ShantanuT01/DACTYL-Pretraining huggingface dataset:
Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must be run on parallel computers. We analyse the problem of parallelising the multiplication of sparse matrices with the sparsity pattern required by linear-scaling techniques. We show that the management of inter-node communications and the effective use of on-node cache are helped by organising the atoms into compact groups. We also discuss how to identify a key part of the code called the `multiplication kernel', which is repeatedly invoked to build up the matrix product, and explicit code is presented for this kernel. Numerical tests of the resulting multiplication code are reported for cases of practical interest, and it is shown that their scaling properties for systems containing up to 20,000 atoms on machines having up to 512 processors are excellent. The tests also show that the cpu efficiency of our code is satisfactory.
In this paper, we first show that the power domination number of a connected $4$-regular claw-free graph on $n$ vertices is at most $\frac{n+1}{5}$, and the bound is sharp. The statement partly disprove the conjecture presented by Dorbec et al. in SIAM J. Discrete Math., 27:1559-1574, 2013. Then we present a dynamic programming style linear-time algorithm for weighted power domination problem in trees.
Measurements of the asymmetry of the emission peaks in the core of the Ca II H line for 105 giant stars are reported. The asymmetry is quantified with the parameter V/R, defined as the ratio between the maximum number of counts in the blueward peak and the redward peak of the emission profile. The Ca II H and K emission lines probe the differential motion of certain chromospheric layers in the stellar atmosphere. Data on V/R for the Ca II K line are drawn from previous papers and compared to the analogous H line ratio, the H and K spectra being from the same sets of observations. It is found that the H line V/R value is +0.04 larger, on average, than the equivalent K line ratio, however, the difference varies with B-V color. Red giants cooler than B-V = 1.2 are more likely to have the H line V/R larger than the K line V/R, whereas the opposite is true for giants hotter than B-V = 1.2. The differences between the Ca II H and K line asymmetries could be caused by the layers of chromospheric material from which these emission features arise moving with different velocities in an expanding outflow.
Heyde proved that a Gaussian distribution on a real line is characterized by the symmetry of the conditional distribution of one linear form given another. The present article is devoted to an analog of the Heyde theorem in the case when random variables take values in a locally compact Abelian group and the coefficients of the linear forms are integers.
Let X be a smooth variety over a field k and D an effective divisor whose support has simple normal crossings. We construct an explicit cycle map from the r-th Nisnevich motivic complex of the pair (X,D) to a shift of the r-th relative Milnor K-sheaf of (X,D). We show that this map induces an isomorphism for all i greater or equal the dimension of X between the motivic Nisnevich cohomology of (X,D) in bidegree (i+r,r) and the i-th Nisnevich cohomology of the r-th relative Minor K-sheaf of (X,D). This generalizes the well-known isomorphism in the case D=0. We use this to prove a certain Zariski descent property for the motivic cohomology of the pair (\A^1_k, (m+1){0}).
Non-Markovian time-evolution of quantum systems is a challenging problem, often mitigated by employing numerical methods or making simplifying assumptions. In this work, we address this problem in waveguide QED by developing a diagrammatic approach, which performs fully analytical non-Markovian time evolution of single-photon states. By revisiting Fermi's two atom problem, we tackle the impeding question of whether rotating-wave approximation violates causality in single-photon waveguide QED. Afterward, we introduce and prove the \emph{no upper half-plane poles (no-UHP) theorem}, which connects the poles of scattering parameters to the causality principle. Finally, we visualize the time-delayed coherent quantum feedback mediated by the field, discuss the Markovian limit for microscopically separated qubits where short-distance causality violations occur and the emergence of collective decay rates in this limit. Our diagrammatic approach is the first method to perform exact and analytical non-Markovian time evolution of multi-emitter systems in waveguide QED.
A significant fraction of compact radio-loud quasars display most of the characteristics of relativistically beamed, high-optical polarization blazars, yet are weakly polarized in the optical regime. We have used the VLBA at 22 and 43 GHz to look for differences in the parsec-scale magnetic field structures of 18 high- and low-optically polarized, compact radio-loud quasars (HPQs and LPRQs, respectively). We find a strong correlation between the polarization level of the unresolved parsec-scale radio core at 43 GHz and overall optical polarization of the source, which suggests a common (possibly co-spatial) origin for the emission at these two wavelengths. The magnetic fields of the polarized 43 GHz radio cores are aligned roughly transverse to the jet axis. Similar orientations are seen in the optical, suggesting that the polarized flux at both wavelengths is due to one or more strong transverse shocks located very close to the base of the jet. In LPRQs, these shocks appear to be weak near the core, and gradually increase in strength down the jet. The LPRQs in our sample tend to have less luminous radio cores than the HPQs, and jet components with magnetic fields predominantly parallel to the flow. The components in HPQ jets, on the other hand, tend to have transverse alignments. These differences cannot be accounted for by a simple model in which HPQs and LPRQs are the same type of object, seen at different angles to the line of sight. A more likely scenario is that LPRQs represent a quiescent phase of blazar activity, in which the inner jet flow does not undergo strong shocks.
We discuss different choices that can be made when matching a general high-energy theory -- with the restriction that it should not contain heavy gauge bosons -- onto a general renormalisable effective field theory at one loop, with particular attention to the quartic scalar couplings and Yukawa couplings. This includes a generalisation of the counterterm scheme that was found to be useful in the case of high-scale/split supersymmetry, but we show the important differences when there are new heavy scalar fields in singlet or triplet representations of $SU(2)$. We also analytically compare our methods and choices with the approach of matching pole masses, proving the equivalence with one of our choices. We outline how to make the extraction of quartic couplings using pole masses more efficient, an approach that we hope will generalise beyond one loop. We give examples of the impact of different scheme choices in a toy model; we also discuss the MSSM and give the threshold corrections to the Higgs quartic coupling in Dirac gaugino models.
We prove that the Dirichlet problem for the Lane-Emden equation in a half-space has no positive solutions which grow at most like the distance to the boundary to a power given by the natural scaling exponent of the equation; in other words, we rule out {\it type~I grow-up} solutions. Such a nonexistence result was previously available only for bounded solutions, or under a restriction on the power in the nonlinearity. Instrumental in the proof are local pointwise bounds for the logarithmic gradient of the solution and its normal derivative, which we also establish.
A functional renormalization group approach to $d$-dimensional, $N$-component, non-collinear magnets is performed using various truncations of the effective action relevant to study their long distance behavior. With help of these truncations we study the existence of a stable fixed point for dimensions between $d= 2.8$ and $d=4$ for various values of $N$ focusing on the critical value $N_c(d)$ that, for a given dimension $d$, separates a first order region for $N<N_c(d)$ from a second order region for $N>N_c(d)$. Our approach concludes to the absence of stable fixed point in the physical - $N=2,3$ and $d=3$ - cases, in agreement with $\epsilon=4-d$-expansion and in contradiction with previous perturbative approaches performed at fixed dimension and with recent approaches based on conformal bootstrap program.
Stellar photospheres of post-asymptotic giant branch stars bear witness to the internal chemical enrichment processes, integrated over their entire stellar evolution. Here we study post-AGB stars in the Large Magellanic Cloud (LMC). With their known distances, these rare objects are ideal tracers of AGB nucleosynthesis and dredge-up phenomena.   We used the UVES spectrograph mounted on the Very Large Telescope (VLT) at the European Southern Observatory (ESO), to obtain high-resolution spectra with high signal-to-noise (S/N) of a sample of four post-AGB stars. The objects display a spectral energy distribution (SED) that indicates the presence of circumstellar dust.   All objects are carbon-rich, and strongly enhanced in s-process elements. We deduced abundances of heavy s-process elements for all stars in the sample, and even found an indication of the presence of Hg in the spectrum of one object. The metallicity of all stars except J053253.51-695915.1 is considerably lower than the average value that is observed for the LMC. The derived luminosities show that we witness the late evolution of low-mass stars with initial masses close to 1 solar mass. An exception is J053253.51-695915.1 and we argue that this object is likely a binary.   We confirmed the correlation between the efficiency of the third-dredge up and the neutron exposure that is detected in Galactic post-AGB stars. The non-existence of a correlation between metallicity and neutron irradiation is also confirmed and expanded to smaller metallicities. We confirm the status of 21-micron stars as post-Carbon stars. Current theoretical AGB models overestimate the observed C/O ratios and fail to reproduce the variety of s-process abundance patterns that is observed in otherwise very similar objects. Similar results have recently been found for a post-AGB star in the Small Magellanic Cloud (SMC).
Black holes formed in dense star clusters, where dynamical interactions are frequent, may have fundamentally different properties than those formed through isolated stellar evolution. Theoretical models for single star evolution predict a gap in the black hole mass spectrum from roughly $40-120\,M_{\odot}$ caused by (pulsational) pair-instability supernovae. Motivated by the recent LIGO/Virgo event GW190521, we investigate whether black holes with masses within or in excess of this "upper-mass gap" can be formed dynamically in young star clusters through strong interactions of massive stars in binaries. We perform a set of $N$-body simulations using the CMC cluster-dynamics code to study the effects of the high-mass binary fraction on the formation and collision histories of the most massive stars and their remnants. We find that typical young star clusters with low metallicities and high binary fractions in massive stars can form several black holes in the upper-mass gap and often form at least one intermediate-mass black hole. These results provide strong evidence that dynamical interactions in young star clusters naturally lead to the formation of more massive black hole remnants.
We consider the spin-Hall current in a disordered two-dimensional electron gas in the presence of Rashba spin-orbit interaction. We derive a generalized Kubo-Greenwood formula for the spin-Hall conductivity $\sigma$ and evaluate it in an systematic way using standard diagrammatic techniques for disordered systems. We find that in the diffusive regime both Boltzmann and the weak localization contributions to $\sigma$ are of the same order and vanish in the zero frequency limit. We show that the uniform spin current is given by the total time derivative of the magnetization from which we can conclude that the spin current vanishes exactly in the stationary limit. This conclusion is valid for arbitrary spin-independent disorder, external electric field strength, and also for interacting electrons.
We address a number of puzzles relating to the proposed formulae for the degeneracies of dyons in orbifold compactifications of the heterotic string to four dimensions with $N =4$ supersymmetry. The partition function for these dyons is given in terms of Siegel modular forms associated with genus-two Riemann surfaces. We point out a subtlety in demonstrating S-duality invariance of the resulting degeneracies and give a prescription that makes the invariance manifest. We show, using M-theory lift of string webs, that the genus-two contribution captures the degeneracy only if a specific irreducibility criterion is satisfied by the charges. Otherwise, in general there can be additional contributions from higher genus Riemann surfaces. We analyze the negative discriminant states predicted by the formula. We show that even though there are no big black holes in supergravity corresponding to these states, there are multi-centered particle-like configurations with subleading entropy in agreement with the microscopic prediction and our prescription for S-duality invariance. The existence of the states is moduli dependent and we exhibit the curves of marginal stability and comment on its relation to S-duality invariance.
We study the effect of the exciton fine-structure splitting on the polarisation-entanglement of photon pairs produced by the biexciton cascade in a single quantum dot. The entanglement is found to persist despite separations between the intermediate energy levels of up to 4 micro-eV. Measurements demonstrate that entanglement of the photon pair is robust to the dephasing of the intermediate exciton state responsible for the first order coherence time of either single photon. We present a theoretical framework taking into account the effects of spin-scattering, background light and dephasing. We distinguish between the first-order coherence time, and a parameter which we measure for the first time and define as the cross-coherence time.
In this paper, a reconstruction method for the spatially distributed dielectric constant of a medium from the back scattering wave field in the frequency domain is considered. Our approach is to propose a globally convergent algorithm, which does not require any knowledge of a small neighborhood of the solution of the inverse problem in advance. The Quasi-Reversibility Method (QRM) is used in the algorithm. The convergence of the QRM is proved via a Carleman estimate. The method is tested on both computationally simulated and experimental data.
In the paper, we consider the free boundary value problem to 3D spherically symmetric compressible isentropic Navier-Stokes-Poisson equations for self-gravitating gaseous stars with $\gamma$-law pressure density function for $6/5 <\gamma \leq 4/3$. For stress free boundary condition and zero flow density continuously across the free boundary, the global existence of spherically symmetric weak solutions is shown, and the regularity and long time behavior of global solution are investigated for spherically symmetric initial data with the total mass smaller than a critical mass.
Biometric identification systems have become immensely popular and important because of their high reliability and efficiency. However person identification at a distance, still remains a challenging problem. Gait can be seen as an essential biometric feature for human recognition and identification. It can be easily acquired from a distance and does not require any user cooperation thus making it suitable for surveillance. But the task of recognizing an individual using gait can be adversely affected by varying view points making this task more and more challenging. Our proposed approach tackles this problem by identifying spatio-temporal features and performing extensive experimentation and training mechanism. In this paper, we propose a 3-D Convolution Deep Neural Network for person identification using gait under multiple view. It is a 2-stage network, in which we have a classification network that initially identifies the viewing point angle. After that another set of networks (one for each angle) has been trained to identify the person under a particular viewing angle. We have tested this network over CASIA-B publicly available database and have achieved state-of-the-art results. The proposed system is much more efficient in terms of time and space and performing better for almost all angles.
We study the relationship between one-dimensional fermion gas-impurity models and quantum dissipative systems, via the method of constructive bosonisation and unitary transformation. Starting from an anisotropic Coqblin-Schrieffer model, a new, exactly solvable, three-level quantum dissipative system is derived as a generalisation of the standard spin-half spin-boson model. The new system has two environmental oscillator baths with ohmic coupling, and admits arbitrary detuning between the three levels. All tunnelling matrix elements are equal, up to one complex phase which is itself a function of the longitudinal and transverse couplings in the integrable limit. Our work underlines the importance of re-examining the detailed structure of fermion-gas impurity models and spin chains, in the light of connections to models for quantum dissipative systems.
Here we present a radio continuum study based on new and archival data from the Australia Telescope Compact Array towards N 103B, a young (<=1000 yrs) spectroscopically confirmed type Ia SNR in the Large Magellanic Cloud (LMC) and proposed to have originated from a single degenerate progenitor. The radio morphology of this SNR is asymmetrical with two bright regions towards the north-west and south-west of the central location as defined by radio emission.   N 103B identified features include: a radio spectral index of -0.75+-0.01 (consistent with other young type Ia SNRs in the Galaxy); a bulk SNR expansion rate as in X-rays; morphology and polarised electrical field vector measurements where we note radial polarisation peak towards the north-west of the remnant at both 5500 and 9000 MHz. The spectrum is concave-up and the most likely reason is the non-linear diffusive shock acceleration effects or presence of two different populations of ultra-relativistic electrons.   We also note unpolarized clumps near the south-west region which is in agreement with this above scenario. We derive a typical magnetic field strength for N 103B, of 16.4 microG for an average rotation measurement of 200 rad m^-2. However, we estimate the equipartition field to be of the order of ~235 microG with an estimated minimum energy of Emin=6.3*10^48 erg. The close (~0.5 degree) proximity of N 103B to the LMC mid-plane indicates that an early encounter with dense interstellar medium may have set an important constrain on SNR evolution.   Finally, we compare features of N 103B, to six other young type Ia SNRs in the LMC and Galaxy, with a range of proposed degeneracy scenarios to highlight potential differences due to a different models. We suggest that the single degenerate scenario might point to morphologically asymmetric type Ia supernova explosions.
We study the interaction of a massless quantized spinor field with the gravitational filed of N parallel static cosmic strings by using a perturbative approach. We show that the presence of more than one cosmic string gives rise to an additional contribution to the energy density of vacuum fluctuations, thereby leading to a vacuum force attraction between two parallel cosmic strings.
We prove the conjecture by M. Yip stating that counting genus one partitions by the number of their elements and parts yields, up to a shift of indices, the same array of numbers as counting genus one rooted hypermonopoles. Our proof involves representing each genus one permutation by a four-colored noncrossing partition. This representation may be selected in a unique way for permutations containing no trivial cycles. The conclusion follows from a general generating function formula that holds for any class of permutations that is closed under the removal and reinsertion of trivial cycles. Our method also provides a new way to count rooted hypermonopoles of genus one, and puts the spotlight on a class of genus one permutations that is invariant under an obvious extension of the Kreweras duality map to genus one permutations.
We investigate the cosmological perturbation theory and calculate the perturbation spectra in the warm $k$-inflation. Unlike the scalar perturbations of $k$-inflation in the cold inflationary scenario, entropy perturbations should be considered in our model. We study how the entropy perturbations affect the evolution of curvature perturbation $\mathcal{R}$ on the comoving hypersurfaces and find the dissipation coefficient $\Gamma$ plays a central role in the entropy perturbations and the evolution equation of $\mathcal{R}$. In the weak dissipation condition, entropy perturbations on the large scale can be neglected such that the primordial spectrum of cosmological perturbations is due only to adiabatic perturbations. Like general warm inflationary models, density fluctuations also mainly originated from the thermal fluctuations of the inflaton field rather than the vacuum fluctuations in our model. Finally, we calculate the perturbation spectra and the tensor-to-scalar ratio, then find the tensor-to-scalar ratio is smaller than that in the $k$-inflation or the general potential-driven cold inflationary models.
Context. Local correlation tracking of granulation (LCT) is an important method for measuring horizontal flows in the photosphere. This method exhibits a systematic error that looks like a flow converging towards disk center, also known as the shrinking-Sun effect.   Aims. We aim at studying the nature of the shrinking-Sun effect for continuum intensity data and at deriving a simple model that can explain its origin.   Methods. We derived LCT flow maps by running the local correlation tracking code FLCT on tracked and remapped continuum intensity maps provided by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory. We also computed flow maps from synthetic continuum images generated from STAGGER code simulations of solar surface convection. We investigated the origin of the shrinking-Sun effect by generating an average granule from synthetic data from the simulations.   Results. The LCT flow maps derived from HMI and from the simulations exhibit a shrinking-Sun effect of comparable magnitude. The origin of this effect is related to the apparent asymmetry of granulation originating from radiative transfer effects when observing with a viewing angle inclined from vertical. This causes, in combination with the expansion of the granules, an apparent motion towards disk center.
Given two weighted k-uniform hypergraphs G, H of order n, how much (or little) can we make them overlap by placing them on the same vertex set? If we place them at random, how concentrated is the distribution of the intersection? The aim of this paper is to investigate these questions.