ShantanuT01/DACTYL-Pretraining huggingface dataset:
With a deep Chandra/HETGS exposure of WR 6, we have resolved emission lines whose profiles show that the X-rays originate from a uniformly expanding spherical wind of high X-ray-continuum optical depth. The presence of strong helium-like forbidden lines places the source of X-ray emission at tens to hundreds of stellar radii from the photosphere. Variability was present in X-rays and simultaneous optical photometry, but neither were correlated with the known period of the system or with each other. An enhanced abundance of sodium revealed nuclear processed material, a quantity related to the evolutionary state of the star. The characterization of the extent and nature of the hot plasma in WR 6 will help to pave the way to a more fundamental theoretical understanding of the winds and evolution of massive stars.
The Hierarchical Dirichlet process is a discrete random measure serving as an important prior in Bayesian non-parametrics. It is motivated with the study of groups of clustered data. Each group is modelled through a level two Dirichlet process and all groups share the same base distribution which itself is a drawn from a level one Dirichlet process. It has two concentration parameters with one at each level. The main results of the paper are the law of large numbers and large deviations for the hierarchical Dirichlet process and its mass when both concentration parameters converge to infinity. The large deviation rate functions are identified explicitly. The rate function for the hierarchical Dirichlet process consists of two terms corresponding to the relative entropies at each level. It is less than the rate function for the Dirichlet process, which reflects the fact that the number of clusters under the hierarchical Dirichlet process has a slower growth rate than under the Dirichlet process.
In conventional formulations of multilayer feedforward neural networks, the individual layers are customarily defined by explicit functions. In this paper we demonstrate that defining individual layers in a neural network \emph{implicitly} provide much richer representations over the standard explicit one, consequently enabling a vastly broader class of end-to-end trainable architectures. We present a general framework of implicitly defined layers, where much of the theoretical analysis of such layers can be addressed through the implicit function theorem. We also show how implicitly defined layers can be seamlessly incorporated into existing machine learning libraries. In particular with respect to current automatic differentiation techniques for use in backpropagation based training. Finally, we demonstrate the versatility and relevance of our proposed approach on a number of diverse example problems with promising results.
Topological indices are a class of numerical invariants that predict certain physical and chemical properties of molecules. Recently, two novel topological indices, named as Sombor index and reduced Sombor index, were introduced by Gutman, defined as $$SO(G)=\sum_{uv\in E(G)}\sqrt{d_{G}^{2}(u)+d_{G}^{2}(v)},$$ $$SO_{red}(G)=\sum_{uv\in E(G)}\sqrt{(d_{G}(u)-1)^{2}+(d_{G}(v)-1)^{2}},$$ where $d_{G}(u)$ denotes the degree of vertex $u$ in $G$.   In this paper, our aim is to order the chemical trees, chemical unicyclic graphs, chemical bicyclic graphs and chemical tricyclic graphs with respect to Sombor index and reduced Sombor index. We determine the first fourteen minimum chemical trees, the first four minimum chemical unicyclic graphs, the first three minimum chemical bicyclic graphs, the first seven minimum chemical tricyclic graphs. At last, we consider the applications of reduced Sombor index to octane isomers.
Efforts are underway to improve the design and sensitivity of gravitational waves detectors, with the hope that the next generation of these detectors will observe a gravitational wave signal. Such a signal will not only provide information on dynamics in the strong gravity regime that characterizes potential sources of gravitational waves, but will also serve as a decisive test for alternative theories of gravitation that are consistent with all other current experimental observations. We study the linearized theory of the tensor-vector-scalar theory of gravity (TeVeS) with generalized vector action, an alternative theory of gravitation designed to explain the apparent deficit of visible matter in galaxies and clusters of galaxies without postulating yet undetected dark matter. We find the polarization states and propagation speeds for gravitational waves in vacuum, and show that in addition to the usual transverse-traceless propagation modes, there are two more transverse modes and two trace modes. Additionally, the propagation speeds are different from c.
We present a deep LBT/LBC U-band imaging survey (9 deg2) covering the NOAO Bootes field. A total of 14,485 Lyman Break Galaxies (LBGs) at z~3 are selected, which are used to measure the rest-frame UV luminosity function (LF). The large sample size and survey area reduce the LF uncertainties due to Poisson statistics and cosmic variance by >3 compared to previous studies. At the bright end, the LF shows excess power compared to the best-fit Schechter function, which can be attributed to the contribution of $z\sim3$ quasars. We compute the rest-frame near-infrared LF and stellar mass function (SMF) of z~3 LBGs based on the R-band and IRAC [4.5 micro m]-band flux relation. We investigate the evolution of the UV LFs and SMFs between z~7 and z~3, which supports a rising star formation history in the LBGs. We study the spatial correlation function of two bright LBG samples and estimate their average host halo mass. We find a tight relation between the host halo mass and the galaxy star formation rate (SFR),which follows the trend predicted by the baryonic accretion rate onto the halo, suggesting that the star formation in LBGs is fueled by baryonic accretion through the cosmic web. By comparing the SFRs with the total baryonic accretion rates, we find that cosmic star formation efficiency is about 5%-20% and it does not evolve significantly with redshift, halo mass, or galaxy luminosity.
In a recent paper by the first two named authors, existence of martingale solutions to a stochastic nonlinear Schr\"odinger equation driven by a L\'evy noise was proved. In this paper, we prove pathwise uniqueness, uniqueness in law and existence of strong solutions to this problem using an abstract uniqueness result of Kurtz.
For two arithmetical functions $f$ and $g$ with absolutely convergent Ramanujan expansions, Murty and Saha have recently derived asymptotic formulas with error term for the convolution sum $\sum_{n \le N} f(n) g(n+h)$ under some suitable conditions (see http://arxiv.org/abs/1506.01945). In this follow up article we improve these results with a weakened hypothesis which is in some sense minimal.
Starting from general considerations about the different concepts which exist for the definition of the quark mass near the pair production threshold, we introduce the definition of a mass with a dynamic degree of freedom that extends the previously given concept of the static PS mass.
In this preliminary work, the determination of physical parameters for the RR Lyrae stars CM, SW, SZ, and UY in Bootes from Stromgren uvby-\beta photometry is presented.
An edge-coloured graph $G$ is {\it rainbow connected} if any two vertices are connected by a path whose edges have distinct colours. This concept was introduced by Chartrand et al. in \cite{ch01}, and it was extended to oriented graphs by Dorbec et al. in \cite{DI}.   In this paper we present some results regarding this extention, mostly for the case of circulant digraphs.
In this paper, we show that 1) additive energy is not appropriate for discussing the validity of Tsallis or R\'enyi statistics for nonextensive systems at meta-equilibrium; 2) $N$-body systems with nonadditive energy or entropy should be described by generalized statistics whose nature is prescribed by the existence of thermodynamic stationarity. 3) the equivalence of Tsallis and R\'enyi entropies is in general not true.
As scene segmentation systems reach visually accurate results, many recent papers focus on making these network architectures faster, smaller and more efficient. In particular, studies often aim at designingreal-time'systems. Achieving this goal is particularly relevant in the context of real-time video understanding for autonomous vehicles, and robots. In this paper, we argue that the commonly used performance metric of mean Intersection over Union (mIoU) does not fully capture the information required to estimate the true performance of these networks when they operate inreal-time'. We propose a change of objective in the segmentation task, and its associated metric that encapsulates this missing information in the following way: We propose to predict the future output segmentation map that will match the future input frame at the time when the network finishes the processing. We introduce the associated latency-aware metric, from which we can determine a ranking. We perform latency timing experiments of some recent networks on different hardware and assess the performances of these networks on our proposed task. We propose improvements to scene segmentation networks to better perform on our task by using multi-frames input and increasing capacity in the initial convolutional layers.
We discuss the morphology and spectrophotometry of 5 comets visible in August, 2001. We decompose comae into coma profiles and azimuthally renormalized images, in which general and local features are quantitatively comparable. Comet 19P/Borrelly showed a strong gas fan toward the solar direction, but no detectable gas in the tail. Dust in its inner coma was collimated toward the antisolar direction and the tail, with no dust in the outer coma. The contribution of spatial variations structure was moderate, about 35%. Comet 29P Schwassmann-Wachmann 1 was observed in outburst: we detected ``spinning'' jet structures. A high level of dust production resulted in an unusually high Af\rho=16600 cm. The spatial variations reached -77%, at the minimum, due in part to a jet and a ring-like structure in 1 arcminute distance from the nucleus. In comet C/2001 A2, we detected a strong post-perihelion increase of dust and gas activity, in which the C_2 profile became one magnitude brighter over a 3-day period. For comets C/2000 SV74 and C/2000 WM1, we present detailed pre-perihelion spectrophotometry and morphological information. Comet C/2000 SV74 showed high dust production (Af\rho=1479 cm). Its coma suggests a steady-state outflow of material, while the low contribution of spatial variations support high level activity. The coma of C/2000 WM1 is dominated by solar effects, and CO+ forms the bulk of its gas activity. Despite its large heliocentric distance, we observed a nice tail.
A crystalline solid exhibits thermally induced localised {\em non-affine} droplets in the absence of external stress. Here we show that upon an imposed shear, the size of these droplets grow until they percolate at a critical strain, well {\em below} the value at which the solid begins to yield. This critical point does not manifest in bulk thermodynamic or mechanical properties, but is {\em hidden} and reveals itself in the onset of inhomogeneities in elastic moduli, marked changes in the appearance and local properties of non-affine droplets and a sudden enhancement in defect pair concentration. Slow relaxation of stress and an-elasticity appear as observable dynamical consequences of this hidden criticality. Our results may be directly verified in colloidal crystals with video microscopy techniques but are expected to have more general validity.
The variational principle for Gibbs point processes with general finite range interaction is proved. Namely, the Gibbs point processes are identified as the minimizers of the free excess energy equals to the sum of the specific entropy and the mean energy. The interaction is very general and includes superstable pairwise potential, finite or infinite multibody potential, geometrical interaction, hardcore interaction. The only restrictive assumption involves the finite range property.
We extend the so called Chen-Jiang decomposition for pushforward of pluricanocanical bundles to abelian varieties to the setting of klt pairs. We also provide a geometric application of this decomposition.
Interface structure at polar/non-polar interfaces has been shown to be a key factor in controlling emergent behavior in oxide heterostructures, including the LaFeO$_3$/$\textit{n}$-SrTiO$_3$ system. We demonstrate via high energy resolution x-ray photoemission that epitaxial LaFeO$_3$/$\textit{n}$-SrTiO$_3$ (001) heterojunctions engineered to have opposite interface polarities exhibit very similar band offsets and potential gradients within the LaFeO$_3$ films. However, differences in the potential gradient within the SrTiO$_3$ layer depending on polarity may promote hole diffusion into LaFeO$_3$ for applications in photocatalysis.
We present deep 3.8 micron observations of the Trapezium cluster in Orion obtained with the ESO VLT. We use these data to search for infrared excess emission and evidence for protoplanetary disks associated with the faint, substellar population of this young cluster, and to investigate the nature and extent of a recently discovered population of deeply embedded sources located in dense molecular gas behind the cluster. Examining the infrared colors of 38 luminosity and 24 spectroscopically selected substellar candidates we determine an infrared excess fraction of 50+/-20% from the JHKsLp colors for both samples. This finding confirms the presence of infrared excess, likely due to circumstellar disks, around a significant fraction of the cluster's substellar population. Our deep Lp imaging survey also provides new information concerning the deeply embedded population of young objects located in the molecular cloud behind the cluster; in particular, it doubles the number of sources in the cluster region known to possess extremely red K-L colors. These objects exhibit K-Lp colors indicative of deeply buried, possibly protostellar, objects that likely mark the site of the most recent and ongoing star formation in the region. We find the surface density distribution of the deeply embedded population to follow that of the background molecular ridge and to be highly structured, consisting of a string of at least 5 significant subclusters. These subclusters may represent the primordial building blocks out of which the cluster was and perhaps still is being assembled. These observations may thus provide insights into the early stages of cluster formation and appear consistent with recent simulations that suggest that the Trapezium cluster may have formed from numerous but small primordial subclusters.
Are some neutron stars produced without a supernova, without ejecting mass in a remnant? Theoretical calculations of core collapse in massive stars often predict this. The observation of the repeating FRB 121102, whose dispersion measure has not changed over several years, suggests that dark core collapses are not just failures of computer codes, but may be real. The existence of one repeating FRB with unchanging dispersion measure is not conclusive, but within a decade hundreds or thousands of FRB are expected to be discovered, likely including scores of repeaters, permitting useful statistical inferences. A na\"{\i}ve supernova remnant model predicts observable decline in dispersion measure for 100 years after its formation. If an upper limit on the decline of 2 pc/cm$^3$-y is set for five repeating FRB, then the na\"{\i}ve model with nominal parameters is rejected at the 95\% level of confidence. This may indicate dark neutron star formation without a supernova or supernova remnant. This hypothesis may also be tested with LSST data that would show, if present, a supernova at an interferometric FRB position if it occurred within the LSST epoch.
We investigate recovery of the bulk S-matrix from the AdS/CFT correspondence, at large radius. It was recently argued that some of the elements of the S-matrix might be read from CFT correlators, given a particular singularity structure of the latter, but leaving the question of more general S-matrix elements. Since in AdS/CFT, data must be specified on the boundary, we find certain limitations on the corresponding bulk wavepackets and on their localization properties. In particular, those we have found that approximately localize have low-energy tails, and corresponding power-law tails in position space. When their scattering is compared to that of "sharper" wavepackets typically used in scattering theory, one finds apparently significant differences, suggesting a possible lack of resolution via these wavepackets. We also give arguments that construction of the sharper wavepackets may require non-perturbative control of the boundary theory, and particular of the N^2 matrix degrees of freedom. These observations thus raise interesting questions about what principle would guarantee the appropriate control, and about how a boundary CFT can accurately approximate the flat space S-matrix.
Some probability distributions have moments, and some do not. For example, the normal distribution has power moments of arbitrary order, but the Cauchy distribution does not have power moments. In this paper, by analogy with the renormalization method in quantum field theory, we suggest a renormalization scheme to remove the divergence in divergent moments. We establish more than one renormalization procedure to renormalize the same moment to prove that the renormalized moment is scheme-independent. The power moment is usually a positive-integer-power moment; in this paper, we introduce nonpositive-integer-power moments by a similar treatment of renormalization. An approach to calculating logarithmic moment from power moment is proposed, which can serve as a verification of the validity of the renormalization procedure. The renormalization schemes proposed are the zeta function scheme, the subtraction scheme, the weighted moment scheme, the cut-off scheme, the characteristic function scheme, the Mellin transformation scheme, and the power-logarithmic moment scheme. The probability distributions considered are the Cauchy distribution, the Levy distribution, the q-exponential distribution, the q-Gaussian distribution, the normal distribution, the Student's t-distribution, and the Laplace distribution.
Two approaches to nonperturbative renormalization are discussed for theories quantized on the light cone. One is tailored specifically to a calculation of the dressed-electron state in quantum electrodynamics, where an invariant-mass cutoff is used as a regulator and a Tamm-Dancoff truncation is made to include no more than two photons. The other approach is based on Pauli-Villars regulators and is applied to Yukawa theory and a related soluble model. In both cases discretized light-cone quantization is used to obtain a finite matrix problem that can be solved nonperturbatively.
The Sun is a magnetically active star and is the source of the solar wind, electromagnetic radiation and energetic particles which affect the heliosphere and the Earths atmosphere. The magnetic field of the Sun is responsible for most of the dynamic activity of the Sun. This thesis research seeks to understand solar magnetic field generation and the role that magnetic fields play in the dynamics of the solar atmosphere. Specifically, this thesis focuses on two themes: in the first part, we study the origin and behaviour of solar magnetic fields using magnetohydrodynamic dynamo theory and modelling, and in the second part, utilizing observations and data analysis we study two major problems in solar physics, namely, the coronal heating problem and initiation mechanisms of solar flares.
Sagittarius A$^*$ in the Galactic center harbors a supermassive black hole and exhibits various active phenomena. Besides quiescent emission in radio and submillimeter radiation, flares in the near infrared (NIR) and X-ray bands are observed to occur frequently. We study a time-dependent model of the flares, assuming that the emission is from a blob ejected from the central object. Electrons obeying a power law with the exponential cutoff are assumed to be injected in the blob for a limited time interval. The flare data of 2007 April 4 were used to determine the values of model parameters. The spectral energy distribution of flare emission is explained by nonthermal synchrotron radiation in the NIR and X-ray bands. The model light curves suggest that electron acceleration is still underway during the rising phase of the flares. GeV gamma-rays are also emitted by synchrotron self-Compton scattering, although its luminosity is not strictly constrained by the current model. If the GeV emission is faint, the plasma blob is dominated by the magnetic energy density over the electron kinetic energy density. Observations in the GeV band will clarify the origin of the blob.
We discuss the non-linear evolution of the angular momentum L acquired by protostructures, like protogalaxies and protoclusters, due to tidal interactions with the surrounding matter inhomogeneities. The primordial density distribution is assumed to be Gaussian and the non-linear dynamics of the collisionless mass fluid is followed using Lagrangian perturbation theory. For a Cold Dark Matter spectrum, the inclusion of the leading-order Lagrangian correction terms results in a value of the rms ensemble average <L^2>^{1/2} which is only a factor of 1.3 higher than the corresponding linear estimate, irrespective of the scale. Consequently, the predictions of linear theory are rather accurate in quantifying the evolution of the angular momentum of protostructures before collapse sets in. In the Einstein-de Sitter universe, the initial torque is a good estimate for the tidal torque over the whole period during which the object is spun up.
We define a spatially-dependent fragmentation process, which involves rectangles breaking up into progressively smaller pieces at rates that depend on their shape. Long, thin rectangles are more likely to break quickly, and are also more likely to split along their longest side. We are interested in how the system evolves over time: how many fragments are there of different shapes and sizes, and how did they reach that state? Our theorem gives an almost sure growth rate along paths, which does not match the growth rate in expectation - there are paths where the expected number of fragments of that shape and size is exponentially large, but in reality no such fragments exist at large times almost surely.
We present a triangle of connections between the Sierpinski triangle, the sum-of-digits function, and the Binomial Theorem via a one-parameter family of Sierpinski matrices, which encodes a digital version of the Binomial Theorem.
We describe recent progress in a program to understand the classification of three-dimensional Fano varieties with $\mathbb{Q}$-factorial terminal singularities using mirror symmetry. As part of this we give an improved and more conceptual understanding of Laurent inversion, a technique that sometimes allows one to construct a Fano variety $X$ directly from a Laurent polynomial $f$ that corresponds to it under mirror symmetry.
We report follow-up observations of the Crab nebula with the PolarLight X-ray polarimeter, which revealed a possible variation in polarization associated with a pulsar glitch in 2019. The new observations confirm that the polarization has recovered roughly 100 days after the glitch. With the new observations, we find that the polarization angle (PA) measured with PolarLight from the total nebular emission has a difference of 18.0 +- 4.6 (deg) from that measured 42 years ago with OSO-8, indicating a secular evolution of polarization with either the Crab nebula or pulsar. The long-term variation in PA could be a result of multiple glitches in the history, magnetic reconnection or movement of synchrotron emitting structures in the nebula, or secular evolution of the pulsar magnetic geometry.