ShantanuT01/DACTYL-Pretraining huggingface dataset:
In a recent paper we derived the free energy or partition function of the $N$-state chiral Potts model by using the infinite lattice ``inversion relation'' method, together with a non-obvious extra symmetry. This gave us three recursion relations for the partition function per site $T_{pq}$ of the infinite lattice. Here we use these recursion relations to obtain the full Riemann surface of $T_{pq}$. In terms of the $t_p, t_q$ variables, it consists of an infinite number of Riemann sheets, each sheet corresponding to a point on a $(2N-1)$-dimensional lattice (for $N > 2$).   The function $T_{pq}$ is meromorphic on this surface: we obtain the orders of all the zeros and poles. For $N$ odd, we show that these orders are determined by the usual inversion and rotation relations (without the extra symmetry), together with a simple linearity ansatz. For $N$ even, this method does not give the orders uniquely, but leaves only $[(N+4)/4]$ parameters to be determined.
To understand the Active Galactic Nuclei (AGN) phenomenon and their impact on the evolution of galaxies, a complete AGN census is required; however, finding heavily obscured AGNs is observationally challenging. Here we use the deep and extensive multi-wavelength data in the COSMOS field to select a complete sample of 578 infrared (IR) quasars ($L_{\rm AGN,IR}>10^{45}\rm \: erg\: s^{-1}$) at $z<3$, with minimal obscuration bias, using detailed UV-to-far IR spectral energy distribution (SED) fitting. We complement our SED constraints with X-ray and radio observations to further investigate the properties of the sample. Overall, 322 of the IR quasars are detected by Chandra and have individual X-ray spectral constraints. From a combination of X-ray stacking and $L_{\rm 2-10\rm keV}$ - $L_{\rm 6\: \mu m}$ analyses, we show that the majority of the X-ray faint and undetected quasars are heavily obscured (many are likely Compton thick), highlighting the effectiveness of the mid-IR band to find obscured AGNs. We find that 355 ($\approx$61%) IR quasars are obscured ($N_{\rm H}>10^{22}\rm \: cm^{-2}$) and identify differences in the average properties between the obscured and unobscured quasars: (1) obscured quasars have star-formation rates $\approx 3$ times higher than unobscured systems for no significant difference in stellar mass and (2) obscured quasars have stronger radio emission than unobscured systems, with a radio-loudness parameter $\approx 0.2 \rm \: dex$ higher. These results are inconsistent with a simple orientation model but in general agreement with either extreme host-galaxy obscuration towards the obscured quasars or a scenario where obscured quasars are an early phase in the evolution of quasars.
The main purpose of this Note is to provide a non-trivial bound on certain Kloosterman sums as considered in the recent paper of E. Fouvry [F], leading to a small improvement of his result on the Pell equation.
We explicitly describe the possible pairs of triangle and square densities for r-regular finite simple graphs. We also prove that every r-regular unimodular random graph can be approximated by r-regular finite graphs with respect to these densities. As a corollary one gets an explicit description of the possible pairs of the third and fourth moments of the spectral measure of r-regular unimodular random graphs.
We study the Josephson effect through a magnetic molecule with anisotropic properties. Performing calculations in the tunneling regime, we show that the exchange coupling between the electron spin on the molecule and the molecular spin can trigger a transition from the $\pi$ state to the 0 state, and we study how the spin anisotropy affects this transition. We show that the behavior of the critical current as a function of an external magnetic field can give access to valuable information about the spin anisotropy of the molecule.
Thermo-electrical nanoantennas have been proposed as an alternative option for conversion solar energy harvesting applications. In this work, the response of a spiral broadband antenna has been obtained from numerical and theoretical simulations perspectives. The results show that this device exhibits a responsivity of 20mV/W under 117W/cm2, for a single-frequency radiation. We discuss strategies for enhanced efficiency.
We analyze the motion of stars in the direction perpendicular to the galactic plane following a spiral arm passage. We show that the fast change in the vertical galactic potential causes a thermalized distribution to develop a distinctive "ringing"-like non-thermal signature. We use A and F-stars from the extended Hipparocos catalogue to show that a spiral arm passage (or passages), with an amplitude (or randomly combined amplitudes) of at least {\delta}{\rho} / {\rho} > ~0.15 must have taken place in the past (with {\rho} being the total background density). Presently, the local stellar distribution within ~100 pc of the plane, appears (at the 2.5{\sigma} level) to be contracting towards it.
We construct a family of map which is shown to be positive when imposing certain condition on the parameters. Then we show that the constructed map can never be completely positive. After tuning the parameters, we found that the map still remain positive but it is not completely positive. We then use the positive but not completely positive map in the detection of bound entangled state and negative partial transpose entangled states.
It has been proposed and demonstrated that path-entangled Fock states (PEFSs) are robust against photon loss over NOON states [S. D. Huver \emph{et al.}, Phys. Rev. A \textbf{78}, 063828 (2008)]. However, the demonstration was based on a measurement scheme which was yet to be implemented in experiments. In this work, we quantitatively illustrate the advantage of PEFSs over NOON states in the presence of photon losses by analytically calculating the quantum Fisher information. To realize such an advantage in practice, we then investigate the achievable sensitivities by employing three types of feasible measurements: parity, photon-number-resolving, and homodyne measurements. We here apply a double-port measurement strategy where the photons at each output port of the interferometer are simultaneously detected with the aforementioned types of measurements.
How much does the curvature perturbation change after it leaves the horizon, and when should one evaluate the power spectrum? To answer these questions we study single field inflation models numerically, and compare the evolution of different curvature perturbations from horizon crossing to the end of inflation. We find that e.g. in chaotic inflation, the amplitude of the comoving and the curvature perturbation on uniform density hypersurfaces differ by up to 180 \% at horizon crossing assuming the same amplitude at the end of inflation, and that it takes approximately 3 efolds for the curvature perturbation to be within 1 \% of its value at the end of inflation.
At doping below 6% the bilayer cuprate YBa2Cu3O{6+y} is a collinear antiferromagnet. Independent of doping the value of the staggered magnetization at zero temperature is about 0.6\mu_B. This is the maximum value of the magnetization allowed by quantum fluctuations of localized spins. In this low doping regime the compound is a normal conductor with a finite resistivity at zero temperature. These experimental observations create a unique opportunity for theory to perform a controlled calculation of the electron spectral function. In the present work we perform this calculation within the framework of the extended t-J model. As one expects the Fermi surface consists of small hole pockets centered at (\pi/2,\pi/2). The electron spectral function is very strongly anisotropic with maximum of intensity located at the inner parts of the pockets and with very small intensity at the outer parts. We also found that the antiferromagnetic correlations act against the bilayer bonding-antibonding splitting destroying it. The bilayer Fermi surface splitting is practically zero.
This paper reviews the NTIRE2021 challenge on burst super-resolution. Given a RAW noisy burst as input, the task in the challenge was to generate a clean RGB image with 4 times higher resolution. The challenge contained two tracks; Track 1 evaluating on synthetically generated data, and Track 2 using real-world bursts from mobile camera. In the final testing phase, 6 teams submitted results using a diverse set of solutions. The top-performing methods set a new state-of-the-art for the burst super-resolution task.
We analyze a game introduced by Andy Niedermaier, where $p$ players take turns throwing a dart at a dartboard. A player is eliminated unless his dart lands closer to the center than all previously thrown darts, in which case he goes to the back of the line, until only one player remains. Using generating functions, we determine the distribution of the number of throws in the game, and we obtain a recursive formula to compute the probability that each player wins.
George Andrews recently proved a new identity between the cardinalities of the set of Semi-Fibonacci partitions and the set of partitions into powers of two with all parts appearing an odd number of times. This paper extends the identity to the set of Semi-$m$-Fibonacci partitions of $n$ and the set of partitions of $n$ into powers of $m$ in which all parts appear with multiplicity not divisible by $m$.
We deduce in this short report the non-asymptotic for exponential tail of distribution for sums of independent centered random variables.
Because of proximity to the Galactic plane, reliable identification of members of the alpha Persei cluster is often problematic. Based primarily on membership evaluations contained in six published papers, we constructed a mostly complete list of high-fidelity members of spectral type G and earlier that lie within 3 arc degrees of the cluster center. Alpha Persei was the one nearby, rich, young open cluster not surveyed with the Spitzer Space Telescope. We examined the first and final data releases of the Wide Field Infrared Survey Explorer (WISE) and found 11, or perhaps 12, alpha Per cluster members that have excess mid-infrared emission above the stellar photosphere attributable to an orbiting dusty debris disk. The most unusual of these is V488 Per, a K-type star with an excess IR luminosity 16% (or more) of the stellar luminosity; this is a larger excess fraction than that of any other known dusty main sequence star. Much of the dust that orbits V488 Per is at a temperature of ~800 K; if these grains radiate like blackbodies, then they lie only ~0.06 AU from the star. The dust is probably the aftermath of a collision of two planetary embryos or planets with small semimajor axes; such orbital radii are similar to those of many of the transiting planets discovered by the Kepler satellite.
In cataclysmic variables (CVs), accretion onto white dwarfs produces high temperature, high density plasmas. They cool down from kT~10 keV via bremsstrahlung continuum and K and L shell line emissions. The small volume around white dwarfs means that the plasma densities are much higher than in, e.g., stellar coronae, probably beyond the range well-described by existing models. I will describe potential diagnostics of the temperatures, the densities, and the optical depths of X-ray emitting plasmas in CVs, and present the recent Chandra grating spectra of the magnetic CV V1223 Sgr as an example.
Global uniform boundedness of solutions to 3D viscous Primitive equations in a bounded cylindrical domain with physical boundary condition is proved in space $H^m$ for any $m\geqslant2$. A bounded absorbing set for the solutions in $H^m$ is obtained. These results seem rather difficult for the methods recently developed in [8] and [10]. A completely different approach based on hydrostatic helmholtz decomposition is presented, which can also be applied to cases with other different boundary conditions. Several important results about hydrostatic Leray projector are obtained and utilized. These results are expected to be of general interest and will be helpful as well for solving some other problems for 3D viscous Primitive equations which appeared hard previously for the cases with non-periodic boundary conditions (see e.g. [9]).
The statistical proprieties of complex systems can differ deeply for those of classical systems governed by Boltzmann-Gibbs entropy. In particular, the probability distribution function observed in several complex systems shows a power law behavior in the tail which disagrees with the standard exponential behavior showed by Gibbs distribution. Recently, a two-parameter deformed family of entropies, previously introduced by Sharma, Taneja and Mittal (STM), has been reconsidered in the statistical mechanics framework. Any entropy belonging to this family admits a probability distribution function with an asymptotic power law behavior. In the present work we investigate the Legendre structure of the thermostatistics theory based on this family of entropies. We introduce some generalized thermodynamical potentials, study their relationships with the entropy and discuss their main proprieties. Specialization of the results to some one-parameter entropies belonging to the STM family are presented.
Chowla~(1962), McEliece~(1974), Evans~(1977, 1981) and Aoki~(1997, 2004, 2012) studied Gauss sums, some integral powers of which are in the field of rational numbers. Such Gauss sums are called {\it pure}. In particular, Aoki (2004) gave a necessary and sufficient condition for a Gauss sum to be pure in terms of Dirichlet characters modulo the order of the multiplicative character involved. In this paper, we study pure Gauss sums with odd extension degree $f$ and classify them for $f=5,7,9,11,13,17,19,23$ based on Aoki's theorem. Furthermore, we characterize a special subclass of pure Gauss sums in view of an application for skew Hadamard difference sets. Based on the characterization, we give a new construction of skew Hadamard difference sets from cyclotomic classes of finite fields.
One of the best-studied jets from all young stellar objects is the jet of DG Tau, which we imaged in the FUV with HST for the first time. These high spatial resolution images were obtained with long-pass filters and allow us to construct images tracing mainly molecular hydrogen and C IV emission. We find that the H2 emission appears as a limb-brightened cone with additional emission close to the jet axis. The length of the rims is about 0.3 arcsec or 42 AU (proj.) before their brightness strongly drops, and the opening angle is about 90 deg. Comparing our FUV data with near-IR data we find that the fluorescent H2 emission likely traces the outer, cooler part of the disk wind while an origin of the H2 emission in the surface layers (atmosphere) of the (flared) disk is unlikely. Furthermore, the spatial shape of the H2 emission shows little variation over six years which suggests that the outer part of the disk wind is rather stable and probably not associated with the formation of individual knots. The C IV image shows that the emission is concentrated towards the jet axis. We find no indications for additional C IV emission at larger distances, which strengthens the association with the X-ray emission observed to originate within the DG Tau jet.
In this paper, we establish $L_p$ estimates and solvability for time fractional divergence form parabolic equations in the whole space when leading coefficients are merely measurable in one spatial variable and locally have small mean oscillations with respect to the other variables. The corresponding results for equations on a half space are also derived.
We prove a uniqueness result of solutions for a system of PDEs of Monge-Kantorovich type arising in problems of mass transfer theory. The results are obtained under very mild regularity assumptions both on the reference set $\Omega\subset\mathbf{R}^n$, and on the (possibly asymmetric) norm defined in $\Omega$. In the special case when $\Omega$ is endowed with the Euclidean metric, our results provide a complete description of the stationary solutions to the tray table problem in granular matter theory.
Interactions between pairs of isolated dwarf galaxies provide a critical window into low-mass hierarchical, gas-dominated galaxy assembly and the buildup of stellar mass in low-metallicity systems. We present the first VLT/MUSE optical IFU observations of the interacting dwarf pair dm1647+21, selected from the TiNy Titans survey. The H$\alpha$ emission is widespread and corresponds to a total unobscured star formation rate (SFR) of 0.44 M$_{\odot}$ yr$^{-1}$, 2.7 times higher than the SFR inferred from SDSS data. The implied specific SFR (sSFR) for the system is elevated by more than an order of magnitude above non-interacting dwarfs in the same mass range. This increase is dominated by the lower-mass galaxy, which has a sSFR enhancement of $>$ 50. Examining the spatially-resolved maps of classic optical line diagnostics, we find the ISM excitation can be fully explained by star formation. The velocity field of the ionized gas is not consistent with simple rotation. Dynamical simulations indicate that the irregular velocity field and the stellar structure is consistent with the identification of this system as an ongoing interaction between two dwarf galaxies. The widespread, clumpy enhancements in star formation in this system point to important differences in the effect of mergers on dwarf galaxies, compared to massive galaxies: rather than the funneling of gas to the nucleus and giving rise to a nuclear starburst, starbursts in low-mass galaxy mergers may be triggered by large-scale ISM compression, and thus be more distributed.
Pretraining Vision Transformers (ViTs) has achieved great success in visual recognition. A following scenario is to adapt a ViT to various image and video recognition tasks. The adaptation is challenging because of heavy computation and memory storage. Each model needs an independent and complete finetuning process to adapt to different tasks, which limits its transferability to different visual domains. To address this challenge, we propose an effective adaptation approach for Transformer, namely AdaptFormer, which can adapt the pre-trained ViTs into many different image and video tasks efficiently. It possesses several benefits more appealing than prior arts. Firstly, AdaptFormer introduces lightweight modules that only add less than 2% extra parameters to a ViT, while it is able to increase the ViT's transferability without updating its original pre-trained parameters, significantly outperforming the existing 100\% fully fine-tuned models on action recognition benchmarks. Secondly, it can be plug-and-play in different Transformers and scalable to many visual tasks. Thirdly, extensive experiments on five image and video datasets show that AdaptFormer largely improves ViTs in the target domains. For example, when updating just 1.5% extra parameters, it achieves about 10% and 19% relative improvement compared to the fully fine-tuned models on Something-Something~v2 and HMDB51, respectively. Code is available at https://github.com/ShoufaChen/AdaptFormer.
We obtain several extensions of Talagrand's lower bound for the small deviation probability using metric entropy. For Gaussian processes, our investigations are focused on processes with sub-polynomial and, respectively, exponential behaviour of covering numbers. The corresponding results are also proved for non-Gaussian symmetric stable processes, both for the cases of critically small and critically large entropy. The results extensively use the classical chaining technique; at the same time they are meant to explore the limits of this method.
In this paper, we focus on unsupervised representation learning for skeleton-based action recognition. Existing approaches usually learn action representations by sequential prediction but they suffer from the inability to fully learn semantic information. To address this limitation, we propose a novel framework named Prototypical Contrast and Reverse Prediction (PCRP), which not only creates reverse sequential prediction to learn low-level information (e.g., body posture at every frame) and high-level pattern (e.g., motion order), but also devises action prototypes to implicitly encode semantic similarity shared among sequences. In general, we regard action prototypes as latent variables and formulate PCRP as an expectation-maximization task. Specifically, PCRP iteratively runs (1) E-step as determining the distribution of prototypes by clustering action encoding from the encoder, and (2) M-step as optimizing the encoder by minimizing the proposed ProtoMAE loss, which helps simultaneously pull the action encoding closer to its assigned prototype and perform reverse prediction task. Extensive experiments on N-UCLA, NTU 60, and NTU 120 dataset present that PCRP outperforms state-of-the-art unsupervised methods and even achieves superior performance over some of supervised methods. Codes are available at https://github.com/Mikexu007/PCRP.
A one-boson-exchange model for the hyperon-nucleon (\Lambda N, \Sigma N) interaction is presented. The model incorporates the standard one boson exchanges of the lowest pseudoscalar and vector meson multiplets with coupling constants fixed by SU(6) flavor symmetry relations. As the main new feature of the model, the contributions in the scalar--isoscalar (\sigma) and vector--isovector (\rho) exchange channels are now constrained by a microscopic model of correlated \pi\pi and K \bar K exchange. Additional short-ranged ingredients of the model in the scalar--isovector (a_0) and scalar--isospin-1/2 (\kappa) channels are likewise viewed as arising from meson-meson correlations but are treated phenomenologically. With this model a satisfactory reproduction of the available hyperon-nucleon data can be achieved.
We investigate the generalization of the Costas property in 3 or more dimensions, and we seek an appropriate definition; the 2 main complications are a) that the number of ``dots'' this multidimensional structure should have is not obvious, and b) that the notion of the multidimensional permutation needs some clarification. After proposing various alternatives for the generalization of the definition of the Costas property, based on the definitions of the Costas property in 1 or 2 dimensions, we also offer some construction methods, the main one of which is based on the idea of reshaping Costas arrays into higher-dimensional entities.
Analysis of the Cassini Ultraviolet Imaging Spectrometer (UVIS) stellar and solar occultations at Titan to date include 12 species: N$_{2}$ (nitrogen), CH$_{4}$ (methane), C$_{2}$H$_{2}$ (acetylene), C$_{2}$H$_{4}$ (ethylene), C$_{2}$H$_{6}$ (ethane), C$_{4}$H$_{2}$ (diacetylene), C$_{6}$H$_{6}$ (benzene), C$_{6}$N$_{2}$ (dicyanodiacetylene), C$_{2}$N$_{2}$ (cyanogen), HCN (hydrogen cyanide), HC$_{3}$N (cyanoacetylene), and aerosols distinguished by a structureless continuum extinction (absorption plus scattering) of photons in the EUV. The introduction of aerosol particles, retaining the same refractive index properties as tholin with radius $\sim$125 \AA and using Mie theory, provides a satisfactory fit to the spectra. The derived vertical profile of aerosol density shows distinct structure, implying a reactive generation process reaching altitudes more than 1000 km above the surface. A photochemical model presented here provides a reference basis for examining the chemical and physical processes leading to the distinctive atmospheric opacity at Titan. We find that dicyanodiacetylene is condensable at $\sim$650 km, where the atmospheric temperature minimum is located. This species is the simplest molecule identified to be condensable. Observations are needed to confirm the existence and production rates of dicyanodiacetylene.