ShantanuT01/DACTYL-Pretraining huggingface dataset:
We introduce a perceptron version of the Generalized Random Energy Model, and prove a quenched Sanov type large deviation principle for the empirical distribution of the random energies. The dual of the rate function has a representation through a variational formula which is closely related to the Parisi variational formula for the SK-model.
Fermi satellite discovered that cosmological gamma-ray bursts (GRBs) are accompanied by long GeV flashes. In two GRBs, an optical counterpart of the GeV flash has been detected. Recent work suggests that the GeV+optical flash is emitted by the external blast wave from the explosion in a medium loaded with copious $e^\pm$ pairs. The full light curve of the flash is predicted by a first-principle radiative transfer simulation and can be tested against observations. Here we examine a sample of 7 bursts with best GeV+optical data and test the model. We find that the observed light curves are in agreement with the theoretical predictions and allow us to measure three parameters for each burst: the Lorentz factor of the explosion, its isotropic kinetic energy, and the external density. With one possible exception of GRB 090510 (which is the only short burst in the sample) the ambient medium is consistent with a wind from a Wolf-Rayet progenitor. The wind density parameter $A=\rho r^2$ varies in the sample around $10^{11}$g/cm. The initial Lorentz factor of the blast wave varies from 200 to 540 and correlates with the burst luminosity. Radiative efficiency of the prompt emission in the sample is between 0.1 and 0.8. For the two bursts with detected optical flash, GRB 120711A and GRB 130427A, we also estimate the magnetization of the external blast wave. Remarkably, the model reproduces the entire optical light curve of GRB 120711A (with its sharp peak, fast decay, plateau, and break) as well as the GeV data. The spectrum of GeV flashes is predicted to extend above 0.1 TeV, where they can be detected by ground-based Cherenkov telescopes.
Routing of photon play a key role in optical communication and quantum networks. Although the quantum routing of signals has been investigated in various systems both in theory and experiment. However, no current theory can route quantum signals between microwave and optical light. Here, we propose an experimentally accessible tunable multi-channel quantum routing proposal using photon-phonon translation in a hybrid opto-electromechanical system. It is the first demonstration that the single-photon of optical frequency can be routed into three different output ports by adjusting microwave power. More important, the two output signals can be selected according to microwave power. Meanwhile, we also demonstrate the vacuum and thermal noise will be insignificant for the optical performance of the single-photon router at temperature of the order of 20 mK. Our proposal may have paved a new avenue towards multi-channel router and quantum network.
The aim of this paper is to introduce truncated degenerate Bell polynomials and numbers and to investigate some of their properties. In more detail, we obtain explicit expressions, identities involving other special polynomials, integral representations, Dobinski-like formula and expressions of the generating function in terms of differential operators and linear incomplete gamma function. In addition, we introduce truncated degenerate modified Bell polynomials and numbers and get similar results for those polynomials. As an application of our results, we show that the truncated degenerate Bell numbers can be expressed as a finite sum involving moments of a beta random variable with certain parameters.
We provide an accurate comparison, against large cosmological $N$-body simulations, of different prescriptions for modelling nonlinear matter power spectra in the presence of massive neutrinos and dynamical dark energy. We test the current most widely used approaches: fitting functions (HALOFIT and HMcode), the halo-model reaction (ReACT) and emulators (baccoemu and EuclidEmulator2). Focussing on redshifts $z\leq2$ and scales $k\lesssim 1 \ h/$Mpc (where the simulation mass resolution provides $\sim 1\%$ accuracy), we find that HMcode and ReACT considerably improve over the HALOFIT prescriptions of Smith and Takahashi (both combined with the Bird correction), with an overall agreement of 2\% for all the cosmological scenarios considered. Concerning emulators, we find that, especially at low redshifts, EuclidEmulator2 remarkably agrees with the simulated spectra at $\lesssim 1\%$ level in scenarios with dynamical dark energy and massless neutrinos, reaching a maximum difference of $\sim 2\%$ at $z=2$. baccoemu has a similar behaviour as EuclidEmulator2, except for a couple of dark energy models. In cosmologies with massive neutrinos, at $z=0$ all the nonlinear prescriptions improve their agreement with respect to the massless neutrino case, except for the Bird and TakaBird models which, however, are not tailored to $w_0$--$w_a$ models. At $z>0$ we do not find a similar improvement when including massive neutrinos, probably due to the lower impact of neutrino free-streaming at higher redshifts; rather at $z=2$ EuclidEmulator2 exceeds $2\%$ agreement for some dark energy equation of state. When considering ratios between the matter power spectrum computed in a given cosmological model and its $\Lambda$CDM counterpart, all the tested prescriptions agree with simulated data, at sub-percent or percent level, depending on $z$. [ABRIDGED]
We present an atlas of ultraviolet and infrared images of ~15,750 local (d < 50 Mpc) galaxies, as observed by NASA's WISE and GALEX missions. These maps have matched resolution (FWHM 7.5'' and 15''), matched astrometry, and a common procedure for background removal. We demonstrate that they agree well with resolved intensity measurements and integrated photometry from previous surveys. This atlas represents the first part of a program (the z=0 Multi-wavelength Galaxy Synthesis) to create a large, uniform database of resolved measurements of gas and dust in nearby galaxies. The images and associated catalogs are publicly available at the NASA/IPAC Infrared Science Archive. This atlas allows us estimate local and integrated star formation rates (SFRs) and stellar masses (M$_\star$) across the local galaxy population in a uniform way. In the appendix, we use the population synthesis fits of Salim et al. (2016, 2018) to calibrate integrated M$_\star$ and SFR estimators based on GALEX and WISE. Because they leverage an SDSS-base training set of >100,000 galaxies, these calibrations have high precision and allow us to rigorously compare local galaxies to Sloan Digital Sky Survey results. We provide these SFR and M$_\star$ estimates for all galaxies in our sample and show that our results yield a "main sequence" of star forming galaxies comparable to previous work. We also show the distribution of intensities from resolved galaxies in NUV-to-WISE1 vs. WISE1-to-WISE3 space, which captures much of the key physics accessed by these bands.
We equip the edges of a deterministic graph $H$ with independent but not necessarily identically distributed weights and study a generalized version of matchings (i.e. a set of vertex disjoint edges) in $H$ satisfying the property that end-vertices of any two distinct edges are at least a minimum distance apart. We call such matchings as strong matchings and determine bounds on the expectation and variance of the minimum weight of a maximum strong matching. Next, we consider an inhomogenous random graph whose edge probabilities are not necessarily the same and determine bounds on the maximum size of a strong matching in terms of the averaged edge probability. We use local vertex neighbourhoods, the martingale difference method and iterative exploration techniques to obtain our desired estimates.
We model the mineralogy and distribution of dust around the white dwarf G29-39 using the infrared spectrum from 1-35 microns and combining a wide range of materials based on spectral studies of comets and debris disks. In order of their contribution to the mid-infrared emission, the most abundant minerals for G29-38 are amorphous carbon, amorphous and crystalline silicates, water ice, and metal sulfides. The amorphous C can be equivalently replaced by other materials (like metallic Fe) with featureless infrared spectra. The best-fitting crystalline silicate is Fe-rich pyroxene. In order to absorb enough starlight to power the observed emission, the disk must either be much thinner than the stellar radius (so that it can be heated from above and below) or it must have an opening angle wider than 2 degrees. A `moderately optically thick' torus model with mass 2x10^19 g fits the spectrum well. A physically thin (less than the white dwarf radius) and optically thick disk can contribute to the near-infrared continuum only; such a disk cannot explain the longer-wavelength continuum or strong silicate features. The silicate composition contains minerals found from cometary spectra and meteorites, but Fe-rich pyroxene is more abundant than enstatite (Mg-rich pyroxene) or forsterite (Mg-rich olivine) in G29-38, in contrast to what is found in most comet or meteorite mineralogies. Enstatite meteorites may be the most similar solar system materials to the G29-38 dust. Finally, we suggest the surviving core of a `hot jupiter' as an alternative (neither cometary nor asteroidal) origin for the debris, though further theoretical work is needed to determine if this hypothesis is viable.
Some superlinear fourth order elliptic equations are considered. Ground states are proved to exist and to concentrate at a point in the limit. The proof relies on variational methods, where the existence and concentration of nontrivial solutions are related to a suitable truncated equation.
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be described effectively by space-time trajectories of interacting particles, such as domain boundaries in two-dimensional growth or river networks. We study trajectories embedded in time-dependent geometries, and the main focus is on uniformly expanding or decreasing domains for which we obtain an exact mapping to simple fixed domain systems while preserving the local scale invariance properties. This approach was recently introduced in [A. Ali et al., Phys. Rev. E 87, 020102(R) (2013)] and here we provide a detailed discussion on its applicability for self-affince Markovian models, and how it can be adapted to self-affine models with memory or explicit time dependence. The mapping corresponds to a non-linear time transformation which convergences to a finite value for a large class of trajectories, enabling an exact analysis of asymptotic properties in expanding domains. We further provide a detailed discussion of different particle interactions and generalized geometries. All our findings are based on exact computations and are illustrated numerically for various examples, including L\'evy processes and fractional Brownian motion.
Given a closed subvariety Y of a n-dimensional torus, we study how the tropical line bundles of Trop(Y) can be induced by line bundles living on a tropical compactification of Y in a toric variety, following the construction of Jenia Tevelev. We then consider the general structure with respect to the Zariski--Riemann space.
With increasing demands for high-quality semantic segmentation in the industry, hard-distinguishing semantic boundaries have posed a significant threat to existing solutions. Inspired by real-life experience, i.e., combining varied observations contributes to higher visual recognition confidence, we present the equipotential learning (EPL) method. This novel module transfers the predicted/ground-truth semantic labels to a self-defined potential domain to learn and infer decision boundaries along customized directions. The conversion to the potential domain is implemented via a lightweight differentiable anisotropic convolution without incurring any parameter overhead. Besides, the designed two loss functions, the point loss and the equipotential line loss implement anisotropic field regression and category-level contour learning, respectively, enhancing prediction consistencies in the inter/intra-class boundary areas. More importantly, EPL is agnostic to network architectures, and thus it can be plugged into most existing segmentation models. This paper is the first attempt to address the boundary segmentation problem with field regression and contour learning. Meaningful performance improvements on Pascal Voc 2012 and Cityscapes demonstrate that the proposed EPL module can benefit the off-the-shelf fully convolutional network models when recognizing semantic boundary areas. Besides, intensive comparisons and analysis show the favorable merits of EPL for distinguishing semantically-similar and irregular-shaped categories.
Recent researches on the solution of Schwinger-Dyson equations, as well as lattice simulations of pure QCD, suggest that the gluon propagator is massive. In this letter, we assume that the classical counterpart of this massive gluon field may be represented with the equation of motion for Yang-Mills theory with a mass term added. A new classical solution is given for this equation. It is discussed that this solution may have some role in confinement.
Cross section of the neutron capture reaction $n+p\rightarrow d+\gamma$ at threshold was calculated with different realistic $^{3}S_{1}$ deuteron and $^{1}S_{0}$ $np$ scattering wave functions stemming from Nijmegen-II, JISP16, Paris, Idaho and Moscow (with forbidden states) potentials. It is found that this reaction with thermal neutrons may be described without a contribution of meson exchange currents.
Using MRI and high-speed video we investigate the motion of a large intruder particle inside a vertically shaken bed of smaller particles. We find a pronounced, non-monotonic density dependence, with both light and heavy intruders moving faster than those whose density is approximately that of the granular bed. For light intruders, we furthermore observe either rising or sinking behavior, depending on intruder starting height, boundary condition and interstitial gas pressure. We map out the phase boundary delineating the rising and sinking regimes. A simple model can account for much of the observed behavior and show how the two regimes are connected by considering pressure gradients across the granular bed during a shaking cycle.
Further evidence is presented supporting the alternative interpretation of superhumps as being due to irradiation modulated periodically variable mass transfer rate. NZ Boo, HT Cas and PU UMa are added to the sample of high inclination dwarf novae showing -- during their superoutbursts -- modulation of the observed brightness of the disk with beat period. Simple model calculations confirm earlier hypothesis that this modulation is due to a non-axisymmetric structure of the outer parts of the disk, involving the azimuthal dependence of their geometrical thickness, rotating with the beat period.   The modulation amplitude $A_{mod}$ is found to decrease during superoutbursts. In particular, it is found that during two superoutbursts of OY Car the rate of decline of the superhump amplitude $dA_{SH}/dt$ was correlated with the rate of decline $dA_{mod}/dt$. This leads to a simple explanation for the decreasing amplitudes of superhumps: it is a consequence of the decreasing modulation amplitude.
Context: It is well known that the so-called s-process is responsible for the production of neutron-rich trans-iron elements, that form the bulk of the "heavy nuclides" (i.e. nuclides more massive than the iron-group nuclei) in the solar-system composition, considered as "standard of reference" dataset for cosmic abundances. In particular, the s-process produces about half of all the trans-iron isotopes by moving along the "valley of stability" through a series of neutron capture reactions and beta decays. More than one s-process "component" (i.e. a nucleosynthesis event with a single set of physical conditions like neutron exposure, initial abundances and neutron density) is required in order to explain the observed solar distribution of s-nuclei abundances. Current views on the subject suggest the existence of several components that, in terms of stellar environments, correspond to distinct categories of stars in different evolutionary phases. Aims: The purpose of the chapter is to review the s-process nucleosynthesis occurring in massive stars (so-called weak component of s-process), pointing particular attention on the recent studies devoted to analyze how the uncertainties due to stellar evolution modeling and, specifically, due to convective overshooting affect the efficiency of this nucleosynthesis process.
Generic properties of the strength function (local density of states (LDOS)) and chaotic eigenstates are analyzed for isolated systems of interacting particles. Both random matrix models and dynamical systems are considered in the unique approach. Specific attention is paid to the quantum-classical correspondence for the form of the LDOS and eigenstates, and to the localization in the energy shell. New effect of the non-ergodicity of individual eigenstates in a deep semiclassical limit is briefly discussed.
An unidentified infrared emission (UIE) feature at 6.0 $\mu$m is detected in a number of astronomical sources showing the UIE bands. In contrast to the previous suggestion that this band is due to C=O vibrational modes, we suggest that the 6.0 $\mu$m feature arises from olefinic double-bond functional groups. These groups are likely to be attached to aromatic rings which are responsible for the major UIE bands. The possibility that the formation of these functional groups is related to the hydrogenation process is discussed.
The renormalization of the Wiedemann-Franz (WF) ratio in strongly correlated electron systems is analyzed within the Landau quasiparticle picture. We demonstrate that the WF law is violated: (i) at the quantum critical point, where the effective mass diverges, and (ii) beyond a point of fermion condensation, where the single-particle spectrum $\epsilon(p)$ becomes flat. Results of the analysis are compared with available experimental data.
We critically discuss the theoretical developments that led to predictions of very deeply bound kaon states and then revise the data of the KEK experiment from where claims for evidence of deeply bound kaon atoms in nuclei were made. We conclude that the peaks seen in the experiment correspond to the absorption of kaons by a pair of nucleons leading to $\Sigma p$ and $\Lambda p$ and leaving the daughter nucleus as a spectator. These conclusions have been reconfirmed by a recent experiment at FINUDA.
Theories with large extra dimensions predict an infinite tower of Kaluza-Klein states in the 1 TeV range, which can consequently have significant implications for experimental observables. One such observable, which gets affected by the exchange of spin-2 Kaluza-Klein particles, is the t t(bar) production cross-section in photon-photon collisions at NLC energies. We study this process and obtain bounds on the effective quantum gravity scale M_S between 700 and 2400 GeV (depending on the centre-of-mass energy). We show that the use of polarisation will further strengthen these bounds.
In this paper, we use counting theorems from the geometry of numbers to extend the Riemann-Roch theorem and the Riemann-Hurwitz formula to global fields of arbitrary characteristic.
We present a detailed analysis of the inner mass structure of the Cosmic Horseshoe (J1148+1930) strong gravitational lens system observed with the Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3). In addition to the spectacular Einstein ring, this systems shows a radial arc. We obtained the redshift of the radial arc counter image $z_\text{s,r} = 1.961 \pm 0.001$ from Gemini observations. To disentangle the dark and luminous matter, we consider three different profiles for the dark matter distribution: a power-law profile, the NFW, and a generalized version of the NFW profile. For the luminous matter distribution, we base it on the observed light distribution that is fitted with three components: a point mass for the central light component resembling an active galactic nucleus, and the remaining two extended light components scaled by a constant M/L. To constrain the model further, we include published velocity dispersion measurements of the lens galaxy and perform a self-consistent lensing and axisymmetric Jeans dynamical modeling. Our model fits well to the observations including the radial arc, independent of the dark matter profile. Depending on the dark matter profile, we get a dark matter fraction between 60 % and 70 %. With our composite mass model we find that the radial arc helps to constrain the inner dark matter distribution of the Cosmic Hoseshoe independently of the dark matter profile.
We propose to study the multiparticle configurations of isovector scalar mesons, saying $a_0(980)$ and $a_0(1450)$, in the charmless three-body $B$ decays by considering the width effects. Two scenarios of $a_0$ configurations are assumed, in which the first one take $a_0(980)$ as the lowest-lying $q{\bar q}$ state and $a_0(1450)$ as the first radial excited state, the second one take $a_0(1450)$ as the lowest-lying $q{\bar q}$ state and $a_0(1950)$ as the first radial excited state while $a_0(980)$ is not a $q{\bar q}$ state. Within these two scenarios, we do the PQCD calculation for the quasi-two-body $B \to a_0 \left[\to K{\bar K}/\pi\eta \right] h$ decays and extract the corresponding branching fractions of two-body $B \to a_0 h$ decays under the narrow width approximation. Our predictions show that the first scenario of $a_0(980)$ configuration can not be excluded by the available measurements in $B$ decays, the contributions from $a_0(1450)$ to the branching fractions in most channels are comparable in the first and second scenarios. Several channels are suggested for the forthcoming experimental measurements to reveal the multiparticle configurations of $a_0$, such as the channel $B^0 \to a_0^-(980) \left[\to \pi^-\eta \right] \pi^+$ with the largest predicted branching fraction, the channels $B^0 \to a_0^{\pm}(1450) \left[\to K^\pm{\bar K}^0, \pi^\pm\eta \right] \pi^\mp$ whose branching fractions obtained in the second scenario is about three times larger in magnitude than that obtained in the first scenario, and also the channels $B^+ \to a_0^+(1950) \left[ K^+{\bar K}^0/\pi^+\eta \right] K^0$ whose branching fractions are linear dependent on the partial width $\Gamma_{a_0(1950) \to KK/\pi\eta}$.
In this paper, we present a learning based approach to depth fusion, i.e., dense 3D reconstruction from multiple depth images. The most common approach to depth fusion is based on averaging truncated signed distance functions, which was originally proposed by Curless and Levoy in 1996. While this method is simple and provides great results, it is not able to reconstruct (partially) occluded surfaces and requires a large number frames to filter out sensor noise and outliers. Motivated by the availability of large 3D model repositories and recent advances in deep learning, we present a novel 3D CNN architecture that learns to predict an implicit surface representation from the input depth maps. Our learning based method significantly outperforms the traditional volumetric fusion approach in terms of noise reduction and outlier suppression. By learning the structure of real world 3D objects and scenes, our approach is further able to reconstruct occluded regions and to fill in gaps in the reconstruction. We demonstrate that our learning based approach outperforms both vanilla TSDF fusion as well as TV-L1 fusion on the task of volumetric fusion. Further, we demonstrate state-of-the-art 3D shape completion results.