and k2 = (0,q2_b,0; q2_b = 0.385-0.396) appears as a minor phase which coexists with ICM1 and the ground state down to the lowestmeasured temperature 5.5 K. No ferroelectric polarization associated with the ICM2 phase was observed in agreement with its nonpolar point group 2221'. Finally, a spiral order with cycloid and proper screw components (ICM3), and k3 = (q3_a,q3_b,0; q3_a = 0.0467, q3_b = 0.349) emerges below 11 K as the ground state of the system. Based on the deduced magnetic point group 21', we conclude that the ferroelectric polarization in ICM3 is parallel to the c axis and is caused by the inverse Dzyloshinskii-Moriya effect with p1 ~ rij x (Si x Sj ). Unlike the rhombohedral 3R-AgFeO2 polytype, the additional contribution to the macroscopic polarization p2 ~ Si x Sj is not allowed in the present case due to the symmetry constraints imposed by the hexagonal lattice of 2H-AgFeO2.
We assume gravity in a $d$-dimensional manifold $M$ and consider a splitting of the form $M=M_{p}\times M_{q}$, with $d=p+q$. The most general two-block metric associated with $M_{p}$ and $M_{q}$ is used to derive the corresponding Einstein-Hilbert action $\mathcal{S}$. We focus on the special case of two distinct conformal factors $\psi $ and $\phi $ ($\psi $ for the metric in $M_{p}$ and $\phi $ for the metric in $M_{q}$), and we write the action $\mathcal{S}$ in the form $\mathcal{S=S}_{p}\mathcal{+S}%_{q} $, where $\mathcal{S}_{p}$ and $\mathcal{S}_{q}$ are actions associated with $M_{p}$ and $M_{q}$, respectively. We show that a simplified action is obtained precisely when $\psi =\phi ^{-1}$. In this case, we find that under the duality transformation $\phi \leftrightarrow \phi ^{-1}$, the action $\mathcal{S}_{p}$ for the $M_{p}$-space or the action $\mathcal{S}%_{q}$ for the $M_{q}$-space remain invariant, but not both. This result establishes an analogy between Farkas property in oriented matroid theory and duality in general relativity. Furthermore, we argue that our approach can be used in several physical scenarios such as 2t physics and cosmology.
Microquasars are stellar-mass black holes accreting matter from a companion star and ejecting plasma jets at almost the speed of light. They are analogues of quasars that contain supermassive black holes of $10^6$ to $10^{10}$ solar masses. Accretion in microquasars varies on much shorter timescales than in quasars and occasionally produces exceptionally bright X-ray flares. How the flares are produced is unclear, as is the mechanism for launching the relativistic jets and their composition. An emission line near 511 kiloelectronvolts has long been sought in the emission spectrum of microquasars as evidence for the expected electron-positron plasma. Transient high-energy spectral features have been reported in two objects, but their positron interpretation remains contentious. Here we report observations of $\gamma$-ray emission from the microquasar V404 Cygni during a recent period of strong flaring activity. The emission spectrum around 511 kiloelectronvolts shows clear signatures of variable positron annihilation, which implies a high rate of positron production. This supports the earlier conjecture that microquasars may be the main sources of the electron-positron plasma responsible for the bright diffuse emission of annihilation $\gamma$-rays in the bulge region of our Galaxy. Additionally, microquasars could be the origin of the observed megaelectronvolt continuum excess in the inner Galaxy.
We give formulas for the degrees of the spaces of foliations in P2 with a dicritical singularity of prescribed order. Blowing up such singularity induces, generically, a foliation with all but finitely many leaves transversal to the exceptional line; we also find the degree of the locus defined by imposing a leaf of total contact with the exceptional line.
Sketch-to-image (S2I) translation plays an important role in image synthesis and manipulation tasks, such as photo editing and colorization. Some specific S2I translation including sketch-to-photo and sketch-to-painting can be used as powerful tools in the art design industry. However, previous methods only support S2I translation with a single level of density, which gives less flexibility to users for controlling the input sketches. In this work, we propose the first multi-level density sketch-to-image translation framework, which allows the input sketch to cover a wide range from rough object outlines to micro structures. Moreover, to tackle the problem of noncontinuous representation of multi-level density input sketches, we project the density level into a continuous latent space, which can then be linearly controlled by a parameter. This allows users to conveniently control the densities of input sketches and generation of images. Moreover, our method has been successfully verified on various datasets for different applications including face editing, multi-modal sketch-to-photo translation, and anime colorization, providing coarse-to-fine levels of controls to these applications.
Let $k \leq n$ be nonnegative integers and let $\lambda$ be a partition of $k$. S. Griffin recently introduced a quotient $R_{n,\lambda}$ of the polynomial ring $\mathbb{Q}[x_1, \dots, x_n]$ in $n$ variables which simultaneously generalizes the Delta Conjecture coinvariant rings of Haglund-Rhoades-Shimozono and the cohomology rings of Springer fibers studied by Tanisaki and Garsia-Procesi. We describe the space $V_{n,\lambda}$ of harmonics attached to $R_{n,\lambda}$ and produce a harmonic basis of $R_{n,\lambda}$ indexed by certain ordered set partitions $\mathcal{OP}_{n,\lambda}$. The combinatorics of this basis is governed by a new extension of the {\em Lehmer code} of a permutation to $\mathcal{OP}_{n, \lambda}$.
We thoroughly analyze the number of independent zero modes and their zero points on the toroidal orbifold $T^2/\mathbb{Z}_N$ ($N = 2, 3, 4, 6$) with magnetic flux background, inspired by the Atiyah-Singer index theorem. We first show a complete list for the number $n_{\eta}$ of orbifold zero modes belonging to $\mathbb{Z}_{N}$ eigenvalue $\eta$. Since it turns out that $n_{\eta}$ quite complicatedly depends on the flux quanta $M$, the Scherk-Schwarz twist phase $(\alpha_1, \alpha_2)$, and the $\mathbb{Z}_{N}$ eigenvalue $\eta$, it seems hard that $n_{\eta}$ can be universally explained in a simple formula. We, however, succeed in finding a single zero-mode counting formula $n_{\eta} = (M-V_{\eta})/N + 1$, where $V_{\eta}$ denotes the sum of winding numbers at the fixed points on the orbifold $T^2/\mathbb{Z}_N$. The formula is shown to hold for any pattern.
A set of electron-correlation energies as large as 10 eV have been measured for a magnetic 2ML Fefilm deposited on Ag(001). By exploiting the spin selectivity in angle-resolved Auger-photoelectroncoincidence spectroscopy and the Cini-Sawatzky theory, the core-valence-valence Auger spectrumof a spin-polarized system have been resolved: correlation energies have been determined for eachindividual combination of the two holes created in the four sub-bands involved in the decay: majorityand minority spin, as well asegandt2g. The energy difference between final states with paralleland antiparallel spin of the two emitted electrons is ascribed to the spin-flip energy for the final ionstate, thus disentangling the contributions of Coulomb and exchange interactions.
Bulk nanocrystalline materials of small and medium ferromagnetic content were produced using severe plastic deformation by high-pressure torsion at roomtemperature. Giant magnetoresistive behavior was found for as deformed materials, which was further improved by adjusting the microstructure with thermal treatments. The adequate range of annealing temperatures was assessed with in-situ synchrotron diffraction measurements. Thermally treated CuCo materials show larger giant magnetoresistance after annealing for 1 h at 300C, while for CuFe this annealing temperature is too high and decreases the magnetoresistive properties. The improvement of magnetoresistivity by thermal treatments is discussed with respect to the microstructural evolution as observed by electron microscopy and ex situ synchrotron diffraction measurements.
Line-narrowing by periodic modulation of nuclear spin interaction Hamiltonians is the central element of various experimental techniques in NMR spectroscopy. In this study, we present a theoretical formulation of coherent averaging to calculate the heights of narrowed spectral peaks. This concept is experimentally demonstrated using proton spectra of solids obtained under fast magic-angle spinning.
Recently there has been a lot of intersest in the superluminal phenomena, and time varying velocity of light cosmological models. More than two decades ago at Einstein centenary symposium, Nagpur I had put forward space-time interaction hypothesis. One of its predictions was that velocity of light decreased with the age of Universe. In view of the profoundness of the hypothesis the original paper is reproduced here. We also mention that in a paper "Quasars, Tachyons and the early universe" proc. Einstein found. Intnl. 2(3), 1985 pp 69-75, it was suggested that, "The boundary region of the universe being the source of radiation, the slowing down of the speed of radiation from $4.4 \times 10^{10}$ cm/sec at $t_A = 10^{10}$ yrs. to the present value of $3 \times 10^{10}$ cm/sec should show up as a large red shifts. The successive boundary region radiations at various epoch will give rise to a wide range of red shifts. Therefore, defining quasars as the objects having two properties: large red shifts and powerful emission of radiations, we would like to identify these objects as the boundary regions of the universe".