Combinatorial structures in loops I. Elements of the decomposition theory

Difference sets have been extensively studied in groups, principally in Abelian groups. Here we extend the notion of a difference set to loops. This entails considering the class of k> systems and the special subclasses of k, [lambda]> principal block partial designs (PBPDs) and k, [lambda]> designs. By means of a certain permutation matrix decomposition of the incidence matrices of a system and its complement, we can isomorphically identify an abstract k> system with a corresponding system in a loop. Special properties of this decomposition correspond to special algebraic properties of the loop. Here we investigate the situation when some or all of the elements of the loop are right inversive. We identify certain classes of k, [lambda]> designs, including skew-Hadamard designs and finite projective planes, with designs and difference sets in right inverse property loops and prove a universal existence theorem for k, [lambda]> PBPDs and corresponding difference sets in such loops.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/33925/1/0000192.pd

Delivery of Dark Material to Vesta via Carbonaceous Chondritic Impacts

NASA's Dawn spacecraft observations of asteroid (4) Vesta reveal a surface with the highest albedo and color variation of any asteroid we have observed so far. Terrains rich in low albedo dark material (DM) have been identified using Dawn Framing Camera (FC) 0.75 {\mu}m filter images in several geologic settings: associated with impact craters (in the ejecta blanket material and/or on the crater walls and rims); as flow-like deposits or rays commonly associated with topographic highs; and as dark spots (likely secondary impacts) nearby impact craters. This DM could be a relic of ancient volcanic activity or exogenic in origin. We report that the majority of the spectra of DM are similar to carbonaceous chondrite meteorites mixed with materials indigenous to Vesta. Using high-resolution seven color images we compared DM color properties (albedo, band depth) with laboratory measurements of possible analog materials. Band depth and albedo of DM are identical to those of carbonaceous chondrite xenolith-rich howardite Mt. Pratt (PRA) 04401. Laboratory mixtures of Murchison CM2 carbonaceous chondrite and basaltic eucrite Millbillillie also show band depth and albedo affinity to DM. Modeling of carbonaceous chondrite abundance in DM (1-6 vol%) is consistent with howardite meteorites. We find no evidence for large-scale volcanism (exposed dikes/pyroclastic falls) as the source of DM. Our modeling efforts using impact crater scaling laws and numerical models of ejecta reaccretion suggest the delivery and emplacement of this DM on Vesta during the formation of the ~400 km Veneneia basin by a low-velocity (<2 km/sec) carbonaceous impactor. This discovery is important because it strengthens the long-held idea that primitive bodies are the source of carbon and probably volatiles in the early Solar System.Comment: Icarus (Accepted) Pages: 58 Figures: 15 Tables:

Black hole solutions in F(R) gravity with conformal anomaly

In this paper, we consider $F(R)=R+f(R)$ theory instead of Einstein gravity with conformal anomaly and look for its analytical solutions. Depending on the free parameters, one may obtain both uncharged and charged solutions for some classes of $F(R)$ models. Calculation of Kretschmann scalar shows that there is a singularity located at $r=0$, which the geometry of uncharged (charged) solution is corresponding to the Schwarzschild (Reissner-Nordstr\"om) singularity. Further, we discuss the viability of our models in details. We show that these models can be stable depending on their parameters and in different epoches of the universe.Comment: 12 pages, one figur

Statistical Theory of Spin Relaxation and Diffusion in Solids

A comprehensive theoretical description is given for the spin relaxation and diffusion in solids. The formulation is made in a general statistical-mechanical way. The method of the nonequilibrium statistical operator (NSO) developed by D. N. Zubarev is employed to analyze a relaxation dynamics of a spin subsystem. Perturbation of this subsystem in solids may produce a nonequilibrium state which is then relaxed to an equilibrium state due to the interaction between the particles or with a thermal bath (lattice). The generalized kinetic equations were derived previously for a system weakly coupled to a thermal bath to elucidate the nature of transport and relaxation processes. In this paper, these results are used to describe the relaxation and diffusion of nuclear spins in solids. The aim is to formulate a successive and coherent microscopic description of the nuclear magnetic relaxation and diffusion in solids. The nuclear spin-lattice relaxation is considered and the Gorter relation is derived. As an example, a theory of spin diffusion of the nuclear magnetic moment in dilute alloys (like Cu-Mn) is developed. It is shown that due to the dipolar interaction between host nuclear spins and impurity spins, a nonuniform distribution in the host nuclear spin system will occur and consequently the macroscopic relaxation time will be strongly determined by the spin diffusion. The explicit expressions for the relaxation time in certain physically relevant cases are given.Comment: 41 pages, 119 Refs. Corrected typos, added reference

Interstellar MHD Turbulence and Star Formation

This chapter reviews the nature of turbulence in the Galactic interstellar medium (ISM) and its connections to the star formation (SF) process. The ISM is turbulent, magnetized, self-gravitating, and is subject to heating and cooling processes that control its thermodynamic behavior. The turbulence in the warm and hot ionized components of the ISM appears to be trans- or subsonic, and thus to behave nearly incompressibly. However, the neutral warm and cold components are highly compressible, as a consequence of both thermal instability in the atomic gas and of moderately-to-strongly supersonic motions in the roughly isothermal cold atomic and molecular components. Within this context, we discuss: i) the production and statistical distribution of turbulent density fluctuations in both isothermal and polytropic media; ii) the nature of the clumps produced by thermal instability, noting that, contrary to classical ideas, they in general accrete mass from their environment; iii) the density-magnetic field correlation (or lack thereof) in turbulent density fluctuations, as a consequence of the superposition of the different wave modes in the turbulent flow; iv) the evolution of the mass-to-magnetic flux ratio (MFR) in density fluctuations as they are built up by dynamic compressions; v) the formation of cold, dense clouds aided by thermal instability; vi) the expectation that star-forming molecular clouds are likely to be undergoing global gravitational contraction, rather than being near equilibrium, and vii) the regulation of the star formation rate (SFR) in such gravitationally contracting clouds by stellar feedback which, rather than keeping the clouds from collapsing, evaporates and diperses them while they collapse.Comment: 43 pages. Invited chapter for the book "Magnetic Fields in Diffuse Media", edited by Elisabete de Gouveia dal Pino and Alex Lazarian. Revised as per referee's recommendation

An Integrated TCGA Pan-Cancer Clinical Data Resource to Drive High-Quality Survival Outcome Analytics

For a decade, The Cancer Genome Atlas (TCGA) program collected clinicopathologic annotation data along with multi-platform molecular profiles of more than 11,000 human tumors across 33 different cancer types. TCGA clinical data contain key features representing the democratized nature of the data collection process. To ensure proper use of this large clinical dataset associated with genomic features, we developed a standardized dataset named the TCGA Pan-Cancer Clinical Data Resource (TCGA-CDR), which includes four major clinical outcome endpoints. In addition to detailing major challenges and statistical limitations encountered during the effort of integrating the acquired clinical data, we present a summary that includes endpoint usage recommendations for each cancer type. These TCGA-CDR findings appear to be consistent with cancer genomics studies independent of the TCGA effort and provide opportunities for investigating cancer biology using clinical correlates at an unprecedented scale. Analysis of clinicopathologic annotations for over 11,000 cancer patients in the TCGA program leads to the generation of TCGA Clinical Data Resource, which provides recommendations of clinical outcome endpoint usage for 33 cancer types

Test-to-Stay After Exposure to SARS-CoV-2 in K-12 Schools

OBJECTIVES: We evaluated the safety and efficacy of a test-to-stay program for unvaccinated students and staff who experienced an unmasked, in-school exposure to someone with confirmed severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection. Serial testing instead of quarantine was offered to asymptomatic contacts. We measured secondary and tertiary transmission rates within participating schools and in-school days preserved for participants. METHODS: Participating staff or students from universally masked districts in North Carolina underwent rapid antigen testing at set intervals up to 7 days after known exposure. Collected data included location or setting of exposure, participant symptoms, and school absences up to 14 days after enrollment. Outcomes included tertiary transmission, secondary transmission, and school days saved among test-to-stay participants. A prespecified interim safety analysis occurred after 1 month of enrollment. RESULTS: We enrolled 367 participants and completed 14-day follow-up on all participants for this analysis. Nearly all (215 of 238, 90%) exposure encounters involved an unmasked index case and an unmasked close contact, with most (353 of 366, 96%) occurring indoors, during lunch (137 of 357, 39%) or athletics (45 of 357, 13%). Secondary attack rate was 1.7% (95% confidence interval: 0.6%-4.7%) based on 883 SARS-CoV-2 serial rapid antigen tests with results from 357 participants; no tertiary cases were identified, and 1628 (92%) school days were saved through test-to-stay program implementation out of 1764 days potentially missed. CONCLUSION: After unmasked in-school exposure to SARS-CoV-2, even in a mostly unvaccinated population, a test-to-stay strategy is a safe alternative to quarantine

The TESS-Keck Survey. II. An Ultra-Short-Period Rocky Planet And Its Siblings Transiting The Galactic Thick-Disk Star TOI-561

We report the discovery of TOI-561, a multiplanet system in the galactic thick disk that contains a rocky, ultra-short-period planet. This bright (V = 10.2) star hosts three small transiting planets identified in photometry from the NASA TESS mission: TOI-561 b (TOI-561.02, P = 0.44 days, Rp = 1.45 ± 0.11 R⊕), c (TOI-561.01, P = 10.8 days, Rp = 2.90 ± 0.13 R⊕), and d (TOI-561.03, P = 16.3 days, Rp = 2.32 ± 0.16 R⊕). The star is chemically ([Fe/H] = −0.41 ± 0.05, [α/Fe] = +0.23 ± 0.05) and kinematically consistent with the galactic thick-disk population, making TOI-561 one of the oldest (10 ± 3 Gyr) and most metal-poor planetary systems discovered yet. We dynamically confirm planets b and c with radial velocities from the W. M. Keck Observatory High Resolution Echelle Spectrometer. Planet b has a mass and density of 3.2 ± 0.8 M⊕ and ${5.5}_{-1.6}^{+2.0}$g cm−3, consistent with a rocky composition. Its lower-than-average density is consistent with an iron-poor composition, although an Earth-like iron-to-silicates ratio is not ruled out. Planet c is 7.0 ± 2.3 M⊕ and 1.6 ± 0.6 g cm−3, consistent with an interior rocky core overlaid with a low-mass volatile envelope. Several attributes of the photometry for planet d (which we did not detect dynamically) complicate the analysis, but we vet the planet with high-contrast imaging, ground-based photometric follow-up, and radial velocities. TOI-561 b is the first rocky world around a galactic thick-disk star confirmed with radial velocities and one of the best rocky planets for thermal emission studies