ShantanuT01/DACTYL-Pretraining huggingface dataset:
Unconventional quantum critical phenomena observed in Yb-based periodic crystals such as YbRh$_2$Si$_2$ and $\beta$-YbAlB$_4$ have been one of the central issues in strongly correlated electron systems. The common criticality has been discovered in quasicrystal Yb$_{15}$Au$_{51}$Al$_{34}$, which surprisingly persists under pressure at least up to $P=1.5$ GPa. The $T/H$ scaling where the magnetic susceptibility can be expressed as a single scaling function of the ratio of temperature $T$ and magnetic field $H$ has been discovered in the quasicrystal, which is essentially the same as that observed in $\beta$-YbAlB$_4$. Recently, the $T/H$ scaling as well as the common criticality has been also observed even in the approximant crystal Yb$_{14}$Au$_{51}$Al$_{35}$ under pressure. The theory of critical Yb-valence fluctuation gives a natural explanation for these striking phenomena in a unified way.
For $a/q\in\mathbb{Q}$ the Estermann function is defined as $D(s,a/q):=\sum_{n\geq1}d(n)n^{-s}\operatorname{e}(n\frac aq)$ if $\Re(s)>1$ and by meromorphic continuation otherwise. For $q$ prime, we compute the moments of $D(s,a/q)$ at the central point $s=1/2$, when averaging over $1\leq a<q$.   As a consequence we deduce the asymptotic for the iterated moment of Dirichlet $L$-functions $\sum_{\chi_1,\dots,\chi_k\mod q}|L(\frac12,\chi_1)|^2\cdots |L(\frac12,\chi_k)|^2|L(\frac12,\chi_1\cdots \chi_k)|^2$, obtaining a power saving error term.   Also, we compute the moments of certain functions defined in terms of continued fractions. For example, writing $f_{\pm}(a/q):=\sum_{j=0}^r (\pm1)^jb_j$ where $[0;b_0,\dots,b_r]$ is the continued fraction expansion of $a/q$ we prove that for $k\geq2$ and $q$ primes one has $\sum_{a=1}^{q-1}f_{\pm}(a/q)^k\sim2 \frac{\zeta(k)^2}{\zeta(2k)} q^k$ as $q\to\infty$.
Hamiltonian of a system in quantum field theory can give rise to infinitely many partition functions which correspond to infinitely many inequivalent representations of the canonical commutator or anticommutator rings of field operators. This implies that the system can theoretically exist in infinitely many Gibbs states. The system resides in the Gibbs state which corresponds to its minimal Helmholtz free energy at a given range of the thermodynamic variables. Individual inequivalent representations are associated with different thermodynamic phases of the system. The BCS Hamiltonian of superconductivity is chosen to be an explicit example for the demonstration of the important role of inequivalent representations in practical applications. Its analysis from the inequivalent representations' point of view has led to a recognition of a novel type of the superconducting phase transition.
Gradually Truncated Power law distribution - Citation of scientists   Hari M. Gupta, Jose R. Campanha and Bianca A. Ferrari Unesp - Physics Dpto. - Rio Claro Sao Paulo - Brazil   Abstract   The number of times, a scientist is cited in other scientific publications is now an important factor in his merit consideration. Normally citation indices of highly cited scientists are available, which in turn give information only about the dynamics of the citation mechanism of this group. In the present work, we studied the statistical distribution of the citation index of Brazilian scientists working in diverse areas, through Zipf-plot technique. As it is a small sub-group within the scientific community, it can better explain the dynamics of citation index. We find that gradually truncated power law distribution can explain well citation index. The distribution of citation of most cited physicist can also be well explained.   We develop a model of citation, based on positive feedback, i.e. highly cited scientist, would get better financial help, and more students, which in turn help to form a large group working in the same topic and paper is cited more times. The limiting factor comes because of limited number of articles which can be published in a particular sub-area due to limited number of scientific journal, where the article can be cited.
The development of advanced 3D sensors has enabled many objects to be captured in the wild at a large scale, and a 3D object recognition system may therefore encounter many objects for which the system has received no training. Zero-Shot Learning (ZSL) approaches can assist such systems in recognizing previously unseen objects. Applying ZSL to 3D point cloud objects is an emerging topic in the area of 3D vision, however, a significant problem that ZSL often suffers from is the so-called hubness problem, which is when a model is biased to predict only a few particular labels for most of the test instances. We observe that this hubness problem is even more severe for 3D recognition than for 2D recognition. One reason for this is that in 2D one can use pre-trained networks trained on large datasets like ImageNet, which produces high-quality features. However, in the 3D case there are no such large-scale, labelled datasets available for pre-training which means that the extracted 3D features are of poorer quality which, in turn, exacerbates the hubness problem. In this paper, we therefore propose a loss to specifically address the hubness problem. Our proposed method is effective for both Zero-Shot and Generalized Zero-Shot Learning, and we perform extensive evaluations on the challenging datasets ModelNet40, ModelNet10, McGill and SHREC2015. A new state-of-the-art result for both zero-shot tasks in the 3D case is established.
We study viscosity solutions to degenerate and singular elliptic equations of $p$-Laplacian type on Riemannian manifolds. The Krylov-Safonov type Harnack inequality for the $p$-Laplacian operators with $1<p<\infty$ is established on the manifolds with Ricci curvature bounded from below based on ABP type estimates. We also prove the Harnack inequality for nonlinear $p$-Laplacian type operators assuming that a nonlinear perturbation of Ricci curvature is bounded below.
A classical theorem of Kempner states that the sum of the reciprocals of positive integers with missing decimal digits converges. This result is extended to much larger families of "missing digits" sets of positive integers with both convergent and divergent harmonic series.
We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG), beyond the cosmological constant scenario. We start with cases where the DE only directly affects the background evolution, considering Taylor expansions of the equation of state, principal component analysis and parameterizations related to the potential of a minimally coupled DE scalar field. When estimating the density of DE at early times, we significantly improve present constraints. We then move to general parameterizations of the DE or MG perturbations that encompass both effective field theories and the phenomenology of gravitational potentials in MG models. Lastly, we test a range of specific models, such as k-essence, f(R) theories and coupled DE. In addition to the latest Planck data, for our main analyses we use baryonic acoustic oscillations, type-Ia supernovae and local measurements of the Hubble constant. We further show the impact of measurements of the cosmological perturbations, such as redshift-space distortions and weak gravitational lensing. These additional probes are important tools for testing MG models and for breaking degeneracies that are still present in the combination of Planck and background data sets. All results that include only background parameterizations are in agreement with LCDM. When testing models that also change perturbations (even when the background is fixed to LCDM), some tensions appear in a few scenarios: the maximum one found is \sim 2 sigma for Planck TT+lowP when parameterizing observables related to the gravitational potentials with a chosen time dependence; the tension increases to at most 3 sigma when external data sets are included. It however disappears when including CMB lensing.
It is suggested that the wavelike character of the recently discovered 2.7-kiloparsec spatially and kinematically coherent complex of interstellar clouds in the solar neighborhood--the Radcliffe Wave--may be the result of a Kelvin-Helmholtz instability arising at the interface between the Galactic disk and non-corotating halo.
We construct sheaf-cohomological analogues of Mathai-Quillen forms, that is, holomorphic bundle-valued differential forms whose cohomology classes are independent of certain deformations, and which are believed to possess Thom-like properties. Ordinary Mathai-Quillen forms are special cases of these constructions, as we discuss. These sheaf-theoretic variations arise physically in A/2 and B/2 pseudo-topological field theories, and we comment on their origin and role.
Inferring 3D locations and shapes of multiple objects from a single 2D image is a long-standing objective of computer vision. Most of the existing works either predict one of these 3D properties or focus on solving both for a single object. One fundamental challenge lies in how to learn an effective representation of the image that is well-suited for 3D detection and reconstruction. In this work, we propose to learn a regular grid of 3D voxel features from the input image which is aligned with 3D scene space via a 3D feature lifting operator. Based on the 3D voxel features, our novel CenterNet-3D detection head formulates the 3D detection as keypoint detection in the 3D space. Moreover, we devise an efficient coarse-to-fine reconstruction module, including coarse-level voxelization and a novel local PCA-SDF shape representation, which enables fine detail reconstruction and one order of magnitude faster inference than prior methods. With complementary supervision from both 3D detection and reconstruction, one enables the 3D voxel features to be geometry and context preserving, benefiting both tasks.The effectiveness of our approach is demonstrated through 3D detection and reconstruction in single object and multiple object scenarios.
This is the first paper of a series presenting a Spheroid's Panchromatic Investigation in Different Environmental Regions (SPIDER). The sample of spheroids consists of 5,080 bright (Mr<-20) Early-Type galaxies (ETGs), in the redshift range of 0.05 to 0.095, with optical (griz) photometry and spectroscopy from SDSS-DR6 and Near-Infrared (YJHK) photometry from UKIDSS-LAS (DR4). We describe how homogeneous photometric parameters (galaxy colors and structural parameters) are derived using grizYJHK wavebands. We find no systematic steepening of the CM relation when probing the baseline from g-r to g-K, implying that internal color gradients drive most of the mass-metallicity relation in ETGs. As far as structural parameters are concerned we find that the mean effective radius of ETGs smoothly decreases, by ~30%, from g through K, while no significant dependence on waveband is detected for the axis ratio, Sersic index, and a4 parameters. Also, velocity dispersions are re-measured for all the ETGs using STARLIGHT and compared to those obtained by SDSS. We compare our (2DPHOT) measurements of total magnitude, effective radius, and mean surface brightness with those obtained as part of the SDSS pipeline (Photo). Significant differences are found and reported, including comparisons with a third and independent part. A full characterization of the sample completeness in all wavebands is presented, establishing the limits of application of the characteristic parameters presented here for the analysis of the global scaling relations of ETGs.
Let p:C' -> C be an unramified double covering of irreducible smooth curves and let P be the attached Prym variety. We prove the schematic theta-dual equalities in the Prym variety T(C')=V^2 and T(V^2)=C', where V^2 is the Brill-Noether locus of P associated to p considered by Welters. As an application we prove a Torelli Theorem analogous to the fact that the g-th symmetric product of a curve D of genus g determines the curve.
We review the present methodology for the use of Sulfur as global metallicity tracer in galaxies, which allows performing a complete abundance analysis using mainly the red to near infrared spectral region, and extending the range of directly derived abundances up to 5 times the S solar photospheric value. The empirical calibration of Sulfur via the S23 parameter is also reviewed.
Fast radio bursts (FRBs) are bright, millisecond-duration radio pulses whose origins are unknown. To date, only one (FRB 121102) out of several dozen has been seen to repeat, though the extent to which it is exceptional remains unclear. We discuss detecting repetition from FRBs, which will be very important for understanding their physical origin, and which also allows for host galaxy localisation. We show how the combination of instrument sensitivity, beamshapes, and individual FRB luminosity functions affect the detection of sources whose repetition is not necessarily described by a homogeneous Poisson process. We demonstrate that the Canadian Hydrogen Intensity Mapping Experiment (CHIME) could detect many new repeating FRBs for which host galaxies could be subsequently localised using other interferometers, but it will not be an ideal instrument for monitoring FRB 121102. If the luminosity distributions of repeating FRBs are given by power-laws with significantly more dim than bright bursts, CHIME's repetition discoveries could preferentially come not from its own discoveries, but from sources first detected with lower-sensitivity instruments like the Australian Square Kilometer Array Pathfinder (ASKAP) in fly's eye mode. We then discuss observing strategies for upcoming surveys, and advocate following up sources at approximately regular intervalsand with telescopes of higher sensitivity, when possible. Finally, we discuss doing pulsar-like periodicity searching on FRB follow-up data, based on the idea that while most pulses are undetectable, folding on an underlying rotation period could reveal the hidden signal.
We study algebraic (Artin) stacks over $\bar{\mathcal M}_g$ giving a functorial way of compactifying the relative degree $d$ Picard variety for families of stable curves. We also describe for every $d$ the locus of genus $g$ stable curves over which we get Deligne-Mumford stacks strongly representable over $\bar{\mathcal M}_g$.
Given a nef and big line bundle $L$ on a projective variety $X$ of dimension $d \geq 2$, we prove that the Seshadri constant of $L$ at a very general point is larger than $(d+1)^{\frac{1}{d}-1}$. This slightly improves the lower bound $1/d$ established by Ein, K\"uchle and Lazarsfeld. The proof relies on the concept of successive minima for line bundles recently introduced by Ambro and Ito.
The integrated shear 3-point correlation function $\zeta_{\pm}$ is a higher-order statistic of the cosmic shear field that describes the modulation of the 2-point correlation function $\xi_{\pm}$ by long-wavelength features in the field. Here, we introduce a new theoretical model to calculate $\zeta_{\pm}$ that is accurate on small angular scales, and that allows to take baryonic feedback effects into account. Our model builds on the realization that the small-scale $\zeta_{\pm}$ is dominated by the nonlinear matter bispectrum in the squeezed limit, which can be evaluated accurately using the nonlinear matter power spectrum and its first-order response functions to density and tidal field perturbations. We demonstrate the accuracy of our model by showing that it reproduces the small-scale $\zeta_{\pm}$ measured in simulated cosmic shear maps. The impact of baryonic feedback enters effectively only through the corresponding impact on the nonlinear matter power spectrum, thereby permitting to account for these astrophysical effects on $\zeta_{\pm}$ similarly to how they are currently accounted for on $\xi_{\pm}$. Using a simple idealized Fisher matrix forecast for a DES-like survey we find that, compared to $\xi_{\pm}$, a combined $\xi_{\pm}\ \&\ \zeta_{\pm}$ analysis can lead to improvements of order $20-40\%$ on the constraints of cosmological parameters such as $\sigma_8$ or the dark energy equation of state parameter $w_0$. We find similar levels of improvement on the constraints of the baryonic feedback parameters, which strengthens the prospects for cosmic shear data to obtain tight constraints not only on cosmology but also on astrophysical feedback models. These are encouraging results that motivate future works on the integrated shear 3-point correlation function towards applications to real survey data.
A simple superasymmetric fission model using microscopically calculated nuclear potentials has shown itself to be outstandingly successful in describing highly asymmetric spontaneous disintegration of nuclei into two composite nuclear fragments. The nuclear interaction potentials required to describe these nuclear decay processes have been calculated by double folding the density distribution functions of the two fragments with a realistic effective interaction. The microscopic nucleus-nucleus potential thus obtained, along with the Coulomb interaction potential and the minimum centrifugal barrier required for the spin-parity conservation, has been used successfully for the lifetime calculations of these nuclear disintegration processes.
A recent derivation of the interpolation between the free energy and conformal anomaly for free fields on spheres is generalised to hemispheres with Neumann (N) and Dirichlet (D) conditions at the rim for GJMS scalar fields. It is shown that the N minus D interpolation is minus a quarter of that for a higher derivative fermion on the spherical rim. In particular, since, for ordinary bosons k=1, the related fermion is irregular propagating according to a second order (pseudo) operator. (2k is the derivative order in the equation of motion.)   It is suggested that the relation has a role to play in the Type--B AdS/CFT mismatch. The DN boundary value problem is enlarged upon in the context of Branson and Gover's construction of the D to N operator. Contact is made with a result of Park and Wojciechowski which is then related to a duality relation of Barvinsky and Nesterov.
Unidirectionally coupled systems which exhibit phase transitions into an absorbing state are investigated at the multicritical point. We find that for initial conditions with isolated particles, each hierarchy level exhibits an inhomogeneous active region, coupled and uncoupled respectively. The particle number of each level increases algebraically in time as $N(t) \sim t^{\eta}$ with different exponents $\eta$ in each domain. This inhomogeneity is a quite general feature of unidirectionally coupled systems and leads to two hyperscaling relations between dynamic and static critical exponents. Using the contact process and the branching-annihilating random walk with two offsprings, which belong to the DP and PC classes respectively, we numerically confirm the scaling relations.
We study tautological classes on the moduli space of stable $n$-pointed hyperelliptic curves of genus $g$ with rational tails. Our result gives a complete description of tautological relations. The method is based on the approach of Yin in comparing tautological classes on the moduli of curves and the universal Jacobian. It is proven that all relations come from the Jacobian side. The intersection pairings are shown to be perfect in all degrees. We show that the tautological algebra coincides with its image in cohomology via the cycle class map. The latter is identified with monodromy invariant classes in cohomology. The connection with recent conjectures by Pixton is also discussed.
We study linearly edge-reinforced random walks on $\mathbb{Z}_+$, where each edge $\{x,x+1\}$ has the initial weight $x^{\alpha} \vee 1$, and each time an edge is traversed, its weight is increased by $\Delta$. It is known that the walk is recurrent if and only if $\alpha \leq 1$. The aim of this paper is to study the almost sure behavior of the walk in the recurrent regime. For $\alpha<1$ and $\Delta>0$, we obtain a limit theorem which is a counterpart of the law of the iterated logarithm for simple random walks. This reveals that the speed of the walk with $\Delta>0$ is much slower than $\Delta=0$. In the critical case $\alpha=1$, our (almost sure) bounds for the trajectory of the walk shows that there is a phase transition of the speed at $\Delta=2$.
To develop a systematic treatment of the self-interaction problem in classical gauge theories and general relativity, we study tenable manifestations of self-interaction: topological phases, and rearrangements of degrees of freedom appearing in the action. We outline the occurrence of topological phases in pure field systems. We show that the rearranged Maxwell-Lorentz electrodynamics is a mathematically consistent and physically satisfactory theory which describes new entities, dressed charged particles and radiation. We extend this analysis to cover different modifications of the Maxwell-Lorentz electrodynamics and the SU(N) Yang-Mills-Wong theory. We take a brief look at a subtle mechanism of self-interaction in classical strings. Turning to general relativity, we note that the total energy and momentum of a system with nontrivial topological content, such as a black hole, are ambiguous, coordinatization-dependent quantities, which resembles the situation with paradoxical decompositions in the Banach-Tarski theorem.
We construct new examples of Kobayashi hyperbolic hypersurfaces in the projective 4-space. They are generic projections of the triple symmetric product of a generic curve of genus at least 7, smoothly embedded in the projective 7-space.
We present a general strategy to extend quantum cluster algorithms for S=1/2 spin systems, such as the loop algorithm, to systems with arbitrary size of spins. In general, the partition function of a high-S spin system is represented in terms of the path integral of a S=1/2 model with special boundary conditions. We introduce additional graphs to be assigned to the boundary part and give the labeling probability explicitly, which completes the algorithm together with an existing S=1/2 cluster algorithm. As a demonstration of the algorithm, we simulate the the integer-spin antiferromagnetic Heisenberg chains. The magnitude of the first excitation gap is estimated as to be 0.41048(6), 0.08917(4), and 0.01002(3) for S=1, 2, and 3, respectively.
We consider cycles on a 3-dimensional Shimura varieties attached to a unitary group, defined over extensions of a CM field $E$, which appear in the context of the conjectures of Gan, Gross, and Prasad \cite{gan-gross-prasad}. We establish a vertical distribution relation for these cycles over an anticyclotomic extension of $E$, complementing the horizontal distribution relation of \cite{jetchev:unitary}, and use this to define a family of norm-compatible cycles over these fields, thus obtaining a universal norm construction similar to the Heegner $\Lambda$-module constructed from Heegner points.
Enforcing exact conservation laws instead of average ones in statistical thermal models for relativistic heavy ion reactions gives raise to so called canonical effect, which can be used to explain some enhancement effects when going from elementary (e.g. pp) or small (pA) systems towards large AA systems. We review the recently developed method for computation of canonical statistical thermodynamics, and give an insight when this is needed in analysis of experimental data.