ShantanuT01/DACTYL-Pretraining huggingface dataset:
The aim of this note is to show that given a positive integer $n \geq 5$, the positive integral solutions of the diophantine equation $4/n = 1/x + 1/y+1/z$ cannot have solution such that $x$ and $y$ are coprime with $xy < \sqrt{z/2}$. The proof uses the continued fraction expansion of $4/n$.
Perfect fluid spacetimes admitting a kinematic self-similarity of infinite type are investigated. In the case of plane, spherically or hyperbolically symmetric space-times the field equations reduce to a system of autonomous ordinary differential equations. The qualitative properties of solutions of this system of equations, and in particular their asymptotic behavior, are studied. Special cases, including some of the invariant sets and the geodesic case, are examined in detail and the exact solutions are provided. The class of solutions exhibiting physical self-similarity are found to play an important role in describing the asymptotic behavior of the infinite kinematic self-similar models.
Given that lung cancer is one of the deadliest illnesses, early identification and diagnosis are critical to preserving a patient's life. However, lung illness diagnosis is time-intensive and requires the expertise of a pulmonary disease specialist, subject to a significant rate of inaccuracy. Our objective is to design a system capable of accurately detecting and classifying lung lesions and segmenting them in CT-scan images. The suggested technique extracts features automatically from the CT-scan image and then classifies them using Ensemble Gradient Boosting methods. Finally, if a lesion is detected in the CT-scan image, it is segmented using a hybrid approach based on Fuzzy Clustering and Level Set. To train and test our models we gathered a dataset that included CT images of patients residing in Mashhad, Iran. Finally, the results indicate 96% accuracy within this dataset. This approach may assist clinicians in diagnosing lung abnormalities and avoiding potential errors.
The abstract Cauchy problem for the fractional evolution equation with the Caputo derivative of order $\beta\in(0,1)$ and operator $-A^\alpha$, $\alpha\in(0,1)$, is considered, where $-A$ generates a strongly continuous one-parameter semigroup on a Banach space. Subordination formulae for the solution operator are derived, which are integral representations containing a subordination kernel (a scalar probability density function) and a $C_0$-semigroup of operators. Some properties of the subordination kernel are established and representations in terms of Mainardi function and L\'evy extremal stable densities are derived. Applications of the subordination formulae are given with a special focus on the multi-dimensional space-time fractional diffusion equation for some special values of the parameters.
A general phenomenon of the Cherenkov radiation known in optics or acoustics of conventional materials is a formation of a forward cone of, respectively, photons or phonons emitted by a particle accelerated above the speed of light or sound in those materials. Here we suggest three-dimensional topological insulators as a unique platform to fundamentally explore and practically exploit the acoustic aspect of the Cherenkov effect. We demonstrate that applying an in-plane magnetic field to a surface of a three-dimensional topological insulator one may suppress the forward Cherenkov sound up to zero at a critical magnetic field. Above the critical field the Cherenkov sound acquires pure backward nature with the polar distribution differing from the forward one generated below the critical field. Potential applications of this asymmetric Cherenkov reverse are in design of low energy electronic devices such as acoustic ratchets or, in general, in low power design of electronic circuits with a magnetic field control of the direction and magnitude of the Cherenkov dissipation.
We consider the two dimensional unsteady Prandtl system. For a special class of outer Euler flows and solutions of the Prandtl system, the trace of the tangential derivative of the tangential velocity along the transversal axis solves a closed one dimensional equation. First, we give a precise description of singular solutions for this reduced problem. A stable blow-up pattern is found, in which the blow-up point is ejected to infinity in finite time, and the solutions form a plateau with growing length. Second, in the case where, for a general analytic solution, this trace of the derivative on the axis follows the stable blow-up pattern, we show persistence of analyticity around the axis up to the blow-up time, and establish a universal lower bound of $(T-t)^{7/4}$ for its radius of analyticity.
Autonomous robotic manipulation in clutter is challenging. A large variety of objects must be perceived in complex scenes, where they are partially occluded and embedded among many distractors, often in restricted spaces. To tackle these challenges, we developed a deep-learning approach that combines object detection and semantic segmentation. The manipulation scenes are captured with RGB-D cameras, for which we developed a depth fusion method. Employing pretrained features makes learning from small annotated robotic data sets possible. We evaluate our approach on two challenging data sets: one captured for the Amazon Picking Challenge 2016, where our team NimbRo came in second in the Stowing and third in the Picking task, and one captured in disaster-response scenarios. The experiments show that object detection and semantic segmentation complement each other and can be combined to yield reliable object perception.
We investigate the emergence of both quantum anomalous Hall and disorder-induced Anderson Chern insulating phases in two dimensional hexagonal lattices, with antiferromagnetically ordered 3Q state and in the absence of spin-orbit coupling. Using tight-binding modeling, we show that such systems display not only a spin-polarized edge-localized current, the chirality of which is energy dependent but also an impurity-induced transition from trivial metallic to topological insulating regimes, through one edge mode plateau. We compute the gaps' phase diagrams, and demonstrate the robustness of the edge channel against deformation and disorder. Our study hints at the 3Q state as a promising building block for dissipationless spintronics based on antiferromagnets.
The multi-branched Husimi recursive lattice has been extended to a virtual structure with fractional numbers of branches joined on one site. Although the lattice is undrawable in real space, the concept is consistent with regular Husimi lattice. The Ising spins of antiferromagnetic interaction on such a sets of lattices were calculated to check the critical temperatures ($T_{c}$) and ideal glass transition temperatures ($T_{k}$) variation with fractional branch numbers. Besides the similar results of two solutions representing the stable state (crystal) and metastable state (supercooled liquid) and indicating the phase transition temperatures, the phase transitions show a well-defined shift with branch number variation. Therefore the fractional branch number as a parameter can be used as an adjusting tool in constructing a recursive lattice model to describe real systems.
We numerically investigate topological phases of periodic lattice systems in tight-binding description under the influence of dissipation. The effects of dissipation are effectively described by $\mathcal{PT}$-symmetric potentials. In this framework we develop a general numerical gauge smoothing procedure to calculate complex Berry phases from the biorthogonal basis of the system's non-Hermitian Hamiltonian. Further, we apply this method to a one-dimensional $\mathcal{PT}$-symmetric lattice system and verify our numerical results by an analytical calculation.
We review the status of quasi-degenerate doublets in nuclei, called pseudospin doublets, which were discovered about thirty years ago and the origins of which have remained a mystery, until recently. We show that pseudospin doublets originate from an SU(2) symmetry of the Dirac Hamiltonian which occurs when the sum of the scalar and vector potentials is a constant. Furthermore, we survey the evidence that pseudospin symmetry is approximately conserved in nuclear spectra and eigenfunctions and in nucleon-nucleus scattering for a Dirac Hamiltonian with realistic nuclear scalar and vector potentials.
The calculation of the Bogoliubov coefficients is a key piece to obtain the reheating temperature of the Universe. In all cases this calculation is performed either in toy models where some derivative of the potential is discontinuous at some points or by making some approximations to the model. The result of these calculations is applied to more realistic models without checking if they really apply to this realistic model because the exact calculation of the Bogoliubov coefficients for a viable model, which is usually depicted by a smooth potential, requires a very complicated numerical calculation. Here we want to point out the difficulties that one encounters when trying to compute numerically these coefficients for a smooth potential without making approximations, which could lead to completely different results.
We introduce a notion of fractional convexity that extends naturally the usual notion of convexity in the Euclidean space to a fractional setting. With this notion of fractional convexity, we study the fractional convex envelope inside a domain of an exterior datum (the largest possible fractional convex function inside the domain that is below the datum outside) and show that the fractional convex envelope is characterized as a viscosity solution to a non-local equation that is given by the infimum among all possible directions of the $1-$dimensional fractional Laplacian. For this equation we prove existence, uniqueness and a comparison principle (in the framework of viscosity solutions). In addition, we find that solutions to the equation for the convex envelope are related to solutions to the fractional Monge-Ampere equation.
We present multi-band results for GRB071010B based on \Swift, \Suzaku, and ground-based optical observations. This burst is an ideal target to evaluate the robustness of the ${\rm E^{src}_{peak}-E_{iso}}$ and ${\rm E^{src}_{peak}-E_{\gamma}}$ relations, whose studies have been in stagnation due to the lack of the combined estimation of $\rm E^{src}_{peak}$ and long term optical monitoring. The joint prompt spectral fitting using \Swift/Burst Alert Telescope and \Suzaku/Wide-band All sky Monitor data yielded the spectral peak energy as E$^{src}_{peak}$ of $86.5^{+6.4}_{-6.3}$ keV and E$_{iso}$ of $2.25^{+0.19}_{-0.16}\times10^{52}$ erg with $z=0.947$. The optical afterglow light curve is well fitted by a simple power law with temporal index $\alpha=-0.60\pm0.02$. The lower limit of temporal break in the optical light curve is 9.8 days. Our multi-wavelength analysis reveals that GRB071010B follows ${\rm E^{src}_{peak}-E_{iso}}$ but violates the ${\rm E^{src}_{peak}-E_{\gamma}}$ and ${\rm E_{iso}-E^{src}_{peak}-t^{src}_{jet}}$ at more than the 3$\sigma$ level.
This paper describes a computation of a part of the QED contribution to the electron anomalous magnetic moment that was performed by the author with the help of a supercomputer. The computed part includes all 5-loop QED Feynman graphs without lepton loops. The calculation has led to the result $A_1^{(10)}[\text{no lepton loops}]=6.793(90)$ that is slightly different than the value $7.668(159)$ presented by T. Aoyama, T. Kinoshita, and M. Nio in 2018. The discrepancy is about $4.8\sigma$. The computation gives the first independent check for that value. A shift in the fine-structure constant prediction is revealed in the paper. The developed calculation method is based on (a) a subtraction procedure for removing all ultraviolet and infrared divergences in Feynman parametric space before integration; (b) a nonadaptive Monte Carlo integration that uses the probability density functions that are constructed for each Feynman graph individually using its combinatorial structure. The method is described briefly in the paper (with the corresponding references to the previous papers). The values for the contributions of nine gauge-invariant classes splitting the whole set are presented in the paper. Moreover, the whole set of all 5-loop graphs without lepton loops is split into 807 subsets for comparison (in the future) of the calculated values with the values obtained by another methods. These detailed results are presented in the supplemental materials. Also, the supplemental materials contain the contribution values for each of 3213 individual Feynman graphs. An "oscillating" nature of these values is discussed. Technical details of the realization are described.
We study inequivalence of canonical and microcanonical ensembles in the mean-field Blume-Emery-Griffiths model. This generalizes previous results obtained for the Blume-Capel model. The phase diagram strongly depends on the value of the biquadratic exchange interaction K, the additional feature present in the Blume-Emery-Griffiths model. At small values of K, as for the Blume-Capel model, lines of first and second order phase transitions between a ferromagnetic and a paramagnetic phase are present, separated by a tricritical point whose location is different in the two ensembles. At higher values of K the phase diagram changes substantially, with the appearance of a triple point in the canonical ensemble which does not find any correspondence in the microcanonical ensemble. Moreover, one of the first order lines that starts from the triple point ends in a critical point, whose position in the phase diagram is different in the two ensembles. This line separates two paramagnetic phases characterized by a different value of the quadrupole moment. These features were not previously studied for other models and substantially enrich the landscape of ensemble inequivalence, identifying new aspects that had been discussed in a classification of phase transitions based on singularity theory. Finally, we discuss ergodicity breaking, which is highlighted by the presence of gaps in the accessible values of magnetization at low energies: it also displays new interesting patterns that are not present in the Blume-Capel model.
We present preliminary results in our long-term project of studying the evolution of matter in a dynamical spacetime. To achieve this, we have developed a new code to evolve axisymmetric initial data sets corresponding to a black hole surrounded by matter fields. The code is based on the coupling of two previously existing codes. The matter fields are evolved with a 2D shock-capturing method which uses the characteristic information of the GR hydro equations to build up a linearized Riemann solver. The spacetime is evolved with a 2D ADM code designed to evolve a wormhole in full general relativity. An example of the kind of problems we are currently investigating is the on axis collision of a star with a black hole.
We study entanglement entropy on the fuzzy sphere. We calculate it in a scalar field theory on the fuzzy sphere, which is given by a matrix model. We use a method that is based on the replica method and applicable to interacting fields as well as free fields. For free fields, we obtain the results consistent with the previous study, which serves as a test of the validity of the method. For interacting fields, we perform Monte Carlo simulations at strong coupling and see a novel behavior of entanglement entropy.
(Abridged) Classical novae (CNe) have recently been reported to represent the major class of supersoft X-ray sources (SSSs) in the central region of our neighbour galaxy M 31. We carried out a dedicated monitoring of the M 31 central region with XMM-Newton and Chandra in order to find SSS counterparts of CNe, determine the duration of their SSS phase and derive physical outburst parameters. We systematically searched our data for X-ray counterparts of CNe and determined their X-ray light curves and spectral properties. Additionally, we determined luminosity upper limits for all novae from previous studies which are not detected anymore and for all CNe in our field of view with optical outbursts between May 2005 and March 2007. We detected eight X-ray counterparts of CNe in M 31, four of which were not previously known. Seven sources can be classified as SSSs, one is a candidate SSS. Two SSSs are still visible more than nine years after the nova outburst, whereas two other nova counterparts show a short SSS phase of less than 150 days. Of the latter sources, M31N 2006-04a exhibits a short-time variable X-ray light curve with an apparent period of (1.6+-0.3) h. This periodicity could indicate the binary period of the system. From the 14 SSS nova counterparts known from previous studies, ten are not detected anymore. Additionally, we found four SSSs in our XMM-Newton data without a nova counterpart, one of which is a new source. Out of eleven SSSs detected in our monitoring, seven are counterparts of CNe. We therefore confirm the earlier finding that CNe are the major class of SSSs in the central region of M 31. We use the measured SSS turn-on and turn-off times to estimate the mass ejected in the nova outburst and the mass burned on the white dwarf. Classical novae with short SSS phases seem to be an important contributor to the overall population.
In this note, we determined the distance signatures of the incidence matrices of affine resolvable designs. This proves a conjecture by Kohei Yamada.
In this work, we study the possibility of realistic text replacement, the goal of which is to replace text present in the image with user-supplied text. The replacement should be performed in a way that will not allow distinguishing the resulting image from the original one. We achieve this goal by developing a novel non-uniform style conditioning layer and apply it to an encoder-decoder ResNet based architecture. The resulting model is a single-stage model, with no post-processing. The proposed model achieves realistic text replacement and outperforms existing approaches on ICDAR MLT.
Binary mass transfer is at the forefront of some of the most exciting puzzles of modern astrophysics, including Type Ia supernovae, gamma-ray bursts, and the formation of most observed exotic stellar populations. Typically, the evolution is assumed to proceed in isolation, even in dense stellar environments such as star clusters. In this paper, we test the validity of this assumption via the analysis of a large grid of binary evolution models simulated with the SeBa code. For every binary, we calculate analytically the mean time until another single or binary star comes within the mean separation of the mass-transferring binary, and compare this time-scale to the mean time for stable mass transfer to occur. We then derive the probability for each respective binary to experience a direct dynamical interruption. The resulting probability distribution can be integrated to give an estimate for the fraction of binaries undergoing mass transfer that are expected to be disrupted as a function of the host cluster properties. We find that for lower-mass clusters ($\lesssim 10^4$ M$_{\odot}$), on the order of a few to a few tens of percent of binaries undergoing mass-transfer are expected to be interrupted by an interloping single, or more often binary, star, over the course of the cluster lifetime, whereas in more massive globular clusters we expect $\ll$ 1% to be interrupted. Furthermore, using numerical scattering experiments performed with the FEWBODY code, we show that the probability of interruption increases if perturbative fly-bys are considered as well, by a factor $\sim 2$.
We study a nonlinear, degenerate cross-diffusion model which involves two densities with two different drift velocities. A general framework is introduced based on its gradient flow structure in Wasserstein space to derive a notion of discrete-time solutions. Its continuum limit, due to the possible mixing of the densities, only solves a weaker version of the original system. In one space dimension, where the densities are guaranteed to be segregated, a stable interface appears between the two densities, and a stronger convergence result, in particular derivation of a standard weak solution to the system, is available. We also study the incompressible limit of the system, which addresses transport under a height constraint on the total density. In one space dimension we show that the problem leads to a two-phase Hele-Shaw type flow.
Observations of magnetically active stars with Chandra and XMM-Newton have deepened our knowledge of the physics of the atmospheres in late-type stars. In this review paper, I discuss two topics that have profited significantly from Chandra and XMM-Newton. Of particular interest, studies of the elemental composition of stellar coronae have taken advantage of the high spectral resolution available with the grating instruments on board these satellites. I summarize the status of our knowledge and discuss the elemental composition in a variety of stellar coronae. I also focus on the topic of flares in stellar coronae, and review the contributions made by XMM-Newton and Chandra to X-ray and multi-wavelength studies.
This work introduces the extended Skorokhod problem (ESP) and associated extended Skorokhod map (ESM) that enable a pathwise construction of reflected diffusions that are not necessarily semimartingales. Roughly speaking, given the closure G of an open connected set in R^J, a non-empty convex cone d(x) in R^J, specified at each point x on the boundary of G, and a cadlag trajectory \psi taking values in R^J, the ESM defines a constrained version \phi of \psi that takes values in G and is such that the increments of \phi - \psi on any interval [s,t] lie in the closed convex hull of the directions d(\phi(u)), u in (s,t]. General deterministic properties of the ESP are first established under the only assumption that the graph of d(.) is closed. Next, for a class of multi-dimensional ESPs on polyhedral domains, pathwise uniqueness and existence of strong solutions to the associated stochastic differential equations is established. In addition, it is also proved that these reflected diffusions are semimartingales on [0,\tau_0], where \tau_0 is the time to hit the set of points x on the boundary for which d(x) contains a line. One motivation for the study of this class of reflected diffusions is that they arise as approximations of queueing networks in heavy traffic that use the so-called generalised processor sharing discipline.
In an effort to develop tools for grand unified model building for the Lie group $E_6$, in this paper we present the computation of the Clebsch-Gordan coefficients for the product (100000) $\otimes$ (000010), where (100000) is the fundamental 27-dimensional representation of $E_6$ and (000010) is its charged conjugate. The results are presented in terms of the dominant weight states of the irreducible representations in this product. These results are necessary for the group analysis of $E_6$ operators involving also higher representations, which is the next step in this project. In this paper we apply the results to the construction of the operator ${\bf 27}^3$.
We present a theoretical study of synchronization dynamics in incoherently pumped exciton-polariton condensates in coupled polariton traps. Our analysis is based on a coupled-mode theory for the generalized Gross-Pitaevskii equation, which employs an expansion in non-Hermitian, pump-dependent modes appropriate for the pumped geometry. We find that polariton-polariton and reservoir-polariton interactions play competing roles and lead to qualitatively different synchronized phases of the coupled polariton modes as pumping power is increased. Crucially, these interactions can also act against each other to hinder synchronization. We map out a phase diagram and discuss the general characteristics of these phases using a generalized Adler equation.
We give a characterization of smooth quadrics in terms of the existence of full exceptional collections of certain type, which generalizes a result of C.Vial for projective spaces.