ShantanuT01/DACTYL-Pretraining huggingface dataset:
We calculate the resonant x-ray scattering (RXS) spectra near the Ce $L_{\rm III}$ absorption edge in CeB$_6$, on the basis of a microscopic model that the $4f$ states of Ce are atomic while the $5d$ states form an energy band with a reasonable density of states. In the initial state, we employ an effective Hamiltonian of Shiina {\it et al}. in the antiferro-quadrupole (AFQ) ordering phase, while we construct the wave function consistent with the neutron scattering experiment in the magnetic ground state. In the intermediate state, we take full account of the intra-atomic Coulomb interaction. Without assuming any lattice distortion, we obtain sufficient RXS intensities on the AFQ superlattice spot. We obtain the spectral shape, the temperature and magnetic field dependences in good agreement with the experiment, thus demonstrating the mechanism that the intensity is brought about by the modulation of $5d$ states through the anisotropic term of the $5d$-$4f$ Coulomb interaction. In the magnetic ground state, a small pre-edge peak is found by the $E_2$ process. On the magnetic superlattice spot, we get a finite but considerably small intensity. The magnetic form factor is briefly discussed.
Let $P(T,X)$ be an irreducible polynomial in two variables with rational coefficients. It follows from Hilbert's Irreducibility Theorem that for most rational numbers $t$ the specialized polynomial $P(t,X)$ is irreducible and has the same Galois group as $P$. We discuss here a method for obtaining an explicit description of the set of exceptional numbers $t$, i.e., those for which $P(t,X)$ is either reducible or has a different Galois group than $P$. To illustrate the method we determine the exceptional specializations of two polynomials of degrees four and six.
In the framework of an equation of state (EoS) constructed from a momentum and density-dependent finite-range two-body effective interaction, the quantitative magnitudes of the different symmetry elements of infinite nuclear matter are explored. The parameters of this interaction are determined from well-accepted characteristic constants associated with homogeneous nuclear matter. The symmetry energy coefficient $a_2$, its density slope $L_0$, the symmetry incompressibility $K_\delta $ as well as the density dependent incompressibility $K(\rho )$ evaluated with this EoS are seen to be in good harmony with those obtained from other diverse perspectives. The higher order symmetry energy coefficients $a_4,~a_6$ etc are seen to be not very significant in the domain of densities relevant to finite nuclei, but gradually build up at supra-normal densities. The analysis carried with a Skyrme-inspired energy density functional obtained with the same input values for the empirical bulk data associated with nuclear matter yields nearly the same results.
We have identified 274 M-type Brown Dwarfs in the Hubble Space Telescope's Wide Field Camera 3 (WFC3) pure parallel fields from the Brightest of Reionizing Galaxies (BoRG) survey for high redshift galaxies. These are near-infrared observations with multiple lines-of-sight out of our Milky Way. Using these observed M-type Brown Dwarfs we fitted a Galactic disk and halo model with a Markov chain Monte Carlo (MCMC) analysis. This model worked best with the scale length of the disk fixed at $h$ = 2.6 kpc. For the scale height of the disk, we found $z_0 = 0.29^{+0.02}_{-0.019}$ kpc and for the central number density $\rho_0 = 0.29^{+0.20}_{-0.13}$ \#/pc$^3$. For the halo we derived a flattening parameter $\kappa$ = 0.45$\pm{0.04}$ and a power-law index $p$ = 2.4$\pm{0.07}$. We found the fraction of M-type brown dwarfs in the local density that belong to the halo to be $f_{h}$ = 0.0075$^{+0.0025}_{-0.0019}$. We found no correlation between subtype of M-dwarf and any model parameters.   The total number of M-type Brown Dwarfs in the disk and halo was determined to be $58.2^{+9.81}_{-6.70} \times10^{9}$. We found an upper limit for the fraction of M-type Brown Dwarfs in the halo of 7$^{+5}_{-4}$\%. The upper limit for the total Galactic Disk mass in M-dwarfs is $4.34^{+0.73}_{-0.5}\times10^{9}$ $M_{\odot}$, assuming all M-type Brown Dwarfs have a mass of $80 M_J$.
Inspired by the latest measurement of muon g-2 by the Fermilab Experiment, we revisit a class of supersymmetric models in which non-universality at M_GUT allows us to realize relatively light sleptons in the few hundred GeV range. These sleptons provide additional contributions to muon g-2 that can be arranged to reconcile theory and experiment. The solutions compatible with the muon g-2 resolution typically predict light sleptons, charginos and neutralinos. We show how these solutions can be probed during LHC-Run3. A direct impact on the chargino mass is observed such that the chargino can be probed up to about 800 GeV during the Run3 experiments. Despite such a direct impact, it is still possible to realize lighter chargino masses which can escape detection due to the chirality mixture of the lighter slepton states. The colored squarks as well as the gluino turn out to be heavier than about 3-4 TeV if the LSP neutralino satisfies the Planck bound on the dark matter relic abundance. We highlight a variety of benchmark points and, in particular, coannihilation scenarios with dark matter candidates that will be tested in the ongoing and planned direct and indirect detection experiments. By relaxing the requirement that the LSP neutralino saturates the relic dark matter abundance, we are able to find solutions with gluino and squark masses in a range that may be accessible at LHC-Run3.
In this paper, we present a novel differential morph detection framework, utilizing landmark and appearance disentanglement. In our framework, the face image is represented in the embedding domain using two disentangled but complementary representations. The network is trained by triplets of face images, in which the intermediate image inherits the landmarks from one image and the appearance from the other image. This initially trained network is further trained for each dataset using contrastive representations. We demonstrate that, by employing appearance and landmark disentanglement, the proposed framework can provide state-of-the-art differential morph detection performance. This functionality is achieved by the using distances in landmark, appearance, and ID domains. The performance of the proposed framework is evaluated using three morph datasets generated with different methodologies.
We develop a new sub-grid model for the growth of supermassive Black Holes (BHs) and their associated Active Galactic Nuclei (AGN) feedback in hydrodynamical cosmological simulations. Assuming that BHs are created in the early stages of galaxy formation, they grow by mergers and accretion of gas at a Eddington-limited Bondi accretion rate. However this growth is regulated by AGN feedback which we model using two different modes: a quasar-heating mode when accretion rates onto the BHs are comparable to the Eddington rate, and a radio-jet mode at lower accretion rates. In other words, our feedback model deposits energy as a succession of thermal bursts and jet outflows depending on the properties of the gas surrounding the BHs. We assess the plausibility of such a model by comparing our results to observational measurements of the coevolution of BHs and their host galaxy properties, and check their robustness with respect to numerical resolution. We show that AGN feedback must be a crucial physical ingredient for the formation of massive galaxies as it appears to be the only physical mechanism able to efficiently prevent the accumulation of and/or expel cold gas out of halos/galaxies and significantly suppress star formation. Our model predicts that the relationship between BHs and their host galaxy mass evolves as a function of redshift, because of the vigorous accretion of cold material in the early Universe that drives Eddington-limited accretion onto BHs. Quasar activity is also enhanced at high redshift. However, as structures grow in mass and lose their cold material through star formation and efficient BH feedback ejection, the AGN activity in the low-redshift Universe becomes more and more dominated by the radio mode, which powers jets through the hot circum-galactic medium.
Deep Neural Networks (DNNs) have revolutionized computer vision. We now have DNNs that achieve top (performance) results in many problems, including object recognition, facial expression analysis, and semantic segmentation, to name but a few. The design of the DNNs that achieve top results is, however, non-trivial and mostly done by trail-and-error. That is, typically, researchers will derive many DNN architectures (i.e., topologies) and then test them on multiple datasets. However, there are no guarantees that the selected DNN will perform well in the real world. One can use a testing set to estimate the performance gap between the training and testing sets, but avoiding overfitting-to-the-testing-data is almost impossible. Using a sequestered testing dataset may address this problem, but this requires a constant update of the dataset, a very expensive venture. Here, we derive an algorithm to estimate the performance gap between training and testing that does not require any testing dataset. Specifically, we derive a number of persistent topology measures that identify when a DNN is learning to generalize to unseen samples. This allows us to compute the DNN's testing error on unseen samples, even when we do not have access to them. We provide extensive experimental validation on multiple networks and datasets to demonstrate the feasibility of the proposed approach.
The expected distribution of Cepheids within the instability strip is affected by several model inputs, reflecting upon the predicted Period-Luminosity relation. On the basis of new and updated sets of evolutionary and pulsational models, we quantitatively evaluated the effects on the theoretical PL relation of current uncertainties on the chemical abundances of Cepheids in the Large Magellanic Cloud and on several physical assumptions adopted in the evolutionary models. We analysed how the different factors influence the evolutionary and pulsational observables and the resulting PL relation. As a result, we found that present uncertainties on the most relevant H and He burning reaction rates do not influence in a relevant way the loop extension in temperature. On the contrary, current uncertainties on the LMC chemical composition significantly affect the loop extension and also reflect in the morphology of the instability strip; however their influence on the predicted pulsational parameters is negligible. We also discussed how overshooting and mass loss influence the ML relation and the pulsational parameters. In summary, the present uncertainties on the physical inputs adopted in the evolutionary codes and in the LMC chemical composition are negligible for the prediction of the main pulsational properties; the inclusion of overshooting in the previous H burning phase and/or of mass loss is expected to significantly change the resulting theoretical pulsational scenario for Cepheids, as well as the calibration of their distance scale. These systematic effects are expected to influence the theoretical Cepheid calibration of the secondary distance indicators and in turn the resulting evaluation of the Hubble constant.
We are interested here in a birth-and-growth process where germs are born according to a Poisson point process with invariant under translation in space intensity measure. The germs can be born in free space and then start growing until occupying the available space. In order to consider various way of growing, we describe the crystals at each time through their geometrical properties. In this general framework, the crystallization process can be caracterized by the random field giving for a point in the space state the first time this point is reached by a crystal. We prove under general conditions that this random field is mixing in the sens of ergodic theory and obtain estimates for the coefficient of absolute regularity.
In the present paper we prove a certain lemma about the structure of "lower level-sets of convolutions", which are sets of the form $\{x \in \Z_N : 1_A*1_A(x) \leq \gamma N\}$ or of the form $\{x \in \Z_N : 1_A*1_A(x) < \gamma N\}$, where $A$ is a subset of $\Z_N$. One result we prove using this lemma is that if $|A| = \theta N$ and $|A+A| \leq (1-\eps) N$, $0 < \eps < 1$, then this level-set contains an arithmetic progression of length at least $N^c$, $c = c(\theta, \eps,\gamma) > 0$. It is perhaps possible to obtain such a result using Green's arithmetic regularity lemma (in combination with some ideas of Bourgain); however, our method of proof allows us to obtain non-tower-type quantitative dependence between the constant $c$ and the parameters $\theta$ and $\eps$. For various reasons (discussed in the paper) one might think, wrongly, that such results would only be possible for level-sets involving triple and higher convolutions.
We present a scheme for multipartite entanglement purification of quantum systems in a Greenberger-Horne-Zeilinger state with quantum nondemolition detectors (QNDs). This scheme does not require the controlled-not gates which cannot be implemented perfectly with linear optical elements at present, but QNDs based on cross-Kerr nonlinearities. It works with two steps, i.e., the bit-flipping error correction and the phase-flipping error correction. These two steps can be iterated perfectly with parity checks and simple single-photon measurements. This scheme does not require the parties to possess sophisticated single photon detectors. These features maybe make this scheme more efficient and feasible than others in practical applications.
We study the images of tautological bundles on Hilbert schemes of points on surfaces and their wedge powers under the derived McKay correspondence. The main observation of the paper is that using a derived equivalence differing slightly from the standard one considerably simplifies both the results and their proofs. As an application, we obtain shorter proofs for known results as well as new formulae for homological invariants of tautological sheaves. In particular, we compute the extension groups between wedge powers of tautological bundles associated to line bundles on the surface.
We study the collapse transition of a polymer on a square lattice with both nearest-neighbor and next nearest-neighbor interactions, by calculating the exact partition function zeros up to chain length 36. The transition behavior is much more pronounced than that of the model with nearest-neighbor interactions only. The crossover exponent and the transition temperature are estimated from the scaling behavior of the first zeros with increasing chain length. The results suggest that the model is of the same universality class as the usual theta point described by the model with only nearest-neighbor interaction.
In this paper we analyze the spin-wave excitations (magnons) of an inhomogeneous spin system within the Boltzmann-Gibbs framework and then connect the results with the nonextensive approach (in the sense of Tsallis statistics). Considering an equivalence between those two frameworks, we could connect the entropic parameter q with moments of the distribution of exchange integrals of the inhomogenous system. It ratifies the idea that the entropic parameter is connected to the microscopic properties of the system.
We prove a general family of congruences for Bernoulli numbers whose index is a polynomial function of a prime, modulo a power of that prime. Our family generalizes many known results, including the von Staudt--Clausen theorem and Kummer's congruence.
Compactness is one of the most versatile tools in the analysis of nonlinear PDEs and systems. Usually, compactness is established by means of some embedding theorem between functional spaces. Such theorems, in turn, rely on appropriate estimates for a function and its derivatives. While a similar result based on simultaneous estimates for the Malliavin and weak Sobolev derivatives is available for the Wiener-Sobolev spaces, it seems that it has not yet been widely used in the analysis of highly nonlinear parabolic problems with stochasticity. In the present work we apply this result in order to study compactness, existence of global solutions, and, as a by-product, the convergence of a semi-discretisation scheme for a prototypical degenerate PDE-SDE coupling.
An analytical formula is derived for particle and energy densities of fermions and bosons, and their ballistic momentum and energy currents for anisotropic energy dispersions in generalized dimensions. The formulation considerably simplifies the comparison of the statistical properties and ballistic particle and energy transport currents of electrons, acoustic phonons, and photons in various dimensions in a unified manner. Assorted examples of its utility are discussed, ranging from blackbody radiation to Schottky diodes and ballistic transistors, quantized electrical and thermal conductance, generalized ballistic Seebeck and Peltier coefficients, their Onsager relations, the generalized Wiedemann-Franz law and the robustness of the Lorenz number, and ballistic thermoelectric power factors, all of which are obtained from the single formula. The new formulation predicts a thermoelectric power factor behaviour of 3D Dirac bands which has not been observed yet.
A lot of research is focused on all-optical signal processing, aiming to obtain effective alternatives to existing data transmission platforms. Amplification of light in fiber optics, such as in Erbium-doped fiber amplifiers, is especially important for an efficient signal transmission. However, the complex fabrication methods, involving high-temperature processes performed in highly pure environment, slow down the fabrication and make amplified components expensive with respect to an ideal, high-throughput and room temperature production. Here, we report on near infrared polymer fiber amplifiers, working over a band of about 20 nm. The fibers are cheap, spun with a process entirely carried out at room temperature, and show amplified spontaneous emission with good gain coefficients as well as low optical losses (a few cm^-1). The amplification process is favoured by the high fiber quality and low self-absorption. The found performance metrics promise to be suitable for short-distance operation, and the large variety of commercially-available doping dyes might allow for effective multi-wavelength operation by electrospun amplified fiber optics.
In the framework of a QCD relativistic potential model we evaluate the form factors describing the exclusive decay B => \pi\pi \ell \nu. The calculation is performed in a phase space region far away from the resonances and therefore is complementary to other decay mechanisms where the pions are produced by intermediate particles, e.g. in the chiral approach. We give an estimate of the contribution of the non resonant channel of the order of BR(B- => \pi+ \pi- \ell \nu) \approx 2.2 x 10^(-4).
We study the thermal partition function of Jackiw-Teitelboim (JT) gravity in asymptotically Euclidean $AdS_2$ background using the matrix model description recently found by Saad, Shenker and Stanford [arXiv:1903.11115]. We show that the partition function of JT gravity is written as the expectation value of a macroscopic loop operator in the old matrix model of 2d gravity in the background where infinitely many couplings are turned on in a specific way. Based on this expression we develop a very efficient method of computing the partition function in the genus expansion as well as in the low temperature expansion by making use of the Korteweg-de Vries constraints obeyed by the partition function. We have computed both these expansions up to very high orders using this method. It turns out that we can take a low temperature limit with the ratio of the temperature and the genus counting parameter held fixed. We find the first few orders of the expansion of the free energy in a closed form in this scaling limit. We also study numerically the behavior of the eigenvalue density and the Baker-Akhiezer function using the results in the scaling limit.
We investigate the effect of pulsar polar cap (PC) heating produced by positrons returning from the upper pair formation front. Our calculations are based on a self-consistent treatment of the pair dynamics and the effect of electric field screening by the returning positrons. We calculate the resultant X-ray luminosities, and discuss the dependence of the PC heating efficiencies on pulsar parameters, such as characteristic spin-down age, spin period, and surface magnetic field strength. In this study we concentrate on the regime where the pairs are produced in a magnetic field by curvature photons emitted by accelerating electrons. Our theoretical results are not in conflict with the available observational X-ray data and suggest that the effect of PC heating should significantly contribute to the thermal X-ray fluxes from middle-aged and old pulsars. The implications for current and future X-ray observations of pulsars are briefly outlined.
Applying the main results of math.AG/0408295, we identify the motives occurring as cones in the co-localization and localization filtrations of the boundary motive of a Shimura variety.
The dominant rational maps of finite degree from a fixed variety to varieties of general type, up to birational isomorphisms, form a finite set. This has been known as the Iitaka-Severi conjecture, and is nowdays an established result, in virtue of some recent advances in the theory of pluricanonical maps. We study the question of finding some effective estimate for the finite number of maps, and to this aim we provide some update and refinement of the classical treatment of the subject.
We first review the results of the tidal stirring model for the transformation of gas-rich dwarf irregulars into dwarf spheroidals, which turns rotationally supported stellar systems into pressure supported ones. We emphasize the importance of the combined effect of ram pressure stripping and heating from the cosmic ultraviolet background in removing the gas and converting the object into a gas poor system as dSphs. We discuss how the timing of infall of dwarfs into the primary halo determines the final mass-to-light ratio and star formation history. Secondly we review the results of recent cosmological simulations of the formation of gas-rich dwarfs. These simulations are finally capable to produce a realistic object with no bulge, an exponential profile and a slowly rising rotation curve. The result owes to the inclusion of an inhomogeneous ISM and a star formation scheme based on regions having the typical density of molecular cloud complexes. Supernovae-driven winds become more effective in such mode, driving low angular momentum baryons outside the virial radius at high redshift and turning the dark matter cusp into a core. Finally we show the first tidal stirring experiments adopting dwarfs formed in cosmological simulations as initial conditions. The latter are gas dominated and have have turbulent thick gaseous and stellar disks disks that cannot develop strong bars, yet they are efficiently heated into spheroids by tidal shocks.