ShantanuT01/DACTYL-Pretraining huggingface dataset:
This article studies the quasi-stationary behaviour of absorbed one-dimensional diffusions. We obtain necessary and sufficient conditions for the exponential convergence to a unique quasi-stationary distribution in total variation, uniformly with respect to the initial distribution. An important tool is provided by one dimensional strict local martingale diffusions coming down from infinity. We prove under mild assumptions that their expectation at any positive time is uniformly bounded with respect to the initial position. We provide several examples and extensions, including the sticky Brownian motion and some one-dimensional processes with jumps.
Dynamics of charged particles in the vicinity of a rotating black hole embedded in the external large-scale magnetic field is numerically investigated. In particular, we consider a non-axisymmetric model in which the asymptotically uniform magnetic field is inclined with respect to the axis of rotation. We study the effect of inclination onto the prevailing dynamic regime of particle motion, i.e. we ask whether the inclined field allows regular trajectories or if instead, the deterministic chaos dominates the motion. In this contribution we further discuss the role of initial condition, particularly, the initial azimuthal angle. To characterize the measure of chaoticness we compute maximal Lyapunov exponents and employ the method of Recurrence Quantification Analysis.
Affine Toda field theories with a purely transmitting integrable defect are considered and the model based on a_2 is analysed in detail. After providing a complete characterization of the problem in a classical framework, a suitable quantum transmission matrix, able to describe the interaction between an integrable defect and solitons, is found. Two independent paths are taken to reach the result. One is an investigation of the triangle equations using the S-matrix for the imaginary coupling bulk affine Toda field theories proposed by Hollowood, and the other uses a functional integral approach together with a bootstrap procedure. Evidence to support the results is collected in various ways: for instance, through the calculation of the transmission factors for the lightest breathers. While previous discoveries within the sine-Gordon model motivated this study, there are several new phenomena displayed in the a_2 model including intriguing disparities between the classical and the quantum pictures. For example, in the quantum framework, for a specific range of the coupling constant that excludes a neighbourhood of the classical limit, there is an unstable bound state.
In the previous blind deconvolution methods, de-blurred images can be obtained by using the edge or pixel information. However, the existing edge-based methods did not take advantage of edge information in ommi-directions, but only used horizontal and vertical edges when recovering the de-blurred images. This limitation lowers the quality of the recovered images. This paper proposes a method which utilizes edges in different directions to recover the true sharp image. We also provide a statistical table score to show how many directions are enough to recover a high quality true sharp image. In order to grade the quality of the deblurring image, we introduce a measurement, namely Haar defocus score that takes advantage of the Haar-Wavelet transform. The experimental results prove that the proposed method obtains a high quality deblurred image with respect to both the Haar defocus score and the Peak Signal to Noise Ratio.
The optical UBVRI photometric analysis has been established using SLOAN DIGITAL SKY SURVEY (SDSS database) in order to estimate the astrophysical parameters of poorly studied open star cluster IC 2156. The results of the present study are compared with a previous one of ours, which relied on the 2MASS JHK infrared photometry. The stellar density distributions and color-magnitude diagrams of the cluster are used to determine the geometrical structure; limited radius, core and tidal radii, the distances from the Sun, from the Galactic plane and from the Galactic center. Also, the main photometric parameters; age, distance modulus, color excesses, membership, total mass, luminosity, mass functions and relaxation time; have been estimated.
In this study, we perform a comparative theoretical study on the thermoelectric performance of materials with Cu$Ch_4$ ($Ch=$ S, Se) tetrahedra, including famous thermoelectric materials BiCuSeO and tetrahedrite Cu$_{12}$Sb$_4$S$_{13}$, by means of first-principles calculations. By comparing these electronic band structures, we find that many of these materials possess a Cu-$t_{2g}$ band structure consisting of quasi-one-dimensional band dispersions and the isotropic (two-dimensional for layered compounds) band dispersion near the valence-band edge. Therefore, the key factors for the thermoelectric performance are the anisotropy of the former band dispersion and the degeneracy of these two kinds of band dispersions. We also find that a large extension of the chalcogen orbitals often improves their thermoelectric performance by improving these two factors or by going beyond such a basic band structure through a large alternation of its shape. Such a large extension of the chalcogen orbitals might partially originate from the anisotropic Cu-$Ch$ bond geometry of a tetrahedron. Our study reveals interesting similarities and differences of materials with Cu$Ch_4$, which provides important knowledge for a future search of high-performance thermoelectric materials.
We present a proper motion and CCD photometric study of stars in the distant halo globular cluster Palomar 13. The absolute proper motion of Pal 13 with respect to the background galaxies, derived from moderate scale photographic plates separated by a 40-year baseline, is $(\mu_{\alpha cos \delta}, \mu_{\delta}) = (+2.30, +0.27) \pm (0.26, 0.25)$ milliarc-seconds per year. The resultant total space velocity (315 km s$^{-1}$) implies that Pal 13 is in the inner part of its orbit near perigalacticon. Orbital integration reveals the cluster to possess an inclined, very eccentric, retrograde orbit. These data confirm that Pal 13 is a paradigm "young halo" globular cluster.   The derived proper motions for cluster stars are used to produce membership probabilities and a cleaned CCD UBV catalogue for Pal 13. With this data set we have made small revisions to Pal 13's distance, metallicity, position and light profile. The membership of four previously reported RR Lyrae variables and a proportionally large group of blue straggler stars are confirmed. As expected, the blue stragglers are centrally concentrated.   The small size of this cluster, combined with the shape of its light profile, which shows a clear departure from a classical King function beyond the tidal radius, suggests that Pal 13 is in the final throes of destruction. This could explain the large blue straggler specific frequency, as destructive processes would preferentially strip less massive stars.
Sputtering of PbTe crystals by Ar plasma with ion energies 50-550 eV is investigated. A dependence of sputter yields of the Te and Pb on the sputtering ion energy and sputtering time is measured. New phenomena: aperiodical oscillations of Pb and Te sputtering; a huge preference of Te sputtering reaching more than two orders of magnitude at the beginning of sputtering process; and a significant excess of Te integrated sputter yield over that of Pb for prolonged sputtering by low energy plasma at 50-160 eV, are observed. It is substantiated that these phenomena can be caused by the peculiarities of the charge states of the interstitial Pb and Te in PbTe crystal matrix and the processes of re-deposition of sputtered atoms on the sputtered surface
Discussion about the convergence and divergence of trajectories generated by certain functions derived from generalized 3x+1 mappings
We prove existence, uniqueness and regularity results for mixed boundary value problems associated with fully nonlinear, possibly singular or degenerate elliptic equations. Our main result is a global H\"older estimate for solutions, obtained by means of the comparison principle and the construction of ad hoc barriers. The global H\"older estimate immediately yields a compactness result in the space of solutions, which could be applied in the study of principal eigenvalues and principal eigenfunctions of mixed boundary value problems.
The peculiar emission-line star MWC 137 with its extended optical nebula was recently classified as B[e] supergiant. To study the spatial distribution of its circumstellar molecular gas on small and large scales, we obtained near-infrared and radio observations using SINFONI and APEX, respectively. We find that the hot CO gas is arranged in moving clumpy ring and shell structures close to the star, while a cold CO envelope is encircling the borders of the optical nebula from the south to the west.
The development, characterization and control of $N$-photon sources are instrumental for quantum technological applications. This work constitutes a step forward in this direction, where we propose a cavity quantum electrodynamics setup designed for the generation of photon pairs. We analyze it both via the scattering and master equation formalisms. From the connection between these two frameworks it naturally arises a physical criterion characterizing when weakly-driven systems behave as continuous antibunched two-photon sources. We find the optimal parameters for which our setup works as an efficient photon-pair source, showing also that it becomes a deterministic down-converter of single photons. We provide a specific implementation based on state-of-the-art superconducting circuits, showing how our proposal is within the reach of current technologies.
We construct and study a matrix model that describes two dimensional string theory in the Euclidean black hole background. A conjecture of V. Fateev, A. and Al. Zamolodchikov, relating the black hole background to condensation of vortices (winding modes around Euclidean time) plays an important role in the construction. We use the matrix model to study quantum corrections to the thermodynamics of two dimensional black holes.
(Abridged) The ACS Virgo Cluster Survey is an HST program to obtain high-resolution, g and z-band images for 100 early-type members of the Virgo Cluster, spanning a range of ~460 in blue luminosity. Based on this large, homogeneous dataset, we present a sharp upward revision in the frequency of nucleation in early-type galaxies brighter than M_B ~ -15 (66 < f_n < 82%), and find no evidence for nucleated dwarfs to be more concentrated to the center of Virgo than their non-nucleated counterparts. Resolved stellar nuclei are not present in galaxies brighter than M_B ~ -20.5, however, there is no clear evidence from the properties of the nuclei, or from the overall incidence of nucleation, for a change at M_B ~ -17.6, the traditional dividing point between dwarf and giant galaxies. On average, nuclei are ~3.5 mag brighter than a typical globular cluster and have a median half-light radius ~4.2 pc. Nuclear luminosities correlate with nuclear sizes and, in galaxies fainter than M_B ~ -17.6, nuclear colors. Comparing the nuclei to the "nuclear clusters" found in late-type spiral galaxies reveals a close match in terms of size, luminosity and overall frequency, pointing to a formation mechanism that is rather insensitive to the detailed properties of the host galaxy. The mean nuclear-to-galaxy luminosity ratio is indistinguishable from the mean SBH-to-bulge mass ratio, calculated in early-type galaxies with detected supermassive black holes (SBHs). We argue that compact stellar nuclei might be the low-mass counterparts of the SBHs detected in the bright galaxies, and that one should think in terms of "Central Massive Objects" -- either SBHs or compact stellar nuclei -- that accompany the formation of almost all early-type galaxies and contain a mean fraction ~0.3% of the total bulge mass.
We consider a singlino dominated neutralino in supersymmetric models with an extra U(1). In case both the $\mu$ term and also the $Z^\prime$ mass are generated by the vacuum expectation value of the scalar component of the same singlet chiral superfield, generically the lightest neutralino is not expected to be dominated by the singlino. However, if the gaugino corresponding to the extra U(1) is sufficiently heavy, the lightest neutralino can be dominated by the singlino and still satisfy the constraints resulting from the $Z^\prime$ phenomenology. We assume a supersymmetry breaking scenario in which the extra U(1) gaugino can be much heavier than other gauginos. In that framework we show that the singlino dominated lightest neutralino may be a good candidate for dark matter in a parameter space where various phenomenological constraints are satisfied.
We study whether a dominant contribution to neutrinoless double beta decay coming from extra heavy degrees of freedom, introduced to generate the light neutrino masses, can dominate over the light neutrino contribution. It has been shown that this may occur at tree-level if the light neutrino contribution partially cancels out. Here we focus on this case, specifically in the context of type-I seesaw models paying special attention to the one-loop corrections to light neutrino masses, their contribution to the process and correlation with the heavy sector. We perform a general analysis without restricting the study to any particular region of the parameter space, although interesting limits associated with inverse and extended seesawlike models are discussed in more detail. It turns out that the heavy neutrinos can dominate the process only in those limits. For the inverse seesaw limit, we find a very constrained allowed region of the parameter space, with heavy neutrino masses around 5 GeV. The extended seesaw case allows for a larger region, but in general, a hierarchical spectrum of heavy neutrinos with masses above and below $\sim100$ MeV is required.
Given an odd prime p, we prove a congruence on the p-residue of the Fermat quotient q_p(a) in base a with 0<a<p, which arises from a generalization of the Voronoi congruences and from some other congruences on sums and weighted sums of divided Bernoulli numbers. As an application in the base 2 case, we retrieve a congruence for the first generalized harmonic number of order (p-1)/2, a generalization originally due to Z-H. Sun of a classical congruence known since long for the harmonic number of order (p-1)/2 as a special case of the Lerch formula. We find a sharpening of the Voronoi congruences which is different from the one of W. Johnson and which is more computationally efficient. We prove an additional related congruence, which specialized to base 2 allows to retrieve several congruences that were originally due to E. Lehmer.
We derive and analyze Noether charges associated with the diffeomorphism invariance for the constrained SO(2,3) BF theory. This result generalizes the Wald approach to the case of the first order gravity with a negative cosmological constant, the Holst modification and topological terms (Nieh-Yan, Euler, and Pontryagin). We show that differentiability of the action is automatically implemented by the the structure of the constrained BF model. Finally, we calculate the AdS--Schwarzschild black hole entropy from the Noether charge and we find that, unexpectedly, it does not depend on the Immirzi parameter.
Autonomous agents interacting with the real world need to learn new concepts efficiently and reliably. This requires learning in a low-data regime, which is a highly challenging problem. We address this task by introducing a fast optimization-based meta-learning method for few-shot classification. It consists of an embedding network, providing a general representation of the image, and a base learner module. The latter learns a linear classifier during the inference through an unrolled optimization procedure. We design an inner learning objective composed of (i) a robust classification loss on the support set and (ii) an entropy loss, allowing transductive learning from unlabeled query samples. By employing an efficient initialization module and a Steepest Descent based optimization algorithm, our base learner predicts a powerful classifier within only a few iterations. Further, our strategy enables important aspects of the base learner objective to be learned during meta-training. To the best of our knowledge, this work is the first to integrate both induction and transduction into the base learner in an optimization-based meta-learning framework. We perform a comprehensive experimental analysis, demonstrating the speed and effectiveness of our approach on four few-shot classification datasets. The Code is available at \href{https://github.com/4rdhendu/FIML}{\textcolor{blue}{https://github.com/4rdhendu/FIML}}.
We are interested in the long time asymptotic behavoir of solutions to the scalar Zakharov system \[ i u_{t} + \Delta u = nu,\] \[n_{tt} - \Delta n= \Delta |u|^2\] and the Klein-Gordon Zakharov system \[ u_{tt} - \Delta u + u = - nu,\] \[ n_{tt} - \Delta n= \Delta |u|^2\] in one dimension of space. For these two systems, we give two results proving decay of solutions for initial data in the energy space. The first result deals with decay over compact intervals asuming smallness and parity conditions ($u$ odd). The second result proves decay in far field regions along curves for solutions whose growth can be dominated by an increasing $C^1$ function. No smallness condition is needed to prove this last result for the Zakharov system. We argue relying on the use of suitable virial identities appropiate for the equations and follow the technics of Kowalczyk-Martel-Mu\~noz and Mu\~noz-Ponce-Saut.
We present a detailed methodology for extracting the full set of Newman-Penrose Weyl scalars from numerically generated spacetimes without requiring a tetrad that is completely orthonormal or perfectly aligned to the principal null directions. We also describe how to implement an extrapolation technique for computing the Weyl scalars' contribution at asymptotic null infinity in postprocessing. These methods have been used to produce $\Psi_4$ and $h$ waveforms for the Simulating eXtreme Spacetimes (SXS) waveform catalog and now have been expanded to produce the entire set of Weyl scalars. These new waveform quantities are critical for the future of gravitational wave astronomy in order to understand the finite-amplitude gauge differences that can occur in numerical waveforms. We also present a new analysis of the accuracy of waveforms produced by the Spectral Einstein Code. While ultimately we expect Cauchy characteristic extraction to yield more accurate waveforms, the extraction techniques described here are far easier to implement and have already proven to be a viable way to produce production-level waveforms that can meet the demands of current gravitational-wave detectors.
We present the panchromatic spectral energy distributions (SEDs) of the Local Volume Legacy (LVL) survey which consists of 258 nearby galaxies ($D<$11 Mpc). The wavelength coverage spans the ultraviolet to the infrared (1500 $\textrm{\AA}$ to 24 $\mu$m) which is utilized to derive global physical properties (i.e., star formation rate, stellar mass, internal extinction due to dust.). With these data, we find color-color relationships and correlated trends between observed and physical properties (i.e., optical magnitudes and dust properties, optical color and specific star formation rate, and ultraviolet-infrared color and metallicity). The SEDs are binned by different galaxy properties to reveal how each property affects the observed shape of these SEDs. In addition, due to the volume-limited nature of LVL, we utilize the dwarf-dominated galaxy sample to test star formation relationships established with higher-mass galaxy samples. We find good agreement with the star-forming "main-sequence" relationship, but find a systematic deviation in the infrared "main-sequence" at low luminosities. This deviation is attributed to suppressed polycyclic aromatic hydrocarbon (PAH) formation in low metallicity environments and/or the destruction of PAHs in more intense radiation fields occurring near a suggested threshold in sSFR at a value of log($sSFR$) $\sim$ $-$10.2.
In this talk, I report on a work done in collaboration with R. Markazi and E.H. Saidi [1].
This submission has been withdrawn by arXiv administrators because it is incomplete and thus violates arXiv policy.
Two $n \times n$ Latin squares $L_1, L_2$ are said to be orthogonal if, for every ordered pair $(x,y)$ of symbols, there are coordinates $(i,j)$ such that $L_1(i,j) = x$ and $L_2(i,j) = y$. A $k$-MOLS is a sequence of $k$ pairwise-orthogonal Latin squares, and the existence and enumeration of these objects has attracted a great deal of attention.   Recent work of Keevash and Luria provides, for all fixed $k$, log-asymptotically tight bounds on the number of $k$-MOLS. To study the situation when $k$ grows with $n$, we bound the number of ways a $k$-MOLS can be extended to a $(k+1)$-MOLS. These bounds are again tight for constant $k$, and allow us to deduce upper bounds on the total number of $k$-MOLS for all $k$. These bounds are close to tight even for $k$ linear in $n$, and readily generalize to the broader class of gerechte designs, which include Sudoku squares.
We present a theory of phonon-assisted optical two-magnon absorption in two-leg spin-ladders. Based on the strong intra-rung-coupling limit we show that collective excitations of total spin S=0, 1 and 2 exist outside of the two-magnon continuum. It is demonstrated that the singlet collective state has a clear signature in the optical spectrum.
Gas-liquid criticality in the ultrasoft restricted primitive model (URPM) of polyelectrolytes is studied using the collective variables-based theory. For the model, an effective Hamiltonian is derived and explicit expressions for all the coefficients are found in a one-loop approximation. Based on this Hamiltonian, the phase and critical behaviour is analysed. Our results provide evidence that the nature of the gas-liquid criticality in the URPM is the same as in the restricted primitive model that includes a hard core.
Breast cancer is one of the leading fatal disease worldwide with high risk control if early discovered. Conventional method for breast screening is x-ray mammography, which is known to be challenging for early detection of cancer lesions. The dense breast structure produced due to the compression process during imaging lead to difficulties to recognize small size abnormalities. Also, inter- and intra-variations of breast tissues lead to significant difficulties to achieve high diagnosis accuracy using hand-crafted features. Deep learning is an emerging machine learning technology that requires a relatively high computation power. Yet, it proved to be very effective in several difficult tasks that requires decision making at the level of human intelligence. In this paper, we develop a new network architecture inspired by the U-net structure that can be used for effective and early detection of breast cancer. Results indicate a high rate of sensitivity and specificity that indicate potential usefulness of the proposed approach in clinical use.