The Energy-Momentum tensor on SpincSpin^c manifolds

On $Spin^c$ manifolds, we study the Energy-Momentum tensor associated with a spinor field. First, we give a spinorial Gauss type formula for oriented hypersurfaces of a $Spin^c$ manifold. Using the notion of generalized cylinders, we derive the variationnal formula for the Dirac operator under metric deformation and point out that the Energy-Momentum tensor appears naturally as the second fundamental form of an isometric immersion. Finally, we show that generalized $Spin^c$ Killing spinors for Codazzi Energy-Momentum tensor are restrictions of parallel spinors.Comment: To appear in IJGMMP (International Journal of Geometric Methods in Modern Physics), 22 page

The Observations Of The X-Ray Source Hz Herculis-Hercules X-1

NASAESASRCAstronom

Rotational symmetry of self-similar solutions to the Ricci flow

Let (M,g) be a three-dimensional steady gradient Ricci soliton which is non-flat and \kappa-noncollapsed. We prove that (M,g) is isometric to the Bryant soliton up to scaling. This solves a problem mentioned in Perelman's first paper.Comment: Final version, to appear in Invent. Mat

Rapid, ultra low coverage copy number profiling of cell-free DNA as a precision oncology screening strategy.

Current cell-free DNA (cfDNA) next generation sequencing (NGS) precision oncology workflows are typically limited to targeted and/or disease-specific applications. In advanced cancer, disease burden and cfDNA tumor content are often elevated, yielding unique precision oncology opportunities. We sought to demonstrate the utility of a pan-cancer, rapid, inexpensive, whole genome NGS of cfDNA approach (PRINCe) as a precision oncology screening strategy via ultra-low coverage (~0.01x) tumor content determination through genome-wide copy number alteration (CNA) profiling. We applied PRINCe to a retrospective cohort of 124 cfDNA samples from 100 patients with advanced cancers, including 76 men with metastatic castration-resistant prostate cancer (mCRPC), enabling cfDNA tumor content approximation and actionable focal CNA detection, while facilitating concordance analyses between cfDNA and tissue-based NGS profiles and assessment of cfDNA alteration associations with mCRPC treatment outcomes. Therapeutically relevant focal CNAs were present in 42 (34%) cfDNA samples, including 36 of 93 (39%) mCRPC patient samples harboring AR amplification. PRINCe identified pre-treatment cfDNA CNA profiles facilitating disease monitoring. Combining PRINCe with routine targeted NGS of cfDNA enabled mutation and CNA assessment with coverages tuned to cfDNA tumor content. In mCRPC, genome-wide PRINCe cfDNA and matched tissue CNA profiles showed high concordance (median Pearson correlation = 0.87), and PRINCe detectable AR amplifications predicted reduced time on therapy, independent of therapy type (Kaplan-Meier log-rank test, chi-square = 24.9, p < 0.0001). Our screening approach enables robust, broadly applicable cfDNA-based precision oncology for patients with advanced cancer through scalable identification of therapeutically relevant CNAs and pre-/post-treatment genomic profiles, enabling cfDNA- or tissue-based precision oncology workflow optimization

High-Resolution Spectroscopy of G191-B2B in the Extreme Ultraviolet

We report a high-resolution (R=3000-4000) spectroscopic observation of the DA white dwarf G191-B2B in the extreme ultraviolet band 220-245 A. A low- density ionised He component is clearly present along the line-of-sight, which if completely interstellar implies a He ionisation fraction considerably higher than is typical of the local interstellar medium. However, some of this material may be associated with circumstellar gas, which has been detected by analysis of the C IV absorption line doublet in an HST STIS spectrum. A stellar atmosphere model assuming a uniform element distribution yields a best fit to the data which includes a significant abundance of photospheric He. The 99-percent confidence contour for the fit parameters excludes solutions in which photospheric He is absent, but this result needs to be tested using models allowing abundance gradients.Comment: LATEX format: 10 pages and 3 figures: accepted for publication in the Astrophysical Journal Letter

Bohm and Einstein-Sasaki Metrics, Black Holes and Cosmological Event Horizons

We study physical applications of the Bohm metrics, which are infinite sequences of inhomogeneous Einstein metrics on spheres and products of spheres of dimension 5 <= d <= 9. We prove that all the Bohm metrics on S^3 x S^2 and S^3 x S^3 have negative eigenvalue modes of the Lichnerowicz operator and by numerical methods we establish that Bohm metrics on S^5 have negative eigenvalues too. We argue that all the Bohm metrics will have negative modes. These results imply that higher-dimensional black-hole spacetimes where the Bohm metric replaces the usual round sphere metric are classically unstable. We also show that the stability criterion for Freund-Rubin solutions is the same as for black-hole stability, and hence such solutions using Bohm metrics will also be unstable. We consider possible endpoints of the instabilities, and show that all Einstein-Sasaki manifolds give stable solutions. We show how Wick rotation of Bohm metrics gives spacetimes that provide counterexamples to a strict form of the Cosmic Baldness conjecture, but they are still consistent with the intuition behind the cosmic No-Hair conjectures. We show how the Lorentzian metrics may be created ``from nothing'' in a no-boundary setting. We argue that Lorentzian Bohm metrics are unstable to decay to de Sitter spacetime. We also argue that noncompact versions of the Bohm metrics have infinitely many negative Lichernowicz modes, and we conjecture a general relation between Lichnerowicz eigenvalues and non-uniqueness of the Dirichlet problem for Einstein's equations.Comment: 53 pages, 11 figure

Discrete molecular dynamics simulations of peptide aggregation

We study the aggregation of peptides using the discrete molecular dynamics simulations. At temperatures above the alpha-helix melting temperature of a single peptide, the model peptides aggregate into a multi-layer parallel beta-sheet structure. This structure has an inter-strand distance of 0.48 nm and an inter-sheet distance of 1.0 nm, which agree with experimental observations. In this model, the hydrogen bond interactions give rise to the inter-strand spacing in beta-sheets, while the Go interactions among side chains make beta-strands parallel to each other and allow beta-sheets to pack into layers. The aggregates also contain free edges which may allow for further aggregation of model peptides to form elongated fibrils.Comment: 15 pages, 8 figure

Habitable Zones in the Universe

Habitability varies dramatically with location and time in the universe. This was recognized centuries ago, but it was only in the last few decades that astronomers began to systematize the study of habitability. The introduction of the concept of the habitable zone was key to progress in this area. The habitable zone concept was first applied to the space around a star, now called the Circumstellar Habitable Zone. Recently, other, vastly broader, habitable zones have been proposed. We review the historical development of the concept of habitable zones and the present state of the research. We also suggest ways to make progress on each of the habitable zones and to unify them into a single concept encompassing the entire universe.Comment: 71 pages, 3 figures, 1 table; to be published in Origins of Life and Evolution of Biospheres; table slightly revise

Colloquium: Nonlinear collective interactions in quantum plasmas with degenerate electron fluids

The current understanding of some important nonlinear collective processes in quantum plasmas with degenerate electrons is presented. After reviewing the basic properties of quantum plasmas, we present model equations (e.g. the quantum hydrodynamic and effective nonlinear Schr\"odinger-Poisson equations) that describe collective nonlinear phenomena at nanoscales. The effects of the electron degeneracy arise due to Heisenberg's uncertainty principle and Pauli's exclusion principle for overlapping electron wavefunctions that result in tunneling of electrons and the electron degeneracy pressure. Since electrons are Fermions (spin-1/2), there also appears an electron spin current and a spin force acting on electrons due to the Bohr magnetization. The quantum effects produce new aspects of electrostatic (ES) and electromagnetic (EM) waves in a quantum plasma that are summarized in here. Furthermore, we discuss nonlinear features of ES ion waves and electron plasma oscillations (ESOs), as well as the trapping of intense EM waves in quantum electron density cavities. Specifically, simulation studies of the coupled nonlinear Schr\"odinger (NLS) and Poisson equations reveal the formation and dynamics of localized ES structures at nanoscales in a quantum plasma. We also discuss the effect of an external magnetic field on the plasma wave spectra and develop quantum magnetohydrodynamic (Q-MHD) equations. The results are useful for understanding numerous collective phenomena in quantum plasmas, such as those in compact astrophysical objects, in plasma-assisted nanotechnology, and in the next-generation of intense laser-solid density plasma interaction experiments.Comment: 25 pages, 14 figures. To be published in Reviews of Modern Physic