ShantanuT01/DACTYL-Pretraining huggingface dataset:
Single layers of hexagonal two-dimensional nanostructures such as graphene, silicene, and germanene exhibit large carrier Fermi velocities and, consequently, large light-matter coupling strength making these materials promising elements for nano-opto-electronics. Although these materials are centrosymmetric, the spatial dispersion turns out to be quite large allowing the second-order nonlinear response of such materials to be comparable to the non-centrosymmetric 2D ones. The second-order response of massless Dirac fermions has been extensively studied, however a general approach correct over the full Brillouin zone is lacking so far. To complete this gap, in the current paper we develop a general quantum-mechanical theory of the in-plane second-order nonlinear response beyond the Dirac cone approximation and applicable to the full Brillouin zone of the hexagonal tight-binding nanostructures. We present explicit calculation of the nonlinear susceptibility tensor of 2D hexagonal nanostructures applicable to arbitrary three-wave mixing processes.
We present a method, based on the positive weight next-to-leading-order matching formalism (POWHEG), to simulate photon production processes at next-to-leading-order (NLO). This technique is applied to the simulation of diphoton production in hadron-hadron collisions. The algorithm consistently combines the parton shower and NLO calculation, producing only positive weight events. The simulation includes both the photon fragmentation contribution and a full implementation of the truncated shower required to correctly describe soft emissions in an angular-ordered parton shower.
Let $K$ be a number field, and let $W$ be a subspace of $K^N$, $N \geq 1$. Let $V_1,...,V_M$ be subspaces of $K^N$ of dimension less than dimension of $W$. We prove the existence of a point of small height in $W \setminus \bigcup_{i=1}^M V_i$, providing an explicit upper bound on the height of such a point in terms of heights of $W$ and $V_1,...,V_M$. Our main tool is a counting estimate we prove for the number of points of a subspace of $K^N$ inside of an adelic cube. As corollaries to our main result we derive an explicit bound on the height of a non-vanishing point for a decomposable form and an effective subspace extension lemma.
Consider stochastic functional differential equations, whose coefficients depend on past histories. The solution determines a non-Markov process. In the present paper, we shall obtain the existence of smooth densities for joint distributions of solutions, under the uniformly elliptic condition on the diffusion coefficients, via the Malliavin calculus. As an application, we shall study the computations of the Greeks on options associated with the asset price dynamics models with delayed effects.
We present high-resolution (1".0) Atacama Large Millimeter/submillimeter Array (ALMA) observations of CO (1-0) and CO (2- 1) rotational transitions toward the nearby IR-luminous merger NGC 1614 supplemented with ALMA archival data of CO (3-2), and CO (6-5) transitions. The CO (6-5) emission arises from the starburst ring (central 590 pc in radius), while the lower-$J$ CO lines are distributed over the outer disk ($\sim$ 3.3 kpc in radius). Radiative transfer and photon dominated region (PDR) modeling reveal that the starburst ring has a single warmer gas component with more intense far-ultraviolet radiation field ($n_{\rm{H_2}}$ $\sim$ 10$^{4.6}$ cm$^{-3}$, $T_{\rm{kin}}$ $\sim$ 42 K, and $G_{\rm{0}}$ $\sim$ 10$^{2.7}$) relative to the outer disk ($n_{\rm{H_2}}$ $\sim$ 10$^{5.1}$ cm$^{-3}$, $T_{\rm{kin}}$ $\sim$ 22 K, and $G_{\rm{0}}$ $\sim$ 10$^{0.9}$). A two-phase molecular interstellar medium with a warm and cold ($>$ 70 K and $\sim$ 19 K) component is also an applicable model for the starburst ring. A possible source for heating the warm gas component is mechanical heating due to stellar feedback rather than PDR. Furthermore, we find evidence for non-circular motions along the north-south optical bar in the lower-$J$ CO images, suggesting a cold gas inflow. We suggest that star formation in the starburst ring is sustained by the bar-driven cold gas inflow, and starburst activities radiatively and mechanically power the CO excitation. The absence of a bright active galactic nucleus can be explained by a scenario that cold gas accumulating on the starburst ring is exhausted as the fuel for star formation, or is launched as an outflow before being able to feed to the nucleus.
The essential point of Bohr-Mottelson theory is to assume a irrotational flow. As was already suggested by Marumori and Watanabe, the internal rotational motion, i.e., the vortex motion, however, may exist also in nuclei. So, we have a necessity of taking the vortex motion into consideration. In a classical fluid dynamics, there are various ways to treat the internal rotational velocity. The Clebsch representation, v(x) = -\nabla \phi(x) + \lambda(x) \nabla \psi(x) (\phi ; velocity potential, \lambda and \psi: Clebsch parameters) is very powerful and has an advantage deriving equations of fluid motion from a Lagransian. Making the best use of the advantage, Kronig-Thellung, Ziman and Ito obtained a Hamiltonian including the internal rotational motion, the vortex motion, through the term \lambda(x) \nabla \psi(x). Going to quantum fluid dynamics, Ziman and Thellung finally derived a roton spectrum of liquid Helium II postulated by Landau. Is it possible to apply such the manner to a description of the collective vortex motion in nuclei? The description of such a collective motion has never been treated in the Bohr-Mottelson model (BMM) for a long time. In this paper, we will investigate a possibility of describing the vortex motion in nuclei basing on the theories of Ziman and Ito together with Marumori's work.
An extensive theoretical literature predicts that X-ray Polarimetry can directly determine relevant physical and geometrical parameters of astrophysical sources, and discriminate between models further than allowed by spectral and timing data only. X-ray Polarimetry can also provide tests of Fundamental Physics. A high sensitivity polarimeter in the focal plane of a New Generation X-ray telescope could open this new window in the High Energy Sky.
In these lectures, we shall present some remarkable results that have been obtained for systems far from equilibrium during the last two decades. We shall put a special emphasis on the concept of large deviation functions that provide us with a unified description of many physical situations. These functions are expected to play, for systems far from equilibrium, a role akin to that of the thermodynamic potentials. These concepts will be illustrated by exact solutions of the Asymmetric Exclusion Process, a paradigm for non-equilibrium statistical physics.
We apply gravity-based and density-based methods to identify clouds in numerical simulations of the star-forming, three-phase interstellar medium (ISM), and compare their properties and their global correlation with the star formation rate over time. The gravity-based method identifies bound objects, which have masses M ~ 10^3 - 10^4 M_solar at densities n_H ~ 100 cm^-3, and traditional virial parameters alpha_v ~ 0.5 - 5. For clouds defined by a density threshold n_H,min , the average virial parameter decreases, and the fraction of material that is genuinely bound increases, at higher n_H,min. Surprisingly, these clouds can be unbound even when alpha_v < 2, and high mass clouds (10^4 - 10^6 M_solar) are generally unbound. This suggests that the traditional alpha_v is at best an approximate measure of boundedness in the ISM. All clouds have internal turbulent motions increasing with size as sigma ~ 1 km/s(R/ pc)^1/2, similar to observed relations. Bound structures comprise a small fraction of the total simulation mass, with star formation efficiency per free-fall time epsilon_ff ~ 0.4. For n_H,min = 10 - 100 cm^-3, epsilon_ff ~ 0.03 - 0.3, increasing with density. Temporal correlation analysis between SFR(t) and aggregate mass M(n_H,min;t) at varying n_H,min shows that time delays to star formation are t_delay ~ t_ff(n_H,min). Correlation between SFR(t) and M(nH,min;t) systematically tightens at higher n_H,min. Considering moderate-density gas, selecting against high virial parameter clouds improves correlation with SFR, consistent with previous work. Even at high n_H,min, the temporal dispersion in (SFR-epsilon_ff M/t_ff )/<SFR> is ~ 50%, due to the large-amplitude variations and inherent stochasticity of the system.
We present a method of adiabatically changing the local phase-space density of an ultracold gas, using a combination of magnetic and optical forces. Applying this method, we observe phase-space density increases in a gas of sodium atoms by as much as 50-fold. The transition to Bose-Einstein condensation was crossed reversibly, attaining condensate fractions of up to 30%. Measurements of the condensate fraction reveal its reduction due to interactions.
We present several bijections, in terms of combinatorial objects counted by the Schr\"oder numbers, that are then used (via coloring) for the construction and enumeration of rational Schr\"oder paths with integer slope, ordered rooted trees, and simple rooted outerplanar maps. On the other hand, we derive partial Bell polynomial identities for the little and large Schr\"oder numbers, which allow us to obtain explicit enumeration formulas.
We have investigated the growth by molecular-beam epitaxy of the II-VI diluted magnetic semiconductor (Zn,Mn)Se on As-passivated Si(100) substrates. The growth start has been optimized by using low-temperature epitaxy. Surface properties were assessed by Nomarski and scanning electron microscopy. Optical properties of (Zn,Mn)Se have been studied by photoluminescence and a giant Zeeman splitting of up to 30 meV has been observed. Our observations indicate a high crystalline quality of the epitaxial films.
In the spirit of general relativity, spacetime should become curved due to the presence of a particle of a given mass and charge, We try to understand this fact in the quantum theory of a thin shell of matter. It leads to a generalization of the potential energy of the shell in the semiclassical highest dominant order of Planck mass. Rather surprisingly, the quantization of charge is obtained as a consequence of the existence of bound states and the quantum of the squared bare electrical charge is $\hbar c/2$
In this paper, we carry out a comparative study of the efficacy of wavelets belonging to Daubechies and Coiflet family in achieving image segmentation through a fast statistical algorithm.The fact that wavelets belonging to Daubechies family optimally capture the polynomial trends and those of Coiflet family satisfy mini-max condition, makes this comparison interesting. In the context of the present algorithm, it is found that the performance of Coiflet wavelets is better, as compared to Daubechies wavelet.
We discuss in this Chapter a series of theoretical developments which motivate the introduction of a quantum evolution equation for which the eikonal approximation results in the geodesics of a four dimensional manifold. This geodesic motion can be put into correspondence with general relativity. One obtains in this way a quantum theory on a flat spacetime, obeying the rules of the standard quantum theory in Lorentz covariant form, with a spacetime dependent Lorentz tensor $g_{\mu\nu}$, somewhat analogous to a gauge field, coupling to the kinetic terms. Since the geodesics predicted by the eikonal approximation, with appropriate choice of $g_{\mu\nu}$, can be those of general relativity, this theory provides a quantum theory which could be underlying to classical gravitation, and coincides with it in this classical ray approximation. In order to understand the possible origin of the structure of this equation, we appeal to the approach of Nelson in constructing a Schroedinger equation from the properties of Brownian motion. Extending the notion of Browninan motion to spacetime in a covariant way, we show that such an equation follows from correlations between spacetime dimensions in the stochastic process.
We analyze pulse properties of Short gamma-ray bursts (GRBs) from a new catalog containing 434 pulses from 387 BATSE Time-Tagged Event (TTE) GRBs. Short GRB pulses exhibit correlated properties of duration, fluence, hardness, and amplitude, and they evolve hard-to-soft while undergoing similar triple-peaked light curves similar to those found in Long/Intermediate bursts. We classify pulse light curves using their temporal complexities, demonstrating that Short GRB pulses exhibit a range of complexities from smooth to highly variable. Most of the bright, hard, chaotic emission seen in complex pulses seems to represent a separate highly-variable emission component. Unlike Long/Intermediate bursts, as many as 90\% of Short GRBs are single-pulsed. However, emission in Short multi-pulsed bursts is coupled such that the first pulse's duration is a predictor of both the interpulse separation and subsequent pulse durations. These results strongly support the idea that external shocks produce the prompt emission seen in Short GRBs. The similarities between the triple-peaked structures and spectral evolution of Long, Short, and Intermediate GRBs then suggests that external shocks are responsible for the prompt emission observed in all GRB classes. In addition to these findings, we identify a new type of gamma-ray transient in which peak amplitudes occur at the end of the burst rather than at earlier times. Some of these "Crescendo" bursts are preceded by rapid-fire "Staccato" pulses, whereas the remaining are preceded by a variable episode that could be unresolved staccato pulses.
This paper tackles the problem of training a deep convolutional neural network with both low-precision weights and low-bitwidth activations. Optimizing a low-precision network is very challenging since the training process can easily get trapped in a poor local minima, which results in substantial accuracy loss. To mitigate this problem, we propose three simple-yet-effective approaches to improve the network training. First, we propose to use a two-stage optimization strategy to progressively find good local minima. Specifically, we propose to first optimize a net with quantized weights and then quantized activations. This is in contrast to the traditional methods which optimize them simultaneously. Second, following a similar spirit of the first method, we propose another progressive optimization approach which progressively decreases the bit-width from high-precision to low-precision during the course of training. Third, we adopt a novel learning scheme to jointly train a full-precision model alongside the low-precision one. By doing so, the full-precision model provides hints to guide the low-precision model training. Extensive experiments on various datasets ( i.e., CIFAR-100 and ImageNet) show the effectiveness of the proposed methods. To highlight, using our methods to train a 4-bit precision network leads to no performance decrease in comparison with its full-precision counterpart with standard network architectures ( i.e., AlexNet and ResNet-50).
We determine, to the first order in the radius of Anti-de-Sitter, the realisation of the $OSp(6,2|2)$ superconformal algebra on vector fields. We then calculate, to this order, the superspace metric describing the background of $AdS_7\times S^4$. The coordinates we work with are adapted to a 6+5 splitting of the eleven dimensional superspace. Finally, we deduce in a manifestly supersymmetric form the equations governing the dynamics of the fivebrane near the boundary of $AdS_7$.
Properties of magnon modes localized on a ferromagnetic skyrmion are studied. Three types of possible asymptotic behavior of the modes eigenfrequencies are found for the case of large skyrmion radius $R_s$, namely $\omega_0\sim R_s^{-2}$ for the breathing mode, $\omega_{-|\mu|}\sim R_s^{-1}$ and $\omega_{|\mu|}\sim R_s^{-3}$ for modes with negative and positive azimuthal quantum numbers, respectively. A number of properties of the magnon eigenfunctions are determined. This enables us to demonstrate that the skyrmion dynamics based on the traveling wave model is described by the massless Thiele equation.
This work is devoted to study the global existence of strong and classical solutions to compressible Navier-Stokes equations with or without density jump on the moving boundary for spherically symmetric motion. We establish a unified method to track the propagation of regularity of strong and classical solutions which works for the cases when density connects to vacuum continuously and with a jump simultaneously. The result we obtain is able to deal with both strong solutions with physical vacuum for which the sound speed is $1/2$-H\"older continuous across the boundary, and classical solutions with physical vacuum when $ 1 < \gamma < 3 $. In contrast to the previous results of global weak solutions, we track the regularity globally-in-time up to the symmetric center and the moving boundary. In particular, the free boundary can be traced.
This article lists all the solution of the Catalan equation $x^p-y^q=1$ for $x,y \in \mathbb{Z}[i]$, when one of the primes $p and q$ is even.
In this paper, we systematically apply Grothendieck duality theorem to simplify the proofs of several theorems in different papers: Including a vanishing theorem in KMM, a theorem of Koll\'{a}r's paper, a vanishing theorem due to Kov\'{a}cs and a theorem of Fujino. We remark that all of the above are achieved by the same trick.
The electric dipole moment of an electron (EDME) is investigated in the supersymmetric extra U(1) models. Neutralino sector is generally extended in these models and then the neutralino contribution will be important for the analysis of the EDME. Kinetic term mixings of abelian gauginos are taken into account in our analysis. Numerical results for the extra U(1) models show that the EDME can be affected by the extra U(1) in a certain range of soft supersymmetry breaking parameters even if the extra U(1) gauge boson is heavy. The EDME may be a clue to find an extended gauge structure in the supersymmetric models.
What is the expected infrared output of elliptical galaxies? Here we report the latest findings obtained in this high time resolution (~10 years) and high spatial resolution (2.5 parsec at center) study. We add a set of grain physics to the MACER code, including (a) dust grains made in passive stellar evolution; (b) dust grain growth due to collision and sticking; (c) grain destruction due to thermal sputtering; (d) dust cooling of hot gas via inelastic collisions; and (e) radiation pressure on dust grains. The code improvements enable us to analyze the effects of dust on metal depletion and AGN obscuration, and also to assess the infrared output of the modeled galaxies. We simulate a representative massive elliptical galaxy of a central stellar velocity dispersion ~ 260 km/s and modest rotation. We find that: (1) the circumnuclear disk (of a size <~ 1 kpc) is dusty in its outer region where most of the metals are in dust grains, while in the inner disk most of the dust grains are destroyed by the AGN irradiation; (2) the dusty disk is optically thick to both the starlight within the disk and the radiation from the central AGN. Thus the AGN will be obscured behind the disk, and the latter is of a covering factor ~ 0.2; (3) the dust infrared emission is mainly due to the AGN irradiation. The median infrared luminosity is ~ 2e44 erg/s, and it can reach >~ 1e46 erg/s during outbursts; (4) the duty cycles of the AGN activities, star formation, and the dust infrared luminosity roughly match observations, e.g., in most of its lifetime, the simulated galaxy is a stereotypical "quiescent" elliptical galaxy with L_{IR} ~ 1e11*L_{solar}, while the star formation rate can exceed 250 M_{solar}/yr during central outbursts.
We present a detailed elemental abundance study of 90 F and G dwarf, turn-off and subgiant stars in the Galactic bulge. Based on high-resolution spectra acquired during gravitational microlensing events, stellar ages and abundances for 11 elements (Na, Mg, Al, Si, Ca, Ti, Cr, Fe, Zn, Y and Ba) have been determined. We find that the Galactic bulge has a wide metallicity distribution with significant peaks at [Fe/H]=-1.09, -0.63, -0.20, +0.12, +0.41. We also find a high fraction of intermediate-age to young stars: at [Fe/H]>0 more than 35 % are younger than 8 Gyr. For [Fe/H]<-0.5 most stars are 10 Gyr or older. We have also identified several episodes when significant star formation in the bulge happened: 3, 6, 8, and 12 Gyr ago. We further find that the "knee" in the alpha-element abundance trends of the sub-solar metallicity bulge is located at about 0.1 dex higher [Fe/H] than in the local thick disk. The Galactic bulge has complex age and abundance properties that appear to be tightly connected to the main Galactic stellar populations. In particular, the peaks in the metallicity distribution, the star formation episodes, and the abundance trends, show similarities with the properties of the Galactic thin and thick disks. At the same time there are additional components not seen outside the bulge region, and that most likely can be associated with the Galactic bar. For instance, the star formation rate appears to have been slightly faster in the bulge than in the local thick disk, which most likely is an indication of the denser stellar environment closer to the Galactic centre. Our results strengthen the observational evidence that support the idea of a secular origin for the Galactic bulge, formed out of the other main Galactic stellar populations present in the central regions of our Galaxy.
Let $X$, $X_1$, $X_2$, $...$ be i.i.d. random variables, and let $S_n=X_1+... + X_n$ be the partial sums and $M_n=\max_{k\le n}|S_k|$ be the maximum partial sums. We give the sufficient and necessary conditions for a kind of limit theorems to hold on the convergence rate of the tail probabilities of both $S_n$ and $M_n$. These results are related to the law of the iterated logarithm. The results of Gut and Spataru (2000) are special cases of ours.
We consider the problem of determining Weierstrass gaps and pure Weierstrass gaps at several points. Using the notion of relative maximality in generalized Weierstrass semigroups due to Delgado \cite{D}, we present a description of these elements which generalizes the approach of Homma and Kim \cite{HK} given for pairs. Through this description, we study the gaps and pure gaps at several points on a certain family of curves with separated variables.
We present a novel method to learn temporally consistent 3D reconstruction of clothed people from a monocular video. Recent methods for 3D human reconstruction from monocular video using volumetric, implicit or parametric human shape models, produce per frame reconstructions giving temporally inconsistent output and limited performance when applied to video. In this paper, we introduce an approach to learn temporally consistent features for textured reconstruction of clothed 3D human sequences from monocular video by proposing two advances: a novel temporal consistency loss function; and hybrid representation learning for implicit 3D reconstruction from 2D images and coarse 3D geometry. The proposed advances improve the temporal consistency and accuracy of both the 3D reconstruction and texture prediction from a monocular video. Comprehensive comparative performance evaluation on images of people demonstrates that the proposed method significantly outperforms the state-of-the-art learning-based single image 3D human shape estimation approaches achieving significant improvement of reconstruction accuracy, completeness, quality and temporal consistency.