ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let W be a projective variety of dimension n+1, L a free line bundle on W, X in $H^0(L^d)$ a hypersurface of degree d which is generic among those given by sums of monomials from $L$, and let $f : Y \to X$ be a generically finite map from a smooth m-fold Y. We suppose that f is r-filling, i.e. upon deforming X in $H^0(L^d)$, f deforms in a family such that the corresponding deformations of $Y^r$ dominate $W^r$. Under these hypotheses we give a lower bound for the dimension of a certain linear system on the Cartesian product $Y^r$ having certain vanishing order on a diagonal locus as well as on a double point locus. This yields as one application a lower bound on the dimension of the linear system |K_{Y} - (d - n + m)f^*L - f^*K_{W}| which generalizes results of Ein and Xu (and in weaker form, Voisin). As another perhaps more surprising application, we conclude a lower bound on the number of quadrics containing certain projective images of Y.
While often the point sources in X-ray surveys are dominated by AGN, with the high sensitivity of modern X-ray telescopes such as Chandra and XMM-Newton normal/starburst galaxies are also being detected in large numbers. We have made use of Bayesian statistics for both the selection of galaxies from deep X-ray surveys and in the analysis of the luminosity functions for galaxies. These techniques can be used to similarly select galaxies from wide-area X-ray surveys and to analyze their luminosity function. The prospects for detecting galaxies and AGN from a proposed ``wide-deep'' XMM-Newton survey and from future wide-area X-ray survey missions (such as WFXT and eRosita) are also discussed.
The twist angle between the monolayers in van der Waals heterostructures provides a new degree of freedom in tuning material properties. We compare the optical properties of WSe2 homobilayers with 2H and 3R stacking using photoluminescence, Raman spectroscopy, and reflectance contrast measurements under ambient and cryogenic temperatures. Clear stacking- dependent differences are evident for all temperatures, with both photoluminescence and reflectance contrast spectra exhibiting a blue shift in spectral features in 2H compared to 3R bilayers. Density functional theory (DFT) calculations elucidate the source of the variations and the fundamental differences between 2H and 3R stackings. DFT finds larger energies for both A and B excitonic features in 2H than in 3R, consistent with experimental results. In both stacking geometries, the intensity of the dominant A1g Raman mode exhibits significant changes as a function of laser excitation wavelength. These variations in intensity are intimately linked to the stacking- and temperature-dependent optical absorption through resonant enhancement effects. The strongest enhancement is achieved when the laser excitation coincides with the C excitonic feature, leading to the largest Raman intensity under 514 nm excitation in 2H stacking and at 520 nm in 3R stacked WSe2 bilayers.
The RNiO$_3$ perovskites are known to order antiferromagnetically below a material-dependent N\'eel temperature $T_\text{N}$. We report experimental evidence indicating the existence of a second magnetically-ordered phase in TlNiO$_3$ above $T_\text{N} = 104$ K, obtained using nuclear magnetic resonance and muon spin rotation spectroscopy. The new phase, which persists up to a temperature $T_\text{N}^* = 202$ K, is suppressed by the application of an external magnetic field of approximately 1 T. It is not yet known if such a phase also exists in other perovskite nickelates.
We study the hole probabilities for ${\mathcal X}_{\infty}^{(\alpha)}$ ($\alpha>0$), a determinantal point process in the complex plane with the kernel $\mathbb K_{\infty}^{(\alpha)}(z,w)=\frac{\alpha}{2\pi}E_{\frac{2}{\alpha},\frac{2}{\alpha}}(z\bar w)e^{-\frac{|z|^{\alpha}}{2}-\frac{|w|^{\alpha}}{2}}$ with respect to Lebesgue measure on the complex plane, where $E_{a,b}(z)$ denotes the Mittag-Leffler function. Let $U$ be an open subset of $D(0,(\frac{2}{\alpha})^{\frac{1}{\alpha}})$ and ${\mathcal X}_{\infty}^{(\alpha)}(rU)$ denote the number of points of ${\mathcal X}_{\infty}^{(\alpha)}$ that fall in $rU$. Then, under some conditions on $U$, we show that $$ \lim_{r\to \infty}\frac{1}{r^{2\alpha}}\log\mathbb P[\mathcal X_{\infty}^{(\alpha)}(rU)=0]=R_{\emptyset}^{(\alpha)}-R_{U}^{(\alpha)}, $$ where $\emptyset$ is the empty set and $$ R_U^{(\alpha)}:=\inf_{\mu\in \mathcal P(U^c)}\left\{\iint \log{\frac{1}{|z-w|}}d\mu(z)d\mu(w)+\int |z|^{\alpha}d\mu(z) \right\}, $$ $\mathcal P(U^c)$ is the space of all compactly supported probability measures with support in $U^c$. Using potential theory, we give an explicit formula for $R_U^{(\alpha)}$, the minimum possible energy of a probability measure compactly supported on $U^c$ under logarithmic potential with an external field $\frac{|z|^{\alpha}}{2}$. In particular, $\alpha=2$ gives the hole probabilities for the infinite ginibre ensemble. Moreover, we calculate $R_U^{(2)}$ explicitly for some special sets like annulus, cardioid, ellipse, equilateral triangle and half disk.
We present a specific periodicity of the Galaxy images in the multipole domain which can be used for separation of the cosmic microwave background (CMB) signal from the Galaxy and foreground component.   This method takes into consideration all the coefficients of the expansion of the signal from the sky \Delta T(\Theta, \phi) into spherical harmonics and dealing with combination of multipoles a_{l,m} and a_{l+\Delta,m} for each multipole mode (\ell, -\ell \le m \le \ell) from the whole sky without galactic cut, masks or any dissection of the whole sky into disjoint regions. For the polar coordinate system we use particular values for \Delta=4n, n=1,2,... which remove all bright point-like sources localized in the Galactic plane and strong diffused component down to the CMB level. To illustrate that significant correlations of the point like sources and foregrounds a_{l,m},a_{l+\Delta,m} coefficients we apply this method to the WMAP Q,V and W bands in order to remove these marks of Galaxy from the maps. We believe that our method would be useful for separation of the CMB signal from different kind of "noises" in the maps.
We prove an unconditional (but slightly weakened) version of the main result of our earlier paper with the same title, which was, starting from dimension $4$, conditional to the Lefschetz standard conjecture. Let $X$ be a variety with trivial Chow groups, (i.e. the cycle class map to cohomology is injective on $CH(X)_\mathbb{Q}$). We prove that if the cohomology of a general very ample hypersurface $Y$ in $X$ is ``parameterized by cycles of dimension $c$'', then the Chow groups $CH_{i}(Y)_\mathbb{Q}$ are trivial for $i\leq c-1$.
Plant classification has a broad application prospective in agriculture and medicine, and is especially significant to the biology diversity research. As plants are vitally important for environmental protection, it is more important to identify and classify them accurately. Plant leaf classification is a technique where leaf is classified based on its different morphological features. The goal of this paper is to provide an overview of different aspects of texture based plant leaf classification and related things. At last we will be concluding about the efficient method i.e. the method that gives better performance compared to the other methods.
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear systems, molecular systems, and two-dimensional electron systems (Wigner-Dyson electrostatic analogy). Measures of quantum chaos and quantum integrability with respect to eigenergies of quantum systems are defined and calculated. Quantum statistical information functional is defined as negentropy (opposite of entropy or minus entropy). The distribution function for the random matrix ensembles is derived from the maximum entropy principle.
This paper is focused on the task of searching for a specific vehicle that appeared in the surveillance networks. Existing methods usually assume the vehicle images are well cropped from the surveillance videos, then use visual attributes, like colors and types, or license plate numbers to match the target vehicle in the image set. However, a complete vehicle search system should consider the problems of vehicle detection, representation, indexing, storage, matching, and so on. Besides, attribute-based search cannot accurately find the same vehicle due to intra-instance changes in different cameras and the extremely uncertain environment. Moreover, the license plates may be misrecognized in surveillance scenes due to the low resolution and noise. In this paper, a Progressive Vehicle Search System, named as PVSS, is designed to solve the above problems. PVSS is constituted of three modules: the crawler, the indexer, and the searcher. The vehicle crawler aims to detect and track vehicles in surveillance videos and transfer the captured vehicle images, metadata and contextual information to the server or cloud. Then multi-grained attributes, such as the visual features and license plate fingerprints, are extracted and indexed by the vehicle indexer. At last, a query triplet with an input vehicle image, the time range, and the spatial scope is taken as the input by the vehicle searcher. The target vehicle will be searched in the database by a progressive process. Extensive experiments on the public dataset from a real surveillance network validate the effectiveness of the PVSS.
We consider a possible (parity conserving) interaction between the electromagnetic field $F$ and a torsion field $T^\alpha$ of spacetime. For generic elementary torsion, gauge invariant coupling terms of lowest order fall into two classes that are both nonminimal and {\it quadratic} in torsion. These two classes are displayed explicitly. The first class of the type $\sim F T^2$ yields (undesirable) modifications of the Maxwell equations. The second class of the type $\sim F^2 T^2$ doesn't touch the Maxwell equations but rather modifies the constitutive tensor of spacetime. Such a modification can be completely described in the framework of metricfree electrodynamics. We recognize three physical effects generated by the torsion: (i) An axion field that induces an {\em optical activity} into spacetime, (ii) a modification of the light cone structure that yields {\em birefringence} of the vacuum, and (iii) a torsion dependence of the {\em velocity of light.} We study these effects in the background of a Friedmann universe with torsion. {\it File tor17.tex, 02 August 2003}
In this paper we consider a sequence of random variables with mean uncertainty in a sublinear expectation space. Without the hypothesis of identical distributions, we show a new central limit theorem under the sublinear expectations.
We review our attempts to discover lost baryons at low redshift with ``X-ray forest'' of absorption lines from the warm-hot intergalactic medium. We discuss the best evidence to date along the Mrk 421 sightline. We then discuss the missing baryons in the Local Group and the significance of the z=0 absorption systems in X-ray spectra. We argue that the debate over the Galactic vs. extragalactic origin of the z=0 systems is premature as these systems likely contain both components. Observations with next generation X-ray missions such as Constellation-X and XEUS will be crucial to map out the warm-hot intergalactic medium.
Naruki gave an explicit construction of the moduli space of marked cubic surfaces, starting from a toric variety and proceeding with blow ups and contractions. Using his result, we compute the Chow groups and the Chern classes of this moduli space.As an application we relate a recent result of Freitag on the Hilbert polynomial of a certain ring of modular forms to the Riemann-Roch theorem for the moduli space.
We consider the incompressible Navier-Stokes equations in the cylinder $\R \times \T$, with no exterior forcing, and we investigate the long-time behavior of solutions arising from merely bounded initial data. Although we do not know if such solutions stay uniformly bounded for all times, we prove that they converge in an appropriate sense to the family of spatially homogeneous equilibria as $t \to \infty$. Convergence is uniform on compact subdomains, and holds for all times except on a sparse subset of the positive real axis. We also improve the known upper bound on the $L^\infty$ norm of the solutions, although our results in this direction are not optimal. Our approach is based on a detailed study of the local energy dissipation in the system, in the spirit of a recent work devoted to a class of dissipative partial differential equations with a formal gradient structure (arXiv:1212.1573).
We study thermodynamics of black holes in the deformed Ho\v{r}ava-Lifshitz gravity with coupling constant $\lambda$.   For $\lambda=1$, the black hole behaves the   Reissner-Norstr\"om black hole. Hence, this is different from the Schwarzschild black hole of Einstein gravity. A connection to the generalized uncertainty principle is explored to understand the Ho\v{r}ava-Lifshitz black holes.
We consider a simple symmetric random walk on a spider, that is a collection of half lines (we call them legs) joined at the origin. Our main question is the following: if the walker makes $n$ steps how high can he go up on all legs. This problem is discussed in two different situations; when the number of legs are increasing, as $n$ goes to infinity and when it is fixed.
We prove the existence of a weak solution to the compressible Navier--Stokes system with singular pressure that explodes when density achieves its congestion level. This is a quantity whose initial value evolves according to the transport equation. We then prove that the "stiff pressure" limit gives rise to the two-phase compressible/incompressible system with congestion constraint describing the free interface. We prescribe of the velocity at the boundary and the value of density at the inflow part of the boundary of a general bounded $C^2$ domain. There are no restrictions on the size of the boundary conditions.
We study spherically symmetric solutions to the Jordan-Brans-Dicke field equations under the assumption that the space-time may possess an arbitrary number of spatial dimensions. Assuming a perfect fluid with the equation of state, we show that there are static interior nontrivial solutions in three dimensional Jordan-Brans-Dicke gravity theory.
These proceedings address a recent publication by the ANITA collaboration of four upward- pointing cosmic-ray-like events observed in the first flight of ANITA. Three of these events were consistent with stratospheric cosmic-ray air showers where the axis of propagation does not inter- sect the surface of the Earth. The fourth event was consistent with a primary particle that emerges from the surface of the ice suggesting a possible {\tau}-lepton decay as the origin of this event. These proceedings follow-up on the modeling and testing of the hypothesis that this event was of {\tau} neutrino origin.
The interpretation of the origin of the light scattering anomalies near the transition from incommensurate (IC) to the alpha-phase of quartz by Dolino et al. (Phys. Rev. Lett. 94, 155701 (2005)) is commented. It is shown that the observed IC structure is a pure transverse acoustic (TA) modulation without any soft optic mode component. Such a modulation cannot be responsible for the observed light scattering contrary to the interpretation by Dolino et al.
In this paper we prove the existence and the multiplicity of radial positive oscillatory solutions for a nonlinear problem governed by the mean curvature operator in the Lorentz-Minkowski space. The problem is set in a ball $B_R$ of $\mathbb R^N$ and is subject to Neumann boundary conditions. The main tool used is the shooting method for ODEs.
Slow light propagation is an important phenomenon in quantum optics. Here, we theoretically study the properties of slow light in a simple optomechanical system considering an effect of non-rotating wave approximation (NRWA) that was ignored in previous related works. With the NRWA effect, the ultraslow light can be easily achieved at the window of optomechanically induced transparency, especially in unresolved sideband regime. From the theoretical results, we find the upper bound of the time delay is exactly the mechanical ringdown time which can last for \textit{several minutes} (mHz linewidth) in recent experiments. Additionally, the interesting phenomena of the perfect optomechanically induced transmission and absorption are studied in the system with the NRWA effect. We believe the results can be used to control optical transmission in modern optical networks.
This work deals with the Mann's stochastic iteration algorithm under strong mixing random errors. We establish the Fuk-Nagaev's inequalities that enable us to prove the almost complete convergence with its corresponding rate of convergence. Moreover, these inequalities give us the possibility of constructing a confidence interval for the unique fixed point. Finally, to check the feasibility and validity of our theoretical results, we consider some numerical examples, namely a classical example from astronomy.
A quasigroup $Q$ is called maximally nonassociative if for $x,y,z\in Q$ we have that $x\cdot (y\cdot z) = (x\cdot y)\cdot z$ only if $x=y=z$. We show that, with finitely many exceptions, there exists a maximally nonassociative quasigroup of order $n$ whenever $n$ is not of the form $n=2p_1$ or $n=2p_1p_2$ for primes $p_1,p_2$ with $p_1\le p_2<2p_1$.
In scattering theory the far field pattern describes the directional dependence of a time-harmonic wave scattered by an obstacle or inhomogeneous medium, when observed sufficiently far away from these objects. Considering plane wave excitations, the far field pattern can be written as a function of two variables, namely the direction of propagation of the incident plane wave and the observation direction, and it is well-known to be separately real analytic with respect to each of them. We show that the far field pattern is in fact a jointly real analytic function of these two variables.
The connection between the scales of $ {\rm SU} (2)\times {\rm U} (1) $ gauge symmetry breaking and supersymmetry breaking is didactically displayed in the framework of a T.O.Y. (Theory Overestimating Yukawas) model, a version of the $ (M+1)SSM $ (supersymmetric extension of the standard model with a gauge singlet) in which the relevant parameters are determined in the fixed point regime. Some conspicuous features of supersymmetric particle physics are reviewed in the light of this simplified model. An alternative theory corresponding to lim $ (M+1)SSM \longrightarrow MSSM, $ leads to interesting inequalities among the supersymmetric breaking parameters of the $ MSSM. $
In a recent work, Gun and co-workers have proposed that $\,\sum_{n=-\infty}^{\infty}{(n+\alpha)^{-k}}\,$ is a transcendental number for all integer $\,k$, $k > 1$, and $\,\alpha \in \mathbb{Q} \backslash \mathbb{Z}$. Here in this work, this proposition is shown to be \emph{false} whenever $\,k\,$ is odd and $\,\alpha\,$ is a half-integer. It is also shown that these are the only counterexamples, which allows for a correct reformulation of the original proposition. This leads to a theorem yielding a closed-form expression for the summation of that series, which determines its arithmetic nature. The result is then extended to a sum of polygamma functions and some related zeta series. In view of the recurrent appearance of these series and functions in different areas of mathematics and applications, the closed-form results put forward here could well be included in modern computer algebra systems (CAS).
Algorithm, based on explicit representations for analytic continuation of the T-matrix Faddeev components on unphysical sheets, is worked out for calculations of resonances in the three-body quantum problem. According to the representations, poles of the T--matrix, scattering matrix and resolvent on unphysical sheets, interpreted as resonances, coincide with those complex energy values where appropriate truncations of the scattering matrix have zero as eigenvalue. Scattering amplitudes on the physical sheet, necessary to construct scattering matrix, are calculated on the basis of the Faddeev differential equations. Effectiveness of the algorithm developed is demonstrated for example of searching for resonances in the system $nnp$ and in a model three-boson system.
A regular clique in a regular graph is a clique such that every vertex outside of the clique is adjacent to the same positive number of vertices inside the clique. We continue the study of regular cliques in edge-regular graphs initiated by A. Neumaier in the 1980s and attracting current interest. We thus define a Neumaier graph to be an non-complete edge-regular graph containing a regular clique, and a strictly Neumaier graph to be a non-strongly regular Neumaier graph. We first prove some general results on Neumaier graphs and their feasible parameter tuples. We then apply these results to determine the smallest strictly Neumaier graph, which has $16$ vertices. Next we find the parameter tuples for all strictly Neumaier graphs having at most $24$ vertices. Finally, we give two sequences of graphs, each with $i^{\text{th}}$ element a strictly Neumaier graph containing a $2^{i}$-regular clique (where $i$ is a positive integer) and having parameters of an affine polar graph as an edge-regular graph. This answers questions recently posed by G. Greaves and J. Koolen.
OB-associations and superbubbles being energetically essential galactic powerhouses are likely to be the important acceleration sites of galactic cosmic rays (CRs). The emission profile of gamma-ray sources related to superbubbles and stellar clusters indicates on continuous particle acceleration by winds of massive stars. One of the most luminous galactic gamma-ray sources is Cygnus Cocoon superbubble, observed by multiple instruments, such as Fermi-LAT, ARGO, and, recently, HAWC. We discuss a model of particle acceleration and transport in a superbubble to explain GeV-TeV gamma-ray spectrum of Cygnus Cocoon, which has a break at the energy of about 1 TeV. It is shown that the gamma rays produced by hadronic interactions of high-energy protons accelerated by an ensemble of shocks from winds of massive stars and supernovae in the Cygnus Cocoon can explain the observations. The proton spectral shape at the highest energies depends on the MHD-fluctuation spectrum in the Cocoon. The viable solutions for Cygnus Cocoon may be applied to some other associations showing similar behaviour. We briefly discuss the similarity and differences of particle acceleration processes in extended superbubbles and compact clusters of young massive stars as represented by Westerlund 1 and 2 gamma-ray sources.