ShantanuT01/DACTYL-Pretraining huggingface dataset:
A Steinhaus matrix is a binary square matrix of size $n$ which is symmetric, with diagonal of zeros, and whose upper-triangular coefficients satisfy $a_{i,j}=a_{i-1,j-1}+a_{i-1,j}$ for all $2\leq i<j\leq n$. Steinhaus matrices are determined by their first row. A Steinhaus graph is a simple graph whose adjacency matrix is a Steinhaus matrix. We give a short new proof of a theorem, due to Dymacek, which states that even Steinhaus graphs, i.e. those with all vertex degrees even, have doubly-symmetric Steinhaus matrices. In 1979 Dymacek conjectured that the complete graph on two vertices $K_2$ is the only regular Steinhaus graph of odd degree. Using Dymacek's theorem, we prove that if $(a_{i,j})_{1\leq i,j\leq n}$ is a Steinhaus matrix associated with a regular Steinhaus graph of odd degree then its sub-matrix $(a_{i,j})_{2\leq i,j\leq n-1}$ is a multi-symmetric matrix, that is a doubly-symmetric matrix where each row of its upper-triangular part is a symmetric sequence. We prove that the multi-symmetric Steinhaus matrices of size $n$ whose Steinhaus graphs are regular modulo 4, i.e. where all vertex degrees are equal modulo 4, only depend on $\lceil \frac{n}{24}\rceil$ parameters for all even numbers $n$, and on $\lceil \frac{n}{30}\rceil$ parameters in the odd case. This result permits us to verify the Dymacek's conjecture up to 1500 vertices in the odd case.
A violation of the Wiedemann-Franz law in a metal can be quantified by comparing the Lorentz ratio, $L=\kappa\rho/T$, where $\kappa$ is the thermal conductivity and $\rho$ is the electrical resistivity, with the universal Sommerfeld constant, $L_0=(\pi^2/3) (k_B/e)^2$. We obtain the Lorentz ratio of a clean compensated metal with intercarrier interaction as the dominant scattering mechanism by solving exactly the system of coupled integral Boltzmann equations. The Lorentz ratio is shown to assume a particular simple form in the forward-scattering limit: $L/L_0=\overline{\Theta^2}/2$, where $\Theta$ is the scattering angle. In this limit, $L/L_0$ can be arbitrarily small. We also show how the same result can be obtained without the benefit of an exact solution. We discuss how a strong downward violation of the Wiedemann-Franz law in a type-II Weyl semimetal WP$_2$ can be explained within our model.
The relativistic precession can be quickly inferred from the nonlinear polar orbit equation without actually solving it.
We analyze complex zebra patterns and fiber bursts during type-IV solar radio bursts on August 1, 2010. It was shown that all of the main details of sporadic zebra patterns can be explained within the model of zebra patterns and fiber bursts during the interaction of plasma waves with whistlers. In addition, it was shown that the major variations in the stripes of the zebra patterns are caused by the scattering mechanism of fast particles on whistlers, which leads to the transition of whistler instability from the normal Doppler effect to an anomalous one.
We use a diagrammatic hopping expansion to calculate finite-temperature Green functions of the Bose-Hubbard model which describes bosons in an optical lattice. This technique allows for a summation of subsets of diagrams, so the divergence of the Green function leads to non-perturbative results for the boundary between the superfluid and the Mott phase for finite temperatures. Whereas the first-order calculation reproduces the seminal mean-field result, the second order goes beyond and shifts the phase boundary in the immediate vicinity of the critical parameters determined by the latest high-precision Monte-Carlo simulations of the Bose-Hubbard model. In addition, our Green's function approach allows for calculating the excitation spectrum at finite temperature and for determining the effective masses of particles and holes.
The exchange interaction between electrons located at different randomly distributed impurities is studied for small density of impurities. The singlet-triplet splitting 2J(R) is calculated for two Coulomb centers at a distance R. Interpolated formulas are found which work for all distances R from zero to infinity. The data from atomic physics are used for the interpolation in three-dimensional case. For two-dimensional case the original calculations are performed to find asymptotic behavior of the splitting at large R, the splitting for the ``two-dimensional helium atom'' (R=0) and the splitting at $R=a_B$, where $a_B$ is the effective Bohr radius. The spin structure of impurity band is described by the Heisenberg Hamiltonian. The ground state of a system consists of localized singlets. The new results are obtained for the distribution of the singlet pairs in the ground state. These results are exact at low density. The problem is reduced to a non-trivial geometric problem which is solved in the mean field approximation and by computer modeling. The density of free electrons is found as a function of temperature and the distribution function of the singlet-triplet transitions energies is calculated. Both functions are given in an analytical form.
A maximal coupling of two diffusion processes makes two diffusion particles meet as early as possible. We study the uniqueness of maximal couplings under a sort of "reflection structure" which ensures the existence of such couplings. In this framework, the uniqueness in the class of Markovian couplings holds for the Brownian motion on a Riemannian manifold whereas it fails in more singular cases. We also prove that a Kendall-Cranston coupling is maximal under the reflection structure.
Given a real curve, we study special linear systems called "very special" for which the dimension does not satisfy a Clifford type inequality. We classify all these very special linear systems when the gonality of the curve is small.
Anomalous Cepheids are a rather rare family of pulsating variables preferably found in dwarf galaxies. Attempts to model these variable stars via single-star evolution scenarios still leave space for improvements to better grasp their origin. Focusing on the LMC with its rich population of Anomalous Cepheids to compare against we probe the role binary stars might play to understand the nature of Anomalous Cepheids. The evolution of donors and accretors undergoing Case-B mass transfer along the first red-giant branch as well as merger-like models were calculated. First results show that in binary scenarios a larger range of star masses and metallicities up to Z < 0.008, higher than deemed possible hitherto, enter and pass through the instability strip. If binary stars play a role in Anomalous Cepheid populations, mass donors, mass accretors, or even mergers are potential candidates to counteract constraints imposed by the single-star approach.
We show how to obtain the critical compressibility factor $Z_c$ for simple and associative Lennard-Jones fluids using the critical characteristics of the Ising model on different lattices. The explanation for the results on the critical point line of the Lennard-Jones fluids and liquid metals is proposed within the global isomorphism approach.
We show analytically that the heat conductivity of oscillator chains diverges with system size N as N^{1/3}, which is the same as for one-dimensional fluids. For long cylinders, we use the hydrodynamic equations for a crystal in one dimension. This is appropriate for stiff systems such as nanotubes, where the eventual crossover to a fluid only sets in at unrealistically large N. Despite the extra equation compared to a fluid, the scaling of the heat conductivity is unchanged. For strictly one-dimensional chains, we show that the dynamic equations are those of a fluid at all length scales even if the static order extends to very large N. The discrepancy between our results and numerical simulations on Fermi-Pasta-Ulam chains is discussed.
Through a series of observations with the Australia Telescope Compact Array we have monitored the variability of ground-state hydroxyl maser emission from G12.889+0.489 in all four Stokes polarisation products. These observations were motivated by the known periodicity in the associated 6.7-GHz methanol maser emission. A total of 27 epochs of observations were made over 16 months. No emission was seen from either the 1612 or 1720 MHz satellite line transitions (to a typical five sigma upper limit of 0.2 Jy). The peak flux densities of the 1665 and 1667 MHz emission were observed to vary at a level of ~20% (with the exception of one epoch which dropped by <40%). There was no distinct flaring activity at any epoch, but there was a weak indication of periodic variability, with a period and phase of minimum emission similar to that of methanol. There is no significant variation in the polarised properties of the hydroxyl, with Stokes Q and U flux densities varying in accord with the Stokes I intensity (linear polarisation, P, varying by <20%) and the right and left circularly polarised components varying by <33% at 1665-MHz and <38% at 1667-MHz. These observations are the first monitoring observations of the hydroxyl maser emission from G12.889+0.489.
Waves propagating in a curved spacetime develop tails. In particular, it is well established that the late-time dynamics of gravitational collapse is dominated by a power-law decaying tail of the form $Mt^{-(2l+3)}$, where $M$ is the black-hole mass. It should be emphasized, however, that in a typical evolution scenario there is a considerable time window in which the signal is no longer dominated by the black-hole quasinormal modes, but the leading order power-law tail has not yet taken over. Higher-order terms may have a considerable contribution to the signal at these intermediate times. It is therefore of interest to analyze these higher-order corrections to the leading-order power-law behavior. We show that the higher-order contamination terms die off at late times as $M^2t^{-4}\ln(t/M)$ for spherical perturbations, and as $M^2t^{-(2l+4)}\ln^2(t/M)$ for non-spherical $(l\neq0)$ perturbations. These results imply that the leading-order power-law tail becomes "pure" (namely, with less than 1% contamination) only at extremely late times of the order of $10^4M$.
The renormalization of the chiral np interaction with Delta-excitations in intermediate states is considered at next-to-leading order (NLO) and next-to-next-to-leading order (N2LO) for central waves. The inclusion of the Delta-excitation as an explicit degree of freedom improves the convergence properties of the effective field theory results for np scattering with respect to Delta-less theory, and allows the existence of a deuteron bound state in the infinite cut-off limit. The 1S_0 singlet and 3S_1 triplet phase shifts reproduce data for p ~ m_pi. The role of spectral function regularization is also discussed.
We search the Planck data for a thermal Sunyaev-Zel'dovich (tSZ) signal due to gas filaments between pairs of Luminous Red Galaxies (LRG's) taken from the Sloan Digital Sky Survey Data Release 12 (SDSS/DR12). We identify $\sim$260,000 LRG pairs in the DR12 catalog that lie within 6-10 $h^{-1} \mathrm{Mpc}$ of each other in tangential direction and within 6 $h^{-1} \mathrm{Mpc}$ in radial direction. We stack pairs by rotating and scaling the angular positions of each LRG so they lie on a common reference frame, then we subtract a circularly symmetric halo from each member of the pair to search for a residual signal between the pair members. We find a statistically significant (5.3$\sigma$) signal between LRG pairs in the stacked data with a magnitude $\Delta y = (1.31 \pm 0.25) \times 10^{-8}$. The uncertainty is estimated from two Monte Carlo null tests which also establish the reliability of our analysis. Assuming a simple, isothermal, cylindrical filament model of electron over-density with a radial density profile proportional to $r_c/r$ (as determined from simulations), where $r$ is the perpendicular distance from the cylinder axis and $r_c$ is the core radius of the density profile, we constrain the product of over-density and filament temperature to be $\delta_c \times (T_{\rm e}/10^7 \, {\rm K}) \times (r_c/0.5h^{-1} \, {\rm Mpc}) = 2.7 \pm 0.5$. To our knowledge, this is the first detection of filamentary gas at over-densities typical of cosmological large-scale structure. We compare our result to the BAHAMAS suite of cosmological hydrodynamic simulations (McCarthy et al. 2017) and find a slightly lower, but marginally consistent Comptonization excess, $\Delta y = (0.84 \pm 0.24) \times 10^{-8}$.
The standard cold dark matter plus cosmological constant model predicts that galaxies form within dark-matter haloes, and that low-mass galaxies are more dark-matter dominated than massive ones. The unexpected discovery of two low-mass galaxies lacking dark matter immediately provoked concerns about the standard cosmology and ignited explorations of alternatives, including self-interacting dark matter and modified gravity. Apprehension grew after several cosmological simulations using the conventional model failed to form adequate numerical analogues with comparable internal characteristics (stellar masses, sizes, velocity dispersions and morphologies). Here we show that the standard paradigm naturally produces galaxies lacking dark matter with internal characteristics in agreement with observations. Using a state-of-the-art cosmological simulation and a meticulous galaxy-identification technique, we find that extreme close encounters with massive neighbours can be responsible for this. We predict that approximately 30 percent of massive central galaxies (with at least 1e11 solar masses in stars) harbour at least one dark-matter-deficient satellite (with 1e8 - 1e9 solar masses in stars). This distinctive class of galaxies provides an additional layer in our understanding of the role of interactions in shaping galactic properties. Future observations surveying galaxies in the aforementioned regime will provide a crucial test of this scenario.
Decomposition of any N-partite state (density operator) into clusters (that do not overlap) is studied in detail with a view to learn as much as possible about the correlations implied by the state. The Wootters-Mermin theorem, stating that the totality of all strings of cluster events (projectors) determines the state in any finite- or infinite-dimensional state space, is a slightly sharpened and generalized form of the original results of Wootters and Mermin. It is applied to tensor factorization of the state into states of clusters (uncorrelated decomposition) and it is shown that a finest uncorrelated decomposition always exists, and that its coarsenings and only they are other possible uncorrelated cluster decompositions. Distant effects witin homogeneous cluster states, which are, by definition, the tensor factors in the finest uncorrelated decomposition, are discussed. The entire study is viewed by the author as a possible further elaboration of Mermin's Ithaca program.
In this letter a late-phase spectrum of SN 2010lp, a subluminous Type Ia supernova (SN Ia), is presented and analysed. As in 1991bg-like SNe Ia at comparable epochs, the spectrum is characterised by relatively broad [FeII] and [CaII] emission lines. However, instead of narrow [FeIII] and [CoIII] lines that dominate the emission from the innermost regions of 1991bg-like SNe, SN 2010lp shows [OI] 6300,6364 emission, usually associated with core-collapse SNe and never observed in a subluminous thermonuclear explosion before. The [OI] feature has a complex profile with two strong, narrow emission peaks. This suggests oxygen to be distributed in a non-spherical region close to the centre of the ejecta, severely challenging most thermonuclear explosion models discussed in the literature. We conclude that given these constraints violent mergers are presently the most promising scenario to explain SN 2010lp.
Gravitational lensing of the cosmic microwave background (CMB) is expected to be amongst the most powerful cosmological tools for ongoing and upcoming CMB experiments. In this work, we investigate a bias to CMB lensing reconstruction from temperature anisotropies due to the kinematic Sunyaev-Zel'dovich (kSZ) effect, that is, the Doppler shift of CMB photons induced by Compton-scattering off moving electrons. The kSZ signal yields biases due to both its own intrinsic non-Gaussianity and its non-zero cross-correlation with the CMB lensing field (and other fields that trace the large-scale structure). This kSZ-induced bias affects both the CMB lensing auto-power spectrum and its cross-correlation with low-redshift tracers. Furthermore, it cannot be removed by multifrequency foreground separation techniques because the kSZ effect preserves the blackbody spectrum of the CMB. While statistically negligible for current datasets, we show that it will be important for upcoming surveys, and failure to account for it can lead to large biases in constraints on neutrino masses or the properties of dark energy. For a Stage 4 CMB experiment, the bias can be as large as $\approx$ 15% or 12% in cross-correlation with LSST galaxy lensing convergence or galaxy overdensity maps, respectively, when the maximum temperature multipole used in the reconstruction is $\ell_{\rm max} = 4000$, and about half of that when $\ell_{\rm max} = 3000$. Similarly, we find that the CMB lensing auto-power spectrum can be biased by up to several percent. These biases are many times larger than the expected statistical errors. Reducing $\ell_{\rm max}$ can significantly mitigate the bias at the cost of a decrease in the overall lensing reconstruction signal-to-noise. Polarization-only reconstruction may be the most robust mitigation strategy.
We present results for response functions and asymmetries in the nuclear reactions 37\vec{Ar}(\vec{e},e'n)36Ar and 37\vec{K}(\vec{e},e' p)36Ar at quasifree kinematics. We compare PWIA results obtained using deformed HF wave functions with PWIA and DWIA results obtained assuming a spherical mean field. We show that the complex structure of the deformed orbitals can be probed by coincidence measurements with polarized beam and targets.
We report the discovery of a gravitationally lensed quasar identified serendipitously in the Sloan Digital Sky Survey (SDSS). The object, SDSS J094604.90+183541.8, was initially targeted for spectroscopy as a luminous red galaxy, but the SDSS spectrum has the features of both a z=0.388 galaxy and a z=4.8 quasar. We have obtained additional imaging that resolves the system into two quasar images separated by 3.06 arcsec and a bright galaxy that is strongly blended with one of the quasar images. We confirm spectroscopically that the two quasar images represent a single lensed source at z=4.8 with a total magnification of 3.2, and we derive a model for the lensing galaxy. This is the highest redshift lensed quasar currently known. We examine the issues surrounding the selection of such an unusual object from existing data and briefly discuss implications for lensed quasar surveys.
In this paper, we present some geometric characterizations of the Moufang quadrangles of mixed type, i.e., the Moufang quadrangles all the points and lines of which are regular. Roughly, we classify generalized quadrangles with enough (to be made precise) regular points and lines with the property that the dual net associated to the regular points satisfy the Axiom of Veblen-Young, or a very weak version of the Axiom of Desargues. As an application we obtain a geometric characterization and axiomatization of the generalized inversive planes arising from the Suzuki-Tits ovoids related to a polarity in a mixed quadrangle. In the perfect case this gives rise to a characterization with one axiom less than in an already known result by the second author.
The recent HEGRA observations of the blazar Mkn 501 show strong curvature in the very high energy gamma-ray spectrum. Applying the gamma-ray opacity derived from an empirically based model of the intergalactic infrared background radiation field (IIRF), to these observations, we find that the intrinsic spectrum of this source is consistent with a power-law: dN/dE~ E^-alpha with alpha=2.00 +/- 0.03 over the range 500 GeV - 20 TeV. Within current synchrotron self-Compton scenarios, the fact that the TeV spectral energy distribution of Mkn 501 does not vary with luminosity, combined with the correlated, spectrally variable emission in X-rays, as observed by the BeppoSAX and RXTE instruments, also independently implies that the intrinsic spectrum must be close to alpha=2. Thus, the observed curvature in the spectrum is most easily understood as resulting from intergalactic absorption.
Aims. To develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods. We consider LSD under the Bayesian framework and we introduce a flexible Gaussian Process (GP) prior for the LSD profile. This prior allows the result to automatically adapt to the presence of signal. We exploit several linear algebra identities to accelerate the calculations. The final algorithm can deal with thousands of spectral lines in a few seconds. Results. We demonstrate the reliability of the method with synthetic experiments and we apply it to real spectropolarimetric observations of magnetic stars. We are able to recover the magnetic signals using a small number of spectral lines, together with the uncertainty at each velocity bin. This allows the user to consider if the detected signal is reliable. The code to compute the Bayesian LSD profile is freely available.
We present the large-scale structure over more than 50 comoving Mpc scale at z $\sim$ 0.9 where the CL1604 supercluster, which is one of the largest structures ever known at high redshifts, is embedded. The wide-field deep imaging survey by the Subaru Strategic Program with Hyper Suprime-Cam reveals that the already-known CL1604 supercluster is a mere part of larger-scale structure extending to both the north and the south. We confirm that there are galaxy clusters at three slightly different redshifts in the northern and southern sides of the supercluster by determining the redshifts of 55 red-sequence galaxies and 82 star-forming galaxies in total by the follow-up spectroscopy with Subaru/FOCAS and Gemini-N/GMOS. This suggests that the structure ever known as the CL1604 supercluster is the tip of the iceberg. We investigate stellar population of the red-sequence galaxies using 4000 A break and Balmer H$\delta$ absorption line. Almost all of the red-sequence galaxies brighter than 21.5 mag in $z$-band show an old stellar population with $\gtrsim2$ Gyr. The comparison of composite spectra of the red-sequence galaxies in the individual clusters show that the galaxies at a similar redshift have similar stellar population age, even if they are located $\sim$50 Mpc apart from each other. However, there could be a large variation in the star formation history. Therefore, it is likely that galaxies associated with the large-scale structure at 50 Mpc scale formed at almost the same time, have assembled into the denser regions, and then have evolved with different star formation history along the hierarchical growth of the cosmic web.
This paper gives a summary of basic concepts of density-functional theory (DFT) and its use in state-of-the-art computations of complex processes in condensed matter physics and materials science. In particular we discuss how microscopic growth parameters can be determined by DFT and how on this basis macroscopic phenomena can be described. To reach the time and length scales of realistic growth conditions, DFT results are complemented by kinetic Monte Carlo simulations.