ShantanuT01/DACTYL-Pretraining huggingface dataset:
This paper presents existence and uniqueness results for reflected backward doubly stochastic differential equations (in short RBDDSEs) in a convex domain D. Moreover, using a stochastic flow approach a probabilistic interpretation for a class of reflected SPDE's in a domain is given via such RBDSDEs. The solution is expressed as a pair (u,{\nu}) where u is a predictable continuous process which takes values in a Sobolev space and m is a random regular measure. The bounded variation process K, component of the solution of the reflected BDSDE, controls the set when u reaches the boundary of D. This bounded variation process determines the measure m from a particular relation by using the inverse of the flow associated to the the diffusion operator.
We describe in this article a new code for evolving axisymmetric isolated systems in general relativity. Such systems are described by asymptotically flat space-times which have the property that they admit a conformal extension. We are working directly in the extended `conformal' manifold and solve numerically Friedrich's conformal field equations, which state that Einstein's equations hold in the physical space-time. Because of the compactness of the conformal space-time the entire space-time can be calculated on a finite numerical grid. We describe in detail the numerical scheme, especially the treatment of the axisymmetry and the boundary.
We devise improved photometric parameters for the morphological classification of galaxies using a bright sample from the First Data Release of the Sloan Digital Sky Survey. In addition to using an elliptical aperture concentration index for classification, we introduce a new texture parameter, coarseness, which quantifies deviations from smooth galaxy isophotes. The elliptical aperture concentration index produces morphological classifications that are in appreciably better agreement with visual classifications than those based on circular apertures. With the addition of the coarseness parameter,the success rate of classifying galaxies into early and late types increases to \~88% with respect to the reference visual classification. A reasonably high success rate ~68% is also attained in classifying galaxies into three types, early-type galaxies (E+S0), early- (Sa+Sb) and late- (Sc+Sdm+Im) type spiral galaxies.
SN2009ku, discovered by Pan-STARRS-1, is a Type Ia supernova (SNIa), and a member of the distinct SN2002cx-like class of SNeIa. Its light curves are similar to the prototypical SN2002cx, but are slightly broader and have a later rise to maximum in g. SN2009ku is brighter (~0.6 mag) than other SN2002cx-like objects, peaking at M_V = -18.4 mag - which is still significantly fainter than typical SNeIa. SN2009ku, which had an ejecta velocity of ~2000 kms^-1 at 18 days after maximum brightness is spectroscopically most similar to SN2008ha, which also had extremely low-velocity ejecta. However, SN2008ha had an exceedingly low luminosity, peaking at M_V = -14.2 mag, ~4 mag fainter than SN2009ku. The contrast of high luminosity and low ejecta velocity for SN2009ku is contrary to an emerging trend seen for the SN2002cx class. SN2009ku is a counter-example of a previously held belief that the class was more homogeneous than typical SNeIa, indicating that the class has a diverse progenitor population and/or complicated explosion physics. As the first example of a member of this class of objects from the new generation of transient surveys, SN2009ku is an indication of the potential for these surveys to find rare and interesting objects.
Supernova remnant (SNR) shock waves are the main place where interstellar dust grains are destroyed. However, the dust destruction efficiency in non-radiative shocks is still not well known. One way to estimate the fraction of dust destroyed is to compare the difference between postshock gas abundances and preshock medium total abundances when the preshock elemental depletion factors are known. We compare the postshock gas abundances of 16 SNRs in Large Magellanic Cloud (LMC) with the LMC interstellar medium abundances that we derived based on 69 slow-rotating early B-type stars. We find that, on average, $\sim$61\% of Si rich dust grains are destroyed in the shock while the fraction of dust destroyed is only $\sim$40\% for Fe rich dust grains. This result supports the idea that the high depletion of Fe in the diffuse neutral medium is not caused by the resilience of Fe rich grains but because of faster growth rate. This work also presents a potential way to constrain the chemical composition of interstellar dust.
Active galactic nuclei (AGN) are one of the most luminous objects in the Universe, emitting powerful continuum and line emission across all wavelength bands. They represent an important link in the investigations of the galaxy evolution and cosmology. The resolving of the AGN inner structure is still a difficult task with current instruments, therefore the spectroscopy and spectropolarimetry are crucial tools to investigate these objects and their components, such as the properties of the supermassive black hole, the broad line region, and the dusty torus. In this review, we present the results of the project "Astrophysical spectroscopy of extragalactic objects", from the observations, data processing and analysis, to the modelling of different regions in AGN.
Let $G$ be a graph of even order and let $K_{G}$ be the complete graph on the same vertex set of $G$. A pairing of a graph $G$ is a perfect matching of the graph $K_{G}$. A graph $G$ has the Pairing-Hamiltonian property (for short, the PH-property) if for each one of its pairings, there exists a perfect matching of $G$ such that the union of the two gives rise to a Hamiltonian cycle of $K_G$. In 2015, Alahmadi \emph{et al.} gave a complete characterisation of the cubic graphs having the PH-property. Most naturally, the next step is to characterise the quartic graphs that have the PH-property. In this work we propose a class of quartic graphs on two parameters, $n$ and $k$, which we call the class of accordion graphs $A[n,k]$. We show that an infinite family of quartic graphs (which are also circulant) that Alahmadi \emph{et al.} stated to have the PH-property are, in fact, members of this general class of accordion graphs. We also study the PH-property of this class of accordion graphs, at times considering the pairings of $G$ which are also perfect matchings of $G$. Furthermore, there is a close relationship between accordion graphs and the Cartesian product of two cycles. Motivated by a recent work by Bogdanowicz (2015), we give a complete characterisation of those accordion graphs that are circulant graphs. In fact, we show that $A[n,k]$ is not circulant if and only if both $n$ and $k$ are even, such that $k\geq 4$.
Quantum interference between time-reversed electron paths in two dimensions leads to the well-known weak localization correction to resistance. If spin-orbit coupling is present, the resistance correction is negative, termed weak anti-localization (WAL). Here we report the observation of WAL coexisting with exchange coupling between itinerant electrons and localized magnetic moments. We use low-temperature magneto-transport measurements to investigate the quasi-two-dimensional, high-electron-density interface formed between SrTiO$_3$ (STO) and the anti-ferromagnetic Mott insulator NdTiO$_3$ (NTO). As the magnetic field angle is gradually tilted away from the sample normal, the data reveals the interplay between strong $k$-cubic Rashba-type spin-orbit coupling and a substantial magnetic exchange interaction from local magnetic regions. The resulting quantum corrections to the conduction are in excellent agreement with existing models and allow sensitive determination of the small magnetic moments (22 $\mu_B$ on average), their magnetic anisotropy and mutual coupling strength. This effect is expected to arise in other 2D magnetic materials systems.
We illustrate a formalism that allows to match the next-to-leading order cross section for the photoproduction of heavy quarks to the cross section obtained by resumming logarithms of $\pt/m$ to the next-to-leading accuracy, thus giving a sensible prediction for any value of $\pt$. We present a comparison between our predictions and H1 and ZEUS data.
Studying the composition of dust in the interstellar medium (ISM) is crucial in understanding the cycle of dust in our galaxy. The mid-infrared spectral signature of amorphous silicates, the most abundant dust species in the ISM, is studied in different lines-of-sight through the Galactic plane, thus probing different conditions in the ISM. We have analysed 10 spectra from the Spitzer archive, of which 6 lines-of-sight probe diffuse interstellar medium material and 4 probe molecular cloud material. The 9.7 um silicate absorption features in 7 of these spectra were studied in terms of their shape and strength. In addition, the shape of the 18 um silicate absorption features in 4 of the diffuse sightline spectra were analysed. The 9.7 um silicate absorption bands in the diffuse sightlines show a strikingly similar band shape. This is also the case for all but one of the 18 um silicate absorption bands observed in diffuse lines-of-sight. The 9.7 um bands in the 4 molecular sightlines show small variations in shape. These modest variations in the band shape are inconsistent with the interpretation of the large variations in {\tau}_9.7/E(J-K) between diffuse and molecular sightlines in terms of silicate grain growth. Instead, we suggest that the large changes in {\tau}_9.7 / E(J-K) must be due to changes in E(J-K).
We study the Ekedahl-Oort stratification on moduli spaces of PEL type. The strata are indexed by cosets in a Weyl group. The main result of this paper is that the dimension of a stratum equals the length of the corresponding Weyl group element. We also discuss some explicit examples.
We present the study for the mass dependence of E$_{bal}$ for various N/Z ratios covering pure symmetric systems to highly neutron-rich ones.
The question of how the scattering cross section changes when the spectra of the colliding nuclei have low-excitation particle-emitting resonances is explored using a multi-channel algebraic scattering (MCAS) method. As a test case, the light-mass nuclear target 8Be, being particle-unstable, has been considered. Nucleon-nucleus scattering cross sections, as well as the spectra of the compound nuclei formed, have been determined from calculations that do, and do not, consider particle emission widths of the target nuclear states. The resonant character of the unstable excited states introduces a problem because the low-energy tails of these resonances can intrude into the sub-threshold, bound-state region. This unphysical behaviour needs to be corrected by modifying, in an energy-dependent way, the shape of the target resonances from the usual Lorentzian one. The resonance function must smoothly reach zero at the elastic threshold. Ways of achieving this condition are explored in this paper.
This paper considers the problem of multiple human target tracking in a sequence of video data. A solution is proposed which is able to deal with the challenges of a varying number of targets, interactions and when every target gives rise to multiple measurements. The developed novel algorithm comprises variational Bayesian clustering combined with a social force model, integrated within a particle filter with an enhanced prediction step. It performs measurement-to-target association by automatically detecting the measurement relevance. The performance of the developed algorithm is evaluated over several sequences from publicly available data sets: AV16.3, CAVIAR and PETS2006, which demonstrates that the proposed algorithm successfully initializes and tracks a variable number of targets in the presence of complex occlusions. A comparison with state-of-the-art techniques due to Khan et al., Laet et al. and Czyz et al. shows improved tracking performance.
In these short, rather informal, expository notes I review the current state of the field regarding the mathematics of Landau damping, based on lectures given at the CIRM Research School on Kinetic Theory, November 14--18, 2022. These notes are mainly on Vlasov-Poisson in $(x,v) \in \mathbb T^d \times \mathbb R^d$ however a brief discussion of the important case of $(x,v) \in \mathbb R^d \times \mathbb R^d$ is included at the end. The focus will be nonlinear and these notes include a proof of Landau damping on $(x,v) \in \mathbb T^d \times \mathbb R^d$ in the Vlasov--Poisson equations meant for graduate students, post-docs, and others to learn the basic ideas of the methods involved. The focus is also on the mathematical side, and so most references are from the mathematical literature with only a small number of the many important physics references included. A few open problems are included at the end.   These notes are not currently meant for publication so they may not be perfectly proof-read and the reference list might not be complete. If there is an error or you have some references which you think should be included, feel free to send me an email and I will correct it when I get a chance.
Organic/inorganic donor-acceptor interfaces are gaining growing attention in organic photovoltaic applications as each component of the interface offers unique attributes. Here we use hybrid-density functional theory to examine the electronic structure of sexithiophene/ZnO interfaces. We find that interfacial molecular orientations strongly influence the adsorption energy, the energy level alignment, and the open circuit voltage. We attribute the orientation dependence to the varied strength of electronic coupling between the molecule and the substrate. Our study suggests that photovoltaic performance can be optimized by controlling the interfacial design of molecular orientations.
A relativistic equation is deduced for the bound state of two particles, by assuming a proper boundary condition for the propagation of the negative-energy states. It reduces to the (one-body)Dirac equation in the infinite limit of one of the constituent mass. It also has the symmetries to assure the existence of the anti-bound-state with the same mass. The interaction kernel(pseudo-potential) is systematically constructed by diagonalizing the Hamiltonian of the background field theory, by which the retardation effects are included in the interaction. Its wave function at the origin(WFO) behaves properly in a manner suggested by the covariant field theory.   The equation can well be applied in the heavy quark effective theory. It can also be used as a starting equation for the unperturbed system in the rigorous perturbation theory of QED.
Viscoelastic subdiffusion governed by a fractional Langevin equation is studied numerically in a random Gaussian environment modeled by stationary Gaussian potentials with decaying spatial correlations. This anomalous diffusion is archetypal for living cells, where cytoplasm is known to be viscoelastic and a spatial disorder also naturally emerges. We obtain some first important insights into it within a model one-dimensional study. Two basic types of potential correlations are studied: short-range exponentially decaying and algebraically slow decaying with an infinite correlation length, both for a moderate (several $k_BT$, in the units of thermal energy), and strong (5-10 $k_BT$) disorder. For a moderate disorder, it is shown that on the ensemble level viscoelastic subdiffusion can easily overcome the medium's disorder. Asymptotically, it is not distinguishable from the disorder-free subdiffusion. However, a strong scatter in single-trajectory averages is nevertheless seen even for a moderate disorder. It features a weak ergodicity breaking, which occurs on a very long yet transient time scale. Furthermore, for a strong disorder, a very long transient regime of logarithmic, Sinai-type diffusion emerges. It can last longer and be faster in the absolute terms for weakly decaying correlations as compare with the short-range correlations. Residence time distributions in a finite spatial domain are of a generalized log-normal type and are reminiscent also of a stretched exponential distribution. They can be easily confused for power-law distributions in view of the observed weak ergodicity breaking. This suggests a revision of some experimental data and their interpretation.
We present an approach to recover absolute 3D human poses from multi-view images by incorporating multi-view geometric priors in our model. It consists of two separate steps: (1) estimating the 2D poses in multi-view images and (2) recovering the 3D poses from the multi-view 2D poses. First, we introduce a cross-view fusion scheme into CNN to jointly estimate 2D poses for multiple views. Consequently, the 2D pose estimation for each view already benefits from other views. Second, we present a recursive Pictorial Structure Model to recover the 3D pose from the multi-view 2D poses. It gradually improves the accuracy of 3D pose with affordable computational cost. We test our method on two public datasets H36M and Total Capture. The Mean Per Joint Position Errors on the two datasets are 26mm and 29mm, which outperforms the state-of-the-arts remarkably (26mm vs 52mm, 29mm vs 35mm). Our code is released at \url{https://github.com/microsoft/multiview-human-pose-estimation-pytorch}.
We report measurements of the four terminal temperature dependent resistance of narrow Au wires implanted with ~100 ppm Fe impurities in proximity to superconducting Al films. The wires show an initial decrease in resistance as the temperature is lowered through the superconducting transition of the Al films, but then show an increase in resistance as the temperature is lowered further. In contrast to the case of pure Au wires in contact with a superconducting film, the resistance at the lowest temperatures rises above the normal state resistance. Analysis of the data shows that, in addition to contributions from magnetic scattering and electron-electron interactions, the temperature dependent resistivity shows a substantial contribution from the superconducting proximity effect, which exists even in the presence of strong spin scattering.
We present results of the $Q^{-1}$ and period shift, $\Delta P$, for $^3$He confined in a 98% nominal open aerogel on a torsion pendulum. The aerogel is compressed uniaxially by 10% along a direction aligned to the torsion pendulum axis and was grown within a 400 $\mu$m tall pancake (after compression) similar to an Andronikashvili geometry. The result is a high $Q$ pendulum able to resolve $Q^{-1}$ and mass coupling of the impurity-limited $^3$He over the whole temperature range. After measuring the empty cell background, we filled the cell above the critical point and observe a temperature dependent period shift, $\Delta P$, between 100 mK and 3 mK that is 2.9$%$ of the period shift (after filling) at 100 mK. The $Q^{-1}$ due to the $^3$He decreases by an order of magnitude between 100 mK and 3 mK at a pressure of $0.14\pm0.03$ bar. We compare the observable quantities to the corresponding calculated $Q^{-1}$ and period shift for bulk $^3$He.
Toroidal 3-orbifolds $(S^1)^6/G$, for $G$ a finite group, were some of the earliest examples of Calabi-Yau 3-orbifolds to be studied in string theory. While much mathematical progress towards the predictions of string theory has been made in the meantime, most of it has dealt with hypersurfaces in toric varieties. As a result, very little is known about curve-counting theories on toroidal orbifolds. In this paper, we initiate a program to study mirror symmetry and the Landau-Ginzburg/Calabi-Yau (LG/CY) correspondence for toroidal orbifolds. We focus on the simplest example $[E^3/\mu_3],$ where $E\subseteq\mathbb{P}^2$ is the elliptic curve $\mathbb{V}(x_0^3+x_1^3+x_2^3).$ We study this orbifold from the point of GIT wall-crossing using the gauged linear sigma model, a collection of moduli spaces generalizing spaces of stable maps. Our main result is a mirror symmetry theorem that applies simultaneously to the different GIT chambers. Using this, we analyze wall-crossing behavior to obtain an LG/CY correspondence relating the genus-zero Gromov-Witten invariants of $[E^3/\mu_3]$ to generalized Fan-Jarvis-Ruan-Witten invariants.
We show how the holomorphic anomaly found in hep-th/0409245 can be used to efficiently compute certain classes of unitarity cuts of one-loop N=4 amplitudes of gluons. These classes include all cuts of n-gluon one-loop MHV amplitudes and of n-gluon next-to-MHV amplitudes with helicities (1+,2+,3+,4-,..., n-). As an application of this method, we present the explicit computation of the (1,2,3)-cut of the n-gluon one-loop N=4 leading-color amplitude A_{n;1}(1+,2+,3+,4-,..., n-). The answer is given in terms of scalar box functions and provides information about the corresponding amplitudes. A possible way to generalize this method to all kinds of unitarity cuts is also discussed.
In this paper, we will prove that a problem deciding whether there is an upper-triangular coordinate in which a character is not in the state of a Hilbert point is NP-hard. This problem is related to the GIT-semistability of a Hilbert point.
Kuroda's formula relates the class number of a multi-quadratic number field $K$ to the class numbers of its quadratic subfields $k_i$. A key component in this formula is the unit group index $Q(K) = [\mathcal{O}_{K}^{\times}: \prod_i\mathcal{O}_{k_i}^{\times}]$. We study how $Q(K)$ behaves on average in certain natural families of totally real biquadratic fields $K$ parametrized by prime numbers.
We present a concept for an imaging gamma-ray polarimeter operating from ~50 MeV to ~1 GeV. Such an instrument would be valuable for the study of high-energy pulsars, active galactic nuclei, supernova remnants, and gamma-ray bursts. The concept makes use of pixelized gas micro-well detectors, under development at Goddard Space Flight Center, to record the electron-positron tracks from pair-production events in a large gas volume. Pixelized micro-well detectors have the potential to form large-volume 3-D track imagers with ~100 micron (rms) position resolution at moderate cost. The combination of high spatial resolution and a continuous low-density gas medium permits many thousands of measurements per radiation length, allowing the particle tracks to be imaged accurately before multiple scattering masks their original directions. The polarization of the incoming radiation may then be determined from the azimuthal distribution of the electron-positron pairs. We have performed Geant4 simulations of these processes to estimate the polarization sensitivity of a simple telescope geometry at 100 MeV.
We first propose a topological term that captures the "intertwinement" between the standard "$\sqrt{3} \times \sqrt{3}$" antiferromagnetic order (or the so-called 120$^\circ$ state) and the "$\sqrt{12}\times \sqrt{12}$" valence solid bond (VBS) order for spin-1/2 systems on a triangular lattice. Then using a controlled renormalization group calculation, we demonstrate that there exists an unfine-tuned direct continuous deconfined quantum critical point (dQCP) between the two ordered phases mentioned above. This dQCP is described by the $N_f = 4$ quantum electrodynamics (QED) with an emergent PSU(4)=SU(4)/$Z_4$ symmetry only at the critical point. The topological term aforementioned is also naturally derived from the $N_f = 4 $ QED. We also point out that physics around this dQCP is analogous to the boundary of a $3d$ bosonic symmetry protected topological state with on-site symmetries only.
The purpose of this article is to give an overview of the series of papers [BK1], [BK2] concerning the $p$-adic Beilinson conjecture of motives associated to Hecke characters of an imaginary quadratic field $K$, for a prime $p$ which splits in $K$.