ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider a conjecture of Kontsevich and Soibelman which is regarded as a foundation of their theory of motivic Donaldson-Thomas invariants for non-commutative 3d Calabi-Yau varieties. We will show that, in some certain cases, the answer to this conjecture is positive.
False alarm is one of the main concerns in intensive care units and can result in care disruption, sleep deprivation, and insensitivity of care-givers to alarms. Several methods have been proposed to suppress the false alarm rate through improving the quality of physiological signals by filtering, and developing more accurate sensors. However, significant intrinsic correlation among the extracted features limits the performance of most currently available data mining techniques, as they often discard the predictors with low individual impact that may potentially have strong discriminatory power when grouped with others. We propose a model based on coalition game theory that considers the inter-features dependencies in determining the salient predictors in respect to false alarm, which results in improved classification accuracy. The superior performance of this method compared to current methods is shown in simulation results using PhysionNet's MIMIC II database.
Bulk magnetite (Fe3O4), the loadstone used in magnetic compasses, has been known to exhibit magnetoelectric (ME) properties below ~10 K; however, corresponding ME effects in Fe3O4 nanoparticles have been enigmatic. We investigate quantitatively the ME coupling of spherical Fe3O4 nanoparticles with uniform diameters (d) from 3 to 15 nm embedded in an insulating host, using a sensitive ME susceptometer. The intrinsic ME susceptibility (MES) of the Fe3O4 nanoparticles is measured, exhibiting a maximum value of ~0.6 ps/m at 5 K for d=15 nm. We found that the MES is reduced with reduced d but remains finite until d=~5 nm, which is close to the critical thickness for observing the Verwey transition. Moreover, with reduced diameter, the critical temperature below which the MES becomes conspicuous increased systematically from 9.8 K in the bulk to 19.7 K in the nanoparticles with d=7 nm, reflecting the core-shell effect on the ME properties. These results point to a new pathway for investigating ME effect in various nanomaterials.
We analyze the cold dark matter density profiles of 54 galaxy halos simulated with FIRE-2 galaxy formation physics, each resolved within $0.5\%$ of the halo virial radius. These halos contain galaxies with masses that range from ultra-faint dwarfs ($M_\star \simeq 10^{4.5} M_{\odot}$) to the largest spirals ($M_\star \simeq 10^{11} M_{\odot}$) and have density profiles that are both cored and cuspy. We characterize our results using a new analytic density profile that extends the standard Einasto form to allow for a pronounced constant-density core in the resolved innermost radius. With one additional core-radius parameter, $r_{c}$, this "core-Einasto" profile is able to characterize the shape and normalization of our feedback-impacted dark matter halos. In order to enable comparisons with observations, we provide fitting functions for $r_{c}$ and other profile parameters as a function of both $M_\star$ and $M_{\star}/M_{\rm halo}$. In agreement with similar studies done in the literature, we find that dark matter core formation is most efficient at the characteristic stellar-mass to halo-mass ratio $M_\star/M_{\rm halo} \simeq 5 \times 10^{-3}$, or $M_{\star} \sim 10^9 \, M_{\odot}$, with cores that are roughly the size of the galaxy half-light radius, $r_{c} \simeq 1-5$ kpc. Furthermore, we find no evidence for core formation at radii $\gtrsim 100\ \rm pc$ in galaxies with $M_{\star}/M_{\rm halo} < 5\times 10^{-4}$ or $M_\star \lesssim 10^6 \, M_{\odot}$. For Milky Way-size galaxies, baryonic contraction often makes halos significantly more concentrated and dense at the stellar half-light radius than dark matter only runs. However, even at the Milky Way scale, FIRE-2 galaxy formation still produces small dark matter cores of $\simeq 0.5-2$ kpc in size. Recent evidence for a ${\sim} 2$ kpc core in the Milky Way's dark matter halo is consistent with this expectation.
Using the Planck far-infrared and Arecibo GALFA 21-cm line surveys, we identified a set of isolated interstellar clouds (approximately degree-sized on the sky and comprising 100 solar masses) and assessed the ratio of gas mass to dust mass. Significant variations of the gas-to-dust ratio are found both from cloud to cloud and within regions of individual clouds; within the clouds, the atomic gas per unit dust decreases by more than a factor of 3 compared to the standard gas-to-dust ratio. Three hypotheses are considered. First, the apparently low gas-to-dust ratio could be due to molecular gas. Comparing to Planck CO maps, the brightest clouds have a H2/CO ratio comparable to galactic plane clouds, but a strong lower limit is placed on the ratio for other clouds, such that the required amount of molecular gas is far higher than would be expected based on the CO upper limits. Second, we consider self-absorbed 21-cm lines and find the optical depth must be approximately 3, significantly higher than found from surveys of radio sources. Third, grain properties may change within the clouds: they become more emissive when they are colder, while not utilizing heavy elements that already have their cosmic abundance fully locked into grains. It is possible all three processes are active, and follow-up studies will be required to disentangle them and measure the true total gas and dust content of interstellar clouds.
At the end of the 1960s, Knuth characterised the permutations that can be sorted using a stack in terms of forbidden patterns. He also showed that they are in bijection with Dyck paths and thus counted by the Catalan numbers. Subsequently, Even \& Itai, Pratt and Tarjan studied permutations that can be sorted using two stacks in parallel. This problem is significantly harder. In particular, a sortable permutation can now be sorted by several distinct sequences of stack operations. Moreover, in order to be sortable, a permutation must avoid infinitely many patterns. The associated counting question has remained open for 40 years. We solve it by giving a pair of functional equations that characterise the generating function of permutations that can be sorted with two parallel stacks. The first component of this system describes the generating function Q(a,u) of square lattice loops confined to the positive quadrant, counted by the length and the number of North-West and East-South factors. Our analysis of the asymptotic number of sortable permutations relies at the moment on two intriguing conjectures dealing with the series Q(a,u). We prove that they hold for loops confined to the upper half plane, or not confined at all. They remain open for quarter plane loops. Given the recent activity on walks confined to cones, we believe them to be attractive per se.
We study the nonstationary solutions of Fokker-Planck equations associated to either stationary or nonstationary quantum states. In particular we discuss the stationary states of quantum systems with singular velocity fields. We introduce a technique that allows to realize arbitrary evolutions ruled by these equations, to account for controlled quantum transitions. The method is illustrated by presenting the detailed treatment of the transition probabilities and of the controlling time-dependent potentials associated to the transitions between the stationary, the coherent, and the squeezed states of the harmonic oscillator. Possible extensions to anharmonic systems and mixed states are briefly discussed and assessed.
The forward-backward multiplicity correlation strength is calculated for arbitrary nucleus-nucleus collision in the framework of the wounded nucleon model. Discussion of our results in the context of the recent STAR data in Au+Au collisions at sqrt{s}=200 GeV is presented. It is suggested that the observed (i) growth of the correlation coefficient with centrality and (ii) approximately flat pseudorapidity dependence of the correlation strength for central collisions are due to the fluctuations of the number of wounded nucleons at a given centrality bin.
We present a tutorial on the principles of crystal growth of intermetallic and oxide compounds from molten solutions, with an emphasis on the fundamental principles governing the underlying phase equilibria and phase diagrams of multicomponent systems.
We investigate the nucleosynthesis in a massive star of 70 M_solar with solar metallicity in the main sequence stage. The helium core mass after hydrogen burning corresponds to 32 M_solar. Nucleosynthesis calculations have been performed during the stellar evolution and the jetlike supernova explosion of a collapsar model, where the weak s-, p-, and r-processes are taken into account. We confirm that s-elements of 60 < A < 90 are highly overproduced relative to the solar abundances in the hydrostatic nucleosynthesis. During oxygen burning, p-elements of A > 90 are produced via photodisintegrations of seed s-elements. However, the produced p-elements are disintegrated in later stages except for ^{180}Ta. In the explosive nucleosynthesis, elements of 90 < A < 160 are significantly overproduced relative to the solar values owing to the r-process. Only heavy p-elements (N > 50) are overproduced via the p-process. Compared with the previous study of r-process nucleosynthesis calculations in the collapsar model of 40 M_solar by Fujimoto et al. 2007, 2008, our jet model cannot contribute to the third peak of the solar r-elements and intermediate p-elements. Averaging the overproduction factors over the progenitor masses with the use of Salpeter's IMF, we suggest that the 70 M_solar star could contribute to the solar weak s-elements of 60 < A < 90 and neutron-rich elements of 90 < A < 160. We confirm the primary synthesis of light p-elements in the ejected matter of high peak temperature. The ejected matter has [Sr/Eu] \sim -0.4, which is different from that of a typical r-process-enriched star CS22892-052 ([Sr/Eu] \sim -1). We find that Sr-Y-Zr isotopes are primarily synthesized in the explosive nucleosynthesis in a similar process of the primary production of light p-elements, which has been considered as one of the sites of a lighter element primary process (LEPP).
We prove a new lower bound for the exponent of growth of the best two-dimensional Diophantine approximations with respect to Euclidean norm.
We investigate segregation behavior of additive elements M (= Ni, Cr) at the C11b/D8m interface for MoSi2- Mo5Si3 alloys, based on first-principles calculation. We first find energetically stable interface structure with interface energy of 0.08 eV/A^2. Based on the stable interface, segregation energy for additive elements is calcu- lated for individual atomic layer, which is applied to Monte Carlo statistical simulation under grand-canonical ensemble to quantitatively predict interface segregation profile. We find that our simulation successfully capture the characteristics in measured segregation tendency of (i) Similarity in strong segregation at interface both for Ni and Cr compared with bulk composition, and (ii) stronger segregation for Ni than for Cr, which can be mainly attributed to differences in calculated segregation energy. The present results indicate that measured segregated interface for MoSi2-Mo5Si3 alloys can be thermodynamically stable.
The role played by the effective residual interaction in the transverse nuclear response for quasi-free electron scattering is discussed. The analysis is done by comparing different calculations performed in the Random--Phase Approximation and Ring Approximation frameworks. The importance of the exchange terms in this energy region is investigated and the changes on the nuclear responses due to the modification of the interaction are evaluated. The calculated quasi-elastic responses show clear indication of their sensibility to the details of the interaction and this imposes the necessity of a more careful study of the role of the different channels of the interaction in this excitation region.
We study valence fluctuations in the extended Anderson model on two-dimensional Penrose lattice, using the real-space dynamical mean-field theory combined with the continuous-time Monte Carlo method. Calculating $f$-electron number, $c$-$f$ spin correlations, and magnetic susceptibility at each site, we find site-dependent formations of the singlet state and valence distribution at low temperatures, which are reflected by the quasiperiodic lattice structure. The bulk magnetic susceptibility is also addressed.
In this paper, we investigate the global properties of Fourier multipliers in the setting of nonharmonic analysis of boundary value problems. We give necessary and sufficient conditions for a Fourier multiplier to be globally hypoelliptic and also to be globally solvable. As an application, we consider operators on $[0,1]^2$ with non-periodic boundary conditions and we obtain results that extend what is already known in the periodic case.
We study the dual complexes of boundary divisors in log resolutions of compactifications of algebraic varieties and show that the homotopy types of these complexes are independent of all choices. Inspired by recent developments in nonarchimedean geometry, we consider relations between these boundary complexes and weight filtrations on singular cohomology and cohomology with compact supports, and give applications to dual complexes of resolutions of isolated singularities that generalize results of Stepanov and Thuillier.
We show that the cyclotomic Iwasawa--Greenberg Main Conjecture holds for a large class of modular forms with multiplicative reduction at $p$, extending previous results for the good ordinary case. In fact, the multiplicative case is deduced from the good case through the use of Hida families and a simple Fitting ideal argument.
We investigate star forming scaling relations using Bayesian inference on a comprehensive data sample of low- (z<0.1) and high-redshift (1<z<5) star forming regions. This full data set spans a wide range of host galaxy stellar mass ($M_{*} \sim10^6-10^{11} M_{\odot}$) and clump star formation rates (SFR $ \sim10^{-5}-10^2 M_\odot yr^{-1}$). We fit the power-law relationship between the size (r$_{H\alpha}$) and luminosity (L$_{H\alpha}$) of the star forming clumps using the Bayesian statistical modeling tool Stan that makes use of Markov Chain Monte Carlo (MCMC) sampling techniques. Trends in the scaling relationship are explored for the full sample and subsets based on redshift and selection effects between samples. In our investigation we find no evidence of redshift evolution of the size-luminosity scaling relationship, nor a difference in slope between lensed and unlensed data. There is evidence of a break in the scaling relationship between high and low star formation rate surface density ($\Sigma_{SFR}$) clumps. The size-luminosity power law fit results are L$_{H\alpha}\sim$ r$_{H\alpha}^{2.8}$ and L$_{H\alpha}\sim$ r$_{H\alpha}^{1.7}$ for low and high $\Sigma_{SFR}$ clumps, respectively. We present a model where star forming clumps form at locations of gravitational instability and produce an ionized region represented by the Str\"{o}mgren radius. A radius smaller than the scale height of the disk results in a scaling relationship of $L \propto r^3$ (high $\Sigma_{SFR}$ clumps), and a scaling of $L \propto r^2$ (low $\Sigma_{SFR}$ clumps) if the radius is larger than the disk scale height.
GRB 131231A was detected by the Large Area Telescope onboard Fermi Space Gamma-ray Telescope. The high energy gamma-ray ($> 100$ MeV) afterglow emission spectrum is $F_\nu \propto \nu^{-0.54\pm0.15}$ in the first $\sim 1300$ s after the trigger and the most energetic photon has an energy $\sim 62$ GeV arriving at $t\sim 520$ s. With reasonable parameters of the GRB outflow as well as the density of the circum-burst medium, the synchrotron radiation of electrons or protons accelerated at an external forward shock have difficulty accounting for the data. The synchrotron self-Compton radiation of the forward shock-accelerated electrons, instead, can account for both the spectrum and temporal behavior of the GeV afterglow emission. We also show that the prospect for detecting GRB 131231A$-$like GRBs with Cherenkov Telescope Array (CTA) is promising.
In this work we implement the Minimal Geometric Deformation method to obtain the isotropic sector and the decoupler matter content of any anisotropic solution of the Einstein field equations with cosmological constant in $2+1$ dimensional space--times. We obtain that the solutions of both sectors can be expressed analytically in terms of the metric functions of the original anisotropic solutions instead of formal integral as in its $3+1$ counterpart. As a particular example we study a regular black hole solution and we show that, depending on the sign of the cosmological constant, the solutions correspond to regular black holes violating the null energy condition or to a non--regular black hole without exotic hair. The exotic/non--exotic and the regular/non--regular black hole dualities are discussed.
A model independent expression for the electromagnetic corrections to a phenomenological hadronic pion-nucleon scattering length, extracted from pionic hydrogen, is obtained. In a non-relativistic approach and using an extended charge distribution, these corrections are derived up to terms of order (alpha)**2 log(alpha) in the limit of a short-range hadronic interaction. We infer a charged pion-proton scattering length of 0.0870(5) in units of inverse pion mass, which gives for the charged pion-proton-neutron coupling, through the GMO relation, a value of 14.04(17).
We describe simple properties of some soups of unoriented Markov loops and of some soups of oriented Markov loops that can be interpreted as a spatial Markov property of these loop-soups. This property of the latter soup is related to well-known features of the uniform spanning trees (such as Wilson's algorithm) while the Markov property of the former soup is related to the Gaussian Free Field and to identities used in the foundational papers of Symanzik, Nelson, and of Brydges, Fr\"ohlich and Spencer or Dynkin, or more recently by Le Jan.
To find the Hermitian phase operatorof a single-mode electromagnetic field in quantum mechanics, the Schroedinger representation is extended to a larger Hilbert space augmented by states with infinite excitation by nonstandard analysis. The Hermitian phase operator is shown to exist on the extended Hilbert space. This operator is naturally considered as the controversial limit of the approximate phase operators on finite dimensional spaces proposed by Pegg and Barnett. The spectral measure of this operator is a Naimark extension of the optimal probability operator-valued measure for the phase parameter found by Helstrom. Eventually, the two promising approaches to the statistics of the phase in quantum mechanics is unified by means of the Hermitian phase operator in the macroscopic extension of the Schroedinger representation.
\noindent The paper establishes weak convergence in $C[0,1]$ of normalized stochastic processes, generated by Toeplitz type quadratic functionals of a continuous time Gaussian stationary process, exhibiting long-range dependence. Both central and non-central functional limit theorems are obtained.
The AGILE gamma-ray satellite provides large sky exposure levels ($\geq 10^9$ cm$^2$ s per year on the Galactic Plane) with sensitivity peaking at $E\sim$100 MeV where the bulk of pulsar energy output is typically released. Its $\sim$1 $\mu$s absolute time tagging capability makes it perfectly suited for the study of gamma-ray pulsars. AGILE collected a large number of gamma-ray photons from EGRET pulsars ($\geq$40,000 pulsed counts for Vela) in two years of observations unveiling new interesting features at sub-millisecond level in the pulsars' high-energy light-curves, gamma-ray emission from pulsar glitches and Pulsar Wind Nebulae. AGILE detected about 20 nearby and energetic pulsars with good confidence through timing and/or spatial analysis. Among the newcomers we find pulsars with very high rotational energy losses, such as the remarkable PSR B1509--58 with a magnetic field in excess of 10$^{13}$ Gauss, and PSR J2229+6114 providing a reliable identification for the previously unidentified EGRET source 3EG 2227+6122. Moreover, the powerful millisecond pulsar B1821--24, in the globular cluster M28, is detected during a fraction of the observations.
We deal with a class of abstract nonlinear stochastic models with multiplicative noise, which covers many 2D hydrodynamical models including the 2D Navier-Stokes equations, 2D MHD models and 2D magnetic B\'enard problems as well as some shell models of turbulence. Our main result describes the support of the distribution of solutions. Both inclusions are proved by means of a general Wong-Zakai type result of convergence in probability for non linear stochastic PDEs driven by a Hilbert-valued Brownian motion and some adapted finite dimensional approximation of this process.
We review recent computations of neutral pion photoproduction and Compton scattering on the deuteron in baryon chiral perturbation theory. Progress in extracting the neutron electric dipole amplitude, which is relevant in neutral pion photoproduction, and the neutron polarizabilities, which are relevant in Compton scattering, is discussed.
Isolated galaxies have not been a hot topic over the past four decades. This is partly due to uncertainties about their existence. Are there galaxies isolated enough to be interesting? Do they exist in sufficient numbers to be statistically useful? Most attempts to compile isolated galaxy lists were marginally successful--too small number and not very isolated galaxies. If really isolated galaxies do exist then their value becomes obvious in a Universe where effects of interactions and environment (i.e. nurture) are important. They provide a means for better quantifying effects of nurture. The Catalog of Isolated Galaxies (CIG) compiled by Valentina Karachentseva appeared near the beginning of the review period. It becomes the focus of this review because of its obvious strengths and because the AMIGA project has increased its utility through a refinement (a vetted CIG). It contains almost 1000 galaxies with nearest neighbor crossing times of 1-3Gyr. It is large enough to serve as a zero-point or control sample. The galaxies in the CIG (and the distribution of galaxy types) may be significantly different than those in even slightly richer environments. The AMIGA-CIG, and future iterations, may be able to tell us something about galaxy formation. It may also allow us to better define intrinsic (natural) correlations like e.g. Fisher-Tully and FIR-OPTICAL. Correlations can be better defined when the dispersion added by external stimuli (nurture) is minimized or removed.
Goldreich-Sridhar model of incompressible turbulence provides an elegant approach to describing strong MHD turbulence. It relies on the fact that interacting Alfvenic waves are independent and have random polarization. However, in case of strong interaction a spontaneous local assymetry can arise. We used direct numerical simulations to show that polarization alignment occurs and it grows larger at smaller scales. This effect would lead to a shallower spectrum and stronger anisotropy. Even small changes in these two properties will have important astrophysical consequencies, e.g. for the cosmic ray physics.