Multiplicity Distributions in Canonical and Microcanonical Statistical Ensembles

The aim of this paper is to introduce a new technique for calculation of observables, in particular multiplicity distributions, in various statistical ensembles at finite volume. The method is based on Fourier analysis of the grand canonical partition function. Taylor expansion of the generating function is used to separate contributions to the partition function in their power in volume. We employ Laplace's asymptotic expansion to show that any equilibrium distribution of multiplicity, charge, energy, etc. tends to a multivariate normal distribution in the thermodynamic limit. Gram-Charlier expansion allows additionally for calculation of finite volume corrections. Analytical formulas are presented for inclusion of resonance decay and finite acceptance effects directly into the system partition function. This paper consolidates and extends previously published results of current investigation into properties of statistical ensembles.Comment: 53 pages, 7 figure

Parallel evolution of chimeric fusion genes

To understand how novel functions arise, we must identify common patterns and mechanisms shaping the evolution of new genes. Here, we take advantage of data from three Drosophila genes, jingwei, Adh-Finnegan, and Adh-Twain, to find evolutionary patterns and mechanisms governing the evolution of new genes. All three of these genes are independently derived from Adh, which enabled us to use the extensive literature on Adh in Drosophila to guide our analyses. We discovered a fundamental similarity in the temporal, spatial, and types of amino acid changes that occurred. All three genes underwent rapid adaptive amino acid evolution shortly after they were formed, followed by later quiescence and functional constraint. These genes also show striking parallels in which amino acids change in the Adh region. We showed that these early changes tend to occur at amino acid residues that seldom, if ever, evolve in Drosophila Adh. Changes at these slowly evolving sites are usually associated with loss of function or hypomorphic mutations in Drosophila melanogaster. Our data indicate that shifting away from ancestral functions may be a critical step early in the evolution of chimeric fusion genes. We suggest that the patterns we observed are both general and predictive

Multiplicity fluctuations in relativistic nuclear collisions

Multiplicity distributions of hadrons produced in central nucleus-nucleus collisions are studied within the hadron-resonance gas model in the large volume limit. In the canonical ensemble conservation of three charges (baryon number, electric charge, and strangeness) is enforced. In addition, in the micro-canonical ensemble energy conservation is included. An analytical method is used to account for resonance decays. Multiplicity distributions and scaled variances for negatively charged hadrons are presented along the chemical freeze-out line of central Pb+Pb (Au+Au) collisions from SIS to LHC energies. Predictions obtained within different statistical ensembles are compared with preliminary NA49 experimental results on central Pb+Pb collisions in the SPS energy range. The measured fluctuations are significantly narrower than a Poisson reference distribution, and clearly favor expectations for the micro-canonical ensemble.Comment: 6 pages, 3 figure

Origin and Spread of de Novo Genes in Drosophila melanogaster Populations

Comparative genomic analyses have revealed that genes may arise from ancestrally non-genic sequence. However, the origin and spread of these de novo genes within populations remain obscure. We identified 142 segregating and 106 fixed testis-expressed de novo genes in a population sample of Drosophila melanogaster. These genes appear to derive primarily from ancestral intergenic, unexpressed open reading frames (ORFs), with natural selection playing a significant role in their spread. These results reveal a heretofore-unappreciated dynamism of gene content

Adaptive Gene Expression Divergence Inferred from Population Genomics

Detailed studies of individual genes have shown that gene expression divergence often results from adaptive evolution of regulatory sequence. Genome-wide analyses, however, have yet to unite patterns of gene expression with polymorphism and divergence to infer population genetic mechanisms underlying expression evolution. Here, we combined genomic expression data—analyzed in a phylogenetic context—with whole genome light-shotgun sequence data from six Drosophila simulans lines and reference sequences from D. melanogaster and D. yakuba. These data allowed us to use molecular population genetics to test for neutral versus adaptive gene expression divergence on a genomic scale. We identified recent and recurrent adaptive evolution along the D. simulans lineage by contrasting sequence polymorphism within D. simulans to divergence from D. melanogaster and D. yakuba. Genes that evolved higher levels of expression in D. simulans have experienced adaptive evolution of the associated 3′ flanking and amino acid sequence. Concomitantly, these genes are also decelerating in their rates of protein evolution, which is in agreement with the finding that highly expressed genes evolve slowly. Interestingly, adaptive evolution in 5′ cis-regulatory regions did not correspond strongly with expression evolution. Our results provide a genomic view of the intimate link between selection acting on a phenotype and associated genic evolution

Novel genes derived from noncoding DNA in Drosophila melanogaster are frequently X-linked and exhibit testis-biased expression

Descriptions of recently evolved genes suggest several mechanisms of origin including exon shuffling, gene fission/fusion, retrotransposition, duplication-divergence, and lateral gene transfer, all of which involve recruitment of preexisting genes or genetic elements into new function. The importance of noncoding DNA in the origin of novel genes remains an open question. We used the well annotated genome of the genetic model system Drosophila melanogaster and genome sequences of related species to carry out a whole-genome search for new D. melanogaster genes that are derived from noncoding DNA. Here, we describe five such genes, four of which are X-linked. Our RT-PCR experiments show that all five putative novel genes are expressed predominantly in testes. These data support the idea that these novel genes are derived from ancestral noncoding sequence and that new, favored genes are likely to invade populations under selective pressures relating to male reproduction

Parallel Geographic Variation in Drosophila melanogaster

Drosophila melanogaster, an ancestrally African species, has recently spread throughout the world, associated with human activity. The species has served as the focus of many studies investigating local adaptation relating to latitudinal variation in non-African populations, especially those from the United States and Australia. These studies have documented the existence of shared, genetically determined phenotypic clines for several life history and morphological traits. However, there are no studies designed to formally address the degree of shared latitudinal differentiation at the genomic level. Here we present our comparative analysis of such differentiation. Not surprisingly, we find evidence of substantial, shared selection responses on the two continents, probably resulting from selection on standing ancestral variation. The polymorphic inversion In(3R)P has an important effect on this pattern, but considerable parallelism is also observed across the genome in regions not associated with inversion polymorphism. Interestingly, parallel latitudinal differentiation is observed even for variants that are not particularly strongly differentiated, which suggests that very large numbers of polymorphisms are targets of spatially varying selection in this species

Bose-Einstein Condensation in the Relativistic Pion Gas: Thermodynamic Limit and Finite Size Effects

We consider the Bose-Einstein condensation (BEC) in a relativistic pion gas. The thermodynamic limit when the system volume $V$ goes to infinity as well as the role of finite size effects are studied. At $V\to \infty$ the scaled variance for particle number fluctuations, $\omega=/$, converges to finite values in the normal phase above the BEC temperature, $T>T_C$. It diverges as $\omega \propto V^{1/3}$ at the BEC line $T=T_C$, and $\omega \propto V$ at $T<T_C$ in a phase with the BE condensate. Possible experimental signals of the pion BEC in finite systems created in high energy proton-proton collisions are discussed

Risk-adjusted CUSUM control charts for shared frailty survival models with application to hip replacement outcomes: a study using the NJR dataset

Background:  Continuous monitoring of surgical outcomes after joint replacement is needed to detect which brands’ components have a higher than expected failure rate and are therefore no longer recommended to be used in surgical practice. We developed a monitoring method based on cumulative sum (CUSUM) chart specifically for this application.  Methods:  Our method entails the use of the competing risks model with the Weibull and the Gompertz hazard functions adjusted for observed covariates to approximate the baseline time-to-revision and time-to-death distributions, respectively. The correlated shared frailty terms for competing risks, corresponding to the operating unit, are also included in the model. A bootstrap-based boundary adjustment is then required for risk-adjusted CUSUM charts to guarantee a given probability of the false alarm rates. We propose a method to evaluate the CUSUM scores and the adjusted boundary for a survival model with the shared frailty terms. We also introduce a unit performance quality score based on the posterior frailty distribution. This method is illustrated using the 2003-2012 hip replacement data from the UK National Joint Registry (NJR). Results:  We found that the best model included the shared frailty for revision but not for death. This means that the competing risks of revision and death are independent in NJR data. Our method was superior to the standard NJR methodology. For one of the two monitored components, it produced alarms four years before the increased failure rate came to the attention of the UK regulatory authorities. The hazard ratios of revision across the units varied from 0.38 to 2.28. Conclusions:  An earlier detection of failure signal by our method in comparison to the standard method used by the NJR may be explained by proper risk-adjustment and the ability to accommodate time-dependent hazards. The continuous monitoring of hip replacement outcomes should include risk adjustment at both the individual and unit level