ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the low-temperature critical behavior of the one-dimensional Hubbard model near half filling caused by enhanced antiferromagnetic fluctuations. We use a mean-field-type approximation with a two-particle self-consistency renormalizing the bare interaction. It allows us to control a transition from high to low temperatures as well as from weak to strong-coupling. We show that there is a crossover temperature $T_{0}= t\exp\{-1/U\rho(0)\}$ for arbitrary interaction $U>0$ and the bare density of states at the Fermi energy $\rho(0)>0$. The solution at lower temperatures goes over to strong coupling and approaches a quantum critical point with the diverging staggered susceptibility and a gap in the excitation spectrum at zero temperature.
In dimension 2, we introduce a distributional Jacobian determinant $\det DV_\beta(Dv)$ for the nonlinear complex gradient $(x_1,x_2)\mapsto |Dv|^\beta(v_{x_1},-v_{x_2})$ for any $\beta>-1$, whenever $v\in W^{1,2 }_{\text{loc}}$ and $\beta |Dv|^{1+\beta}\in W^{1,2}_{\text{loc}}$. Then for any planar $\infty$-harmonic function $u$, we show that such distributional Jacobian determinant is a nonnegative Radon measure with some quantitative local lower and upper bounds. We also give the following two applications.   (i) Applying this result with $\beta=0$, we develop an approach to build up a Liouville theorem, which improves that of Savin [33]. Precisely, if $u$ is $\infty$-harmonic functions in whole ${\mathbb R}^2$ with $$ \liminf_{R\to\infty}\inf_{c\in\mathbb R}\frac1 {R^3}\int_{B(0,R)}|u(x)-c|\,dx<\infty,$$ then $u=b+a\cdot x$ for some $b\in{\mathbb R}$ and $a\in{\mathbb R}^2$.   (ii) Denoting by $u_p$ the $p$-harmonic function having the same nonconstant boundary condition as $u$, we show that $\det DV_\beta(Du_p) \to \det DV_\beta(Du)$ as $p\to\infty$ in the weak-$\star$ sense in the space of Radon measure. Recall that $V_\beta(Du_p)$ is always quasiregular mappings, but $V_\beta(Du)$ is not in general.
(Abridged) We present a detailed study of the host galaxy of GRB 011121 (at z = 0.36) based on high-resolution imaging in 5 broad-band, optical and near-infrared filters with HST and VLT/ISAAC. The surface brightness profile of this galaxy is best fitted by a Sersic law with index ~ 2 - 2.5 and a rather large effective radius (~ 7.5 kpc). Both the morphological analysis and the F450W - F702W colour image suggest that the host galaxy of GRB 011121 is either a disk-system with a rather small bulge, or one hosting a central, dust-enshrouded starburst. Hence, we modeled the integrated spectral energy distribution of this galaxy by combining stellar population and radiative transfer models, assuming properties representative of nearby starburst or normal star-forming, Sbc-like galaxies. A range of plausible fitting solutions indicates that the host galaxy of GRB 011121 has a stellar mass of 3.1 - 6.9 x10^9 Msun, stellar populations with a maximum age ranging from 0.4 to 2 Gyr, and a metallicity ranging from 1 to 29 per cent of the solar value. Starburst models suggest this galaxy to be nearly as opaque as local starbursts (with an A_V = 0.27 - 0.76 mag). Alternatively, normal star-forming Sbc-like models suggest a high central opacity whereas A_V = 0.12$ -- 0.57 mag along the line of sight. For this subluminous galaxy (with L_B/Lstar_B = 0.26), we determine a model-dependent SFR of 2.4 - 9.4 Msun/yr. The SFR per unit luminosity (9.2 - 36.1 Msun/yr/(L_B/Lstar_B)) is high compared to those of most GRB host galaxies, but consistent with those of most of the hosts at similar low redshift. Our results suggest that the host galaxy of GRB 011121 is a rather large disk-system in a relatively early phase of its star formation history.
One of the main problems in any quantum resource theory is the characterization of the conversions between resources by means of the free operations of the theory. In this work, we advance on this characterization within the quantum coherence resource theory by introducing the generalized coherence vector of an arbitrary quantum state. The generalized coherence vector is a probability vector that can be interpreted as a concave roof extension of the pure states coherence vector. We show that it completely characterizes the notions of being incoherent, as well as being maximally coherent. Moreover, using this notion and the majorization relation, we obtain a necessary condition for the conversion of general quantum states by means of incoherent operations. These results generalize the necessary conditions of conversions for pure states given in the literature, and show that the tools of the majorization lattice are useful also in the general case. Finally, we introduce a family of coherence quantifiers by considering concave and symmetric functions applied to the generalized coherence vector. We compare this proposal with the convex roof measure of coherence and others quantifiers given in the literature.
Symmetry energy coefficients of asymmetric nuclear matter are investigated as the inverse of nuclear matter polarizabilities with two different approaches. Firstly a general calculation shows they may depend on the neutron-proton asymmetry itself. The choice of particular prescriptions for the density fluctuations lead to certain isospin (n-p asymmetry) dependences of the polarizabilities. Secondly, with Skyrme type interactions, the static limit of the dynamical polarizability is investigated corresponding to the inverse symmetry energy coefficient which assumes different values at different asymmetries (and densities and temperatures). The symmetry energy coefficient (in the isovector channel) is found to increase as n-p asymmetries increase. The spin symmetry energy coefficient is also briefly investigated.
The Born approximation, based on $\bar\alpha \equiv\alpha (m_Z)$ instead of $\alpha$, reproduces all electroweak precision measurements within their $(1\sigma)$ accuracy. The low upper limits for the genuinely electroweak corrections constitute one of the major achievements of LEP. The astonishing smallness of these corrections results from the cancellation of a large positive contribution from the heavy top quark and large negative contributions from all other virtual particles. It is precisely the non-observation of electroweak radiative corrections that places stringent upper and lower limits on the top mass.
The affine Gaussian derivative model can in several respects be regarded as a canonical model for receptive fields over a spatial image domain: (i) it can be derived by necessity from scale-space axioms that reflect structural properties of the world, (ii) it constitutes an excellent model for the receptive fields of simple cells in the primary visual cortex and (iii) it is covariant under affine image deformations, which enables more accurate modelling of image measurements under the local image deformations caused by the perspective mapping, compared to the more commonly used Gaussian derivative model based on derivatives of the rotationally symmetric Gaussian kernel.   This paper presents a theory for discretizing the affine Gaussian scale-space concept underlying the affine Gaussian derivative model, so that scale-space properties hold also for the discrete implementation.   Two ways of discretizing spatial smoothing with affine Gaussian kernels are presented: (i) by solving semi-discretized affine diffusion equation, which has derived by necessity from the requirements of a semi-group structure over scale as parameterized by a family of spatial covariance matrices and obeying non-creation of new structures from any finer to any coarser scale in terms of non-enhancement of local extrema and (ii) approximating these semi-discrete affine receptive fields by parameterized families of 3x3-kernels as obtained from an additional discretization along the scale direction. The latter discrete approach can be optionally complemented by spatial subsampling at coarser scales, leading to the notion of affine hybrid pyramids.   Using these theoretical results, we outline hybrid architectures for discrete approximations of affine covariant receptive field families, to be used as a first processing layer for affine covariant and affine invariant visual operations at higher levels.
In a series of four papers we determine structures whose existence is dual, in the sense of complementary, to the existence of stars or combs. In the first paper of our series we determined structures that are complementary to arbitrary stars or combs. Stars and combs can be combined, positively as well as negatively. In the second and third paper of our series we provided duality theorems for all but one of the possible combinations.   In this fourth and final paper of our series, we complete our solution to the problem of finding complementary structures for stars, combs, and their combinations, by presenting duality theorems for the missing piece: for undominating stars. Our duality theorems are phrased in terms of end-compactified subgraphs, tree-decompositions and tangle-distinguishing separators.
Data assimilation techniques, developed in the last two decades mainly for weather prediction, produce better forecasts by taking advantage of both theoretical/numerical models and real-time observations. In this paper, we explore the possibility of applying the data-assimilation techniques known as 4D-VAR to the prediction of solar flares. We do so in the context of a continuous version of the classical cellular-automaton-based self-organized critical avalanche models of solar flares introduced by Lu and Hamilton (Astrophys. J., 380, L89, 1991). Such models, although a priori far removed from the physics of magnetic reconnection and magneto-hydrodynamical evolution of coronal structures, nonetheless reproduce quite well the observed statistical distribution of flare characteristics. We report here on a large set of data assimilation runs on synthetic energy release time series. Our results indicate that, despite the unpredictable (and unobservable) stochastic nature of the driving/triggering mechanism within the avalanche model, 4D-VAR succeeds in producing optimal initial conditions that reproduce adequately the time series of energy released by avalanches/flares. This is an essential first step towards forecasting real flares.
Deep ConvNets have shown its good performance in image classification tasks. However it still remains as a problem in deep video representation for action recognition. The problem comes from two aspects: on one hand, current video ConvNets are relatively shallow compared with image ConvNets, which limits its capability of capturing the complex video action information; on the other hand, temporal information of videos is not properly utilized to pool and encode the video sequences. Towards these issues, in this paper, we utilize two state-of-the-art ConvNets, i.e., the very deep spatial net (VGGNet) and the temporal net from Two-Stream ConvNets, for action representation. The convolutional layers and the proposed new layer, called frame-diff layer, are extracted and pooled with two temporal pooling strategy: Trajectory pooling and line pooling. The pooled local descriptors are then encoded with VLAD to form the video representations. In order to verify the effectiveness of the proposed framework, we conduct experiments on UCF101 and HMDB51 datasets. It achieves the accuracy of 93.78\% on UCF101 which is the state-of-the-art and the accuracy of 65.62\% on HMDB51 which is comparable to the state-of-the-art.
The principle purpose of this work is to investigate a "viscous" version of a "simple" but still realistic bi-fluid model described in [Bresch, Desjardin, Ghidaglia, Grenier, Hillairet] whose "non-viscous" version is derived from physical considerations in \cite[Ishii, Hibiki]{ISHI} as a particular sample of a multifluid model with algebraic closure. The goal is to show existence of weak solutions for large initial data on an arbitrarily large time interval. We achieve this goal by transforming the model to an academic system which resembles to the compressible Navier-Stokes equations, with however two continuity equations and a momentum equation endowed with pressure of complicated structure dependent on two variable densities. The new "academic system" is then solved by an adaptation of the Lions--Feireisl approach for solving compressible Navier--Stokes equation, completed with several observations related to the DiPerna--Lions transport theory inspired by [Maltese, Michalek, Mucha, Novotny, Pokorny, Zatorska] and [Vasseur, Wen, Yu]. We also explain how these techniques can be generalized to a model of mixtures with more then two species.   This is the first result on the existence of weak solutions for any realistic multifluid system.
The baryonic acoustic peak in the correlation function of galaxies and galaxy clusters provides a standard ruler to probe the space-time geometry of the Universe, jointly constraining the angular diameter distance and the Hubble expansion rate. Moreover, non-linear effects can systematically shift the peak position, giving us the opportunity to exploit this clustering feature also as a dynamical probe. We investigate the possibility of detecting interactions in the dark sector through an accurate determination of the baryonic acoustic scale. Making use of the public halo catalogues extracted from the CoDECS simulations -- the largest suite of N-body simulations of interacting dark energy models to date -- we determine the position of the baryonic scale fitting a band-filtered correlation function, specifically designed to amplify the signal at the sound horizon. We analyze the shifts due to non-linear dynamics, redshift-space distortions and Gaussian redshift errors, in the range 0 < z < 2. Since the coupling between dark energy and dark matter affects in a particular way the clustering properties of haloes and, specifically, the amplitude and location of the baryonic acoustic oscillations, the cosmic evolution of the baryonic peak position might provide a direct way to discriminate interacting dark energy models from the standard \Lambda CDM framework. To maximize the efficiency of the baryonic peak as a dynamic probe, the correlation function has to be measured in redshift-space, where the baryonic acoustic shift due to non-linearities is amplified. The typical redshift errors of spectroscopic galaxy surveys do not significantly impact these results.
We prove the q-aspect analogue of Heath-Brown's result on the twelfth power moment of the Riemann zeta function for Dirichlet L-functions to odd prime power moduli. Our results rely on the p-adic method of stationary phase for sums of products and complement Nunes' bound for smooth square-free moduli.
We show that every monic polynomial of degree three with complex coefficients and no repeated roots is either a (vertical and horizontal) translation of $y=x^3$ or can be composed with a linear function to obtain a Ramanujan cubic. As a result, we gain some new insights into the roots of cubic polynomials.
We study the zero-temperature Ising chain evolving according to the Swendsen-Wang dynamics. We determine analytically the domain length distribution and various ``historical'' characteristics, e.g., the density of unreacted domains is shown to scale with the average domain length as <l>^{-d} with d=3/2 (for the q-state Potts model, d=1+1/q). We also compute the domain length distribution for the Ising chain endowed with the zero-temperature Wolff dynamics.
We show that a system consisting of two interacting particles with mass ratio $3$ or $1/3$ in a hard-wall box can be exactly solved by using Bethe-type ansatz. The ansatz is based on a finite superposition of plane waves associated with a dihedral group $D_{6}$, which enforces the momentums after a series of scattering and reflection processes to fulfill the $D_{6}$ symmetry. Starting from a two-body elastic collision model in a hard-wall box, we demonstrate how a finite momentum distribution is related to the $D_{2n}$ symmetry for permitted mass ratios. For a quantum system with mass ratio $3$, we obtain exact eigenenergies and eigenstates by solving Bethe-type-ansatz equations for arbitrary interaction strength. A many-body excited state of the system is found to be independent of the interaction strength, i.e. the wave function looks exactly the same for non-interacting two particles or in the hard-core limit.
Biconformal supergravity models provide a new gauging of the superconformal group relevant to the Maldacena conjecture. Using the group quotient method to biconformally gauge SU(2,2|N), we generate a 16-dim superspace. We write the most general even- and odd-parity actions linear in the curvatures, the bosonic sector of which is known to descend to general relativity on a 4-dim manifold.
We propose two conjectures on a moduli theoretic approach to constructing Lagrangian subvarieties of hyperk\"ahler varieties arising from the Kuznetsov components of cubic fourfolds or Gushel--Mukai fourfolds. Then we verify the conjectures in several cases, recovering classical examples. As a corollary, we confirm a conjecture of O'Grady in several instances on the existence of Lagrangian covering families for hyperk\"ahler varieties.
We present an improved Minimal Variance (MV) method for using a radial peculiar velocity sample to estimate the average of the three-dimensional velocity field over a spherical volume, which leads to an easily interpretable bulk flow measurement. The only assumption required is that the velocity field is irrotational. The resulting bulk flow estimate is particularly insensitive to smaller scale flows. We also introduce a new constraint into the MV method that ensures that bulk flow estimates are independent of the value of the Hubble constant $H_o$; this is important given the tension between the locally measured $H_o$ and that obtained from the cosmic background radiation observations. We apply our method to the \textit{CosmicFlows-3} catalogue and find that, while the bulk flows for shallower spheres are consistent with the standard cosmological model, there is some tension between the bulk flow in a spherical volume with radius $150$\hmpc\ and its expectations; we find only a $\sim 2\%$ chance of obtaining a bulk flow as large or larger in the standard cosmological model with \textit{Planck} parameters
Within Takahashi's spin-wave theory we study finite size and temperature effects near the quantum critical point in the $J_{1}-J_{2}$ Heisenberg antiferromagnet defined on a strip ($L\times\infty$). In the continuum limit, the theory predicts universal finite size and temperature corrections and describes the dimensional crossover in magnetic properties from 2+1 to 1+1 space-time dimensions.
In this paper we present a connection between the results obtained from a semiclassical study of a relativistic, two-body system, and the leptons masses. Some possible consequences are also discussed.
The Type II Superstring amplitude to 1-loop order is given by an integral of $\vartheta$-functions over the moduli space of tori, which diverges for real momenta. We construct the analytic continuation which renders this amplitude well defined and finite, and we find the expected poles and cuts in the complex momentum plane.
Let $H$ and $G$ be graphs on $n$ vertices, where $n$ is sufficiently large. We prove that if $H$ has Ore-degree at most 5 and $G$ has minimum degree at least $2n/3$ then $H\subset G.$
Studies of disks around young brown dwarfs are of paramount importance to our understanding of the origin, diversity and early evolution of sub-stellar objects. Here we present first results from a systematic search for disk emission in a spectroscopically confirmed sample of young objects near or below the sub-stellar boundary in a variety of star-forming regions. Our VLT and Keck L'-band observations of the sigma Orionis and TW Hydrae associations suggest that if a majority of brown dwarfs are born with disks, at least the inner regions of those disks evolve rapidly, possibly clearing out within a few million years.
The goal of this PhD thesis is to study a diophantine approximation problem stated by Schmidt in 1967. The problem aim to study the approximation of a subspace of $\mathbb{R}^n$ by rational subspaces, not necessarily of the same dimension, by determining the exponents of approximation associated to the various angles between the subspaces.
We have derived equations for nonadiabatic Ehrenfest molecular dynamics which conserve the total energy in the case of time-dependent discretization for electrons. A discretization is time-dependent in all cases where it or part of it depends on the positions of the nuclei, for example, in atomic orbital basis sets, and in the projector augmented-wave (PAW) method, where the augmentation functions depend on the nuclear positions. We have derived, implemented, and analyzed the energy conserving equations and their most common approximations for a 1D test system where we can achieve numerical results converged to a high accuracy. Based on the observations in 1D, we implement and analyze the Ehrenfest molecular dynamics in 3D using the PAW method and the time-dependent density functional formalism. We demonstrate the applicability of our method by carrying out calculations for small and medium sized molecules in both the adiabatic and the nonadiabatic regime.
We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth, and prove a rigorous reduction of these equations to Birkhoff normal form up to degree four. This proves a conjecture of Zakharov-Dyachenko [55] suggested by the formal Birkhoff integrability of the water waves Hamiltonian truncated at order four. As a consequence, we also obtain a long-time stability result: periodic perturbations of a flat interface that are of size $\varepsilon$ in a sufficiently smooth Sobolev space lead to solutions that remain regular and small up to times of order $\varepsilon^{-3}$. This time scale is expected to be optimal. Main difficulties in the proof are the presence of non-trivial resonant four-waves interactions, the so-called Benjamin-Feir resonances, the small divisors arising from near-resonances and the quasilinear nature of the equations. Some of the main ingredients that we use are: (1) a reduction procedure to constant coefficient operators up to smoothing remainders, that, together with the verification of key algebraic cancellations of the system, implies the integrability of the equations at non-negative orders; (2) a Poincar\'e-Birkhoff normal form of the smoothing remainders that deals with near-resonances; (3) an a priori algebraic identification argument of the above Poincar\'e- Birkhoff normal form equations with the formal Hamiltonian computations of [55, 19, 27, 17], that allows us to handle the Benjamin-Feir resonances.