Random number generators for the generalized Birnbaum-Saunders distribution

The generalized Birnbaum-Saunders distribution pertains to a class of lifetime models including both lighter and heavier tailed distributions. This model adapts well to lifetime data, even when outliers exist, and has other good theoretical properties and application perspectives. However, statistical inference tools may not exist in closed form for this model. Hence, simulation and numerical studies are needed, which require a random number generator. Three different ways to generate observations from this model are considered here. These generators are compared by utilizing a goodness-of-fit procedure as well as their effectiveness in predicting the true parameter values by using Monte Carlo simulations. This goodness-of-fit procedure may also be used as an estimation method. The quality of this estimation method is studied here. Finally, through a real data set, the generalized and classical Birnbaum-Saunders models are compared by using this estimation method.

Stochastic stability for Markovian jump linear systems associated with a finite number of jump times

This paper deals with a stochastic stability concept for discrete-time Markovian jump linear systems. The random jump parameter is associated to changes between the system operation modes due to failures or repairs, which can be well described by an underlying finite-state Markov chain. In the model studied, a fixed number of failures or repairs is allowed, after which, the system is brought to a halt for maintenance or for replacement. The usual concepts of stochastic stability are related to pure infinite horizon problems, and are not appropriate in this scenario. A new stability concept is introduced, named stochastic tau-stability that is tailored to the present setting. Necessary and sufficient conditions to ensure the stochastic tau-stability are provided, and the almost sure stability concept associated with this class of processes is also addressed. The paper also develops equivalences among second order concepts that parallels the results for infinite horizon problems. (C) 2003 Elsevier B.V. All rights reserved.

Differences in the number of some antennal sensilla of four honey bee (Apis mellifera) types and comparisons with the defensive behaviour

The number of sensilla coeloconica, ampullacea and campaniformia of flagellomeres 3 to 10 of the antennae of workers of four honey bee types (Italian, Caucasian, African and Africanized) was studied by scanning electron microscopy. Comparisons of the four bee types showed that only African and Africanized honey bees did not differ from one another with respect to the number of sensilla coeloconica and ampullacea of flagellomere 10. African and Africanized honey bees and Caucasian and Italian honey bees also did not differ from one another in terms of flagellomere 9. In the other flagellomeres there were no differences among bee types. Italian and Caucasian honey bees differed from Africanized honey bees in terms of number of sensilla campaniformia on flagellomere 6, and Caucasian honey bees differed from African and Africanized honey bees in terms of flagellomere 3. Five significant but random correlation values were obtained between number of antennal sensilla and defensive behaviour in Africanized honey bees. Thus,there is no relationship between antennal structures and defence behaviour.

Random amplification of polymorphic DNA reveals clonal relationships among enteropathogenic Escherichia coli isolated from non-human primates and humans

Enteropathogenic Escherichia coli ( EPEC) strains are important agents of infantile diarrhea all over the world, gaining even greater importance in developing countries. EPEC have also been isolated from various animal species, but most isolates belong to serotypes that differ from those recovered from humans. However, it has been demonstrated that several isolates from non- human primates belong to the serogroups and/ or serotypes related to those implicated in human disease. The objective of this study was to evaluate the genetic differences between thirteen strains isolated from non- human primates and the same number of strains isolated from human infections. Human isolates belonged to the same serogroup/ serotype as the monkey strains and the evaluation was done by analysis of random amplified polymorphic DNA. Dendrogram analysis showed that there was no clustering between human and monkey strains. Human and non- human isolates of the EPEC serotypes O127:H40 and O128:H2 shared 90 and 87% of their bands, respectively, indicating strong genomic similarity between the strains, leading to the speculation that they may have arisen from the same pathogenic clone. To our knowledge, this study is the first one comparing genomic similarity between human and non- human primate strains and the results provide further evidence that monkey EPEC strains correlate with human EPEC, as suggested in a previous investigation.

Effective number of accessed nodes in complex networks

The measurement called accessibility has been proposed as a means to quantify the efficiency of the communication between nodes in complex networks. This article reports results regarding the properties of accessibility, including its relationship with the average minimal time to visit all nodes reachable after h steps along a random walk starting from a source, as well as the number of nodes that are visited after a finite period of time. We characterize the relationship between accessibility and the average number of walks required in order to visit all reachable nodes (the exploration time), conjecture that the maximum accessibility implies the minimal exploration time, and confirm the relationship between the accessibility values and the number of nodes visited after a basic time unit. The latter relationship is investigated with respect to three types of dynamics: traditional random walks, self-avoiding random walks, and preferential random walks.

Decreasing the number of false positives in sequence classification

Abstract Background A large number of probabilistic models used in sequence analysis assign non-zero probability values to most input sequences. To decide when a given probability is sufficient the most common way is bayesian binary classification, where the probability of the model characterizing the sequence family of interest is compared to that of an alternative probability model. We can use as alternative model a null model. This is the scoring technique used by sequence analysis tools such as HMMER, SAM and INFERNAL. The most prevalent null models are position-independent residue distributions that include: the uniform distribution, genomic distribution, family-specific distribution and the target sequence distribution. This paper presents a study to evaluate the impact of the choice of a null model in the final result of classifications. In particular, we are interested in minimizing the number of false predictions in a classification. This is a crucial issue to reduce costs of biological validation. Results For all the tests, the target null model presented the lowest number of false positives, when using random sequences as a test. The study was performed in DNA sequences using GC content as the measure of content bias, but the results should be valid also for protein sequences. To broaden the application of the results, the study was performed using randomly generated sequences. Previous studies were performed on aminoacid sequences, using only one probabilistic model (HMM) and on a specific benchmark, and lack more general conclusions about the performance of null models. Finally, a benchmark test with P. falciparum confirmed these results. Conclusions Of the evaluated models the best suited for classification are the uniform model and the target model. However, the use of the uniform model presents a GC bias that can cause more false positives for candidate sequences with extreme compositional bias, a characteristic not described in previous studies. In these cases the target model is more dependable for biological validation due to its higher specificity.

Optical quantum random number generator

A physical random number generator based on the intrinsic randomness of quantum mechanics is described. The random events are realized by the choice of single photons between the two outputs of a beamsplitter. We present a simple device, which minimizes the impact of the photon counters’ noise, dead-time and after pulses.

Detection of nonrandom association of alleles from the distribution of the number of heterozygous loci in a sample.

The distribution of the number of heterozygous loci in two randomly chosen gametes or in a random diploid zygote provides information regarding the nonrandom association of alleles among different genetic loci. Two alternative statistics may be employed for detection of nonrandom association of genes of different loci when observations are made on these distributions: observed variance of the number of heterozygous loci (s2k) and a goodness-of-fit criterion (X2) to contrast the observed distribution with that expected under the hypothesis of random association of genes. It is shown, by simulation, that s2k is statistically more efficient than X2 to detect a given extent of nonrandom association. Asymptotic normality of s2k is justified, and X2 is shown to follow a chi-square (chi 2) distribution with partial loss of degrees of freedom arising because of estimation of parameters from the marginal gene frequency data. Whenever direct evaluations of linkage disequilibrium values are possible, tests based on maximum likelihood estimators of linkage disequilibria require a smaller sample size (number of zygotes or gametes) to detect a given level of nonrandom association in comparison with that required if such tests are conducted on the basis of s2k. Summarization of multilocus genotype (or haplotype) data, into the different number of heterozygous loci classes, thus, amounts to appreciable loss of information.

High Performance FPGA-oriented mersenne twister uniform random number generator

Mersenne Twister (MT) uniform random number generators are key cores for hardware acceleration of Monte Carlo simulations. In this work, two different architectures are studied: besides the classical table-based architecture, a different architecture based on a circular buffer and especially targeting FPGAs is proposed. A 30% performance improvement has been obtained when compared to the fastest previous work. The applicability of the proposed MT architectures has been proven in a high performance Gaussian RNG.

The Malthusian parameter of ascents: What prevents the exponential increase of one’s ancestors?

The reason that the indefinite exponential increase in the number of one’s ancestors does not take place is found in the law of sibling interference, which can be expressed by the following simple equation:\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}\begin{matrix}{\mathit{N}}_{{\mathit{n}}} \enskip & \\ {\mathit{{\blacksquare}}} \enskip & \\ {\mathit{ASZ}} \enskip & \end{matrix} {\mathrm{\hspace{.167em}{\times}\hspace{.167em}2\hspace{.167em}=\hspace{.167em}}}{\mathit{N_{n+1},}}\end{equation*}\end{document} where Nn is the number of ancestors in the nth generation, ASZ is the average sibling size of these ancestors, and Nn+1 is the number of ancestors in the next older generation (n + 1). Accordingly, the exponential increase in the number of one’s ancestors is an initial anomaly that occurs while ASZ remains at 1. Once ASZ begins to exceed 1, the rate of increase in the number of ancestors is progressively curtailed, falling further and further behind the exponential increase rate. Eventually, ASZ reaches 2, and at that point, the number of ancestors stops increasing for two generations. These two generations, named AN SA and AN SA + 1, are the most critical in the ancestry, for one’s ancestors at that point come to represent all the progeny-produced adults of the entire ancestral population. Thereafter, the fate of one’s ancestors becomes the fate of the entire population. If the population to which one belongs is a successful, slowly expanding one, the number of ancestors would slowly decline as you move toward the remote past. This is because ABZ would exceed 2. Only when ABZ is less than 2 would the number of ancestors increase beyond the AN SA and AN SA + 1 generations. Since the above is an indication of a failing population on the way to extinction, there had to be the previous AN SA involving a far greater number of individuals for such a population. Simulations indicated that for a member of a continuously successful population, the AN SA ancestors might have numbered as many as 5.2 million, the AN SA generation being the 28th generation in the past. However, because of the law of increasingly irrelevant remote ancestors, only a very small fraction of the AN SA ancestors would have left genetic traces in the genome of each descendant of today.

On the time to reach a critical number of infections in epidemic models with infective and susceptible immigrants.

In this paper we examine the time T to reach a critical number K0 of infections during an outbreak in an epidemic model with infective and susceptible immigrants. The underlying process X, which was first introduced by Ridler-Rowe (1967), is related to recurrent diseases and it appears to be analytically intractable. We present an approximating model inspired from the use of extreme values, and we derive formulae for the Laplace-Stieltjes transform of T and its moments, which are evaluated by using an iterative procedure. Numerical examples are presented to illustrate the effects of the contact and removal rates on the expected values of T and the threshold K0, when the initial time instant corresponds to an invasion time. We also study the exact reproduction number Rexact,0 and the population transmission number Rp, which are random versions of the basic reproduction number R0.

Random number generation on the I.B.M. 360.

"Errata" ([3] p.) inserted.

The phasevarion: A genetic system controlling coordinated, random switching of expression of multiple genes

Several host-adapted bacterial pathogens contain methyltransferases associated with type III restriction-modification (R-M) systems that are subject to reversible, high-frequency on/off switching of expression (phase variation). To investigate the role of phase-variable expression of R-M systems, we made a mutant strain lacking the methyltransferase (mod) associated with a type III R-M system of Haemophilus influenzae and analyzed its phenotype. By microarray analysis, we identified a number of genes that were either up- or down-regulated in the mod mutant strain. This system reports the coordinated random switching of a set of genes in a bacterial pathogen and may represent a widely used mechanism.

Random vibration of the functionally graded laminates in thermal environments

This work deals with the random free vibration of functionally graded laminates with general boundary conditions and subjected to a temperature change, taking into account the randomness in a number of independent input variables such as Young's modulus, Poisson's ratio and thermal expansion coefficient of each constituent material. Based on third-order shear deformation theory, the mixed-type formulation and a semi-analytical approach are employed to derive the standard eigenvalue problem in terms of deflection, mid-plane rotations and stress function. A mean-centered first-order perturbation technique is adopted to obtain the second-order statistics of vibration frequencies. A detailed parametric study is conducted, and extensive numerical results are presented in both tabular and graphical forms for laminated plates that contain functionally graded material which is made of aluminum and zirconia, showing the effects of scattering in thermo-clastic material constants, temperature change, edge support condition, side-to-thickness ratio, and plate aspect ratio on the stochastic characteristics of natural frequencies. (c) 2005 Elsevier B.V. All rights reserved.

Incoherent fibre supercontinuum generation for all-optical random number generation

Random number generation is a central component of modern information technology, with crucial applications in ensuring communications and information security. The development of new physical mechanisms suitable to directly generate random bit sequences is thus a subject of intense current research, with particular interest in alloptical techniques suitable for the generation of data sequences with high bit rate. One such promising technique that has received much recent attention is the chaotic semiconductor laser systems producing high quality random output as a result of the intrinsic nonlinear dynamics of its architecture [1]. Here we propose a novel complementary concept of all-optical technique that might dramatically increase the generation rate of random bits by using simultaneously multiple spectral channels with uncorrelated signals - somewhat similar to use of wave-division-multiplexing in communications. We propose to exploit the intrinsic nonlinear dynamics of extreme spectral broadening and supercontinuum (SC) generation in optical fibre, a process known to be often associated with non-deterministic fluctuations [2]. In this paper, we report proof-of concept results indicating that the fluctuations in highly nonlinear fibre SC generation can potentially be used for random number generation.