Reaction-diffusion equation for quark-hadron transition in heavy-ion collisions

Reaction-diffusion equations with suitable boundary conditions have special propagating solutions which very closely resemble the moving interfaces in a first order transition. We show that the dynamics of chiral order parameter for chiral symmetry breaking transition in heavy-ion collisions, with dissipative dynamics, is governed by one such equation, specifically, the Newell-Whitehead equation. Further, required boundary conditions are automatically satisfied due to the geometry of the collision. The chiral transition is, therefore, completed by a propagating interface, exactly as for a first order transition, even though the transition actually is a crossover for relativistic heavy-ion collisions. Same thing also happens when we consider the initial confinement-deconfinement transition with Polyakov loop order parameter. The resulting equation, again with dissipative dynamics, can then be identified with the reaction-diffusion equation known as the Fitzhugh-Nagumo equation which is used in population genetics. We discuss the implications of these results for heavy-ion collisions. We also discuss possible extensions for the case of early universe.Comment: 7 pages, 3 figure

Setting Initial Conditions for Inflation with Reaction-Diffusion Equation

We discuss the issue of setting appropriate initial conditions for inflation. Specifically, we consider natural inflation model and discuss the fine tuning required for setting almost homogeneous initial conditions over a region of order several times the Hubble size which is orders of magnitude larger than any relevant correlation length for field fluctuations. We then propose to use the special propagating front solutions of reaction-diffusion equations for localized field domains of smaller sizes. Due to very small velocities of these propagating fronts we find that the inflaton field in such a ${\it field domain}$ changes very slowly, contrary to naive expectation of rapid roll down to the true vacuum. Continued expansion leads to the energy density in the Hubble region being dominated by the vacuum energy, thereby beginning the inflationary phase. Our results show that inflation can occur even with a single localized field domain of size smaller than the Hubble size. We discuss possible extensions of our results for different inflationary models, as well as various limitations of our analysis (e.g. neglecting self gravity of the localized field domain).Comment: 17 pages, 12 figures, some important modifications in the paper, published in General relativity and Gravitation, Volume 50, Issue 3, March 2018, Article:2

Random-set methods identify distinct aspects of the enrichment signal in gene-set analysis

A prespecified set of genes may be enriched, to varying degrees, for genes that have altered expression levels relative to two or more states of a cell. Knowing the enrichment of gene sets defined by functional categories, such as gene ontology (GO) annotations, is valuable for analyzing the biological signals in microarray expression data. A common approach to measuring enrichment is by cross-classifying genes according to membership in a functional category and membership on a selected list of significantly altered genes. A small Fisher's exact test $p$-value, for example, in this $2\times2$ table is indicative of enrichment. Other category analysis methods retain the quantitative gene-level scores and measure significance by referring a category-level statistic to a permutation distribution associated with the original differential expression problem. We describe a class of random-set scoring methods that measure distinct components of the enrichment signal. The class includes Fisher's test based on selected genes and also tests that average gene-level evidence across the category. Averaging and selection methods are compared empirically using Affymetrix data on expression in nasopharyngeal cancer tissue, and theoretically using a location model of differential expression. We find that each method has a domain of superiority in the state space of enrichment problems, and that both methods have benefits in practice. Our analysis also addresses two problems related to multiple-category inference, namely, that equally enriched categories are not detected with equal probability if they are of different sizes, and also that there is dependence among category statistics owing to shared genes. Random-set enrichment calculations do not require Monte Carlo for implementation. They are made available in the R package allez.Comment: Published at http://dx.doi.org/10.1214/07-AOAS104 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Statistical Use of Argonaute Expression and RISC Assembly in microRNA Target Identification

MicroRNAs (miRNAs) posttranscriptionally regulate targeted messenger RNAs (mRNAs) by inducing cleavage or otherwise repressing their translation. We address the problem of detecting m/miRNA targeting relationships in homo sapiens from microarray data by developing statistical models that are motivated by the biological mechanisms used by miRNAs. The focus of our modeling is the construction, activity, and mediation of RNA-induced silencing complexes (RISCs) competent for targeted mRNA cleavage. We demonstrate that regression models accommodating RISC abundance and controlling for other mediating factors fit the expression profiles of known target pairs substantially better than models based on m/miRNA expressions alone, and lead to verifications of computational target pair predictions that are more sensitive than those based on marginal expression levels. Because our models are fully independent of exogenous results from sequence-based computational methods, they are appropriate for use as either a primary or secondary source of information regarding m/miRNA target pair relationships, especially in conjunction with high-throughput expression studies.</p

Single Read and Paired End mRNA-Seq Illumina Libraries from 10 Nanograms Total RNA

Whole transcriptome sequencing by mRNA-Seq is now used extensively to perform global gene expression, mutation, allele-specific expression and other genome-wide analyses. mRNA-Seq even opens the gate for gene expression analysis of non-sequenced genomes. mRNA-Seq offers high sensitivity, a large dynamic range and allows measurement of transcript copy numbers in a sample. Illumina’s genome analyzer performs sequencing of a large number (> 107) of relatively short sequence reads (< 150 bp).The "paired end" approach, wherein a single long read is sequenced at both its ends, allows for tracking alternate splice junctions, insertions and deletions, and is useful for de novo transcriptome assembly

Statistical Use of Argonaute Expression and RISC Assembly in microRNA Target Identification

MicroRNAs (miRNAs) posttranscriptionally regulate targeted messenger RNAs (mRNAs) by inducing cleavage or otherwise repressing their translation. We address the problem of detecting m/miRNA targeting relationships in homo sapiens from microarray data by developing statistical models that are motivated by the biological mechanisms used by miRNAs. The focus of our modeling is the construction, activity, and mediation of RNA-induced silencing complexes (RISCs) competent for targeted mRNA cleavage. We demonstrate that regression models accommodating RISC abundance and controlling for other mediating factors fit the expression profiles of known target pairs substantially better than models based on m/miRNA expressions alone, and lead to verifications of computational target pair predictions that are more sensitive than those based on marginal expression levels. Because our models are fully independent of exogenous results from sequence-based computational methods, they are appropriate for use as either a primary or secondary source of information regarding m/miRNA target pair relationships, especially in conjunction with high-throughput expression studies

A study of the relationships between oligonucleotide properties and hybridization signal intensities from NimbleGen microarray datasets

Well-defined relationships between oligonucleotide properties and hybridization signal intensities (HSI) can aid chip design, data normalization and true biological knowledge discovery. We clarify these relationships using the data from two microarray experiments containing over three million probes from 48 high-density chips. We find that melting temperature (Tm) has the most significant effect on HSI while length for the long oligonucleotides studied has very little effect. Analysis of positional effect using a linear model provides evidence that the protruding ends of probes contribute more than tethered ends to HSI, which is further validated by specifically designed match fragment sliding and extension experiments. The impact of sequence similarity (SeqS) on HSI is not significant in comparison with other oligonucleotide properties. Using regression and regression tree analysis, we prioritize these oligonucleotide properties based on their effects on HSI. The implications of our discoveries for the design of unbiased oligonucleotides are discussed. We propose that isothermal probes designed by varying the length is a viable strategy to reduce sequence bias, though imposing selection constraints on other oligonucleotide properties is also essential