ShantanuT01/DACTYL-Pretraining huggingface dataset:
This work is a companion paper of Gamboa, Nagel, Rouault (J. Funct. Anal. 2016). We continue to explore the connections between large deviations for random objects issued from random matrix theory and sum rules. Here, we are concerned essentially with measures on the unit circle whose support is an arc that is possibly proper. We particularly focus on two matrix models. The first one is the Gross-Witten ensemble. In the gapped regime we give a probabilistic interpretation of a Simon sum rule. The second matrix model is the Hua-Pickrell ensemble. Unlike the Gross-Witten ensemble the potential is here infinite at one point. Surprisingly, but as in the above mentioned paper, we obtain a completely new sum rule for the deviation to the equilibrium measure of the Hua-Pickrell ensemble. The extension to matrix measures is also studied.
Existing approaches for fine-grained visual recognition focus on learning marginal region-based representations while neglecting the spatial and scale misalignments, leading to inferior performance. In this paper, we propose the spatial-scale aligned network (SSANET) and implicitly address misalignments during the recognition process. Especially, SSANET consists of 1) a self-supervised proposal mining formula with Morphological Alignment Constraints; 2) a discriminative scale mining (DSM) module, which exploits the feature pyramid via a circulant matrix, and provides the Fourier solver for fast scale alignments; 3) an oriented pooling (OP) module, that performs the pooling operation in several pre-defined orientations. Each orientation defines one kind of spatial alignment, and the network automatically determines which is the optimal alignments through learning. With the proposed two modules, our algorithm can automatically determine the accurate local proposal regions and generate more robust target representations being invariant to various appearance variances. Extensive experiments verify that SSANET is competent at learning better spatial-scale invariant target representations, yielding superior performance on the fine-grained recognition task on several benchmarks.
We give a representation of the classical theory of multiplicative arithmetic functions (MF)in the ring of symmetric polynomials. The basis of the ring of symmetric polynomials that we use is the isobaric basis, a basis especially sensitive to the combinatorics of partitions of the integers. The representing elements are recursive sequences of Schur polynomials evaluated at subrings of the complex numbers. The multiplicative arithmetic functions are units in the Dirichlet ring of arithmetic functions, and their properties can be described locally, that is, at each prime number $p$. Our representation is, hence, a local representation. One such representing sequence is the sequence of generalized Fibonacci polynomials. In general the sequences consist of Schur-hook polynomials. This representation enables us to clarify and generalize classical results, e.g., the Busche-Ramanujan identity, as well as to give a richer structural description of the convolution group of multiplicative functions. It is a consequence of the representation that the MF's can be defined in a natural way on the negative powers of the prime $p$.
We study fluctuations of conserved charges including baryon number, electric charge, and strangeness as well as the correlations among these conserved charges in the 2+1 flavor Polyakov--Nambu--Jona-Lasinio model at finite temperature. The calculated results are compared with those obtained from recent lattice calculations performed with an improved staggered fermion action at two values of the lattice cutoff with almost physical up and down quark masses and a physical value for the strange quark mass. We find that our calculated results are well consistent with those obtained in lattice calculations except for some quantitative differences for fluctuations related with strange quarks. Our calculations indicate that there is a pronounced cusp in the ratio of the quartic to quadratic fluctuations of baryon number, i.e. $\chi_{4}^{B}/\chi_{2}^{B}$, at the critical temperature during the phase transition, which confirms that $\chi_{4}^{B}/\chi_{2}^{B}$ is a useful probe of the deconfinement and chiral phase transition.
In this paper, we carry out a study of viable cosmological models in $f(R)$-gravity at the background level. We use observable parameters like $\Omega$ and $\gamma$ to form autonomous system of equations and show that the models under consideration exhibit two different regimes in their time evolution, namely, a phantom phase followed by a quintessence like behavior. We employ statefinder parameters to emphasize a characteristic discriminative signature of these models.
It is pointed out that the concepts and methods introduced by Bachelier and by Mandelbrot to Finance and Economics can be used to examine the fluctuations observed in high-energy hadron production processes. Theoretical arguments and experimental evidences are presented which show that the relative variations of hadron-numbers between successive rapidity intervals are non-Gaussian stable random variables, which exhibit stationarity and scaling. The implications of the obtained results are discussed.
We discuss effects of fragmentation and hard gluon radiation on the signal for the pair production of the lighter scalar top eigenstate $\tilde{t}_1$ at e^+e^- colliders. The main emphasis is on scenarios with small stop--LSP mass splitting, where strong interaction effects can considerably modify kinematical properties of the final state.
We simulate scattering of electrons by a chain of antiferromagnetically coupled quantum Heisenberg spins, to analyze spin-transfer effects not described by the classical models of magnetism. Our simulations demonstrate efficient excitation of dynamical states that would be forbidden by the semiclassical symmetries, such as generation of multiple magnetic excitation quanta by a single electron. Furthermore, quantum interference of spin wavefunctions enables generation of magnetization dynamics with amplitudes exceeding the transferred magnetic moment. The efficiency of excitation is almost independent of the electron spin polarization, and is governed mainly by the transfer of energy. Non-classical spin transfer may thus enable efficient electronic control of antiferromagnets not limited by the classical constraints.
We report on a combined experimental and theoretical investigation into the normal modes of an all-fiber coupled cavity-quantum-electrodynamics system. The interaction between atomic ensembles and photons in the same cavities, and that between the photons in these cavities and the photons in the fiber connecting these cavities, generates five non-degenerate normal modes. We demonstrate our ability to excite each normal mode individually. We study particularly the `cavity dark mode', in which the two cavities coupled directly to the atoms do not exhibit photonic excitation. Through the observation of this mode, we demonstrate remote excitation and nonlocal saturation of atoms.
We employ meson-nucleon scattering data to deduce the properties of the low-mass vector mesons in nuclear matter, and present results for the $\rho$ and $\omega$ in-medium spectral functions. The corresponding thermal emission rate for lepton pairs is also discussed.
Resonant activation is one of classical effects demonstrating constructive role of noise. In resonant activation cooperative action of barrier modulation process and noise lead to the optimal escape kinetics as measured by the mean first passage time. Resonant activation has been observed in versatilities of systems for various types of barrier modulation processes and noise types. Here, we show that resonant activation is also observed in 2D and 3D systems driven by bi-variate and tri-variate $\alpha$-stable noises. Strength of resonant activation is sensitive to the exact value of the noise parameters. In particular, the decrease in the stability index $\alpha$ results in the disappearance of the resonant activation.
The two-nucleon spectral function in nuclear matter is studied using Correlated Basis Function perturbation theory, including central and tensor correlations produceded by a realistic hamiltonian. The factorization property of the two-nucleon momentum distribution into the product of the two single nucleon distributions shows up in an analogous property of the spectral function. The correlated model yields a two-hole contribution quenched whith respect to Fermi gas model, while the peaks acquire a quasiparticle width that vanishes as the two momenta approach $k_F$. In addition, three-hole one-particle and more complicated intermediate states give rise to a background, spread out in energy and absent in the uncorrelated models. The possible connections with one- and two-nucleon emission processes are briefly discussed.
The stability of the excitonic condensation at low temperature driven by a coupling of electrons to vibrational degrees of freedom in semimetal two-dimensional electronic system is discussed. In the framework of the unrestricted Hartree-Fock approximation, we derive a set of equations to determine both the excitonic condensate order parameter and lattice displacement self-consistently. By lowering temperature we find out a semimetal-insulator transition in the system if the coupling is large enough. The insulating state typifies an excitonic condensation accompanied by a finite lattice distortion. Increasing temperature, both excitonic condensate order parameter and the lattice distortion decrease and then disappear in the same manner. Microscopic analysis in momentum space strongly specifies that the excitonic condensate driven by the lattice distortion favours the BCS type.
Video deblurring is still an unsolved problem due to the challenging spatio-temporal modeling process. While existing convolutional neural network-based methods show a limited capacity for effective spatial and temporal modeling for video deblurring. This paper presents VDTR, an effective Transformer-based model that makes the first attempt to adapt Transformer for video deblurring. VDTR exploits the superior long-range and relation modeling capabilities of Transformer for both spatial and temporal modeling. However, it is challenging to design an appropriate Transformer-based model for video deblurring due to the complicated non-uniform blurs, misalignment across multiple frames and the high computational costs for high-resolution spatial modeling. To address these problems, VDTR advocates performing attention within non-overlapping windows and exploiting the hierarchical structure for long-range dependencies modeling. For frame-level spatial modeling, we propose an encoder-decoder Transformer that utilizes multi-scale features for deblurring. For multi-frame temporal modeling, we adapt Transformer to fuse multiple spatial features efficiently. Compared with CNN-based methods, the proposed method achieves highly competitive results on both synthetic and real-world video deblurring benchmarks, including DVD, GOPRO, REDS and BSD. We hope such a Transformer-based architecture can serve as a powerful alternative baseline for video deblurring and other video restoration tasks. The source code will be available at \url{https://github.com/ljzycmd/VDTR}.
Over the last few years, optical, mid-infrared and X-ray surveys have brought to light a significant number of candidate obscured AGN and, among them, many Type 2 quasars, the long-sought after "big cousins'' of local Seyfert 2 galaxies. However, despite the large amount of multi-wavelength data currently available, a proper census and a panchromatic view of the obscured AGN/quasar population are still missing, mainly due to observational limitations. Here we provide a review of recent results on the identification of obscured AGN, focusing primarily on the population of Type 2 quasars selected in the optical band from the Sloan Digital Sky Survey.
We show that the heating effect of spontaneous wave-function collapse models implies an experimentally significant increment $\Delta T$ of equilibrium temperature in a mechanical oscillator. The obtained form $\Delta T$ is linear in the oscillator's relaxation time $\tau$ and independent of the mass. The oscillator can be in a classical thermal state, the effect $\Delta T$ is classical for a wide range of frequencies and quality factors. We note that the test of $\Delta T$ does not necessitate quantum state monitoring but tomography. In both gravity-related (DP) and continuous spontaneous localization (CSL) models the strong-effect edge of their parameter range can be challenged in existing experiments on classical oscillators. For the CSL theory, the conjectured highest collapse rate parameter values become immediately constrained by evidences from current experiments on extreme slow-ring-down oscillators.
We prove that a Fano variety (with arbitrary singularities) of dimension $n$ in positive characteristic is isomorphic to $\mathbb{P}^n$ if the Seshadri constant of the anti-canonical divisor at some smooth point is greater than $n$ and classify Fano varieties whose anti-canonical divisors have Seshadri constants $n$. In characteristic $p>5$ and dimension $3$, we also show that Fano varieties $X$ with Seshadri constants $\epsilon(-K_X,x)>2+\epsilon$ at some smooth point $x\in X$ (for some fixed $\epsilon>0$) have bounded anti-canonical degrees.
At the LHC Multiple Parton Interactions will represent an important feature of the minimum bias and of the underlying event and will give important contributions in many channels of interest for the search of new physics. Different numbers of multiple collision may contribute to the production of a given final state and one should expect important interference effects in the regime where different contributions have similar rates. We show, on the contrary, that, once multiple parton interactions are identified by their different topologies, terms with different numbers of multiple parton interactions do not interfere in the final cross section.
We extend the use of random evolving sets to time-varying conductance models and utilize it to provide tight heat kernel upper bounds. It yields the transience of any uniformly lazy random walk, on Z^d, d>=3, equipped with uniformly bounded above and below, independently time-varying edge conductances, of (effectively) non-decreasing in time vertex conductances (i.e. reversing measure), thereby affirming part of [ABGK, Conj. 7.1].
We evaluate the large momentum transfer $J/\psi$ photoproduction with rapidity gaps in ultraperipheral proton-ion collisions at the LHC which provides an effective method of probing dynamics of large t elastic hard QCD Pomeron interactions. It is shown that the experimental studies of this process would allow to investigate the energy dependence of cross section of elastic scattering of a small $c\bar c$ dipole off the gluon over a wide range of invariant energies 10^3 < s_{c\bar c - gluon} < 10^6 GeV^2. The accessible energy range exceeds the one reached in \gamma p at HERA by a factor of 10 and allows the kinematic cuts which improve greatly sensitivity to the Pomeron dynamics as compared to the HERA measurements. The cross section is expected to change by a factor \ge 20 throughout this interval and our estimates predict quite reasonable counting rates for this process with the several of the LHC detectors.
We consider a Stochastic Differential Equation driven by a L\'evy process whose L\'evy measure satisfy a tempered stable domination. We study how a perturbation of the coefficients reflects on the density of the solution. We quantify the distance between the densities in term of the proximity of the coefficients. This extend to the stable case the works of [KKM15], where the noise is Gaussian.
{\bf Background} Deuteron induced reactions are widely used to probe nuclear structure and astrophysical information. Those (d,p) reactions may be viewed as three-body reactions and described with Faddeev techniques.   {\bf Purpose} Faddeev-AGS equations in momentum space have a long tradition of utilizing separable interactions in order to arrive at sets of coupled integral equations in one variable. However, it needs to be demonstrated that observables calculated based on separable interactions agree exactly with those based on nonseparable forces.   {\bf Methods} Momentum space AGS equations are solved with separable and nonseparable forces as coupled integral equations.   {\bf Results} Deuteron-alpha scattering is calculated via momentum space AGS equations using the CD-Bonn neutron-proton force and a Woods-Saxon type neutron(proton)-$^4$He force, for which the Pauli-forbidden S-wave bound state is projected out. Elastic as well as breakup observables are calculated and compared to results in which the interactions in the two-body sub-systems are represented by separable interactions derived in the Ernst-Shakin-Thaler (EST) framework. {\bf Conclusions} We find that the calculations based on the separable representation of the interactions and the original interactions give results that are in excellent agreement. Specifically, integrated cross sections and angular distributions for elastic scattering agree within $\approx$ 1\%, which is well below typical experimental errors. In addition, the five-fold differential cross sections corresponding to breakup of the deuteron agree extremely well.
Embedded clusters are groups of stars which have not dispersed yet the residual of the parental cloud where they were born so getting precise distances and properties of these groups turns out to be an essential task. We present results for five embedded clusters: [DBS2003]5, [DBS2003]60, [DBS2003]98, [DBS2003]116 and [DBS2003]117. Results come from a combination of deep CCD UBVI photometry suitable to identify blue faint stars and infrared information from available surveys. In turn photometry was linked with proper motions and parallaxes from Gaia DR2. Each object was treated in a multi-space using ASteCA, a code especially designed to perform an automatic data analysis and aimed at providing the fundamental parameters of star groups, in case they compose a real entity.
Berkovich-Uncu have recently proved a companion of the well-known Capparelli's identities as well as refinements of Savage-Sills' new little G\"ollnitz identities. Noticing the connection between their results and Boulet's earlier four-parameter partition generating functions, we discover a new class of partitions, called $k$-strict partitions, to generalize their results. By applying both horizontal and vertical dissections of Ferrers' diagrams with appropriate labellings, we provide a unified combinatorial treatment of their results and shed more lights on the intriguing conditions of their companion to Capparelli's identities.
We analyze a mean-field model of electrons with pure forward scattering interactions on a square lattice which exhibits spontaneous Fermi surface symmetry breaking with a d-wave order parameter: the surface expands along the kx-axis and shrinks along the ky-axis (or vice versa). The symmetry-broken phase is stabilized below a dome-shaped transition line Tc(mu), with a maximal Tc near van Hove filling. The phase transition is usually first order at the edges of the transition line, and always second order around its center. The d-wave compressibility of the Fermi surface is however strongly enhanced even near the first order transition down to zero temperature. In the weak coupling limit the phase diagram is fully determined by a single non-universal energy scale, and hence dimensionless ratios of different characteristic quantities are universal. Adding a uniform repulsion to the forward scattering interaction, the two tricritical points at the ends of the second order transition line are shifted to lower temperatures. For a particularly favorable choice of hopping and interaction parameters one of the first order edges is replaced completely by a second order transition line, leading to a quantum critical point.
We present F110W (~J) and F160W (~H) observations of ten submillimeter galaxies (SMGs) obtained with the Hubble Space Telescope's (HST's) NICMOS camera. Our targets have optical redshifts in the range 2.20<z<2.81 confirmed by millimeter CO or mid-IR spectroscopy, guaranteeing that the two bands sample the rest-frame optical with the Balmer break falling between them. Eight of ten are detected in both bands, while two are detected in F160W only. We study their F160W morphologies, applying a maximum-deblending detection algorithm to distinguish multiple- from single-component configurations, leading to reassessments for several objects. Based on our NICMOS imaging and/or previous dynamical evidence we identify five SMGs as multiple sources, which we interpret as merging systems. Additionally, we calculate morphological parameters asymmetry (A) and Gini coefficient (G); thanks to our sample's limited redshift range we recover the trend that multiple-component, merger-like morphologies are reflected in higher asymmetries. We analyze the stellar populations of nine objects with F110W/F160W photometry, using archival HST optical data when available. For multiple systems, we are able to model the individual components that build up an SMG. With the available data we cannot discriminate among star formation histories, but we constrain stellar masses and mass ratios for merger-like SMG systems, obtaining a mean log(M_*/M_sun)=10.9+/-0.2 for our full sample, with individual values log(M_*/M_sun)~9.6-11.8. The morphologies and mass ratios of the least and most massive systems match the predictions of the major-merger and cold accretion SMG formation scenarios, respectively, suggesting that both channels may have a role in the population's origin.
Time-series \emph{VI} CCD photometry of the globular cluster NGC 1261 is employed to study its variable star population. A membership analysis of most variables based on Gaia~DR2 proper motions and colours, was performed prior to the estimation of the mean cluster distance and metallicity. For the member RR Lyrae, their light curves were Fourier decomposed to calculate their individual values of distance, [Fe/H], radius and mass. The $I$-band P-L for RR Lyrae stars was also employed. Our best estimates of the metallicity and distance of this Oo I cluster are [Fe/H]$_{\rm ZW}$=$-1.42 \pm 0.05$ dex and $d=17.2 \pm 0.4$ kpc. No mixture of fundamental and first overtone RR Lyrae stars in the either-or or bimodal region is seen in this cluster, as it seems to be the rule for Oo~I clusters with a red horizontal branch. A multi-approach search in a region of about 10$\times$10 arcmin$^2$ around the cluster revealed no new variable stars within the limitations of our CCD photometry.