A General Method for the Calculation of Axis-crossing Moments Technical Report No. 5

Calculating axis-crossing moments by stochastic proces

Development of reliability methodology for systems engineering. Volume III - Theoretical investigations - An approach to a class of reliability problems Final report

Random quantities from continuous time stochastic process with application to reliability and probabilit

On certain functionals of normal processes Technical report no. 1

Probabilistic modeling and stochastic process investigations to provide measures of quality of performance and reliability for systems engineering - Chebyshev approximatio

Theory of spike timing based neural classifiers

We study the computational capacity of a model neuron, the Tempotron, which classifies sequences of spikes by linear-threshold operations. We use statistical mechanics and extreme value theory to derive the capacity of the system in random classification tasks. In contrast to its static analog, the Perceptron, the Tempotron's solutions space consists of a large number of small clusters of weight vectors. The capacity of the system per synapse is finite in the large size limit and weakly diverges with the stimulus duration relative to the membrane and synaptic time constants.Comment: 4 page, 4 figures, Accepted to Physical Review Letters on 19th Oct. 201

On smoothed probability density estimation for stationary processes

Aspects of estimation of the (marginal) probability density for a stationary sequence or continuous parameter process, are considered in this paper. Consistency and asymptotic distributional results are obtained using a class of smoothed function estimators including those of kernel type, under various decay of dependence conditions for the process. Some of the consistency results contain convergence rates which appear to be more delicate than those previously available, even for i.i.d. sequences

Freezing Transition, Characteristic Polynomials of Random Matrices, and the Riemann Zeta-Function

We argue that the freezing transition scenario, previously explored in the statistical mechanics of 1/f-noise random energy models, also determines the value distribution of the maximum of the modulus of the characteristic polynomials of large N x N random unitary (CUE) matrices. We postulate that our results extend to the extreme values taken by the Riemann zeta-function zeta(s) over sections of the critical line s=1/2+it of constant length and present the results of numerical computations in support. Our main purpose is to draw attention to possible connections between the statistical mechanics of random energy landscapes, random matrix theory, and the theory of the Riemann zeta function.Comment: published version with a few misprints corrected and references adde

Extreme value statistics and return intervals in long-range correlated uniform deviates

We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to minimum are such that the reference point from which the maximum is measured is itself a random quantity. We analytically calculate the limiting distributions for independent and identically distributed random variables, and use these as a reference point for correlated cases. The distributions are different from that of the maximum itself i.e., a Weibull distribution, reflecting the fact that the distribution of the reference point either dominates over or convolves with the distribution of the maximum. The functional form of the limiting distributions is unaffected by correlations, although the convergence is slower. We show that our findings can be directly generalized to a wide class of stochastic processes. We also analyze return interval distributions, and compare them to recent conjectures of their functional form

Extreme value distributions for weakly correlated fitnesses in block model

We study the limit distribution of the largest fitness for two models of weakly correlated and identically distributed random fitnesses. The correlated fitness is given by a linear combination of a fixed number of independent random variables drawn from a common parent distribution. We find that for certain class of parent distributions, the extreme value distribution for correlated random variables can be related either to one of the known limit laws for independent variables or the parent distribution itself. For other cases, new limiting distributions appear. The conditions under which these results hold are identified.Comment: Expanded, added reference

Analysis of genes of tetrahydrofolate-dependent metabolism from cultivated spirochaetes and the gut community of the termite Zootermopsis angusticollis

The hindguts of wood-feeding termites are the sites of intense, CO_2-reductive acetogenesis. This activity profoundly influences host nutrition and methane emissions. Homoacetogens previously isolated from diverse termites comprised novel taxa belonging to two distinct bacterial phyla, Firmicutes and Spirochaetes. Little else is known about either the diversity or abundance of homoacetogenic species present in any given termite or the genetic details underlying CO_2-reductive acetogenesis by Spirochaetes. A key enzyme of CO_2-reductive acetogenesis is formyltetrahydrofolate synthetase (FTHFS). A previously designed primer set was used to amplify FTHFS genes from three isolated termite-gut spirochaetes. Sequencing DNA flanking the FTHFS gene of Treponema strain ZAS-2 revealed genes encoding two acetogenesis-related enzymes, methenyltetrahydrofolate cyclohydrolase and methylenetetrahydrofolate dehydrogenase. Although termite-gut spirochaetes are only distantly related to clostridia at the ribosomal level, their tetrahydrofolate-dependent enzymes appear to be closely related. In contrast, homologous proteins identified in the non-homoacetogenic oral spirochaete Treponema denticola were only distantly related to those from clostridia and the termite-gut treponemes. Having demonstrated their utility with spirochaete pure cultures, the FTHFS primers were used to construct a 91-clone library from the termite-gut community DNA. From this, 19 DNA and eight amino acid FTHFS types were identified. Over 75 % of the retrieved clones formed a novel, coherent cluster with the FTHFS homologues obtained from the termite-gut treponemes. Thus, FTHFS gene diversity in the gut of the termite Zootermopsis angusticollis appears to be dominated by spirochaetes. The homoacetogenic capacity of termite-gut spirochaetes may have been acquired via lateral gene transfer from clostridia

Characterization, Comparative Genomics and Genome Mining for Antibiotics and Secondary Metabolite of two Actinomycetales isolates

Actinomycetes are ubiquitous Gram (+) bacteria commonly found to have high G+C content and best known for their metabolic by-products and novel enzymes [1]. Isolates CCMMD2014 & MRMD2014 were co-cultured from soil impacted by a rusty fire hydrant in Woods Hole, MA. The Streptomyces sp. and Curtobacterium sp. isolates were identified by marker genes for 16S rRNA, rpoB, xylose isomerase, tryptophan synthase beta chain and Cytochrome P450 monooxygenase. Both isolates showed lactic acid fermentation and urease activity. The co-isolates were separated by selective culturing with antibiotics. In addition, whole genome sequencing revealed distinct inherent metabolic pathways in each culture that allowed for mutually exclusive selective culture conditions. Assembly was done using HGAP3 with Celera8 assembler using SMRT portal [2,3]. Annotation was done using the RAST server [4], with 7540 and 3969 CDS for Streptomyces sp. and Curtobacterium sp. respectively being revealed by AMIGene and BASys [5,6]. Subsequently, antiSMASH [7], was used to predict 52 and 26 secondary metabolite biosynthetic clusters that included genes for lantipeptides, terpenes, siderophores, polyketide synthases type I and II, bacteriocin and nonribosomal peptide synthase genes for Streptomyces sp. and Curtobacterium sp. respectively. The isolates have genes of potentially beneficial traits that could help study, among others, the role of fimbrial adhesins and iron in biofilm formation and investigation on natural products