ShantanuT01/DACTYL-Pretraining huggingface dataset:
The source-count distribution as a function of their flux, dN/dS, is one of the main quantities characterizing gamma-ray source populations. We employ statistical properties of the Fermi Large Area Telescope (LAT) photon counts map to measure the composition of the extragalactic gamma-ray sky at high latitudes (|b|>30 deg) between 1 GeV and 10 GeV. We present a new method, generalizing the use of standard pixel-count statistics, to decompose the total observed gamma-ray emission into (a) point-source contributions, (b) the Galactic foreground contribution, and (c) a truly diffuse isotropic background contribution. Using the 6-year Fermi-LAT data set (P7REP), we show that the dN/dS distribution in the regime of so far undetected point sources can be consistently described with a power law of index between 1.9 and 2.0. We measure dN/dS down to an integral flux of ~2x10^{-11} cm^{-2}s^{-1}, improving beyond the 3FGL catalog detection limit by about one order of magnitude. The overall dN/dS distribution is consistent with a broken power law, with a break at 2.1^{+1.0}_{-1.3}x10^{-8} cm^{-2}s^{-1}. The power-law index n_1=3.1^{+0.7}_{-0.5} for bright sources above the break hardens to n_2=1.97+-0.03 for fainter sources below the break. A possible second break of the dN/dS distribution is constrained to be at fluxes below 6.4x10^{-11} cm^{-2}s^{-1} at 95% confidence level. The high-latitude gamma-ray sky between 1 GeV and 10 GeV is shown to be composed of ~25% point sources, ~69.3% diffuse Galactic foreground emission, and ~6% isotropic diffuse background.
We present the next-to-leading order full results in Chiral Perturbation Theory for the charged Kaon K --> 3 pi slope g CP violating asymmetries. We discuss the constraints that a measurement of these asymmetries would impose on the Standard Model results of epsilon_K' and search for new physics. We also study the kind of information that such measurement can provide on Im G_8, Im (e^2 G_E) and higher order weak couplings.
It is known that much of the structure of string theory can be derived from three-dimensional topological field theory and gravity. We show here that, at least for simple topologies, the string diffeomorphism ghosts can also be explained in terms of three-dimensional physics.
We will show that for exponential type potentials, which are used to depict quintessential inflation, the solutions whose initial conditions take place during the slow roll phase in order to describe correctly the inflationary period do not belong to the basin of attraction of the scaling solution -a solution of the scalar field equation whose energy density scale as the one of the fluid component of the universe during radiation or the matter domination period-, meaning that a late time mechanism to exit this behavior and depict correctly the current cosmic acceleration is not needed.
Recent experimental results find strong indications that the universe is flat, while other experimental results from supernovae Ia observations have been interpreted to show that, not only that there is an accelerating expansion of the universe, but also that the universe is strongly curved. By means of a recently proposed metric, I am able to show that the experimental results which had previously been analyzed to give a strong curvature are quite consistent with a flat universe, thus resolving the apparent mismatch. The conclusion of these latter authors which indicated an accelerating expansion of the universe remains unchanged.
To understand the nature of transient obscuring outflows in active galactic nuclei, we observed the Seyfert 1 galaxy NGC 3783 on two occasions in December 2016 triggered by Swift monitoring indicating strong soft X-ray absorption in November. We obtained ultraviolet spectra using COS on HST and optical spectra using FEROS on the MPG/ESO 2.2-m telescope that were simultaneous with X-ray spectra from XMM-Newton and NuSTAR. We find new components of broad, blue-shifted absorption associated with Ly$\alpha$, \ion{N}{v}, \ion{Si}{iv}, and \ion{C}{iv} in our COS spectra. The absorption extends from velocities near zero in the rest-frame of the host galaxy to $-6200$ $\rm km~s^{-1}$. These features appear for the first time in NGC 3783 at the same time as the heavy soft X-ray absorption seen in the XMM-Newton X-ray spectra. The X-ray absorption has a column density of $\sim 10^{23}~\rm cm^{-2}$, and it partially covers the X-ray continuum source. The X-ray absorption becomes more transparent in the second observation, as does the UV absorption. Combining the X-ray column densities with the UV spectral observations yields an ionization parameter for the obscuring gas of log $\xi =1.84^{+0.4}_{-0.2}$ $\rm erg~cm~s^{-1}$. Despite the high intensity of the UV continuum in NGC 3783, F(1470 \AA)=$8 \times 10^{-14}~\rm erg~cm^{-2}~s^{-1}~\AA^{-1}$, the well known narrow UV absorption lines are deeper than in earlier observations in unobscured states, and low ionization species such as \ion{C}{iii} appear, indicating that the narrow-line gas is more distant from the nucleus and is being shadowed by the gas producing the obscuration. Despite the high continuum flux levels in our observations of NGC 3783, moderate velocities in the UV broad line profiles have substantially diminished. We suggest that a collapse of the broad line region has led to the outburst and triggered the obscuring event.
We provide a squeeze-like transformation that allows one to remove a position dependent mass from the Hamiltonian. Methods to solve the Schr\"{o}dinger equation may then be applied to find the respective eigenvalues and eigenfunctions. As an example, we consider a position-dependent-mass that leads to the integrable Morse potential and therefore to well-known solutions.
References to the works of Iliev-Ranestad and Kuznetsov added.   -----   In a first part we detail the construction, on a general Fano 4-fold of genus 9, of a canonical set of four stable vector bundles of rank 2, and prove that they are rigid. Those results were already known by Iliev-Ranestad and Kuznetsov with different purposes.   In a second part we show that its variety of lines is an hyperplane section of P1xP1xP1xP1. Then we compute the Chow ring of a general Fano 4-fold, which appears to have a rich structure in codimension 2.   The 4-bundles gives embeddings in a Grassmannian G(2,6), and the link with the order one congruence discovered by E. Mezzeti and P de Poi is done. We will also describe in this part the normalization of the non quadraticaly normal variety they constructed, and also its variety of plane cubics and detail the zak duality in this case.
We study Liouville-type theorem for polyharmonic H\'enon-Lane-Emden system $(-\Delta)^mu=|x|^av^p,\; (-\Delta)^mv=|x|^bu^q$ when $m,p,q\geq 1, pq\ne 1$, and $a,b\geq 0$. It is a natural conjecture that the nonexistence of positive solutions should be true if and only if $(N+a)/(p+1)+$ $(N+b)/(q+1)>N-2m$. It is shown by Fazly [6] that the conjecture holds for radial solutions in all dimensions and for classical solutions in dimension $N\leq 2m+1$. We here give some partial results in dimension $N\geq 2m+2$.
The phenomenon of finite time extinction of bounded and non-negative solutions to the diffusion equation with strong absorption $$\partial_t u-\Delta u^m+|x|^{\sigma}u^q=0, \qquad (t,x)\in(0,\infty)\times\mathbb{R}^N,$$ with $m\geq1$, $q\in(0,1)$ and $\sigma>0$, is addressed. Introducing the critical exponent $\sigma^* := 2(1-q)/(m-1)$ for $m>1$ and $\sigma_*=\infty$ for $m=1$, extinction in finite time is known to take place for $\sigma\in [0,\sigma^*)$ and an alternative proof is provided therein. When $m>1$ and $\sigma\ge \sigma^*$, the occurrence of finite time extinction is proved for a specific class of initial conditions, thereby supplementing results on non-extinction that are available in that range of $\sigma$ and showing their sharpness.
We consider almost sure convergence of the SDE $dX_t=\alpha_t d t + \beta_t d W_t$ under the existence of a $C^2$-Lyapunov function $F:\mathbb R^d \to \mathbb R$. More explicitly, we show that on the event that the process stays local we have almost sure convergence in the Lyapunov function $(F(X_t))$ as well as $\nabla F(X_t)\to 0$, if $|\beta_t|=\mathcal O( t^{-\beta})$ for a $\beta>1/2$. If, additionally, one assumes that $F$ is a Lojasiewicz function, we get almost sure convergence of the process itself, given that $|\beta_t|=\mathcal O(t^{-\beta})$ for a $\beta>1$. The assumptions are shown to be optimal in the sense that there is a divergent counterexample where $|\beta_t|$ is of order $t^{-1}$.
We develop a formalism wherein the solution of the equations of equilibrium for a self-gravitating, magnetized interstellar cloud may be accomplished analytically, under the only hypotheses that (a) the cloud is scale-free, and (b) is electrically neutral. All variables are represented as series of scalar and vector spherical harmonics, and the equilibrium equations are reduced to a set of coupled algebraic equations for the expansion coefficients of the density and the magnetic vector potential. Previously known axisymmetric solutions are recovered and new non-axisymmetric solutions are found and discussed as models for pre-protostellar molecular cloud cores.
We have identified epitaxially grown elemental Te as a capping material that is suited to protect the topological surface states of intrinsically insulating Bi$_2$Te$_3$. By using angle-resolved photoemission, we were able to show that the Te overlayer leaves the dispersive bands of the surface states intact and that it does not alter the chemical potential of the Bi$_2$Te$_3$ thin film. From in-situ four-point contact measurements, we observed that the conductivity of the capped film is still mainly determined by the metallic surface states and that the contribution of the capping layer is minor. Moreover, the Te overlayer can be annealed away in vacuum to produce a clean Bi$_2$Te$_3$ surface in its pristine state even after the exposure of the capped film to air. Our findings will facilitate well-defined and reliable ex-situ experiments on the properties of Bi$_2$Te$_3$ surface states with nontrivial topology.
We study the Fourier transforms of indicator functions of some special high-dimensional finite type domains and obtain estimates of the associated lattice point discrepancy.
We address a model for adhesive unilateral frictionless Signorini-type contact between bodies of heat-conductive viscoelastic material, in the linear Kelvin-Voigt rheology, undergoing thermal expansion. The flow-rule for debonding the adhesion is considered rate-independent and unidirectional, and a thermodynamically consistent model is derived and analysed as far as the existence of a weak solution is concerned.
Facial expression spotting is the preliminary step for micro- and macro-expression analysis. The task of reliably spotting such expressions in video sequences is currently unsolved. The current best systems depend upon optical flow methods to extract regional motion features, before categorisation of that motion into a specific class of facial movement. Optical flow is susceptible to drift error, which introduces a serious problem for motions with long-term dependencies, such as high frame-rate macro-expression. We propose a purely deep learning solution which, rather than tracking frame differential motion, compares via a convolutional model, each frame with two temporally local reference frames. Reference frames are sampled according to calculated micro- and macro-expression duration. As baseline for MEGC2021 using leave-one-subject-out evaluation method, we show that our solution achieves F1-score of 0.105 in a high frame-rate (200 fps) SAMM long videos dataset (SAMM-LV) and is competitive in a low frame-rate (30 fps) (CAS(ME)2) dataset. On unseen MEGC2022 challenge dataset, the baseline results are 0.1176 on SAMM Challenge dataset, 0.1739 on CAS(ME)3 and overall performance of 0.1531 on both dataset.
In materials science, wedge disclinations are defects caused by angular mismatches in the crystallographic lattice. To describe such disclinations, we introduce an atomistic model in planar domains. This model is given by a nearest-neighbor-type energy for the atomic bonds with an additional term to penalize change in volume. We enforce the appearance of disclinations by means of a special boundary condition.   Our main result is the discrete-to-continuum limit of this energy as the lattice size tends to zero. Our proof method is relaxation of the energy. The main mathematical novelty of our proof is a density theorem for the special boundary condition. In addition to our limit theorem, we construct examples of planar disclinations as solutions to numerical minimization of the model and show that classical results for wedge disclinations are recovered by our analysis.
We revisit effective scenarios for the origin of heavy tails in stationary velocity distributions. A first analysis combines localization with diffusive acceleration. That gets realized in space plasmas to find the so-called kappa-distributions having power-law decay at high speeds. There, localization at high energy already takes place for the reversible dynamics but becomes effective by an active diffusion in velocity space. A model for vibrating granular gases and giving rise to stretched exponential tails is also briefly discussed, where negative friction is the energizer. In all cases, the resulting nonMaxwellian velocity distributions are frenetically caused by the dependence on the speed of kinetic parameters.
Let X\subsetneq\mathbb{P}_{\mathbb{C}}^{N} be an n-dimensional nondegenerate smooth projective variety containing an m-dimensional subvariety Y. Assume that either m>\frac{n}{2} and X is a complete intersection or that m\geq\frac{N}{2}, we show deg(X)|deg(Y) and codim_{span(Y)}Y\geq codim_{\mathbb{P}^{N}}X, where span(Y) is the linear span of Y. These bounds are sharp. As an application, we classify smooth projective n-dimensional quadratic varieties swept out by m\geq[\frac{n}{2}]+1 dimensional quadrics passing through one point.
We report on the realization of silicon nitride membranes with enhanced and electrically tunable reflectivity. A subwavelength one-dimensional grating is directly patterned on a suspended 200 nm-thick, high stress commercial film using electron beam lithography. A Fano resonance is observed in the transmission spectrum of TM polarized light impinging on the membrane at normal incidence, leading to an increase in its reflectivity from 10% to 78% at 937 nm. The observed spectrum is compared to the results of rigorous coupled wave analysis simulations based on measurements of the grating transverse profile through localized cuts of the suspended film with a Focused Ion Beam. By mounting the membrane chip on a ring piezoelectric transducer and applying a compressive force to the substrate we subsequently observe a shift of the transmission spectrum by 0.23 nm.
This article contains a proof of the basic lemma. This lemma, discovered by Beilinson, yields a motivic proof of the Andreotti-Frankel theorem for affine varieties. Next, it is shown that the category of Cohomologically Constructible Sheaves (as it is referred to in the Riemann-Hilbert correspondence) coincides with the derived category of bounded complexes of constructible sheaves. It is also shown that higher direct images and the sheaf-Ext groups are effaceable in the category of constructible sheaves.
We construct models of molecular clouds that are considered as ensembles of transient cores. Each core is assumed to develop in the background gas of the cloud, grow to high density and decay into the background. The chemistry in each core responds to the dynamical state of the gas and to the gas-dust interaction. Ices are deposited on the dust grains in the core's dense phase, and this material is returned to the gas as the core expands to low density. The cores of the ensemble number typically one thousand and are placed randomly in position within the cloud, and are assigned a random evolutionary phase.   The models are used to generate molecular line contour maps of a typical dark cloud. These maps are found to represent extremely well the characteristic features of observed maps of the dark cloud L673, which has been observed at both low and high resolutions. The computed maps are found to exhibit the general morphology of the observed maps, and to generate similar sizes of emitting regions, molecular column densities, and the separations between peaks of emissions of various molecular species. The models give insight into the nature of molecular clouds and the dynamical processes occurring within them, and significantly constrain dynamical and chemical processes in the interstellar medium.
Graphs with few distinct eigenvalues have been investigated extensively. In this paper, we focus on another relevant topic: characterizing graphs with some eigenvalue of large multiplicity. Specifically, the normalized Laplacian matrix of a graph is considered here. Let $\rho_{n-1}(G)$ and $\nu(G)$ be the second least normalized Laplacian eigenvalue and the independence number of a graph $G$, respectively. As the main conclusions, two families of $n$-vertex connected graphs with some normalized Laplacian eigenvalue of multiplicity $n-3$ are determined: graphs with $\rho_{n-1}(G)=-1$ and graphs with $\rho_{n-1}(G)\neq -1$ and $\nu(G)\neq 2$. Moreover, it is proved that these graphs are determined by their spectrum.
The galaxy distributions along the line-of-sight are significantly contaminated by the uncertainty on redshift measurements obtained through multiband photometry, which makes it difficult to get cosmic distance information measured from baryon acoustic oscillations, or growth functions probed by redshift distortions. We investigate the propagation of the uncertainties into large scale clustering by exploiting all known estimators, and propose the wedge approach as a promising analysis tool to extract cosmic distance information still remaining in the photometric galaxy samples. We test our method using simulated galaxy maps with photometric uncertainties of $\sigma_{0} =\left(0.01, 0.02, 0.03\right)$. The measured anisotropy correlation function $\xi$ is binned into the radial direction of $s$ and the angular direction of $\mu$, and the variations of $\xi(s,\mu)$ with perpendicular and radial cosmic distance measures of $D_A$ and $H^{-1}$ are theoretically estimated by an improved RSD model. Although the radial cosmic distance $H^{-1}$ is unable to be probed from any of the three photometric galaxy samples, the perpendicular component of $D_A$ is verified to be accurately measured even after the full marginalisation of $H^{-1}$. We measure $D_A$ with approximately 6% precision which is nearly equivalent to what we can expect from spectroscopic DR12 CMASS galaxy samples.
We have studied the interstellar extinction in a field of 3' x 3' located about 6' SW of 30 Doradus in the Large Magellanic Cloud (LMC). Hubble Space Telescope observations in the U, B, V, I and Halpha bands reveal patchy extinction in this field. The colour-magnitude diagram (CMD) shows an elongated stellar sequence, almost parallel to the main sequence (MS), which is in reality made up of stars of the red giant clump (RC) spread across the CMD by the uneven levels of extinction in this region. Since these objects are all at the same distance from us and share very similar physical properties, we can derive quantitatively both the extinction law in the range 3000 - 8000 Angstrom and the absolute extinction towards about 100 objects, setting statistically significant constraints on the dust grains properties in this area. We find an extinction curve considerably flatter than the standard Galactic one and than those obtained before for the LMC. The derived value of Rv = 5.6 +/- 0.3 implies that in this region larger grains dominate. Upper MS stars span a narrower range of E(B-V) values than RC objects, at variance with what has been found elsewhere in the LMC.
Parking spaces are costly to build, parking payments are difficult to enforce, and drivers waste an excessive amount of time searching for empty lots. Accurate quantification would inform developers and municipalities in space allocation and design, while real-time measurements would provide drivers and parking enforcement with information that saves time and resources. In this paper, we propose an accurate and real-time video system for future Internet of Things (IoT) and smart cities applications. Using recent developments in deep convolutional neural networks (DCNNs) and a novel vehicle tracking filter, we combine information across multiple image frames in a video sequence to remove noise introduced by occlusions and detection failures. We demonstrate that our system achieves higher accuracy than pure image-based instance segmentation, and is comparable in performance to industry benchmark systems that utilize more expensive sensors such as radar. Furthermore, our system shows significant potential in its scalability to a city-wide scale and also in the richness of its output that goes beyond traditional binary occupancy statistics.
The effect of electron-phonon interactions in the conductance through metallic atomic wires is theoretically analyzed. The proposed model allows to consider an atomic size region electrically and mechanically coupled to bulk electrodes. We show that under rather general conditions the features due to electron-phonon coupling are described by universal functions of the system transmission coefficients. It is predicted that the reduction of the conductance due to electron-phonon coupling which is observed close to perfect transmission should evolve into an enhancement at low transmission. This crossover can be understood in a transparent way as arising from the competition between elastic and inelastic processes.
An electro-mechanical setup for the measurement of AC-forces in a low-temperature tunnelling microscope has been developed, which enables extremely high force resolution. The crosstalk of vibrations onto the tunnelling current is used to measure the deflection of a force-sensing cantilever beam. We demonstrate its capability to measure the noise of the force at a tunnelling contact using polycrystalline Iridium. Depending on temperature, spring constant and current, a resolution in the range of $\rm {fN}/\sqrt{\rm Hz}$ is possible. We observe peak levels of the force-noise at the energy of the expected phonon maximal density of states, which suggests that inelastic transport processes contribute to force fluctuations.
We give the algebra of quasimodular forms a collection of Rankin-Cohen operators. These operators extend those defined by Cohen on modular forms and, as for modular forms, the first of them provide a Lie structure on quasimodular forms. They also satisfy a ``Leibniz rule'' for the usual derivation. Rankin-Cohen operators are useful for proving arithmetic identities. In particular we give an interpretation of the Chazy equation and explain why such an equation has to exist.