ShantanuT01/DACTYL-Pretraining huggingface dataset:
This paper is devoted to improvements of functional inequalities based on scalings and written in terms of relative entropies. When scales are taken into account and second moments fixed accordingly, deficit functionals provide explicit stability measurements, i.e., bound with explicit constants distances to the manifold of optimal functions. Various results are obtained for the Gaussian logarithmic Sobolev inequality and its Euclidean counterpart, for the Gaussian generalized Poincar{\'e} inequalities and for the Gagliardo-Nirenberg inequalities. As a consequence, faster convergence rates in diffusion equations (fast diffusion, Ornstein-Uhlenbeck and porous medium equations) are obtained.
Charm and bottom baryons and mesons are studied within the framework of a relativistically covariant 3D reduction of the Bethe-Salpeter equation. We carry out an analysis of semileptonic decays of heavy hadrons within this framework using explicit oscillator-type wave functions where we calculate Isgur-Wise functions, decay rates and asymmetry parameters. Within this model we also study the effect of interactions between the light quarks inside the heavy baryon and how they affect the values of the computed heavy baryon observables. We also elaborate on the role of relativistic effects in the calculation of the heavy baryon Isgur-Wise function.
We perform a global analysis of the $b\to c\tau\nu$ data using the recent lattice results on the $B_c\to J/\psi$ vector and axial-vector form factors. To explore the effects from the tensor operator of new physics beyond the standard model, we determine the tensor form factors by using the non-relativistic QCD (NRQCD) relations between tensor and (axial-)vector form factors. Based on the lattice+NRQCD form factors, we fit the Wilson coefficients and the new physics couplings in $R_2$, $S_1$ and $U_1$ leptoquark models by including the recently measured $R(\Lambda_c)$ and imposing the relaxed constraint $\mathcal B(B_c\to J/\psi)<30\%$ in light of the recent studies on LEP1 data and $B_c$ lifetime. We give predictions for the experimental observables including $R(J/\psi)$, $P_\tau(J/\psi)$, $F_L(J/\psi)$ and $\mathcal A_{FB}(J/\psi)$ as well as their $q^2$ distribution in new physics scenarios/models. Our results suggest that the longitudinal $\tau$ polarization fraction $P_\tau(J/\psi)$ and the forward-backward asymmetry $\mathcal A_{FB}(J/\psi)$ are useful for testing the $R_2$ leptoquark model.
This paper is an adaptation of a method used in \cite{K} to the model of random quadrangulations. We prove local weak convergence of uniform measures on quadrangulations and show that the local growth of quadrangulation is governed by certain critical time-reversed branching process and the rescaled profile converges to the reversed continuous-state branching process. As an intermediate result we derieve a biparametric generating function for certain class of quadrangulations with boundary.
We formulate a version of the Random Wave Conjecture for the fourth moment of Eisenstein series which is based on Zagier's regularized inner product. We prove an asymptotic formula expressing the regularized fourth moment as a mean value of L-functions. This is an advantage over previous work in the literature, which has approached the fourth moment problem through truncated Eisenstein series and not yielded a suitable expression in terms of L-functions.
We prove that self-diffusion constants of interacting Brownian particles in $ \mathbb{R}$ always vanish if the particles do not collide with each other. We represent self-diffusion constants by additive functionals of reversible Markov processes as obtained in O. 1998.
Minimum-uncertainty squeezed states, related to a broad class of observables, are analyzed. Methods for characterizing such states are developed, which are based on numerical solutions of ordinary differential equations. As typical examples we deal with nonlinear generalizations of quadrature squeezed states and deformed nonlinear squeezed states. In this manner one may derive those squeezed states which are directly related to given observables. This can be useful for optimized measurements at a reduced level of quantum-noise.
We extend the formulation of relativistic Coulomb sum rules to account for the average effects of nuclear binding on the initial and final states of ejected nucleons. Relativistic interactions are included by using a Dirac representation adapted from a vector-scalar field theory. The scalar field reduces the effective nucleon mass $M^*$ and increases the relativistic effects of recoil and Fermi motion. We consider two models for the off-shell behavior of the nuclear electromagnetic current, and demonstrate that the sum rule is accurate for applications to data over the interesting range of $M^*$ and three momentum $q$. We further indicate that the form of the sum rule is sufficiently general to accommodate a broad class of off-shell form factor models.
In the last decade, several ultra faint objects (UFOs, $M_V\gtrsim-3.5$) have been discovered in the outer halo of the Milky Way. For some of these objects it is not clear whether they are star clusters or (ultra-faint) dwarf galaxies. In this work we quantify the contribution of star clusters to the population of UFOs. We extrapolated the mass and Galactocentric radius distribution of the globular clusters using a population model, finding that the Milky Way contains about $3.3^{+7.3}_{-1.6}$ star clusters with $M_V\gtrsim-3.5$ and Galactocentric radius $\geq20\,$kpc. To understand whether dissolving clusters can appear as UFOs, we run a suite of direct $N$-body models, varying the orbit, the Galactic potential, the binary fraction and the black hole (BH) natal kick velocities. In the analyses, we consider observational biases such as: luminosity limit, field stars, and line-of-sight projection. We find that star clusters contribute to both the compact and the extended population of UFOs: clusters without BHs appear compact with radii $\sim5\,$pc, while clusters that retain their BHs after formation have radii $\gtrsim20\,$pc. The properties of the extended clusters are remarkably similar to those of dwarf galaxies: high inferred mass-to-light ratios due to binaries; binary properties mildly affected by dynamical evolution; no observable mass segregation; and flattened stellar mass function. We conclude that the slope of the stellar mass function as a function of Galactocentric radius and the presence/absence of cold streams can discriminate between DM free and DM dominated UFOs.
We produce numerical evidence that the joint spike transitions between Kasner eras of $G_2$ cosmologies are described by the non-orthogonally transitive $G_2$ spike solution. A new matching procedure is developed for this purpose.
We extend the concept of entanglement spectrum from the geometrical to the particle bipartite partition. We apply this to several Fractional Quantum Hall (FQH) wavefunctions on both sphere and torus geometries to show that this new type of entanglement spectra completely reveals the physics of bulk quasihole excitations. While this is easily understood when a local Hamiltonian for the model state exists, we show that the quasiholes wavefunctions are encoded within the model state even when such a Hamiltonian is not known. As a nontrivial example, we look at Jain's composite fermion states and obtain their quasiholes directly from the model state wavefunction. We reach similar conclusions for wavefunctions described by Jack polynomials.
We show how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment. This result holds for several variants of the walk algorithm and for a wide range of parameters. The growth mechanism is based on using local graph information only, so this is a process of self-organisation. The standard mean-field equations are an excellent approximation for network growth using these rules. We discuss the effects of finite size on the degree distribution, and compare analytical results to simulated networks. Finally, we generalise the random walk algorithm to produce weighted networks with power-law distributions of both weight and degree.
We show that the linearity of an evolution of Quantum Mechanics follows from the definition of kinematics. The same result is obtained for an arbitrary theory with the state space that includes mixtures of different preparations. Next, we formulate the non-signaling theorem and show that the theorem poses no additional restriction on Quantum Mechanics provided the kinematics is given. We also discuss validity of the postulate for the case of more general theories.
We present the first APOKASC catalog of spectroscopic and asteroseismic properties of 1916 red giants observed in the Kepler fields. The spectroscopic parameters provided from the Apache Point Observatory Galactic Evolution Experiment project are complemented with asteroseismic surface gravities, masses, radii, and mean densities determined by members of the Kepler Asteroseismology Science Consortium. We assess both random and systematic sources of error and include a discussion of sample selection for giants in the Kepler fields. Total uncertainties in the main catalog properties are of order 80 K in Teff , 0.06 dex in [M/H], 0.014 dex in log g, and 12% and 5% in mass and radius, respectively; these reflect a combination of systematic and random errors. Asteroseismic surface gravities are substantially more precise and accurate than spectroscopic ones, and we find good agreement between their mean values and the calibrated spectroscopic surface gravities. There are, however, systematic underlying trends with Teff and log g. Our effective temperature scale is between 0-200 K cooler than that expected from the Infrared Flux Method, depending on the adopted extinction map, which provides evidence for a lower value on average than that inferred for the Kepler Input Catalog (KIC). We find a reasonable correspondence between the photometric KIC and spectroscopic APOKASC metallicity scales, with increased dispersion in KIC metallicities as the absolute metal abundance decreases, and offsets in Teff and log g consistent with those derived in the literature. We present mean fitting relations between APOKASC and KIC observables and discuss future prospects, strengths, and limitations of the catalog data.
A theory for treating the unconventional non-Fermi liquid temperature dependence of physical quantities, such as the resistivity, in the Pr-based two-channel Anderson impurities system is developed. It is shown that their temperature dependences are essentially the same as those in the pure lattice system except for the case of extremely low concentration of Pr ions that is difficult to realize by a controlled experiments. This result is consistent with recent observations in diluted Pr-1-2-20 system Y$_{1-x}$Pr$_x$Ir$_2$Zn$_{20}$ ($x=0.024,\,0.044,\,0.085,$ and $0.44$) reported in Yamane $et\ al$. Phys. Rev. Lett. ${\bf 121}$, 077206 (2018), and is quite different from that in the case of single-channel Anderson impurities system in which the crossover between behaviors of the local Fermi liquid and heavy Fermi liquid occurs at around moderate concentration of impurities as observed in Ce-based heavy fermion system La$_{1-x}$Ce$_x$Cu$_6$.
With $M(t):=\sup_{s\in[0,t]}A(s)-s$ denoting the running maximum of a fractional Brownian motion $A(\cdot)$ with negative drift, this paper studies the rate of convergence of $\mathbb {P}(M(t)>x)$ to $\mathbb{P}(M>x)$. We define two metrics that measure the distance between the (complementary) distribution functions $\mathbb{P}(M(t)>\cdot)$ and $\mathbb{P}(M>\cdot)$. Our main result states that both metrics roughly decay as $\exp(-\vartheta t^{2-2H})$, where $\vartheta$ is the decay rate corresponding to the tail distribution of the busy period in an fBm-driven queue, which was computed recently [Stochastic Process. Appl. (2006) 116 1269--1293]. The proofs extensively rely on application of the well-known large deviations theorem for Gaussian processes. We also show that the identified relation between the decay of the convergence metrics and busy-period asymptotics holds in other settings as well, most notably when G\"artner--Ellis-type conditions are fulfilled.
A suggestive phenomenological relation is found among the lepton and quark masses which suggests a new insight into the problem of generations and also gives a prediction for the top quark mass in agreement with the range of values which is actually expected.
We develop a first-principles model of thermally-activated cross-slip in magnesium in the presence of a random solute distribution. Electronic structure methods provide data for the interaction of solutes with prismatic dislocation cores and basal dislocation cores. Direct calculations of interaction energies are possible for solutes---K, Na, and Sc---that lower the Mg prismatic stacking fault energy to improve formability. To connect to thermally activated cross-slip, we build a statistical model for the distribution of activation energies for double kink nucleation, barriers for kink migration, and roughness of the energy landscape to be overcome by an athermal stress. These distributions are calculated numerically for a range of concentrations, as well as alternate approximate analytic expressions for the dilute limit. The analytic distributions provide a simplified model for the maximum cross-slip softening for a solute as a function of temperature. The direct interaction calculations predict lowered forming temperatures for Mg-0.7at.%Sc, Mg-0.4at.%K, and Mg-0.6at.%Na of approximately 250C.
Given a function $f$ on the vertex set of some graph $G$, a scenery, let a simple random walk run over the graph and produce a sequence of values. Is it possible to, with high probability, reconstruct the scenery $f$ from this random sequence? To show this is impossible for some graphs, Gross and Grupel, call a function $f:V\to\{0,1\}$ on the vertex set of a graph $G=(V,E)$ $p$-biased if for each vertex $v$ the fraction of neighbours on which $f$ is 1 is exactly $p$. Clearly, two $p$-biased functions are indistinguishable based on their sceneries. Gross and Grupel construct $p$-biased functions on the hypercube $\{0,1\}^n$ and ask for what $p\in[0,1]$ there exist $p$-biased functions on $\mathbb{Z}^n$ and additionally how many there are. We fully answer this question by giving a complete characterization of these values of $p$. We show that $p$-biased functions exist for all $p=c/2n$ with $c\in\{0,\dots,2n\}$ and, in fact, there are uncountably many of them for every $c\in\{1,\dots,2n-1\}$. To this end, we construct uncountably many partitions of $\mathbb{Z}^n$ into $2n$ parts such that every element of $\mathbb{Z}^n$ has exactly one neighbour in each part. This additionally shows that not all sceneries on $\mathbb{Z}^n$ can be reconstructed from a sequence of values on attained on a simple random walk.
We report anomalous quantum transport features in bilayer graphene in presence of a random distribution of structural vacancies. By using an efficient real-space Kubo-Greenwood transport methodology, the impact of a varying density of dimer versus non-dimer vacancies is investigated in very large scale disordered models. While non-dimer vacancies are shown to induce localization regimes, dimer vacancies result in an unexpected ballistic regime whose energy window surprisingly enlarges with increasing impurity density. Such counterintuitive phenomenon is explained by the formation of an effective linear dispersion in the bilayer bandstructure, which roots in the symmetry breaking effects driven by dimer vacancies, and provides a novel realization of Dirac semimetals in high dimension.
In this paper, we study the ill-posdness of the Cauchy problem for semilinear wave equation with very low regularity, where the nonlinear term depends on $u$ and $\partial_t u$. We prove a ill-posedness result for the "defocusing" case, and give an alternative proof for the supercritical "focusing" case, which improves our previous result in Chin. Ann. Math. Ser. B 26(3), 361-378, 2005.
Recent work on globular cluster systems in dwarf galaxies outside the Local Group is reviewed. Recent large imaging surveys with the Hubble Space Telescope and follow-up spectroscopy with 8-m class telescopes now allow us to compare the properties of massive star clusters in a wide range of galaxy types and environments. This body of work provides important constraints for theories of galaxy and star cluster formation and evolution.
We report on the tuning of magnetic interactions in superlattices composed of single and bilayer SrIrO$_3$ inter-spaced with SrTiO$_3$. Magnetic scattering shows predominately $c$-axis antiferromagnetic orientation of the magnetic moments for the bilayer justifying these systems as viable artificial analogues of the bulk Ruddlesden-Popper series iridates. Magnon gaps are observed in both superlattices, with the magnitude of the gap in the bilayer being reduced to nearly half that in its bulk structural analogue, Sr$_3$Ir$_2$O$_7$. We assign this to modifications in the anisotropic exchange driven by bending of the $c$-axis Ir-O-Ir bond and subsequent local environment changes, as detected by x-ray diffraction and modeled using spin wave theory. These findings explain how even subtle structural modulations driven by heterostructuring in iridates are leveraged by spin orbit coupling to drive large changes in the magnetic interactions.
This is the second paper of two reporting results from a study of the HI content and stellar properties of nearby galaxies detected by the Arecibo Legacy Fast ALFA blind 21-cm line survey and the Sloan Digital Sky Survey in a 2160 deg^2 region covered by both surveys. We apply strategies of multivariate data analysis to a complete HI flux-limited subset of 1624 objects extracted from the control sample of HI emitters assembled by Toribio et al. (2011a) in order to: i) investigate the correlation structure of the space defined by an extensive set of observables describing gas-rich systems; ii) identify the intrinsic parameters that best define their HI content; and iii) explore the scaling relations arising from the joint distributions of the quantities most strongly correlated with the HI mass. The principal component analysis performed over a set of five galaxy properties reveals that they are strongly interrelated, supporting previous claims that nearby HI emitters show a high degree of correlation. The best predictors for the expected value of MHI are the diameter of the stellar disk, D25r, followed by the total luminosity (both in the r-band), and the maximum rotation speed, while morphological proxies such as color show only a moderately strong correlation with the gaseous content attenuated by observational error. The simplest and most accurate prescription is log(MHI/Msun)= 8.72 + 1.25*log(D25r/kpc). We find a slope of $-8.2 \pm 0.5$ for the relation between optical magnitude and log rotation speed, in good agreement with Tully-Fisher studies, and a log slope of $1.55 \pm 0.06$ for the HI mass-optical galaxy size relation. Given the homogeneity of the measurements and the completeness of our dataset, the latter outcome suggests that the constancy of the average (hybrid) HI surface density advocated by some authors for the spiral population is a crude approximation.
A solar neutron detector has been launched on the Japan Exposure Module (JEM) of the International Space Station (ISS) in August 4, 2009. The detector works satsifactory. The detector comprises scintillation fiber and is designated as the Space Environment Data Acquisition (SEDA)-FIB. It tracks the recoil protons induced by neutrons and measurement of the proton energy using the range method. The energy resolution of the detector was measured using the proton beam at Riken. Herein, we report the energy resolution of the FIB detector by two different methods.
Let $A' = \varprojlim_n$ be the projective limit of the $p$-parts of the ideal class groups of the $p$ integers in the $\Z_p$-cyclotomic extension $\K_{\infty}/\K$ of a CM number field $\K$. We prove in this paper that the $T$ part $(A')^-(T) = 0$. This fact has been explicitly conjecture by Kuz'min in 1972 and was proved by Greenberg in 1973, for abelian extensions $\K/\Q$. Federer and Gross had shown in 1981 that $(A')^-(T) = 0$ is equivalent to the non-vanishing of the $p$-adic regulator of the $p$-units of $\K$.
We derive loop quantum gravity corrections to the Raychaudhuri equation in the interior of a Schwarzschild black hole and near the classical singularity. We show that the resulting effective equation implies defocusing of geodesics due to the appearance of repulsive terms. This prevents the formation of conjugate points, renders the singularity theorems inapplicable, and leads to the resolution of the singularity for this spacetime.
We use a suite of cosmological, hydrodynamical simulations to investigate the chemical enrichment history of the Universe. Specifically, we trace the origin of the metals back in time to investigate when various gas phases were enriched and by what halo masses. We find that the age of the metals decreases strongly with the density of the gas in which they end up. At least half of the metals that reside in the diffuse intergalactic medium (IGM) at redshift zero (two) were ejected from galaxies above redshift two (three). The mass of the haloes that last contained the metals increases rapidly with the gas density. More than half of the mass in intergalactic metals was ejected by haloes with total masses less than 1e11 solar masses and stellar masses less than 1e9 solar masses. The range of halo masses that contributes to the enrichment is wider for the hotter part of the IGM. By combining the `when' and `by what' aspects of the enrichment history, we show that metals residing in lower density gas were typically ejected earlier and by lower mass haloes.
We show that the Weak Gravity Conjecture (WGC) implies a nontrivial upper bound on the volumes of the minimal-volume cycles in certain homology classes that admit no calibrated representatives. In compactification of type IIB string theory on an orientifold $X$ of a Calabi-Yau threefold, we consider a homology class $[\Sigma] \in H_4(X,\mathbb{Z})$ represented by a union $\Sigma_{\cup}$ of holomorphic and antiholomorphic cycles. The instanton form of the WGC applied to the axion charge $[\Sigma]$ implies an upper bound on the action of a non-BPS Euclidean D3-brane wrapping the minimal-volume representative $\Sigma_{\mathrm{min}}$ of $[\Sigma]$. We give an explicit example of an orientifold $X$ of a hypersurface in a toric variety, and a hyperplane $\mathcal{H} \subset H_4(X,\mathbb{Z})$, such that for any $[\Sigma] \in H$ that satisfies the WGC, the minimal volume obeys $\mathrm{Vol}(\Sigma_{\mathrm{min}}) \ll \mathrm{Vol}(\Sigma_{\cup})$: the holomorphic and antiholomorphic components recombine to form a much smaller cycle. In particular, the sub-Lattice WGC applied to $X$ implies large recombination, no matter how sparse the sublattice. Non-BPS instantons wrapping $\Sigma_{\mathrm{min}}$ are then more important than would be predicted from a study of BPS instantons wrapping the separate components of $\Sigma_{\cup}$. Our analysis hinges on a novel computation of effective divisors in $X$ that are not inherited from effective divisors of the toric variety.
We compute the Nash blow-up of a cominuscule Schubert variety. In particular, we show that the Nash blow-up is algebraically isomorphic to another Schubert variety of the same Lie type. As a consequence, we give a new characterization of the smooth locus and, for Grassmannian Schubert varieties, determine when the Nash blow-up is a resolution of singularities. We also study the induced torus action on the Nash blow-up and give a bijection between its torus fixed points and Peterson translates on the Schubert variety.