ShantanuT01/DACTYL-Pretraining huggingface dataset:
We show that if ${\mathcal A},{\mathcal B},{\mathcal C}$ are increasing subsets of $\Omega:=\{0,1\}^n$ with ${\mathcal A}\neq\emptyset$, then with respect to any product probability measure on $\Omega$, \[ \mbox{if each of the pairs $\{{\mathcal A}\cap{\mathcal B},{\mathcal C}\}$, $\{{\mathcal A}\cap {\mathcal C},{\mathcal A}\}$ is independent, then ${\mathcal B}$ and ${\mathcal C}$ are independent.} \] This implies an answer to a motivating question of J. Steif, and is related to a basic, still open variant of that question, and to a well-known conjecture of S. Sahi.
We present a generic reweighting method for nonequilibrium Markov processes. With nonequilibrium Monte Carlo simulations at a single temperature, one calculates the time evolution of physical quantities at different temperatures, which greatly saves the computational time. Using the dynamical finite-size scaling analysis for the nonequilibrium relaxation, one can study the dynamical properties of phase transitions together with the equilibrium ones. We demonstrate the procedure for the Ising model with the Metropolis algorithm, but the present formalism is general and can be applied to a variety of systems as well as with different Monte Carlo update schemes.
In some low-luminosity accreting supermassive black hole systems, the supply of plasma in the funnel region can be a problem. It is believed that a local region with unscreened electric field can exist in the black hole magnetosphere, accelerating particles and producing high energy gamma-rays that can create $e^{\pm}$ pairs. We carry out time-dependent self-consistent 1D PIC simulations of this process, including inverse Compton scattering and photon tracking. We find a highly time-dependent solution where a macroscopic gap opens quasi-periodically to create $e^{\pm}$ pairs and high energy radiation. If this gap is operating at the base of the jet in M87, we expect an intermittency on the order of a few $r_g/c$, which coincides with the time scale of the observed TeV flares from the same object. For Sagittarius A* the gap electric field can potentially grow to change the global magnetospheric structure, which may explain the lack of a radio jet at the center of our galaxy.
The observational mass-radius relation of main sequence stars with masses between ~0.3 and 1.0 Msun reveals deviations between the stellar radii predicted by models and the observed radii of stars in detached binaries. We generate an accurate physical model of the low-mass eclipsing binary T-Cyg1-12664 in the Kepler mission field to measure the physical parameters of its components and to compare them with the prediction of theoretical stellar evolution models. We analyze the Kepler mission light curve of T-Cyg1-12664 to accurately measure the times and phases of the primary and secondary eclipse. In addition, we measure the rotational period of the primary component by analyzing the out-of-eclipse oscillations that are due to spots. We accurately constrain the effective temperature of the system using ground-based absolute photometry in B, V, Rc, and Ic. We also obtain and analyze V, Rc, Ic differential light curves to measure the eccentricity and the orbital inclination of the system, and a precise Teff ratio. From the joint analysis of new radial velocities and those in the literature we measure the individual masses of the stars. Finally, we use the PHOEBE code to generate a physical model of the system. T-Cyg1-12664 is a low eccentricity system, located d=360+/-22 pc away from us, with an orbital period of P=4.1287955(4) days, and an orbital inclination i=86.969+/-0.056 degrees. It is composed of two very different stars with an active G6 primary with Teff1=5560+/-160 K, M1=0.680+/-0.045 Msun, R1=0.799+/-0.017 Rsun, and a M3V secondary star with Teff2=3460+/-210 K, M2=0.376+/-0.017 Msun, and R2=0.3475+/-0.0081 Rsun. The primary star is an oversized and spotted active star, hotter than the stars in its mass range. The secondary is a cool star near the mass boundary for fully convective stars (M~0.35 Msun), whose parameters appear to be in agreement with low-mass stellar model.
We study the impact of an exchange-reducing defect on a skyrmion for a thin film of finite thickness. Attraction of the skyrmion to a defect is demonstrated in a lattice model by computing the micromagnetic energy accounting for the exchange, Dzyaloshinskii-Moriya interaction, magnetic anisotropy, and dipole-dipole coupling. The spiraling dynamics of the skyrmion towards the defect is illustrated by solving numerically the full Landau-Lifshitz-Gilbert equations on a lattice and, independently, the Thiele equation, with the two methods in agreement with each other. We find that the skyrmion deforms when approaching the defect. Deformation is small in the parameter space far from the phase boundary that determines stability of skyrmions. It increases dramatically near the phase boundary, leading to the transformation of the skyrmion by the defect into a snake-like magnetic domain.
Utilizing the unbiased time-dependent density-matrix renormalization group technique, we examine the photoemission spectra in the extended Falicov-Kimball model at zero and finite temperatures, particularly with regard to the excitonic insulator state most likely observed in the quasi-one-dimensional material Ta$_2$NiSe$_5$. Working with infinite boundary conditions, we are able to simulate all dynamical correlation functions directly in the thermodynamic limit. For model parameters best suited for Ta$_2$NiSe$_5$ the photoemission spectra show a weak but clearly visible two-peak structure, around the Fermi momenta $k\simeq\pm k_{\rm F}$, which suggests that Ta$_2$NiSe$_5$ develops an excitonic insulator of BCS-like type. At higher temperatures, the leakage of the conduction-electron band beyond the Fermi energy becomes distinct, which provides a possible explanation for the bare non-interacting band structure seen in time- and angle-resolved photoemission spectroscopy experiments.
Recent calculations of accretion-induced collapse of an oxygen-neon-magnesium white dwarf into a neutron star [Piro & Thompson 2014] allow for a potentially detectable transient electromagnetic signal. Motivated by these results, I present theoretical rates and physical properties of binary stars that can produce accretion-induced collapse. The rates are presented for various types of host galaxies (e.g. old ellipticals versus spirals) and are differentiated by the donor star type (e.g. large giant star versus compact helium-rich donor). Results presented in this thesis may help to guide near-future electromagnetic transient search campaigns to find likely candidates for accretion-induced collapse events. My predictions are based on binary evolution calculations that include the most recent updates on mass accretion and secular mass growth of white dwarfs. I find that the most likely systems that undergo accretion-induced collapse consist of an ONeMg white dwarf with a Hertzsprung gap star or a red giant companion. Typical rates are of the order ~1-5 x 10^-5 1/yr and ~10^-4-10^-5 1/yr in large spiral galaxies and old ellipticals, respectively. The brightest electromagnetic signals are predicted for evolved giant type donors for which I find rates of the order ~2.5 x 10^-5 1/yr (large spirals) and ~1.3 x 10^-5 1/yr (old ellipticals).
In this paper, we discuss initial-boundary value problems for linear diffusion equation with multiple time-fractional derivatives. By means of the Mittag-Leffler function and the eigenfunction expansion, we reduce the problem to an integral equation for a solution, and we apply the fixed-point theorem to prove the unique existence and the H\"older regularity of solution. For the case of the homogeneous equation, the solution can be analytically extended to a sector $\{z\in\mathbb{C};z\neq0,|\arg z|<\frac{\pi}{2}\}$. In the case where all the coefficients of the time-fractional derivatives are positive constants, by the Laplace transform and the analyticity, we can prove that if a function satisfies the fractional diffusion equation and the homogeneous Neumann boundary condition on arbitrary subboundary as well as the homogeneous Dirichlet boundary condition on the whole boundary, then it vanishes identically.
We derive the optimal exponent of the error probability of the quantum fixed-length pure state source coding in both cases of blind coding and visible coding. The optimal exponent is universally attained by Jozsa et al. (PRL, 81, 1714 (1998))'s universal code. In the direct part, a group representation theoretical type method is essential. In the converse part, Nielsen and Kempe (PRL, 86, 5184 (2001))'s lemma is essential.
A pair of non-thermal radio bubbles recently discovered in the inner few hundred parsecs of the Galactic center bears a close spatial association with elongated, thermal X-ray features called the X-ray chimneys. While their morphology, position, and orientation vividly point to an outflow from the Galactic center, the physical processes responsible for the outflow remain to be understood. We use three-dimensional magnetohydrodynamic simulations to test the hypothesis that the radio bubbles/X-ray chimneys are the manifestation of an energetic outflow driven by multiple core-collapsed supernovae in the nuclear stellar disk, where numerous massive stars are known to be present. Our simulations are run with different combinations of two main parameters, the supernova birth rate and the strength of a global magnetic field being vertically oriented with respect to the disk. The simulation results show that a hot gas outflow can naturally form and acquire a vertically elongated shape due to collimation by the magnetic pressure. In particular, the simulation with an initial magnetic field strength of 80 $\mu$G and a supernova rate of 1 $kyr^{-1}$ can well reproduce the observed morphology, internal energy and X-ray luminosity of the bubbles after an evolutionary time of 330 kyr. On the other hand, a magnetic field strength of 200 $\mu$G gives rise to an overly elongated outflow that is inconsistent with the observed bubbles. The simulations also reveal that, inside the bubbles, mutual collisions between the shock waves of individual supernovae produce dense filaments of locally amplified magnetic field. Such filaments may account for a fraction of the synchrotron-emitting radio filaments known to exist in the Galactic center.
This paper concerns the generation and evolution of the cosmological (large-scale $\sim Mpc$) magnetic fields in an inflationary universe. The universe during inflation is represented by de Sitter space-time. We started with the Maxwell equations in spatially flat Friedmann-Robertson-Walker (FRW) Cosmologies. Then we calculated the wave equations of the magnetic field and electric field for the evolution. We consider the input current that was produced from a massless charged scalar complex field. This field minimally coupled to both gravity and the electromagnetic fields. The Lagrangian for massless scalar electrodynamics is then $L=\sqrt{-g}(D_\mu\phi(D^\mu\phi)^*-{1/4}F_{\mu\nu}F^{\mu\nu})$ . The complex scalar field couples to electromagnetism through the usual gauge covariant derivative $D_\mu=\partial_\mu-ieA_\mu$ . After the quantum field theoretical deduction for the current, we put it back into the wave equation of the magnetic field.   After solving this wave equation, our result is $a^2B\sim \frac{eH}{\sqrt{2}k^2}\mid\sin\sqrt{2}k\eta\mid$ . At the time $\eta_{RH}$ we have $B_{RH}=\frac{e}{k_{phys}}$. This may imply that the breaking of the conformal invariance due to the minimal coupling of a massless charged scalar complex field to both gravitational and electromagnetic fields is not sufficient for the production of seed galactic magnetic fields during inflation. But since we are interested in the large-scale cosmological magnetic field, this could be still a candidate, because of the $1/k$ factor.
Differential and total breakup cross sections as well as vector and tensor analyzing powers for p-d scattering are studied for energies above the deuteron breakup threshold up to E(lab)=28 MeV. The p-d scattering wave function is expanded in terms of the correlated hyperspherical harmonic basis and the elastic S-matrix is obtained using the Kohn variational principle in its complex form. The effects of the Coulomb interaction, which are expected to be important in this energy range, have been rigorously taken into account. The Argonne AV18 interaction and the Urbana URIX three-nucleon potential have been used to perform a comparison to the available experimental data.
Suppose that $p$ is an odd prime and $\genfrac{(}{)}{}{}{\cdot}{p}$ denotes the Legendre symbol modulo $p$. If $p$ is has the form $p= n^2+1$ then one easily verifies that $\genfrac{(}{)}{}{}{a}{p} = \genfrac{(}{)}{}{}{-a}{p}$ for all $a\in \mathbb Z/p\mathbb Z$. We identify various symmetry properties of sequential matrices over $\mathbb Z/(n^2+1)\mathbb Z$ regardless of whether $n^2+1$ is prime. We deduce from these results a collection of symmetries involving Jacobi symbol modulo $n^2+1$ which generalize our above observation on the Legendre symbol.
We determine Tur\'an numbers for the family of 3-uniform minimal paths of length four \emph{for all $n$}. We also establish the second and third order Tur\'an numbers and use them to compute the corresponding Ramsey numbers for up to four colors.
We present a new method for identifying blazar candidates by examining the locus, i.e. the region occupied by the Fermi gamma-ray blazars in the three-dimensional color space defined by the WISE infrared colors. This method is a refinement of our previous approach that made used of the two-dimensional projection of the the distribution of WISE gamma-ray emitting blazars (the Strip) in the three WISE color-color planes. In this paper, we define the three-dimensional locus by means of a Principal Component analysis of the the colors distribution of a large sample of blazars composed by all the ROMA-BZCAT sources with counterparts in the WISE All-Sky Catalog and associated to a gamma-ray source in the second Fermi LAT catalog (2FGL) (the WISE Fermi Blazars sample, WFB). Our new procedure, as reported in [D'Abrusco et al. 2013], yields a total completeness of c=81% and total efficiency of e=97%.
The problem of identifying measurement scenarios capable of revealing state-independent contextuality in a given Hilbert space dimension is considered. We begin by showing that for any given dimension $d$ and any measurement scenario consisting of projective measurements, (i) the measure of contextuality of a quantum state is entirely determined by its spectrum, so that pure and maximally mixed states represent the two extremes of contextual behavior, and that (ii) state-independent contextuality is equivalent to the contextuality of the maximally mixed state up to a global unitary transformation. We then derive a necessary and sufficient condition for a measurement scenario represented by an orthogonality graph to reveal state-independent contextuality. This condition is given in terms of the fractional chromatic number of the graph $\chi_f(G)$ and is shown to identify all state-independent contextual measurement scenarios including those that go beyond the original Kochen-Specker paradigm \cite{Yu-Oh}.
We assess the influence of massive black hole (MBH) ejections from galaxy centres, due to the gravitational radiation recoil, along the cosmic merger history of the MBH population. We discuss the 'danger' of the recoil for MBHs as a function of different MBH spin/orbit configurations and of the host halo cosmic bias, and on how that reflects on the 'occupation fraction' of MBHs. We assess ejection probabilities for mergers occurring in a gas-poor environment, where the MBH binary coalescence is driven by stellar dynamical processes, and the spin/orbit configuration is expected to be isotropically distributed. We contrast this case with the 'aligned' case. The latter is the most realistic situation for 'wet', gas-rich mergers, which are the expectation for high-redshift galaxies. We find that if all halos at z>5-7 host a MBH, the probability of the Milky Way (or similar size galaxy) to host a MBH today is less than 50%, unless MBHs form continuously in galaxies. The 'occupation fraction' of MBHs, intimately related to halo bias and MBH formation efficiency, plays a crucial role in increasing the retention fraction. Small halos, with shallow potential wells and low escape velocities, have a high ejection probability, but the MBH merger rate is very low along their galaxy formation merger hierarchy: MBH formation processes are likely inefficient in such shallow potential wells. Recoils can decrease the overall frequency of MBHs in small galaxies to ~60%, while they have little effect on the frequency of MBHs in large galaxies (at most a 20% effect).
We consider a generalisation of the classical Lehmer problem about the parity distribution of an integer and its modular inverse. We use some known estimates of exponential sums to study a more general question of simultaneous distribution of the residues of any fixed number of negative and positive powers of integers in prescribed arithmetic progressions. In particular, we improve and generalise a recent result of Y. Yi and W. Zhang.
Rapid, non-destructive characterization of molecular level chemistry for organic matter (OM) is experimentally challenging. Raman spectroscopy is one of the most widely used techniques for non-destructive chemical characterization, although it currently does not provide detailed identification of molecular components in OM, due to the combination of diffraction-limited spatial resolution and poor applicability of peak-fitting algorithms. Here, we develop a genome-inspired collective molecular structure fingerprinting approach, which utilizes ab initio calculations and data mining techniques to extract molecular level chemistry from the Raman spectra of OM. We illustrate the power of such an approach by identifying representative molecular fingerprints in OM, for which the molecular chemistry is to date inaccessible using non-destructive characterization techniques. Chemical properties such as aromatic cluster size distribution and H/C ratio can now be quantified directly using the identified molecular fingerprints. Our approach will enable non-destructive identification of chemical signatures with their correlation to the preservation of biosignatures in OM, accurate detection and quantification of environmental contamination, as well as objective assessment of OM with respect to their chemical contents.
The kinematics of molecular gas are crucial for setting the stage for star formation. One key question related to the kinematic properties of gas is how they depend on the spatial scale. We aim to describe the CO spectra, velocity dispersions, and especially the linewidth-size relation, of molecular gas from cloud (parsec-) scales to kiloparsec scales in a complete region within the Milky Way disk. We utilise the census of molecular clouds within 2 kpc from our earlier work, together with CO emission data for them from the literature. We study the kinematics and the Larson's relations for the sample of individual clouds. We also mimic a face-on view of the Milky Way and analyse the kinematics of the clouds within apertures of 0.25-2 kpc in size. In this way, we describe the scale-dependency of the CO gas kinematics and Larson's relations. We describe the spectra of CO gas at cloud scales and in apertures between 0.25-2 kpc in our survey area. The spectra within the apertures are relatively symmetric but show non-Gaussian high-velocity wings. At cloud-scales, our sample shows a linewidth-size relation \sigma_v=1.5*R^{0.3\pm0.1} with a large scatter. The mass-size relation in the sample of clouds is M_{CO}= 794*R^{1.5\pm0.5}. The relations are also present for the apertures at kpc-scales. A suggestive dependency on galactic environment is seen, with apertures closer to the Galactic centre and the Sagittarius spiral arm having slightly higher velocity dispersions. We explore the possible effect of a diffuse component in the survey area, and find that such a component would widen the CO spectra and could flatten the linewidth-size relation. Understanding the nature of the possible diffuse CO component and its effects on observations is crucial for connecting Galactic and extragalactic data.
In 2010, Hrushovski--Loeser showed that the Berkovich analytification of a quasi-projective variety over a non-Archimedean valued field admits a deformation retraction onto a finite simplicial complex. In this article, we adapt the tools and methods developed by Hrushovski--Loeser to study if such deformation retractions can be obtained to be compatible with respect to a given morphism. Amongst other results, we show that compatible deformation retractions exist over a constructible partition of the base and prove the general statement in the case of a morphism of relative dimension 1 where the target is a smooth connected curve.
We discuss a new method for setting limits on small signals in the presence of background noise. The method is based on a combination of a two dimensional confidence region and the large sample approximation to the likelihood ratio test statistic. It automatically quotes upper limits for small signals and two-sided confidence intervals for larger samples. We show that this method gives the correct coverage and also has good power.
We conducted an analysis of the distribution of elements from lithium to europium in 200 dwarfs in the solar neighbourhood ~20 pc with temperatures in the range 4800-6200 K and metallicities [Fe/H] higher than -0.5 dex. Determinations of atmospheric parameters and the chemical composition of the dwarfs were taken from our previous studies. We found that the lithium abundances in the planet-hosting solar-analog stars of our sample were lower than those in the stars without planetary systems. Our results reveal no significant differences exceeding the determination errors for the abundances of investigated elements, except for aluminium and barium, which are more and less abundant in the planet-hosting stars, respectively. We did not find confident dependences of the lithium, aluminium and barium abundances on the ages of our target stars (which is probable because of the small number of stars). Furthermore, we found no correlation between the abundance differences in [El/Fe] and the condensation temperature (Tcond) for stars in the 16 Cyg binary system, unlike the case for 51 Peg (HD 217014), for which a slight excess of volatile elements and a deficit of refractories were obtained relative to those of solar twins. We found that one of the components of 16 Cyg exhibits a slightly higher average abundance than its counterpart (<[El/H](A-B)> = 0.08+/-0.02 dex); however, no significant abundance trend versus Tcond was observed. Owing to the relatively large errors, we cannot provide further constraints for this system.
The relativistic perturbative approach based on the Bethe-Salpeter (BS) equation is developed for the study of the characteristics of the hadronic pi+ pi- atom. The general expression for the atom lifetime is derived. Lowest-order corrections to the relativistic Deser-type formula for the atom lifetime are evaluated within the Chiral Perturbation Theory. The lifetime of the pi+ pi- atom in the two-loop order of the Chiral Perturbation Theory is predicted to be tau_1=(3.03\pm 0.10)\times 10^{-15}~s.