ShantanuT01/DACTYL-Pretraining huggingface dataset:
Traditional patch-based sparse representation modeling of natural images usually suffer from two problems. First, it has to solve a large-scale optimization problem with high computational complexity in dictionary learning. Second, each patch is considered independently in dictionary learning and sparse coding, which ignores the relationship among patches, resulting in inaccurate sparse coding coefficients. In this paper, instead of using patch as the basic unit of sparse representation, we exploit the concept of group as the basic unit of sparse representation, which is composed of nonlocal patches with similar structures, and establish a novel sparse representation modeling of natural images, called group-based sparse representation (GSR). The proposed GSR is able to sparsely represent natural images in the domain of group, which enforces the intrinsic local sparsity and nonlocal self-similarity of images simultaneously in a unified framework. Moreover, an effective self-adaptive dictionary learning method for each group with low complexity is designed, rather than dictionary learning from natural images. To make GSR tractable and robust, a split Bregman based technique is developed to solve the proposed GSR-driven minimization problem for image restoration efficiently. Extensive experiments on image inpainting, image deblurring and image compressive sensing recovery manifest that the proposed GSR modeling outperforms many current state-of-the-art schemes in both PSNR and visual perception.
We use molecular dynamics simulations of the SPC-E model of liquid water to derive probability distributions for water density fluctuations in probe volumes of different shapes and sizes, both in the bulk as well as near hydrophobic and hydrophilic surfaces. To obtain our results, we introduce a biased sampling of coarse-grained densities, which in turn biases the actual solvent density. The technique is easily combined with molecular dynamics integration algorithms. Our principal result is that the probability for density fluctuations of water near a hydrophobic surface, with or without surface-water attractions, is akin to density fluctuations at the water-vapor interface. Specifically, the probability of density depletion near the surface is significantly larger than that in bulk. In contrast, we find that the statistics of water density fluctuations near a model hydrophilic surface are similar to that in the bulk.
I study the dynamics of the violation of the CHSH inequality for two qubits interacting with a common zero-temperature non-Markovian environment. I demonstrate sudden violation of the inequality for two qubits initially prepared in a factorized state. Due to the strong coupling between the qubits and the reservoir, the dynamics is characterized by numerous sharp revivals. Furthermore I focus on a more realistic physical system in which the spontaneous emission for the qubits is taken into account. When including spontaneous emission even for small decay parameters, revivals in the violation are heavily damped out. If the decay rates exceed a certain threshold, the inequality turns out to be always satisfied.
We prove the following. If $f$ is a harmonic quasiconformal mapping between the unit ball in $\mathbb{R}^n$ and a spatial domain with $C^{1,\alpha}$ boundary, then $f$ is Lipschitz continuous in $B$. This generalizes some known results for $n=2$ and improves some others in higher dimensional case.
We study the gravitational waves in the 10-dimensional target space of the superstring theory. Some of these waves have unbroken supersymmetries. They consist of Brinkmann metric and of a 2-form field. Sigma-model duality is applied to such waves. The corresponding solutions we call dual partners of gravitational waves, or dual waves. Some of these dual waves upon Kaluza-Klein dimensional reduction to 4 dimensions become equivalent to the conformo-stationary solutions of axion-dilaton gravity. Such solutions include dilaton extreme black holes, axion-dilaton Israel-Werner-Perjes-type spacetimes and extreme charged axion-dilaton Taub-Nut solutions. The unbroken supersymmetry of the gravitational waves transfers to the unbroken supersymmetry of axion-dilaton IWP solutions. More general supersymmetric 4-dimensional configurations derivable from 10-dimensional waves are described.
Using hard x-ray (HX ; $h\nu$ = 5.95 keV) synchrotron photoemission spectroscopy (PES), we study the intrinsic electronic structure of La$_{1-x}$Sr$_x$MnO$_3$ (LSMO) thin films. Comparison of Mn 2$p$ core-levels with Soft x-ray (SX ; $h\nu$ $\sim$ 1000 eV) -PES shows a clear additional well-screened feature only in HX-PES. Take-off-angle dependent data indicate its bulk ($\ge$ 20 {\AA}) character. The doping and temperature dependence track the ferromagnetism and metallicity of the LSMO series. Cluster model calculations including charge transfer from doping induced states show good agreement, confirming this picture of bulk properties reflected in Mn 2$p$ core-levels using HX-PES.
Ideas and techniques from Khare's and Wintenberger's article on the proof of Serre's conjecture for odd conductors are used to establish that for a fixed prime l infinitely many of the groups PSL_2(F_{l^r}) (for r running) occur as Galois groups over the rationals such that the corresponding number fields are unramified outside a set consisting of l, the infinite place and only one other prime.
If dark matter is composed of neutralinos, one of the most exciting prospects for its detection lies in observations of the gamma-ray radiation created in pair annihilations between neutralinos, a process that may contribute significantly to the extragalactic gamma-ray background (EGB) radiation. We here use the high-resolution Millennium-II simulation of cosmic structure formation to produce the first full-sky maps of the expected radiation coming from extragalactic dark matter structures. Our map making procedure takes into account the total gamma-ray luminosity from all haloes and their subhaloes, and includes corrections for unresolved components of the emission as well as an extrapolation to the damping scale limit of neutralinos. Our analysis also includes a proper normalization of the signal according to a specific supersymmetric model based on minimal supergravity. The new simulated maps allow a study of the angular power spectrum of the gamma-ray background from dark matter annihilation, which has distinctive features associated with the nature of the annihilation process and may be detectable in forthcoming observations by the recently launched FERMI satellite. Our results are in broad agreement with analytic models for the gamma-ray background, but they also include higher-order correlations not readily accessible in analytic calculations and, in addition, provide detailed spectral information for each pixel. In particular, we find that difference maps at different energies can reveal cosmic large-scale structure at low and intermediate redshifts. If the intrinsic emission spectrum is characterized by an emission peak, cosmological tomography with gamma ray annihilation radiation is in principle possible.
This note places primary emphasis on improving the asymptotic behavior of a multi-dimensional delayed wave equation in the absence of any displacement term. In the first instance, the delay is assumed to occur in the boundary. Then, invoking a geometric condition BLR on the domain, the exponential convergence of solutions to their equilibrium state is proved. The strategy adopted of the proof is based on an interpolation inequality combined with a resolvent method. In turn, an internal delayed wave equation is considered in the second case, where the domain possesses trapped ray and hence (BLR) geometric condition does not hold. In such a situation polynomial convergence results are established. These finding improve earlier results of Ammari-Chentouf and Phung.
Scanning tunneling microscopy (STM) is a fundamental tool for determination of the surface atomic structure. However, the interpretation of high resolution microscopy images is not straightforward. In this paper we provide a physical insight on how STM images can suggest atomic locations which are distinctively different from the real ones. This effect should be taken into account when interpreting high-resolution STM images obtained on surfaces with directional bonds. It is shown that spurious images are formed in the presence of polarized surface radicals showing a pronounced angle with respect to the surface normal. This issue has been overlooked within the surface science community and often disregarded by experimentalists working with STM. Without loss of generality, we illustrate this effect by the magnification observed for pentamer-like structures on (110), (113) and (331) surfaces of silicon and germanium.
We review some recent results on the equilibrium shapes of charged liquid drops. We show that the natural variational model is ill-posed and how this can be overcome by either restricting the class of competitors or by adding penalizations in the functional. The original contribution of this note is twofold. First, we prove existence of an optimal distribution of charge for a conducting drop subject to an external electric field. Second, we prove that there exists no optimal conducting drop in this setting.
We derive an explicit upper bound for the number of systems of Hecke eigenvalues coming from Siegel modular forms (mod p) of dimension g and level N relatively prime to p. In the special case of elliptic modular forms (g=1), our result agrees with recent work of G. Herrick.
Kondo insulators are predicted to undergo an insulator-to-metal transition under applied magnetic field, yet the extremely high fields required to date have prohibited a comprehensive investigation of the nature of this transition. Here we show that Ce3Bi4Pd3 provides an ideal platform for this investigation, owing to the unusually small magnetic field of B ~ 11 T required to overcome its Kondo insulating gap. Above Bc, we find a magnetic field-induced Fermi liquid state whose characteristic energy scale T_FL collapses near Bc in a manner indicative of a magnetic field-tuned quantum critical point. A direct connection is established with the process of Kondo singlet formation, which yields a broad maximum in the magnetic susceptibility as a function of temperature in weak magnetic fields that evolves progressively into a sharper transition at Bc as T -> 0.
We discuss the problem of counting {\em incidence matrices}, i.e. zero-one matrices with no zero rows or columns. Using different approaches we give three different proofs for the leading asymptotics for the number of matrices with $n$ ones as $n\to\infty$. We also give refined results for the asymptotic number of $i\times j$ incidence matrices with $n$ ones.
We investigate all the brane instanton solutions--an Einstein brane inhabiting at different positions in 5-dimensional negative curvature Einstein bulk. We construct a brane instanton model consisting of a brane with asymmetric bulk along two sides of the brane. And the junction condition of the resulting space-time is analyzed in the frame of induced gravity. In spirits of quantum gravity of path integral formulism we calculate the Euclidean actions on three canonical paths and then compare the Euclidean actions of different instantons per unit 4-volume. We also compare the Euclidean actions per unit 4-volume of instantons consisting of a brane gluing a fixed half with other halves possessing different cosmological constants.
We present the calculation of the electroweak corrections for squark-antisquark pair production at the LHC within the Minimal Supersymmetric Standard Model. Taking into account all possible chirality and light-flavor configurations, we evaluate the NLO EW corrections, which are of O(a_s^2 a), as well as the subleading tree-level contributions of O(a_s a) and O(a^2). Numerical results are presented for several scans in the SUSY parameter space and relevant differential distributions are investigated. The impact of the electroweak corrections is nonnegligible and strongly depends on the chirality configuration of the produced squarks. Our analysis includes a discussion of photon-gluon initiated processes with a focus on the impact of the corresponding large PDF uncertainties.
In the CDM paradigm, the halo mass function is a sensitive probe of the cosmic structure. In observations, halo mass is typically estimated from its relation with other observables. The resulting halo mass function is subject to systematic bias, such as the Eddington bias, due to the scatter or uncertainty in the observable - mass relation. Exact correction for the bias is not easy, as predictions for the observables are typically model-dependent in simulations. In this paper, we point out an interesting feature in the halo mass function of the concordence $\Lambda$CDM model: the total halo mass within each evenly-spaced logarithmic mass bin is approximately the same over a large mass range. We show that this property allows us to construct an almost bias-free halo mass function using only an observable (as a halo mass estimator) and stacked weak lensing measurements as long as the scatter between the true halo mass and the observable-inferred mass has a stable form in logarithmic units. The method is not sensitive to the form of the mass-observable relation. We test the idea using cosmological simulations, and show that the method performs very well for realistic observables.
Ubiquitous graphene is a stricly 2D material representing an ideal adsorbing platform due to its large specific surface area as well as its mechanical strength and resistance to both thermal and chemical stresses. However, graphene as a bulk material has the tendency to form irreversible agglomerates leading to 3D graphitic structures with a significant decrease of the area available for adsorption and no room for gas intercalation. In this paper a novel nanoporous graphite formed by graphtriyne sheets is introduced: its 3D structure is theoretically assessed by means of electronic structure and molecular dynamics computations within the DFT level of theory. It is found that the novel layered carbon allotrope is almost as compact as pristine graphite but the inherent porosity of the 2D graphyne sheets and its relative stacking leads to nanochannels that cross the material and whose sub-nanometer size could allow the diffusion and storage of gas species. A molecular prototype of the nanochannel is used to accurately determine first principles adsorption energies and enthalpies for CO2, N2, H2O and H2 within the pores. The proposed porous graphite presents no significant barrier for gas diffusion and it shows a high propensity for CO2 physisorption with respect to the other relevant components in both pre- and post-combustion gas streams.
An exact study of charge-spin separation, pairing fluctuations and pseudogaps is carried out by combining the analytical eigenvalues of the four-site Hubbard clusters with the grand canonical and canonical ensemble approaches in a multidimensional parameter space of temperature (T), magnetic field (h), on-site interaction (U) and chemical potential. Our results, near the average number of electrons <N>=3, strongly suggest the existence of a critical parameter U_{c}(T) for the localization of electrons and a particle-hole binding (positive) gap at U>U_{c}(T), with a zero temperature quantum critical point, U_{c}(0)=4.584. For U<U_{c}(T), particle-particle pair binding is found with a (positive) pairing gap. The ground state degeneracy is lifted at U>U_c(T) and the cluster becomes a Mott-Hubbard like insulator due to the presence of energy gaps at all (allowed) integer numbers of electrons. In contrast, for U< U_c(T), we find an electron pair binding instability at finite temperature near <N>=3, which manifests a possible pairing mechanism, a precursor to superconductivity in small clusters.   In addition, the resulting phase diagram consisting of charge and spin pseudogaps, antiferromagnetic correlations, hole pairing with competing hole-rich (<N>=2), hole-poor (<N>=4) and magnetic (<N>=3) regions in the ensemble of clusters near 1/8 filling closely resembles the phase diagrams and inhomogeneous phase separation recently found in the family of doped high T_c cuprates.
En utilisant des approximants de Hermite-Pad\'e de fonctions exponentielles, ainsi que des d\'eterminants d'interpolation de Laurent, nous minorons la distance entre un nombre alg\'ebrique et l'exponentielle d'un nombre alg\'ebrique non nul.   -----   We use Hermite-Pad\'e approximants of exponential functions along with Laurent's interpolation determinants to obtain lower bounds for the distance between an algebraic number and the exponential of another non-zero algebraic number.
The generalization to N colors of a recently proposed non unitary two color model for the gravitational interaction in non relativistic quantum mechanics is considered. The N->Infinity limit is proven to be equivalent to the Schroedinger-Newton model, which, though sharing localization properties with the N=2 model, cannot produce decoherence.
We present the first VLBI detection of HCN molecular absorption in the nearby active galactic nucleus NGC 1052. Utilizing the 1 milliarcsecond resolution achieved by the Korean VLBI Network, we have spatially resolved the HCN absorption against a double-sided nuclear jet structure. Two velocity features of HCN absorption are detected significantly at the radial velocity of 1656 and 1719 km/s, redshifted by 149 and 212 km/s with respect to the systemic velocity of the galaxy. The column density of the HCN molecule is estimated to be 10^{15}-10^{16} cm^{-2}, assuming the excitation temperature of 100-230 K. The absorption features show high optical depth localized on the receding jet side, where the free-free absorption occurred due to the circumnuclear torus. The size of the foreground absorbing molecular gas is estimated to be on approximately one-parsec scales, which agrees well with the approximate size of the circumnuclear torus. HCN absorbing gas is likely to be several clumps smaller than 0.1 parsec inside the circumnuclear torus. The redshifted velocities of the HCN absorption features imply that HCN absorbing gas traces ongoing infall motion inside the circumnuclear torus onto the central engine.
A normalized positive operator measure $X\mapsto E(X)$ has the norm-1-property if $\no{E(X)}=1$ whenever $E(X)\ne O$. This property reflects the fact that the measurement outcome probabilities for the values of such observables can be made arbitrary close to one with suitable state preparations. Some general implications of the norm-1-property are investigated. As case studies, localization observables, phase observables, and phase space observables are considered.
This is the first in a series of papers studying the variable stars in Large Magellanic Cloud globular clusters. The primary goal of this series is to better understand how the RR Lyrae stars in Oosterhoff-intermediate systems compare to those in Oosterhoff I/II systems. In this paper we present the results of our new time-series BV photometric study of NGC 1466. A total of 62 variables were identified in the cluster, of which 16 are new discoveries. The variables include 30 RRab stars, 11 RRc's, 8 RRd's, 1 candidate RR Lyrae, 2 long-period variables, 1 potential anomalous Cepheid, and 9 variables of undetermined classification. We present photometric parameters for these variables.   For the RR Lyrae stars physical properties derived from Fourier analysis of their light curves are presented. The RR Lyrae stars were used to determine a reddening-corrected distance modulus of (m-M)0 = 18.43 +/- 0.15. We discuss several different indicators of Oosterhoff type and find NGC 1466 to be an Oosterhoff-intermediate object.
Let A be a standard Borel space, and consider the space A^{\bbN^{(k)}} of A-valued arrays indexed by all size-k subsets of \bbN. This paper concerns random measures on such a space whose laws are invariant under the natural action of permutations of \bbN. The main result is a representation theorem for such `exchangeable' random measures, obtained using the classical representation theorems for exchangeable arrays due to de Finetti, Hoover, Aldous and Kallenberg.   After proving this representation, two applications of exchangeable random measures are given. The first is a short new proof of the Dovbysh-Sudakov Representation Theorem for exchangeable PSD matrices. The second is in the formulation of a natural class of limit objects for dilute mean-field spin glass models, retaining more information than just the limiting Gram-de Finetti matrix used in the study of the Sherrington-Kirkpatrick model.
In these lectures we cover basics of the theory of heights starting with the heights in the projective space, heights of polynomials, and heights of the algebraic curves. We define the minimal height of binary forms and moduli height for algebraic curves and prove that the moduli height of superelliptic curves $\mathcal H (f) \leq c_0 \tilde H (f)$ where $c_0$ is a constant and $\tilde H$ the minimal height of the corresponding binary form. For genus $g=2$ and 3 such constant is explicitly determined. Furthermore, complete lists of curves of genus 2 and genus 3 hyperelliptic curves with height 1 are computed.
We present an extensive study of the two-impurity Kondo problem for spin-1 adatoms on square lattice using an exact canonical transformation to map the problem onto an effective one-dimensional system that can be numerically solved using the density matrix renormalization group method. We provide a simple intuitive picture and identify the different regimes, depending on the distance between the two impurities, Kondo coupling $J_K$, longitudinal anisotropy $D$, and transverse anisotropy $E$. In the isotropic case, two impurities on opposite(same) sublattices have a singlet(triplet) ground state. However, the energy difference between the triplet ground state and the singlet excited state is very small and we expect an effectively four-fold degenerate ground state, i.e., two decoupled impurities. For large enough $J_K$ the impurities are practically uncorrelated forming two independent underscreened states with the conduction electrons, a clear non-perturbative effect. When the impurities are entangled in an RKKY-like state, Kondo correlations persists and the two effects coexist: the impurities are underscreened, and the dangling spin-$1/2$ degrees of freedom are responsible for the inter-impurity entanglement. We analyze the effects of magnetic anisotropy in the development of quasi-classical correlations.
We classify the point objects in the derived category $D(X)$ of a torsor under an abelian variety over a field of characteristic $0$.
The formation history of the Small Magellanic cloud (SMC) is unraveled based on the results of our new chemical evolution models constructed for the SMC, highlighting the observed anomaly in the age-metallicity relation for star clusters in the SMC. We first propose that evidence of a major merger is imprinted in the age-metallicity relation as a dip in [Fe/H]. Our models predict that the major merger with a mass ratio of 1:1 to 1:4 occurred at ~7.5 Gyr ago, with a good reproduction of the abundance distribution function of field stars in the SMC. Furthermore, our models predict a relatively large scatter in [Mg/Fe] for -1.4 < [Fe/H] <-1.1 as a reflection of a looping feature resulting from the temporally inverse progress of chemical enrichment, which can be tested against future observational results. Given that the observed velocity dispersion (~30 km/s) of the SMC is much smaller than that (~160 km/s) of the Galactic halo, our finding strongly implies that the predicted merger event happened in a small group environment that was far from the Galaxy and contained a number of small gas-rich dwarfs comparable to the SMC. This theoretical view is extensively discussed in the framework that considers a connection with the formation history of the Large Magellanic cloud.