ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider an extension of the Monge-Kantorovitch optimal transportation problem. The mass is transported along a continuous semimartingale, and the cost of transportation depends on the drift and the diffusion coefficients of the continuous semimartingale. The optimal transportation problem minimizes the cost among all continuous semimartingales with given initial and terminal distributions. Our first main result is an extension of the Kantorovitch duality to this context. We also suggest a finite-difference scheme combined with the gradient projection algorithm to approximate the dual value. We prove the convergence of the scheme, and we derive a rate of convergence. We finally provide an application in the context of financial mathematics, which originally motivated our extension of the Monge-Kantorovitch problem. Namely, we implement our scheme to approximate no-arbitrage bounds on the prices of exotic options given the implied volatility curve of some maturity.
We report the most detailed $1-3$ GHz radio continuum emission map of the nearest region of massive star formation, the Carina Nebula. As part of a large program with the Australia Telescope Compact Array, we have covered $\sim$ 12 deg$^2$, achieving an angular resolution of $\sim$ 16 arcsec, representing the largest and most complete map of the radio continuum to date. Our continuum map shows a spectacular and complex distribution of emission across the nebula, with multiple structures such as filaments, shells, and fronts across a wide range of size scales. The ionization fronts have advanced far into the southern and northern region of the Galactic Plane, as fronts are clearly detected at distances $\sim$ 80 pc from the stellar clusters in the center. We estimated an ionization photon luminosity $Q_\mathrm{H}=(7.8 \pm 0.8) \times 10^{50}$ s$^{-1}$ which corresponds to $\sim 85\%$ of the total value obtained from stellar population studies. Thus, approximately $15\%$ of the ionizing flux has escaped from the nebula into the diffuse Galactic Interstellar Medium. Comparison between radio continuum and the hydrogen atomic and molecular gas maps offers a clear view of the bipolar outflow driven by the energy released by the massive stellar clusters that also affects the fraction of molecular gas across the nebula. Comparison between 8$\mu$m and 70$\mu$m emission maps and the radio continuum reveals how the hot gas permeates through the molecular cloud, shapes the material into features such as pillars, small shells and arc-like structures, and ultimately, escapes.
We analyze a pair of reflected Brownian motions in a planar domain $D$, for which the increments of both processes form mirror images of each other when the processes are not on the boundary. We show that for $D$ in a class of smooth convex planar domains, the two processes remain ordered forever, according to a certain partial order.   This is used to prove that the second eigenvalue is simple for the Laplacian with Neumann boundary conditions for the same class of domains.
We consider the creation of polarization entangled light from parametric down- conversion driven by an intense pulsed pump inside a cavity. The multi-photon states produced are close approximations to singlet states of two very large spins. A criterion is derived to quantify the entanglement of such states. We study the dynamics of the system in the presence of losses and other imperfections, concluding that the creation of strongly entangled states with photon numbers up to a million seems achievable.
It is proved that there exist graphs of bounded degree with arbitrarily large queue-number. In particular, for all $\Delta\geq3$ and for all sufficiently large $n$, there is a simple $\Delta$-regular $n$-vertex graph with queue-number at least $c\sqrt{\Delta}n^{1/2-1/\Delta}$ for some absolute constant $c$.
More then forty years ago R.I. Pimenov introduced a new geometry -- semi-Riemannian one -- as a set of geometrical objects consistent with a fibering $ pr: M_n \to M_m.$ He suggested the heuristic principle according to which the physically different quantities (meter, second, coulomb etc.) are geometrically modelled as space coordinates that are not superposed by automorphisms. As there is only one type of coordinates in Riemannian geometry and only three types of coordinates in pseudo-Riemannian one, a multiple fibered semi-Riemannian geometry is the most appropriate one for the treatment of more then three different physical quantities as unified geometrical field theory.   Semi-Euclidean geometry $^{3}R_5^4$ with 1-dimensional fiber $x^5$ and 4-dimensional Minkowski space-time as a base is naturally interpreted as classical electrodynamics. Semi-Riemannian geometry $^{3}V_5^4$ with the general relativity pseudo-Riemannian space-time $^{3}V^4,$ and 1-dimensional fiber $x^5,$ responsible for the electromagnetism, provides the unified field theory of gravitation and electromagnetism. Unlike Kaluza-Klein theories, where the 5-th coordinate appears in nondegenerate Riemannian or pseudo-Riemannian geometry, the theory based on semi-Riemannian geometry is free from defects of the former. In particular, scalar field does not arise.   PACS: 04.50.Cd, 02.40.-k, 11.10.Kk
The production scale and internal structure of jets produced in high energy collisions are studied using Jetset7.4 and Herwig5.9 Monte Carlo generators. Two scales are found. One is the jet-development scale, which determines the size of the jet developed from a mother-parton. The other one is the jet-production scale, the jets produced with this scale are the most consistent with QCD jet-production dynamics and will provide the most reliable dynamical information about their mother-partons.
The role of tensor force on the collision dynamics of $^{16}$O+$^{16}$O is investigated in the framework of a fully three-dimensional time-dependent Hartree-Fock theory. The calculations are performed with modern Skyrme energy functional plus tensor terms. Particular attention is given on the analysis of dissipation dynamics in heavy-ion collisions. The energy dissipation is found to decrease as an initial bombarding energy increases in deep-inelastic collisions for all the Skyrme parameter sets studied here because of the competition between the collective motion and the single-particle degrees of freedom.   We reveal that the tensor forces may either enhance or reduce the energy dissipation depending on the different parameter sets. The fusion cross section without tensor force overestimates the experimental value by about 25\%, while the calculation with tensor force T11 has good agreement with experimental cross section.
In the article we present chaotic decomposition and analog of the Clark formula for the local time of Gaussian integrators. Since the integral with respect to Gaussian integrator is understood in Skorokhod sense, then there exist more than one Clark representation for the local time. We present different representations and discuss the representation with the minimal L_2-norm.
Compared with direct-gap semiconductors, the valley degeneracy of silicon and germanium opens up new channels for spin relaxation that counteract the spin degeneracy of the inversion-symmetric system. Here the symmetries of the electron-phonon interaction for silicon and germanium are identified and the resulting spin lifetimes are calculated. Room-temperature spin lifetimes of electrons in silicon are found to be comparable to those in gallium arsenide, however, the spin lifetimes in silicon or germanium can be tuned by reducing the valley degeneracy through strain or quantum confinement. The tunable range is limited to slightly over an order of magnitude by intravalley processes.
We propose a unified realistic shell-model Hamiltonian employing the pairing plus multipole Hamiltonian combined with the monopole interaction constructed starting from the monopole-based universal force by Otsuka it et al. (Phys. Rev. Lett. 104, 012501 (2010)). It is demonstrated that the proposed PMMU model can consistently describe a large amount of spectroscopic data as well as binding energies in the pf and pf5/2g9/2 shell spaces, and could serve as a practical shell model for even heavier mass regions.
A strong $k$-edge-coloring of a graph $G$ is a mapping from $E(G)$ to $\{1,2,\ldots,k\}$ such that every pair of distinct edges at distance at most two receive different colors. The strong chromatic index $\chi'_s(G)$ of a graph $G$ is the minimum $k$ for which $G$ has a strong $k$-edge-coloring. Denote $\sigma(G)=\max_{xy\in E(G)}\{\operatorname{deg}(x)+\operatorname{deg}(y)-1\}$. It is easy to see that $\sigma(G) \le \chi'_s(G)$ for any graph $G$, and the equality holds when $G$ is a tree. For a planar graph $G$ of maximum degree $\Delta$, it was proved that $\chi'_s(G) \le 4 \Delta +4$ by using the Four Color Theorem. The upper bound was then reduced to $4\Delta$, $3\Delta+5$, $3\Delta+1$, $3\Delta$, $2\Delta-1$ under different conditions for $\Delta$ and the girth. In this paper, we prove that if the girth of a planar graph $G$ is large enough and $\sigma(G)\geq \Delta(G)+2$, then the strong chromatic index of $G$ is precisely $\sigma(G)$. This result reflects the intuition that a planar graph with a large girth locally looks like a tree.
We present an implementation of a truncated unity parquet solver (TUPS) which solves the parquet equations using a truncated form-factor basis for the fermionic momenta. This way fluctuations from different scattering channels are treated on an equal footing. The essentially linear scaling of computational costs in the number of untruncated bosonic momenta allows us to treat system sizes of up to 76x76 discrete lattice momenta, unprecedented by previous unbiased methods that include the frequency dependence of the vertex. With TUPS, we provide the first numerical evidence that the parquet approximation might indeed respect the Mermin-Wagner theorem and further systematically analyze the convergence with respect to the number of form factors. Using a single form factor seems to qualitatively describe the physics of the half-filled Hubbard model correctly, including the pseudogap behaviour. Quantitatively, using a single or a few form factors only is not sufficient at lower temperatures or stronger coupling.
Charge exchange is an important process for the modeling of X-ray spectra obtained by the Chandra, XMM-Newton, and Suzaku X-ray observatories, as well as the anticipated Astro-H mission. The understanding of the observed X-ray spectra produced by many astrophysical environments is hindered by the current incompleteness of available atomic and molecular data -- especially for charge exchange. Here, we implement a streamlined program set that applies quantum defect methods and the Landau-Zener theory to generate total, n-resolved, and nlS-resolved cross sections for any given projectile ion/ target charge exchange collision. Using this data in a cascade model for X-ray emission, theoretical spectra for such systems can be predicted. With these techniques, Fe25+ and Fe26+ charge exchange collisions with H, He, H2, N2, H2O, and CO are studied for single electron capture. These systems have been selected as they illustrate computational difficulties for high projectile charges. Further, Fe XXV and Fe XXVI emission lines have been detected in the Galactic center and Galactic ridge. Theoretical X-ray spectra for these collision systems are compared to experimental data generated by an electron beam ion trap study. Several l- distribution models have been tested for Fe25+ and Fe26+ single electron capture. Such analysis suggests that commonly used l-distribution models struggle to accurately reflect the true distribution of electron capture as understood by more advanced theoretical methods.
This paper presents a workforce planning model scalable to an entire hierarchical organization. Its main objective is to design a cost optimal target which leverages flexible workforce solutions while ensuring an efficient promotional flux. The value of this paper lies in its proposal of an adequate flexibility rate using various solution types and in its discussion about external hiring ratios. The mathematical structures of the models are analyzed and numerical simulations illustrate the theoretical background.
We study non-relativistic limits of the N=6 Chern-Simons-Matter theory that arises as a low-energy limit of the M2-brane gauge theory with background flux. The model admits several different non-relativistic limits and we find that the maximal supersymmetry we construct has 14 components of supercharges, which is a novel example of non-relativistic superconformal algebra in (1+2) dimension. We also investigate the other limits that realize less supersymmetries.
We show that logarithmic derivative of the Zeta function of any regular graph is given by a power series about infinity whose coefficients are given in terms of the traces of powers of the graph's Hashimoto matrix.   We then consider the expected value of this power series over random, $d$-regular graph on $n$ vertices, with $d$ fixed and $n$ tending to infinity. Under rather speculative assumptions, we make a formal calculation that suggests that for fixed $d$ and $n$ large, this expected value should have simple poles of residue $-1/2$ at $\pm (d-1)^{-1/2}$. We shall explain that calculation suggests that for fixed $d$ there is an $f(d)>1/2$ such that a $d$-regular graph on $n$ vertices is Ramanujan with probability at least $f(d)$ for $n$ sufficiently large.   Our formal computation has a natural analogue when we consider random covering graphs of degree $n$ over a fixed, regular "base graph." This again suggests that for $n$ large, a strict majority of random covering graphs are relatively Ramanujan.   We do not regard our formal calculations as providing overwhelming evidence regarding the frequency of Ramanujan graphs. However, these calculations are quite simple, and yield intiguing suggestions which we feel merit further study.
We present the first set of results of solving the Hartree-Fock-Bogoliubov equations, which describe the self-consistent mean field theory with pairing interaction. Calculations for even-even nuclei are carried out on a two-dimensional axially symmetric lattice, in coordinate space. An important aspect of our method is the proper representation of the quasi-particle continuum wavefunctions, which are considered for energies up to 60 MeV. This stage is essential for a proper description of nuclei near the drip lines, due to the strong coupling between weakly bound states and the particle continuum for such nuclei. High accuracy is achieved by representing the operators and wavefunctions using the technique of basis-splines. Calculations for Sn isotopes are presented to demonstrate the reliability of the method.
In this paper, we study the dynamics of a hollow spherical matter collapsing with very large initial velocity. The spacetime is initially very similar to the Vaidya solution, and the deviations from this background are treated perturbatively. The equations of state for radial pressure $p_{\rm R}=k\rho$ and tangential one $p_{\rm T}=w\rho$ with constant $k$ and $w$ are assumed. We find for the case of equations of state $k< 1$ and $0<w\leq1$ that the initial velocity, which is nearly the speed of light, is strongly decelerated. This result implies that the pressure is essential to the property of singularity formation in gravitational collapse even for initially nearly light-speed collapse. By contrast, in cases with the negative tangential pressure, the present result implies that the central naked singularity similar to that of the Vaidya spacetime can be formed, even though the radial pressure is positive, and the weak, strong and dominant energy conditions hold. Especially, in the case of $w<-(1-k)/4$, the high-speed collapse will produce the spacetime structure very similar to that of the Vaidya spacetime.
Newman and Rovelli have used singular Hamilton-Jacobi transformations to reduce the phase space of general relativity in terms of the Ashtekar variables. Their solution of the gauge constraint cannot be inverted and indeed has no Minkowski space limit. Nonetheless, we exhibit an explicit Hamilton-Jacobi solution of all the linearized constraints. The result does not encourage an iterative solution, but it does indicate the origin of the singularity of the Newman-Rovelli result.
We consider a higher dimensional gravity theory with a negative kinetic energy scalar field and a cosmological constant. We find that the theory admits an exact cosmological solution for the scale factor of our universe. It has the feature that the universe undergoes a continuous transition from deceleration to acceleration at some finite time. This transition time can be interpreted as that of recent acceleration of our universe.
We study the behaviour of multiple radiative cooling algorithms implemented in seven Semi-Analytic Models (SAMs) of galaxy formation, including a new model we propose in this paper. We use versions of the models without feedback and apply them to dark matter haloes growing in a cosmological context, which have final masses that range from 10^{11}Msun to 10^{14}Msun. First, using simplified smoothly-growing halo models, we demonstrate that the different algorithms predict cooling rates and final cold gas masses that differ by a factor of ~5 for massive haloes (>10^{12}Msun). The algorithms are in better agreement for less massive haloes because they cool efficiently and, therefore, their cooling rates are largely limited by the halo accretion rate. However, for less massive haloes, all the SAMs predict less cooling than corresponding 1D hydrodynamic models. Second, we study the gas accretion history of the central galaxies of dark matter haloes using merger trees. The inclusion of mergers alters the cooling history of haloes by locking up gas in galaxies within small haloes at early times. For realistic halo models, the dispersion in the cold gas mass predicted by the algorithms is 0.5 dex for high mass haloes and 0.1 dex for low mass haloes, while the dispersion in the accretion rate is about two times larger. Comparing to cosmological SPH simulations, we find that most SAMs systematically under-predict the gas accretion rates for low-mass haloes but over-predict the gas accretion rates for massive haloes. Although the models all include both "rapid" and "slow" mode accretion, the transition between the two accretion modes varies between models and also differs from the simulations. Finally, we construct a new model that explicitly incorporates cold halo gas to illustrate that such a class of models can better match the results from cosmological hydrodynamic simulations.
The recent detection of the "cosmic dawn" redshifted 21 cm signal at 78 MHz by the EDGES experiment differs significantly from theoretical predictions. In particular, the absorption trough is roughly a factor of two stronger than the most optimistic theoretical models. The early interpretations of the origin of this discrepancy fall into two categories. The first is that there is increased cooling of the gas due to interactions with dark matter, while the second is that the background radiation field includes a contribution from a component in addition to the cosmic microwave background. In this paper we examine the feasibility of the second idea using new data from the first station of the Long Wavelength Array. The data span 40 to 80 MHz and provide important constraints on the present-day background in a frequency range where there are few surveys with absolute temperature calibration suitable for measuring the strength of the radio monopole. We find support for a strong, diffuse radio background that was suggested by the ARCARDE 2 results in the 3 to 10 GHz range. We find that this background is well modeled by a power law with a spectral index of $-$2.58$\pm$0.05 and a temperature at the rest frame 21 cm frequency of 603$^{+102}_{-92}$ mK.
We present new photometric and spectroscopic observations of an unusual luminous blue variable (LBV) in NGC 3432, covering three major outbursts in October 2008, April 2009 and November 2009. Previously, this star experienced an outburst also in 2000 (known as SN 2000ch). During outbursts the star reached an absolute magnitude between -12.1 and -12.8. Its spectrum showed H, He I and Fe II lines with P-Cygni profiles during and soon after the eruptive phases, while only intermediate-width lines in pure emission (including He II 4686A were visible during quiescence. The fast-evolving light curve soon after the outbursts, the quasi-modulated light curve, the peak magnitude and the overall spectral properties are consistent with multiple episodes of variability of an extremely active LBV. However, the widths of the spectral lines indicate unusually high wind velocities (1500-2800 km/s), similar to those observed in Wolf-Rayet stars. Although modulated light curves are typical of LBVs during the S-Dor variability phase, the luminous maxima and the high frequency of outbursts are unexpected in S-Dor variables. Such extreme variability may be associated with repeated ejection episodes during a giant eruption of an LBV. Alternatively, it may be indicative of a high level of instability shortly preceding the core-collapse or due to interaction with a massive, binary companion. In this context, the variable in NGC 3432 shares some similarities with the famous stellar system HD 5980 in the Small Magellanic Cloud, which includes an erupting LBV and an early Wolf-Rayet star.
Viscosity plays a critical role in determining the stability of rotating neutron stars. We report the results of a calculation of the shear viscosity of $\beta$~-~stable matter, carried out using an effective interaction based on a state-of-the-art nucleon-nucleon potential and the formalism of correlated basis functions. Within our approach the equation of state, determining the proton fraction, and the nucleon-nucleon scattering probability are consistently obtained from the same dynamical model. The results show that, while the neutron contribution to the viscosity is always dominant, above nuclear saturation density the electron contribution becomes appreciable.
Recently, deep learning has been widely used in the field of vehicle re-identification. When training a deep model, softmax loss is usually used as a supervision tool. However, the softmax loss performs well for closed-set tasks, but not very well for open-set tasks. In this paper, we sum up five shortcomings of center loss and solved all of them by proposing a dual distance center loss (DDCL). Especially we solve the shortcoming that center loss must combine with the softmax loss to supervise training the model, which provides us with a new perspective to examine the center loss. In addition, we verify the inconsistency between the proposed DDCL and softmax loss in the feature space, which makes the center loss no longer be limited by the softmax loss in the feature space after removing the softmax loss. To be specifically, we add the Pearson distance on the basis of the Euclidean distance to the same center, which makes all features of the same class be confined to the intersection of a hypersphere and a hypercube in the feature space. The proposed Pearson distance strengthens the intra-class compactness of the center loss and enhances the generalization ability of center loss. Moreover, by designing a Euclidean distance threshold between all center pairs, which not only strengthens the inter-class separability of center loss, but also makes the center loss (or DDCL) works well without the combination of softmax loss. We apply DDCL in the field of vehicle re-identification named VeRi-776 dataset and VehicleID dataset. And in order to verify its good generalization ability, we also verify it in two datasets commonly used in the field of person re-identification named MSMT17 dataset and Market1501 dataset.