ShantanuT01/DACTYL-Pretraining huggingface dataset:
Calculations of the number of equivalence classes of Sudoku boards has to this point been done only with the aid of a computer, in part because of the unnecessarily large symmetry group used to form the classes. In particular, the relationship between relabeling symmetries and positional symmetries such as row/column swaps is complicated. In this paper we focus first on the smaller Shidoku case and show first by computation and then by using connectivity properties of simple graphs that the usual symmetry group can in fact be reduced to various minimal subgroups that induce the same action. This is the first step in finding a similar reduction in the larger Sudoku case and for other variants of Sudoku.
We present a survey of atomic hydrogen HI) emission in the direction of the Galactic Center conducted with the CSIRO Australia Telescope Compact Array (ATCA). The survey covers the area -5 deg < l < +5, -5 deg < b <+5 deg over the velocity range -309 < v_{LSR} < 349 km/s with a velocity resolution of 1 km/s. The ATCA data are supplemented with data from the Parkes Radio Telescope for sensitivity to all angular scales larger than the 145 arcsec angular resolution of the survey. The mean rms brightness temperature across the field is 0.7 K, except near (l,b)=(0 deg, 0 deg) where it increases to ~2 K. This survey complements the Southern Galactic Plane Survey to complete the continuous coverage of the inner Galactic plane in HI at ~2 arcmin resolution. Here we describe the observations and analysis of this Galactic Center survey and present the final data product. Features such as Bania's Clump 2, the far 3 kiloparsec arm and small high velocity clumps are briefly described.
We proved the explicit formulas in Laplace transform of the hitting times for the birth and death processes on a denumerable state space with $\ift$ the exit or entrance boundary. This extends the well known Keilson's theorem from finite state space to infinite state space.   We also apply these formulas to the fastest strong stationary time for strongly ergodic birth and death processes, and obtain the explicit convergence rate in separation.
We report the first results of a multi-epoch search for wide (separations greater than a few tens of AU), low-mass tertiary companions of a volume-limited sample of 118 known spectroscopic binaries within 30 pc of the Sun, using the 2MASS Point Source Catalog and follow-up observations with the KPNO and CTIO 4m telescopes. Note that this sample is not volume-complete but volume-limited, and, thus, there is incompleteness in our reported companion rates. We are sensitive to common proper motion companions with separations from roughly 200 AU to 10,000 AU (~10" -> ~10'). From 77 sources followed-up to date, we recover 11 previously known tertiaries, three previously known candidate tertiaries, of which two are spectroscopically confirmed and one rejected, and three new candidates, of which two are confirmed and one rejected. This yields an estimated wide tertiary fraction of 19.5^+5.2%_-3.7%. This observed fraction is consistent with predictions set out in star formation simulations where the fraction of wide, low-mass companions to spectroscopic binaries is >10%, and is roughly twice the wide companion rate of single stars.
Consider a homogeneous Poisson process in $\mathbb{R}^d$, $d \ge 1$. Let $R_1 < R_2 < \dots$ be the distances of the points from the origin, and let $S = R_1^{-\gamma} + R_2^{-\gamma} + \dots$, where $\gamma > d$ is a parameter. Let $\overline{S}^{(r)} = \sum_k R_k^{-\gamma} \, \mathbf{1}_{R_k \ge r}$ be the contribution to $S$ outside radius $r$. For large enough $r$, and any $\overline{s}$ in the support of $\overline{S}^{(r)}$, consider the change of measure that shifts the mean to $\overline{s}$. We derive rigorous error estimates for the Edgeworth expansion of the transformed random variable. Our error terms are uniform in $\overline{s}$, and we give explicitly the dependence of the error on $r$ and the order $k$ of the expansion. As an application, we provide a scheme that approximates the conditional distribution of $R_1$ given $S = s$ to any desired accuracy, with error bounds that are uniform in $s$. Along the way, we prove a stochastic comparison between $(R_1, R_2, \dots)$ given $S = s$ and unconditioned radii $(R'_1, R'_2, \dots)$.
A short review of recent results on exact solutions in multidimensional cosmology and overview of reports at workshop in MG8 (held by the author) are presented.
The Neutron Star Interior Composition Explorer (NICER) on the International Space Station (ISS) observed strong photospheric expansion of the neutron star in 4U 1820-30 during a Type I X-ray burst. A thermonuclear helium flash in the star's envelope powered a burst that reached the Eddington limit. Radiation pressure pushed the photosphere out to ~200 km, while the blackbody temperature dropped to 0.45 keV. Previous observations of similar bursts were performed with instruments that are sensitive only above 3 keV, and the burst signal was weak at low temperatures. NICER's 0.2-12 keV passband enables the first complete detailed observation of strong expansion bursts. The strong expansion lasted only 0.6 s, and was followed by moderate expansion with a 20 km apparent radius, before the photosphere finally settled back down at 3 s after the burst onset. In addition to thermal emission from the neutron star, the NICER spectra reveal a second component that is well fit by optically thick Comptonization. During the strong expansion, this component is six times brighter than prior to the burst, and it accounts for 71% of the flux. In the moderate expansion phase, the Comptonization flux drops, while the thermal component brightens, and the total flux remains constant at the Eddington limit. We speculate that the thermal emission is reprocessed in the accretion environment to form the Comptonization component, and that changes in the covering fraction of the star explain the evolution of the relative contributions to the total flux.
We show that pseudo - spin symmetry in nuclei could arise from nucleons moving in a relativistic mean field which has an attractive scalar and repulsive vector potential nearly equal in magnitude.
We discuss the existence and characterization of quasi-stationary distributions and Yaglom limits of self-similar Markov processes that reach 0 in finite time. By Yaglom limit, we mean the existence of a deterministic function $g$ and a non-trivial probability measure $\nu$ such that the process rescaled by $g$ and conditioned on non-extinction converges in distribution towards $\nu$. If the study of quasi-stationary distributions is easy and follows mainly from a previous result by Bertoin and Yor \cite{BYFacExp} and Berg \cite{bergI}, that of Yaglom limits is more challenging. We will see that a Yaglom limit exits if and only if the extinction time at 0 of the process is in the domain of attraction of an extreme law and we will then treat separately three cases, according whether the extinction time is in the domain of attraction of a Gumbel law, a Weibull law or a Fr\'echet law. In each of these cases, necessary and sufficient conditions on the parameters of the underlying L\'evy process are given for the extinction time to be in the required domain of attraction. The limit of the process conditioned to be positive is then characterized by a multiplicative equation which is connected to a factorization of the exponential distribution in the Gumbel case, a factorization of a Beta distribution in the Weibull case and a factorization of a Pareto distribution in the Fr\'echet case. This approach relies partly on results on the tail distribution of the extinction time, which is known to be distributed as the exponential integral of a L\'evy process. In that aim, new results on such tail distributions are given, which may be of independent interest. Last, we present applications of the Fr\'echet case to a family of Ornstein-Uhlenbeck processes.
$\delta$-AlOOH is of significant crystallochemical interest due to a subtle structural transition near 10 GPa from a $P2_1nm$ to a $Pnnm$ structure, the nature and origin of hydrogen disorder, the symmetrization of the O-H$\cdots$O hydrogen bond and their interplay. We perform a series of density functional theory based simulations in combination with high-pressure nuclear magnetic resonance experiments on $\delta$-AlOOH up to 40 GPa with the goal to better characterize the hydrogen potential and therefore the nature of hydrogen disorder. Simulations predict a phase transition in agreement with our nuclear magnetic resonance experiments at $10-11$ GPa and hydrogen bond symmetrization at $14.7$ GPa. Calculated hydrogen potentials do not show any double-well character and there is no evidence for proton tunneling in our nuclear magnetic resonance data.
Cosmic microwave background (CMB) anisotropies probe the primordial density field at the edge of the observable Universe. There is a limiting precision (``cosmic variance'') with which anisotropies can determine the amplitude of primordial mass fluctuations. This arises because the surface of last scatter (SLS) probes only a finite two-dimensional slice of the Universe. Probing other SLSs observed from different locations in the Universe would reduce the cosmic variance. In particular, the polarization of CMB photons scattered by the electron gas in a cluster of galaxies provides a measurement of the CMB quadrupole moment seen by the cluster. Therefore, CMB polarization measurements toward many clusters would probe the anisotropy on a variety of SLSs within the observable Universe, and hence reduce the cosmic-variance uncertainty.
Granular media are examined with the focus on polydisperse mixtures in the presence of two localized heat-baths. If the two driving energies are similar, the large particles prefer to stay in the `cold' regions of the system -- as far away from the energy source as possible. If one of the temperatures is larger than the other, the cold region is shifted towards the colder reservoir; if the temperature of one source is much higher, a strong, almost constant temperature gradient builds up between the two reservoirs and the large particles are found close to the cold reservoir. Furthermore, clustering is observed between the heat reservoirs, if dissipation is strong enough.
We consider the following Liouville-type equation with exponential Neumann boundary condition: $$ -\Delta\tilde u = \varepsilon^2 K(x) e^{2\tilde u}, \quad x\in D, \qquad \frac{\partial \tilde u}{\partial n} + 1 = \varepsilon \kappa(x) e^{\tilde u}, \quad x\in\partial D, $$ where $D\subset \mathbb R^2$ is the unit disc, $\varepsilon^2 K(x)$ and $\varepsilon \kappa(x)$ stand for the prescribed Gaussian curvature and the prescribed geodesic curvature of the boundary, respectively. We prove the existence of concentration solutions if $\kappa(x) + \sqrt{K(x)+\kappa(x)^2}$ ($x\in\partial D$) has a strictly local extremum point, which is a total new result for exponential Neumann boundary problem.
The Pb-radioactivity in the superheavy mass region is studied within the frame work of PCM model,the calculation of Pb-Radioactivity looks favorably for the cluster decay studies in superheavy mass region as in the heavy mass region.
An exhaustive analysis of 9-year optical R-band photopolarimetric data of the flat-spectrum radio quasar 3C279 from 2008 February 27 to 2017 May 25 is presented, alongside with multiwavelength observing campaigns performed during the flaring activity exhibited in 2009 February/March, 2011 June, 2014 March/April, 2015 June and 2017 February. In the R-band, this source showed the maximum brightness state of $13.68\pm 0.11$ mag ($1.36\pm0.20$ mJy) on 2017 March 02, and the lowest brightness state ever recorded of $18.20\pm 0.87$ mag ($0.16\pm0.03$ mJy) on 2010 June 17. During the entire period of observations, the polarization degree varied between $0.48\pm0.17$% and $31.65\pm0.77$% and the electric vector position angle exhibited large rotations between $82.98^\circ \pm0.92$ and $446.32^\circ \pm1.95$. Optical polarization data show that this source has a stable polarized component that varied from $\sim$6% (before the 2009 flare) to $\sim$13% after the flare. The overall behavior of our polarized variability data supports the scenario of jet precessions as responsible of the observed large rotations of the electric vector position angle. Discrete correlation function analysis show that the lags between gamma-rays and X-rays compared to the optical R-band fluxes are $\Delta t \sim$ 31 d and $1$ d in 2009. Lags were also found among gamma-rays compared with X-rays and radio of $\Delta t \sim$ 30 d and $43$ d in 2011, and among radio and optical-R band of $\Delta t \sim$ 10 d in 2014. A very intense flare in 2017 was observed in optical bands with a dramatic variation in the polarization degree (from $\sim$ 6% to 20%) in 90 days without exhibiting flaring activity in other wavelengths.
The Galactic HII region G353.2+0.9 is excited by the massive open cluster Pismis-24. By analyzing (sub-)mm molecular-line and -continuum we study the detailed morphology of the gas and dust, as well as their physical parameters and their variation across the PDR. We observed various molecules and transitions to derive the physical properties of the molecular gas through line ratios, and both LTE and non-LTE analyses. The physical properties of the gas were derived with a Bayesian approach for the non-LTE analysis. Based on the continuum data at 870 micron, we derived the dust mass and the column density of H2, and thus the molecular abundances. The total mass of the gas in the region is ca. 2000 Mo, while that of the dust is ca. 21 Mo. A velocity gradient in the region suggests that the expansion of the ionized gas is pushing the molecular gas away from the observer. We unambiguously identify the ionization front, at the location of which we detect an increase in gas density and temperature. We find at least 14 clumps at different positions and LSR velocities. We derive kinetic temperatures in the ranges 11-45 K (CS) and 20-45 K (CN). The H2 number density is typically around 1e5 cm^-3 from CS and few 1e5 cm^-3 from CN, with maxima above 1e6 cm^-3. The abundances of the molecules observed vary across the region, and appear to be higher in regions further away from the ionization front.
We develop an effective version of the Chabauty--Kim method which gives explicit upper bounds on the number of $S$-integral points on a hyperbolic curve in terms of dimensions of certain Bloch--Kato Selmer groups. Using this, we give a new "motivic" proof that the number of solutions to the $S$-unit equation is bounded uniformly in terms of $\#S$.
The current status of the scientific results of the Auger Observatory will be discussed which include spectrum, anisotropy in arrival directions, chemical composition analyses, and limits on neutrino and photon fluxes. A review of the Observatory detection systems will be presented. Auger has started the construction of its second phase which encompasses antennae for radio detection of cosmic rays, high-elevation telescopes, and surface plus muon detectors. Details will be presented on the latter, AMIGA (Auger Muons and Infill for the Ground Array), an Auger project consisting of 85 detector pairs each one composed of a surface water-Cherenkov detector and a buried muon counter. The detector pairs are arranged in an array with spacings of 433 and 750 m in order to perform a detailed study of the 10^17 eV to 10^19 eV spectrum region. Preliminary results on the performance of the 750 m array of surface detectors and the first muon counter prototype will be presented.
We present a comprehensive structural characterization of ferromagnetic SiC single crystals induced by Ne ion irradiation. The ferromagnetism has been confirmed by electron spin resonance and possible transition metal impurities can be excluded to be the origin of the observed ferromagnetism. Using X-ray diffraction and Rutherford backscattering/channeling spectroscopy, we estimate the damage to the crystallinity of SiC which mutually influences the ferromagnetism in SiC.
We calculate the masses of $J^{PC}=1^{-+}$ light exotic mesons by QCD sum rules; the masses are extracted from four-quark--hybrid mixing correlation functions. We construct several $1^{-+}$ four-quark currents and hybrid currents, and get two masses around $1.2\text{-}1.4\text{GeV}$ and $1.45\text{-}1.67\text{GeV}$; they can be identified as $\pi_1(1400)$ and $\pi_1(1600)$.
Neutrino air showers can be formed in any part of the atmosphere passing a long was in the matter due to its physical properties. In general, air showers produced by neutrinos are highly inclined and formed near the ground level, i.e. young showers. Therefore, one should expect a large number of peaks in the signal of such air showers [1, 2, 3].   The goal of our work is to search for air shower candidates produced by neutrino. For this purposes, we analyzed large amount of data from scintillation detectors with different area and energy thresholds [1, 2].   Preliminary analysis of Yakutsk array data indicated the absence of air shower produced by neutrino, but it does not mean that such air showers does not exist. It is going to need a further analysis of highly inclined showers. In order to do that improved methodology for recording and processing of air showers required.
Nanoparticles of very small size (below 10 nm) of TiO2 material are nowadays the functional building blocks of many developing technological applications. Nano is clearly different from bulk or extended systems as regards surface area, molecular binding properties, charge separation efficiency, electron/hole transport, photochemical conversion properties, etc. In this work, we investigate the life path of energy (excitons) and charge (electrons and holes) carriers in anatase TiO2 nanoparticles of different size (2-3 nm) and shape (faceted vs spherical), by means of a wide set of hybrid density functional theory calculations. The attention is focused on the exciton/charge carriers formation, separation, recombination, self-trapping processes, which are analyzed in terms of structural deformations, energy gain or cost, charge localization/delocalization and electronic transitions involved. The computational models are corroborated by an extensive comparison with available experimental data based on photoluminescence measurements, electron paramagnetic resonance and transient absorption spectroscopies. Peculiar differences are observed for spherical nanoparticles with respect to faceted ones because of the higher disorder and larger diversity of coordination sites present on the surface. For example, charge delocalization on several lattice sites is more competitive with self-trapping processes in faceted than in spherical nanoparticles. This relates to the fact that selective compression or elongation of Ti-O bonds play a key role in determining the effectiveness of trapping sites, with spherical nanoparticles being more flexible. Moreover, hydroxyl groups on surface five-fold coordinated Ti sites are also found to be good hole trapping sites.
We have measured magnetotransport at half-filled high Landau levels in a quantum well with two occupied electric subbands. We find resistivities that are {\em isotropic} in perpendicular magnetic field but become strongly {\em anisotropic} at $\nu$ = 9/2 and 11/2 on tilting the field. The anisotropy appears at an in-plane field, $B_{ip} \sim$ 2.5T, with the easy-current direction {\em parallel} to $B_{ip}$ but rotates by 90$^{\circ}$ at $B_{ip} \sim$ 10T and points now in the same direction as in single-subband samples. This complex behavior is in quantitative agreement with theoretical calculations based on a unidirectional charge density wave state model.
We present the results of a spectroscopic survey to characterize chromospheric activity, as measured by H$\alpha$ emission, in low-mass members of the 500-Myr-old open cluster M37. Combining our new measurements of H$\alpha$ luminosities ($L_{H\alpha}$) with previously cataloged stellar properties, we identify saturated and unsaturated regimes in the dependence of the $L_{H\alpha}$-to-bolometric-luminosity ratio, $L_{H\alpha}/L_{bol}$, on the Rossby number $R_o$. All rotators with Ro smaller than 0.03$\pm$0.01 converge to an activity level of $L_{H\alpha}/L_{bol}$ = (1.27$\pm$0.02) x 10$^{-4}$. This saturation threshold ($R_{o,sat}$ = 0.03$\pm$0.01) is statistically smaller than that found in most studies of the rotation-activity relation. In the unsaturated regime, slower rotators have lower levels of chromospheric activity, with $L_{H\alpha}/L_{bol}$($R_o$) following a power-law of index $\beta$ = -0.51$\pm$0.02, slightly shallower than the one found for a combined $\approx$650-Myr-old sample of Hyades and Praesepe stars. By comparing this unsaturated behavior to that previously found for coronal activity in M37 (as measured via the X-ray luminosity, $L_X$), we confirm that chromospheric activity decays at a much slower rate than coronal activity with increasing $R_o$. While a comparison of $L_{H\alpha}$ and $L_X$ for M37 members with measurements of both reveals a nearly 1:1 relation, removing the mass-dependencies by comparing instead $L_{H\alpha}/L_{bol}$ and $L_X/L_{bol}$ does not provide clear evidence for such a relation. Finally, we find that $R_{o,sat}$ is smaller for our chromospheric than for our coronal indicator of activity ($R_{o,sat}$ = 0.03$\pm$0.01 versus 0.09$\pm$0.01). We interpret this as possible evidence for coronal stripping.
We identify seven new ultracool white dwarfs discovered in the Sloan Digital Sky Survey (SDSS). The SDSS photometry, spectra, and proper motions are presented, and additional BVRI data are given for these and other previously discovered ultracool white dwarfs. The observed colors span a remarkably wide range, qualitatively similar to colors predicted by models for very cool white dwarfs. One of the new stars (SDSS J1251+44) exhibits strong collision-induced absorption (CIA) in its spectra, while the spectra and colors of the other six are consistent with mild CIA. Another of the new discoveries (SDSS J2239+00A) is part of a binary system -- its companion is also a cool white dwarf, and other data indicate that the companion exhibits an infrared flux deficiency, making this the first binary system composed of two CIA white dwarfs. A third discovery (SDSS J0310-00) has weak Balmer emission lines. The proper motions of all seven stars are consistent with membership in the disk or thick disk.
We review the physics of GRB production by relativistic jets that start highly opaque near the central source and then expand to transparency. We discuss dissipative and radiative processes in the jet and how radiative transfer shapes the observed nonthermal spectrum released at the photosphere. A comparison of recent detailed models with observations gives estimates for important parameters of GRB jets, such as the Lorentz factor and magnetization. We also discuss predictions for GRB polarization and neutrino emission.
In 1964 (Solar Cycle 20; SC 20), Patrick McIntosh began creating hand-drawn synoptic maps of solar magnetic features, based on H$\alpha$ images. These synoptic maps were unique in that they traced magnetic polarity inversion lines, and connected widely separated filaments, fibril patterns, and plage corridors to reveal the large-scale organization of the solar magnetic field. Coronal hole boundaries were later added to the maps, which were produced, more or less continuously, into 2009 (i.e., the start of SC 24). The result was a record of $\sim45$ years ($\sim570$ Carrington rotations), or nearly four complete solar cycles of synoptic maps. We are currently scanning, digitizing and archiving these maps, with the final, searchable versions publicly available at NOAA's National Centers for Environmental Information. In this paper we present preliminary scientific studies using the archived maps from SC 23. We show the global evolution of closed magnetic structures (e.g., sunspots, plage, and filaments) in relation to open magnetic structures (e.g., coronal holes), and examine how both relate to the shifting patterns of large-scale positive and negative polarity regions.