ShantanuT01/DACTYL-Pretraining huggingface dataset:
We propose and apply the finite-element discrete variable representation to express the nonequilibrium Green's function for strongly inhomogeneous quantum systems. This method is highly favorable against a general basis approach with regard to numerical complexity, memory resources, and computation time. Its flexibility also allows for an accurate representation of spatially extended hamiltonians, and thus opens the way towards a direct solution of the two-time Schwinger/Keldysh/Kadanoff-Baym equations on spatial grids, including e.g. the description of highly excited states in atoms. As first benchmarks, we compute and characterize, in Hartree-Fock and second Born approximation, the ground states of the He atom, the H$_2$ molecule and the LiH molecule in one spatial dimension. Thereby, the ground-state/binding energies, densities and bond-lengths are compared with the direct solution of the time-dependent Schr\"odinger equation.
Let X be a Fano variety of dimension n, pseudoindex i_X and Picard number \rho_X. A generalization of a conjecture of Mukai says that \rho_X(i_X-1)\le n. We prove that the conjecture holds if: a) X has pseudoindex i_X \ge \frac{n+3}{3} and either has a fiber type extremal contraction or does not have small extremal contractions b) X has dimension five.
We present an analysis of over 150 ks of data on the planetary nebula WeBo 1 (PN G135.6+01.0) obtained with the Swift Ultraviolet Optical Telescope (UVOT). The central object of this nebula has previously been described as a late-type K giant barium star with a possible hot companion, most likely a young pre-white dwarf. UVOT photometry shows that while the optical photometry is consistent with a large cool object, the near-ultraviolet (UV) photometry shows far more UV flux than could be produced by any late-type object. Using model stellar atmospheres and a comparison to UVOT photometry for the pre-white dwarf PG 1159-035, we find that the companion has a temperature of at least 40,000 K and a radius of, at most, 0.056 R_sun. While the temperature and radius are consistent with a hot compact stellar remnant, they are lower and larger, respectively, than expected for a typical young pre-white dwarf. This likely indicates a deficiency in the assumed UV extinction curve. We find that higher temperatures more consistent with expectations for a pre-white dwarf can be derived if the foreground dust has a strong "blue bump" at 2175 AA and a lower R_V. Our results demonstrate the ability of Swift to both uncover and characterize hot hidden companion stars and to constrain the UV extinction properties of foreground dust based solely on UVOT photometry.
We generalise to signed graphs a classical result of Tutte [Canad. J. Math. 8 (1956), 13--28] stating that every integer flow can be expressed as a sum of characteristic flows of circuits. In our generalisation, the r\^ole of circuits is taken over by signed circuits of a signed graph which occur in two types -- either balanced circuits or pairs of disjoint unbalanced circuits connected with a path intersecting them only at its ends. As an application of this result we show that a signed graph $G$ admitting a nowhere-zero $k$-flow has a covering with signed circuits of total length at most $2(k-1)|E(G)|$.
In two-dimensional systems, it is possible transmute bosons into fermions by use of a Chern-Simons gauge field. Such a mapping is used to compute magnetization processes of two-dimensional magnets. The calculation of the magnetization curve then involves the structure of the Hofstadter problem for the lattice under consideration. Certain features of the Hofstadter butterfly are shown to imply the appearance of magnetization plateaus. While not always successfull, this approach leads to interesting results when applied to the 2D AF magnet SrCu2(BO3)2.
We present a study of the effect of an electric field on the binding energy of a shallow hydrogenic impurity in GaAs/Ga_{1-x}Al_{x}As quantum well wires. The wire is considered to be of length L and radius R and the electric field F is applied along the z-axis, the axis of the wire.
Nonlinear perturbations of Friedmann-Lemaitre cosmologies with dust and a positive cosmological constant have recently attracted considerable attention. In this paper our first goal is to compare the evolution of the first and second order perturbations by determining their asymptotic behaviour at late times in ever-expanding models. We show that in the presence of spatial curvature K or a positive cosmological constant, the density perturbation approaches a finite limit both to first and second order, but the rate of approach depends on the model, being power law in the scale factor if the cosmological constant is positive but logarithmic if it is zero and and K<0. Scalar perturbations in general contain a growing and a decaying mode. We find, somewhat surprisingly, that if the cosmological constant is positive the decaying mode does not die away, i.e. it contributes on an equal footing as the growing mode to the asymptotic expression for the density perturbation. On the other hand, the future asymptotic regime of the Einstein-de Sitter universe (for which the cosmological constant and the spatial curvature are both zero) is completely different, as exemplified by the density perturbation which diverges; moreover, the second order perturbation diverges faster than the first order perturbation, which suggests that the Einstein-de Sitter universe is unstable to perturbations, and that the perturbation series do not converge towards the future. We conclude that the presence of spatial curvature or a cosmological constant stabilizes the perturbations. Our second goal is to derive an explicit expression for the second order density perturbation that can be used to study the effects of including a cosmological constant and spatial curvature.
The "nonlinear complex heat equation" $A_t=i|A|^2A+A_{xx}$ was introduced by P. Coullet and L. Kramer as a model equation exhibiting travelling fronts induced by non-variational effects, called "retracting fronts". In this paper we study the existence of such fronts. They go by one-parameter families, bounded at one end by the slowest and "steepest" front among the family, a situation presenting striking analogies with front propagation into unstable states.
We report a comprehensive catalog of emission episodes within long gamma-ray bursts (GRBs) that are separated by a quiescent period during which gamma-ray emission falls below the background level. We use a fully automated identification method for an unbiased, large scale and expandable search. We examine a comprehensive sample of long GRBs from the BATSE, Swift and Fermi missions, assembling a total searched set of 2710 GRBs, the largest catalog of isolated emission episodes so far. Our search extends out to [-1000s,750s] around the burst trigger, expanding the covered time interval beyond previous studies and far beyond the nominal durations (T90) of most bursts. We compare our results to previous works by identifying pre-peak emission (or precursors), defined as isolated emission periods prior to the episode with the highest peak luminosity of the burst. We also systematically search for similarly defined periods after the burst's peak emission. We find that the pre-peak and post-peak emission periods are statistically similar, possibly indicating a common origin. For the analyzed GRBs, we identify 24% to have more than one isolated emission episode, with 11% having at least one pre-peak event and 15% having at least one post-peak event. We identify GRB activity significantly beyond their T90, which can be important for understanding the central engine activity as well as, e.g., gravitational-wave searches.
Motivated by applications in noncommutative geometry we prove several value range estimates for even convergents and tails, and odd reverse sequences of Stieltjes type continued fractions with bounded ratio of consecutive elements, and show how those estimates control growth of solutions of a system of discrete Dirac equations.
We have carried out \textit{ab-initio} calculations of local structure of Mn and Ni in Mn$_{2}$Ni$_{1.5}$In$_{0.5}$ alloy with different site occupancies in order to understand the similarities in martensitic and magnetic properties of Mn$_{2}$Ni$_{1+x}$In$_{1-x}$ and Ni$_2$Mn$_{1+x}$In$_{1-x}$ alloys. Our results show that in Mn$_{2}$Ni$_{1+x}$In$_{1-x}$ alloys there is a strong possibility of Mn atoms occupying all the three, X, Y and Z sites of X$_2$YZ Heusler structure while Ni atoms preferentially occupy the X sites. Such a site occupancy disorder of Mn atoms is in addition to a local structural disorder due to size differences between Mn and In atoms which is also present in Ni$_2$Mn$_{1+x}$In$_{1-x}$ alloys. Further, a comparison of the calculations with experimental XAFS at the Mn and Ni K edges in Mn$_{2-y}$Ni$_{1.6+y}$In$_{0.4}$ ($-0.08 \le y \le 0.08$) indicate a strong connection between martensitic transformation and occupancy of Z sites by Mn atoms.
We calculate the first and second moments of L-functions in the family of quadratic twists of a fixed elliptic curve E over F_q[x], asymptotically in the limit as the degree of the twists tends to infinity. We also compute moments involving derivatives of L-functions over quadratic twists, enabling us to deduce lower bounds on the correlations between the analytic ranks of the twists of two distinct curves.
After a brief review of population synthesis of close-by cooling neutron stars, I focus on the interpretation of dichotomy of spin periods of near-by coolers. The existence of two well separated groups -- short period ($\sim$0.1-0.3 s) radio pulsars and long period ($\sim$3-10 s) radio quiet sources, aka the Magnificent seven, -- can not be easily explained in unified models developed recently (Popov et al. 2010, Gull{\'o}n et al. 2014). I speculate that the most natural solution of the problem can be in bimodal initial magnetic field distribution related to the existence of an additional mechanism of field generation in magnetars.
Macroscopic loop correlators are investigated in the hermitian one matrix model with the potential perturbed by the higher order curvature term. In the phase of smooth surfaces the model is equivalent to the minimal conformal matter coupled to gravity. The properties of the model in the intermediate phase are similar to that of the discretized bosonic string with the central charge $C > 1.$ Loop correlators describe the effect of the splitting of the random surfaces. It is shown, that the properties of the surfaces are changed in the intermediate phase because the perturbation modifies the spectrum of the scaling operators.
In \cite{davis19}, the author constructed an elliptic version of the Grothendieck-Springer resolution for the stack $\mathrm{Bun}_G$ of principal bundles under a simply connected simple group $G$ on an elliptic curve $E$. This is a simultaneous log resolution of a map from $\mathrm{Bun}_G$ to the union of the coarse moduli space of semistable $G$-bundles and a single stacky point. In this paper, we study singularities, resolutions and deformations coming from subregular slices of this elliptic Grothendieck-Springer resolution. More precisely, we construct explicit slices of $\mathrm{Bun}_G$ through all subregular unstable bundles, for every $G$. For $G \neq SL_2$, we describe the pullbacks of the elliptic Grothendieck-Springer resolution to these slices as concrete varieties, extending and refining earlier work of I. Grojnowski and N. Shepherd-Barron, who related these varieties to del Pezzo surfaces in type $E$. We use the resolutions to identify the singularities of the unstable locus of the subregular slices, and prove that that the extended coarse moduli space map gives deformations that are miniversal among torus-equivariant deformations with appropriate weights.
Consider an urn initially containing $b$ black and $w$ white balls. Select a ball at random and observe its color. If it is black, stop. Otherwise, return the white ball together with another white ball to the urn. Continue selecting at random, each time adding a white ball, until a black ball is selected. Let $T_{b,w}$ denote the number of draws until this happens. Surprisingly, the expectation of $T_{b,w}$ is infinite for the "fair" initial scenario $b =w=1$, but finite if $b=2$ and $w=10^9$. In fact, $\mathbb{E}[T_{b,w}]$ is finite if and only if $b\ge 2$, and the variance of $T_{b,w}$ is finite if and only if $b \ge 3$, regardless of the number $w$ of white balls. These observations extend to higher moments.
We study the thermodynamics of an exact hairy black hole solution in Anti-deSitter (AdS) spacetime. We use the counterterm method supplemented with boundary terms for the scalar field to obtain the thermodynamic quantities and stress tensor of the dual field theory. We then extend our analysis by considering a dynamical cosmological constant and verify the isoperimetric inequality. Unlike the thermodynamics of Reissner-N\"{o}rdstrom (RN) black hole in this `extended' framework, the presence of the scalar field and its self-interaction make also the criticality possible in the grand canonical ensemble. In the canonical ensemble, we prove that, in fact, there exist two critical points. Finally we comment on a different possible interpretation that is more natural in the context of string theory.
Using RXTE observations, we investigate the evolution of inner disk radius R_in of Cir X-1 during two cycles and find obvious orbital modulation. We argue that the modulation is attributed to its high orbital eccentricity. The disk luminosity is inversely with the inner disk temperature kT_in, which is ascribed to the slow increase of kT_in and, however, the rapid decrease of R_in during the passage for the neutron star to depart from the companion star.
When an emitting spherical shell with a constant Lorentz factor turns off emission abruptly at some radius, its high-latitude emission would obey the relation of $\hat{\alpha}$ (the temporal index) = $2 + \hat{\beta}$ (the spectral index). However, this relation is violated by the X-ray fares in some gamma-ray bursts (GRBs), whose $\hat{\alpha}$ is much more steeper. We show that the synchrotron radiation should be anisotropic when the angular distribution of accelerated electrons has preferable orientation, and this anisotropy would naturally lead to the steeper decay for the high-latitude emission if the the intrinsic emission is limb-brightened. We use our simple toy model to reproduce the temporal and the spectral evolution of the X-ray flares. We show that our model can well interpret the steep decay of the X-ray flares in the three GRBs selected as example. Recent simulations on particle acceleration may support the specific anisotropic distribution of the electrons adopted in our work. Reversely, confirmation of the anisotropy in the radiation would give meaningful clues to the details of electron acceleration in the emitting region.
A $k\ell$-subset partition, or $(k,\ell)$-subpartition, is a $k\ell$-subset of an $n$-set that is partitioned into $\ell$ distinct classes, each of size $k$. Two $(k,\ell)$-subpartitions are said to $t$-intersect if they have at least $t$ classes in common. In this paper, we prove an Erd\H{o}s-Ko-Rado theorem for intersecting families of $(k,\ell)$-subpartitions. We show that for $n \geq k\ell$, $\ell \geq 2$ and $k \geq 3$, the largest $1$-intersecting family contains at most $\frac{1}{(\ell-1)!}\binom{n-k}{k}\binom{n-2k}{k}\cdots\binom{n-(\ell-1)k}{k}$ $(k,\ell)$-subpartitions, and that this bound is only attained by the family of $(k,\ell)$-subpartitions with a common fixed class, known as the \emph{canonical intersecting family of $(k,\ell)$-subpartitions}. Further, provided that $n$ is sufficiently large relative to $k,\ell$ and $t$, the largest $t$-intersecting family is the family of $(k,\ell)$-subpartitions that contain a common set of $t$ fixed classes.
Faraday tomography of polarimetric observations at low frequency is a unique tool to study the structure of the magneto-ionic interstellar medium (ISM) based on Faraday depth. LOFAR data below 200 MHz revealed a plethora of features in polarization, whose origin remains unknown. Previous studies highlighted the remarkable association of such features to tracers of the magnetized-neutral ISM, as interstellar dust and atomic hydrogen (HI). However, the physical conditions responsible for the correlation between magneto-ionic and neutral media are yet to be clarified. In this letter we investigate further the correlation between LOFAR data and HI observations at 21cm from the Effelsberg-Bonn HI Survey (EBHIS). We focus on the multiphase properties of the HI gas. We present the first statistical study on the morphological correlation between LOFAR tomographic data and the cold (CNM), luke-warm (LNM), and warm (WNM) HI phases, separately. We use the Regularized Optimization for Hyper-Spectral Analysis (ROHSA) approach to decompose the HI phases based on the Gaussian decomposition of the HI spectra. In at least two fields of view -- Fields 3C196 and A -- out of four -- Fields B and C -- we find a significant correlation between LOFAR and EBHIS data using the Histograms of Oriented Gradients (HOG). The absence of correlation in Fields B and C is caused by low signal-to-noise ratio in polarization. The observed HOG correlation in Fields 3C196 and A is associated with all HI phases and it is surprisingly dominant in the CNM and LNM phases. We discuss possible mechanisms that would explain the correlation between CNM, LNM, and WNM, with polarized emission at Faraday depths up to 10 rad m$^{-2}$. Our results show how the complex structure of the ionic medium seen by LOFAR data is tightly related to phase transition in the diffuse and magnetized neutral ISM traced by HI spectroscopic data.
The Monge-Kantorovich transportation problem involves optimizing with respect to a given a cost function. Uniqueness is a fundamental open question about which little is known when the cost function is smooth and the landscapes containing the goods to be transported possess (non-trivial) topology. This question turns out to be closely linked to a delicate problem (# 111) of Birkhoff [14]: give a necessary and sufficient condition on the support of a joint probability to guarantee extremality among all measures which share its marginals. Fifty years of progress on Birkhoff's question culminate in Hestir and Williams' necessary condition which is nearly sufficient for extremality; we relax their subtle measurability hypotheses separating necessity from sufficiency slightly, yet demonstrate by example that to be sufficient certainly requires some measurability. Their condition amounts to the vanishing of the measure \gamma outside a countable alternating sequence of graphs and antigraphs in which no two graphs (or two antigraphs) have domains that overlap, and where the domain of each graph / antigraph in the sequence contains the range of the succeeding antigraph (respectively, graph). Such sequences are called numbered limb systems. We then explain how this characterization can be used to resolve the uniqueness of Kantorovich solutions for optimal transportation on a manifold with the topology of the sphere.
We have investigated the volume collapse occurring in LaMnO3 unit cell using the anisotropic Potts model modified by two types of anisotropic interactions which has been used to study the change of Mn-O bonds lengths as function of temperature. The bond lengths are related to the occupation of the orbits. The lattice parameters and the distortion modes have been investigated as well. We have shown that the collapse is due to the change of Mn-O bonds lengths change as the temperature is raised through the transition. It has been shown that all the parameters studied here decrease with increasing temperature in a narrow temperature range below TJT, and then undergoes a collapse at TJT. These results are in a good agreement with the published experimental results.
Effect of a complicated many-body environment is analyzed on the electron random scattering by a 2D mesoscopic open ballistic structure. A new mechanism of decoherence is proposed. The temperature of the environment is supposed to be zero whereas the energy of the incoming particle $E_{in}$ can be close to or somewhat above the Fermi surface in the environment. The single-particle doorway resonance states excited in the structure via external channels are damped not only because of escape through such channels but also due to the ulterior population of the long-lived environmental states. Transmission of an electron with a given incoming $E_{in}$ through the structure turns out to be an incoherent sum of the flow formed by the interfering damped doorway resonances and the retarded flow of the particles re-emitted into the structure by the environment. Though the number of the particles is conserved in each individual event of transmission, there exists a probability that some part of the electron's energy can be absorbed due to environmental many-body effects. In such a case the electron can disappear from the resonance energy interval and elude observation at the fixed transmission energy $E_{in}$ thus resulting in seeming loss of particles, violation of the time reversal symmetry and, as a consequence, suppression of the weak localization. The both decoherence and absorption phenomena are treated within the framework of a unit microscopic model based on the general theory of the resonance scattering. All the effects discussed are controlled by the only parameter: the spreading width of the doorway resonances, that uniquely determines the decoherence rate
We motivate and address a human-in-the-loop variant of the monocular viewpoint estimation task in which the location and class of one semantic object keypoint is available at test time. In order to leverage the keypoint information, we devise a Convolutional Neural Network called Click-Here CNN (CH-CNN) that integrates the keypoint information with activations from the layers that process the image. It transforms the keypoint information into a 2D map that can be used to weigh features from certain parts of the image more heavily. The weighted sum of these spatial features is combined with global image features to provide relevant information to the prediction layers. To train our network, we collect a novel dataset of 3D keypoint annotations on thousands of CAD models, and synthetically render millions of images with 2D keypoint information. On test instances from PASCAL 3D+, our model achieves a mean class accuracy of 90.7%, whereas the state-of-the-art baseline only obtains 85.7% mean class accuracy, justifying our argument for human-in-the-loop inference.
In this paper we present a method for the estimation of the color of the illuminant in RAW images. The method includes a Convolutional Neural Network that has been specially designed to produce multiple local estimates. A multiple illuminant detector determines whether or not the local outputs of the network must be aggregated into a single estimate. We evaluated our method on standard datasets with single and multiple illuminants, obtaining lower estimation errors with respect to those obtained by other general purpose methods in the state of the art.
We prove local-wellposedness of the mKdV equation in $\mathcal{F}L^{s,p}$ spaces using the new method of M. Christ.