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

Methods to study event-by-event fluctuations in the NA61/SHINE experiment at the CERN SPS

Theoretical calculations locate the critical point of strongly interacting matter (CP) at energies accessible at the CERN SPS. Event-by-event transverse momentum and multiplicity fluctuations are considered as one of the most important tools to search for the CP. Pilot studies of the energy dependence and the system size dependence of both $p_T$ and multiplicity fluctuations were performed by the NA49 experiment. The NA61/SHINE ion program is a continuation of these efforts. After briefly recalling the essential NA49 results on fluctuations we will discuss the technical methods (removing Non-Target interactions) which we plan to apply for future transverse momentum and multiplicity fluctuation analyses.Comment: Proceedings of CPOD 2010, 23-29 August, JINR, Dubn

Multiplicity Fluctuations in the Pion-Fireball Gas

The pion number fluctuations are considered in the system of pions and large mass fireballs decaying finally into pions. A formulation which gives an extension of the model of independent sources is suggested. The grand canonical and micro-canonical ensemble formulations of the pion-fireball gas are considered as particular examples.Comment: 13 pages, 4 figure

Strongly Intensive Measures for Multiplicity Fluctuations

The recently proposed two families of strongly intensive measures of fluctuations and correlations are studied within Hadron-String-Dynamics (HSD) transport approach to nucleus-nucleus collisions. We consider the measures $\Delta^{K\pi}$ and $\Sigma^{K\pi}$ for kaon and pion multiplicities in Au+Au collisions in a wide range of collision energies and centralities. These strongly intensive measures appear to cancel the participant number fluctuations. This allows to enlarge the centrality window in the analysis of event-by-event fluctuations up to at least of 10% most central collisions. We also present a comparison of the HSD results with the data of NA49 and STAR collaborations. The HSD describes $\Sigma^{K\pi}$ reasonably well. However, the HSD results depend monotonously on collision energy and do not reproduce the bump-deep structure of $\Delta^{K\pi}$ observed from the NA49 data in the region of the center of mass energy of nucleon pair $\sqrt{s_{NN}}= 8\div 12$ GeV. This fact deserves further studies. The origin of this `structure' is not connected with simple geometrical or limited acceptance effects, as these effects are taken into account in the HSD simulations

Critical Exponents and Particle Multiplicity Distributions in High Energy Collisions

Data from the L3, Tasso, Opal and Delphi collaborations are analyzed in terms of a statistical model of high energy collisions. The model contains a power law critical exponent tau and Levy index alpha. These data are used to study values of tau and alpha. The very high multiplicity events in L3, Opal and Delphi are consistent with a model based on a Feynman-Wilson gas which has a tail exponent tau=3/2 and alpha=1/2.Comment: 10 pages, new table adde

Resonances and fluctuations at SPS and RHIC

We perform an analysis of preliminary data on hadron yields and fluctuations within the Statistical hadronization ansatz. We describe the theoretical disagreements between different statistical models currently on the market, and show how the simultaneous analysis of yields and fluctuations can be used to determine if one of them can be connected to underlying physics. We perform such an analysis on preliminary RHIC and SPS A-A data that includes particle yields, ratios and event by event fluctuations. We show that the equilibrium statistical model can not describe the $K/\pi$ fluctuation measured at RHIC and SPS, unless an unrealistically small volume is assumed. Such small volume then makes it impossible to describe the total particle multiplicity. The non-equilibrium model,on the other hand, describes both the $K/\pi$ fluctuation and yields acceptably due to the extra boost to the $\pi$ fluctuation provided by the high pion chemical potential. We show, however, that both models significantly over-estimate the $p/\pi$ fluctuation measured at the SPS, and speculate for the reason behind this.Comment: Presented at Hot Quarks, 2006 In press, European Physical Journal

Comparative Population Genetics of the Immunity Gene, Relish: Is Adaptive Evolution Idiosyncratic?

The frequency of adaptive evolution acting on common loci in distant lineages remains an outstanding question in evolutionary biology. We asked whether the immunity factor, Relish, a gene with a history of directional selection in Drosophila simulans, shows evidence of a similar selective history in other Drosophila species. We found only weak evidence of recurrent adaptive protein evolution at the Relish locus in three sister species pairs, suggesting that this key component of the insect immune system has an idiosyncratic evolutionary history in Drosophila

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

Population Genomic Inferences from Sparse High-Throughput Sequencing of Two Populations of Drosophila melanogaster

Short-read sequencing techniques provide the opportunity to capture genome-wide sequence data in a single experiment. A current challenge is to identify questions that shallow-depth genomic data can address successfully and to develop corresponding analytical methods that are statistically sound. Here, we apply the Roche/454 platform to survey natural variation in strains of Drosophila melanogaster from an African (n = 3) and a North American (n = 6) population. Reads were aligned to the reference D. melanogaster genomic assembly, single nucleotide polymorphisms were identified, and nucleotide variation was quantified genome wide. Simulations and empirical results suggest that nucleotide diversity can be accurately estimated from sparse data with as little as 0.2× coverage per line. The unbiased genomic sampling provided by random short-read sequencing also allows insight into distributions of transposable elements and copy number polymorphisms found within populations and demonstrates that short-read sequencing methods provide an efficient means to quantify variation in genome organization and content. Continued development of methods for statistical inference of shallow-depth genome-wide sequencing data will allow such sparse, partial data sets to become the norm in the emerging field of population genomics

De Novo ORFs in Drosophila Are Important to Organismal Fitness and Evolved Rapidly from Previously Non-coding Sequences

Funding for Open Access provided by the UMD Libraries Open Access Publishing Fund.How non-coding DNA gives rise to new protein-coding genes (de novo genes) is not well understood. Recent work has revealed the origins and functions of a few de novo genes, but common principles governing the evolution or biological roles of these genes are unknown. To better define these principles, we performed a parallel analysis of the evolution and function of six putatively protein-coding de novo genes described in Drosophila melanogaster. Reconstruction of the transcriptional history of de novo genes shows that two de novo genes emerged from novel long non-coding RNAs that arose at least 5 MY prior to evolution of an open reading frame. In contrast, four other de novo genes evolved a translated open reading frame and transcription within the same evolutionary interval suggesting that nascent open reading frames (proto-ORFs), while not required, can contribute to the emergence of a new de novo gene. However, none of the genes arose from proto-ORFs that existed long before expression evolved. Sequence and structural evolution of de novo genes was rapid compared to nearby genes and the structural complexity of de novo genes steadily increases over evolutionary time. Despite the fact that these genes are transcribed at a higher level in males than females, and are most strongly expressed in testes, RNAi experiments show that most of these genes are essential in both sexes during metamorphosis. This lethality suggests that protein coding de novo genes in Drosophila quickly become functionally important.This work was supported by NSF Grant #mcb0920196 and a Royster Society Fellowship from the University of North Carolina. Open Access publication fees were provided by the University of Maryland Libraries Open Access Publishing Fund. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript