ShantanuT01/DACTYL-Pretraining huggingface dataset:
By introducing a ubiquity property for rectangles, we prove the mass transference principle from rectangles to rectangles, i.e., if a sequence of rectangles forms a ubiquity system (a full measure property), then the limsup set defined by shrinking these rectangles to smaller rectangles has full Hausdorff measure or to say transfer a full measure property to a full Hausdorff measure property for brevity.   The limsup sets generated by balls or generated by rectangles appear at the most fundamental level in Diophantine approximation: one follows from Dirichlet's theorem, the other follows from Minkowski's theorem. So the result sets up a general principle for the Hausdorff measure theory for high dimensional Diophantine approximation which, together with the landmark work of Beresnevich & Velani in 2006 where a transference principle from balls to balls is established, gives a coherent Hausdorff measure theory for metric Diophantine approximation.   The dimensional theory for limsup sets generated by rectangles also underpins the dimensional theory in multiplicative Diophantine approximation where unexpected phenomenon occurs and the usually used methods or even their generalizations fail to work.
The aim of this study is to accurately calculate the rotational period of CS\,Vir by using {\sl STEREO} observations and investigate a possible period variation of the star with the help of all accessible data. The {\sl STEREO} data that cover five-year time interval between 2007 and 2011 are analyzed by means of the Lomb-Scargle and Phase Dispersion Minimization methods. In order to obtain a reliable rotation period and its error value, computational algorithms such as the Levenberg-Marquardt and Monte-Carlo simulation algorithms are applied to the data sets. Thus, the rotation period of CS\,Vir is improved to be 9.29572(12) days by using the five-year of combined data set. Also, the light elements are calculated as $HJD_\mathrm{max} = 2\,454\,715.975(11) + 9_{\cdot}^\mathrm{d}29572(12) \times E + 9_{\cdot}^\mathrm{d}78(1.13) \times 10^{-8} \times E^2$ by means of the extremum times derived from the {\sl STEREO} light curves and archives. Moreover, with this study, a period variation is revealed for the first time, and it is found that the period has lengthened by 0.66(8) s y$^{-1}$, equivalent to 66 seconds per century. Additionally, a time-scale for a possible spin-down is calculated around $\tau_\mathrm{SD} \sim 10^6$ yr. The differential rotation and magnetic braking are thought to be responsible of the mentioned rotational deceleration. It is deduced that the spin-down time-scale of the star is nearly three orders of magnitude shorter than its main-sequence lifetime ($\tau_\mathrm{MS} \sim 10^9$ yr). It is, in return, suggested that the process of increase in the period might be reversible.
Let $P$ be a partially ordered set. We prove that if $n$ is sufficiently large, then there exists a packing $\mathcal{P}$ of copies of $P$ in the Boolean lattice $(2^{[n]},\subset)$ that covers almost every element of $2^{[n]}$: $\mathcal{P}$ might not cover the minimum and maximum of $2^{[n]}$, and at most $|P|-1$ additional points due to divisibility. In particular, if $|P|$ divides $2^{n}-2$, then the truncated Boolean lattice $2^{[n]}-\{\emptyset,[n]\}$ can be partitioned into copies of $P$. This confirms a conjecture of Lonc from 1991.
Recently, in a study the X-ray flaring activity of Sgr A* with Chandra and XMM-Newton public observations from 1999 to 2014 and 2014 Swift data, it has been argued that the "bright and very bright" flaring rate raised from 2014 Aug. 31. Thanks to 482ks of observations performed in 2015 with Chandra, XMM-Newton and Swift, we test the significance of this rise of flaring rate and determine the threshold of unabsorbed flare flux or fluence leading to any flaring-rate change. The mean unabsorbed fluxes of the 107 flares detected in the 1999-2015 observations are consistently computed from the extracted spectra and calibration files, assuming the same spectral parameters. We construct the observed flare fluxes and durations distribution for the XMM-Newton and Chandra flares and correct it from the detection biases to estimate the intrinsic distribution from which we determine the average flare detection efficiency for each observation. We apply the BB algorithm on the flare arrival times corrected from the corresponding efficiency. We confirm a constant overall flaring rate in 1999-2015 and a rise in the flaring rate for the most luminous/energetic flares from 2014 Aug. 31 (4 months after the passage of the DSO/G2 close to Sgr A*). We also identify a decay of the flaring rate for the less luminous and less energetic flares from 2013 Aug. and Nov., respectively (10 and 7 months before the pericenter of the DSO/G2). The decay of the faint flaring rate is difficult to explain by the tidal disruption of the DSO/G2, whose stellar nature is now well established, since it occurred well before its pericenter. Moreover, a mass transfer from the DSO/G2 to Sgr A* is not required to produce the rise in the bright flaring rate since the energy saved by the decay of the number of faint flares during a long time period may be later released by several bright flares during a shorter time period. (abridged)
We study the N = 2 gauge theories obtained by engineering the Type IIB superstring on the quasi-homogeneous elements of Arnold's list of bimodal singularities. All these theories have finite BPS chambers and we describe, along the lines of [arXiv:1107.5747], the algebraically obvious ones.   Our results leads to the prediction of 11 new periodic Y-systems, providing additional evidence for the correspondence in between thermodinamical Bethe ansatz periodic Y-systems and N = 2 superconformal theories with a finite BPS chamber whose chiral primaries have dimensions of the form $\mathbb{N}/\ell$.
Within the chiral soliton model the SU(3) breaking collective hamiltonian introduces representation mixing in the baryonic wave functions. We calculate ${\cal{O}}(m_s)$ effects of this mixing on the decay widths of decuplet and antidecuplet baryons. We find importance of the 27-plet admixture in the $\Theta^+$ and $\Xi_{\bar{10}}$ decays. The role of the $1/N_c$ nonleading terms in ${\cal{O}}(m_s)$ transition matrix elements is discussed.
We have performed our spectroscopic and multi-color photometric observations of the recurrent nova U Scorpii at the earliest stage of the 2010 outburst. 0.37 days after the discovery of the outburst, we can see broad and prominent emission lines of Balmer series, He I, N II, N III, O I and Mg II on the spectra. The FWHM of H$\alpha$ line yields an expansion velocity of approximately 6200 km/s. This line also accompanies a blue shifted absorption line (so called P Cygni profile). 1.37 days after the discovery, H$\alpha$ line shows a nearly flat-topped profile in contrast to the previous day. From our multi-color photometry, we can see its rapid decline (one magnitude per day) of the brightness in each color band.
Motion blur from camera shake is a major problem in videos captured by hand-held devices. Unlike single-image deblurring, video-based approaches can take advantage of the abundant information that exists across neighboring frames. As a result the best performing methods rely on aligning nearby frames. However, aligning images is a computationally expensive and fragile procedure, and methods that aggregate information must therefore be able to identify which regions have been accurately aligned and which have not, a task which requires high level scene understanding. In this work, we introduce a deep learning solution to video deblurring, where a CNN is trained end-to-end to learn how to accumulate information across frames. To train this network, we collected a dataset of real videos recorded with a high framerate camera, which we use to generate synthetic motion blur for supervision. We show that the features learned from this dataset extend to deblurring motion blur that arises due to camera shake in a wide range of videos, and compare the quality of results to a number of other baselines.
Using the local spin-density approximation (LSDA) and the (non self-consistent) GW approach, the (quasi-particle) band structure is calculated for MnTe in zinc-blende geometry. Different parameters characterizing the electronic structure are computed for an antiferromagnetic and the ferromagnetic phase and compared with the experiment. The strong Hubbard-type repulsion on the Mn-3d orbitals and the p-d hybridization are seen to be responsible for substantial defects found in the LSDA picture. It is discussed to which extent these can be improved upon by means of the GW approach.
We define a scheme for labelling and ordering integral ideals of number fields, including prime ideals as a special case. The order we define depends only on the choice of a monic irreducible integral defining polynomial for each field $K$, and we start by defining for each field its unique reduced defining polynomial, after Belabas. We define a total order on the set of prime ideals of $K$ and then extend this to a total order on the set of all nonzero integral ideals of $K$. This order allows us to give a unique label of the form $N.i$, where $N$ is its norm and $i$ is the index of the ideal in the ordered list of all ideals of norm $N$. Our ideal labelling scheme has several nice properties: for a given norm, prime ideals always appear first, and given the factorisation of the norm, the bijection between ideals of norm $N$ and labels is computable in polynomial time.   Our motivation for this is to have a well-defined and concise way to sort and label ideals for use in databases such as the LMFDB. We have implemented algorithms which realise this scheme, in Sage, Magma and Pari.
We prove that the sum of the series $\sum_{n=0}^{\infty}\, p^{v_p(n!)}$ is a $p$-adic irrational for all primes $p$, where $v_p(n!)$ denotes the exponent of the highest power of $p$ dividing $n!$.
Atomic layer deposition (ALD) provides uniform and conformal thin films that are of interest for a range of applications. To better understand the properties of amorphous ALD films, we need improved understanding of their local atomic structure. Previous work demonstrated measurement of how the local atomic structure of ALD-grown aluminum oxide (AlOx) evolves in operando during growth by employing synchrotron high energy X-ray diffraction (HE-XRD). In this work, we report on efforts to employ electron diffraction pair distribution function (ePDF) measurements using more broadly available transmission electron microscope (TEM) instrumentation to study the atomic structure of amorphous ALD-AlOx. We observe electron beam damage in the ALD-coated samples during ePDF at ambient temperature and successfully mitigate this beam damage using ePDF at cryogenic temperatures (cryo-ePDF). We employ cryo-ePDF and Reverse Monte Carlo (RMC) modeling to obtain structural models of ALD-AlOx coatings formed at a range of deposition temperatures from 150-332{\deg}C. From these model structures, we derive structural metrics including stoichiometry, pair distances, and coordination environments in the ALD-AlOx films as a function of deposition temperature. The structural variations we observe with growth temperature are consistent with temperature-dependent changes in the surface hydroxyl density on the growth surface. The sample preparation and cryo-ePDF procedures we report here can be used for routine measurement of ALD-grown amorphous thin films to improve our understanding of the atomic structure of these materials, establish structure-property relationships, and help accelerate the timescale for the application of ALD to address technological needs.
We study the problem of test-particle motion in the Nonsymmetric Gravitational Theory (NGT) assuming the four-velocity of the particle is parallel-transported along the trajectory. The predicted motion is studied on a static, spherically symmetric background field, with particular attention paid to radial and circular motions. Interestingly, it is found that the proper time taken to travel between any two non-zero radial positions is finite. It is also found that circular orbits can be supported at lower radii than in General Relativity for certain forms of motion.   We present three interactions which could be used as alternate methods for coupling a test-particle to the antisymmetric components of the NGT field. One of these takes the form of a Yukawa force in the weak-field limit of a static, spherically symmetric field, which could lead to interesting phenomenology.
The Color Glass Condensate is a theory of the dynamical properties of partons in the Regge limit of QCD: x_{\rm Bj}\to 0$, $Q^2 >> \Lambda_{\rm QCD}^2={\rm fixed} and the center of mass energy squared s\to \infty. We provide a brief introduction to the theoretical ideas underlying the Color Glass Condensate and discuss the application of these ideas to high energy scattering in QCD.
Scale-space representation has been popular in computer vision community due to its theoretical foundation. The motivation for generating a scale-space representation of a given data set originates from the basic observation that real-world objects are composed of different structures at different scales. Hence, it's reasonable to consider learning features with image pyramids generated by smoothing and down-sampling operations. In this paper we propose Laplacian pyramid auto-encoders, a straightforward modification of the deep convolutional auto-encoder architecture, for unsupervised representation learning. The method uses multiple encoding-decoding sub-networks within a Laplacian pyramid framework to reconstruct the original image and the low pass filtered images. The last layer of each encoding sub-network also connects to an encoding layer of the sub-network in the next level, which aims to reverse the process of Laplacian pyramid generation. Experimental results showed that Laplacian pyramid benefited the classification and reconstruction performance of deep auto-encoder approaches, and batch normalization is critical to get deep auto-encoders approaches to begin learning.
We have studied the reversal time of the magnetisation in two dimensional Ising ferromagnet in the presence of externally applied uniform magnetic field using Monte Carlo simulation based on Metropolis single spin flip algorithm. Then we have investigated the change in reversal time due to the presence of quenched random field in addition to the uniform magnetic field. We report the results of statistical distribution of reversal times in the presence of three different types of the distributions (namely, uniform, bimodal and normal) of random fields and compared the results with those obtained for uniform field only. We have observed that the reversal time decreases due to the presence of any kind (of distribution) of the random fields. The metastable volume fraction is observed to follow the Avrami's law. Dependence of reversal times on temperature and different widths of the distributions of random fields are also reported. We have also checked whether the system obeyed Becker-Doring theory of classical nucleation in presence of additional random field and tried to investigate the range of the width of the distribution of random field. For larger width of the distribution of random field, the system fails to show the reversal via the nucleation of a single droplet (for small values of uniform field only). The possible reason is analysed.
We compute the semi-classical quantum amplitude to go from an initial spherically symmetric bosonic matter and gravitational field configuration to a final radiation configuration, corresponding to the relic Hawking radiation from a non-rotating, chargeless black hole which evaporates completely. This is obtained via the classical action integral which is solely a boundary term. On discretising the classical action, the quantum amplitude can be expressed in terms of generalised coherent states of the harmonic oscillator. A squeezed-state representation is obtained by complexifying the proper time separation T at spatial infinity between the initial and final space-like hypersurfaces. Such a procedure is deemed necessary as the two-surface problem for Dirichlet boundary data and wave-like perturbations is not well posed. We find that infinitesimal rotation into the lower complex T plane is equivalent to a highly-squeezed final state for the relic radiation, similar to the relic gravitational-wave background in cosmology. This final state is a pure state, and so the unpredictability associated with the final momentarily-naked singularity is avoided. The cosmological analogy is the tunnelling from an initial smooth Euclidean or timeless state to a classical universe. The high-squeezing limit corresponds to a final state of the Hawking flux which is indistinguishable from a stochastic collection of standing waves. The phases conjugate to the field amplitudes are squeezed to discrete values. We also discuss the entropy of the final radiation in the high-squeezing limit.
We extend some classical results dealing with boundary Harnack inequatilities to a class of quasilinear elliptic equations and derive some new estimates for solutions of such equations with an isolated singularity on the boundary of a domain.
The Density Dependent Relativistic Hadron Field (DDRH) theory, previously introduced and applied to isospin nuclei, is extended to hypernuclei by including the octet hyperons. Infinite matter Dirac-Brueckner theory for octet baryons and the derivation of in-medium DDRH baryon-meson vertices is discussed. From the properties of Dirac-Brueckner interactions it is found that hyperon and nucleon self-energies and vertices are related by the ratios of free space coupling constants. This leads to simple scaling laws for the in-medium hyperon and nucleon vertices. The model is applied in relativistic DDRH mean-field calculations to singl$\Lambda nuclei. Free space N-Lambda T-matrix results are used for the scalar vertex. As the only free parameter the hyperon vector vertex scaling factor is adjusted to a selected set of hypernuclear data. Spectroscopic data of single Lambda hypernuclei over the full mass range are well described. The reduced Lambda spin-orbit splitting is reproduced and found to be related closely the medium dependence of scalar and vector interactions.
Spectroscopic observations of a sample of 42 flat-spectrum radio sources from the Cosmic Lens All-Sky Survey (CLASS) have yielded a mean redshift of $<z> = 1.27$ with an RMS spread of 0.95, at a completeness level of 64%. The sample consists of sources with a 5-GHz flux density of 25-50 mJy, making it the faintest flat-spectrum radio sample for which the redshift distribution has been studied. The spectra, obtained with the Willam Herschel Telescope (WHT), consist mainly of broad-line quasars at $z>1$ and narrow-line galaxies at $z<0.5$. Though the mean redshift of flat-spectrum radio sources exhibits little variation over more than two orders of magnitude in radio flux density, there is evidence for a decreasing fraction of quasars at weaker flux levels. In this paper we present the results of our spectroscopic observations, and discuss the implications for constraining cosmological parameters with statistical analyses of the CLASS survey.
We construct effective hydrodynamics for composite particles in (2+1) dimensions carrying a magnetic flux by employing a holographic approach. The hydrodynamics is obtained by perturbation of the dyonic black brane solutions in the derivative expansion. We introduce a consistent way to avoid mixing of different orders in the expansion. Thanks to this method, it is possible to take the strong external magnetic field limit in the dual field theory. To compare our result with those for a composite particle system, we study several cases that correspond to special solutions of Einstein's equation and Maxwell's equations.
We investigate transport properties of the junctions in which the graphene nanoribbon with the zigzag shaped edges consisting of the $N$ legs is sandwiched by the two normal metals by means of recursive Green's function method. The conductance and the transmission probabilities are found to have the remarkable properties depending on the parity of $N$. The singular behaviors close to E=0 with $E$ being the Fermi energy are demonstrated. The channel filtering is shown to occur in the case with $N=$ even.
Change detection is the process of identifying pixelwise differences in bitemporal co-registered images. It is of great significance to Earth observations. Recently, with the emergence of deep learning (DL), the power and feasibility of deep convolutional neural network (CNN)-based methods have been shown in the field of change detection. However, there is still a lack of effective supervision for change feature learning. In this work, a feature constraint change detection network (FCCDN) is proposed. We constrain features both in bitemporal feature extraction and feature fusion. More specifically, we propose a dual encoder-decoder network backbone for the change detection task. At the center of the backbone, we design a nonlocal feature pyramid network to extract and fuse multiscale features. To fuse bitemporal features in a robust way, we build a dense connection-based feature fusion module. Moreover, a self-supervised learning-based strategy is proposed to constrain feature learning. Based on FCCDN, we achieve state-of-the-art performance on two building change detection datasets (LEVIR-CD and WHU). On the LEVIR-CD dataset, we achieve an IoU of 0.8569 and an F1 score of 0.9229. On the WHU dataset, we achieve an IoU of 0.8820 and an F1 score of 0.9373. Moreover, for the first time, the acquisition of accurate bitemporal semantic segmentation results is achieved without using semantic segmentation labels. This is vital for the application of change detection because it saves the cost of labeling.
With the large-scale explosion of images and videos over the internet, efficient hashing methods have been developed to facilitate memory and time efficient retrieval of similar images. However, none of the existing works uses hashing to address texture image retrieval mostly because of the lack of sufficiently large texture image databases. Our work addresses this problem by developing a novel deep learning architecture that generates binary hash codes for input texture images. For this, we first pre-train a Texture Synthesis Network (TSN) which takes a texture patch as input and outputs an enlarged view of the texture by injecting newer texture content. Thus it signifies that the TSN encodes the learnt texture specific information in its intermediate layers. In the next stage, a second network gathers the multi-scale feature representations from the TSN's intermediate layers using channel-wise attention, combines them in a progressive manner to a dense continuous representation which is finally converted into a binary hash code with the help of individual and pairwise label information. The new enlarged texture patches also help in data augmentation to alleviate the problem of insufficient texture data and are used to train the second stage of the network. Experiments on three public texture image retrieval datasets indicate the superiority of our texture synthesis guided hashing approach over current state-of-the-art methods.
Let K be a complete discrete valuation field of mixed characteristic (0,p) with perfect residue field. Let (\pi_n)_{n\ge 0} be a system of p-power roots of a uniformizer \pi=\pi_0 of K with \pi^p_{n+1}=\pi_n, and define G_s (resp.\ G_{\infty}) the absolute Galois group of K(\pi_s) (resp.\ K_{\infty}:=\bigcup_{n\ge 0} K(\pi_n)). In this paper, we study G_s-equivatiantness properties of G_{\infty}-equivariant homomorphisms between torsion (potentially) crystalline representations