ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let G be a split semisimple linear algebraic group over a field k0. Let E be a G-torsor over a field extension k of k0. Let h be an algebraic oriented cohomology theory in the sense of Levine-Morel. Consider a twisted form E/B of the variety of Borel subgroups G/B over k.   Following the Kostant-Kumar results on equivariant cohomology of flag varieties we establish an isomorphism between the Grothendieck groups of the h-motivic subcategory generated by E/B and the category of finitely generated projective modules of certain Hecke-type algebra H which depends on the root datum of G, on the torsor E and on the formal group law of the theory h.   In particular, taking h to be the Chow groups with finite coefficients Fp and E to be a generic G-torsor we prove that all indecomposable submodules of an affine nil-Hecke algebra H of G with coefficients in Fp are isomorphic to each other and correspond to the (non-graded) generalized Rost-Voevodsky motive for (G,p).
Configurations of the molecules on the wall of a vacancy, formed by removing a central and its first and second nearest-neighbor (NN) molecules in solid CO2 with the Pa3 structure, were calculated by the Monte Carlo simulation technique at T = 0, 100, and 200 K and a nominal pressure of P = 1 bar. It was found that the deviations of both the center-of-mass and the orientational coordinates of the molecules from the unperturbed coordinates had a three-fold symmetry about a body diagonal axis of the crystal. It was also found that a single CO2 molecule, initially placed in the center of the vacancy, was stabilized at a position close to the vacancy wall. This paper is a continuation of arXiv:1711.04976 [cond-mat.mtrl-sci] (2017) and arXiv:1809.04291 [cond-mat.mtrl-sci] (2018).
We measure the neutral absorption towards the black hole X-ray binary system LMC X-1 from six archival soft X-ray spectra obtained with the gratings and/or CCD detectors on Chandra, XMM-Newton, and Swift. Four spectral models for the soft continuum have been investigated. While the powerlaw model may overestimate NH considerably, the others give consistent results. Taking the lower metalicity of the Large Magellanic Cloud into account, we find equivalent hydrogen column densities of N_H = (1.0-1.3)*10^22 cm^-2, with a systematic dependence on the orbital phase. This variation of the neutral absorption can nearly explain the orbital modulation of the soft X-ray flux recently detected with the All Sky Monitor (ASM) on the Rossi X-ray Timing Explorer (RXTE).
We study the optimal stopping time problem $v(S)={\rm ess}\sup_{\theta \geq S} E[\phi(\theta)|\mathcal {F}_S]$, for any stopping time $S$, where the reward is given by a family $(\phi(\theta),\theta\in\mathcal{T}_0)$ \emph{of non negative random variables} indexed by stopping times. We solve the problem under weak assumptions in terms of integrability and regularity of the reward family. More precisely, we only suppose $v(0) < + \infty$ and $ (\phi(\theta),\theta\in \mathcal{T}_0)$ upper semicontinuous along stopping times in expectation. We show the existence of an optimal stopping time and obtain a characterization of the minimal and the maximal optimal stopping times. We also provide some local properties of the value function family. All the results are written in terms of families of random variables and are proven by only using classical results of the Probability Theory.
This paper provides a construction of a Fleming--Viot measure valued diffusion process, for which the transition function is known, by extending recent ideas of the Gibbs sampler based Markov processes. In particular, we concentrate on the Chapman--Kolmogorov consistency conditions which allows a simple derivation of such a Fleming--Viot process, once a key and apparently new combinatorial result for P\'{o}lya-urn sequences has been established.
We investigate the process of an inhomogeneous planetesimal disk evolution caused by the planetesimal-planetesimal gravitational scattering. We develop a rather general approach based on the kinetic theory which self-consistently describes the evolution in time and space of both the disk surface density and its kinematic properties -- dispersions of eccentricity and inclination. The gravitational scattering of planetesimals is assumed to be in the dispersion-dominated regime which considerably simplifies analytical treatment. The resultant equations are of advection-diffusion type. Distance dependent scattering coefficients entering these equations are calculated analytically under the assumption of two-body scattering in the leading order in Coulomb logarithm. They are essentially nonlocal in nature. Our approach allows one to explore the dynamics of nonuniform planetesimal disks with arbitrary mass and random velocity distributions. It can also naturally include other physical mechanisms which are important for the evolution of such disks -- gas drag, migration, and so on.
We elaborate the problem of energy-momentum in general relativity by energy-momentum prescriptions theory. In this regard, we calculate M\oller,Landau-Lifshitz, Papapetrou, Einstein, Bergman, Tolman, and Weinberg's energy-momentum complexes in static and nonstatic cosmic string space-times. We obtain strong coincidences between the results. These coincidences can be considered as an extension of Virbhadra's viewpoint that different energy-momentum prescriptions may provide some basis to define a unique quantity. In addition, our results disagree with Lessner's belief about M\oller's prescription and support the Virbhadra's conclusion about the power of Einstein's prescription.
We argue that the emission and the absorption components of he N II lines recently observed in Eta Carinae can originate in the secondary's wind acceleration zone. We base this claim in part on the presence of these lines in hot nitrogen rich stars, such as WN 8 stars, and on the expected clumpy nature of such winds. The envelope of the secondary star in Eta Carinae is expected to be nitrogen rich due to accretion of few solar masses of the primary luminous blue variable's nitrogen rich material during the nineteenth century Great Eruption. Another argument in support of N II lines origin in the acceleration zone of the secondary wind is the behavior of the emission components. The emission components of the lines show the same Doppler shift variation as that of the absorption components. The secondary's-wind origin of the N II lines is compatible with the binary orientation in which the secondary is closer to us near periastron passage.
The analysis of tagged B_s -> J/psi phi decays determines the CP phase phi_s in B_s-anti-B_s mixing with a two-fold ambiguity. The solutions differ in the sign of cos(phi_s) which equals the sign of the width difference Delta Gamma_s among the two B_s mass eigenstates. We point out that this ambiguity can be removed with the help of B_s -> D_s K decays. We compare untagged and tagged strategies and find the tagged analysis more promising. The removal of the sign ambiguity in Delta Gamma_s can be done with relatively low statistics and could therefore be a target for the early stage of B_s -> D_s K studies.
CeB(6) is a model compound exhibiting antiferroquadrupolar (AFQ) order, its magnetic properties being typically interpreted within localized models. More recently, the observation of strong and sharp magnetic exciton modes forming in its antiferromagnetic (AFM) state at both ferromagnetic and AFQ wave vectors suggested a significant contribution of itinerant electrons to the spin dynamics. Here we investigate the evolution of the AFQ excitation upon the application of an external magnetic field and the substitution of Ce with non-magnetic La, both parameters known to suppress the AFM phase. We find that the exciton energy decreases proportionally to T_N upon doping. In field, its intensity is suppressed, while its energy remains constant. Its disappearance above the critical field of the AFM phase is preceded by the formation of two modes, whose energies grow linearly with magnetic field upon entering the AFQ phase. These findings suggest a crossover from itinerant to localized spin dynamics between the two phases, the coupling to heavy-fermion quasiparticles being crucial for a comprehensive description of the magnon spectrum.
Using the amplification technique, we prove that `mass' of the pullback of the Saito-Kurokawa lift of a Hecke eigen form $g\in S_{2k}$ is bounded by $k^{1-\frac{1}{210}+\epsilon}$. This improves the previously known bound $k$ for this quantity.
The next decade will be an exciting time for computational physicists. After 50 years of being forced to use standardized commercial equipment, it will finally become relatively straightforward to adapt one's computing tools to one's own needs. The breakthrough that opens this new era is the now wide-spread availability of programmable chips that allow virtually every computational scientist to design his or her own special-purpose computer.
This is not a research article. This is a partial version of a mini-cours which I gave at a meeting of the ACI Jeunes Chercheurs "Dynamique des applications polynomiales" in Toulouse in november 2004. This text includes two parts of that mini-cours: the first one collects some preliminaries on Fano threefolds with cyclic Picard group, the second one discusses some methods to obtain bounds for the degree of a morphism onto such a Fano threefold (different from projective space). The mini-cours also had a third part - the boundedness theorem of Hwang and Mok for morphisms between Fano manifolds which have rational curves with trivial normal bundles; this part is not included here, as the Hwang and Mok's paper in Journal of Algebraic Geometry 12 (2003) is concise, clear and self-contained.
We present a model describing the dark sector (DS) featured by two interactions remaining efficient until late times in the matter-dominated era after recombination: the interaction among dark radiations (DR), and the interaction between a small fraction of dark matter and dark radiation. The dark sector consists of (1) a dominant component cold collisionless DM (DM1), (2) a sub-dominant cold DM (DM2) and (3) a self-interacting DR. When a sufficient amount of DR is ensured and a few percent of the total DM density is contributed by DM2 interacting with DR, this set-up is known to be able to resolve both the Hubble and $\sigma_{8}$ tension. In light of this, we propose a scenario which is logically natural and has an intriguing theoretical structure with a hidden unbroken gauge group ${\rm SU}(5)_{\rm X}\otimes {\rm U}(1)_{\rm X}$. Our model of the dark sector does not introduce any new scalar field, but contains only massless chiral fermions and gauge fields in the ultraviolet (UV) regime. As such, it introduces a new scale (DM2 mass, $m_{\rm DM2}$) based on the confinement resulting from the strong dynamics of ${\rm SU}(5)_{\rm X}$. Both DM2-DR and DR-DR interactions are attributed to an identical long range interaction of ${\rm U}(1)_{\rm X}$. We show that our model can address the cosmological tensions when it is characterized by $g_{\rm X}=\mathcal{O}(10^{-3})-\mathcal{O}(10^{-2})$, $m_{\rm DM2}=\mathcal{O}(1)-\mathcal{O}(100){\rm GeV}$ and $T_{\rm DS}/T_{\rm SM}\simeq0.3-0.4$ where $g_{\rm X}$ is the gauge coupling of ${\rm U}(1)_{\rm X}$ and $T_{\rm DS}$ ($T_{\rm SM}$) is a temperature of the DS (Standard Model sector). Our model explains candidates of DM2 and DR, and DM1 can be any kind of CDM.
It is shown that in a rational conformal field theory every torus one-point function of a given highest weight state satisfies a modular differential equation. We derive and solve these differential equations explicitly for some Virasoro minimal models. In general, however, the resulting amplitudes do not seem to be expressible in terms of standard transcendental functions.
Based on density functional theory the noncentrosymmetric superconductor Mo_3Al_2C in its well established {\beta}-Mn type ($P4_{1}32$) crystal structure is investigated. In particular, its thermodynamical and dynamical stabilities are studied by calculating lattice vibrations within the harmonic approximation. It is found that the fully stoichiometric compound is dynamically unstable. However, compounds with carbon vacancies, i.e., Mo_3Al_2C_{1-x}, can be dynamically stabilized for vacancy concentrations x > 0.09. By means of a simple thermodynamical model we estimate x ~ 0.13-0.14 for Mo_3Al_2C_{1-x} at the experimental preparation temperatures. The influence of the carbon vacancy concentration on the electronic structure is investigated.
The knowledge of electron g factor is essential for spin manipulation in the field of spintronics and quantum computing. While there exist technical difficulties in determining the sign of g factor in semiconductors by the established magneto-optical spectroscopic methods. We develop a time resolved Kerr rotation technique to precisely measure the sign and the amplitude of electron g factor in semiconductors.
In this paper, we introduce the STN-Homography model to directly estimate the homography matrix between image pair. Different most CNN-based homography estimation methods which use an alternative 4-point homography parameterization, we use prove that, after coordinate normalization, the variance of elements of coordinate normalized $3\times3$ homography matrix is very small and suitable to be regressed well with CNN. Based on proposed STN-Homography, we use a hierarchical architecture which stacks several STN-Homography models and successively reduce the estimation error. Effectiveness of the proposed method is shown through experiments on MSCOCO dataset, in which it significantly outperforms the state-of-the-art. The average processing time of our hierarchical STN-Homography with 1 stage is only 4.87 ms on the GPU, and the processing time for hierarchical STN-Homography with 3 stages is 17.85 ms. The code will soon be open sourced.
We have used density functional theory to study the energetics and electronic structure of aluminium dopants in crystalline silicon. We present data regarding the atomic and electronic structure and properties of pairs of substitutional aluminium dopants. We find that pairs of dopants, when occupying nearest neighbouring subsitutional sites in a high spin state, can bond to form aluminium pairs. This suggests that such a configuration of dopants will be electrically active when made to occupy a high spin state, whereas in the low spin state the neighbouring dopant pairs are found to be self compensating.
We analyze the phase diagram of multilayer-graphene sandwiched between identical transition metal dichalcogenides. Recently realized in all van-der-Wall heterostructures, these sandwiches induce sizable (1-15 meV) spin orbit coupling in the graphene, offering a way to engineer topological band-structures in a pristine and gate-tunable platform. We find a rich phase diagram that depends on the number of layers $N$ and the gate-tunable perpendicular electric field. For $N > 1$ and odd, the system is a strong 2D topological insulator with a gap equal to the strength of proximity-induced Ising spin-orbit coupling, which reverts to a trivial phase at moderate electric fields. For $N$-even, the low energy bands exhibit a recently proposed form of "fragile" crystalline topology, as well as electric-field tuned symmetry-protected phase transitions between distinct atomic insulators. Hence AB-stacked bilayer and ABC-stacked trilayer graphene are predicted to provide controllable experimental realizations of fragile and strong topology.
We introduce a notion of nonlinear expectation --G--expectation-- generated by a nonlinear heat equation with infinitesimal generator G. We first discuss the notion of G-standard normal distribution. With this nonlinear distribution we can introduce our G-expectation under which the canonical process is a G--Brownian motion. We then establish the related stochastic calculus, especially stochastic integrals of Ito's type with respect to our G--Brownian motion and derive the related Ito's formula. We have also give the existence and uniqueness of stochastic differential equation under our G-expectation. As compared with our previous framework of g-expectations, the theory of G-expectation is intrinsic in the sense that it is not based on a given (linear) probability space.
Our knowledge of the Galaxy is being revolutionised by a series of photometric, spectroscopic and astrometric surveys. Already an enormous body of data is available from completed surveys, and data of ever increasing quality and richness will accrue at least until the end of this decade. To extract science from these surveys we need a class of models that can give probability density functions in the space of the observables of a survey -- we should not attempt to "invert" the data from the space of observables into the physical space of the Galaxy. Currently just one class of model has the required capability, so-called "torus models". A pilot application of torus models to understanding the structure of the Galaxy's thin and thick discs has already produced two significant results: a major revision of our best estimate of the Sun's velocity with respect to the Local Standard of Rest, and a successful prediction of the way in which the vertical velocity dispersion in the disc varies with distance from the Galactic plane.
Finite amplitude method based on the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc-FAM) is developed and applied to study isoscalar giant monopole resonance in exotic nuclei. Validation of the numerical implementation is examined for $^{208}\textrm{Pb}$. The isoscalar giant monopole resonances for even-even calcium isotopes from $^{40}\textrm{Ca}$ to the last bound neutron-rich nucleus $^{80}\textrm{Ca}$ are calculated, and a good agreement with the available experimental centroid energies is obtained for $^{40-48}\textrm{Ca}$. For the exotic calcium isotopes, e.g., $^{68}\textrm{Ca}$ and $^{80}\textrm{Ca}$, the DRHBc-FAM calculated results are closer to the energy weighted sum rule than the calculations on the harmonic oscillator basis, which highlights the advantages of DRHBc-FAM in describing giant resonances for exotic nuclei. In order to explore the soft monopole mode in the exotic nuclei, the giant monopole resonance for the deformed exotic nucleus $^{200}\textrm{Nd}$ is investigated, where the prolate shape and the oblate shape coexist. A soft monopole mode near 6.0 MeV is found in the prolate case, and another one near 4.5 MeV is found in the oblate case. The transition density of the soft monopole mode shows in phase or out-of-phase vibrations near the surface region, which is generated by quadrupole vibrations.
The spin-1 Heisenberg model on a triangular lattice with the ferromagnetic nearest, $J_1=-(1-p)J,$ $J>0$, and antiferromagnetic third-nearest-neighbor, $J_3=pJ$, exchange interactions is studied in the range of the parameter $0 \leqslant p \leqslant 1$. Mori's projection operator technique is used as a method, which retains the rotation symmetry of spin components and does not anticipate any magnetic ordering. For zero temperature several phase transitions are observed. At $p\approx 0.2$ the ground state is transformed from the ferromagnetic spin structure into a disordered state, which in its turn is changed to an antiferromagnetic long-range ordered state with the incommensurate ordering vector ${\bf Q = Q^\prime} \approx (1.16, 0)$ at $p\approx 0.31$. With the further growth of $p$ the ordering vector moves along the line ${\bf Q^\prime-Q_c}$ to the commensurate point ${\bf Q_c}=(\frac{2\pi}{3}, 0)$, which is reached at $p = 1$. The final state with an antiferromagnetic long-range order can be conceived as four interpenetrating sublattices with the $120^\circ$ spin structure on each of them. Obtained results are used for interpretation of the incommensurate magnetic ordering observed in NiGa$_2$S$_4$.
The double pulsar J0737-3039A/B is a unique system with which to test gravitational theories in the strong-field regime. However, the accuracy of such tests will be limited by knowledge of the distance and relative motion of the system. Here we present very long baseline interferometry observations which reveal that the distance to PSR J0737-3039A/B is 1150+220-160 pc, more than double previous estimates, and confirm its low transverse velocity (~9 km/s). Combined with a decade of pulsar timing, these results will allow tests of gravitational radiation emission theories at the 0.01% level, putting stringent constraints on theories which predict dipolar gravitational radiation. They also allow insight into the system's formation and the source of its high-energy emission.
Let $\sigma(n)$ be the sum of the positive divisors of $n$, and let $A(t)$ be the natural density of the set of positive integers $n$ satisfying $\sigma(n)/n \ge t$. We give an improved asymptotic result for $\log A(t)$ as $t$ grows unbounded. The same result holds if $\sigma(n)/n$ is replaced by $n/\phi(n)$, where $\phi(n)$ is Euler's totient function.
Recent studies of the circumgalactic gaseous environment of the Milky Way have concentrated on the distribution, chemical composition, and physical properties of the most massive neutral gas clouds and the highly-ionized halo absorbers. Relatively little effort has been put so far in exploring the circumgalactic neutral and weakly ionized metal absorbers at low HI column densities.   With our work we systematically study the distribution and physical properties of neutral and ionised low-column density gas in the halo of the Milky Way. We combine CaII and NaI absorption line measurements with HI 21-cm emission line data. For some of the sight lines high-resolution radio synthesis observations were performed allowing us to study small-scale structures that cannot be resolved with single dish telescopes.   In total 177 lines of sight were observed, providing a large absorption-selected data sample for the analysis of IVC and HVC gas in the circumgalactic environment of the Milky Way. The study allows us to compare the observed absorption column density distribution (CDD) of gas in the Milky Way halo with the overall CDD of intervening absorbers towards quasars. The sensitive absorption line analysis enables us to identify the neutral and ionised gaseous structures at low column densities and small angular extent that possibly remain unseen in large 21-cm all-sky surveys. If this gas cover a significant portion of the sky, it possibly has a large influence on the evolution of the Milky Way.
The process $e^+e^-\to H t\bar t$ can be used at the Next Linear Collider to measure the Higgs-top Yukawa coupling. In this paper, we compute $2\to 8$ processes of the form $e^+e^-\to b\bar b b\bar b W^+W^-\to b\bar b b\bar b \ell^\pm\nu_\ell q\bar q'$, accounting for the Higgs-top-antitop signal as well as several irreducible backgrounds in the semi-leptonic top-antitop decay channel. We restrict ourselves to the case of a light Higgs boson in the range 100 GeV $\le M_H \le$ 140 GeV. We use helicity amplitude techniques to compute exactly such processes at tree level in the framework of the Standard Model. Total rates and differential spectra of phenomenological interest are given and discussed