bluuebunny/crossref_metadata_2025 huggingface dataset:
On the non-existence of consistent estimates in Galton-Watson processes
Authors: Lockhart Richard
Published: April 2006

Estimation of the offspring distribution from a single realization of a supercritical Galton-Watson process is studied. It is shown that, based on population totals, a parameter of the offspring distribution cannot be estimated unless it is determined by the mean, variance, lattice size and lattice offset of the offspring distribution.
Comparison of percolation probabilities
Authors: Rüschendorf Ludger
Published: April 2006

Some recent results of Oxley and Welsh (1979) and McDiarmid (1981) concerning Bernoulli percolation on clutters are generalized. Our results allow to consider quantitative aspects of percolation on graphs and clutters.
A note describing the marginal benefits of spares on availability
Authors: Stulman A. , Mehrez A.
Published: April 2006

In this note we consider the marginal effect of adding an additional spare to a system containing operating units and their spares. We shall see that under the circumstance that the number of spares is greater than the number of repair facilities, the marginal effect will assume a simple interesting structure.
Inequalities and bounds for the scheduling of stochastic jobs on parallel machines
Authors: Pinedo Michael , Schechner Zvi
Published: April 2006

Consider n jobs and m machines. The m machines are identical and set up in parallel. All n jobs are available at t = 0 and each job has to be processed on one of the machines; any one can do. The processing time of job j is Xj, a random variable with distribution Fj. The sequence in which the jobs start with their processing is predetermined and preemptions are not allowed. We investigate the effect of the variability of the processing times on the expected makespan and the expected time to first idleness. Bounds are presented for these quantities in case the distributions of the processing times of the jobs are new better (worse) than used.
The limiting behaviour of the maximal spacing generated by an i.i.d. sequence of Gaussian random variables
Authors: Deheuvels Paul
Published: April 2006

Let Mn be the maximal spacing generated in the sample's range by Χ1,· ··, Χ n, independent and identically distributed Gaussian N(0, 1) random variables. We obtain the limiting distribution of and show that

according to whether ε> 0 or ε < 0.
On regenerative and ergodic properties of the k-server queue with non-stationary Poisson arrivals
Authors: Thorisson Hermann
Published: April 2006

We consider the stable k-server queue with non-stationary Poisson arrivals and i.i.d. service times and show that the non-time-homogeneous Markov process Zt = (the queue length and residual service times at time t) can be subordinated to a stable time-homogeneous regenerative process. As an application we show that if the system starts from given conditions at time s then the distribution of Zt stabilizes (but depends on t) as s tends backwards to –∞. Also moment and stochastic domination results are established for the delay and recurrence times of the regenerative process leading to results on uniform rates of convergence.
A note on the probability of extinction in a class of population-size-dependent Galton-Watson processes
Authors: Höpfner R.
Published: April 2006

In a class of population-size-dependent Galton-Watson processes where extinction does not occur with probability 1 we describe the rate of decay of qi (the probability that the process starting from i ancestors will become extinct) as the number i of ancestors increases.

The results are related to the asymptotic behavior of the Green's function of the critical Galton-Watson process with immigration.
The convex hull of a uniform sample from the interior of a simple d-polytope
Authors: Van Wel Barthold F.
Published: April 2006

An asymptotic expression is given for the expected number of vertices of the convex hull of a uniform sample from the interior of a d-dimensional simple polytope. This extends a result derived by Rényi and Sulanke for sample points in the plane.
A stochastic population projection system based on general age-dependent branching processes
Authors: Mode Charles J. , Jacobson Marc E. , Pickens Gary T.
Published: April 2006

Algorithms for a stochastic population process, based on assumptions underlying general age-dependent branching processes in discrete time with time inhomogeneous laws of evolution, are developed through the use of a new representation of basic random functions involving birth cohorts and random sums of random variables. New algorithms provide a capability for computing the mean age structure of the process as well as variances and covariances, measuring variation about means. Four exploratory population projections, testing the implications of the algorithms for the case of time-homogeneous laws of evolution, are presented. Formulas extending mean and variance functions for unit population projections to an arbitrary initial population size are also presented. These formulas show that, in population processes with non-random laws of evolution, stochastic fluctuations about the mean function are negligible when initial population size is large. Further extensions of these formulas to the case of randomized laws of evolution suggest that stochastic fluctuations about the mean function can be significant even for large initial populations.
A modified repair strategy for two-component systems with revealed and unrevealed faults
Authors: Johnson Norman L. , Kotz Samuel
Published: April 2006

Some consequences of a modified repair system for Phillips' (1981a, b) model for a two-component system are discussed. In the original model, both components are repaired whenever a revealed fault occurs; in the modified model only faulty components are repaired. Specifically (i) the distribution of time from the initial state up to discovery of an unrevealed fault, (ii) the expected proportion of time during which there exists an unrepaired fault, and (iii) the distribution of number of revealed faults up to and including the one which leads to a discovery of an unrevealed fault, are obtained. The theory is illustrated by examples, based on specific distributions for the times between repairs and occurrences of the two types of faults. A characterization of the exponential distribution is indicated.
A martingale characterization of mixed Poisson processes
Authors: Pfeifer Dietmar , Heller Ursula
Published: April 2006

It is shown that an elementary pure birth process is a mixed Poisson process iff the sequence of post-jump intensities forms a martingale with respect to the σ -fields generated by the jump times of the process. In this case, the post-jump intensities converge almost surely to the mixing random variable of the process.
A note on continuous search algorithms
Authors: Garey L. E. , Gupta R. D.
Published: April 2006

Continuous random search methods with an average complexity given by O(log(1/ε)) for ε → 0 where ε is a given accuracy were presented in a recent paper. In this article an example of an O(log log(1/ε)) method is presented and illustrated.
Asymptotic results for non-linear processes of the McKean tagged-molecule type
Authors: Giroux Gaston
Published: April 2006

McKean's tagged-molecule process is a non-linear homogeneous two-state Markov chain in continuous time, constructed with the aid of a binary branching process. For each of a large class of branching processes we construct a similar process. The construction is carefully done and the weak homogeneity is deduced. A simple probability argument permits us to show convergence to the equidistribution (½, ½) and to note that this limit is a strong equilibrium. A non-homogeneous Markov chain result is also used to establish the geometric rate of convergence. A proof of a Boltzmann H-theorem is also established.
Stein's method and poisson process convergence
Authors: Barbour A. D.
Published: April 2006

Stein's method of obtaining rates of convergence, well known in normal and Poisson approximation, is considered here in the context of approximation by Poisson point processes, rather than their one-dimensional distributions. A general technique is sketched, whereby the basic ingredients necessary for the application of Stein's method may be derived, and this is applied to a simple problem in Poisson point process approximation.
A note on the asymptotic eigenvalues and eigenvectors of the dispersion matrix of a second-order Stationary Process on a d-dimensional Lattice
Authors: Martin R. J.
Published: April 2006

A sufficiently large finite second-order stationary time series process on a line has approximately the same eigenvalues and eigenvectors of its dispersion matrix as its counterpart on a circle. It is shown here that this result can be extended to second-order stationary processes on a d-dimensional lattice.
Modelling the flow of coalescing data streams through a processor
Authors: Anantharam V.
Published: April 2006

In a data processing network, two data streams A and B arrive at a node independently at the same Poisson rate λ. Service at exponential rate µ can take place iff there is at least one of each of A and B present. The output is the combined processed data AB. We consider models of this situation with finite buffers, with infinite buffers and with finite buffers for the excess of each input type over the other. We apply the filtering theory for point process functionals of a Markov chain to study whether the output flow is Poisson in equilibrium. The motivation is to examine, if the output is to subsequently be processed by a queueing system, whether it can be treated as an independent Poisson input to that system.

A result of independent interest is that a subset of transitions of a countable-state Markov process does not yield a Poisson process when counted, if the rate matrix of counted transitions is nilpotent, and we prove a generalization of Pakes' lemma for countable-state Markov chains.
On the probability of covering the circle by random arcs
Authors: Huffer F. W. , Shepp L. A.
Published: April 2006

Arcs of length lk, 0 < lk < 1, k = 1, 2, ···, n, are thrown independently and uniformly on a circumference having unit length. Let P(l1, l2, · ··, ln) be the probability that is completely covered by the n random arcs. We show that P(l1, l2,· ··, ln) is a Schur-convex function and that it is convex in each argument when the others are held fixed.
A note on waiting times in systems with queues in parallel
Authors: Blanc J. P. C.
Published: April 2006

Numerical data are presented concerning the mean and the standard deviation of the waiting-time distribution for multiserver systems with queues in parallel, in which customers choose one of the shortest queues upon arrival. Moreover, a new numerical method is outlined for calculating state probabilities and moments of queue-length distributions. This method is based on power series expansions and recursion. It is applicable to many systems with more than one waiting line.
Upper bounds on work in system for multichannel queues
Authors: Wolff Ronald W.
Published: April 2006

Previously derived sample path upper bounds for multi-channel work in system and work in queue are shown to be false. A new proof is given for the corresponding stochastic bounds on these quantities.
Scheduling jobs with exponential processing times on parallel machines
Authors: Lehtonen Tapani
Published: April 2006

We consider a system where jobs are processed by parallel machines. The processing times are exponentially distributed. An essential feature is that the assignment of the jobs to the machines is decided before the system starts to work. We consider both the flow time and the makespan. In the case of the flow time we allow both the machines and the jobs to be non-homogeneous. The optimization is by minimizing the flow time in the sense of stochastic order and the optimal assignment is obtained for this case. The case of the makespan is harder. We consider the expected makespan and as a partial solution we prove an optimality result for the case where there are two non-homogeneous machines and the jobs are homogeneous. It turns out that the optimal assignment can be expressed by using a quantile of a binomial distribution.
Comparisons of replacement policies
Authors: Langberg Naftali A.
Published: April 2006

For independent random lifelengths of the units in use stochastic comparisons of the number of failures and removal in [0,s] under age and block replacement policies are performed. A new concept of NBU (NWU) in sequence is introduced.
A cost relationship between age and block replacement policies
Authors: Savits Thomas H.
Published: April 2006

The general cost structure of a unit on line is assumed to be governed by a stochastic process , where R(t) denotes the operating cost on [0, t)and ζ denotes the time of an unscheduled (or unplanned) replacement by a new unit at a cost c1. For an age replacement maintenance policy, scheduled (or planned) replacements occur whenever an operating unit reaches age T, whereas in the block replacement case, scheduled replacements occur every T units of time. Such scheduled replacements cost c2. The expected long-run cost per unit time can then be expressed in the form A(T)/Ε [min(ζ, T)] and B(T)/T respectively. Our main result shows that where U is the associated renewal function generated by ζ.
Non-singularity and asymptotic independence
Authors: Bloomfield Peter
Published: April 2006

A stationary stochastic process must satisfy various requirements to make it a realistic model for a phenomenon in the real world. Some of these requirements are quantitative, such as agreement of distribution or moments. Other, more qualitative requirements deal with the general behavior of the process. Two such requirements are non-singularity and asymptotic independence. Each will be discussed from a variety of points of view, and given precise definition in a succession of progressively stronger forms.
The comparison of transient responses to stimuli
Authors: Cameron Murray A.
Published: April 2006

In some experiments an ‘observation' is a time series and the ‘treatments' are stimuli which elicit changes in the nature of the time series for only a short period. One approach to analysing data from such experiments is presented here. Tests are given for detecting responses in such experiments, and for comparing responses elicited under different treatment regimes. The tests are based on frequency-domain estimates of the prediction variance for stationary time series. If several stimuli are applied within each observed time series at regular intervals, then the method of analysis may be designed so that the estimates of the different responses are orthogonal and most of the calculations can be performed using standard analysis of variance programs.
Approximate distributions of Student's t-statistics for autoregressive coefficients calculated from regression residuals
Authors: Durbin J.
Published: April 2006

We consider a multiple regression model in which the regressors are Fourier cosine vectors. These regressors are intended as approximations to ‘slowly changing' regressors of the kind often found in time series regression applications. The errors in the model are assumed to be generated by a special type of autoregressive model defined so that the regressors are eigenvectors of the quadratic forms occurring in the exponent of the probability density of the errors. This autoregression is intended as an approximation to the usual stationary autoregression. Both approximations are adopted for the sake of mathematical convenience.

Student's t-statistics are constructed for the autoregressive coefficients in a manner analogous to ordinary regression. It is shown that these statistics are distributed as Student's t to the first order of approximation, that is with errors in the density of order T−1/2, where T is the sample size, while the squares of the statistics are distributed as the square of Student's t to the second order of approximation, that is with errors in the density of order Τ–1.
Circuit-switching networks with priorities on a one-dimensional lattice
Authors: Shamsiev Rahim
Published: April 2006

We prove existence and uniqueness of a stationary regime for a model of a circuit-switching network with infinitely many nodes.
On the limiting behaviour of Downton's carrier epidemic in the case of a general infection mechanism
Authors: Booth James G.
Published: April 2006

A generalization of Downton's (1968) carrier-borne epidemic process is considered in which the assumption of homogeneous mixing is replaced by a general infection mechanism. Using a method and notation similar to that of Gani and Purdue (1984), a recursive algorithm for the joint distribution of the total size and the total observed size of the epidemic is obtained.
Stationary increments in the accumulated work process in processor-sharing queues
Authors: Foley R. D. , Klutke Georgia-Ann
Published: April 2006

We present a new approach to the processor-sharing queue that allows us to study the accumulated work process of a job that requires an amount of processing time x. Our approach simplifies the proofs of some earlier results on expected conditional response times and extends them to the M/G/φ (·) class. The approach illuminates some of the paradoxical features of these systems.
The distribution of evolutionarily stable strategies
Authors: Haigh John
Published: April 2006

Suppose the n × n matrix A gives the payoffs for some evolutionary game, and its entries are the values of independent, identically distributed, continuous random variables. The distribution of the pattern of evolutionarily stable strategies for A will depend, if n ≧ 3, on this underlying distribution. A fairly complete picture for n = 3 is found, and some results are obtained for n ≧ 4.
Optimal stopping in the parking problem with U-turn
Authors: Tamaki Mitsushi
Published: April 2006

A motorist drives his car toward his destination along a street and looks for a motor pool. Motor pools are assumed to occur independently, with probabilityp.Observing whether there exists a motor pool or not, the driver decides either to stop (i.e., return to the latest motor pool observed so far and park there) or continue driving. Once the driver stops, he walks the remaining distance to his destination. Letr, 0 <r< 1, be the relative speed of driving a car compared with that on foot. Then the time duration required to reach the destination is measured byr· (distance driven) + (distance on foot) and the objective of the driver is to find a parking policy which minimizes the expected time duration. It is shown that, under an optimal policy, a U-turn never occurs before the destination, but may occur beyond the destination. Moreover, the expected time is computed and some comparisons are made between our problem and the classical parking problem.
A model for random instantaneous growth on an interval
Authors: Quine M. P.
Published: April 2006

Points arrive in succession on an interval and immediately ‘cover' a region of length ½ to each side (less if they are close to the boundary or to a covered part). The location of a new point is uniformly distributed on the uncovered parts. We study the mean and variance of the total number of points ever formed, in particular as a → 0, in which case we also establish asymptotic normality.
Markov processes for modeling and analyzing a new genetic mapping method
Authors: Feingold Eleanor
Published: April 2006

This paper describes a set of stochastic processes that is useful for modeling and analyzing a new genetic mapping method. Some of the processes are Markov chains, and some are best described as functions of Markov chains. The central issue is boundary-crossing probabilities, which correspond top-values for the existence of genes for particular traits. The methods elaborated by Aldous (1989) provide very accurate approximatep-values, as spot-checked against simulations.
Sums and maxima of discrete stationary processes
Authors: McCormick William P. , Sun Jiayang
Published: April 2006

This paper considers the joint limiting behavior of sums and maxima of stationary discrete-valued processes. The asymptotic behavior is a cross between a central limit theorem and asymptotic bounds for the distribution of the maxima. Some applications and simulations are also included.
The first-passage density of the Brownian motion process to a curved boundary
Authors: Durbin J. , Williams D.
Published: April 2006

An expression for the first-passage density of Brownian motion to a curved boundary is expanded as a series of multiple integrals. Bounds are given for the error due to truncation of the series when the boundary is wholly concave or wholly convex. Extensions to the Brownian bridge and to continuous Gauss–Markov processes are given. The series provides a practical method for calculating the probability that a sample path crosses the boundary in a specified time-interval to a high degree of accuracy. A numerical example is given.
Contact and chord length distributions of the Poisson Voronoi tessellation
Authors: Muche Lutz , Stoyan Dietrich
Published: April 2006

This paper presents the form of some characteristics of the Voronoi tessellation which is generated by a stationary Poisson process in. Expressions are given for the spherical and linear contact distribution functions. These formulae lead to numerically tractable double-integral formulae for chord length probability density functions.
On renewal processes relating to counter models: the case of phase-type interarrival times
Authors: Kao Edward P. C. , Smith Marion Spokony
Published: April 2006

The Type I and Type II counter models of Pyke (1958) have many applications in applied probability: in reliability, queueing and inventory models, for example. In this paper, we study the case in which the interarrival time distribution is of phase type. For the two counter models, we derive the renewal functions of the related renewal processes and propose approaches for their computations.
The limit distribution of the number of rare mutants
Authors: Finkelstein Mark , Tucker Howard G. , Veeh Jerry Alan
Published: April 2006

We study the number of mutants in a mutation process in which reverse mutation is allowed and in which both normal and mutant organisms reproduce at the same rate. Under a mild side condition on the rate of forward mutation we find necessary and sufficient conditions for the number of mutants to converge in distribution. We find the probability generating function of the limit distribution, when it exists. We present an example which shows that the mild side condition cannot be relaxed.
Compensator conditions for stochastic ordering of point processes
Authors: Kwieciński A. , Szekli R.
Published: April 2006

Sufficient conditions are given under which two simple point processes on the positive half-line can be stochastically compared as random elements of D(0,∞) or R∞+ Using a martingale approach to point processes, the conditions are proposed via a compensator function family. Appropriate versions of the processes being compared are constructed on the same probability space. The results are illustrated by replacement policies and semi-Markov point processes.
Some monotonicity properties of the delayed renewal function
Authors: Hansen B. G. , Frenk J. B. G.
Published: April 2006

Analogues of some theorems of Brown (1980) concerning renewal measures with DFR or IMRL underlying distributions are proved for delayed renewal measures. Some related results, such as partial converses of the main theorems, are also presented.
Distribution of the number of alleles in multigene families
Authors: Griffiths R. C.
Published: April 2006

The distribution of the number of alleles in samples fromrchromosomes is studied. The stochastic model used includes gene conversion within chromosomes and mutation at loci on the chromosomes. A method is described for simulating the distribution of alleles and an algorithm given for computing lower bounds for the mean number of alleles.

A formula is derived for the expected number of samples fromrchromosomes which contain the allele type of a locus chosen at random.
Asymptotic analysis of extremes from autoregressive negative binomial processes
Authors: McCormick William P. , Park You Sung
Published: April 2006

It is well known that most commonly used discrete distributions fail to belong to the domain of maximal attraction for any extreme value distribution. Despite this negative finding, C. W. Anderson showed that for a class of discrete distributions including the negative binomial class, it is possible to asymptotically bound the distribution of the maximum. In this paper we extend Anderson's result to discrete-valued processes satisfying the usual mixing conditions for extreme value results for dependent stationary processes. We apply our result to obtain bounds for the distribution of the maximum based on negative binomial autoregressive processes introduced by E. McKenzie and Al-Osh and Alzaid. A simulation study illustrates the bounds for small sample sizes.
A Pólya urn model and the coalescent
Authors: Trieb Gudrun
Published: April 2006

In recent papers by Hoppe and Donnelly it has been shown that a Pólya urn model generating the Ewens sampling formula (population genetics) parallels a construction of Kingman using a Poisson–Dirichlet ‘paintbox'. Even the jump chain of Kingman's n-coalescent can be constructed using the urn. The properties of a certain process based on the coalescent also are derived. This process was introduced by Hoppe.
Sur certaines fonctionnelles exponentielles du mouvement brownien réel
Authors: Yor Marc
Published: April 2006

Dufresne [1] recently showed that the integral of the exponential of Brownian motion with negative drift is distributed as the reciprocal of a gamma variable. In this paper, it is shown that this result is another formulation of the distribution of last exit times for transient Bessel processes. A bivariate distribution of such integrals of exponentials is also obtained explicitly.
Limit laws for the maxima of chain-dependent sequences with positive extremal index
Authors: Turkman K. F. , Oliveira M. F.
Published: April 2006

We extend the results on the extremal properties of chain-dependent sequences considered in Turkman and Walker (1983) by assuming conditions similar to those given by Leadbetter and Nandagopalan (1987) which permit clustering of high values.
An ergodic L2-theorem for simulated annealing in bayesian image reconstruction
Authors: Winkler Gerhard
Published: April 2006

An ergodic L2-theorem for inhomogeneous Markov chains covering simulated annealing with or without constraints and stochastic relaxation with or without constraints arising in Bayesian image reconstruction is proved. The derivation is self-contained.
Note on the strong limiting behaviour of busy periods in GI/G/1 queues under heavy traffic
Authors: Steinebach Josef , Zhang Hanqin
Published: April 2006

In this note, the strong limiting behaviour of busy periods in GI/G/1 queues is studied under the condition that the traffic intensity equals unity.
On a discrete-time non-zero-sum Dynkin problem with monotonicity
Authors: Ohtsubo Yoshio
Published: April 2006

We consider a monotone case of the non-zero-sum stopping game with discrete time parameter which is called the Dynkin problem. Marner (1987) has investigated a stopping game with general monotone reward structures, but his monotonicity is too strong to apply our problem. We establish that there exists an explicit equilibrium point in our monotone case. We also give a simple example applicable to a duopolistic exit game.
A martingale approach to the slow server problem
Authors: Stockbridge Richard H.
Published: April 2006

A Markov queueing system having heterogeneous servers under a long-run average criterion is analyzed. A direct proof of the optimality of a stationary, Markov policy is given using martingale methods. Simultaneously, the problem is reduced to a linear programming problem. Analysis of the LP for a system having finite queueing length shows the optimal policy is not always of threshold type.
Branching processes and functional differential equations determining steady-size distributions in cell populations
Authors: Taib Ziad
Published: April 2006

The functional differential equation y′(x) = ay(λx) + by(x) arises in many different situations. The purpose of this note is to show how it arises in some multitype branching process cell population models. We also show how its solution can be given an intuitive interpretation as the probability density function of an infinite sum of independent but not identically distributed random variables.
Characterization of convergence rates for the approximation of the stationary distribution of infinite monotone stochastic matrices
Authors: Simonot F. , Song Y. Q.
Published: April 2006

Let P be an infinite irreducible stochastic matrix, recurrent positive and stochastically monotone and Pn be any n × n stochastic matrix with Pn ≧ Tn, where Tn denotes the n × n northwest corner truncation of P. These assumptions imply the existence of limit distributions π and πn for P and Pn respectively. We show that if the Markov chain with transition probability matrix P meets the further condition of geometric recurrence then the exact convergence rate of πn to π can be expressed in terms of the radius of convergence of the generating function of π. As an application of the preceding result, we deal with the random walk on a half line and prove that the assumption of geometric recurrence can be relaxed. We also show that if the i.i.d. input sequence (A(m)) is such that we can find a real number r0 > 1 with , then the exact convergence rate of πn to π is characterized by r0. Moreover, when the generating function of A is not defined for |z| > 1, we derive an upper bound for the distance between πn and π based on the moments of A.
Mechanical models for cell movement – locomotion, translocation, migration
Authors: Watkins Joseph C.
Published: April 2006

This paper provides a detailed stochastic analysis of leucocyte cell movement based on the dynamics of a rigid body. The cell's behavior is studied in two relevant anisotropic environments displaying adhesion mediated movement (haptotaxis) and stimulus mediated movement (chemotaxis). This behavior is modeled by diffusion processes on three successively longer time scales, termed locomotion, translocation, and migration.
Rough limit results for level-crossing probabilities
Authors: Nyrhinen Harri
Published: April 2006

Let Y1, Y2, · ·· be a stochastic process and M a positive real number. Define TM = inf{n | Yn > M} (TM = + ∞ if for n = 1, 2, ···)· We are interested in the probabilities P(TM <∞) and in particular in the case when these tend to zero exponentially fast when M tends to infinity. The techniques of large deviations theory are used to obtain conditions for this and to find out the rate of convergence. The main hypotheses required are given in terms of the generating functions associated with the process (Yn).
Approximating gamma distributions by normalized negative binomial distributions
Authors: Adell José A. , De La Cal Jesús
Published: April 2006

Let F be the gamma distribution function with parameters a > 0 and α > 0 and let Gs be the negative binomial distribution function with parameters α and a/s, s > 0. By combining both probabilistic and approximation-theoretic methods, we obtain sharp upper and lower bounds for . In particular, we show that the exact order of uniform convergence is s–p, where p = min(1, α). Various kinds of applications concerning charged multiplicity distributions, the Yule birth process and Bernstein-type operators are also given.
Stability of feed-forward fluid networks with Lévy input
Authors: Kaspi Haya , Kella Offer
Published: April 2006

We consider a stochastic fluid network with independent subordinator inputs to the various stations and deterministic internal flow which is of feed-forward type. We show that under suitable conditions the process of fluid contents in the station has a limiting distribution, where the limit holds in total variation and is independent of the initial condition. We also show that this limiting distribution is of product form only for trivial setups.
Reliability bounds for the ℒ-class and Laplace order
Authors: Sengupta Debasis
Published: April 2006

Sharp upper and lower reliability bounds for the ℒ- and -classes of life distributions with a given mean are provided. Bounds are also given for a distribution which is related to a known distribution (not necessarily exponential) through the Laplace order.
Records from a power model of independent observations
Authors: Weissman Ishay
Published: April 2006

Records from are analyzed, where {Yj} is an independent sequence of random variables. Each Yj has a continuous distribution function Fj = Fλj for some distribution F and some λ j > 0. We study records, record times and related quantities for this sequence. Depending on the sequence of powers , a wide spectrum of behaviour is exhibited.
Crossings of max-stable processes
Authors: Davis Richard A. , Resnick Sidney I.
Published: April 2006

The expected number of upcrossings for a max-stable process is computed and compared with known results for stable processes. Asymptotically the formulas are of the same order.
On improvements of the order of approximation in the Poisson limit theorem
Authors: Borovkov K. , Pfeifer D.
Published: April 2006

In this paper we consider improvements in the rate of approximation for the distribution of sums of independent Bernoulli random variables via convolutions of Poisson measures with signed measures of specific type. As a special case, the distribution of the number of records in an i.i.d. sequence of length n is investigated. For this particular example, it is shown that the usual rate of Poisson approximation of O(1/log n) can be lowered to O(1/n2). The general case is discussed in terms of operator semigroups.
Limiting behavior of some measures of system availability
Authors: Mi Jie
Published: April 2006

Availability is an important characteristic of a system. Different types of availability are defined. For the case when a sequence of bivariate random variables of lifetime and repair time are i.i.d. certain properties have been established previously. In practice, however, we need to consider the situation where these bivariate random variables are independent but not identically distributed. Properties of two measures of availability for the i.i.d. case are extended to this more general case.
Detecting optimal and non-optimal actions in average-cost Markov decision processes
Authors: Lasserre Jean B.
Published: April 2006

We present two sufficient conditions for detection of optimal and non-optimal actions in (ergodic) average-cost MDPs. They are easily interpreted and can be implemented as detection tests in both policy iteration and linear programming methods. An efficient implementation of a recent new policy iteration scheme is discussed.
Some results on the relative ageing of two life distributions
Authors: Sengupta Debasis , Deshpande Jayant V.
Published: April 2006

Kalashnikov and Rachev (1986) have proposed a partial ordering of life distributions which is equivalent to an increasing hazard ratio, when the ratio exists. This model can represent the phenomenon of crossing hazards, which has received considerable attention in recent years. In this paper we study this and two other models of relative ageing. Their connections with common partial orderings in the reliability literature are discussed. We examine the closure properties of the three orderings under several operations. Finally, we give reliability and moment bounds for a distribution when it is ordered with respect to a known distribution.
On the full information best-choice problem
Authors: Gnedin Alexander V.
Published: April 2006

We introduce the optimal stopping problem of an infinite sequence of records associated with a planar Poisson process. This problem serves as a limiting form of the classical full information best-choice problem. A link between the finite problem and its limiting form is established via embedding n i.i.d. observations into the planar process.
Finite-time optimal control of a process leaving an interval
Authors: Mcbeth Douglas W. , Weerasinghe Ananda P. N.
Published: April 2006

Consider the optimal control problem of leaving an interval (– a, a) in a limited playing time. In the discrete-time problem, a is a positive integer and the player's position is given by a simple random walk on the integers with initial position x. At each time instant, the player chooses a coin from a control set where the probability of returning heads depends on the current position and the remaining amount of playing time, and the player is betting a unit value on the toss of the coin: heads returning +1 and tails − 1. We discuss the optimal strategy for this discrete-time game. In the continuous-time problem the player chooses infinitesimal mean and infinitesimal variance parameters from a control set which may depend upon the player's position. The problem is to find optimal mean and variance parameters that maximize the probability of leaving the interval [— a, a] within a finite time T > 0.
A Bayesian analysis of layered defense systems
Authors: Al-mutairi Dhaifalla K. , Al-khamis Talal M. , Abdel-Hameed Mohamed S.
Published: April 2006

A Bayesian approach for analyzing layered defense systems is presented. This approach incorporates the dependence of penetration probabilities on the size of attackers going into any layer. A general formula is developed for computing the predictive distribution of the number of attackers surviving any layer as well as the posterior distribution of the penetration probabilities under the a priori assumptions that: (i) the probabilities are dependent and their joint distribution is Dirichlet, and (ii) the probabilities are independent. Positive dependence of the penetration probabilities as well as the number of attackers surviving the different layers is also established.
Shape measurements of live pigs using 3-D image capture
Authors: McFarlane N. J. B. , Wu J. , Tillett R. D. , Schofield C. P. , Siebert J. P. , Ju X.
Published: April 2006

A photogrammetric stereo imaging system was used to capture 3-D models of live pigs, and quantitative shape measurements were extracted from cross sections of the models. Stereo images were captured of 32 pigs, divided into high-lysine and low-lysine diet groups, and 3-D models were built from the images. Each pig was imaged once per week for 14 weeks. After slaughter, 10 of the pigs were dissected for muscle and fat measurements. A sequence of algorithms was applied to the 3-D models: differential geometry to reveal surface curvature features and detect the spine; manual landmark placement; fitting a curve to the spine; determining the vertical axis of the body; placing a slice plane across the abdomen close to the P2 position; extracting a cross section; and fitting a shape model to the cross section. Differential geometry revealed many qualitative features of the musculature. The spine was a line of minimum curvature along the back. The high-lysine pigs had higher height-to-width ratios and flatter backs than the low-lysine pigs. The dissected total muscle mass had a -0·66 correlation with the flatness-of-back shape parameter, and a 0·64 correlation with weight.
A study on associations between PrP genotypes and meat traits in French sheep breeds
Authors: Vitezica Z. G. , Moreno C. R. , Bouix J. , Barillet F. , Perret G. , Elsen J. M.
Published: April 2006

In this study the potential association of PrP genotypes with meat traits has been investigated. The data included young rams from individual testing stations of three breeds: Ile de France, Préalpes du Sud and Blanc du Massif Central. These breeds were chosen due to their large number of available animals (with performance records and PrP genotypes) and their differential ARR haplotype frequency. Two analyses differing in the PrP genotype classes considered were carried out. Firstly, animals were categorized into three classes: ARR homozygous, ARR heterozygous, and animals without the ARR haplotype. The data for this analysis included 725, 534 and 832 animals for Ile de France, Préalpes du Sud and Blanc du Massif Central breeds, respectively. Secondly, as the two predominant haplotypes in these breeds are ARR and AR- (and AR- includes ARQ and ARH haplotypes), the effect of substituting 1 or 2 ARR haplotypes for AR- haplotypes was studied. These comparisons involved three genotype classes: ARR homozygous, ARR/AR-, and AR-homozygous. The data for this analysis included 532, 509 and 620 animals of Ile de France, Préalpes du Sud and Blanc du Massif Central breeds, respectively. Meat traits were analysed using an animal model (where the PrP genotype was included as a fixed effect) and they included growth rate, ultrasonic fat depth, and ultrasonic muscle depth. The results of this study indicate no evidence of association between PrP genotypes and the meat traits studied in these sheep breeds.
Agreement between parent and child report of quality of life in children with attention‐deficit/hyperactivity disorder
Authors: Klassen A. F. , Miller A. , Fine S.
Published: April 2006

Background  There is little information in the research literature of agreement between parent and child in reports of child quality of life (QOL) for a sample of children diagnosed with attention‐deficit/hyperactivity disorder (ADHD). The aim of our study was to determine whether parent and child concordance is greater for physical domains of QOL than for psychosocial domains; whether parents rate their child’s QOL better or poorer than their child’s ratings; and whether concordance is related to demographic, socioeconomic or clinical factors.

Methods  The study was a questionnaire survey of children aged 10–17 referred to the ADHD clinic and diagnosed with ADHD in the province of British Columbia (Canada) between November 2001 and October 2002 and their parent.

Results  Fifty‐eight children diagnosed with ADHD and their parents completed our study questionnaire. The main outcome measure was the Child Health Questionnaire, which permitted comparisons on eight QOL domains and one single item. Intraclass correlation coefficients were moderate for five domains (range from 0.40 to 0.51), and good for three domains (range from 0.60 to 0.75). Children rated their QOL significantly better than their parents in four areas and poorer in one. Standardized Response Means indicated clinically important differences in mean scores for Behaviour and Self‐esteem. Compared with population norms, across most domains, children with ADHD reported comparable health. Discrepancies between parent–child ratings were related to the presence of a comorbid oppositional/defiant disorder, a psychosocial stressor and increased ADHD symptoms.

Conclusions  Although self‐report is an important means of eliciting QOL data, in children with ADHD, given the discrepancies in this study between parent and child report, measuring both perspectives seems appropriate.
Highly structured nucleotide variation within and among Arabidopsis lyrata populations at the FAH1 and DFR gene regions
Authors: BALAÑÁ‐ALCAIDE D. , RAMOS‐ONSINS S. E. , BOONE Q. , AGUADÉ M.
Published: April 2006

Nucleotide variation at the FAH1 and DFR gene regions was surveyed in four populations of Arabidopsis lyrata (two European A. l. petraea and two North American A. l. lyrata populations). In contrast to previous results, levels of variation were not consistently lower in A. l. lyrata than in A. l. petraea, and similar degrees of genetic differentiation were detected between and within subspecies. These observations and the significant genetic differentiation detected among populations suggest population substructure and no real subdivision between subspecies. For each gene studied, genotypic data were obtained, which allowed comparing nucleotide diversity within individuals (between sequences from the same individual) and within populations (between sequences from the same population). The generally lower level of variation within than among individuals detected in each population yielded a significant deviation from panmixia within populations. In three of the four populations studied, two highly divergent alleles were detected within populations at the highly variable DFR locus. This pattern and the significant excess of derived variants detected in most populations suggest that most variation segregating within populations results from rare migration events between relatively small and isolated populations exhibiting reduced panmixia.
Phytochrome‐mediated agravitropism in Arabidopsis hypocotyls requires GIL1 and confers a fitness advantage
Authors: Allen Trudie , Ingles Patricia J. , Praekelt Uta , Smith Harry , Whitelam Garry C.
Published: April 2006

Plants use specialized photoreceptors to detect the amount, quality, periodicity and direction of light and to modulate their growth and development accordingly. These regulatory light signals often interact with other environmental cues. Exposure of etiolated Arabidopsis seedlings to red (R) or far‐red (FR) light causes hypocotyls to grow in random orientations with respect to the gravitational vector, thus overcoming the signal from gravity to grow upwards. This light response, mediated by either phytochrome A or phytochrome B, represents a prime example of cross‐talk between environmental signalling systems. Here, we report the isolation the mutant gil1 (for gravitropic in the light) in which hypocotyls continue to grow upwards after exposure of seedlings to R or FR light. The gil1 mutant displays no other phenotypic alterations in response to gravity or light. Cloning of GIL1 has identified a novel gene that is necessary for light‐dependent randomization of hypocotyl growth orientation. Using gil1, we have demonstrated that phytochrome‐mediated randomization of Arabidopsis hypocotyl orientation provides a fitness advantage to seedlings developing in patchy, low‐light environments.
Colourful male guppies produce faster and more viable sperm
Authors: Locatello L. , Rasotto M. B. , Evans J. P. , Pilastro A.
Published: April 2006

In guppies (Poecilia reticulata) precopulatory sexual selection (via female choice) and post-copulatory selection (via sperm competition) both favour males with relatively high levels of carotenoid (orange) pigmentation, suggesting that colourful males produce more competitive ejaculates. Here we test whether there is a positive association between male orange pigmentation and sperm quality. Our analysis of sperm quality focused on sperm swimming speeds (using CASA: computer-assisted sperm analysis to estimate three parameters of sperm velocity in vitro), sperm viability (proportion of live sperm per stripped ejaculate) and sperm lengths. We found that males with relatively large areas of orange pigmentation had significantly faster and more viable sperm than their less ornamented counterparts, suggesting a possible link between dietary carotenoid intake and sperm quality. By contrast, we found no relationship between sperm length (head length and total sperm length) and male phenotype. These findings, in conjunction with previous work showing that highly ornamented male guppies sire higher quality offspring, suggest that female preference for colourful males and sperm competition work in concert to favour intrinsically higher quality males.