ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $X$ be a smooth projective curve over a finite field $\mathbb{F}$ with $q$ elements. For $m\geq 1,$ let $X_m$ be the curve $X$ over the finite field $\mathbb{F}_m$, the $m$-th extension of $\mathbb{F}.$ Let $K_n(m)$ be the $K$-group $K_n(X_m)$ of the smooth projective curve $X_m.$   In this paper, we study the structure of the groups $K_n(m).$ If $l$ is a prime, we establish an analogue of Iwasawa theorem in algebraic number theory for the orders of the $l$-primary part $K_n(l^m)\{l\}$ of $K_n(l^m)$. In particular, when $X$ is an elliptic curve $E$ defined over $\mathbb{F},$ our method determines the structure of $K_n(E).$ Our results can be applied to construct an efficient {\bf DL} system in elliptic cryptography.
The Adam-Gibbs view of the glass transition relates the relaxation time to the configurational entropy, which goes continuously to zero at the so-called Kauzmann temperature. We examine this scenario in the context of a dimer model with an entropy vanishing phase transition, and stochastic loop dynamics. We propose a coarse-grained master equation for the order parameter dynamics which is used to compute the time-dependent autocorrelation function and the associated relaxation time. Using a combination of exact results, scaling arguments and numerical diagonalizations of the master equation, we find non-exponential relaxation and a Vogel-Fulcher divergence of the relaxation time in the vicinity of the phase transition. Since in the dimer model the entropy stays finite all the way to the phase transition point, and then jumps discontinuously to zero, we demonstrate a clear departure from the Adam-Gibbs scenario. Dimer coverings are the "inherent structures" of the canonical frustrated system, the triangular Ising antiferromagnet. Therefore, our results provide a new scenario for the glass transition in supercooled liquids in terms of inherent structure dynamics.
In this work we discuss the recent criticism by Zdziarski of the maximal jet model derived in Falcke & Biermann (1995). We agree with Zdziarski that in general a jet's internal energy is not bounded by its rest-mass energy density. We describe the effects of the mistake on conclusions that have been made using the maximal jet model and show when a maximal jet is an appropriate assumption. The maximal jet model was used to derive a 1-D hydrodynamical model of jets in agnjet, a model that does multiwavelength fitting of quiescent/hard state X-ray binaries and low-luminosity active galactic nuclei. We correct algebraic mistakes made in the derivation of the 1-D Euler equation and relax the maximal jet assumption. We show that the corrections cause minor differences as long as the jet has a small opening angle and a small terminal Lorentz factor. We find that the major conclusion from the maximal jet model, the jet-disk symbiosis, can be generally applied to astrophysical jets. We also show that isothermal jets are required to match the flat radio spectra seen in low-luminosity X-ray binaries and active galactic nuclei, in agreement with other works.
We report on variations in important X-ray emission lines in a series of Chandra grating spectra of the supermassive colliding wind binary star Eta Carinae, including key phases around the X-ray minimum/periastron passage in 2003.5. The X-rays arise from the collision of the slow, dense wind of Eta Car with the fast, low-density wind of an otherwise hidden companion star. The X-ray emission lines provide the only direct measure of the flow dynamics of the companion's wind along the wind-wind collision zone. We concentrate here on the silicon and sulfur lines, which are the strongest and best resolved lines in the X-ray spectra. Most of the line profiles can be adequately fit with symmetric Gaussians with little significant skewness. Both the silicon and sulfur lines show significant velocity shifts and correlated increases in line widths through the observations. The R = forbidden-to-intercombination ratio from the Si XIII and S XV triplets is near or above the low-density limit in all observations, suggesting that the line-forming region is >1.6 stellar radii from the companion star. We show that simple geometrical models cannot simultaneously fit both the observed centroid variations and changes in line width as a function of phase. We show that the observed profiles can be fitted with synthetic profiles with a reasonable model of the emissivity along the wind-wind collision boundary. We use this analysis to help constrain the line formation region as a function of orbital phase, and the orbital geometry.
Only eleven O-type stars have been confirmed to possess large-scale organized magnetic fields. The presence of a -600G longitudinal magnetic field in the O9.7V star HD54879 with a lower limit of the dipole strength of ~2kG, was discovered a few years ago in the framework of the ESO large program "B-fields in OB stars". Our FORS2 spectropolarimetric observations from 2017 October 4 to 2018 February 21 reveal the presence of short and long-term spectral variability and a gradual magnetic field decrease from about -300G down to about -90G. Surprisingly, we discover on the night of 2018 February 17 a sudden, short-term increase of the magnetic field strength and measure a longitudinal magnetic field of -833G. The inspection of the FORS2 spectrum acquired during the observed magnetic field increase indicates a very strong change in spectral appearance with a significantly lower photospheric temperature and a decrease of the radial velocity by several 10km/s. Different scenarios are discussed in an attempt to interpret our observations. The FORS2 radial velocity measurements indicate that HD54879 is a member of a long-period binary.
We study 2-player impartial games, so called \emph{invariant subtraction games}, of the type, given a set of allowed moves the players take turn in moving one single piece on a large Chess board towards the position $\boldsymbol 0$. Here, invariance means that each allowed move is available inside the whole board. Then we define a new game, $\star$ of the old game, by taking the $P$-positions, except $\boldsymbol 0$, as moves in the new game. One such game is $\W^\star=$ (Wythoff Nim)$^\star$, where the moves are defined by complementary Beatty sequences with irrational moduli. Here we give a polynomial time algorithm for infinitely many $P$-positions of $\W^\star$. A repeated application of $\star$ turns out to give especially nice properties for a certain subfamily of the invariant subtraction games, the \emph{permutation games}, which we introduce here. We also introduce the family of \emph{ornament games}, whose $P$-positions define complementary Beatty sequences with rational moduli---hence related to A. S. Fraenkel's `variant' Rat- and Mouse games---and give closed forms for the moves of such games. We also prove that ($k$-pile Nim)$^{\star\star}$ = $k$-pile Nim.
We study the patch dynamics on the whole plane and on the half-plane for a family of active scalars called modified SQG equations. These involve a parameter $\alpha$ which appears in the power of the kernel in their Biot-Savart laws and describes the degree of regularity of the equation. The values $\alpha=0$ and $\alpha=\frac 12$ correspond to the 2D Euler and SQG equations, respectively. We establish here local-in-time regularity for these models, for all $\alpha\in(0,\frac 12)$ on the whole plane and for all small $\alpha>0$ on the half-plane. We use the latter result in [16], where we show existence of regular initial data on the half-plane which lead to a finite time singularity.
The challenges of learning a robust 6D pose function lie in 1) severe occlusion and 2) systematic noises in depth images. Inspired by the success of point-pair features, the goal of this paper is to recover the 6D pose of an object instance segmented from RGB-D images by locally matching pairs of oriented points between the model and camera space. To this end, we propose a novel Bi-directional Correspondence Mapping Network (BiCo-Net) to first generate point clouds guided by a typical pose regression, which can thus incorporate pose-sensitive information to optimize generation of local coordinates and their normal vectors. As pose predictions via geometric computation only rely on one single pair of local oriented points, our BiCo-Net can achieve robustness against sparse and occluded point clouds. An ensemble of redundant pose predictions from locally matching and direct pose regression further refines final pose output against noisy observations. Experimental results on three popularly benchmarking datasets can verify that our method can achieve state-of-the-art performance, especially for the more challenging severe occluded scenes. Source codes are available at https://github.com/Gorilla-Lab-SCUT/BiCo-Net.
We discuss a scalar Dark Matter candidate from the Inert Doublet Model in light of discovery of a 125 GeV SM-like Higgs boson at the LHC. We explore the possibility of using the recent and future data from LHC experiments, namely the Higgs diphoton decay measurements, to constrain the properties of Dark Matter particles.
A continuous-state polynomial branching process is constructed as the pathwise unique solution of a stochastic integral equation with absorbing boundary condition. The extinction and explosion probabilities and the mean extinction and explosion times are computed explicitly, which are also new in the classical branching case. We present necessary and sufficient conditions for the process to extinguish or explode in finite times. In the critical or subcritical case, we give a construction of the process coming down from infinity. Finally, it is shown that the continuous-state polynomial branching process arises naturally as the rescaled limit of a sequence of discrete-state processes.
The multiplicative non-linearity term is usually assumed to be globally Lipschitz in most results on SPDEs. This work proves that the solutions fail to exist if the non-linearity term grows faster than linear growth. The global non-existence of the solution occurs for some non-linear conditions on $\sigma$ . Some precise conditions for existence and uniqueness of the solutions were stated and we have established that the solutions grow in time at most a precise exponential rate at some time interval; and if the solutions satisfy some non-linear conditions then they cease to exist at some finite time t . Our result also compares the non-existence of global solutions for both the compensated and non-compensated Poisson noise equations
The supernova remnant Kes 73 and/or the magnetar 1E 1841-045 at its center can deposit a large amount of energy to the surroundings and is potentially responsible for particle acceleration. Using the data taken with the Fermi Large Area Telescope (LAT), we confirmed the presence of an extended source whose centroid position is highly consistent with this magnetar/supernova-remnant pair. Its emission is intense from 100 MeV to $>$100 GeV. Its LAT spectrum can be decoupled into two components which are respectively governed by two different mechanisms. According to the young age of this system, the magnetar is seemingly a necessary and sufficient source for the downward-curved spectrum below 10 GeV, as the observed $<$10 GeV flux is too high for the supernova remnant to account for. On the other hand, the supernova remnant is reasonably responsible for the hard spectrum above 10 GeV. Further studies of this region in the TeV regime is required, so that we can perform physically meaningful comparisons of the $>$10 GeV spectrum and the TeV spectrum.
We have undertaken an imaging survey of 34 nearby galaxies in far-ultraviolet (FUV, ~1500A) and optical (UBVRI) passbands to characterize galaxy morphology as a function of wavelength. This sample, which includes a range of classical Hubble types from elliptical to irregular with emphasis on spirals at low inclination angle, provides a valuable database for comparison with images of high-z galaxies whose FUV light is redshifted into the optical and near- infrared bands. Ultraviolet data are from the UIT Astro-2 mission. We present images and surface brightness profiles for each galaxy, and we discuss the wavelength-dependence of morphology for different Hubble types in the context of understanding high-z objects. In general, the dominance of young stars in the FUV produces the patchy appearance of a morphological type later than that inferred from optical images. Prominent rings and circumnuclear star formation regions are clearly evident in FUV images of spirals, while bulges, bars, and old, red stellar disks are faint to invisible at these short wavelengths. However, the magnitude of the change in apparent morphology ranges from dramatic in early--type spirals with prominent optical bulges to slight in late-type spirals and irregulars, in which young stars dominate both the UV and optical emission. Starburst galaxies with centrally concentrated, symmetric bursts display an apparent ``E/S0'' structure in the FUV, while starbursts associated with rings or mergers produce a peculiar morphology. We briefly discuss the inadequacy of the optically-defined Hubble sequence to describe FUV galaxy images and estimate morphological k-corrections, and we suggest some directions for future research with this dataset.
An algorithm to create difficult Sudoku puzzles is proposed. An Ising spin-glass like Hamiltonian describing difficulty of puzzles is defined, and difficult puzzles are created by minimizing the energy of the Hamiltonian. We adopt the replica exchange Monte Carlo method with simultaneous temperature adjustments to search lower energy states efficiently, and we succeed in creating a puzzle which is the world hardest ever created in our definition, to our best knowledge. (Added on Mar. 11, the created puzzle can be solved easily by hand. Our definition of the difficulty is inappropriate.)
In this note we propose a two-spine decomposition of the critical Galton-Watson tree and use this decomposition to give a probabilistic proof of Yaglom's theorem.
We formulate a martingale problem that describes a diffusion process in a multidimensional Euclidean space with a membrane located on a given smooth surface and having the properties of skewing and delaying. The theorem on the existence of no more than one solution to the problem is proved.
VERITAS (Very Energetic Radiation Imaging Telescope Array System) is one of the most sensitive currently operating arrays of imaging atmospheric Cherenkov telescopes, which detect very high-energy (VHE; E > 100 GeV) gamma rays. VERITAS is currently in its 11th year of full-array operations with four 12m-diameter telescopes. Many Galactic sources of VHE gamma rays have been detected by VERITAS, such as pulsar wind nebulae, binary systems, and supernova remnants, and the study of VHE emission from these objects has enabled a deeper understanding of the underlying physical processes responsible for the observed gamma rays. Recent highlights from the VERITAS Galactic science program will be presented, including results on pulsar searches, follow-up of sources detected by HAWC, and the 50-year-period binary PSR J2032+4127.
We investigate collective multipole excitations for closed shell nuclei from 16O to 208Pb using correlated realistic nucleon -nucleon interactions in the framework of the random phase approximation (RPA). The dominant short-range central and tensor correlations a re treated explicitly within the Unitary Correlation Operator Method (UCOM), which provides a phase-shift equivalent correlated interaction V_UCOM adapted to simple uncorrelated Hilbert spaces. The same unitary transformation that defines the correlated interaction is used to derive correlated transition operators. Using V_UCOM we solve the Hartree-Fock problem and employ the single-particle state s as starting point for the RPA. By construction, the UCOM-RPA is fully self-consistent, i.e. the same correlated nucleon-nucleon interact ion is used in calculations of the HF ground state and in the residual RPA interaction. Consequently, the spurious state associated with t he center-of-mass motion is properly removed and the sum-rules are exhausted within +-3%. The UCOM-RPA scheme results in a collective character of giant monopole, dipole, and quadrupole resonances in closed-shell nuclei across the nuclear chart. For the isoscalar giant monopole resonance, the resonance energies are in agreement with experiment hinting at a reasonable compressibility. However, in the 1- and 2+ channels the resonance energies are overestimated due to missing long-range correlations and three-body contributions.
In this article we shall outline a derivation of the analogue of discrete torsion for the M-theory three-form potential. We find that some of the differences between orbifold group actions on the C field are classified by H^3(G, U(1)). We also compute the phases that the low-energy effective action of a membrane on T^3 would see in the analogue of a twisted sector, and note that they are invariant under the obvious SL(3,Z) action.
The primary Kepler Mission provided nearly continuous monitoring of ~200,000 objects with unprecedented photometric precision. We present the final catalog of eclipsing binary systems within the 105 square degree Kepler field of view. This release incorporates the full extent of the data from the primary mission (Q0-Q17 Data Release). As a result, new systems have been added, additional false positives have been removed, ephemerides and principal parameters have been recomputed, classifications have been revised to rely on analytical models, and eclipse timing variations have been computed for each system. We identify several classes of systems including those that exhibit tertiary eclipse events, systems that show clear evidence of additional bodies, heartbeat systems, systems with changing eclipse depths, and systems exhibiting only one eclipse event over the duration of the mission. We have updated the period and galactic latitude distribution diagrams and included a catalog completeness evaluation. The total number of identified eclipsing and ellipsoidal binary systems in the Kepler field of view has increased to 2878, 1.3% of all observed Kepler targets. An online version of this catalog with downloadable content and visualization tools is maintained at http://keplerEBs.villanova.edu.
The process of atomic-to-molecular (HI-to-H$_2$) gas conversion is fundamental for molecular-cloud formation and star formation. 21 cm observations of the star-forming region W43 revealed extremely high HI column densities, of 120-180 M$_{\odot}$ pc$^{-2}$, a factor of 10-20 larger than predicted by HI-to-H$_2$ transition theories. We analyze the observed HI with an HI-to-H$_2$ transition theoretical model, and show that the theory-observation discrepancy cannot be explained by the intense radiation in W43, nor by variations of the assumed volume density or H$_2$ formation-rate coefficient. We show that the large observed HI columns are naturally explained by several ($9-22$) HI-to-H$_2$ transition layers, superimposed along the sightlines of W43. We discuss other possible interpretations such as a non-steady-state scenario, and inefficient dust absorption. The case of W43 suggests that HI thresholds reported in extra-galactic observations are probably not associated with a single HI-to-H$_2$ transition, but are rather a result of several transition layers (clouds) along the sightlines, beam-diluted with diffuse inter-cloud gas.
We present a necessary and sufficient condition for three qutrit density matrices to be the one-particle reduced density matrices of a pure three-qutrit quantum state. The condition consists of seven classes of inequalities satisfied by the eigenvalues of these matrices. One of them is a generalization of a known inequality for the qubit case. Some of these inequalities are proved algebraically whereas the proof of the others uses the fact that a continuous function of the state must have a minimum. Construction of states satisfying these inequalities relies on a representation of the convex set of the allowed set of eigenvalues in terms of corner points. We also present a result for a more general quantum system concerning the nature of the boundary surface of the set of the allowed set of eigenvalues.
The usefulness of the spectral function S in the process 3He(e,e'N) has been investigated in a kinematical regime constrained by the conditions that the three-nucleon center-of-mass energy is less than 150 MeV and the magnitude of the three-momentum transfer smaller than 600 MeV/c. Results based on a full treatment of the final state interaction are compared to the spectral function approximation. In the case of proton knockout in the direction of the photon kinematical conditions have been identified where both response functions, RL and RT, can be well approximated by S. These conditions occur for certain low missing momenta and missing energies but not in all cases. So care is required. In case of neutron knockout only RT is a candidate for an approximate treatment by S. In the case of RL the concept of using S is not valid in the studied kinematical regime. This does not exclude the possibility that beyond that regime it might be useful. Possible applications using S for the extraction of electromagnetic form factors of the nucleons are pointed out.
The three-state majority-vote model with noise on Erdos-Renyi's random graphs has been studied. Using Monte Carlo simulations we obtain the phase diagram, along with the critical exponents. Exact results for limiting cases are presented, and shown to be in agreement with numerical values. We find that the critical noise qc is an increasing function of the mean connectivity z of the graph. The critical exponents beta/nu, gamma/nu and 1/nu are calculated for several values of connectivity. We also study the globally connected network, which corresponds to the mean-field limit z = N-1 -> infinity. Our numerical results indicate that the correlation length scales with the number of nodes in the graph, which is consistent with an effective dimensionality equal to unity.
The main focus of this thesis is the IR spectral regime, which since the 70's and 80's has revolutionised our understanding of the Universe. A multi-wavelength analysis on Extremely Red Galaxy populations is first presented in one of the most intensively observed patch of the sky, the Chandra Deep Field South. By adopting a purely statistical methodology, we consider all the photometric and spectroscopic information available on large samples of Extremely Red Objects (EROs, 553 sources), IRAC EROs (IEROs, 259 sources), and Distant Red Galaxies (DRGs, 289 sources). We derive general properties: redshift distributions, AGN host fraction, star-formation rate densities, dust content, morphology, mass functions and mass densities. The results point to the fact that EROs, IEROs, and DRGs all belong to the same population, yet seen at different phases of galaxy evolution. The second part of this thesis is dedicated to the AGN selection in the IR, with particular relevance to the James Webb Space Telescope, to be launched in 2018. We develop an improved IR criterion (using K and IRAC bands) as an alternative to existing IR AGN criteria for the z<2.5 regime, and develop another IR criterion which reliably selects AGN hosts at 0<z<7 (using K, Spitzer-IRAC, and Spitzer-MIPS24um bands, KIM). The ability to track AGN activity since the end of reionization holds great advantages for the study of galaxy evolution. The thesis then focus on the importance of dust. Based on deep IR data on the Cosmological Survey, we derive rest-frame 1.6, 3.3, and 6.2um luminosity functions and their dependency on redshift. We estimate the dust contribution to those wavelengths and show that the hot dust luminosity density evolves since z=1-2 with a much steeper drop than the star-formation history of the Universe. Future prospects are finally discussed in the last chapter.