ShantanuT01/DACTYL-Pretraining huggingface dataset:
By using the Sloan Digital Sky Survey (SDSS) first year type Ia supernova (SN Ia) compilation, we compare two different approaches (traditional \chi^2 and complete likelihood) to determine parameter constraints when the magnitude dispersion is to be estimated as well. We consider cosmological constant + Cold Dark Matter (\Lambda CDM) and spatially flat, constant w Dark Energy + Cold Dark Matter (FwCDM) cosmological models and show that, for current data, there is a small difference in the best fit values and $\sim$ 30% difference in confidence contour areas in case the MLCS2k2 light-curve fitter is adopted. For the SALT2 light-curve fitter the differences are less significant ($\lesssim$ 13% difference in areas). In both cases the likelihood approach gives more restrictive constraints. We argue for the importance of using the complete likelihood instead of the \chi^2 approach when dealing with parameters in the expression for the variance.
We numerically and analytically calculate the properties of the bipolaron in an extended Hubbard Holstein model, which has a longer range electron-phonon coupling like the Fr\" ohlich model. In the strong coupling regime, the effective mass of the bipolaron in the extended model is much smaller than the Holstein bipolaron mass. In contrast to the Holstein bipolaron, the bipolaron in the extended model has a lower binding energy and remains bound with substantial binding energy even in the large-U limit. In comparison with the Holstein model where only a singlet bipolaron is bound, in the extended Holstein model a triplet bipolaron can also form a bound state. We discuss the possibility of phase separation in the case of finite electron doping.
We derive necessary-and-sufficient conditions on characteristic initial data for Friedrich's conformal field equations in $3+1$ dimensions to have no logarithmic terms in an asymptotic expansion at null infinity.
Observations of the Vela pulsar-wind nebula (PWN) with the Chandra X-ray Observatory have revealed a complex, variable PWN structure, including inner and outer arcs, a jet in the direction of the pulsar's proper motion, and a counter-jet in the opposite direction, embedded in diffuse nebular emission.   From the analysis of thirteen Chandra observations spread over about 2.5 years we found that this outer jet shows particularly strong variability, changing its shape and brightness. We observed bright blobs in the outer jet moving away from the pulsar with apparent speeds (0.3-0.6)c and fading on time-scales of days to weeks. The spectrum of the outer jet fits a power-law model with a photon index of 1.3. The X-ray emission of the outer jet can be interpreted as synchrotron radiation of ultrarelativistic electrons/positrons. This interpretation allows one to estimate the magnetic field, ~100 microGauss, maximum energy of X-ray emitting electrons, $2 \times 10^{14}$ eV, and energy injection rate, $8\times 10^{33}$ erg/s, for the outer jet. In the summed PWN image, we see a faint, strongly bent, extension of the outer jet. The more extreme bends closer to the pulsar, as well as the apparent side motions of the outer jet, can be associated with kink instabilities of a magnetically confined, pinched jet flow. Another feature found in the summed image is a dim, 2'-long outer counter-jet, which also shows a power-law spectrum with photon index of 1.2-1.5. Southwest of the jet/counter-jet (i.e., approximately perpendicular to the direction of pulsar's proper motion), an extended region of diffuse emission is seen. Relativistic particles responsible for this radiation are apparently supplied by the outer jet.
We derive a system of stochastic partial differential equations satisfied by the eigenvalues of the symmetric matrix whose entries are the Brownian sheets. We prove that the sequence $\left\{L_{d}(s,t), (s,t)\in[0,S]\times [0,T]\right\}_{d\in\mathbb N}$ of empirical spectral measures of the rescaled matrices is tight on $C([0,S]\times [0,T], \mathcal P(\mathbb R))$ and hence is convergent as $d$ goes to infinity by Wigner's semicircle law. We also obtain PDEs which are satisfied by the high-dimensional limiting measure.
We consider the Cauchy problem for a pseudo-differential operator which has a translation-invariant and analytic symbol. For a certain set of initial conditions, a formal solution is obtained by a perturbative expansion. The series so obtained can be re-expressed in terms of generalized Feynman graphs and Feynman rules. The logarithm of the solution can then be represented by a series containing only the connected Feynman graphs. Under some conditions, it is shown that the formal solution uniquely determines the real solution by means of Borel transforms. The formalism is then applied to probabilistic L\'{e}vy distributions. Here, the Gaussian part of such a distribution is re-interpreted as a initial condition and a large diffusion expansion for L\'{e}vy densities is obtained. It is outlined how this expansion can be used in statistical problems that involve L\'{e}vy distributions.
We prove that the irreducible components of the moduli space of polarized Calabi-Yau pairs are projective.
Because of their Yukawa interactions, third generation squarks may be substantially lighter than those of the first two generations. Assuming that $\tb_1 \to b\tz_1$ and $\tz_1$ escapes experimental detection, we show that experiments at the Main Injector upgrade (integrated luminosity of $2 fb^{-1}$) of the Tevatron should be sensitive to $b$-squark masses up to 210 GeV for $m_{\tz_1} \leq 120$ GeV. For integrated luminosities of $10 fb^{-1}$ (25 $fb^{-1}$) the sbottom mass reach increases by 20 GeV (35 GeV). If the channel $\tb_1 \to b\tz_2$ is also accessible, the reach becomes model-dependent and may be degraded relative to the case where only the decay to $\tz_1$ is allowed. In models with gaugino mass unification and $\mu$ much larger than gaugino masses, we argue that this degradation is unlikely to be larger than 30-40 GeV.
By means of density-functional simulations for half-doped manganites, such as pseudocubic Pr0.5Ca0.5MnO3 and bilayer PrCa2Mn2O7, we discuss the occurrence of ferroelectricity and we explore its crucial relation to the crystal structure and to peculiar charge/spin/orbital ordering effects. In pseudocubic Pr0.5Ca0.5MnO3, ferroelectricity is induced in the Zener polaron type structure, where Mn ions are dimerized. In marked contrast, in bilayer PrCa2Mn2O7, it is the displacements of apical oxygens bonded to either Mn3+ or Mn4+ ions that play a key role in the rising of ferroelectricity. Importantly, local dipoles due to apical oxygens are also intimately linked to charge and orbital ordering patterns in MnO2 planes, which in turn contribute to polarization. Finally, an important outcome of our work consists in proposing Born effective charges as a valid mean to quantify charge disproportionation effects, in terms of anisotropy and size of electronic clouds around Mn ions.
In this paper we discuss some aspects of the behavior of superconformal N=1 models under Seiberg's duality. Our claim is that if an electric gauge theory is superconformal on some marginal subspace of all coupling constants then its magnetic dual must be also superconformal on a corresponding moduli space of dual couplings. However this does not imply that the magnetic dual of a completely finite N=1 gauge theory is again finite. Moreover we generalize this statement conjecturing that also for non-superconformal N=1 models the determinant of the beta-function equations is invariant under Seiberg duality. During the course of this investigation we construct some superconformal N=1 gauge theories which were not yet discussed before.
We propose an action-conditional human motion generation method using variational implicit neural representations (INR). The variational formalism enables action-conditional distributions of INRs, from which one can easily sample representations to generate novel human motion sequences. Our method offers variable-length sequence generation by construction because a part of INR is optimized for a whole sequence of arbitrary length with temporal embeddings. In contrast, previous works reported difficulties with modeling variable-length sequences. We confirm that our method with a Transformer decoder outperforms all relevant methods on HumanAct12, NTU-RGBD, and UESTC datasets in terms of realism and diversity of generated motions. Surprisingly, even our method with an MLP decoder consistently outperforms the state-of-the-art Transformer-based auto-encoder. In particular, we show that variable-length motions generated by our method are better than fixed-length motions generated by the state-of-the-art method in terms of realism and diversity. Code at https://github.com/PACerv/ImplicitMotion.
Given $s \in (0,1)$, we discuss the embedding of $\mathcal D^{s,p}_0(\Omega)$ in $L^q(\Omega)$. In particular, for $1\le q < p$ we deduce its compactness on all open sets $\Omega\subset \mathbb R^N$ on which it is continuous. We then relate, for all q up the fractional Sobolev conjugate exponent, the continuity of the embedding to the summability of the function solving the fractional torsion problem in $\Omega$ in a suitable weak sense, for every open set $\Omega$. The proofs make use of a non-local Hardy-type inequality in $\mathcal D^{s,p}_0(\Omega)$, involving the fractional torsion function as a weight.
Self-consistent hydrodynamic one-loop quantum corrections to the Gross-Pitaevskii equation due to the interaction of the condensate with collective excitations are calculated. It is done by making use a formalism of effective action and $\zeta$-function regularization for a contribution from Bogoliubov particles in hydrodynamic approximation. It turns out to be possible to reduce the problem to the investigation of a determinant of Laplace operator on curved space where a metric is defined by density and velocity of the condensate. Standard methods of quantum gravity let us get the leading logarithmic contribution of the determinant and corresponding quantum corrections. They describe an additional quantum pressure in the condensate, local heating-cooling and evaporation-condensation effects of the Bose-condensed fraction. The effects of these corrections are studied for the correction from excited states in equilibrium situation. Response functions and form factors are discussed in the same approximation.
We present a class of Gauss-Markov processes which can be represented as space-time scaled stationary Ornstein-Uhlenbeck processes defined on the real line. We give several explicit examples of the representation for certain Gauss bridge processes. As an application, we derive a formula for the density function of the supremum location of certain standardized Gauss-Markov processes on compact time intervals. We also present some sufficient conditions under which mean centered Gauss-Markov processes take zero at a fixed time with probability one.
We have attempted to extend the parameter space of the elements of the texture 4 zero Hermitian quark mass matrices, to include the case of `weak hierarchy' amongst them along with the usually considered `strong hierarchy' case. This has been carried out by giving wide variation to the hierarchy defining parameters D_U and D_D, having implications for the structural features of the mass matrices. We find that not only the weakly hierarchical mass matrices are able to reproduce the strongly hierarchical mixing angles but also both the phases having their origin in the mass matrices have to be non zero to achieve compatibility of these matrices with recent quark mixing data. Further noting the difference between the exclusive and inclusive values of V_ub, we have carried out separate analyses corresponding to these.
The binary (one-bit-per-photon) encoding that most existing quantum key distribution (QKD) protocols employ puts a fundamental limit on their achievable key rates, especially under high channel loss conditions associated with long-distance fiber-optic or satellite-to-ground links. Inspired by the pulse-position-modulation (PPM) approach to photon-starved classical communications, we design and demonstrate the first PPM-QKD, whose security against collective attacks is established through continuous-variable entanglement measurements that also enable a novel decoy-state protocol performed conveniently in post processing. We achieve a throughput of 8.0 Mbit/s (2.5 Mbit/s for loss equivalent to 25 km of fiber) and secret-key capacity up to 4.0 bits per detected photon, thus demonstrating the significant enhancement afforded by high-dimensional encoding. These results point to a new avenue for realizing high-throughput satellite-based or long-haul fiber-optic quantum communications beyond their photon-reception-rate limits.
In this note, we give a necessary and sufficient condition for a matrix A in M to be finitely G-determined, where M is the ring of 2 x 2 matrices whose entries are formal power series over an infinite field, and G is a group acting on M by change of coordinates together with multiplication by invertible matrices from both sides.
Given a gallery of face images of missing children, state-of-the-art face recognition systems fall short in identifying a child (probe) recovered at a later age. We propose a feature aging module that can age-progress deep face features output by a face matcher. In addition, the feature aging module guides age-progression in the image space such that synthesized aged faces can be utilized to enhance longitudinal face recognition performance of any face matcher without requiring any explicit training. For time lapses larger than 10 years (the missing child is found after 10 or more years), the proposed age-progression module improves the closed-set identification accuracy of FaceNet from 16.53% to 21.44% and CosFace from 60.72% to 66.12% on a child celebrity dataset, namely ITWCC. The proposed method also outperforms state-of-the-art approaches with a rank-1 identification rate of 95.91%, compared to 94.91%, on a public aging dataset, FG-NET, and 99.58%, compared to 99.50%, on CACD-VS. These results suggest that aging face features enhances the ability to identify young children who are possible victims of child trafficking or abduction.
We extend recently proposed variational coupled-cluster method to describe excitation states of quantum antiferromagnetic bipartite lattices. We reproduce the spin-wave excitations (i.e., magnons with spin $\pm 1$). In addition, we obtain a new, spin-zero excitation (magnon-density waves) which has been missing in all existing spin-wave theories. Within our approximation, this magnon-density-wave excitation has a nonzero energy gap in a cubic lattice and is gapless in a square lattice, similar to those charge-density-wave excitations (plasmons) in quantum electron gases.
I propose a simple and manageable method that allows for deriving coupling constants of model energy density functionals (EDFs) directly from ab initio calculations performed for finite fermion systems. A proof-of-principle application allows for linking properties of finite nuclei, determined by using the nuclear nonlocal Gogny functional, to the coupling constants of the quasilocal Skyrme functional. The method does not rely on properties of infinite fermion systems but on the ab initio calculations in finite systems. It also allows for quantifying merits of different model EDFs in describing the ab initio results.
We propose a plausible mechanism to explain the formation of the so-called "obscuring tori" around active galactic nuclei (AGNs) based on three-dimensional hydrodynamic simulations including radiative feedback from the central source. The X-ray heating and radiation pressure on the gas are explicitly calculated using a ray-tracing method. This radiation feedback drives a "fountain", that is, a vertical circulation of gas in the central a few to tens parsecs. Interaction between the non-steady outflows and inflows causes the formation of a geometrically thick torus with internal turbulent motion. As a result, the AGN is obscured for a wide range of solid angles. In a quasi-steady state, the opening angles for the column density toward a black hole < 10^23 cm^-2 are approximately +-30 deg and +-50 deg for AGNs with 10% and 1% Eddington luminosity, respectively. Mass inflows through the torus coexist with the outflow and internal turbulent motion, and the average mass accretion rate to the central parsec region is 2x10^-4 ~ 10^-3, M_sun/yr this is about ten times smaller than accretion rate required to maintain the AGN luminosity. This implies that relatively luminous AGN activity is intrinsically intermittent or that there are other mechanisms, such as stellar energy feedback, that enhance the mass accretion to the center.
We discuss the dynamics of finite systems within molecular dynamics models. Signatures of a critical behavior are analyzed and compared to experimental data both in nucleus-nucleus and metallic cluster collisions. We suggest the possibility to explore the instability region via tunneling. In this way we can obtain fragments at very low temperatures and densities. We call these fragments quantum drops.
We investigate when the energy that pins a superfluid vortex to the lattice of nuclei in the inner crust of neutron stars can be approximated by the energy that binds the vortex to a single nucleus. Indeed, although the pinning energy is the quantity relevant to the theory of pulsar glitches, so far full quantum calculations have been possible only for the binding energy. Physically, the presence of nearby nuclei can be neglected if the lattice is dilute, namely with nuclei sufficiently distant from each other. We find that the dilute limit is reached only for quite large Wigner-Seitz cells, with radii > 55 fm; these are found only in the outermost low-density regions of the inner crust. We conclude that present quantum calculations do not correspond to the pinning energies in almost the entire inner crust and thus their results are not predictive for the theory of glitches.
We consider a system of fermions with mass m and model repulsive interaction U(q) = g/\sqrt{q^2 + q_0^2}, where q is the momentum transfer, q_0 the screening constant, and g > 0 the coupling constant. It is shown that at g > g_cr > 3\pi^2/m the system ground state is changed from fully occupied Fermi sphere to multiconnected Fermi sphere (MFS), consisting in N fully occupied spherical layers (icebergs) separated by empty spacers. An effective description is developed for such states at N >> 1, showing their tendency at N \to \infty to the Fermi condensate (FC) state known for the model U(q) = g/q [Khodel, Shaginyan, JETP Lett., 51, 553, 1990]. At finite temperatures, a crossover is predicted from the Fermi liquid behavior of MFS with effective mass m^* \sim m N/ln(N) to non-Fermi-liquid behavior with m^* \propto 1/T at T > T^* \sim T_F ln(N)/N.
We study the time evolution of unstable $dS_p$ \times $S^q$ configurations with flux in theories of gravity with a cosmological constant. For certain values of the flux, we identify a stable configuration to which these unstable solutions flow. For other values of the flux the sphere wants to decompactify, regardless of the sign of the initial perturbation.
AstroSat spectra of the black hole system GRS 1915+105 during the heartbeat state (with a varying oscillation period from 150 to 100 secs) were analysed using a truncated relativistic disc model along with a Comptonization component. Spectra were fitted for segments of length ~ 24 secs. The oscillation can be described as coordinated variations of the accretion rate, Comptonised flux, and the inner disc radius, with the latter ranging from 1.235-5 gravitational radii. Comparison with results from the $\chi$ and Intermediate states shows that while the accretion rate and the high energy photon index were similar, the inner disc radius and the fraction of Comptonised photons were larger for these states than for the heartbeat one. The coronal efficiency $\eta \equiv L_{ac}/\dot M c^2$, where $L_{ac}$ is the radiative luminosity generated in the corona is found to be approximately $\propto \dot M^{-2/3}$ for all the observations. The efficiency decreases with inner radii for the heartbeat state but has similar values for the $\chi$ and Intermediate states where the inner radii is larger. The implications of these results are discussed.
In the present paper, the Hawking radiation of massive bosons from 4-dimensional and 5-dimensional black strings are studied in quantum tunneling formalism. Firstly, we derive the Hamilton-Jacobi equation set via the Proca equation and WKB approximation. Then, the tunneling rates and Hawking temperature of the black strings are obtained. Our calculations show that the tunneling rates and Hawking temperatures are related to the properties of black strings' spacetime. When compare our results with those of scalars and fermions cases, it finds that they are the same.
In this paper, we first use PDE techniques and probabilistic methods to identify a kind of quasi-continuous random variables. Then we give a characterization of the $G$-integrable processes and get a kind of quasi-continuous processes by Krylov's estimates. This result is useful for the development of $G$-stochastic analysis theory. Moreover, it also provides a tool for the study of the non-Markovian It\^o processes.
We analyze the massive 4D scalar multiplet in 'reformulated' projective N=2 superspace (hyperspace) from both 4D and 6D perspectives.
The production of J/Psi mesons in gamma gamma collisions allows for a test of factorization in color-octet processes as predicted by NRQCD and observed at the Tevatron. We calculate the cross sections for J/Psi production with direct and resolved photons, including also the feed-down from chi_{cJ} and Psi' decays. Our NRQCD predictions are nicely confirmed by recent data from the DELPHI collaboration at CERN LEP2.
We investigate the Coulomb excitation of low-lying states of unstable nuclei in intermediate energy collisions ($E_{lab}\sim10-500$ MeV/nucleon). It is shown that the cross sections for the $E1$ and $E2$ transitions are larger at lower energies, much less than 10 MeV/nucleon. Retardation effects and Coulomb distortion are found to be both relevant for energies as low as 10 MeV/nucleon and as high as 500 MeV/nucleon. Implications for studies at radioactive beam facilities are discussed.
Recent measurements of the autocorrelation function of the Ly-alpha clouds are analyzed from the point of view of a simple model with strong clustering on the small scales. It is shown that this toy model reproduces fairly well the important linear relation between amplitude of the absorber autocorrelation function and neutral hydrogen column density. In addition, it predicts a correct evolutionary trend of correlation amplitudes. Some possible ramifications of these results are discussed.
We examine the effects of the linear and the cosmological redshift-space distortions on the power spectrum of cosmological objects on a light cone. We develop theoretical formulae for the power spectrum in linear theory of density perturbations in a rigorous manner starting from first principle corresponding to Fourier analysis. Approximate formulae, which are useful properly to incorporate the redshift-space distortion effects into the power spectrum are derived, and the validity is examined. Applying our formulae to galaxy and quasar samples which roughly match the SDSS survey, we will show how the redshift-space distortions distort the power spectrum on the light cone quantitatively.