ShantanuT01/DACTYL-Pretraining huggingface dataset:
It is proven that encoding images and videos through Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, can lead to increased classification performance. Taking into account manifold geometry is typically done via embedding the manifolds in tangent spaces, or Reproducing Kernel Hilbert Spaces (RKHS). Recently, it was shown that embedding such manifolds into a Random Projection Spaces (RPS), rather than RKHS or tangent space, leads to higher classification and clustering performance. However, based on structure and dimensionality of the randomly generated hyperplanes, the classification performance over RPS may vary significantly. In addition, fine-tuning RPS is data expensive (as it requires validation-data), time consuming, and resource demanding. In this paper, we introduce an approach to learn an optimized kernel-based projection (with fixed dimensionality), by employing the concept of subspace clustering. As such, we encode the association of data points to the underlying subspace of each point, to generate meaningful hyperplanes. Further, we adopt the concept of dictionary learning and sparse coding, and discriminative analysis, for the optimized kernel-based projection space (OPS) on SPD manifolds. We validate our algorithm on several classification tasks. The experiment results also demonstrate that the proposed method outperforms state-of-the-art methods on such manifolds.
BES Collaboration has collected 58 million $J/\psi$ events at the Beijing Electron-Positron Collider (BEPC). $J/\psi$ decays provide an excellent place for studying excited nucleons and hyperons -- $N^*$, $\Lambda^*$, $\Sigma^*$ and $\Xi^*$ resonances. Physics motivation, data status, partial wave analyses and future prospects are presented for the baryon resonance program at BES.
The first hours following a neutron star merger are considered to provide several UV/optical/NIR signals: $ \beta $-decay emission from free neutrons, radioactive decay of shocked heavy elements in the cocoon and cocoon's cooling emission. Here we consider two additional emission sources: $ \beta $-decay of free neutrons in the cocoon and synchrotron by the $ \beta $-decay electrons. We present 3D RHD simulations of jets that propagate in a multi-layer ejecta from the merger and calculate semi-analytically the resulting light curves. We find that the free neutrons emission at high latitudes is enhanced by the cocoon by a factor of a few to power a wide ($ \lesssim 60^\circ $) and brief ($ \sim 1 $ hour) UV signal that can reach an absolute magnitude of $\gtrsim$ -15, comparable with the cooling emission. If the ejected neutron matter mass is $ M_n \gtrsim 10^{-4}{\rm M_\odot} $, the synchrotron emission may yield a long ($ \sim 8 $ hours) quasi-isotropic UV/optical signal with an absolute magnitude between -12 and -15, depending on the magnetic field. Such a high mass of a mildly-relativistic component may partly obscure the cocoon's shocked r-process elements, thereby attenuating its radioactive decay emission. Future observations on these timescales, including null detections, may place constraints on the ejected neutron matter mass and shed light on the ejecta and jet-cocoon characteristics.
Consider a non-CM elliptic curve $E$ defined over $\mathbb{Q}$. For each prime $\ell$, there is a representation $\rho_{E,\ell}: G \to GL_2(\mathbb{F}_\ell)$ that describes the Galois action on the $\ell$-torsion points of $E$, where $G$ is the absolute Galois group of $\mathbb{Q}$. A famous theorem of Serre says that $\rho_{E,\ell}$ is surjective for all large enough $\ell$. We will describe all known, and conjecturally all, pairs $(E,\ell)$ such that $\rho_{E,\ell}$ is not surjective. Together with another paper, this produces an algorithm that given an elliptic curve $E/\mathbb{Q}$, outputs the set of such exceptional primes $\ell$ and describes all the groups $\rho_{E,\ell}(G)$ up to conjugacy. Much of the paper is dedicated to computing various modular curves of genus $0$ with their morphisms to the $j$-line.
Given a solution of a semilinear dispersive partial differential equation with a real analytic nonlinearity, we relate its Cauchy data at two different times by nonlinear representation formulas in terms of convergent series. These series are constructed by means of generating functions. All this theory is based on a new suitable formulation of the dynamics of solutions of dispersive equations.
Property by design is one appealing idea in material synthesis but hard to achieve in practice. A recent successful example is the demonstration of van der Waals (vdW) heterostructures,1-3 in which atomic layers are stacked on each other and different ingredients can be combined beyond symmetry and lattice matching. This concept, usually described as a nanoscale Lego blocks, allows to build sophisticated structures layer by layer. However, this concept has been so far limited in two dimensional (2D) materials. Here we show a class of new material where different layers are coaxially (instead of planarly) stacked. As the structure is in one dimensional (1D) form, we name it "1D vdW heterostructures". We demonstrate a 5 nm diameter nanotube consisting of three different materials: an inner conductive carbon nanotube (CNT), a middle insulating hexagonal boron nitride nanotube (BNNT) and an outside semiconducting MoS2 nanotube. As the technique is highly applicable to other materials in the current 2D libraries,4-6 we anticipate our strategy to be a starting point for discovering a class of new semiconducting nanotube materials. A plethora of function-designable 1D heterostructures will appear after the combination of CNTs, BNNTs and semiconducting nanotubes.
Stanley considered suitably normalized characters of the symmetric groups on Young diagrams having a special geometric form, namely multirectangular Young diagrams. He proved that the character is a polynomial in the lengths of the sides of the rectangles forming the Young diagram and he conjectured an explicit form of this polynomial. This Stanley character polynomial and this way of parametrizing the set of Young diagrams turned out to be a powerful tool for several problems of the dual combinatorics of the characters of the symmetric groups and asymptotic representation theory, in particular to Kerov polynomials.
We model the exchange-correlation (XC) energy density of the Si crystal and atom as calculated by variational Monte Carlo (VMC) methods with a gradient analysis beyond the local density approximation (LDA). We find the Laplacian of the density to be an excellent predictor of the discrepancy between VMC and LDA energy densities in each system. A simple Laplacian-based correction to the LDA energy density is developed by means of a least square fit to the VMC XC energy density for the crystal, which fits the homogeneous electron gas and Si atom without further effort.
It has been debated for a decade whether there is a large overabundance of strongly lensed arcs in galaxy clusters, compared to expectations from LambdaCDM cosmology. We perform ray tracing through the most massive halos of the Millennium simulation at several redshifts in their evolution, using the Hubble Ultra Deep Field as a source image, to produce realistic simulated lensed images. We compare the lensed arc statistics measured from the simulations to those of a sample of 45 X-ray selected clusters, observed with the Hubble Space Telescope, that we have analysed in Horesh et al. (2010). The observations and the simulations are matched in cluster masses, redshifts, observational effects, and the algorithmic arc detection and selection. At z=0.6 there are too few massive-enough clusters in the Millennium volume for a proper statistical comparison with the observations. At redshifts 0.3<z<0.5, however, we have large numbers of simulated and observed clusters, and the latter are an unbiased selection from a complete sample. For these redshifts, we find excellent agreement between the observed and simulated arc statistics, in terms of the mean number of arcs per cluster, the distribution of number of arcs per cluster, and the angular separation distribution. At z ~ 0.2 some conflict remains, with real clusters being ~3 times more efficient arc producers than their simulated counterparts. This may arise due to selection biases in the observed subsample at this redshift, to some mismatch in masses between the observed and simulated clusters, or to physical effects that arise at low redshift and enhance the lensing efficiency, but which are not represented by the simulations.
For renewal-reward processes with a power-law decaying waiting time distribution, anomalously large probabilities are assigned to atypical values of the asymptotic processes. Previous works have reveals that this anomalous scaling causes a singularity in the corresponding large deviation function. In order to further understand this problem, we study in this article the scaling of variance in several renewal-reward processes: counting processes with two different power-law decaying waiting time distributions and a Knudsen gas (a heat conduction model). Through analytical and numerical analyses of these models, we find that the variances show an anomalous scaling when the exponent of the power law is -3. For a counting process with the power-law exponent smaller than -3, this anomalous scaling does not take place: this indicates that the processes only fluctuate around the expectation with an error that is compatible with a standard large deviation scaling. In this case, we argue that anomalous scaling appears in higher order cumulants. Finally, many-body particles interacting through soft-core interactions with the boundary conditions employed in the Knudsen gas are studied using numerical simulations. We observe that the variance scaling becomes normal even though the power-law exponent in the boundary conditions is -3.
Quantum paraelectrics are materials in which a long-range ferroelectric/antiferroelectric order is suppressed by quantum fluctuations, i.e. zero-point motion of the lattice prevents condensation of the soft polar phonon mode even at T = 0 K. The most prominent quantum paraelectric materials are SrTiO3, KTaO3, and CaTiO3. Here we focus on peculiar properties of the pseudo-cubic perovskite CaTi1-xRuxO3 system. Namely, as soon as any concentration of either Ru or Ti is introduced into the pure compounds, a concentration-independent ferromagnetic-like transition occurs at low temperatures. We present the experimental evidence of the spin-polarized ground state of CaTi1-xRuxO3 induced by coupling of magnetic moments of Ru impurities with quantum paraelectric fluctuations in the host compound CaTiO3.
For an affine toric variety $\spec(A)$, we give a convex geometric interpretation of the Gerstenhaber product $\HH^2(A)\times \HH^2(A)\to \HH^3(A)$ between the Hochschild cohomology groups. In the case of Gorenstein toric surfaces we prove that the Gerstenhaber product is the zero map. As an application in commutative deformation theory we find the equations of the versal base space (in special lattice degrees) up to second order for not necessarily isolated toric Gorenstein singularities. Our construction reproves and generalizes results obtained in [1] and [13].
We prove an identity of Segre classes for zero-schemes of compatible sections of two vector bundles. Applications include bounds on the number of equations needed to cut out a scheme with the same Segre class as a given subscheme of (for example) a projective variety, and a `Segre-Bertini' theorem controlling the behavior of Segre classes of singularity subschemes of hypersurfaces under general hyperplane sections.   These results interpolate between an observation of Samuel concerning multiplicities along components of a subscheme and facts concerning the integral closure of corresponding ideals. The Segre-Bertini theorem has applications to characteristic classes of singular varieties. The main results are motivated by the problem of computing Segre classes explicitly and applications of Segre classes to enumerative geometry.
More than 30 million of high-energy muons collected with the MACRO detector at the underground Gran Sasso Laboratory have been used to search for flux variations of different natures. Two kinds of studies were carried out: search for periodic variations and for the occurrence of clusters of events. Different analysis methods, including Lomb-Scargle spectral analysis and Scan Test statistics have been applied to the data.
Based on results from the physics and mathematics literature which suggest a series of clearly defined conjectures, we formulate three simple scenarios for the fate of hard sphere crystallization in high dimension: (A) crystallization is impeded and the glass phase constitutes the densest packing, (B) crystallization from the liquid is possible, but takes place much beyond the dynamical glass transition and is thus dynamically implausible, or (C) crystallization is possible and takes place before (or just after) dynamical arrest, thus making it plausibly accessible from the liquid state. In order to assess the underlying conjectures and thus obtain insight into which scenario is most likely to be realized, we investigate the densest sphere packings in dimension $d=3$-$10$ using cell-cluster expansions as well as numerical simulations. These resulting estimates of the crystal entropy near close-packing tend to support scenario C. We additionally confirm that the crystal equation of state is dominated by the free volume expansion and that a meaningful polynomial correction can be formulated.
A non-Hermitian PT-symmetric system can have full real spectrum but does not ensure probability preserving time evolution, in contrast to that of a Hermitian system. We present a non-Hermitian two-band model, which is comprised of dimerized hopping terms and staggered imaginary on-site potentials, and study the dynamics in the exact PT-symmetric phase based on the exact solution. It is shown that an initial state, which does not involve two equal-momentum-vector eigenstates in different bands, obeys perfectly probability-preserving time evolution in terms of the Dirac inner product. Beyond this constriction, the quasi-Hermitian dynamical behaviors, such as non-spreading propagation and fractional revival of a Gaussian wave packet, are also observed.
Correlations between low-lying electric dipole (E1) strength and neutron skin thickness are systematically investigated with the fully self-consistent random-phase approximation using the Skyrme energy functionals. The presence of strong correlation among these quantities is currently under dispute. We find that the strong correlation is present in properly selected nuclei, namely in spherical neutron-rich nuclei in the region where the neutron Fermi levels are located at orbits with low orbital angular momenta. The significant correlation between the fraction of the energy-weighted sum value and the slope of the symmetry energy is also observed. The deformation in the ground state seems to weaken the correlation.
The quasipotential formalism for elastic scattering from relativistic bound states is formulated based on the instant constraint in the Breit frame. The quasipotential electromagnetic current is derived from Mandelstam's five-point kernel and obeys a two-body Ward identity. Breit-frame wave functions are obtained directly by solving integral equations with nonzero total three-momentum, thus accomplishing a dynamical boost. Calculations of electron-deuteron elastic form factors illustrate the importance of the dynamical boost versus kinematic boosts of the rest frame wave functions.
In this paper, we consider the following symmetric non-local Dirichlet forms of pure jump type on metric measure space $(M,d,\mu)$: $$\mathcal{E}(f,g)=\int_{M\times M} (f(x)-f(y))(g(x)-g(y))\,J(dx,dy),$$ where $J(dx,dy)$ is a symmetric Radon measure on $M\times M\setminus {\rm diag}$ that may have different scalings for small jumps and large jumps. Under general volume doubling condition on $(M,d,\mu)$ and some mild quantitative assumptions on $J(dx, dy)$ that are allowed to have light tails of polynomial decay at infinity, we establish stability results for two-sided heat kernel estimates as well as heat kernel upper bound estimates in terms of jumping kernel bounds, the cut-off Sobolev inequalities, and the Faber-Krahn inequalities (resp.\ the Poincar\'e inequalities). We also give stable characterizations of the corresponding parabolic Harnack inequalities.
This study aims to provide further evidence for the potential influence of the global solar magnetic field on localised chromospheric jets, the macrospicules (MS). To find a connection between the long-term variation of properties of MS and other solar activity proxies, including e.g. the temporal variation of the frequency shift of solar global oscillations, sunspot area, etc., a database overarching seven years of observations was built up. This database contains 362 MS, based on observations at the 30.4 nm of the Atmospheric Imaging Assembly (AIA) on-board the Solar Dynamics Observatory (SDO). Three of the five investigated physical properties of MS show a clear long-term temporal variation after smoothing the raw data. Wavelet analysis of the temporal variation of maximum length, maximum area and average velocity is carried out. The results reveal a strong pattern of periodicities at around 2-year (also referred to as Quasi-Biennial Oscillations -- QBOs). Comparison to solar activity proxies, that also possess the properties of QBOs, provides some interesting features: the minima and maxima of QBOs of MS properties occur at around the same epoch as the minima and maxima of these activity proxies. For most of the time span investigated, the oscillations are out-of-phase. This out-of-phase behaviour was also corroborated by a cross-correlation analysis. These results suggest that the physical processes, that generate and drive the long-term evolution of the global solar activity proxies, may be coupled to the short-term local physical processes driving the macrospicules, and, therefore modulate the properties of local dynamics.
The structure of the models of section 3.2 has been found to be richer than previously thought; a revised version has appeared as hep-th/9808087.
We use data from the DESI Legacy Survey imaging to probe the galaxy density field in tomographic slices covering the redshift range $0<z<0.8$. After careful consideration of completeness corrections and galactic cuts, we obtain a sample of $4.9\times 10^7$ galaxies covering 17 739 deg$^2$. We derive photometric redshifts with precision $\sigma_z/(1+z)=0.012 - 0.015$, and compare with alternative estimates. Cross-correlation of the tomographic galaxy maps with Planck maps of CMB temperature and lensing convergence probe the growth of structure since $z=0.8$. The signals are compared with a fiducial Planck $\Lambda$CDM model, and require an overall scaling in amplitude of $A_\kappa=0.901\pm 0.026$ for the lensing cross-correlation and $A_{\rm ISW} = 0.984 \pm 0.349$ for the temperature cross-correlation, interpreted as the Integrated Sachs-Wolfe effect. The ISW amplitude is consistent with the fiducial $\Lambda$CDM prediction, but lies significantly below the prediction of the AvERA model of R\'acz et al. (2017), which has been proposed as an alternative explanation for cosmic acceleration. Within $\Lambda$CDM, our low amplitude for the lensing cross-correlation requires a reduction either in fluctuation normalization or in matter density compared to the Planck results, so that $\Omega_m^{0.78}\sigma_8=0.297\pm 0.009$. In combination with the total amplitude of CMB lensing, this favours a shift mainly in density: $\Omega_m=0.274\pm0.024$. We discuss the consistency of this figure with alternative evidence. A conservative compromise between lensing and primary CMB constraints would require $\Omega_m=0.296\pm0.006$, where the 95% confidence regions of both probes overlap.
The crystalline structure, anisotropic magnetoresistance (AMR), and magnetization of La0.7Sr0.3MnO3/SrTiO3 (LSMO/STO) superlattices grown by an rf sputtering system are systematically analyzed to study the spin polarization of manganite at interfaces. A perfectly epitaxial growth with sharp interfaces between LSMO and STO layers is confirmed by the transmission electron microscopy (TEM) image and the x-ray diffraction. The presence of positive low-temperature AMR in LSMO/STO superlattices with thinner LSMO layers or thicker STO layers implies that two bands of majority and minority character contribute to the transport properties, leading to a reduced spin polarization. Furthermore, the magnetization of superlattices follows the T3/2 law at low temperatures and decays more quickly as the thickness ratio dSTO/dLSMO increases, corresponding to a reduced exchange coupling. The results clearly show that the spin polarization is strongly correlated with the influence of interface-induced strain on the structure.
We present a worldvolume effective action suitable for the study of the confined phase of a Dp-anti-Dp system at weak coupling. We identify the mechanism by which the fundamental string arises from this action as a confined electric flux string when the Dp and the anti-Dp annihilate. We construct an explicit dual action, more suitable for the study of the strong coupling regime, and show that it realizes a generalized Higgs-Stueckelberg phase for the (relative) (p-2)-form field dual to the (overall) BI vector. This is the mechanism put forward by Yi and collaborators based on duality arguments in order to explain the breaking of the overall U(1) gauge group at strong coupling. Indeed, in our dual description the Goldstone boson is a (p-3)-form magnetically charged with respect to the overall BI vector field. This indicates that the condensing tachyonic objects originate from open D(p-2)-branes stretched between the brane and the anti-brane. Our results provide an explicit realization of the breaking of the overall U(1) gauge group perturbatively, in a way consistent with the duality symmetries of String Theory.
Thermal fluctuations of charged particles, fluctuations akin to Brownian motion, can excite optical surface-states leading to the concept of the thermal near-field, which is a highly localized, and, therefore, evanescent optical density of states that exist at distances much less than the thermal emission wavelength. By tunneling the surface charge emitted photons into nearby waveguides, the thermally excitable near-field optical density of states can be enhanced, engineered, and efficiently extracted to the far-field for observation. With this technique, the plasmonic thermal near-field of a 10nm thick ITO film, known to have plasmonic activity in the 1500nm wavelength region, was probed under external illumination and by thermal excitation at 873K. The results confirm that waveguides provide a large density of optical channels with spatial overlap and k-vector matching to facilitate plasmon de-excitation in the near-field through photon tunneling for extraction into the far-field. Furthermore, it is shown that the thermal near-field can be observed without the introduction of a vacuum-gap, a feature unique to this particular method.
We consider self-avoiding Nambu-Goto open strings on a random surface. We have shown that the partition function of such a string theory can be calculated exactly. The string susceptibility for the disk is evaluated to be $-\frac{1}{2}$. We also consider modifications of the Nambu-Goto action which are exactly soluble on a random surface.
We prove matrix and scalar differential Harnack inequalities for linear parabolic equations on Riemannian and K\"ahler manifolds.