ShantanuT01/DACTYL-Pretraining huggingface dataset:
For any set $S$ of positive integers, a mixed hypergraph ${\cal H}$ is a one-realization of $S$ if its feasible set is $S$ and each entry of its chromatic spectrum is either 0 or 1. In this paper, we determine the minimum size of 3-uniform bi-hypergraphs which are one-realizations of a given set $S$. As a result, we partially solve an open problem proposed by Bujt$\acute{\rm a}$s and Tuza in 2008.
Using the HST STIS spectrograph we have obtained a grid of [O III] and H-beta emission-line spectra at 0"05x0"19 and 60 km/s (FWHM) resolution that covers much of the NLR of NGC 1068. We find emitting knots that have blueshifted radial velocities up to 3200 km/s relative to galaxy systemic, are 70-150 pc NE of the nucleus and up to 40 pc from the radio jet, emit several percent of the NLR line flux but no significant continuum, span velocity extents of up to 1250 km/s but a small fraction of the sky seen from the nucleus, coincide with a region of enhanced IR coronal-line emission, and have ionized masses $\sim$200 Msun/ne4 (ne4=10^4 cm^{-3}). We argue that the blueshifted knots are ablata from disintegrating molecular clouds that are being photoionized by the AGN, and are being accelerated readiatively by the AGN or mechanically by the radio jet. In their kinematic properties, the knots resemble the associated absorbers seen projected on the UV continua of some AGN. Between 2"5-4"5 from the nucleus, emission is redshifted relative to systemic, a pattern that we interpret as gas in the galaxy disk being pushed away from us by the NE radio lobe.
Using a detailed Galactic model in which we consider distinct contributions from the bulge, thin disc, thick disc, and halo, and a population synthesis approach, we determined the birth rates, numbers, and period distributions of double white dwarfs (DWDs) within each component. In the Galaxy as a whole, our model predicts the current birth rate of DWDs to be 3.21x10^{-2} yr^{-1}, the local density to be 2.2x10^{-4} pc^{-3} and the total number to be 2.76x10^{8}. Assuming SNIa are formed from the merger of two CO white dwarfs, the SNIa rate should be 0.0013 yr^{-1}. The frequency spectra of DWD strain amplitude and number distribution are presented as a function of galactic component, DWD type, formation channel, and metallicity. We confirm that CO+He and He+He white dwarf (WD) pairs should dominate the GW signal at very high frequencies (log f Hz^{-1} > -2.3), while CO+CO and ONeMg WD pairs have a dominant contribution at log f Hz^{-1} < -2.3. Formation channels involving two common-envelope (CE) phases or a stable Roche lobe overflow phase followed by a CE phase dominate the production of DWDs detectable by LISA at log f Hz^{-1} > -4.5. DWDs with the shortest orbital periods will come from the CE+CE channel. The Exposed Core plus CE channel is a minor channel. A number of resolved DWDs would be detected, making up 0.012% of the total number of DWDs in the Galaxy. The majority of these would be CO+He and He+He pairs formed through the CE+CE channel.
The concepts of an instanton vacuum and F-invariance are used to derive a complete effective theory of massless edge excitations in the quantum Hall effect. We establish, for the first time, the fundamental relation between the instanton vacuum approach and the theory of chiral edge bosons. Two longstanding problems of smooth disorder and Coulomb interactions are addressed. We introduce a two dimensional network of chiral edge states and tunneling centers (saddlepoints) as a model for the plateau transitions. We derive a mean field theory including the Coulomb interactions and explain the recent empirical fits to transport at low temperatures. Secondly, we address the problem of electron tunneling into the quantum Hall edge. We express the problem in terms of an effective Luttinger liquid with conductance parameter (g) equal to the filling fraction (\nu) of the Landau band. Hence, even in the integral regime our results for tunneling are completely non-Fermi liquid like, in sharp contrast to the predictions of single edge theories.
We study the propagation in time of $1/2$-Gelfand-Shilov singularities, i.e. global analytic singularities, of tempered distributional solutions of the initial value problem \begin{align*} \begin{cases} u_t + q^w(x,D) u = 0 \\ u|_{t=0} = u_0, \end{cases} \end{align*} on $\mathbb{R}^n$, where $u_0$ is a tempered distribution on $\mathbb{R}^n$, $q=q(x,\xi)$ is a complex-valued quadratic form on $\mathbb{R}^{2n} = \mathbb{R}^n_x \times \mathbb{R}^n_\xi$ with nonnegative real part $\textrm{Re} \ q \ge 0$, and $q^w(x,D)$ is the Weyl quantization of $q$. We prove that the $1/2$-Gelfand-Shilov singularities of the initial data that are contained within a distinguished linear subspace of the phase space $\mathbb{R}^{2n}$, called the singular space of $q$, are transported by the Hamilton flow of $\textrm{Im} \ q$, while all other $1/2$-Gelfand-Shilov singularities are instantaneously regularized. Our result extends the observation of Hitrik, Pravda-Starov, and Viola '18 that this evolution is instantaneously globally analytically regularizing when the singular space of $q$ is trivial.
In this paper we address the problem of finding well approximating lattices for a given finite set $A$ of points in ${\mathbb R}^n$. More precisely, we search for $\v{o},\v{d_1}, \dots,\v{d_n}\in \mathbb{R}^n$ such that $\v{a}-\v{o}$ is close to $\Lambda=\v{d_1}\mathbb{Z}+\dots+\v{d_n}\mathbb{Z}$ for every $\v{a}\in A$. First we deal with the one-dimensional case, where we show that in a sense the results are almost the best possible. These results easily extend to the multi-dimensional case where the directions of the axes are given, too. Thereafter we treat the general multi-dimensional case. Our method relies on the LLL algorithm. Finally we apply the least squares algorithm to optimize the results. We give several examples to illustrate our approach.
In this paper we focus on the open symmetric exclusion process with parameter $m$ (open SEP($m/2$)), which allows $m$ particles each site and has an open boundary. We generalize the result about hydrodynamic limit for the open SEP$(m/2)$ that was originally raised in Theorem 4.12 of arXiv:1908.02359. We prove that the hydrodynamic limit of the density profile for a $d-$dimensional open SEP$(m/2)$ solves the $(d+1)-$dimensional heat equation with certain initial condition and boundary condition.
We report magneto-dielectric properties of partially B-site ordered monoclinic Tb2CoMnO6 double perovskite thin film epitaxially grown by metalorganic aerosol deposition technique. Transmission electron microscopy and electron energy loss spectroscopy mapping shows the presence and distribution of both Co2+ and Co3+ ions in the film, evidencing a partial B-site disorder, which was further confirmed by the observation of reduced saturation magnetization at low temperatures. The ferromagnetic Curie temperature, TC=110 K, is slightly higher as compared to the bulk value (100 K) probably due to an in plane tensile strain. Remarkably, a short range ordering of spins at T*~190 K>>TC was established and assigned to the B-site disorder in the film. Two different dielectric relaxation peaks have been observed; they merge at the same temperature T* of short range spin correlations. Moreover, an unexpected high temperature dipolar relaxor-glass-like transition at T~T* was observed, at which a coupling to short range magnetic correlations results in a 4% magneto-dielectric coupling.
The compelling experimental evidences for oscillations of solar, reactor, atmospheric and accelerator neutrinos imply the existence of 3-neutrino mixing in the weak charged lepton current. The current data on the 3-neutrino mixing parameters are summarised and the phenomenology of 3-$\nu$ mixing is reviewed. The properties of massive Majorana neutrinos and of their various possible couplings are discussed in detail. Two models of neutrino mass generation with massive Majorana neutrinos - the type I see-saw and the Higgs triplet model, are briefly reviewed. The problem of determining the nature - Dirac or Majorana, of massive neutrinos is considered. The predictions for the effective Majorana mass $\meff$ in neutrinoless double beta ($\betabeta-$) decay in the case of 3-neutrino mixing and massive Majorana neutrinos are summarised. The physics potential of the experiments, searching for $\betabeta-$decay for providing information on the type of the neutrino mass spectrum, on the absolute scale of neutrino masses and on the Majorana CP-violation phases in the PMNS neutrino mixing matrix, is also briefly discussed. The opened questions and the main goals of future research in the field of neutrino physics are outlined.
Low-mass members of young stellar associations exhibit a wide spread of rotation periods. Such a spread originates from distributions of masses and initial rotation periods. However, multiplicity can also play a significant role. We investigate the role played by physical companions in shortening the primordial disc lifetime. We have compiled the most extensive list of low-mass members of the young 25-Myr beta Pictoris association. We have measured the rotation periods of about all members and used updated UVWXYZ components to assess their membership. We built the rotation period distribution distinguishing between bona fide members and candidate members and according to their multiplicity status. We found that single stars and components of multiple systems in wide orbits (>80 AU) have rotation periods that exhibit a well defined sequence arising from mass distribution. All components of multiple systems in close orbits (<80 AU) have rotation periods significantly shorter than their equal-mass single counterparts. A comparison with the younger 13 Myr h Per cluster and with the older 40-Myr open clusters/stellar associations NGC2547, IC2391, Argus, and IC2602 and the 130-Myr Pleiades shows that whereas the evolution of F-G stars is well reproduced by angular momentum evolution models, this is not the case for the slow K and early-M stars. Finally, we found that the amplitude of their light curves is correlated neither with rotation nor with mass. Once single stars and wide components of multiple systems are separated from close components of multiple systems, the rotation period distributions exhibit a well defined dependence on mass that allows to make a meaningful comparison with similar distributions of either younger or older associations/clusters. Such cleaned distributions allow to use the stellar rotation period as age indicator, meaningfully for F and G type stars.
Observations indicate that roughly 60% of the baryons may exist in a Warm-Hot Intergalactic Medium (WHIM) at low redshifts. Following up on previous results showing that gas is released through galaxy mergers, we use a semi-analytic technique to estimate the fraction of gas mass lost from haloes solely due to mergers. We find that up to ~25% of the gas in a halo can unbind over the course of galaxy assembly. This process does not act preferentially on smaller mass haloes; bigger haloes \emph{always} release larger amounts of gas in a given volume of the Universe. However, if we include multi-phase gas accretion onto haloes, we find that only a few percent is unbound. We conclude that either non-gravitational processes may be in play to heat up the gas in the galaxies prior to unbinding by mergers or most of the baryons in the WHIM have never fallen into virialised dark matter haloes. We present a budget for stocking the WHIM compiled from recent work.
The exclusive production of double excited quarkonium is comprehensive studied, i.e., the production of double excitedcharmonium, double excited bottomonium, and double excited $Bc$-mesons via $e^+e^-\to \gamma^*/Z^0 \to|(Q\bar{Q'})[n]\rangle +|(Q'\bar{Q})[n']\rangle$ ($Q/Q'=c$- or $b$-quarks) at a future $Z$ factory under the nonrelativistic quantum chromodynamics framework, where the $[n]$~/$[n']$ represents the color-singlet heavy quarkonium states $[^1S_0]\rangle, ~[^3S_1]\rangle, ~[^1P_1]\rangle$, and $[^3P_J]\rangle$ ($J=0,1,2$). The "improved trace technology" is adopted for calculating the complicated $P$-wave channels for derive the analytic expressions at the amplitude level. According to our study, the production rates of double heavy quarkonium are considerable at the future $Z$ factory. We obtain the cross sections for the production of double excited charmonium for $\sigma{(|(c\bar{c})[n]\rangle+|(c\bar{c})[n']\rangle)_{total}}=1.167^{+0.113}_{-0.164}\times 10^{-2}~fb$, the cross sections of double excited bottomonium for $\sigma{(|(b\bar{b})[n]\rangle+|(b\bar{b})[n']\rangle)_{total}}=0.1132^{+0.0139}_{-0.0130}~fb$, and the cross sections of double excited $Bc$-mesons for $\sigma{(|(c\bar{b})[n]\rangle+|(b\bar{c})[n']\rangle)_{total}}=3.692^{+0.124}_{-0.097}~fb$. The main uncertainties come from the mass of the heavy quarkonium and the radial wave functions at the origin and their derivatives at the origin under different potential models. The numerical results show that such the super $Z$ factory should be a good platform to study the properties of the double excited charmonium, the double excited bottomonium , especially the double excited $Bc$-mesons.
The optical conductivity \sigma(\omega) in the two-dimensional Hubbard model is examined by applying the exact diagonalization technique to small square clusters with periodic boundary conditions up to \sqrt{20} X \sqrt{20} sites. Spectral-weight distributions at half filling and their doping dependence in the 20-site cluster are found to be similar to those in a \sqrt{18} X \sqrt{18} cluster, but different from 4 X 4 results. The results for the 20-site cluster enable us to perform a systematic study of the doping dependence of the spectral-weight transfer from the region of the Mott-gap excitation to lower-energy regions. We discuss the dependence of the Drude weight and the effective carrier number on the electron density at a large on-site Coulomb interaction.
In this paper, we study a class of nonlocal dispersion equation with monostable nonlinearity in $n$-dimensional space u_t - J\ast u +u+d(u(t,x))= \int_{\mathbb{R}^n} f_\beta (y) b(u(t-\tau,x-y)) dy, u(s,x)=u_0(s,x), s\in[-\tau,0], \ x\in \mathbb{R}^n} \] where the nonlinear functions $d(u)$ and $b(u)$ possess the monostable characters like Fisher-KPP type, $f_\beta(x)$ is the heat kernel, and the kernel $J(x)$ satisfies ${\hat J}(\xi)=1-\mathcal{K}|\xi|^\alpha+o(|\xi|^\alpha)$ for $0<\alpha\le 2$. After establishing the existence for both the planar traveling waves $\phi(x\cdot{\bf e}+ct)$ for $c\ge c_*$ ($c_*$ is the critical wave speed) and the solution $u(t,x)$ for the Cauchy problem, as well as the comparison principles, we prove that, all noncritical planar wavefronts $\phi(x\cdot{\bf e}+ct)$ are globally stable with the exponential convergence rate $t^{-n/\alpha}e^{-\mu_\tau}$ for $\mu_\tau>0$, and the critical wavefronts $\phi(x\cdot{\bf e}+c_*t)$ are globally stable in the algebraic form $t^{-n/\alpha}$. The adopted approach is Fourier transform and the weighted energy method with a suitably selected weight function. These rates are optimal and the stability results significantly develop the existing studies for nonlocal dispersion equations.
We review the current high-significance X-ray detections of Warm-Hot Intergalactic Medium (WHIM) filaments at z>0 along the lines of sight to the two blazars Mrk 421 (z=0.03) and 1ES 1028+511 (z=0.361). For these WHIM filaments, we derive ionization corrections and, when possible, metallicity estimates. This allows us to obtain refined estimates of the number density of O VII WHIM systems down to the O VII column density sensitivity of our observations, and most importantly, a measurement of the cosmological mass density Omega_b^{WHIM} in the WHIM, at redshift z<0.361. These estimates agree well with model predictions and with the total estimated amount of missing baryons in the local Universe, although errors are large, due to the still limited number of systems. We conclude discussing future observational strategies and mission designs for WHIM studies.
Let $f\in L^1(\R^d)$ be real. The Rudin-Osher-Fatemi model is to minimize $\|u\|_{\dot{BV}}+\lambda\|f-u\|_{L^2}^2$, in which one thinks of $f$ as a given image, $\lambda > 0$ as a "tuning parameter", $u$ as an optimal "cartoon" approximation to $f$, and $f-u$ as "noise" or "texture". Here we study variations of the R-O-F model having the form $\inf_u\{\|u\|_{\dot{BV}}+\lambda \|K*(f-u)\|_{L^p}^q\}$ where $K$ is a real analytic kernel such as a Gaussian. For these functionals we characterize the minimizers $u$ and establish several of their properties, including especially their smoothness properties. In particular we prove that on any open set on which $u \in W^{1,1}$ and $\nabla u \neq 0$ almost every level set $\{u =c\}$ is a real analytic surface. We also prove that if $f$ and $K$ are radial functions then every minimizer $u$ is a radial step function.
We study the response of the antiferromagnetism of CeAuSb$_2$ to orthorhombic lattice distortion applied through in-plane uniaxial pressure. The response to pressure applied along a $\langle 110 \rangle$ lattice direction shows a first-order transition at zero pressure, which shows that the magnetic order lifts the $(110)/(1\bar{1}0)$ symmetry of the unstressed lattice. Sufficient $\langle 100 \rangle$ pressure appears to rotate the principal axes of the order from $\langle 110 \rangle$ to $\langle 100 \rangle$. At low $\langle 100 \rangle$ pressure, the transition at $T_N$ is weakly first-order, however it becomes continuous above a threshold $\langle 100 \rangle$ pressure. We discuss the possibility that this behavior is driven by order parameter fluctuations, with the restoration of a continuous transition a result of reducing the point-group symmetry of the lattice.
Factorization in gauge theories holds at the amplitude or amplitude-squared level for states of given soft or collinear momenta. When performing phase-space integrals over such states, one would generally like to avoid putting in explicit cuts to separate soft from collinear momenta. Removing these cuts induces an overcounting of the soft-collinear region and adds new infrared-ultraviolet divergences in the collinear region. In this paper, we first present a regulator-independent subtraction algorithm for removing soft-collinear overlap at the amplitude level which may be useful in pertubative QCD. We then discuss how both the soft-collinear and infrared-ultraviolet overlap can be undone for certain observables in a way which respects factorization. Our discussion clarifies some of the subtleties in phase-space subtractions and includes a proof of the infrared finiteness of a suitably subtracted jet function. These results complete the connection between factorized QCD and Soft-Collinear Effective Theory.
The main goal of this paper is to prove a formula that expresses the limit behaviour of Dedekind zeta functions for $\Re s > 1/2$ in families of number fields, assuming that the Generalized Riemann Hypothesis holds. This result can be viewed as a generalization of the Brauer--Siegel theorem. As an application we obtain a limit formula for Euler--Kronecker constants in families of number fields.
We study the dynamics of one-dimensional (1D) interacting particles simulated with the event-chain Monte Carlo algorithm (ECMC). We argue that previous versions of the algorithm suffer from a mismatch in the factor potential between different particle pairs (factors) and show that in 1D models, this mismatch is overcome by factor fields. ECMC with factor fields is motivated, in 1D, for the harmonic model, and validated for the Lennard-Jones model as well as for hard spheres. In 1D particle systems with short-range interactions, autocorrelation times generally scale with the second power of the system size for reversible Monte Carlo dynamics, and with its first power for regular ECMC and for molecular-dynamics. We show, using numerical simulations, that they grow only with the square root of the systems size for ECMC with factor fields. Mixing times, which bound the time to reach equilibrium from an arbitrary initial configuration, grow with the first power of the system size.
We prove the boundedness theorem for Fano threefolds with log-terminal singularities of any fixed index. This is an improvement of our earlier result, where we required additionally that the variety is Q-factorial, with Picard number 1. The new ideas of the paper include the following.   1. Using Alexeev Minimal Model program with suitable boundary to find horizontal extremal contractions.   2. Using Koll\'ar's effective Base Point Freeness theorem.   3. Using Kawamata's result on the length of extremal curves with suitable boundary to avoid gluing curves in some cases.
Solar flare accelerated electrons escaping into the interplanetary space and seen as type III solar radio bursts are often detected near the Earth. Using numerical simulations we consider the evolution of energetic electron spectrum in the inner heliosphere and near the Earth. The role of Langmuir wave generation, heliospheric plasma density fluctuations, and expansion of magnetic field lines on the electron peak flux and fluence spectra is studied to predict the electron properties as could be observed by Solar Orbiter and Solar Probe Plus. Considering various energy loss mechanisms we show that the substantial part of the initial energetic electron energy is lost via wave-plasma processes due to plasma inhomogeneity. For the parameters adopted, the results show that the electron spectra changes mostly at the distances before $\sim20 R_\odot$. Further into the heliosphere, the electron flux spectra of electrons forms a broken power-law relatively similar to what is observed at 1 AU.
The nebular phase of lanthanide-rich ejecta of a neutron star merger (NSM) is studied by using a one-zone model, in which the atomic properties are represented by a single species, neodymium (Nd). Under the assumption that beta-decay of r-process nuclei is the heat and ionization source, we solve the ionization and thermal balance of the ejecta under non-local thermodynamic equilibrium. The atomic data including energy levels, radiative transition rates, collision strengths, and recombination rate coefficients, are obtained by using atomic structure codes, GRASP2K and HULLAC. We find that both permitted and forbidden lines roughly equally contribute to the cooling rate of Nd II and Nd III at the nebular temperatures. We show that the kinetic temperature and ionization degree increase with time in the early stage of the nebular phase while these quantities become approximately independent of time after the thermalization break of the heating rate because the processes relevant to the ionization and thermalization balance are attributed to two-body collision between electrons and ions at later times. As a result, in spite of the rapid decline of the luminosity, the shape of the emergent spectrum does not change significantly with time after the break. We show that the emission-line nebular spectrum of the pure Nd ejecta consists of a broad structure from $0.5\,\mu m$ to $20\,\mu m$ with two distinct peaks around $1\,\mu m$ and $10\,\mu m$.
The time evolution of low energy spin states of a single molecular magnet in a local electric field is investigated. The decoherence of the driven single molecular magnet weakly coupled to a thermal bosonic environment is analyzed by the second-order time-convolutionless non-Markovian master equation. If the characteristic time of the system is much smaller than the correlation time of the environment, the analytical expression of the reduced density matrix of the system is obtained. The non-Markovian dynamics of the spin states at low temperatures is induced by the memory effects in the decay rates. The non-Markovian oscillation of the Bloch vector is presented. The quantum decoherence can be effectively restrained with the help of the reasonable manipulation of the environment spectral density function and local electric field. The influence of the dissipation on the pointer states are investigated by the von Neumann entropy. The pointer states can be selected by the environment.