ShantanuT01/DACTYL-Pretraining huggingface dataset:
Starting from a detailed model for the kinetics of a step edge or island boundary, we derive a Gibbs-Thomson type formula and the associated step stiffness as a function of the step edge orientation angle, $theta$. Basic ingredients of the model are: (i) the diffusion of point defects (``adatoms'') on terraces and along step edges; (ii) the convection of kinks along step edges; and (iii) constitutive laws that relate adatom fluxes, sources for kinks, and the kink velocity with densities via a mean-field approach. This model has a kinetic (nonequilibrium) steady-state solution that corresponds to epitaxial growth through step flow. The step stiffness, $\tbe(\theta)$, is determined via perturbations of the kinetic steady state for small edge Peclet number, P, which is the ratio of the deposition to the diffusive flux along a step edge. In particular, $\tbe$ is found to satisfy $\tbe =O(\theta^{-1})$ for $O(P^{1/3}) <\theta \ll 1$, which is in agreement with independent, equilibrium-based calculations.
This is the first in a series of papers in which we investigate the resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds with applications to the restriction theorem, spectral multiplier results and Strichartz estimates. In this first paper, we use semiclassical Lagrangian distributions and semiclassical intersecting Lagrangian distributions, along with Mazzeo-Melrose 0-calculus, to construct the high energy resolvent on general non- trapping asymptotically hyperbolic manifolds, generalizing the work due to Melrose, Sa Barreto and Vasy. We note that there is an independent work by Y. Wang which also constructs the high-energy resolvent.
This paper reports a study on the truncated Israel-Stewart formalism for bulk viscosity using the extended holographic Ricci dark energy (EHRDE), where the density of dark energy is given as a combination of the Hubble parameter and its derivative. The equations of motion are integrated and the resulting model is analysed under many aspects, including the state finder parameters and the generalised thermodynamics second law. Under the consideration that the universe is dominated by EHRDE the evolution equation for the bulk viscous pressure $\Pi$ in the framework of the truncated Israel-Stewart theory has been taken as $\tau \dot{\Pi}+\Pi=-3\xi H$, where $\tau$ is the relaxation time and $\xi$ is the bulk viscosity coefficient. Considering effective pressure as a sum of thermodynamic pressure of EHRDE and bulk viscous pressure it has been observed that under the influence of bulk viscosity the EoS parameter $w_{DE}$ is behaving like phantom i.e. $w_{DE}\leq -1$. It has been observed that the magnitude of the effective pressure $p_{eff}=p+\Pi$ is decaying with time. We also investigated the case for a specific choice of scale factor namely $a(t)=(t-t_0)^{\frac{\beta}{1-\alpha}}$. For this choice we have observed that a transition from quintessence to phantom is possible for the equation of state parameter. However, the $\Lambda$CDM phase is not attainable by the statefinder trajectories for this choice. Finally it has been observed that in both of the cases the generalized second law of thermodynamics is valid for the viscous EHRDE dominated universe enveloped by the apparent horizon.
HD 141569 is a Herbig Ae/Be star that straddles the boundary between the transition disks and debris disks. It is a low dust mass disk that reveals numerous structural elements (e.g. gaps and rings) that may point to young planets. It also exhibits a reservoir of CO gas observed at both millimeter and IR wavelengths. Previous observations (Goto et al. 2006) reported a possible asymmetry in the CO gas emission. Herein the IR ro-vibrational emission lines are analyzed and modeled both spectroscopically and spectroastrometrically. We find emission features from both 12CO and 13CO isotopologues heated to a temperature of approximately 200 K in the radial extent of 13 to 60 au. We do not see evidenceof the previously reported asymmetry in CO emission, our results being consistent with a Keplerian, axisymmetric emitting region. This raises the question of whether the emission profile may be evolving in time, possibly as a result of an orbiting feature in the inner disk such as a planet.
We show that for Eve to get information in one basis about a state, she must cause errors in all bases that are mutually unbiased to that basis. Our result holds in any dimension. We also show that this result holds for all functions of messages that are encrypted with a key.
SN1998bw shot to fame by claims of association with GRB980425. Independent of its presumed association with a GRB, this SN is unusual in its radio properties. A simple interpretation of the unusually bright radio emission leads us to the conclusion that there are two shocks in this SN: a slow moving shock containing most of the ejecta and a relativistic shock (Gamma=2) which is responsible for the radio emission. This is the first evidence for the existence of relativistic shocks in supernovae. It is quite plausible that this shock may produce high energy emission (at early times and by inverse Compton scattering). As with other supernovae, we expect radio emission at much later times powered primarily by the slow moving ejecta. This expectation has motivated us to continue monitoring this unusual SN.
A subclass of recently discovered class of solutions in multidimensional gravity with intersecting p-branes related to Lie algebras and governed by a set of harmonic functions is considered. This subclass in case of three Euclidean p-branes (one electric and two magnetic) contains a cosmological-type solution (in 11-dimensional model with two 4-forms) related to hyperbolic Kac-Moody algebra ${\cal F}_3$ (of rank 3). This solution describes the non-Kasner power-law inflation.
We study stochastic reaction--diffusion equation $$ \partial_tu_t(x)=\frac12 \partial^2_{xx}u_t(x)+b(u_t(x))+\dot{W}_{t}(x), \quad t>0,\, x\in D $$ where $b$ is a generalized function in the Besov space $\mathcal{B}^\beta_{q,\infty}({\mathbb R})$, $D\subset{\mathbb R}$ and $\dot W$ is a space-time white noise on ${\mathbb R}_+\times D$. We introduce a notion of a solution to this equation and obtain existence and uniqueness of a strong solution whenever $\beta-1/q\ge-1$, $\beta>-1$ and $q\in[1,\infty]$. This class includes equations with $b$ being measures, in particular, $b=\delta_0$ which corresponds to the skewed stochastic heat equation. For $\beta-1/q > -3/2$, we obtain existence of a weak solution. Our results extend the work of Bass and Chen (2001) to the framework of stochastic partial differential equations and generalizes the results of Gy\"ongy and Pardoux (1993) to distributional drifts. To establish these results, we exploit the regularization effect of the white noise through a new strategy based on the stochastic sewing lemma introduced in L\^e~(2020).
We find that the one-loop correction to the ratio of Yukawa coupling and gauge coupling in the gauge-Higgs unification, "gauge-Yukawa universality violation", is finite and calculable in any space-time dimension. Applying this result to the ratio of top quark and W-boson masses, we show that the order one correction required to generate a viable top quark mass is indeed possible if the fermion embedding top quark belongs to the large dimensional representation of the gauge group and a vacuum expectation value of Higgs scalar field is very small comparing to the compactification scale.
Dyck paths are among the most heavily studied Catalan families. We work with peaks and valleys to uniquely decompose Dyck paths into the simplest objects - prime fragments with a single peak. Each Dyck path is uniquely characterized by a set of peaks or a set of valleys. The appendix contains a python program with which the reader can factorize Dyck paths online.
The influence functional method of Feynman and Vernon is used to obtain a quantum master equation for a Brownian system subjected to a Levy stable random force. The corresponding classical transport equations for the Wigner function are then derived, both in the limit of weak and strong friction. These are fractional extensions of the Klein-Kramers and the Smoluchowski equations. It is shown that the fractional character acquired by the position in the Smoluchowski equation follows from the fractional character of the momentum in the Klein-Kramers equation. Connections among fractional transport equations recently proposed are clarified.
Discriminative least squares regression (DLSR) has been shown to achieve promising performance in multi-class image classification tasks. Its key idea is to force the regression labels of different classes to move in opposite directions by means of the proposed the joint use of the $\epsilon$-draggings technique, yielding discriminative regression model exhibiting wider margins, and the Fisher criterion. The $\epsilon$-draggings technique ignores an important problem: its non-negative relaxation matrix is dynamically updated in optimization, which means the dragging values can also cause the labels from the same class to be uncorrelated. In order to learn a more powerful discriminative projection, as well as regression labels, we propose a Fisher regularized DLSR (FDLSR) framework by constraining the relaxed labels using the Fisher criterion. On one hand, the Fisher criterion improves the intra-class compactness of the relaxed labels during relaxation learning. On the other hand, it is expected further to enhance the inter-class separability of $\epsilon$-draggings technique. FDLSR for the first time ever attempts to integrate the Fisher discriminant criterion and $\epsilon$-draggings technique into one unified model because they are absolutely complementary in learning discriminative projection. Extensive experiments on various datasets demonstrate that the proposed FDLSR method achieves performance that is superior to other state-of-the-art classification methods. The Matlab codes of this paper are available at https://github.com/chenzhe207/FDLSR.
We show that B-model topological strings on local Calabi-Yau threefolds are large N duals of matrix models, which in the planar limit naturally give rise to special geometry. These matrix models directly compute F-terms in an associated N=1 supersymmetric gauge theory, obtained by deforming N=2 theories by a superpotential term that can be directly identified with the potential of the matrix model. Moreover by tuning some of the parameters of the geometry in a double scaling limit we recover (p,q) conformal minimal models coupled to 2d gravity, thereby relating non-critical string theories to type II superstrings on Calabi-Yau backgrounds.
A microscopic four-body description of near-threshold coherent photoproduction of the $\eta$ meson on the (3N)-nuclei is given. The photoproduction cross-section is calculated using the Finite Rank Approximation (FRA) of the nuclear Hamiltonian. The results indicate that the final state interaction of the $\eta$ meson with the residual nucleus plays an important role in the photoproduction process. Sensitivity of the results to the choice of the $\eta N$ T-matrix is investigated. The importance of obeying the condition of $\eta N$ unitarity is demonstrated.
We present follow-up time-series photometric observations that confirm and extend the results of the significant discovery made by Barlow et al.(2008) that the Hot DQ white dwarfs SDSS J220029.08-074121.5 and SDSS J234843.30-094245.3 are luminosity variable. These are the second and third known members of a new class of pulsating white dwarfs, after the prototype SDSS J142625.71+575218.3 (Montgomery et al. 2008). We find that the light curve of SDSS J220029.08-074121.5 is dominated by an oscillation at 654.397+-0.056 s, and that the light pulse folded on that period is highly nonlinear due to the presence of the first and second harmonic of the main pulsation. We also present evidence for the possible detection of two additional pulsation modes with low amplitudes and periods of 577.576+-0.226 s and 254.732+-0.048 s in that star. Likewise, we find that the light curve of SDSS J234843.30-094245.3 is dominated by a pulsation with a period of 1044.168+-0.012 s, but with no sign of harmonic components. A new oscillation, with a low amplitude and a period of 416.919+-0.004 s, is also probably detected in that second star. We argue, on the basis of the very different folded pulse shapes, that SDSS J220029.08-074121.5 is likely magnetic, while SDSS J234843.30-094245.3 is probably not.
We discuss the effect of the recent change of $V_{\rm us}$ by three standard deviations on the standard model predictions for neutron beta decay observables. We also discuss the effect the experimental error bars of $V_{\rm us}$ have on such predictions. Refined precision tests of the standard model will be made by a combined effort to improve measurements in neutron beta decay and in strangeness-changing decays. By itself the former will yield very precise measurements of $V_{\rm ud}$ and make also very precise predictions for $V_{\rm us}$.
We show experimentally and theoretically that the persistence of large deviations in equilibrium step fluctuations is characterized by an infinite family of independent exponents. These exponents are obtained by carefully analyzing dynamical experimental images of Al/Si(111) and Ag(111) equilibrium steps fluctuating at high (970K) and low (320K) temperatures respectively, and by quantitatively interpreting our observations on the basis of the corresponding coarse-grained discrete and continuum theoretical models for thermal surface step fluctuations under attachment/detachment (``high-temperature'') and edge-diffusion limited kinetics (``low-temperature'') respectively.
Perceptron model is a fundamental linear classifier in machine learning and also the building block of artificial neural networks. Recently, Wiebe et al. (arXiv:1602.04799) proposed that the training of a perceptron can be quadratically speeded using Grover search with a quantum computer, which has potentially important big-data applications. In this paper, we design a quantum circuit for implementing this algorithm. The Grover oracle, the central part of the circuit, is realized by Quantum-Fourier-Transform based arithmetics that specifies whether an input weight vector can correctly classify all training data samples. We also analyze the required number of qubits and universal gates for the algorithm, as well as the success probability using uniform sampling, showing that it has higher possibility than spherical Gaussian distribution $N(0,1)$. The feasibility of the circuit is demonstrated by a testing example using the IBM-Q cloud quantum computer, where 16 qubits are used to classify four data samples.
The beta-decay of a tritium nucleus produces an entangled quantum system, a beta electron, a helium nucleus, and an antineutrino. For finite collapse times, the post-collapse beta electron energy can originate from a range of pre-collapse energies due to the uncertainty principle. Long collapse times give negligible uncertainty, so the pre-collapse spectrum must approach that of isolated nuclei. We calculate the post-collapse electron spectrum which shows a collapse-dependent pileup near the endpoint. Comparison with observation shows that a collapse time of 1 x 10^-17 s explains the observed pileup. The collapse of the entangled quantum system must be triggered by the environment: most likely an atomic (molecular) electron initially bound to the atomic (molecular) tritium source or perhaps ambient gas molecules. Coincidentally, the 40 eV tritium atom-helium ion energy level shift is unobservably small for times shorter than the system collapse time. We conclude that an atomic (molecular) electron triggers the collapse once the 40 eV shift becomes detectible and the electron detects the helium nucleus. Thus collapse may explain the tritium endpoint pileup.
A new, more general derivation of the spin-statistics and PCT theorems is presented. It uses the notion of the analytic wave front set of (ultra)distributions and, in contrast to the usual approach, covers nonlocal quantum fields. The fields are defined as generalized functions with test functions of compact support in momentum space. The vacuum expectation values are thereby admitted to be arbitrarily singular in their space-time dependence. The local commutativity condition is replaced by an asymptotic commutativity condition, which develops generalizations of the microcausality axiom previously proposed.
We introduce the notion of K-correspondence, and show that many Calabi-Yau varieties carry a lot of self-K-isocorrespondences, which furthermore satisfy the property of multiplying the canonical volume form by a constant of modulus different from 1. This leads to the introduction of a modified Kobayashi-Eisenman pseudovolume form, for which we are able to prove many instances of the Kobayashi conjecture.
A proof that a new kind of non-removable {\it "regularity singularity"} forms when two shock waves collide within the theory of General Relativity, was first announced in ProcRoySoc A \cite{ReintjesTemple}. In the present paper we give complete proofs of the claims in \cite{ReintjesTemple} and extend the results on the regularity of the Einstein curvature tensor to the full Riemann curvature tensor. The main result is that, in a neighborhood of a point where two shock waves collide in a spherically symmetric spacetime, the gravitational metric tensor cannot be lifted from C0,1 to C1 within the class of C1,1 coordinate transformations. This contrasts Israel's celebrated theorem \cite{Israel}, which states that around each point on a {\it single} shock surface there exist a coordinate system in which the metric is C1,1 regular. Moreover, at points of shock wave interaction, delta function sources exist in the second derivatives of the gravitational metric tensor in all coordinate systems of the C1,1-atlas, but due to cancellation, the Einstein and Riemann curvature tensor remain sup-norm bounded. We conclude that points of shock wave interaction are a new kind of spacetime singularity, (which we name "regularity singularity"), singularities that can form from the evolution of smooth initial data for perfect fluids and that lie in physical spacetime, but at such points {\it locally inertial} coordinates fail to exist.
We consider the problem of optimal estimation of the linear functional $A_N{\xi}=\sum_{k=0}^Na(k)\xi(k)$ depending on the unknown values of a stochastic sequence $\xi(m)$ with stationary increments from observations of the sequence $\xi(m)+\eta (m)$ at points of the set $\mathbb{Z}\setminus\{0,1,2,\ldots,N\}$, where $\eta(m)$ is a stationary sequence uncorrelated with $\xi(m)$. We propose formulas for calculating the mean square error and the spectral characteristic of the optimal linear estimate of the functional in the case of spectral certainty, where spectral densities of the sequences are exactly known. We also consider the problem for a class of cointegrated sequences. We propose relations that determine the least favorable spectral densities and the minimax spectral characteristics in the case of spectral uncertainty, where spectral densities are not exactly known while a set of admissible spectral densities is specified.
The Rubik's cube was invented in 1974 by Erno Rubik, who had no idea of the incredible popularity and mathematical fascinations his toy would bring. Through the years of study on the mathematical properties of the cube, the Rubik's Cube group was introduced to represent all possible moves one could perform on the cube. In this paper, we define a planar analogue to the Rubik's cube, which we dub the Rubik's Square, and prove that the Rubik's square is complete in the sense that given any two configurations there is a sequence of moves which changes one to the other. The Rubik's cube does not have this property. We then abstract the concept of the Rubik's Square to a Rubik's Shape and analyse the completeness in this more general setting.
We present results from integral field spectroscopy with the Potsdam Multi-Aperture Spectrograph at the 3.5m telescope at Calar Alto Observatory of the intense star-forming region [HL90] 111 at the center of the starburst galaxy IC 10. We have obtained maps with a spatial sampling of 1" x 1" = 3.9 pc x 3.9 pc of different emission lines and analyzed the extinction, physical conditions, nature of the ionization, and chemical abundances of the ionized gas, as well determined locally the age of the most recent star-formation event. By defining several apertures, we study the main integrated properties of some regions within [HL90] 111. Two contiguous spaxels show an unambiguous detection of the broad He II 4686 emission line, this feature seems to be produced by a single WNL star. We also report a probable N and He enrichment in the precise spaxels where the WR features are detected. The enrichment pattern is roughly consistent with that expected for the pollution of the ejecta of a single or a very small number of WR stars. Furthermore, this chemical pollution is very localized (~2"~7.8 pc) and it should be difficult to detect in star-forming galaxies beyond the Local Volume. We also discuss the use of the most-common empirical calibrations to estimate the oxygen abundances of the ionized gas in nearby galaxies from 2D spectroscopic data. The ionization degree of the gas plays an important role when applying these empirical methods, as they tend to give lower oxygen abundances with increasing ionization degree.
In this manuscript we present the technique to detect and analyze the DNA rich structure in Haemotoxylin & Eosin (H&E) image of a tissue treated with anti CD4 green antigen. The detection of DNA rich structure can be considered as a detection of blue nuclei present through the biomedical signal/image processing technique performed on the image of the tissue obtained by the Scanning Electron Microscope(SEM). Earlier the tissue treated with the anti CD4 green antigen, is stained with the H&E staining solution.
With rapid development of techniques for astronomical observations, the precision of measurements has been significantly increasing. Theories of astronomical relativistic reference systems, which are the foundation for processing and interpreting these data now and in the future, may require extensions to satisfy the needs of these trends. Besides building a framework compatible with alternative theories of gravity and the pursuit of higher order post-Newtonian approximation, it will also be necessary to make the first order post-Newtonian multipole moments of celestial bodies be explicitly expressed in the astronomical relativistic reference systems. This will bring some convenience into modeling the observations and experiments and make it easier to distinguish different contributions in measurements. As the first step, the global solar system reference system is multipolarly expanded and the post-Newtonian mass and spin moments are shown explicitly in the metric which describes the coordinates of the system. The full expression of the global metric is given.
We present a model for dressing the nucleon propagator and vertices. In the model the use of a K-matrix approach (unitarity) and dispersion relations (analyticity) are combined. The principal application of the model lies in pion-nucleon scattering where we discuss effects of the dressing on the phase shifts.