ShantanuT01/DACTYL-Pretraining huggingface dataset:
In the framework of density functional theory, the structural and magnetic properties of Fe$_{100-x}$Al$_x$ alloys (${5 \leq x \leq 25}$~at.\%) with the different structural order are investigated. Using the Korringa-Kohn-Rostoker Green's function method with a coherent potential approximation, the equilibrium lattice parameters, ground-state energy, and shear moduli for D0$_3$, B2, and A2 structures are calculated. For all structures, the optimized lattice constant increases while the shear modulus demonstrates a decreasing behavior with increasing Al content. The tetragonal magnetostriction constants are estimated by the torque method. The A2 and B2 structures provide a positive contribution to the tetragonal magnetostriction. With the help of Monte Carlo simulations of the Heisenberg model, the Curie temperatures are obtained in a wide concentration range.
We consider tunneling transport through a Mn$_{12}$ molecular magnet using spin density functional theory. A tractable methodology for constructing many-body wavefunctions from Kohn-Sham orbitals allows for the determination of spin-dependent matrix elements for use in transport calculations. The tunneling conductance at finite bias is characterized by peaks representing transitions between spin multiplets, separated by an energy on the order of the magnetic anisotropy. The energy splitting of the spin multiplets and the spatial part of their many-body wave functions, describing the orbital degrees of freedom of the excess charge, strongly affect the electronic transport, and can lead to negative differential conductance.
The chemical evolution in high-mass star-forming regions is still poorly constrained. Studying the evolution of deuterated molecules allows to differentiate between subsequent stages of high-mass star formation regions due to the strong temperature dependence of deuterium isotopic fractionation. We observed a sample of 59 sources including 19 infrared dark clouds, 20 high-mass protostellar objects, 11 hot molecular cores and 9 ultra-compact HII regions in the (3-2) transitions of the four deuterated molecules, DCN, DNC, DCO+ and N2D+ as well as their non-deuterated counterpart. The overall detection fraction of DCN, DNC and DCO+ is high and exceeds 50% for most of the stages. N2D+ was only detected in a few infrared dark clouds and high-mass protostellar objects. It can be related to problems in the bandpass at the frequency of the transition and to low abundances in the more evolved, warmer stages. We find median D/H ratios of ~0.02 for DCN, ~0.005 for DNC, ~0.0025 for DCO+ and ~0.02 for N2D+. While the D/H ratios of DNC, DCO+ and N2D+ decrease with time, DCN/HCN peaks at the hot molecular core stage. We only found weak correlations of the D/H ratios for N2D+ with the luminosity of the central source and the FWHM of the line, and no correlation with the H2 column density. In combination with a previously observed set of 14 other molecules (Paper I) we fitted the calculated column densities with an elaborate 1D physico-chemical model with time-dependent D-chemistry including ortho- and para-H2 states. Good overall fits to the observed data have been obtained the model. It is one of the first times that observations and modeling have been combined to derive chemically based best-fit models for the evolution of high-mass star formation including deuteration.
The multi-phase-field approach is generalized to treat capillarity-driven diffusion parallel to the surfaces and phase-boundaries, i.e. the boundaries between a condensed phase and its vapor and the boundaries between two or multiple condensed phases. The effect of capillarity is modeled via curvature-dependence of the chemical potential whose gradient gives rise to diffusion. The model is used to study thermal grooving on the surface of a polycrystalline body. Decaying oscillations of the surface profile during thermal grooving, postulated by Hillert long ago but reported only in few studies so far, are observed and discussed. Furthermore, annealing of multi-nano-clusters on a deformable free surface is investigated using the proposed model. Results of these simulations suggest that the characteristic crater-like structure with an elevated perimeter, observed in recent experiments, is a transient non-equilibrium state during the annealing process.
Gamma-positivity appears frequently in finite geometries, combinatorics and number theory. Motivated by the recent work of Sagan and Tirrell (Adv. Math., 374 (2020), 107387), we study the relationships between gamma-positivity and alternating gamma-positivity. As applications, we derive several alternatingly gamma-positive polynomials related to Narayana polynomials and Eulerian polynomials. In particular, we show the alternating gamma-positivity and Hurwitz stability of a combination of the modified Narayana polynomials of types A and B. By using colored $2\times n$ Young diagrams, we present a unified combinatorial interpretations of three identities involving Narayana numbers of type B. A general result of this paper is that every gamma-positive polynomial is also alternatingly semi-gamma-positive. At the end of this paper, we pose two conjectures, one concerns the Boros-Moll polynomials and the other concerns the enumerators of permutations by descents and excedances.
We have introduced a class of exactly soluble Hamiltonian with either SO(2n+1) or SU(2) symmetry, whose ground states are the SO(2n+1) symmetric matrix product states. The hidden topological order in these states can be fully identified and characterized by a set of nonlocal string order parameters. The Hamiltonian possesses a hidden $(Z_{2}\times Z_{2})^{n} $ topological symmetry. The breaking of this hidden symmetry leads to $4^{n}$ degenerate ground states with disentangled edge states in an open chain system. Such matrix product states can be regarded as cluster states, applicable to measurement-based quantum computation.
In the past decade, weak gravitational lensing has become an important tool in the study of the universe at the largest scale, giving insights into the distribution of dark matter, the expansion of the universe, and the nature of dark energy. This thesis research explores several applications of Karhunen-Loeve (KL) analysis to speed and improve the comparison of weak lensing shear catalogs to theory in order to constrain cosmological parameters in current and future lensing surveys. After providing a brief introduction to cosmology and to KL analysis, this work addresses three related aspects of weak lensing analysis: (1) Three-dimensional tomographic mapping (based on work published in Vanderplas et al. 2011); (2) Shear peak statistics with incomplete/gappy data (based on work published in Vanderplas et al. 2012); and (3) two-point parameter estimation from gappy data using KL modes (previously unpublished)... [this abstract has been abbreviated; please see the thesis for the full abstract].
In this article we study a transport-diffusion equation in the framework of the stratified Lie groups. For this equation we will study the existence of the solutions, a maximum principle, a positivity principle and H\"older regularity.
We construct a tower of fields from the rings $R_n$ which parametrize pairs $(X,\lambda)$, where $X$ is a deformation of a fixed one-dimensional formal group $\mathbb{X}$ of finite height $h$, together with a Drinfeld level-$n$ structure $\lambda$. We choose principal prime ideals $\mathfrak{p}_n \mid (p)$ in each ring $R_n$ in a compatible way and consider the field $K'_n$ obtained by localizing $R_n$ at $\mathfrak{p}_n$, completing, and passing to the fraction field. By taking the compositum $K_n = K'_n K_0$ of each field with the completion $K_0$ of a certain unramified extension of $K'_0$, we obtain a tower of fields $(K_n)_n$ which we prove to be strictly deeply ramified in the sense of Anthony Scholl. When $h=2$ we also investigate the question of whether this is a Kummer tower.
The dilatancy angle describes the propensity of a granular medium to dilate under an applied shear. Using a simple spin model (the ``tetris'' model) which accounts for geometrical ``frustration'' effects, we study such a dilatancy angle as a function of density. An exact mapping can be drawn with a directed percolation process which proves that there exists a critical density $\rho_c$ above which the system expands and below which it contracts under shear. When applied to packings constructed by a random deposition under gravity, the dilatancy angle is shown to be strongly anisotropic, and it constitutes an efficient tool to characterize the texture of the medium.
In this paper we consider the possibility that the structure of the largest radio galaxy J1420-0545 is formed by a restarted rather than a primary jet activity. This hypothesis is motivated by the unusual morphological properties of the source, suggesting almost ballistic propagation of powerful jets in a particularly low-density environment. New radio observations of J1420-0545 confirm its morphology consisting of only two narrow lobes; no trace of any outer low-density cavity due to the previous jet activity is therefore detected. Different model fits performed using the newly accessed radio data imply relatively young age of the source, its exceptionally high expansion velocity, large jet kinetic power, and confirm particularly low-density environment. We find that it is possible to choose a realistic set of the model parameters for which the hypothetical outer lobes of J1420-0545 are old enough so that their expected radio surface brightness is substantially below the rms noise level of the available radio maps. On the other hand, the extremely low density of the gas surrounding the J1420-0545 lobes is consistent with the mean density of the baryonic matter in the Universe. This suggests that the source may be instead located in a real void of the galaxy and matter distribution. In both cases the giant radio lobes of J1420-0545 are expected to modify substantially the surrounding matter by driving strong shocks and heating the gas located at the outskirts of the filamentary galactic distribution. Finally, we also find that the energetic requirements for the source are severe in terms of the total jet power and the total energy deposited by the outflows far away from the central engine.
We discuss the classicalization of a quantum state induced by an environment in the inflationary stage of the universe. The classicalization is necessary for the homogeneous ground sate to become classical non-homogeneous one accompanied with the statistical fluctuation, which is a plausible candidate for the seeds of structure formation. Using simple models, we show that i) the two classicalization criteria, the classical correlation and quantum decoherence, are simultaneously satisfied by the environment and that ii) the power spectrum of the resultant statistical fluctuation depends upon the detail of the classicalization process. Especially, the result ii) means that, taking account of the classicalization process, the inflationary scenario does not necessarily predict the unique spectrum which is usually believed.
We study the noise of the cotunneling current through one or several tunnel-coupled quantum dots in the Coulomb blockade regime. We consider the regime of weak (elastic and inelastic) cotunneling, and prove a non-equilibrium fluctuation-dissipation theorem which leads to a universal expression for the noise-to-current ratio (Fano factor).
Let $X$ be a smooth, projective, geometrically connected curve over a finite field $\mathbb{F}_q$, and let $G$ be a split semisimple algebraic group over $\mathbb{F}_q$. Its dual group $\hat{G}$ is a split reductive group over $\mathbb{Z}$. Conjecturally, any $l$-adic $\hat{G}$-local system on $X$ (equivalently, any conjugacy class of continuous homomorphisms $\pi_1(X) \to \hat{G}(\bar{\mathbb{Q}}_l)$) should be associated to an everywhere unramified automorphic representation of the group $G$.   We show that for any homomorphism $\pi_1(X) \to \hat{G}(\bar{\mathbb{Q}}_l)$ of Zariski dense image, there exists a finite Galois cover $Y \to X$ over which the associated local system becomes automorphic.
Simple linear second-order differential equations have been written down for FRW cosmologies with barotropic fluids by Faraoni. His results have been extended by Rosu, who employed techniques belonging to nonrelativistic supersymmetry to obtain time-dependent adiabatic indices. Further extensions are presented here using the known connection between the linear second-order differential equations and Dirac-like equations in the same supersymmetric context. These extensions are equivalent to adding an imaginary part to the adiabatic index which is proportional to the mass parameter of the Dirac spinor. The natural physical interpretation of the imaginary part is related to the particular dissipation and instabilities of the barotropic FRW hydrodynamics that are introduced by means of this supersymmetric scheme
We give results on the question of code optimality for linear codes over finite Frobenius rings for the homogeneous weight. This article improves on the existing Plotkin bound derived in an earlier paper, and suggests a version of a Singleton bound. We also present some families of codes meeting these new bounds.
We consider the standard repulsive Hubbard model with a flat lowest-energy band for two one-dimensional lattices (diamond chain and ladder) as well as for a two-dimensional lattice (bilayer) at half filling of the flat band. The considered models do not fall in the class of Mielke-Tasaki flat-band ferromagnets, since they do not obey the connectivity conditions. However, the ground-state ferromagnetism can emerge, if the flat band becomes dispersive. To study this kinetic-energy-driven ferromagnetism we use perturbation theory and exact diagonalization of finite lattices. We find as a typical scenario that small and moderate dispersion may lead to a ferromagnetic ground state for sufficiently large on-site Hubbard repulsion $U>U_c$, where $U_c$ increases monotonically with the acquired bandwidth. However, we also observe for some specific parameter cases, that (i) ferromagnetism appears at already very small $U_c$, (ii) ferromagnetism does not show up at all, (iii) the critical on-site repulsion $U_c$ is a nonmonotonic function of the bandwidth, or that (iv) a critical bandwidth is needed to open the window for ground-state ferromagnetism.
Pedestrian detection relying on deep convolution neural networks has made significant progress. Though promising results have been achieved on standard pedestrians, the performance on heavily occluded pedestrians remains far from satisfactory. The main culprits are intra-class occlusions involving other pedestrians and inter-class occlusions caused by other objects, such as cars and bicycles. These result in a multitude of occlusion patterns. We propose an approach for occluded pedestrian detection with the following contributions. First, we introduce a novel mask-guided attention network that fits naturally into popular pedestrian detection pipelines. Our attention network emphasizes on visible pedestrian regions while suppressing the occluded ones by modulating full body features. Second, we empirically demonstrate that coarse-level segmentation annotations provide reasonable approximation to their dense pixel-wise counterparts. Experiments are performed on CityPersons and Caltech datasets. Our approach sets a new state-of-the-art on both datasets. Our approach obtains an absolute gain of 9.5% in log-average miss rate, compared to the best reported results on the heavily occluded (HO) pedestrian set of CityPersons test set. Further, on the HO pedestrian set of Caltech dataset, our method achieves an absolute gain of 5.0% in log-average miss rate, compared to the best reported results. Code and models are available at: https://github.com/Leotju/MGAN.
In this paper we show some multiplicity estimates theorems for a connected algebraic group (not necessarily commutative) $G$ over an algebraically closed subfield of $\mathbb{C}$. More specifically, under particular assumptions on the parameters and the points where the polynomial has high order with respect to a Lie subalgebra of the Lie algebra associated to $G$, we present a series of results where we find obstruction varieties with different properties. Some of the results obtained in this paper improve the multiplicity estimates theorem for arbitrary connected algebraic groups that already exist and also they shall be important tools in transcendence theory for noncommutative algebraic groups.
CMB observables have largely fixed the expansion history of the universe in the deceleration regime and provided two self-calibrated absolute standards for dark energy studies: the sound horizon at recombination as a standard ruler and the amplitude of initial density fluctuations. We review these inferences and expose the testable assumptions about recombination and reionization that underly them. Fixing the deceleration regime with CMB observables, deviations in the distance and growth observables appear most strongly at z=0 implying that accurate calibration of local and CMB standards may be more important than redshift range or depth. The single most important complement to the CMB for measuring the dark energy equation of state at z~0.5 is a determination of the Hubble constant to better than a few percent. Counterintuitively, with fixed fractional distance errors and relative standards such as SNe, the Hubble constant measurement is best achieved in the high redshift deceleration regime. Degeneracies between the evolution and current value of the equation of state or between its value and spatial curvature can be broken if percent level measurement and calibration of distance standards can be made at intermediate redshifts or the growth function at any redshift in the acceleration regime. We compare several dark energy probes available to a wide and deep optical survey: baryon features in galaxy angular power spectra and the growth rate from galaxy-galaxy lensing, shear tomography and the cluster abundance.
The Grothendieck ring of Chow motives admits two natural opposite $\lambda$-ring structures, one of which is a special structure allowing the definition of Adams operations on the ring. In this work I present algorithms which allow an effective simplification of expressions that involve both $\lambda$-ring structures, as well as Adams operations. In particular, these algorithms allow the symbolic simplification of algebraic expressions in the sub-$\lambda$-ring of motives generated by a finite set of curves into polynomial expressions in a small set of motivic generators. As a consequence, the explicit computation of motives of some moduli spaces is performed, allowing the computational verification of some conjectural formulas for these spaces.
We consider the focusing $L^2$-supercritical Schr\"odinger equation in the exterior of a smooth, compact, strictly convex obstacle. We construct a solution behaving asymptotically as a solitary waves on $R^3$, as large time. When the velocity of the solitary wave is high, the existence of such a solution can be proved by a classical fixed point argument. To construct solutions with arbitrary nonzero velocity, we use a compactness argument similar to the one that was introduced by F.Merle in 1990 to construct solution of NLS blowing up at several blow-up point together with a topological argument using Brouwer's theorem to control the unstable direction of the linearized operator at soliton. These solutions are arbitrarily close to the scattering threshold given by a previous work of R.Killip, M.Visan and X.Zhang which is the same as the one on whole Euclidean space.
Stellar oscillations appear all across the Hertzsprung-Russell diagram. Recent theoretical studies support their existence also in the atmospheres of M dwarfs. These studies predict for them short periodicities ranging from 20~min to 3~h. Our Cool Tiny Beats (CTB) programme aims at finding these oscillations for the very first time. With this goal, CTB explores the short time domain of M dwarfs using radial velocity data from the HARPS-ESO and HARPS-N high-precision spectrographs. Here we present the results for the two most long-term stable targets observed to date with CTB, GJ~588 and GJ~699 (i.e. Barnard's star). In the first part of this work we detail the correction of several instrumental effects. These corrections are specially relevant when searching for sub-night signals. Results show no significant signals in the range where M dwarfs pulsations were predicted. However, we estimate that stellar pulsations with amplitudes larger than $\sim0.5\,\mathrm{m\,s}^{-1}$ can be detected with a 90% completeness with our observations. This result, along with the excess of power regions detected in the periodograms, open the possibility of non-resolved very low amplitude pulsation signals. Next generation more precise instrumentation would be required to detect such oscillations. However, the possibility of detecting pulsating M-dwarf stars with larger amplitudes is feasible due to the short size of the analysed sample. This motivates the need for completeness of the CTB survey.
As we resolve ever smaller structures in the solar atmosphere, it has become clear that magnetism is an important component of those small structures. Small-scale magnetism holds the key to many poorly understood facets of solar magnetism on all scales, such as the existence of a local dynamo, chromospheric heating, and flux emergence, to name a few. Here, we review our knowledge of small-scale photospheric fields, with particular emphasis on quiet-sun field, and discuss the implications of several results obtained recently using new instruments, as well as future prospects in this field of research.
We report the observation of a magnetic polarization of the O\,$2p$-states in YMn$_2$O$_5$ through the use of soft X-ray resonant scattering at the oxygen $K$-edge. Remarkably, we find that the temperature dependence of the integrated intensity of this signal closely follows the macroscopic electric polarization, and hence is proportional to the ferroelectric order parameter. This is in contrast to the temperature dependence observed at the Mn\,$L_3$-edge, which reflects the Mn magnetic order parameter. First principle calculations provide a microscopic understanding of these results and show that a spin-dependent hybridization of O\,$2p$- and Mn\, 3d-states results in a purely electronic contribution to the ferroelectric polarization, which can exist in the absence of lattice distortions.
Mean Average Precision (mAP) is the primary evaluation measure for object detection. Although object detection has a broad range of applications, mAP evaluates detectors in terms of the performance of ranked instance retrieval. Such the assumption for the evaluation task does not suit some downstream tasks. To alleviate the gap between downstream tasks and the evaluation scenario, we propose Optimal Correction Cost (OC-cost), which assesses detection accuracy at image level. OC-cost computes the cost of correcting detections to ground truths as a measure of accuracy. The cost is obtained by solving an optimal transportation problem between the detections and the ground truths. Unlike mAP, OC-cost is designed to penalize false positive and false negative detections properly, and every image in a dataset is treated equally. Our experimental result validates that OC-cost has better agreement with human preference than a ranking-based measure, i.e., mAP for a single image. We also show that detectors' rankings by OC-cost are more consistent on different data splits than mAP. Our goal is not to replace mAP with OC-cost but provide an additional tool to evaluate detectors from another aspect. To help future researchers and developers choose a target measure, we provide a series of experiments to clarify how mAP and OC-cost differ.