ShantanuT01/DACTYL-Pretraining huggingface dataset:
We calculate bulk transport properties of two-dimensional topological insulators based on HgTe quantum wells in the ballistic regime. Interestingly, we find that the conductance and the shot noise are distinctively different for the so-called normal regime (the topologically trivial case) and the so-called inverted regime (the topologically non-trivial case). Thus, it is possible to verify the topological order of a two-dimensional topological insulator not only via observable edge properties but also via observable bulk properties. This is important because we show that under certain conditions the bulk contribution can dominate the edge contribution which makes it essential to fully understand the former for the interpretation of future experiments in clean samples.
We give the lower bound on Seshadri constants for the case of very ample line bundles on threefolds. We consider the situation when the Seshadri constant is strictly less than 2 and give a version of Bauer's theorem \cite[Theorem 2.1]{B1} for singular surfaces so we can prove the same result for smooth threefolds.
After a short review of experimental foundations of metric theories of gravity, the choice of general relativity as a theory to be used for the routine modeling of Gaia observations is justified. General principles of relativistic modeling of astronomical observations are then sketched and compared to the corresponding Newtonian principles. The fundamental reference system -- Barycentric Celestial Reference System, which has been chosen to be the relativistic reference system underlying the future Gaia reference frame is presented. Principal relativistic effects in each constituent of a relativistic model of astronomical observations are briefly elucidated. The structure of a relativistic model of positional observations which can be used as a standard relativistic model for Gaia is sketched. The physical meaning of the Gaia reference frame is discussed. It is discussed also how Gaia observations can be used to verify general relativity.
We present results obtained from our newly developed Galactic cosmic-ray transport code PICARD, that solves the cosmic-ray transport equation. This code allows for the computation of cosmic-ray spectra and the resulting gamma-ray emission. Relying on contemporary numerical solvers allows for efficient computation of models with deca-parsec resolution. PICARD can handle locally anisotropic spatial diffusion acknowledging a full diffusion tensor. We used this framework to investigate the transition from axisymmetric to spiral-arm cosmic-ray source distributions. Wherever possible we compare model predictions with constraining observables in cosmic-ray astrophysics.
An important problem in the theory of compressible gas flows is to understand the singular behavior of vacuum states. The main difficulty lies in the fact that the system becomes degenerate at the vacuum boundary, where the characteristics coincide and have unbounded derivative. In this paper, we overcome this difficulty by presenting a new formulation and new energy spaces. We establish the local in time well-posedness of one-dimensional compressible Euler equations for isentropic flows with the physical vacuum singularity in some spaces adapted to the singularity.
Line emission from dark matter is well motivated for some candidates e.g. sterile neutrinos. We present the first search for dark matter line emission in the 3-80keV range in a pointed observation of the Bullet Cluster with NuSTAR. We do not detect any significant line emission and instead we derive upper limits (95% CL) on the flux, and interpret these constraints in the context of sterile neutrinos and more generic dark matter candidates. NuSTAR does not have the sensitivity to constrain the recently claimed line detection at 3.5keV, but improves on the constraints for energies of 10-25keV.
Hybrid inverse problems are based on the interplay of two types of waves, in order to allow for imaging with both high resolution and high contrast. The inversion procedure often consists of two steps: first, internal measurements involving the unknown parameters and some related quantities are obtained, and, second, the unknown parameters have to be reconstructed from the internal data. The reconstruction in the second step requires the solutions of certain PDE to satisfy some non-zero constraints, such as the absence of nodal or critical points, or a non-vanishing Jacobian.   In this work, we consider a second-order elliptic PDE and show that it is possible to satisfy these constraints with overwhelming probability by choosing the boundary values randomly, following a sub-Gaussian distribution. The proof is based on a new quantitative estimate for the Runge approximation, a result of independent interest.
Let $p$ be a odd prime such that 2 is a primitive element of finite field $F_p*$. In this short note we propose a new algorithm for the computation of discrete logarithm in $F_p*$. This algorithm is based on elementary properties of finite fields and is purely theoretical in nature.
We explore the warm molecular and ionized gas in the centers of two megamaser disk galaxies using K-band spectroscopy. Our ultimate goal is to determine how gas is funneled onto the accretion disk, here traced by megamaser spots on sub-pc scales. We present NIR IFU data with a resolution of ~50 pc for two galaxies: NGC 4388 with VLT/SINFONI and NGC 1194 with Keck/OSIRIS+AO. The high spatial resolution and rich spectral diagnostics allow us to study both the stellar and gas kinematics as well as gas excitation on scales only an order of magnitude larger than the maser disk. We find a drop in the stellar velocity dispersion in the inner ~100 pc of NGC 4388, a common signature of a dynamically cold central component seen in many active nuclei. We also see evidence for non-circular gas motions in the molecular hydrogen on similar scales, with the gas kinematics on 100-pc scales aligned with the megamaser disk. In contrast, the high ionization lines and Br-gamma trace outflow along the 100 pc-scale jet. In NGC 1194, the continuum from the accreting black hole is very strong, making it difficult to measure robust two-dimensional kinematics, but the spatial distribution and line ratios of the molecular hydrogen and Br-gamma have consistent properties between the two galaxies.
In this work we develop a compact multi-orbital tight-binding model for phosphorene that accurately describes states near the main band gap. The model parameters are adjusted using as reference the band structure obtained by a density-functional theory calculation with the hybrid HSE06 functional. We use the optimized tight-binding model to study the effects of disorder on the anisotropic transport properties of phosphorene. In particular, we evaluate how the longitudinal resistivity depends on the lattice orientation for two typical disorder models: dilute scatterers with high potential fluctuation amplitudes, mimicking screened charges in the substrate, and dense scatterers with lower amplitudes, simulating weakly bounded adsorbates. We show that the intrinsic anisotropy associated to the band structure of this material, although sensitive to the type and intensity of the disorder, is robust.
In order to establish face recognition system in rehabilitation nursing robots beds and achieve real-time monitor the patient on the bed. We propose a face recognition method based on partial matching Hu moments which apply for rehabilitation nursing robots beds. Firstly we using Haar classifier to detect human faces automatically in dynamic video frames. Secondly we using Otsu threshold method to extract facial features (eyebrows, eyes, mouth) in the face image and its Hu moments. Finally, we using Hu moment feature set to achieve the automatic face recognition. Experimental results show that this method can efficiently identify face in a dynamic video and it has high practical value (the accuracy rate is 91% and the average recognition time is 4.3s).
Here we present a comparative study of the magnetic and crystal chemical properties of two Co2+ containing garnets, NaCa2Co2V3O12 and CaY2Co2Ge3O12. Both phases exhibit the onset of antiferromagnetic order at 8K and 6K respectively, as well as field-induced transitions in their magnetization at 1T and around 11 T. We find these field-dependent transitions correspond to quantum critical points that result in the suppression of antiferromagnetic order and that these transitions can be clearly seen using magnetocapacitance measurements. Finally, we perform detailed crystal chemistry analyses and complimentary density functional theory calculations to show that changes in the local environment of the Co-ions are responsible for differences in the two magnetic structures and their respective properties.
Probabilistic point cloud registration methods are becoming more popular because of their robustness. However, unlike point-to-plane variants of iterative closest point (ICP) which incorporate local surface geometric information such as surface normals, most probabilistic methods (e.g., coherent point drift (CPD)) ignore such information and build Gaussian mixture models (GMMs) with isotropic Gaussian covariances. This results in sphere-like GMM components which only penalize the point-to-point distance between the two point clouds. In this paper, we propose a novel method called CPD with Local Surface Geometry (LSG-CPD) for rigid point cloud registration. Our method adaptively adds different levels of point-to-plane penalization on top of the point-to-point penalization based on the flatness of the local surface. This results in GMM components with anisotropic covariances. We formulate point cloud registration as a maximum likelihood estimation (MLE) problem and solve it with the Expectation-Maximization (EM) algorithm. In the E step, we demonstrate that the computation can be recast into simple matrix manipulations and efficiently computed on a GPU. In the M step, we perform an unconstrained optimization on a matrix Lie group to efficiently update the rigid transformation of the registration. The proposed method outperforms state-of-the-art algorithms in terms of accuracy and robustness on various datasets captured with range scanners, RGBD cameras, and LiDARs. Also, it is significantly faster than modern implementations of CPD. The source code is available at https://github.com/ChirikjianLab/LSG-CPD.git.
We present an improved photometric redshift estimator code, CuBAN$z$, that is publicly available at https://goo.gl/fpk90V}{https://goo.gl/fpk90V. It uses the back propagation neural network along with clustering of the training set, which makes it more efficient than existing neural network codes. In CuBAN$z$, the training set is divided into several self learning clusters with galaxies having similar photometric properties and spectroscopic redshifts within a given span. The clustering algorithm uses the color information (i.e. $u-g$, $g-r$ etc.) rather than the apparent magnitudes at various photometric bands as the photometric redshift is more sensitive to the flux differences between different bands rather than the actual values. Separate neural networks are trained for each cluster using all possible colors, magnitudes and uncertainties in the measurements. For a galaxy with unknown redshift, we identify the closest possible clusters having similar photometric properties and use those clusters to get the photometric redshifts using the particular networks that were trained using those cluster members. For galaxies that do not match with any training cluster, the photometric redshifts are obtained from a separate network that uses entire training set. This clustering method enables us to determine the redshifts more accurately. SDSS Stripe 82 catalog has been used here for the demonstration of the code. For the clustered sources with redshift range $z_{\rm spec}<0.7$, the residual error ($\langle (z_{{\rm spec}}-z_{{\rm phot}})^2\rangle^{1/2} $) in the training/testing phase is as low as 0.03 compared to the existing ANNz code that provides residual error on the same test data set of 0.05. Further, we provide a much better estimate of the uncertainty of the derived photometric redshift.
This key-issues review is a plea for a new focus on simpler and more realistic models of glass-forming fluids. It seems to me that we have too often been led astray by sophisticated mathematical models that beautifully capture some of the most intriguing features of glassy behavior, but are too unrealistic to provide bases for predictive theories. As illustrations of what I mean, the first part of this article is devoted to brief summaries of imaginative, sensible, but disparate and often contradictory ideas for solving glass problems. Almost all of these ideas remain alive today, with their own enthusiastic advocates. I then describe numerical simulations, mostly by H. Tanaka and coworkers, in which it appears that very simple, polydisperse systems of hard disks and spheres develop long range, Ising-like, bond-orientational order as they approach glass transitions. Finally, I summarize my recent proposal that topologically ordered clusters of particles, in disordered environments, tend to become aligned with each other as if they were two-state systems, and thus produce the observed Ising-like behavior. Neither Tanaka's results nor my proposed interpretation of them fit comfortably within any of the currently popular glass theories.
[Abridged] In galactic nuclei with sufficiently short relaxation times, binary supermassive black holes can evolve beyond their stalling radii via continued interaction with stars. We study this "collisional" evolutionary regime using both fully self-consistent N-body integrations and approximate Fokker-Planck models. The N-body integrations employ particle numbers up to 0.26M and a direct-summation potential solver; close interactions involving the binary are treated using a new implementation of the Mikkola-Aarseth chain regularization algorithm. Even at these large values of N, two-body scattering occurs at high enough rates in the simulations that they can not be simply scaled to the large-N regime of real galaxies. The Fokker-Planck model is used to bridge this gap; it includes, for the first time, binary-induced changes in the stellar density and potential. The Fokker-Planck model is shown to accurately reproduce the results of the N-body integrations, and is then extended to the much larger N regime of real galaxies. Analytic expressions are derived that accurately reproduce the time dependence of the binary semi-major axis as predicted by the Fokker-Planck model. Gravitational wave coalescence is shown to occur in <10 Gyr in nuclei with velocity dispersions below about 80 km/s. Formation of a core results from a competition between ejection of stars by the binary and re-supply of depleted orbits via two-body scattering. Mass deficits as large as ~4 times the binary mass are produced before coalescence. After the two black holes coalesce, a Bahcall-Wolf cusp appears around the single hole in one relaxation time, resulting in a nuclear density profile consisting of a flat core with an inner, compact cluster, similar to what is observed at the centers of low-luminosity spheroids.
Let $X$ be a K3 surface, and $H$ its primitive polarization of the degree $H^2=8$. The moduli space of sheaves over $X$ with the isotropic Mukai vector $(2,H,2)$ is again a K3 surface, $Y$. In math.AG/0206158 we gave necessary and sufficient conditions in terms of Picard lattice of $X$ when $Y$ is isomorphic to $X$. The proof of sufficient condition in math.AG/0206158, when $Y$ is isomorphic to $X$, used Global Torelli Theorem for K3 surfaces, and it was not effective.   Here we give an effective variant of these results: its sufficient part gives an explicit isomorphism between $Y$ and $X$.   We hope that our similar results in math.AG/0304415, math.AG/0307355, math.AG/0309348 for arbitrary primitive isotropic Mukai vector on a K3 surface also can be made effective.
We fit a functional form for a universal ICM entropy profile to the scaled entropy profiles of a catalogue of X-ray galaxy cluster outskirts results, which are all relaxed cool core clusters at redshift below 0.25. We also investigate the functional form suggested by Lapi et al. and Cavaliere et al. for the behaviour of the entropy profile in the outskirts and find it to fit the data well outside 0.3r200 . We highlight the discrepancy in the entropy profile behaviour in the outskirts between observations and the numerical simulations of Burns et al., and show that the entropy profile flattening due to gas clumping calculated by Nagai & Lau is insufficient to match observations, suggesting that gas clumping alone cannot be responsible for all of the entropy profile flattening in the cluster outskirts. The entropy profiles found with Suzaku are found to be consistent with ROSAT, XMM-Newton and Planck results.
This paper presents a model for the outcome of collisions between planetesimals in a debris disk and assesses the impact of collisional processes on the structure and size distribution of the disk. The model is presented by its application to Fomalhaut's collisionally replenished dust disk; a recent 450 micron image of this disk shows a clump embedded within it with a flux ~5 per cent of the total. The following conclusions are drawn: (i) SED modelling is consistent with Fomalhaut's disk having a collisional cascade size distribution extending from bodies 0.2 m in diameter down to 7 micron-sized dust. (ii) Collisional lifetime arguments imply that the cascade starts with planetesimals 1.5-4 km in diameter. Any larger bodies must be predominantly primordial. (iii) Constraints on the timescale for the ignition of the cascade are consistent with these primordial planetesimals having a distribution that extends up to 1000km, resulting in a disk mass of 5-10 times the minimum mass solar nebula. (iv) The debris disk is expected to be intrinsically clumpy, since planetesimal collisions result in dust clumps. The intrinsic clumpiness of Fomalhaut's disk is below current detection limits, but could be detectable by future observatories such as the ALMA, and could provide the only way of determining the primordial planetesimal population. (v) The observed clump could have originated in a collision between two runaway planetesimals, both larger than 1400 km diameter. It is unlikely that we should witness such an event unless both the formation of these runaways and the ignition of the collisional cascade occurred within the last ~10 Myr. (vi) Another explanation for Fomalhaut's clump is that ~5 per cent of the planetesimals in the ring are trapped in 1:2 resonance with a planet orbiting at 80 AU.
We have used Virtual Observatory technology to analyse the disk scale length and central surface brightness for a sample of 29955 bright disk galaxies from the Sloan Digital Sky Survey. We use the results in the r-band and revisit the relation between these parameters and the galaxy morphology, and find the average disk surface brightness of 20.2(0.7) mag/arcsec^2. We confirm that late type spirals populate the lower left corner of the scale length-mu0 plane and that the early and intermediate spirals are mixed in this diagram, with disky ellipticals at the top left corner. We further investigate the Freeman Law and affirm that it indeed defines an upper limit for the disk central surface brightness in bright galaxies, and that disks in late type spirals have fainter central surface brightness. Our results are based on a volume corrected sample of galaxies in the local universe (z < 0.3) that is two orders of magnitudes larger than any sample previously studied, and deliver statistically significant implications that provide a comprehensive test bed for future theoretical studies and numerical simulations of galaxy formation and evolution.
In this tutorial it is explained the procedure to analyze an optical emission-line spectrum produced by a nebula ionized by massive star formation. Particularly, it is described the methodology used to derive physical properties, such as electron density and temperature, and the ionic abundances of the most representative elements whose emission lines are present in the optical spectrum. The tutorial is focused on the direct method,based on the measurement of the electron temperature to derive the abundances, given that the ionization and thermal equilibrium of the ionized gas is dominated by the metallicity. The ionization correction factors used to obtain total abundances from the abundances of some of their ions are also given. Finally, some strong-line methods to derive abundances are described. These are used when no estimation of the temperature can be derived, but that can be consistent with the direct method if they are calibrated.
Let $C$ be a hyperelliptic curve of genus $g \geq 3$. We give a new description of the theta map for moduli spaces of rank 2 semistable vector bundles with trivial determinant. In orther to do this, we describe a fibration of (a birational model of) the moduli space, whose fibers are GIT quotients $(\mathbb{P}^1)^{2g}//\operatorname{PGL(2)}$. Then, we use recent results of Kumar to identify the restriction of the theta map to these GIT quotients with some explicit osculating projection. As a corollary of this construction, we obtain a birational equivalence between the ramification locus of the theta map and a fibration in Kummer $(g-1)$-varieties over $\mathbb{P}^g$.
Consider the parabolic free boundary problem $$ \Delta u - \partial_t u = 0 \textrm{in} \{u>0\}, |\nabla u|=1 \textrm{on} \partial\{u>0\} . $$ For a realistic class of solutions, containing for example {\em all} limits of the singular perturbation problem $$\Delta u_\epsilon - \partial_t u_\epsilon = \beta_\epsilon(u_\epsilon) \textrm{as} \epsilon\to 0,$$ we prove that one-sided flatness of the free boundary implies regularity.   In particular, we show that the topological free boundary $\partial\{u>0\}$ can be decomposed into an {\em open} regular set (relative to $\partial\{u>0\}$) which is locally a surface with H\"older-continuous space normal, and a closed singular set.   Our result extends the main theorem in the paper by H.W. Alt-L.A. Caffarelli (1981) to more general solutions as well as the time-dependent case. Our proof uses methods developed in H.W. Alt-L.A. Caffarelli (1981), however we replace the core of that paper, which relies on non-positive mean curvature at singular points, by an argument based on scaling discrepancies, which promises to be applicable to more general free boundary or free discontinuity problems.
In this paper, we study various twisted A-harmonic sums, named following the seminal log-algebraicity papers of G. Anderson. These objects are partial sums of new types of special zeta values introduced by the first author and linked to certain rank one Drinfeld modules over Tate algebras in positive characteristic by Angl\`es, Tavares Ribeiro and the first author. We prove, by using techniques introduced by the second author, that various infinite families of such sums may be interpolated by polynomials, and we deduce, among several other results, properties of analogues of finite zeta values but inside the framework of the Carlitz module. In the theory of finite multi-zeta values in characteristic zero, finite zeta values are all zero. In the Carlitzian setting, there exist non-vanishing finite zeta values, and we study some of their properties in the present paper.
In X-ray CT scan with metallic objects, it is known that direct application of the filtered back-projection (FBP) formula leads to streaking artifacts in the reconstruction. These are characterized mathematically in terms of wave front sets in [13]. In this work, we give a quantitative microlocal analysis of such artifacts. We consider metal regions with strictly convex smooth boundaries and show that the streaking artifacts are conormal distributions to straight lines tangential to at least two boundary curves. For metal regions with piecewise smooth boundaries, we analyze the streaking artifacts especially due to the corner points. Finally, we study the reduction of the artifacts using appropriate filters.