Small BGK waves and nonlinear Landau damping

Consider 1D Vlasov-poisson system with a fixed ion background and periodic condition on the space variable. First, we show that for general homogeneous equilibria, within any small neighborhood in the Sobolev space W^{s,p} (p>1,s<1+(1/p)) of the steady distribution function, there exist nontrivial travelling wave solutions (BGK waves) with arbitrary minimal period and traveling speed. This implies that nonlinear Landau damping is not true in W^{s,p}(s<1+(1/p)) space for any homogeneous equilibria and any spatial period. Indeed, in W^{s,p} (s<1+(1/p)) neighborhood of any homogeneous state, the long time dynamics is very rich, including travelling BGK waves, unstable homogeneous states and their possible invariant manifolds. Second, it is shown that for homogeneous equilibria satisfying Penrose's linear stability condition, there exist no nontrivial travelling BGK waves and unstable homogeneous states in some W^{s,p} (p>1,s>1+(1/p)) neighborhood. Furthermore, when p=2,we prove that there exist no nontrivial invariant structures in the H^{s} (s>(3/2)) neighborhood of stable homogeneous states. These results suggest the long time dynamics in the W^{s,p} (s>1+(1/p)) and particularly, in the H^{s} (s>(3/2)) neighborhoods of a stable homogeneous state might be relatively simple. We also demonstrate that linear damping holds for initial perturbations in very rough spaces, for linearly stable homogeneous state. This suggests that the contrasting dynamics in W^{s,p} spaces with the critical power s=1+(1/p) is a trully nonlinear phenomena which can not be traced back to the linear level

Friedmann Equation and Stability of Inflationary Higher Derivative Gravity

Stability analysis on the De Sitter universe in pure gravity theory is known to be useful in many aspects. We first show how to complete the proof of an earlier argument based on a redundant field equation. It is shown further that the stability condition applies to $k \ne 0$ Friedmann-Robertson-Walker spaces based on the non-redundant Friedmann equation derived from a simple effective Lagrangian. We show how to derive this expression for the Friedmann equation of pure gravity theory. This expression is also generalized to include scalar field interactions.Comment: Revtex, 6 pages, Add two more references, some typos correcte

Ginzburg-Landau functional for nearly antiferromagnetic perfect and disordered Kondo lattices

Interplay between Kondo effect and trends to antiferromagnetic and spin glass ordering in perfect and disordered bipartite Kondo lattices is considered. Ginzburg-Landau equation is derived from the microscopic effective action written in three mode representation (Kondo screening, antiferromagnetic correlations and spin liquid correlations). The problem of local constraint is resolved by means of Popov-Fedotov representation for localized spin operators. It is shown that the Kondo screening enhances the trend to a spin liquid crossover and suppresses antiferromagnetic ordering in perfect Kondo lattices and spin glass ordering in doped Kondo lattices. The modified Doniach's diagram is constructed, and possibilities of going beyond the mean field approximation are discussed.Comment: 18 pages, RevTeX, 7 EPS figures include

Metastable States in Spin Glasses and Disordered Ferromagnets

We study analytically M-spin-flip stable states in disordered short-ranged Ising models (spin glasses and ferromagnets) in all dimensions and for all M. Our approach is primarily dynamical and is based on the convergence of a zero-temperature dynamical process with flips of lattice animals up to size M and starting from a deep quench, to a metastable limit. The results (rigorous and nonrigorous, in infinite and finite volumes) concern many aspects of metastable states: their numbers, basins of attraction, energy densities, overlaps, remanent magnetizations and relations to thermodynamic states. For example, we show that their overlap distribution is a delta-function at zero. We also define a dynamics for M=infinity, which provides a potential tool for investigating ground state structure.Comment: 34 pages (LaTeX); to appear in Physical Review

Abuse-related post-traumatic stress during the childbearing year

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75405/1/j.1365-2648.2004.03051.x.pd

Largest GWAS of PTSD (N=20 070) yields genetic overlap with schizophrenia and sex differences in heritability

The Psychiatric Genomics Consortium-Posttraumatic Stress Disorder group (PGC-PTSD) combined genome-wide case-control molecular genetic data across 11 multiethnic studies to quantify PTSD heritability, to examine potential shared genetic risk with schizophrenia, bipolar disorder, and major depressive disorder and to identify risk loci for PTSD. Examining 20 730 individuals, we report a molecular genetics-based heritability estimate (h 2 SNP) for European-American females of 29% that is similar to h 2 SNP for schizophrenia and is substantially higher than h 2 SNP in European-American males (estimate not distinguishable from zero). We found strong evidence of overlapping genetic risk between PTSD and schizophrenia along with more modest evidence of overlap with bipolar and major depressive disorder. No single-nucleotide polymorphisms (SNPs) exceeded genome-wide significance in the transethnic (overall) meta-analysis and we do not replicate previously reported associations. Still, SNP-level summary statistics made available here afford the best-available molecular genetic index of PTSD - for both European- and African-American individuals - and can be used in polygenic risk prediction and genetic correlation studies of diverse phenotypes. Publication of summary statistics for 1/410 000 African Americans contributes to the broader goal of increased ancestral diversity in genomic data resources. In sum, the results demonstrate genetic influences on the development of PTSD, identify shared genetic risk between PTSD and other psychiatric disorders and highlight the importance of multiethnic/racial samples. As has been the case with schizophrenia and other complex genetic disorders, larger sample sizes are needed to identify specific risk loci

A putative causal relationship between genetically determined female body shape and posttraumatic stress disorder

Background: The nature and underlying mechanisms of the observed increased vulnerability to posttraumatic stress disorder (PTSD) in women are unclear. Methods: We investigated the genetic overlap of PTSD with anthropometric traits and reproductive behaviors and functions in women. The analysis was conducted using female-specific summary statistics from large genome-wide association studies (GWAS) and a cohort of 3577 European American women (966 PTSD cases and 2611 trauma-exposed controls). We applied a high-resolution polygenic score approach and Mendelian randomization analysis to investigate genetic correlations and causal relationships. Results: We observed an inverse association of PTSD with genetically determined anthropometric traits related to body shape, independent of body mass index (BMI). The top association was related to BMI-adjusted waist circumference (WCadj; R = -0.079, P &lt; 0.001, Q = 0.011). We estimated a relative decrease of 64.6% (95% confidence interval = 27.5-82.7) in the risk of PTSD per 1-SD increase in WCadj. MR-Egger regression intercept analysis showed no evidence of pleiotropic effects in this association (Ppleiotropy = 0.979). We also observed associations of genetically determined WCadj with age at first sexual intercourse and number of sexual partners (P = 0.013 and P &lt; 0.001, respectively). Conclusions: There is a putative causal relationship between genetically determined female body shape and PTSD, which could be mediated by evolutionary mechanisms involved in human sexual behaviors

Epigenome-wide association of PTSD from heterogeneous cohorts with a common multi-site analysis pipeline

Compelling evidence suggests that epigenetic mechanisms such as DNA methylation play a role in stress regulation and in the etiologic basis of stress related disorders such as Post traumatic Stress Disorder (PTSD). Here we describe the purpose and methods of an international consortium that was developed to study the role of epigenetics in PTSD. Inspired by the approach used in the Psychiatric Genomics Consortium, we brought together investigators representing seven cohorts with a collective sample size of N = 1147 that included detailed information on trauma exposure, PTSD symptoms, and genome-wide DNA methylation data. The objective of this consortium is to increase the analytical sample size by pooling data and combining expertise so that DNA methylation patterns associated with PTSD can be identified. Several quality control and analytical pipelines were evaluated for their control of genomic inflation and technical artifacts with a joint analysis procedure established to derive comparable data over the cohorts for meta-analysis. We propose methods to deal with ancestry population stratification and type I error inflation and discuss the advantages and disadvantages of applying robust error estimates. To evaluate our pipeline, we report results from an epigenome-wide association study (EWAS) of age, which is a well-characterized phenotype with known epigenetic associations. Overall, while EWAS are highly complex and subject to similar challenges as genome-wide association studies (GWAS), we demonstrate that an epigenetic meta-analysis with a relatively modest sample size can be well-powered to identify epigenetic associations. Our pipeline can be used as a framework for consortium efforts for EWAS

Search for a W' boson decaying to a bottom quark and a top quark in pp collisions at sqrt(s) = 7 TeV

Results are presented from a search for a W' boson using a dataset corresponding to 5.0 inverse femtobarns of integrated luminosity collected during 2011 by the CMS experiment at the LHC in pp collisions at sqrt(s)=7 TeV. The W' boson is modeled as a heavy W boson, but different scenarios for the couplings to fermions are considered, involving both left-handed and right-handed chiral projections of the fermions, as well as an arbitrary mixture of the two. The search is performed in the decay channel W' to t b, leading to a final state signature with a single lepton (e, mu), missing transverse energy, and jets, at least one of which is tagged as a b-jet. A W' boson that couples to fermions with the same coupling constant as the W, but to the right-handed rather than left-handed chiral projections, is excluded for masses below 1.85 TeV at the 95% confidence level. For the first time using LHC data, constraints on the W' gauge coupling for a set of left- and right-handed coupling combinations have been placed. These results represent a significant improvement over previously published limits.Comment: Submitted to Physics Letters B. Replaced with version publishe