ShantanuT01/DACTYL-Pretraining huggingface dataset:
This article examines a recent body of work on stochastic processes indexed by a tree. Emphasis is on the application of this new framework to existing probability models. Proofs are largely omitted, with references provided.
We analyze the propagation of waves in sunspots from the photosphere to the chromosphere using time series of co-spatial Ca II H intensity spectra (including its line blends) and polarimetric spectra of Si I 10827 and the He I 10830 multiplet. From the Doppler shifts of these lines we retrieve the variation of the velocity along the line-of-sight at several heights. Phase spectra are used to obtain the relation between the oscillatory signals. Our analysis reveals standing waves at frequencies lower than 4 mHz and a continuous propagation of waves at higher frequencies, which steepen into shocks in the chromosphere when approaching the formation height of the Ca II H core. The observed non-linearities are weaker in Ca II H than in He I lines. Our analysis suggests that the Ca II H core forms at a lower height than the He I 10830 line: a time delay of about 20 s is measured between the Doppler signal detected at both wavelengths. We fit a model of linear slow magnetoacoustic wave propagation in a stratified atmosphere with radiative losses according to Newton's cooling law to the phase spectra and derive the difference in the formation height of the spectral lines. We show that the linear model describes well the wave propagation up to the formation height of Ca II H, where non-linearities start to become very important.
We study effects of the oft-neglected cubic Dresselhaus spin-orbit coupling (i.e., $\propto p^3$) in GaAs/AlGaAs quantum dots. Using a semiclassical billiard model, we estimate the magnitude of the spin-orbit induced avoided crossings in a closed quantum dot in a Zeeman field. Using these results, together with previous analyses based on random matrix theory, we calculate corresponding effects on the conductance through an open quantum dot. Combining our results with an experiment on conductance through an 8 um^2 quantum dot [D M Zumbuhl et al., Phys. Rev. B 72, 081305 (2005)] suggests that 1) the GaAs Dresselhaus coupling constant, $\gamma$, is approximately 9 eVA^3, significantly less than the commonly cited value of 27.5 eVA^3 and 2) the majority of the spin-flip component of spin-orbit coupling can come from the cubic Dresselhaus term.
We study Talenti's type symmetrization properties for solutions of linear stationary and evolution problems. Our main result establishes the comparison in norm between the solution of a problem and its symmetric version when nonlocal diffusion defined through integrable kernels is replacing the usual local diffusion defined by a second order differential operator. Using an approximation argument, we recover, as a corollary of our results, the classical Talenti's theorem. A novelty of our approach is that we replace the measure geometric tools employed in Talenti's proof by the use of the Riesz's rearrangement inequality, giving thus an alternative and somehow simpler proof than Talenti's one.
Recent results have revealed a critical way in which lower order terms affect the well-posedness of the characteristic initial value problem for the scalar wave equation. The proper choice of such terms can make the Cauchy problem for scalar waves well posed even on a background spacetime with closed lightlike curves. These results provide new guidance for developing stable characteristic evolution algorithms. In this regard, we present here the finite difference version of these recent results and implement them in a stable evolution code. We describe test results which validate the code and exhibit some of the interesting features due to the lower order terms.
In this note we study the prospect of high-precision measurements of W boson mass, top quark mass, and forward-backward asymmetry in Z->ee decays and the search for the Higgs boson during Run 2 to challenge the standard model.
A time-dependent Synchrotron Self Compton model (SSC) which is able to motivate the used electron spectra of many SSC models as a balance of acceleration and radiative losses is introduced. Using stochastic acceleration as well as Fermi-I processes even electron spectra with a rising part can be explained, which are mandatory to fit the lowstate spectral energy distribution (SED) of PKS 2155-304 as constrained from Fermi LAT observations. Due to the time resolution the outburst of PKS 2155-304 observed by H.E.S.S. in 2006 can be modelled selfconsistently as fluctuations along the jet axis without introducing new sets of parameters. The model makes the time evolution of the SED also accessible. Hence giving new insights into the flaring behavior of blazars.
Let K be a finite extension of Q_p and X a smooth projective variety over K. We define the notion of totally degenerate reduction of such an X and the associated Chow complexes of the special fibre of a suitable regular proper model of X over the ring of integers of K. If X has such reduction, we then show that for all l, the Q_l-adic etale cohomology of X has a filtration whose graded quotients are isomorphic, as Galois modules, to the tensor product of a finite dimensional Q-vector space (with a finite unramified action of Galois) with twists of Q_l by the cyclotomic character.
It has been suggested recently (Phys. Rev. Lett. 91, 232501 (2003)) that charge symmetry of nucleon-nucleon interactions relates the Asymptotic Normalization Coefficients (ANCs) of proton and neutron virtual decays of mirror nuclei. This relation is given by a simple analytical formula which involves proton and neutron separation energies, charges of residual nuclei and the range of their strong interaction with the last nucleon. Relation between mirror ANCs, if understood properly, can be used to predict astrophysically relevant direct proton capture cross sections using neutron ANCs measured with stable beams. In this work, we calculate one-nucleon ANCs for several light mirror pairs, using microscopic two-, three- and four-cluster models, and compare the ratio of mirror ANCs to the predictions of the simple analytic formula. We also investigate mirror symmetry between other characteristics of mirror one-nucleon overlap integrals, namely, spectroscopic factors and single-particle ANCs.
We solve the Faddeev equations for 11Li (n+n+9Li) using hyperspherical coordinates and analytical expressions for distances much larger than the effective ranges of the interactions. The lowest resonances are found at 0.65 MeV (1/2+, 3/2+, 5/2+) and 0.89 MeV (3/2+, 3/2-) with widths of about 0.35 MeV. A number of higher-lying broader resonances are also obtained and related to the Efimov effect. The dipole strength function and the Coulomb dissociation cross section are also calculated. PACS numbers: 21.45.+v, 11.80.Jy, 21.60.Gx
The observed baryon asymmetry of the Universe is suitably created in thermal leptogenesis through the out-of-equilibrium decay of $N_1$, the lightest of the three heavy singlet neutral fermions which anchor the seesaw mechanism to obtain small Majorana neutrino masses. However, this scenario suffers from the incompatibility of a generic lower bound on the mass of $N_1$ and the upper bound on the reheating temperature of the Universe after inflation. A modest resolution of this conundrum is proposed.
Leptoquarks arise naturally in models attempting the unification of the quark and lepton sectors of the standard model of particle physics. Such particles could be produced in the interaction of high energy quasi-horizontal cosmic neutrinos with the atmosphere, via their direct coupling to a quark and a neutrino. The hadronic decay products of the leptoquark, and possibly its leptonic decay products would originate an extensive air shower, observable in large cosmic ray experiments. In this letter, the sensitivity of present and planned very high energy cosmic ray experiments to the production of leptoquarks of different types is estimated and discussed.
We establish an approach theoretic version of Anscombe's theorem, which we apply to justify the use of confidence intervals based on the sample mean after a group sequential trial.
It is well-known that many famous pooling designs are constructed from mathematical structures by the "containment matrix" method. In this paper, we propose another method and obtain a family of pooling designs with surprisingly high degree of error correction based on a finite set. Given the numbers of items and pools, the error-tolerant property of our designs is much better than that of Macula's designs when the size of the set is large enough.
An on-demand single-photon source is a key requirement for scaling many optical quantum technologies. A promising approach to realize an on-demand single-photon source is to multiplex an array of heralded single-photon sources using an active optical switching network. However, the performance of multiplexed sources is degraded by photon loss in the optical components and the non-unit detection efficiency of the heralding detectors. We provide a theoretical description of a general multiplexed single-photon source with lossy components and derive expressions for the output probabilities of single-photon emission and multi-photon contamination. We apply these expressions to three specific multiplexing source architectures and consider their tradeoffs in design and performance. To assess the effect of lossy components on near- and long-term experimental goals, we simulate the multiplexed sources when used for many-photon state generation under various amounts of component loss. We find that with a multiplexed source composed of switches with ~0.2-0.4 dB loss and high efficiency number-resolving detectors, a single-photon source capable of efficiently producing 20-40 photon states with low multi-photon contamination is possible, offering the possibility of unlocking new classes of experiments and technologies.
The generating function for $S_n$-equivariant Euler characteristics of moduli spaces of pointed hyperelliptic curves for any genus g>1 is calculated. This answer generalizes the known ones for genera 2 and 3 and answers obtained by J. Bergstrom for any genus and n<8 points.
We construct the non-BPS black brane representation from the Kerr metric using the U-duality and symmetries in string or M-theory. We give the general rule to get the brane configuration and we apply it especially for Kerr metric. We find the three charged solution in M-theory and after the compactification it becomes rotating black string solution in five dimension. We also find the four charged solution containing the pp-wave in M-theory, and we can find charged dilaton rotating black hole solution in four dimension after the torus compactification. This solution has the other representation in string theory, which is easy to apply the AdS/CFT correspondence.
We present evidence that the spectroscopically identified bipolar jets of the pre-main sequence binary KH 15D are a common product of the whole binary system, rather than being launched from either star individually. They may be launched from the innermost part of the circumbinary disk (CBD) or may result from the merging of two outflows driven by the individual stars. This evidence is based on high-resolution H-alpha and [OI] 6300A line profiles obtained during eclipse phases of this nearly edge-on system. The occultation of star A (the only currently visible star) by the disk strongly suppresses the stellar H-alpha and continuum emission and allows one to study the faint redshifted and blueshifted emission components of the bipolar jets. The strongest evidence for jet production by the whole binary system comes from the observed radial velocity symmetry of the two jet components relative to the systemic velocity of the binary, in combination with current accretion models from the CBD onto a binary system.
We calculate the orbital angular momentum of dark matter subhaloes in the Aquarius simulations of cold dark matter galactic haloes. We calculate the orientation of their angular momentum relative to that of the spin vector of their host halo and find a variety of different configurations. All six Aquarius haloes contain statistically significant populations of subhalo orbits that are aligned with the main halo spin. All haloes posses a population of subhaloes that rotates in the same direction as the main halo and three of them possess, in addition, a population that rotates in the opposite direction. These configurations arise from the filamentary accretion of subhaloes. Quasi-planar distributions of coherently rotating satellites, such as those inferred in the Milky Way and other galaxies, arise naturally in simulations of a $\Lambda$CDM universe.
Using the FDTD method, we investigate the electromagnetic propagation in two-dimensional photonic crystals, formed by parallel air cylinders in a dielectric medium. The corresponding frequency band structure is computed using the standard plane-wave expansion method. It is shown that within partial bandgaps, waves tend to bend away from the forbidden directions. This phenomenon perhaps need not be explained in terms of negative refraction or `superlensing' behavior, contrast to what has been conjectured.
Fermi-edge absorption theory predicting the spectrum, A(\omega)\propto \omega^{-2\delta_0/\pi+\delta^2_0/\pi^2}, relies on the assumption that scattering phase, \delta_0, is frequency-independent. Dependence of \delta_0 on \omega becomes crucial near the resonant condition, where the phase changes abruptly by \pi. In this limit, due to finite time spent by electron on a resonant level, the scattering is dynamic. We incorporate this time delay into the theory, solve the Dyson equation with a modified kernel and find that, near the resonance, A(\omega) behaves as \omega^{-3/4} |\ln \omega|. Resonant scattering off the core hole takes place in 1D and 2D in the presence of an empty subband above the Fermi level; then attraction to hole splits off a resonant level from the bottom of the empty subband. Fermi-edge absorption in the regime when resonant level transforms into a Kondo peak is discussed.
A large number of pulsars and X-rays sources are detected in globular clusters. To understand the structure and content of these clusters, accurate distances are required. We derive the distances of Terzan 5, Liller 1 and UKS 1 using as a reference a recent distance determination of NGC 6528, based on HST/NICMOS and NTT/SOFI infrared photometry. The distance of the metal-poor cluster Terzan 4 was derived from a comparison with M92 in NICMOS bands. Distances of the metal-rich clusters are obtained by comparison of the Horizontal Branch (HB) level of the clusters, relative to the reddening line passing through the HB of NGC 6528. We use methods based on NICMOS bands and transformations to J and H magnitudes with different assumptions. Liller~1 and Terzan~4 are found to be at the central bulge distance, UKS~1 is beyond the Galactic center, while Terzan 5 is closer to the Sun than the other four clusters. The distance of Terzan 5 is of paramount importance, given the impact of its population of 21 pulsars, which is related to the high cluster density. The distance of Terzan 5 is found to be d$_{\odot}$=5.5$\pm$0.9 kpc from the Sun, thus closer to us than values given in studies of pulsars in Terzan 5. As a consequence, the higher cluster density is even more favourable for formation of the millisecond pulsars recently detected in this cluster.
Using the analogy with stationary axisymmetric solutions, we present a method to generate new analytic cosmological solutions of Einstein's equation belonging to the class of $T^3$ Gowdy cosmological models. We show that the solutions can be generated from their data at the initial singularity and present the formal general solution for arbitrary initial data. We exemplify the method by constructing the Kantowski-Sachs cosmological model and a generalization of it that corresponds to an unpolarized $T^3$ Gowdy model.
We have previously proposed a conjecture stating that quantum mechanical transition amplitudes can be parametrized in terms of a quantum action. Here we give a proof of the conjecture and establish the existance of a local quantum action in the case of imaginary time in the Feynman-Kac limit (when temperature goes to zero). Moreover we discuss some symmetry properties of the quantum action.
A new method is devised for calculating the Igusa local zeta function $Z_f$ of a polynomial $f(x_1,\dots,x_n)$ over a $p$-adic field. This involves a new kind of generating function $G_f$ that is the projective limit of a family of generating functions, and contains more data than $Z_f$. This $G_f$ resides in an algebra whose structure is naturally compatible with operations on the underlying polynomials, facilitating calculation of local zeta functions. This new technique is used to expand significantly the set of quadratic polynomials whose local zeta functions have been calculated explicitly. Local zeta functions for arbitrary quadratic polynomials over $p$-adic fields with $p$ odd are presented, as well as for polynomials over unramified $2$-adic fields of the form $Q+L$ where $Q$ is a quadratic form and $L$ is a linear form where $Q$ and $L$ have disjoint variables. For a quadratic form over an arbitrary $p$-adic field with odd $p$, this new technique makes clear precisely which of the three candidate poles are actual poles.
In this summary, we present the main topics of the talks presented in the parallel session "Black holes - 5" of the 14th Marcel Grossmann Meeting held in Rome, Italy in July 2015. We first present a short review of the main approaches used to understand thermodynamics by using differential geometry. Then, we present a brief summary of each presentation, including some general remarks and comments.
Facial Expression Recognition (FER) is crucial in many research domains because it enables machines to better understand human behaviours. FER methods face the problems of relatively small datasets and noisy data that don't allow classical networks to generalize well. To alleviate these issues, we guide the model to concentrate on specific facial areas like the eyes, the mouth or the eyebrows, which we argue are decisive to recognise facial expressions. We propose the Privileged Attribution Loss (PAL), a method that directs the attention of the model towards the most salient facial regions by encouraging its attribution maps to correspond to a heatmap formed by facial landmarks. Furthermore, we introduce several channel strategies that allow the model to have more degrees of freedom. The proposed method is independent of the backbone architecture and doesn't need additional semantic information at test time. Finally, experimental results show that the proposed PAL method outperforms current state-of-the-art methods on both RAF-DB and AffectNet.
[Abridged and Edited] We investigate nuclear light profiles in 135 ATLAS3D galaxies for which the Hubble Space Telescope (HST) imaging is available and compare them to the large scale kinematics obtained with the SAURON integral-field spectrograph. Specific angular momentum, lambda_R, correlates with the shape of nuclear light profiles, where cores are typically found in slow rotators and core-less galaxies are fast rotators. Cores are found only in massive galaxies and only in systems with the stellar mass M>8x10^10 Msun. Based on our sample, we, however, see no evidence for a bimodal distribution of nuclear slopes. The best predictor for finding a core is based on the stellar velocity dispersion within an effective radius, sigma_e, and specific angular momentum, where cores are found for lambda_R<0.25 and sigma_e>160 km/s. We estimate that only about 10% of nearby early-type galaxies contain cores. Furthermore, we show that there is a genuine population of fast rotators with cores. We also show that core fast rotators are morphologically, kinematically and dynamically different from core slow rotators. The cores of fast rotators could harbour black holes of similar masses to those in core slow rotators, but typically more massive than those found in core-less fast rotators. Core-less galaxies, and especially core-less fast rotators, are under-luminous in the diffuse X-ray emission, but the presence of a core does not imply high X-ray luminosities. We postulate a possible population of core-less galaxies among slow rotators, which can not be explained as face-on discs, but comprise a genuine sub-population of slow rotators. These galaxies are typically less massive and flatter than core slow rotators, and show evidence for dynamical cold structures and exponential photometric components. We discuss possible processes for formation of cores and their subsequent preservation.
Following Brown, in this paper we give an overview of how to modify standard hyperbolic formulations of the 3+1 evolution equations of General Relativity in such a way that all auxiliary quantities are true tensors, thus allowing for these formulations to be used with curvilinear sets of coordinates such as spherical or cylindrical coordinates. After considering the general case for both the Nagy-Ortiz-Reula (NOR) and the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulations, we specialize to the case of spherical symmetry and also discuss the issue of regularity at the origin. Finally, we show some numerical examples of the modified BSSN formulation at work in spherical symmetry.
Using a simple exactly solvable model, we show that event-dependent time delays may lead to significant non-Poisson effects in the statistics of polymer chain growth. The results are confirmed by stochastic simulation of various growth scenarios.
Nuclear effects and QCD perturbative corrections to the Paschos-Wolfenstein relationship are discussed. We argue that perturbative corrections largely cancel out in this relationship for total cross sections while the neutron excess correction in heavy nuclei is enhanced by Fermi motion and nuclear binding effects. These observations are discussed in the context of NuTeV measurement of the Weinberg mixing angle.
We extend results of R. Holley beyond the integer lattice to a large class of groups which includes free groups. In particular we show that a shift-invariant measure is Gibbs if and only if it is Glauber-invariant. Moreover, any shift-invariant measure converges weakly to the set of Gibbs measures when evolved under Glauber dynamics. These results are proven using a new notion of free energy density relative to a sofic approximation by homomorphisms. Any measure which minimizes free energy density is Gibbs.
The microscopic center-of-mass (c.m.) correction energies for nuclei ranging from Oxygen to Calcium are systematically calculated by both spherical and axially deformed relativistic mean-field (RMF) models with the effective interaction PK1. The microscopic c.m. correction energies strongly depend on the isospin as well as deformation and deviate from the phenomenological ones. The deformation effect is discussed in detail by comparing the deformed with the spherical RMF calculation. It is found that the direct and exchange terms of the c.m. correction energies are strongly correlated with the density distribution of nuclei and are suppressed in the deformed case.
In this paper we deal with a singular nonlocal phase field system with inertial term. The system has the logarithm of the absolute temperature $\theta$ under time derivative. Although the system has a difficult mathematical point caused by the combination of $(\ln \theta)_{t}$, the inertial term and the nonlocal diffusion term for the order parameter $\varphi$ (see Section 1.1), we can establish existence of solutions by a key estimate (see Remark 1.1).