ShantanuT01/DACTYL-Pretraining huggingface dataset:
We report the results of our follow-up campaign for the neutron star - black hole (NSBH) merger GW200115 detected during the O3 run of the Advanced LIGO and Advanced Virgo detectors. We obtained wide-field observations with the Deca-Degree Optical Transient Imager (DDOTI) covering ~20% of the total probability area down to a limiting magnitude of $w$=20.5 AB at ~23 h after the merger. Our search for counterparts returns a single candidate (AT2020aeo), likely not associate to the merger. In total, only 25 sources of interest were identified by the community and later discarded as unrelated to the GW event. We compare our upper limits with the emission predicted by state-of-the-art kilonova simulations and disfavor high mass ejecta (>0.1$M_{\odot}$), indicating that the spin of the system is not particularly high. By combining our optical limits with gamma-ray constraints from $Swift$ and $Fermi$, we disfavor the presence of a standard short duration burst for viewing angles $\lesssim$15 deg from the jet axis. Our conclusions are however limited by the large localization region of this GW event, and accurate prompt positions remain crucial to improving the efficiency of follow-up efforts.
We demonstrate that a temperature schedule for single-spin flip transition matrix calculations can be simply and rapidly generated by monitoring the average size of the Wolff clusters at a set of discrete temperatures. Optimizing this schedule yields a potentially interesting quantity related to the fractal structure of Ising clusters. We also introduce a technique in which the transition matrix is constructed at a sequence of discrete temperatures at which Wolff cluster reversals are alternated with certain series of single-spin flip steps. The single spin-flip transitions are then employed to construct a single transition matrix.
A practical number is a positive integer $n$ such that all positive integers less than $n$ can be written as a sum of distinct divisors of $n$. Leonetti and Sanna proved that, as $x \to +\infty$, the central binomial coefficient $\binom{2n}{n}$ is a practical number for all positive integers $n \leq x$ but at most $O(x^{0.88097})$ exceptions. We improve this result by reducing the number of exceptions to $\exp\!\big(C (\log x)^{4/5} \log \log x\big)$, where $C > 0$ is a constant.
Compressible disturbances propagate in a plasma in the form of magnetoacoustic waves driven by both gas pressure and magnetic forces. In partially ionized plasmas the dynamics of ionized and neutral species are coupled due to ion-neutral collisions. As a consequence, magnetoacoustic waves propagating through a partially ionized medium are affected by the ion-neutral coupling. The degree to which the behavior of the classic waves is modified depends on the physical properties of the various species and on the relative value of the wave frequency compared to the ion-neutral collision frequency. Here, we perform a comprehensive theoretical investigation of magnetoacoustic wave propagation in a partially ionized plasma using the two-fluid formalism. We consider an extensive range of values for the collision frequency, ionization ratio, and plasma $\beta$, so that the results are applicable to a wide variety of astrophysical plasmas. We determine the modification of the wave frequencies and study the frictional damping due to ion-neutral collisions. Approximate analytic expressions to the frequencies are given in the limit case of strongly coupled ions and neutrals, while numerically obtained dispersion diagrams are provided for arbitrary collision frequencies. In addition, we discuss the presence of cutoffs in the dispersion diagrams that constrain wave propagation for certain combinations of parameters. A specific application to propagation of compressible waves in the solar chromosphere is given.
Global classical solutions to the viscous Hamilton-Jacobi equation with homogenious Dirichlet boundary conditions are shown to converge to zero at the same speed as the linear heat semigroup when p > 1. For p = 1, an exponential decay to zero is also obtained in one space dimension but the rate depends on a and differs from that of the linear heat equation. Finally, if 0 < p < 1 and a < 0, finite time extinction occurs for non-negative solutions.
We investigate the role of angular momentum in the clustering of dark matter haloes. We make use of data from two high-resolution N-body simulations spanning over four orders of magnitude in halo mass, from $10^{9.8}$ to $10^{14}\ h^{-1}\ \text{M}_\odot$. We explore the hypothesis that mass accretion in filamentary environments alters the angular momentum of a halo, thereby driving a correlation between the spin parameter $\lambda$ and the strength of clustering. However, we do not find evidence that the distribution of matter on large scales is related to the spin of haloes. We find that a halo's spin is correlated with its age, concentration, sphericity, and mass accretion rate. Removing these correlations strongly affects the strength of secondary spin bias at low halo masses. We also find that high spin haloes are slightly more likely to be found near another halo of comparable mass. These haloes that are found near a comparable mass neighbour - a \textit{twin} - are strongly spatially biased. We demonstrate that this \textit{twin bias}, along with the relationship between spin and mass accretion rates, statistically accounts for halo spin secondary bias.
We show that chiral symmetry and gauge invariance enforce relations between the short-distance physics that occurs in a number of electroweak and pionic reactions on light nuclei. Within chiral perturbation theory this is manifested via the appearance of the same axial isovector two-body contact term in pi- d -> n n gamma, p-wave pion production in NN collisions, tritium beta decay, pp fusion, nu d scattering, and the hep reaction. Using a Gamow-Teller matrix element obtained from calculations of pp fusion as input we compute the neutron spectrum obtained in pi- d -> n n gamma. With the short-distance physics in this process controlled from p p -> d e+ nu_e the theoretical uncertainty in the nn scattering length extracted from pi- d -> n n gamma is reduced by a factor larger than three, to <~0.05 fm.
We study the relationship between long cycles and Bose-Einstein condensation (BEC) in the case of several models. A convenient expression for the density of particles on cycles of length $q$ is obtained, in terms of $q$ unsymmetrised particles coupled with a boson field. Using this formulation we reproduce known results on the Ideal Bose Gas, Mean-Field and Perturbed Mean-Field Models, where the condensate density exactly equals the long cycle density.   Then we consider the Infinite-Range-Hopping Bose-Hubbard model, with and without hard-cores. For the hard-core case, we find we can disregard the hopping contribution of the q unsymmetrised particles to obtain an exact expression for the density of particles on long cycles. It is shown that only the cycle of length one contributes to the cycle density. We conclude that while the existence of a non-zero long cycle density coincides with the occurrence of Bose-Einstein condensation, the respective densities are not necessarily equal.   For the case of a finite on-site repulsion, we obtain an expression for the cycle density by neglecting the $q$ unsymmetrised hop. Inspired by the Approximating Hamiltonian method we conjecture a simplified expression for the short cycle density as a ratio of single-site partition functions. In the absence of condensation we prove that this simplification is exact and find that in this case the long-cycle density vanishes. In the presence of condensation we justify this simplification when a gauge-symmetry breaking term is introduced in the Hamiltonian. Assuming our conjecture is correct, we compare numerically the long-cycle density with the condensate and again find that though they coexist, in general they are not equal.
Most emergent properties of the materials discovered since the 1980s are related to the existence of electron-electron interactions which are large with respect to the kinetic energies and could not be thoroughly studied before. The occurrence of metal insulator transitions, of exotic magnetic and/or superconducting properties in many new compounds have stimulated a large series of ex- perimental and theoretical developments to grasp their physical significance. We present here a simple introduction to the elementary aspects of the physics of electron-electron interactions, which could be a starting point for typical undergraduate students.
We show that deciding the equality of two Dedekind sums $S(c,b)$, $S(d,b)$ is equivalent to deciding whether a Dedekind sum defined by $b, c, d$ takes a certain value. By means of this result we construct infinite sequences of pairwise equal Dedekind sums. Moreover, we prove a result that says how many Dedekind sums $S(d,b)$, $1\le d\le b-1$, may be equal to a given $S(c,b)$ if $b$ is a square-free number.
We study cosmologies in modified theories of gravity considering Lagrangian density $f(R)$ which is a polynomial function of scalar curvature ($R$) in the Einstein-Hilbert action in vacuum. The field equation obtained from the modified action corresponding to a Robertson-Walker metric is highly non-linear and not simple enough to obtain analytic solution. Consequently we adopt a numerical technique to study the evolution of the FRW universe.   A number of evolutionary phases of the universe including the present accelerating phase are found to exist in the higher derivative theories of gravity. The cosmological solutions obtained here are new and interesting. We study modified theory of gravity as a toy model to explore the past, the present and predict the future evolution. It is found that all the models analyzed here can reproduce the current accelerating phase of expansion of the universe. The duration of the present accelerating phase is found to depend on the coupling constants of the gravitational action. The physical importance of the coupling parameters those considered in the action are also discussed.
Significant numbers of high-velocity HI clouds (HVCs) have now been detected in H-alpha, with a subset seen in low ionization lines (e.g. [NII]). It was originally hoped that the observed H-alpha strength would provide a distance constraint to individual clouds. This idea requires that a useful fraction (f_esc > 1%) of ionizing photons escape the Galaxy, and that the halo ionizing field is relatively smooth, as we discuss. Most HVCs which are known to be close to the Sun are H-alpha; the brightest clouds also show enhanced [NII] emission, in contrast to the Magellanic Stream where the low ionization emission lines are always weak compared to H-alpha. But an acute complication for H-alpha distances is the apparent H-alpha brightness of the Magellanic Stream along several sight lines. To account for this, we present three possible configurations for the Magellanic Stream and propose a follow-up experiment. If we normalize the distances to local HVCs, some HVCs appear to be scattered throughout the Galactic halo on scales of tens of kiloparsecs.
The pressure effects on the JT distortion of three representative compounds belonging to the LaMn_1-xGa_xO_3 (x= 0.2, 0.3, 0.4) family was widely investigated by means of X-ray diffraction and Raman spectroscopy. A compound with a fully JT distorted structure (x=0.2), one with regular octahedra (x=0.6) and one in an intermediate configuration (x=0.3) were selected. A pressure induced transitions from the orthorhombic Pbnm phase towards structures with higher symmetry were observed in all the samples. Both Raman and X-ray data confirm that the most important structural effect of pressure is that of reducing the octahedral distortion. The appearance of a feature in the lattice parameter behavior connected to a structural instability was also detected, pointing out the key role of the JT distortion in stabilizing the manganite structures. On the other hand, the complete suppression of the JT distortion in the high-pressure phases cannot be claimed. The Raman spectra collected from more distorted compounds (x=0.2, 0.3) reveal clearly the coexistence of domains of distorted and more regular octahedra in a certain pressure range. The first sketch of the Pressure vs. Ga-content phase diagram was drawn.
Adiabatic quantum gate implementation generally takes longer time, which is disadvantageous in view of decoherence. In this report we implement several essential one-qubit quantum gates nonadiabatically by making use of a dynamical invariant associated with a Hamiltonian. Moreover we require that these gates be holonomic, that is, the dynamical phases associated with the gates vanish. Our implementation is based on our recent work [J. Phys. Soc. Jpn. 83, 034001 (2014)] and the gate parameters required for the implementations are found by numerical optimization.
Euler's equations of motion are derived exactly for a rigid, triaxial, internally frictionless neutron star spinning down electromagnetically in vacuo. It is shown that the star precesses, but not freely: its regular precession relative to the principal axes of inertia couples to the component of the radiation torque associated with the near-zone radiation fields and is modified into an anharmonic wobble. The wobble period \tau_1 typically satisfies \tau_1 < 10^{-2}\tau_0, where \tau_0 is the braking time-scale; the wobble amplitude evolves towards a constant non-zero value, oscillates, or decreases to zero, depending on the degree of oblateness or prolateness of the star and its initial spin state; and the (negative) angular frequency derivative d{\omega}/dt oscillates as well, exhibiting quasi-periodic spikes for triaxial stars of a particular figure. In light of these properties, a young, Crab-like pulsar ought to display fractional changes of order unity in the space of a few years in its pulse profile, magnetic inclination angle, and d{\omega}/dt. Such changes are not observed, implying that the wobble is damped rapidly by internal friction, if its amplitude is initially large upon crystallization of the stellar crust. If the friction is localized in the inner and outer crusts, the thermal luminosity of the neutron star increases by a minimum amount \Delta L = 3*10^{31} (\epsilon / 10^{-12}) (\omega / 10^3 rad s^{-1})^2 (\tau_d / 1 yr)^{-1} erg s^{-1}, where epsilon is the ellipticity and \tau_d is the damping time-scale, with the actual value of \Delta L determined in part by the thermal conduction time \tau_cond. The increased luminosity is potentially detectable as thermal X-rays lasting for a time max(tau_d,tau_cond) following crystallization of the crust.
Using a result of Blanchet and Wallwater (2015: Exact sampling of stationary and time-reversed queues. ACM TOMACS, 25, 26) for exactly simulating the maximum of a negative drift random walk queue endowed with independent and identically distributed (iid) increments, we extend it to a multi-dimensional setting and then we give a new algorithm for simulating exactly the stationary distribution of a first-in-first-out (FIFO) multi-server queue in which the arrival process is a general renewal process and the service times are iid; the FIFO GI/GI/c queue with 2 \le c < 1. Our method utilizes dominated coupling from the past (DCFP) as well as the Random Assignment (RA) discipline, and complements the earlier work in which Poisson arrivals were assumed, such as the recent work of Connor and Kendall (2015: Perfect simulation of M/G/c queues. Advances in Applied Probability, 47, 4). We also consider the models in continuous-time and show that with mild further assumptions, the exact simulation of those stationary distributions can also be achieved. We also give, using our FIFO algorithm, a new exact simulation algorithm for the stationary distribution of the infinite server case, the GI/GI/\infty model. Finally, we even show how to handle Fork-Join queues, in which each arriving customer brings c jobs, one for each server.
In this paper we report on the observations performed with INTEGRAL and Swift of the first outburst detected from the hard X-ray transient MAXI J1828-249. During the first about two days of the outburst, the source was observed by MAXI to undergo a very rapid transition from a hard to a softer spectral state. While the hard state was not efficiently monitored because the transition occurred so rapidly, the evolution of the source outburst in the softer state was covered quasi-simultaneously in a broad energy range (0.6-150 keV) by the instruments on-board INTEGRAL and Swift. During these observations, the spectra measured from the source displayed both a prominent thermal emission with temperature kT 0.7 keV and a power-law hard component with a photon index gamma 2.2 extending to 200 keV. The properties of the source in the X-ray domain are reminiscent of those displayed by black hole transients during the soft intermediate state, which supports the association of MAXI J1828-249 with this class of objects.
We present a new efficient method to compute the angular power spectra of large-scale structure observables that circumvents the numerical integration over Bessel functions, expanding on a recently proposed algorithm based on FFTlog. This new approach has better convergence properties. The method is explicitly implemented in the CLASS code for the case of number count $C_\ell$'s (including redshift-space distortions, weak lensing, and all other relativistic corrections) and cosmic shear $C_\ell$'s. In both cases our approach speeds up the calculation of the exact $C_\ell$'s (without the Limber approximation) by a factor of order 400 at a fixed precision target of 0.1%.
In this paper we prove a new strong uniqueness result and a weak existence result for possibly {\it degenerate} multidimensional stochastic differential equations with Sobolev diffusion coefficients and rough drifts. In particular, examples with H\"older diffusion coefficients are provided to show our results.
Electrical resistivity measurements were performed on single crystals of URu$_2-x$Os$_x$Si$_2$ up to $x$ = 0.28 under hydrostatic pressure up to $P$ = 2 GPa. As the Os concentration, $x$ , is increased, (1) the lattice expands, creating an effective negative chemical pressure $P_{ch}$($x$), (2) the hidden order (HO) phase is enhanced and the system is driven toward a large-moment antiferromagnetic (LMAFM) phase, and (3) less external pressure $P_{c}$ is required to induce the HO to LMAFM phase transition. We compare the $T(x)$, $T(P)$ phase behavior reported here for the URu$_2-x$Os$_x$Si$_2$ system with previous reports of enhanced HO in URu$_2$Si$_2$ upon tuning with $P$, or similarly in URu$_2-x$Fe$_x$Si$_2$ upon tuning with positive $P_{ch}$($x$). It is noted that pressure, Fe substitution, and Os substitution are the only known perturbations that enhance the HO phase and induce the first order transition to the LMAFM phase in URu$_2$Si$_2$. We present a scenario in which the application of pressure or the isoelectronic substitution of Fe and Os ions for Ru results in an increase in the hybridization of the U-5$f$- and transition metal $d$-electron states which leads to electronic instability in the paramagnetic phase and a concurrent stability of HO (and LMAFM) in URu$_2$Si$_2$. Calculations in the tight binding approximation are included to determine the strength of hybridization between the U-5$f$ electrons and each of the isoelectronic transition metal $d$-electron states of Fe, Ru, and Os.
We propose a new way of looking at the quantum Maxwell's demon problem in terms of conditional action. A "conditional action" on a system is a unitary time evolution, selected according to the result of a previous measurement, which can reduce the entropy of the system. However, any conditional action can be realized by an (unconditional) unitary time evolution of a larger system and a subsequent L\"uders measurement, whereby the entropy of the entire system is either increased or remains constant. We give some examples that illustrate and confirm our proposal, including the erasure of $N$ qubits and the Szilard engine, thus relating the present approach to the Szilard principle and the Landauer principle that have been discussed as possible solutions of the Maxwell's demon problem.
We develop the free boundary regularity for nonnegative minimizers of the Alt-Phillips functional for negative power potentials   $$\int_\Omega \left(\frac 1 2 |\nabla u|^2 + u^{\gamma} \chi_{\{u>0\}}\right) \, dx, \quad \quad \gamma \in (-2,0),$$   and establish a $\Gamma$-convergence result of the rescaled energies to the perimeter functional as $\gamma \to -2$.
The paper considers the integration theory for $G$-L\'evy processes with finite activity. We introduce the It\^o-L\'evy integrals, give the It\^o formula for them and establish SDE's, BSDE's and decoupled FBSDE's driven by $G$-L\'evy processes. In order to develop such a theory, we prove two key results: the representation of the sublinear expectation associated with a $G$-L\'evy process and a characterization of random variables in $L^p_G(\Omega)$ in terms of their quasi-continuity.
We compare the fluctuations in the velocity and in the fraction of time spent at a given position for minimal models of a passive and an active particle: an asymmetric random walker and a run-and-tumble particle in continuous time and on a 1D lattice. We compute rate functions and effective dynamics conditioned on large deviations for these observables. While generally different, for a unique and non-trivial choice of rates (up to a rescaling of time) the velocity rate functions for the two models become identical, whereas the effective processes generating the fluctuations remain distinct. This equivalence coincides with a remarkable parity of the spectra of the processes' generators. For the occupation-time problem, we show that both the passive and active particles undergo a prototypical dynamical phase transition when the average velocity is non-vanishing in the long-time limit.
Recurrent mutations are a common phenomenon in population genetics. They may be at the origin of the fixation of a new genotype, if they give a phenotypic advantage to the carriers of the new mutation. In this paper, we are interested in the genetic signature left by a selective sweep induced by recurrent mutations at a given locus from an allele A to an allele a, depending on the mutation frequency. We distinguish three possible scales for the mutation probability per reproductive event, which entail distinct genetic signatures. Besides, we study the hydrodynamic limit of the A- and a-population size dynamics when mutations are frequent, and find non trivial equilibria leading to several possible patterns of polymorphism.
The present paper is devoted to the study of the combinatorics of 216 maximal $C^3$ circular codes --- a particular type of structure arising in the analysis of genomic sequences. Their circularity property is believed to be intimately connected to the protection against the reading frame shift in the process of RNA translation. We present some new observations concerning the internal structure of circular codes, which give a way to construct all of them in a relatively simple manner.