ShantanuT01/DACTYL-Pretraining huggingface dataset:
We introduce semi-perfect obstruction theory of a Deligne-Mumford stack $X$ consisting of local perfect obstruction theories with weak comparisons on overlaps. We show that semi-perfect obstruction theory shares similar properties with perfect obstruction theory. We use semi-perfect obstruction theory to construct virtual cycles of moduli of derived objects on Calabi-Yau threefolds.   In the revision, we assume the existence of obstruction sheaf and put the (coarse moduli of the) intrinsic normal cone inside the obstruction sheaf. This avoids the issue of descent of bundle stacks of the local obstruction complexes.
The non-uniform ground state of the two-dimensional three-band Hubbard model for the oxide high-Tc superconductors is investigated using a variational Monte Carlo method. We examine the effect produced by holes doped into the antiferromagnetic (AF) background in the underdoped region. It is shown that the AF state with spin modulations and stripes is stabilized du to holes travelling in the CuO plane. The structures of the modulated AF spins are dependent upon the parameters used in the model. The effect of the boundary conditions is reduced for larger systems. We show that there is a region where incommensurability is proportional to the hole density. Our results give a consistent description of stripes observed by the neutron- scattering experiments based on the three-band model for CuO plane.
We have obtained deep photometry in two 1x1 degree fields covering the close pair of dwarf spheroidal galaxies (dSph) Leo IV and Leo V and part of the area in between. We find that both systems are significantly larger than indicated by previous measurements based on shallower data and also significantly elongated. With half-light radii of r_h=4'.6 +- 0'.8 (206 +- 36 pc) and r_h=2'.6 +- 0'.6 (133 +- 31 pc), respectively, they are now well within the physical size bracket of typical Milky Way dSph satellites. Their ellipticities of epsilon ~0.5 are shared by many faint (M_V>-8) Milky Way dSphs. The large spatial extent of our survey allows us to search for extra-tidal features with unprecedented sensitivity. The spatial distribution of candidate red giant branch and horizontal branch stars is found to be non-uniform at the ~3 sigma level. This substructure is aligned along the direction connecting the two systems, indicative of a possible `bridge' of extra-tidal material. Fitting the stellar distribution with a linear Gaussian model yields a significance of 4 sigma for this overdensity, a most likely FWHM of ~16 arcmin and a central surface brightness of ~32 mag arcsec^{-2}. We investigate different scenarios to explain the close proximity of Leo IV and Leo V and the possible tidal bridge between them. Orbit calculations demonstrate that they are unlikely to be remnants of a single disrupted progenitor, while a comparison with cosmological simulations shows that a chance collision between unrelated subhalos is negligibly small. Leo IV and Leo V could, however, be a bound `tumbling pair' if their combined mass exceeds 8 +- 4 x 10^9 M_sun. The scenario of an internally interacting pair appears to be the most viable explanation for this close celestial companionship. (abridged)
We present a histories version of the connection formalism of general relativity. Such an approach introduces a spacetime description--a characteristic feature of the histories approach--and we discuss the extent to which the usual loop variables are compatible with a spacetime description. In particular, we discuss the definability of the Barbero connection without any gauge fixing. Although it is not the pullback of a spacetime connection onto the three-surface and it does not have a natural spacetime interpretation, this does not mean that the Barbero connection is not suitable variable for quantisation; it appears naturally in the formalism even in absence of gauge fixing. It may be employed therefore, to define loop variables similar to those employed in loop quantum gravity. However, the loop algebra would have to be augmented by the introduction of additional variables.
String theory suggests the existence of gravitational-strength scalar fields ("dilaton" and "moduli") whose couplings to matter violate the equivalence principle. This provides a new motivation for high-precision clock experiments, as well as a generic theoretical framework for analyzing their significance.
We present tables of record (maximal) gaps between densest prime constellations, or k-tuplets. The tables contain all maximal gaps between prime k-tuplets up to 10^15, for each k<=7.
Positive results of dark matter searches in experiments DAMA/NaI and DAMA/LIBRA taken together with negative results of other groups can imply nontrivial particle physics solutions for cosmological dark matter. Stable particles with charge -2 bind with primordial helium in O-helium "atoms" (OHe), representing a specific Warmer than Cold nuclear-interacting form of dark matter. Slowed down in the terrestrial matter, OHe is elusive for direct methods of underground Dark matter detection like those used in CDMS experiment, but its low energy binding with nuclei can lead to annual variations of energy release in the interval of energy 2-6 keV in DAMA/NaI and DAMA/LIBRA experiments. Schrodinger equation for system of nucleus and OHe is solved for a spherically symmetrical potential, formed by the Yukawa tail of nuclear scalar isoscalar attraction potential, acting on He beyond the nucleus, and dipole Coulomb repulsion between the nucleus and OHe at distances from the nuclear surface, smaller than the size of OHe. The values of coupling strength and mass of meson, mediating scalar isoscalar, are rather uncertain. Within the uncertainties of parameters of nuclear potential we find a range of these parameters, at which the sodium and/or iodine nuclei have a few keV binding energy with OHe. At nuclear parameters, reproducing DAMA results, the energy release predicted for detectors with chemical content other than NaI differ in the most cases from the one in DAMA detector. In particular, it is shown that in the case of CDMS germanium state has binding energy with OHe beyond the range of 2-6 keV and its formation should not lead to ionization in the energy range of DAMA signal. (abridged)
We obtain a Beale-Kato-Majda-type criterion with optimal frequency and temporal localization for the 3D Navier-Stokes equations. Compared to previous results our condition only requires the control of Fourier modes below a critical frequency, whose value is explicit in terms of time scales. As applications it yields a strongly frequency-localized condition for regularity in the space $B^{-1}_{\infty,\infty}$ and also a lower bound on the decaying rate of $L^p$ norms $2\leq p <3$ for possible blowup solutions. The proof relies on new estimates for the cutoff dissipation and energy at small time scales which might be of independent interest.
Measuring the respiratory signal from a video based on body motion has been proposed and recently matured in products for video health monitoring. The core algorithm for this measurement is the estimation of tiny chest/abdominal motions induced by respiration, and the fundamental challenge is motion sensitivity. Though prior arts reported on the validation with real human subjects, there is no thorough/rigorous benchmark to quantify the sensitivities and boundary conditions of motion-based core respiratory algorithms that measure sub-pixel displacement between video frames. In this paper, we designed a setup with a fully-controllable physical phantom to investigate the essence of core algorithms, together with a mathematical model incorporating two motion estimation strategies and three spatial representations, leading to six algorithmic combinations for respiratory signal extraction. Their promises and limitations are discussed and clarified via the phantom benchmark. The insights gained in this paper are intended to improve the understanding and applications of camera-based respiration measurement in health monitoring.
We report the statistical properties of stars and brown dwarfs obtained from four radiation hydrodynamical simulations of star cluster formation that resolve masses down to the opacity limit for fragmentation. The calculations are identical except for their dust and gas opacities. Assuming dust opacity is proportional to metallicity, the calculations span a range of metallicities from 1/100 to 3 times solar, although we emphasise that changing the metallicity has other thermodynamic effects that the calculations do not capture (e.g. on the thermal coupling between gas and dust).   All four calculations produce stellar populations whose statistical properties are difficult to distinguish from observed stellar systems, and we find no significant dependence of stellar properties on opacity. The mass functions and properties of multiple stellar systems are consistent with each other. However, we find protostellar mergers are more common with lower opacities. Combining the results from the three calculations with the highest opacities, we obtain a stellar population consisting of more than 500 stars and brown dwarfs. Many of the statistical properties of this population are in good agreement with those observed in our Galaxy, implying that gravity, hydrodynamics, and radiative feedback may be the primary ingredients for determining the statistical properties of low-mass stars. However, we do find indications that the calculations may be slightly too dissipative. Although further calculations will be required to understand all of the effects of metallicity on stellar properties, we conclude that stellar properties are surprisingly resilient to variations of the dust and gas opacities.
This work prepares new probability bounds for sums of random, independent, Hermitian tensors. These probability bounds characterize large-deviation behavior of the extreme eigenvalue of the sums of random tensors. We extend Lapalace transform method and Lieb's concavity theorem from matrices to tensors, and apply these tools to generalize the classical bounds associated with the names Chernoff, Bennett, and Bernstein from the scalar to the tensor setting. Tail bounds for the norm of a sum of random rectangular tensors are also derived from corollaries of random Hermitian tensors cases. The proof mechanism can also be applied to tensor-valued martingales and tensor-based Azuma, Hoeffding and McDiarmid inequalities are established.
We study the Chow group of 1-cycles of the moduli space of semistable parabolic vector bundles of fixed rank, determinant and a generic weight over a nonsingular projective curve over $\mathbb{C}$ of genus at least 3. We show that, the Chow group of 1-cycles remains isomorphic as we vary the generic weight. As a consequence, we can give an explicit description of the Chow group in the case of rank 2 and determinant $\mathcal{O}(x)$, where $x\in X$ is a fixed point.
Explaining observed properties in terms of underlying shape degrees of freedom is a well--established prism with which to understand atomic nuclei. Self--consistent mean--field models provide one tool to understand nuclear shapes, and their link to other nuclear properties and observables. We present examples of how the time--dependent extension of the mean--field approach can be used in particular to shed light on nuclear shape properties, particularly looking at the giant resonances built on deformed nuclear ground states, and at dynamics in highly-deformed fission isomers. Example calculations are shown of $^{28}$Si in the first case, and $^{240}$Pu in the latter case.
We studied the non-equilibrium dynamics of the q-state Potts model in the square lattice, after a quench to sub-critical temperatures. By means of a continuous time Monte Carlo algorithm (non-conserved order parameter dynamics) we analyzed the long term behavior of the energy and relaxation time for a wide range of quench temperatures and system sizes. For q>4 we found the existence of different dynamical regimes, according to quench temperature range. At low (but finite) temperatures and very long times the Lifshitz-Allen-Cahn domain growth behavior is interrupted with finite probability when the system stuck in highly symmetric non-equilibrium metastable states, which induce activation in the domain growth, in agreement with early predictions of Lifshitz [JETP 42, 1354 (1962)]. Moreover, if the temperature is very low, the system always gets stuck at short times in a highly disordered metastable states with finite life time, which have been recently identified as glassy states. The finite size scaling properties of the different relaxation times involved, as well as their temperature dependency are analyzed in detail.
This paper withdrawn by the authors due to errors in the TEM measurements of the densities and sizes of small islands.
Differentiability of semigroups is useful for many applications. Here we focus on stochastic differential equations whose diffusion coefficient is the square root of a differentiable function but not differentiable itself. For every $m\in\{0,1,2\}$ we establish an upper bound for a $C^m$-norm of the semigroup of such a diffusion in terms of the $C^m$-norms of the drift coefficient and of the squared diffusion coefficient. The constants in our upper bound are often dimension-independent. Our estimates are thus suitable for analyzing certain high-dimensional and infinite-dimensional degenerate stochastic differential equations.
It is possible to construct L\'evy white noises as generalized random processes in the sense of Gel'fand and Vilenkin, or as an independently scattered random measures introduced by Rajput and Rosinski. In this article, we unify those two approaches by extending the L\'evy white noise, defined as a generalized random process, to an independently scattered random measure. We are then able to give general integrability conditions for L\'evy white noises, thereby maximally enlarging their domain of definition. Based on this connection, we provide new criteria for the practical determination of the domain of definition, including specific results for the subfamilies of Gaussian, symmetric-{\alpha}-stable, generalized Laplace, and compound Poisson white noises. We also apply our results to formulate a general criterion for the existence of generalized solutions of linear stochastic partial differential equations driven by a L\'evy white noise.
We establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation $u_{tt} - c(u)(c(u)u_x)_x=0$, for initial data of finite energy. Here $c(\cdot)$ is any smooth function with uniformly positive bounded values.
We introduce the notion of Artin motives and cohomological motives over a scheme X. Given a cohomological motive M over X, we construct its punctual weight zero part $\omega^0_X(M)$ as the universal Artin motive mapping to M. We use this to define a motive E_X over X which is an invariant of the singularities of X. The first half of the paper is devoted to the study of the functors $\omega^0_X$ and the computation of the motives E_X.   In the second half of the paper, we develop the application to locally symmetric varieties. Specifically, let Y be a locally symmetric variety and denote by p:W-->Z the projection of its reductive Borel-Serre compactification W onto its Baily-Borel Satake compactification Z. We show that $Rp_*(\Q_W)$ is naturally isomorphic to the Betti realization of the motive E_Z, where Z is viewed as a scheme. In particular, the direct image of E_Z along the projection of Z to Spec(C) gives a motive whose Betti realization is naturally isomorphic to the cohomology of W.
Type Ibn supernova SN~2010al is explored to infer parameters of supernova and a circumstellar (CS) shell. The CS interaction model combined with the spectral model of 4600\AA\ blend suggests the explosion of a WR star with the energy of $(1-1.5)\times10^{51}$ erg inside a dense confined CS shell with the mass of $\sim0.1$\msun\ and kinetic energy of $\sim 10^{48}$ erg. The confined CS shell has been formed during the last 0.4 yr prior to the core collapse.
We present an investigation on electronic structure of 1T-TiTe2 material via high-resolution angle-resolved photoemission spectroscopy (ARPES), utilizing tunable photon energy excitations. The typical semimetal-like electronic structure is observed and examined, where multiple hole pockets related to Te 5p bands and one electron pockets related to Ti 3d band are populated. The obtained results reveals i) a pronounced three-dimensional (3D) electronic structure of 1T-TiTe2 with typical semi-metallic features, for both the Ti 3d and the Te 5p states; ii) multiple Fermi surface (FS) sheets and complex band structure; and iii) an obvious kink in dispersion at an energy of about 18 meV below the Fermi energy, the first experimental observation of a kink structure in 1T-TiTe2, which may originate from electron-phonon coupling. These important and significant findings can help us to gain an in-depth understanding of the 3D electronic structure of semimetallic 1T- TiTe2.
We consider the transport equation driven by the fractional Brownian motion. We study the existence and the uniqueness of the weak solution and, by using the tools of the Malliavin calculus, we prove the existence of the density of the solution and we give Gaussian estimates from above and from below for this density.
Graphitization of the 6H-SiC(0001) surface as a function of annealing temperature has been studied by ARPES, high resolution XPS, and LEED. For the initial stage of graphitization - the 6root3 reconstructed surface - we observe sigma-bands characteristic of graphitic sp2-bonded carbon. The pi-bands are modified by the interaction with the substrate. C1s core level spectra indicate that this layer consists of two inequivalent types of carbon atoms. The next layer of graphite (graphene) formed on top of the 6root3 surface at TA=1250-1300 degree C has an unperturbed electronic structure. The annealing at higher temperatures results in the formation of a multilayer graphite film. It is shown that the atomic arrangement of the interface between graphite and the SiC(0001) surface is practically identical to that of the 6root3 reconstructed layer.
Carmichael quotients for an integer $m\ge 2$ are introduced analogous to Fermat quotients, by using Carmichael function $\lambda(m)$. Various properties of these new quotients are investigated, such as basic arithmetic properties, sequences derived from Carmichael quotients, Carmichael-Wieferich numbers, and so on. Finally, we link Carmichael quotients to perfect nonlinear functions.
Egocentric videos are characterised by their ability to have the first person view. With the popularity of Google Glass and GoPro, use of egocentric videos is on the rise. Recognizing action of the wearer from egocentric videos is an important problem. Unstructured movement of the camera due to natural head motion of the wearer causes sharp changes in the visual field of the egocentric camera causing many standard third person action recognition techniques to perform poorly on such videos. Objects present in the scene and hand gestures of the wearer are the most important cues for first person action recognition but are difficult to segment and recognize in an egocentric video. We propose a novel representation of the first person actions derived from feature trajectories. The features are simple to compute using standard point tracking and does not assume segmentation of hand/objects or recognizing object or hand pose unlike in many previous approaches. We train a bag of words classifier with the proposed features and report a performance improvement of more than 11% on publicly available datasets. Although not designed for the particular case, we show that our technique can also recognize wearer's actions when hands or objects are not visible.
The classical Michael-Simon and Allard inequality is a Sobolev inequality for functions defined on a submanifold of Euclidean space. It is governed by a universal constant independent of the manifold, but displays on the right-hand side an additional $L^p$ term weighted by the mean curvature of the underlying manifold. We prove here a fractional version of this inequality on hypersurfaces of Euclidean space that are boundaries of convex sets. It involves the Gagliardo semi-norm of the function, as well as its $L^p$ norm weighted by the fractional mean curvature of the hypersurface.   As an application, we establish a new upper bound for the maximal time of existence in the smooth fractional mean curvature flow of a convex set. The bound depends on the perimeter of the initial set instead of on its diameter.
High quality fake videos and audios generated by AI-algorithms (the deep fakes) have started to challenge the status of videos and audios as definitive evidence of events. In this paper, we highlight a few of these challenges and discuss the research opportunities in this direction.
Using a multidimensional large sieve inequality, we obtain a bound for the mean square error in the Chebotarev theorem for division fields of elliptic curves that is as strong as what is implied by the Generalized Riemann Hypothesis. As an application we prove a theorem to the effect that, according to height, almost all elliptic curves are Serre curves, where a Serre curve is an elliptic curve whose torsion subgroup, roughly speaking, has as much Galois symmetry as possible.
Flare stars were discovered in the late 1940s in the solar vicinity and were named UV Cet-type variables (classical FSs). Among the FSs within 100 pc we search for young stars. For the search we take spectra with sufficient resolution to resolve Lithium at 6707 \AA and Calcium at 6718 \AA of all the stars. The real young stars are prime targets for the search of extra-solar planets by direct imaging.
We study the first excited state of He4 in a microscopic {H3+p,He3+n} cluster model, including H3 and He3 distortions. The phenomenological 1S0 H3+p scattering phase shift is well reproduced. We localize a complex pole of the S-matrix between the H3+p and He3+n thresholds. The corresponding resonance parameters are E_r=93 keV position relative to H3+p, and Gamma=390 keV width. A pole search is also performed in an extended R-matrix method, and a resonance is found with parameters E_r=114 keV and Gamma=392 keV. The R-matrix approach gives several additional poles, some of which may be connected with an enhanced threshold effect.
We study magnetic behaviour of the Yb$^{3+}$ ions on a frustrated pyrochlore lattice in the spinel {\CYS}. The crystal-electric field parameters deduced from high-energy inelastic neutron scattering reveal well-isolated ytterbium ground state doublet with a weakly Ising character. Magnetic order studied by powder neutron diffraction evolves from the $XY$-type antiferromagnetic $\Gamma_5$ state to a splayed ice-like ferromagnet (both with k=0) in applied magnetic field with $B_c$=3 T. Low-energy inelastic neutron scattering identifies weakly dispersive magnetic bands around 0.72 meV starting at $\mid\bf{Q}\mid$ = 1.1 \AA$^{-1}$~ at zero field, which diminish with field and vanish above 3 T. We explain the observed magnetic behaviour in framework of the nearest-neighbour anisotropic exchange model for effective $S=1/2$ Kramers doublets on the pyrochlore lattice. The estimated exchanges position the {\CYS} spinel close to the phase boundary between the $\Gamma_5$ and splayed ferromagnet states, similar to the Yb-pyrochlores suggesting an important role of the competition between these phases.