ShantanuT01/DACTYL-Pretraining huggingface dataset:
Recent work of Bettin and Conrey on the period functions of Eisenstein series naturally gave rise to the Dedekind-like sum \[   c_{a}\left(\frac{h}{k}\right) \ = \   k^{a}\sum_{m=1}^{k-1}\cot\left(\frac{\pi mh}{k}\right)\zeta\left(-a,\frac{m}{k}\right), \] where $a\in\mathbb{C}$, $h$ and $k$ are positive coprime integers, and $\zeta(a,x)$ denotes the Hurwitz zeta function. We derive a new reciprocity theorem for these Bettin--Conrey sums, which in the case of an odd negative integer $a$ can be explicitly given in terms of Bernoulli numbers. This, in turn, implies explicit formulas for the period functions appearing in Bettin--Conrey's work. We study generalizations of Bettin--Conrey sums involving zeta derivatives and multiple cotangent factors and relate these to special values of the Estermann zeta function.
The HAWC observatory recently published their second source catalog with 39 very high energy gamma-ray sources based on 507 days of exposure time. Among these, there were 16 sources that are more than one degree away from any known TeV source. We studied 13 of these 16 sources with VERITAS and \textit{Fermi}-LAT data. VERITAS, an array of four imaging atmospheric Cherenkov telescopes observing gamma rays with energies higher than 85 GeV, can provide a more detailed image of the source with much shorter exposure time and with better angular resolution. With \textit{Fermi}-LAT data, we searched for the counterparts at lower energies (E>10 GeV). The exposure of VERITAS varies among the 13 sources, and we used eight years of \textit{Fermi}-LAT data. VERITAS found weak gamma-ray emission in the region of PWN~DA~495 coinciding with 2HWC J1953+294 in this follow-up study. We will discuss the results especially focusing on the PWN~DA~495 region and the SNR~G~54.1+0.3 region where \textit{Fermi}-LAT detected a GeV counterpart of SNR~G~54.1+0.3, a known TeV source detected by both VERITAS and HAWC.
The hypothesis is explored that fermion rest mass is due entirely to self-interaction via virtual excitation of gauge bosons. This requires revising the standard model to treat both chiral projections of a fermion field as SU(2) doublets, which precludes Yukawa coupling to a scalar (Higgs) boson field. The estimated self-interaction mass of the electron neutrino is $0.291\times10^{-5}m_e$. The implied self-interaction mass of the Higgs boson itself is very small, comparable to the neutrino. Because there is no direct coupling to fermions, only to the $Z^0$ gauge boson, this can be reconciled with failure to detect low-mass Higgs bosons. This argument eliminates many undetermined parameters of the standard model, but requires an {\it ad hoc} Lagrangian term to account for neutral current asymmetries. The proposed algebraic formalism is consistent with fermion generations defined by distinct eigenvalues of a self-interaction mass operator.
We consider the map of three-dimensional N=4 superfields to N=3 harmonic superspace. The left and right representations of the N=4 superconformal group are constructed on N=3 analytic superfields. These representations are convenient for the description of N=4 superconformal couplings of the Abelian gauge superfields with hypermultiplets. We analyze the N=4 invariance in the non-Abelian N=3 Yang-Mills theory.
We present analytical results for the lowest cumulants of a stochastic process described by a Fokker-Planck equation with nonlinear drift. We show that, in the limit of small fluctuations, the mean, the variance and the covariance of the process can be expressed in compact form with the help of the Lambert W function. As an application, we discuss the interplay of noise and nonlinearity far from equilibrium.
We consider a simple modification of the amplitude defining the dynamics of loop quantum gravity, corresponding to the introduction of the cosmological constant, and possibly related to the SL(2,C)q extension of the theory recently considered by Fairbairn-Meusburger and Han. We show that in the context of spinfoam cosmology, this modification yields the de Sitter cosmological solution.
We present a search for infrared dust emission associated with the Leo cloud, a large intergalactic cloud in the M96 group. Mid-infrared and far-infrared images were obtained with IRAC and MIPS on the Spitzer Space Telescope. Our analysis of these maps is done at each wavelength relative to the HI spatial distribution. We observe a probable detection at 8 microns and a marginal detection at 24 microns associated with the highest HI column densities in the cloud. At 70 and 160 microns, upper limits on the dust emission are deduced. The level of the detection is low so that the possibility of a fortuitous cirrus clump or of an overdensity of extragalactic sources along the line of sight can not be excluded. If this detection is confirmed, the quantities of dust inferred imply a dust to gas ratio in the intergalactic cloud up to a few times solar but no less than 1/20 solar. A confirmed detection would therefore exclude the possibility that the intergalactic cloud has a primordial origin. Instead, this large intergalactic cloud could therefore have been formed through interactions between galaxies in the group.
The combination of global and partial features has been an essential solution to improve discriminative performances in person re-identification (Re-ID) tasks. Previous part-based methods mainly focus on locating regions with specific pre-defined semantics to learn local representations, which increases learning difficulty but not efficient or robust to scenarios with large variances. In this paper, we propose an end-to-end feature learning strategy integrating discriminative information with various granularities. We carefully design the Multiple Granularity Network (MGN), a multi-branch deep network architecture consisting of one branch for global feature representations and two branches for local feature representations. Instead of learning on semantic regions, we uniformly partition the images into several stripes, and vary the number of parts in different local branches to obtain local feature representations with multiple granularities. Comprehensive experiments implemented on the mainstream evaluation datasets including Market-1501, DukeMTMC-reid and CUHK03 indicate that our method has robustly achieved state-of-the-art performances and outperformed any existing approaches by a large margin. For example, on Market-1501 dataset in single query mode, we achieve a state-of-the-art result of Rank-1/mAP=96.6%/94.2% after re-ranking.
Stars with initial masses between $\sim0.8$ and 8~$M_\odot$ present copious mass loss during the asymptotic giant branch (AGB) at the end of their lives. The accepted mass-loss mechanism requires radiation pressure acting on dust grains that form in the extended AGB stellar atmospheres. The details of this process are not yet well understood, however. Using the extreme-adaptive-optics imager and polarimeter SPHERE/ZIMPOL, we observed light polarised by grains around W\,Hya, SW\,Vir, and R\,Crt, which have mass-loss rates between 10$^{-7}$ and 10$^{-6}~M_\odot~{\rm yr^{-1}}$. We find the distribution of dust to be asymmetric around the three targets. A biconical morphology is seen for R Crt, with a position angle that is very similar to those inferred from interferometric observations of maser emission and of mid-infrared continuum emission. The cause of the biconical outflow cannot be directly inferred from the ZIMPOL data. The dust grains polarise light more efficiently at 0.65~$\mu$m for R\,Crt and SW\,Vir and at 0.82~$\mu$m for W\,Hya. This indicates that at the time of the observations, the grains around SW\,Vir and R\,Crt had sizes $< 0.1~\mu$m, while those around W\,Hya were larger, with sizes $\gtrsim 0.1~\mu$m. The asymmetric distribution of dust around R\,Crt makes the interpretation more uncertain for this star, however. We find that polarised light is produced already from within the visible photosphere of W~Hya, which we reproduce using models with an inner dust shell that is optically thick to scattering. The radial profile of the polarised light observed around W\,Hya reveal a steep dust density profile. We find the wind-acceleration region of W\,Hya to extend to at least $\sim 7~R_\star$, in agreement with theoretical predictions of acceleration up to $\sim 12~R_\star$.
What distribution of graphical degree sequence is invariant under ``scaling''? Are these graphs always power-law graphs? We show the answer is a surprising ``yes'' for sparse graphs if we ignore isolated vertices, or more generally, the vertices with degrees less than a fixed constant $k$. We obtain a concentration result on the degree sequence of a random induced subgraph. The case of hypergraphs (or set-systems) is also examined.
In recent years, neural implicit surface reconstruction methods have become popular for multi-view 3D reconstruction. In contrast to traditional multi-view stereo methods, these approaches tend to produce smoother and more complete reconstructions due to the inductive smoothness bias of neural networks. State-of-the-art neural implicit methods allow for high-quality reconstructions of simple scenes from many input views. Yet, their performance drops significantly for larger and more complex scenes and scenes captured from sparse viewpoints. This is caused primarily by the inherent ambiguity in the RGB reconstruction loss that does not provide enough constraints, in particular in less-observed and textureless areas. Motivated by recent advances in the area of monocular geometry prediction, we systematically explore the utility these cues provide for improving neural implicit surface reconstruction. We demonstrate that depth and normal cues, predicted by general-purpose monocular estimators, significantly improve reconstruction quality and optimization time. Further, we analyse and investigate multiple design choices for representing neural implicit surfaces, ranging from monolithic MLP models over single-grid to multi-resolution grid representations. We observe that geometric monocular priors improve performance both for small-scale single-object as well as large-scale multi-object scenes, independent of the choice of representation.
Neutron scattering is used to investigate the single-ion spin and orbital excitations below the Mott-Hubbard gap in CoO. Three excitations are reported at 0.870 $\pm$ 0.009 eV, 1.84 $\pm$ 0.03, and 2.30 $\pm$ 0.15 eV. These were parameterized within a weak crystal field scheme with an intra-orbital exchange of $J(dd)$=1.3 $\pm$ 0.2 eV and a crystal field splitting 10Dq=0.94 $\pm$ 0.10 eV. A reduced spin-orbit coupling of \lambda=-0.016 $\pm$ 0.003 eV is derived from dilute samples of Mg$_{0.97}$Co$_{0.03}$O, measured to remove complications due to spin exchange and structural distortion parameters which split the cubic phase degeneracy of the orbital excitations complicating the inelastic spectrum. The 1.84 eV, while reported using resonant x-ray and optical techniques, was absent or weak for non resonant x-ray experiments and overlaps with the expected position of a $^{4}A_{2}$ level. This transition is absent in the dipolar approximation but expected to have a finite quadrupolar matrix element that can be observed with neutron scattering techniques at larger momentum transfers. Our results agree with a crystal field analysis (in terms of Racah parameters and Tanabe-Sugano diagrams) and with previous calculations performed using local-density band theory for Mott insulating transition metal oxides. The results also demonstrate the use of neutron scattering for measuring dipole forbidden transitions in transition metal oxide systems.
We consider the influence of a power-law deviation from the critical coupling such that the system is critical at its surface. We develop a scaling theory showing that such a perturbation introduces a new length scale which governs the scaling behaviour of the density profiles as well as the finite-size behaviour of the surface properties. Exact results are obtained for the Ising quantum chain when the perturbation varies linearly whereas the quadratic perturbation is mainly studied numerically. The scaling theory is well confirmed in both cases.
We propose a two-photon beating experiment based upon biphotons generated from a resonant pumping two-level system operating in a backward geometry. On the one hand, the linear optical-response leads biphotons produced from two sidebands in the Mollow triplet to propagate with tunable refractive indices, while the central-component propagates with unity refractive index. The relative phase difference due to different refractive indices is analogous to the pathway-length difference between long-long and short-short in the original Franson interferometer. By subtracting the linear Rayleigh scattering of the pump, the visibility in the center part of the two-photon beating interference can be ideally manipulated among [0, 100%] by varying the pump power, the material length, and the atomic density, which indicates a Bell-type inequality violation. On the other hand, the proposed experiment may be an interesting way of probing the quantum nature of the detection process. The interference will disappear when the separation of the Mollow peaks approaches the fundamental timescales for photon absorption in the detector.
We study the effect of site dilution and quantum fluctuations in an antiferromagnetic spin system on a square lattice within the linear spin-wave approximation. By performing numerical diagonalization in real space and finite-size scaling, we characterize the nature of the low-energy spin excitations for different dilution fractions up to the classical percolation threshold. We find nontrivial signatures of fractonlike excitations at high frequencies. Our simulations also confirm the existence of an upper bound for the amount of quantum fluctuations in the ground state of the system, leading to the persistence of long-range order up to the percolation threshold. This result is in agreement with recent neutron-scattering experimental data and quantum Monte Carlo numerical calculations. We also show that the absence of a quantum critical point below the classical percolation threshold holds for a large class of systems whose Hamiltonians can be mapped onto a system of coupled noninteracting massless bosons.
A set S of vertices of a connected graph G is convex, if for any pair of vertices u; v 2 S, every shortest path joining u and v is contained in S . The convex hull CH(S) of a set of vertices S is defined as the smallest convex set in G containing S. The set S is geodetic, if every vertex of G lies on some shortest path joining two vertices in S, and it is said to be a hull set if its convex hull is V(G). The geodetic and the hull numbers of G are the cardinality of a minimum geodetic and a minimum hull set, respectively. In this work, we investigate the behavior of both geodetic and hull sets with respect to the strong product operation for graphs. We also stablish some bounds for the geodetic number and the hull number and obtain the exact value of these parameters for a number of strong product graphs.
In this paper, we classify all continuous Galois representations $\rho:\mathrm{Gal}(\overline{\mathbf{Q}}/\mathbf{Q})\to \mathrm{GL}_2(\overline{\mathbf{Q}}_p)$ which are unramified outside $\{p,\infty\}$ and locally induced at $p$, under the assumption that $\overline{\rho}$ is exceptional, that is, has image of order prime to $p$. We prove two results. If $f$ is a level one cuspidal eigenform and one of the $p$-adic Galois representations $\rho_f$ associated to $f$ has exceptional residual image, then $\rho_f$ is not locally induced and $a_p(f)\neq 0$. If $\rho$ is locally induced at $p$ and with exceptional residual image, and furthermore certain subfields of the fixed field of the kernel of $\overline{\rho}$ are assumed to have class numbers prime to $p$, then $\rho$ has finite image up to a twist.
Context: In the last six years, the VVV survey mapped 562 sq. deg. across the bulge and southern disk of the Galaxy. However, a detailed study of these regions, which includes $\sim 36$ globular clusters (GCs) and thousands of open clusters is by no means an easy challenge. High differential reddening and severe crowding along the line of sight makes highly hamper to reliably distinguish stars belonging to different populations and/or systems. Aims: The aim of this study is to separate stars that likely belong to the Galactic GC NGC 6544 from its surrounding field by means of proper motion (PM) techniques. Methods: This work was based upon a new astrometric reduction method optimized for images of the VVV survey. Results: Photometry over the six years baseline of the survey allowed us to obtain a mean precision of $\sim0.51$ mas/yr, in each PM coordinate, for stars with Ks < 15 mag. In the area studied here, cluster stars separate very well from field stars, down to the main sequence turnoff and below, allowing us to derive for the first time the absolute PM of NGC 6544. Isochrone fitting on the clean and differential reddening corrected cluster color magnitude diagram yields an age of $\sim$ 11-13 Gyr, and metallicity [Fe/H] = -1.5 dex, in agreement with previous studies restricted to the cluster core. We were able to derive the cluster orbit assuming an axisymmetric model of the Galaxy and conclude that NGC 6544 is likely a halo GC. We have not detected tidal tail signatures associated to the cluster, but a remarkable elongation in the galactic center direction has been found. The precision achieved in the PM determination also allows us to separate bulge stars from foreground disk stars, enabling the kinematical selection of bona fide bulge stars across the whole survey area. Our results show that VVV data is perfectly suitable for this kind of analysis.
We explore combinatorial formulas for deformations of highest weight characters of the odd orthogonal group $SO(2n+1)$. Our goal is to represent these deformations of characters as partition functions of statistical mechanical models -- in particular, two-dimensional solvable lattice models. In Cartan type $A$, Hamel and King [8] and Brubaker, Bump, and Friedberg [3] gave square ice models on a rectangular lattice which produced such a deformation. Outside of type $A$, ice-type models were found using rectangular lattices with additional boundary conditions that split into two classes -- those with `nested' and `non-nested bends.' Our results fill a gap in the literature, providing the first such formulas for type $B$ with non-nested bends. In type $B$, there are many known combinatorial parameterizations of highest weight representation basis vectors as catalogued by Proctor [19]. We show that some of these permit ice-type models via appropriate bijections (those of Sundaram [21] and Koike-Terada [15]) while other examples due to Proctor do not.
Individual dark matter halos in cosmological simulations vary widely in their detailed structural properties such as shape, rotation, substructure and degree of internal relaxation. Recent non-parametric (principal component) analyses suggest that a few principal components explain a large fraction of the scatter in halo properties. The main principal component is closely linked with concentration, which in turn is known to be related to the mass accretion history of the halo. Here we examine more generally the connection between mass accretion history and structural parameters. The space of mass accretion histories has principal components of its own. We find that the strongest two can be interpreted as the overall age of the halo and the acceleration or deceleration of growth at late times. These two components only account for $\sim70$%\ of the scatter in mass accretions histories however, due to the stochastic effect of major mergers. Relating structural parameters to formation history, we find that concentration correlates strongly with the early history of the halo, while relaxation correlates with the late history. We examine the inferences about formation history that can be drawn by splitting haloes into subsamples, based on observable properties such as concentration and shape at some final time. This approach suggests interesting possibilities, such as the possibility of defining young and old samples of galaxy clusters in a rigorous, quantitative way, or testing the dynamical assumptions of galaxy formation models empirically.
We give a brief review on the development of phenomenological NN interactions and the corresponding quantification of statistical uncertainties. We look into the uncertainty of effective interactions broadly used in mean field calculations through the Skyrme parameters and effective field theory counter-terms by estimating both statistical and systematic uncertainties stemming from the NN interaction. We also comment on the role played by different fitting strategies on the light of recent developments.
The temperature dependencies of magnetic susceptibility in temperature range 4.2-250 K along the principal magnetic axes as well as frequency-field dependence EPR spectrum at helium temperature in basic plane was studied. It is found that ground state of CsPr(MoO4)2, is the quasi-doublet. The experimental values of g-factors gc=1.54; ga<0.1; gb<0.1 and energy gap 0,2 cm-1 was determined
In this paper for each $n\ge g\ge 0$ we consider the moduli stack $\widetilde{\mathcal U}^{ns}_{g,n}$ of curves $(C,p_1,\ldots,p_n,v_1,\ldots,v_n)$ of arithmetic genus $g$ with $n$ smooth marked points $p_i$ and nonzero tangent vectors $v_i$ at them, such that the divisor $p_1+\ldots+p_n$ is nonspecial (has no $h^1$) and ample. With some mild restrictions on the characteristic we show that it is a scheme, affine over the Grassmannian $G(n-g,n)$. We also construct an isomorphism of $\widetilde{\mathcal U}^{ns}_{g,n}$ with a certain relative moduli of $A_\infty$-structures (up to an equivalence) over a family of graded associative algebras parametrized by $G(n-g,n)$.
The in-medium masses of the bottomonium ground states [$1S$ ($\Upsilon (1S), \eta_b$) and $1P$ ($\chi_{b0},\chi_{b1}$)] are investigated in the magnetized vacuum (nuclear medium), using the QCD sum rule framework. In QCD sum rule approach, the mass modifications are calculated in terms of the medium modifications of the scalar and twist-2 gluon condensates, which are obtained in the nuclear medium, from the medium change of a scalar dilaton field, $\chi$ within a chiral effective model. The in-medium masses of the bottomonium ground states are observed to decrease with increasing density. P-wave states are observed to have more appreciable mass-shifts than the S-wave states. In the present investigation, the effects of spin-mixing between 1S bottomonium states, $\Upsilon(1S)$ and $\eta_b$ are taking into account in presence of an external magnetic field. The contribution of magnetic fields are seen to be dominant via spin-magnetic field interaction effects, which leads to an appreciable rise and drop in the in-medium masses of the longitudinal component of vector $1S$ state ($\Upsilon$) and pseudoscalar state ($\eta_b$) respectively. For zero magnetic field, the effects of baryon density on the bottomonium ground states in isospin asymmetric nuclear medium are observed to be quite appreciable. These should have observable consequences for the production of the open and hidden bottom meson states resulting from high energy asymmetric nuclear collisions in facilities which probe high density baryonic matter. There is observed to be large contributions to the masses of the longitudinal component of the vector bottomonium state, $\Upsilon (1S)$ and pesudoscalar state $\eta_b$ in strong magnetic fields.