ShantanuT01/DACTYL-Pretraining huggingface dataset:
Asteroseismology has started to provide constraints on stellar properties that will be essential to accurately reconstruct the history of the Milky Way. Here we look at the information content in data sets representing current and future space missions (CoRoT, Kepler, K2, TESS, and PLATO) for red giant stars. We describe techniques for extracting the information in the frequency power spectrum and apply these techniques to {\it Kepler} data sets of different observing length to represent the different space missions. We demonstrate that for KIC 12008916, a low-luminosity red giant branch star, we can extract useful information from all data sets, and for all but the shortest data set we obtain good constraint on the g-mode period spacing and core rotation rates. We discuss how the high precision in these parameters will constrain the stellar properties of stellar radius, distance, mass and age. We show that high precision can be achieved in mass and hence age when values of the g-mode period spacing are available. We caution that tests to establish the accuracy of asteroseismic masses and ages are still "work in progress".
We study the influence of the liquid-vapor surface on the crystallization kinetics of supercooled metal alloys. While a good glass former, $\rm{Cu}_{50}\rm{Zr}_{50}$, shows no evidence of surface enhancement of crystallization, $\rm{Ni}_{50}\rm{Al}_{50}$ exhibits an increased rate of crystallization due to heterogeneous nucleation at the free liquid surface. The difference in the compositional fluctuations at the interface is proposed as the explanation of the distinction between the two alloys. Specifically, we observe compositional ordering at the surface of $\rm{Ni}_{50}\rm{Al}_{50}$ while the $\rm{Cu}_{50}\rm{Zr}_{50}$ alloy only exhibits a diffuse adsorption of the Cu at the interface. We argue that the general difference in composition susceptibilities at planar surfaces represents an important factor in understanding the difference in the glass forming ability of the two alloys.
We present an imaging framework which converts three images from a gated camera into high-resolution depth maps with depth accuracy comparable to pulsed lidar measurements. Existing scanning lidar systems achieve low spatial resolution at large ranges due to mechanically-limited angular sampling rates, restricting scene understanding tasks to close-range clusters with dense sampling. Moreover, today's pulsed lidar scanners suffer from high cost, power consumption, large form-factors, and they fail in the presence of strong backscatter. We depart from point scanning and demonstrate that it is possible to turn a low-cost CMOS gated imager into a dense depth camera with at least 80m range - by learning depth from three gated images. The proposed architecture exploits semantic context across gated slices, and is trained on a synthetic discriminator loss without the need of dense depth labels. The proposed replacement for scanning lidar systems is real-time, handles back-scatter and provides dense depth at long ranges. We validate our approach in simulation and on real-world data acquired over 4,000km driving in northern Europe. Data and code are available at https://github.com/gruberto/Gated2Depth.
We first consider the basic requirements for a quantum computer, arguing for the attractiveness of nuclear spins as information-bearing entities, and light for the coupling which allows quantum gates. We then survey the strengths of and immediate prospects for quantum information processing in ion traps. We discuss decoherence and gate rates in ion traps, comparing methods based on the vibrational motion with a method based on exchange of photons in cavity QED. We then sketch the main features of a quantum computer designed to allow an algorithm needing 10^6 Toffoli gates on 100 logical qubits. We find that around 200 ion traps linked by optical fibres and high-finesse cavities could perform such an algorithm in a week to a month, using components at or near current levels of technology.
While Random Matrix Theory has successfully modeled many quantities of families of L-functions, it frequently cannot see the family's arithmetic. In some situations this requires an extended theory that inserts arithmetic factors depending on the family, while in other cases these factors result in contributions which vanish in the limit, and are thus not detected. We review the general theory associated to one of the most important statistics, the n-level density of zeros near the central point. According to the Katz-Sarnak density conjecture, to each family of L-functions there is a corresponding symmetry group such that the behavior of zeros near the central point as the conductors tend to infinity agrees with the behavior of eigenvalues near 1 as the matrix size tends to infinity. We show how these calculations are done, emphasizing the techniques, methods and obstructions to improving the results, by considering in full detail a family of Dirichlet characters. We then describe how we may associate a symmetry constant to each family, and how to determine the symmetry group of a compound family in terms of the symmetries of the constituents. These calculations explain the remarkable universality of behavior, where the main terms are independent of the arithmetic (only the first two moments of the Satake parameters contribute in the limit; similar to the Central Limit Theorem, the higher moments are only felt in the rate of convergence). We end by exploring lower order terms in families of elliptic curves. We present evidence supporting a conjecture that the average second moment in one-parameter families without complex multiplication has, when appropriately viewed, a negative bias, and end with a discussion of the consequences of this bias on the distribution of low-lying zeros, in particular relations between such a bias and the observed excess rank in families.
We propose a phenomenological technique for modelling the emergence of active regions within a three-dimensional, kinematic dynamo framework. By imposing localised velocity perturbations, we create emergent flux-tubes out of toroidal magnetic field at the base of the convection zone, leading to the eruption of active regions at the solar surface. The velocity perturbations are calibrated to reproduce observed active region properties (including the size and flux of active regions, and the distribution of tilt angle with latitude), resulting in a more consistent treatment of flux-tube emergence in kinematic dynamo models than artificial flux deposition. We demonstrate how this technique can be used to assimilate observations and drive a kinematic 3D model, and use it to study the characteristics of active region emergence and decay as a source of poloidal field. We find that the poloidal components are strongest not at the solar surface, but in the middle convection zone, in contrast with the common assumption that the poloidal source is located near the solar surface. We also find that, while most of the energy is contained in the lower convection zone, there is a good correlation between the evolution of the surface and interior magnetic fields.
We review the relations between a family of domain-wall solutions to M-theory and gravitational instantons with special holonomy. When oxidized into the maximal-dimension parent supergravity, the transverse spaces of these domain walls become cohomogeneity-one spaces with generalized Heisenberg symmetries and a homothetic conformal symmetry. These metrics may also be obtained as scaling limits of generalized Eguchi-Hanson metrics, or, with appropriate discrete identifications, from generalized Atiyah-Hitchin metrics, thus providing field-theoretic realizations of string-theory orientifolds.
Using the Galerkin method, we obtain the unique existence of the weak solution to a time fractional wave problem, and establish some regularity estimates which reveal the singularity structure of the weak solution in time.
Aims. In this work we develop a technique to obtain high precision determinations of both metallicity and effective temperature of M dwarfs in the optical.   Methods. A new method is presented that makes use of the information of 4104 lines in the 530-690 nm spectral region. It consists in the measurement of pseudo equivalent widths and their correlation with established scales of [Fe/H] and $T_{eff}$.   Results. Our technique achieves a $rms$ of 0.08$\pm$0.01 for [Fe/H], 91$\pm$13 K for $T_{eff}$, and is valid in the (-0.85, 0.26 dex), (2800, 4100 K), and (M0.0, M5.0) intervals for [Fe/H], $T_{eff}$ and spectral type respectively. We also calculated the RMSE$_{V}$ which estimates uncertainties of the order of 0.12 dex for the metallicity and of 293 K for the effective temperature. The technique has an activity limit and should only be used for stars with $\log{L_{H_{\alpha}}/L_{bol}} < -4.0$. Our method is available online at \url{http://www.astro.up.pt/resources/mcal}.
We present the idea of intertwining of two diffusions by Feynman-Kac operators. We present some variations and implications of the method and give examples of its applications. Among others, it turns out to be a very useful tool for finding the expectations of some functionals of diffusions, especially for computing the Laplace transforms of stochastic processes. The examples give new results on marginal distributions of many stochastic processes including a generalized squared Bessel processes and joint distribution for squared Bessel bridge and its integral - the close formulae of the Laplace transforms are presented. We finally present a general version of the method and its applications to PDE of the second order. A new dependence between diffusions and solutions of hyperbolic partial differential equations is presented. In particular, the version of Feynman-Kac representation for hyperbolic PDE is given. It is presented, among others, the simple form of Laplace transform of wave equation with axial symmetry.
A spacelike surface with cylinder topology can be described by various sets of canonical variables within pure AdS3 gravity. Each is made of one real coordinate and one real momentum. The Hamiltonian can be either $H=0$ or it can be nonzero and we display the canonical transformations that map one into the other, in two relevant cases. In a choice of canonical coordinates, one of them is the cylinder aspect $q$, which evolves nontrivially in time. The time dependence of the aspect is an analytic function of time $t$ and an "angular momentum" $J$. By analytic continuation in both $t$ and $J$ we obtain a Euclidean evolution that can be described geometrically as the motion of a cylinder inside the region of the 3D hyperbolic space bounded by two "domes" (i.e. half spheres), which is topologically a solid torus. We find that for a given $J$ the Euclidean evolution cannot connect an initial aspect to an arbitrary final aspect; moreover, there are infinitely many Euclidean trajectories that connect any two allowed initial and final aspects. We compute the transition amplitude in two independent ways; first by solving exactly the time-dependent Schr\"odinger equation, then by summing in a sensible way all the saddle contributions, and we discuss why both approaches are mutually consistent.
We study the first "derived functors of unramified cohomology" in the sense of arXiv:1506.08385 [math.AG], applied to the sheaves $\mathbf{G}_m$ and $\mathcal{K}_2$. We find interesting connections with classical cycle-theoretic invariants of smooth projective varieties, involving notably a version of the Griffiths group, and the indecomposable $(2,1)$-cycles.
Building on earlier work, we construct linear sigma models for strings on curved spaces in the presence of branes. Our models include an extremely general class of brane-worldvolume gauge field configurations. We explain in an accessible manner the mathematical ideas which suggest appropriate worldsheet interactions for generating a given open string background. This construction provides an explanation for the appearance of the derived category in D-brane physics complementary to that of recent work of Douglas.
Instead of directly utilizing an observed image including some outliers, noise or intensity inhomogeneity, the use of its ideal value (e.g. noise-free image) has a favorable impact on clustering. Hence, the accurate estimation of the residual (e.g. unknown noise) between the observed image and its ideal value is an important task. To do so, we propose an $\ell_0$ regularization-based Fuzzy $C$-Means (FCM) algorithm incorporating a morphological reconstruction operation and a tight wavelet frame transform. To achieve a sound trade-off between detail preservation and noise suppression, morphological reconstruction is used to filter an observed image. By combining the observed and filtered images, a weighted sum image is generated. Since a tight wavelet frame system has sparse representations of an image, it is employed to decompose the weighted sum image, thus forming its corresponding feature set. Taking it as data for clustering, we present an improved FCM algorithm by imposing an $\ell_0$ regularization term on the residual between the feature set and its ideal value, which implies that the favorable estimation of the residual is obtained and the ideal value participates in clustering. Spatial information is also introduced into clustering since it is naturally encountered in image segmentation. Furthermore, it makes the estimation of the residual more reliable. To further enhance the segmentation effects of the improved FCM algorithm, we also employ the morphological reconstruction to smoothen the labels generated by clustering. Finally, based on the prototypes and smoothed labels, the segmented image is reconstructed by using a tight wavelet frame reconstruction operation. Experimental results reported for synthetic, medical, and color images show that the proposed algorithm is effective and efficient, and outperforms other algorithms.
We investigate the relationship between the energy spectrum of a local Hamiltonian and the geometric properties of its ground state. By generalizing a standard framework from the analysis of Markov chains to arbitrary (non-stoquastic) Hamiltonians we are naturally led to see that the spectral gap can always be upper bounded by an isoperimetric ratio that depends only on the ground state probability distribution and the range of the terms in the Hamiltonian, but not on any other details of the interaction couplings. This means that for a given probability distribution the inequality constrains the spectral gap of any local Hamiltonian with this distribution as its ground state probability distribution in some basis (Eldar and Harrow derived a similar result in order to characterize the output of low-depth quantum circuits). Going further, we relate the Hilbert space localization properties of the ground state to higher energy eigenvalues by showing that the presence of k strongly localized ground state modes (i.e. clusters of probability, or subsets with small expansion) in Hilbert space implies the presence of k energy eigenvalues that are close to the ground state energy. Our results suggest that quantum adiabatic optimization using local Hamiltonians will inevitably encounter small spectral gaps when attempting to prepare ground states corresponding to multi-modal probability distributions with strongly localized modes, and this problem cannot necessarily be alleviated with the inclusion of non-stoquastic couplings.
The role of soft biometrics to enhance person recognition systems in unconstrained scenarios has not been extensively studied. Here, we explore the utility of the following modalities: gender, ethnicity, age, glasses, beard, and moustache. We consider two assumptions: 1) manual estimation of soft biometrics and 2) automatic estimation from two commercial off-the-shelf systems (COTS). All experiments are reported using the labeled faces in the wild (LFW) database. First, we study the discrimination capabilities of soft biometrics standalone. Then, experiments are carried out fusing soft biometrics with two state-of-the-art face recognition systems based on deep learning. We observe that soft biometrics is a valuable complement to the face modality in unconstrained scenarios, with relative improvements up to 40%/15% in the verification performance when using manual/automatic soft biometrics estimation. Results are reproducible as we make public our manual annotations and COTS outputs of soft biometrics over LFW, as well as the face recognition scores.
The growth index $\gamma_L$ was proposed to investigate the possible deviation from the standard $\Lambda$CDM model and Einstein's gravity theory in a dynamical perspective. Recently, thanks to the measurement of the cosmic growth rate via the redshift-space distortion, one can understand the evolution of density contrast through $f\sigma_8(z)$, where $f(z)=d\ln \delta/d \ln a$ is the growth rate of matter and $\sigma_8(z)$ is the rms amplitude of the density contrast $\delta$ at the comoving $8h^{-1}$ Mpc scale. In this paper, we use the redshift space distortion data points to study the growth index on the bases of Einstein's gravity theory and a modified gravity theory under the assumption of $f=\Omega_m(a)^{\gamma_L}$. The cosmic background evolution is fixed by the cosmic observations from the type Ia supernovae SNLS3, cosmic microwave background radiation data from {\it Planck} and baryon acoustic oscillations. Via the Markov Chain Monte Carlo method, we found the $\gamma_L$ values for Einstein's gravity with a cosmological constant, $w=constant$ dark energy and a modified gravity theory in the $1,2,3\sigma$ regions respectively: $0.675_{-0.0662-0.120-0.155}^{+0.0611+0.129+0.178}$, $0.745_{-0.0819-0.146-0.190}^{+0.0755+0.157+0.205}$ and $0.555_{-0.0167-0.0373-0.0516}^{+0.0193+0.0335+0.0436}$. In the Einstein's gravity theory, the values of growth index $\gamma_L$ show almost $2\sigma$ deviation from the theoretical prediction 6/11 for the $\Lambda$CDM model. However in the modified gravity framework, a deviation from the Einstein's relativity is not detected in $1\sigma$ region. That implies that the currently available cosmic observations don't expect an alternative modified gravity theory beyond the $\Lambda$CDM model under Einstein's gravity, but that the simple assumption of $f=\Omega_m^{\gamma_L}$ should be improved.
The paper proposes an image-guided depth completion method to estimate accurate dense depth maps with fast computation time. The proposed network has two-stage structure. The first stage predicts a first depth map. Then, the second stage further refines the first depth map using the confidence maps. The second stage consists of two layers, each of which focuses on different regions and generates a refined depth map and a confidence map. The final depth map is obtained by combining two depth maps from the second stage using the corresponding confidence maps. Compared with the top-ranked models on the KITTI depth completion online leaderboard, the proposed model shows much faster computation time and competitive performance.
It has long been known that matter charged under a broken U(1) gauge symmetry collapsing to form a black hole will radiate away the associated external (massive) gauge field. We show that the timescale for the radiation of the monopole component of the field will be on the order of the inverse Compton wavelength of the gauge boson (assuming natural units). Since the Compton wavelength for a massive gauge boson is directly related to the scale of symmetry breaking, the timescale for a black hole to lose its gauge field "hair" is determined only by this scale. The timescale for Hawking radiation, however, is set by the mass of the black hole. These different dependencies mean that for any (sub-Planckian) scale of symmetry breaking we can define a mass below which black holes radiate quickly enough to discharge themselves via the Hawking process before the gauge field is radiated away. This has important implications for the extrapolation of classical black hole physics to Planck-scale virtual black holes. In particular, we comment on the implications for protecting protons from gravitationally mediated decay.
Most Video Super-Resolution (VSR) methods enhance a video reference frame by aligning its neighboring frames and mining information on these frames. Recently, deformable alignment has drawn extensive attention in VSR community for its remarkable performance, which can adaptively align neighboring frames with the reference one. However, we experimentally find that deformable alignment methods still suffer from fast motion due to locally loss-driven offset prediction and lack explicit motion constraints. Hence, we propose a Matching-based Flow Estimation (MFE) module to conduct global semantic feature matching and estimate optical flow as coarse offset for each location. And a Flow-guided Deformable Module (FDM) is proposed to integrate optical flow into deformable convolution. The FDM uses the optical flow to warp the neighboring frames at first. And then, the warped neighboring frames and the reference one are used to predict a set of fine offsets for each coarse offset. In general, we propose an end-to-end deep network called Flow-guided Deformable Alignment Network (FDAN), which reaches the state-of-the-art performance on two benchmark datasets while is still competitive in computation and memory consumption.
13\,Tau is a rarely studied bright B9V type star ({\sl V} = 5.68 mag), which shows a weak and double-peaked H{$\alpha$} emission profile in its spectra. In this study, we presented high-precision photometric data of 13\,Tau taken by the {\sl STEREO} satellite between 2007 and 2011, and compared the results to the spectroscopic findings to shed light on the Be phenomenon in the star. From the frequency analysis of the five-year data, we detected that 13\,Tau has exhibited a mono-periodic light variation ($f$ = 1.80487(1) cd$^{-1}$; A $\sim$ 2.76(8) mmag). The analysis revealed that frequency and amplitude values of the seasonal light curves varied from one year to another. From the spectroscopic data, we figured out that the equivalent widths of the H{$\alpha$} lines also showed variability, which seemed connected to the changes seen in both frequency and amplitude.
Internal diffusion-limited aggregation is a growth model based on random walk in Z^d. We study how the shape of the aggregate depends on the law of the underlying walk, focusing on a family of walks in Z^2 for which the limiting shape is a diamond. Certain of these walks -- those with a directional bias toward the origin -- have at most logarithmic fluctuations around the limiting shape. This contrasts with the simple random walk, where the limiting shape is a disk and the best known bound on the fluctuations, due to Lawler, is a power law. Our walks enjoy a uniform layering property which simplifies many of the proofs.
We consider $n$ independent, identically distributed one-dimensional Brownian motions, $B_j(t)$, where $B_j(0)$ has a rapidly decreasing, smooth density function $f$. The empirical quantiles, or pointwise order statistics, are denoted by $B_{j:n}(t)$, and we are interested in a sequence of quantiles $Q_n(t) = B_{j(n):n}(t)$, where $j(n)/n \to \alpha \in (0,1)$. This sequence converges in probability in $C[0,\infty)$ to $q(t)$, the $\alpha$-quantile of the law of $B_j(t)$. Our main result establishes the convergence in law in $C[0,\infty)$ of the fluctuation processes $F_n = n^{1/2}(Q_n - q)$. The limit process $F$ is a centered Gaussian process and we derive an explicit formula for its covariance function. We also show that $F$ has many of the same local properties as $B^{1/4}$, the fractional Brownian motion with Hurst parameter $H = 1/4$. For example, it is a quartic variation process, it has H\"older continuous paths with any exponent $\gamma < 1/4$, and (at least locally) it has increments whose correlation is negative and of the same order of magnitude as those of $B^{1/4}$.