bluuebunny/crossref_metadata_2025 huggingface dataset:
An unusual stochastic order relation with some applications in sampling and epidemic theory
Authors: Lefevre Claude , Picard Philippe
Published: April 2006

One expects, intuitively, that the total damage caused by an epidemic increases, in a certain sense, with the infection intensity exerted by the infectives during their lifelength. The original object of the present work is to make precise in which probabilistic terms such a statement does indeed hold true, when the spread of the disease is described by a collective Reed–Frost model and the global cost is represented by the final size and severity. Surprisingly, this problem leads us to introduce an order relation for -valued random variables, unusual in the literature, based on the descending factorial moments. Further applications of the ordering occur when comparing certain sampling procedures through the number of un-sampled individuals. In particular, it is used to reinforce slightly comparison results obtained earlier for two such samplings.
Monotone stopping-allocation problems
Authors: Benhenni Robert A.
Published: April 2006

Stopping-allocation problems are concerned with how best to allocate observations among some K competing stochastic populations and when to stop the observation process. The goal of the decision-maker is to choose a stopping–allocation rule to maximize the expected value of a payoff function. First the stopping rule is fixed, and the local and global optimality of the myopic allocation rule are derived under some monotonicity conditions. An application is considered, namely the inspection problem and its use in solving a computer scheduling problem. Next, optimization is done with respect to both the allocation rule and the stopping rule. For any given stopping-allocation rule, it is shown that under some monotonicity conditions, the decision-maker can improve on it by using a ‘partial' myopic allocation rule and a generalized one-stage-look-ahead stopping rule; this result is then extended, under the same conditions and other monotonicity requirements, to derive the joint optimality of the myopic allocation rule and the one-stage-look-ahead stopping rule. Finally this latter result is applied to the inspection problem.
Induced rare events: analysis via large deviations and time reversal
Authors: Shwartz Adam , Weiss Alan
Published: April 2006

When a subsystem goes into an infrequent state, how does the remainder of the system behave? We show how to calculate the relevant distributions using the notions of reversed time for Markov processes and large deviations. For ease of exposition, most of the work deals with a specific queueing model due to Flatto, Hahn, and Wright. However, we show how the theorems may be applied to much more general jump-Markov systems.

We also show how the tools of time-reversal and large deviations complement each other to yield general theorems. We show that the way a constant coefficient process approaches a rare event is roughly by following the path of another constant coefficient process. We also obtain some properties, including apriori bounds, for the change of measure associated with some large deviations functionals; these are useful for accelerating simulations.
Stability condition for a single-server retrial queue
Authors: Liang Huei-Mei , Kulkarni V. G.
Published: April 2006

A single-server retrial queue consists of a primary queue, an orbit and a single server. Assume the primary queue capacity is 1 and the orbit capacity is infinite. Customers can arrive at the primary queue either from outside the system or from the orbit. If the server is busy, the arriving customer joins the orbit and conducts a retrial later. Otherwise, he receives service and leaves the system.

We investigate the stability condition for a single-server retrial queue. Let λ be the arrival rate and 1/μ be the mean service time. It has been proved that λ/μ < 1 is a sufficient stability condition for the M/G/1/1 retrial queue with exponential retrial times. We give a counterexample to show that this stability condition is not valid for general single-server retrial queues. Next we show that λ /μ < 1 is a sufficient stability condition for the stability of a single-server retrial queue when the interarrival times and retrial times are finite mixtures of Erlangs.
Some results on the bomber problem
Authors: Simons Gordon , Yao Yi-Ching
Published: April 2006

The problem of optimally allocating partially effective, defensive weapons against randomly arriving enemy aircraft so that a bomber maximizes its probability of reaching its designated target is considered in the usual continuous-time context, and in a discrete-time context. The problem becomes that of determining the optimal number of missiles K(n, t) to use against an enemy aircraft encountered at time (distance) t away from the target when n is the number of remaining weapons (missiles) in the bomber's arsenal. Various questions associated with the properties of the function K are explored including the long-standing, unproven conjecture that it is a non-decreasing function of its first variable.
A repair replacement model
Authors: Yeh Lam
Published: April 2006

In this paper, we study a similar replacement model in which the successive survival times of the system form a process with non-increasing means, whereas the consecutive repair times after failure constitute a process with non-decreasing means. The system is replaced at the time of the Nth failure since the installation or last replacement. Based on the long-run average cost per unit time, we determine the optimal replacement policy N∗ and the maximum of the long-run average reward explicitly. Under additional conditions, the policy N∗ is even optimal among all replacement policies.
Convergence in Distribution of the One-Dimensional Kohonen Algorithms when the Stimuli are not Uniform
Authors: Bouton Catherine , Pagès Gilles
Published: April 2006

We show that the one-dimensional self-organizing Kohonen algorithm (with zero or two neighbours and constant step ε) is a Doeblin recurrent Markov chain provided that the stimuli distribution μ is lower bounded by the Lebesgue measure on some open set. Some properties of the invariant probability measure vε (support, absolute continuity, etc.) are established as well as its asymptotic behaviour as ε ↓ 0 and its robustness with respect to μ.
A stochastic simulation for solving scalar reaction–diffusion equations
Authors: Chauvin B. , Rouault
Published: April 2006

A recent Monte Carlo method for solving one-dimensional reaction–diffusion equations is considered here as a convergence problem for a sequence of spatial branching processes with interaction. The martingale problem is studied and a limit theorem is proved by embedding spaces of measures in Sobolev spaces.
A description of the long-term behaviour of absorbing continuous-time Markov chains using a centre manifold
Authors: Pollett P. K. , Roberts A. J.
Published: April 2006

We use the notion of an invariant manifold to describe the long-term behaviour of absorbing continuous-time Markov processes with a denumerable infinity of states. We show that there exists an invariant manifold for the forward differential equations and we are able to describe the evolution of the state probabilities on this manifold. Our approach gives rise to a new method for calculating conditional limiting distributions, one which is also appropriate for dealing with processes whose transition probabilities satisfy a system of non-linear differential equations.
Exponential approximation of waiting time and queue size for queues in heavy traffic
Authors: Szczotka Władysław
Published: April 2006

An exponential approximation for the stationary waiting time distribution and the stationary queue size distribution for single-server queues in heavy traffic is given for a wide class of queues. This class contains for example not only queues for which the generic sequence, i.e. the sequence of service times and interarrival times, is stationary but also such queues for which the generic sequence is asymptotically stationary in some sense. The conditions ensuring the exponential approximation of the characteristics considered in heavy traffic are expressed in terms of the invariance principle for the stationary representation of the generic sequence and its first two moments.
Phase-type distributions and invariant polytopes
Authors: O'Cinneide Colm Art
Published: April 2006

The notion of an invariant polytope played a central role in the proof of the characterization of phase-type distributions. The purpose of this paper is to develop invariant polytope techniques further. We derive lower bounds on the number of states needed to represent a phase-type distribution based on poles of its Laplace–Stieltjes transform. We prove that every phase-type distribution whose transform has only real poles has a bidiagonal representation. We close with three short applications of the invariant polytope idea. Taken together, the results of this paper show that invariant polytopes provide a natural approach to many questions about phase-type distributions.
The multitype branching random walk: temporal and spatial limit theorems
Authors: Ivanoff B. Gail
Published: April 2006

We consider a multitype branching random walk with independent Poisson random fields of each type of particle initially. The existence of limiting random fields as the generation number, is studied, when the intensity of the initial field is renormalized in such a way that the mean measures converge. Spatial laws of large numbers and central limit theorems are given for the limiting random field, when it is non-trivial.
Some power series with random gaps
Authors: Holgate Philip
Published: April 2006

Power series ΣzXn are studied, where {Xn} is a strictly increasing integer-valued stochastic process.
Aggregated semi-Markov processes incorporating time interval omission
Authors: Ball Frank , Milne Robin K. , Yeo Geoffrey F.
Published: April 2006

We consider a semi-Markov process with finite state space, partitioned into two classes termed ‘open' and ‘closed'. It is possible to observe only which class the process is in. We show that complete information concerning the aggregated process is contained in an embedded Markov renewal process, whose parameters, moments and equilibrium behaviour are determined. Such processes have found considerable application in stochastic modelling of single ion channels. In that setting there is time interval omission, i.e. brief sojourns in either class failed to be detected. Complete information on the aggregated process incorporating time interval omission is contained in a Markov renewal process, whose properties are derived, obtained from the above Markov renewal process by a further embedding. The embedded Markov renewal framework is natural, and its invariance to time interval omission leads to considerable economy in the derivation of properties of the observed process. The results are specialised to the case when the underlying process is a continuous-time Markov chain.
On a job resequencing issue in parallel processor stochastic scheduling
Authors: Xu Susan H.
Published: April 2006

In flexible assembly systems, it is often necessary to coordinate jobs and materials so that specific jobs are matched with specific materials. This requires that jobs depart from upstream parallel workstations in some predetermined order. One way to satisfy this requirement is to temporarily hold the serviced jobs getting out of order at a resequencing buffer and to release them to downstream workstations as soon as all their predecessors are serviced. In this paper we consider the problem of scheduling a fixed number of non-preemptive jobs on two IHR non-identical processors with the resequencing requirement. We prove that the individually optimal policy, in which each job minimizes its own expected departure time subject to the constraint that available processors are offered to jobs in their departure order, is of a threshold type. The policy is independent of job weights and the jobs residing at the resequencing buffer and possesses the monotonicity property which states that a job will never utilize a processor in the future once it has declined the processor. Most importantly, we prove that the individually optimal policy has the stability property; namely: if at any time a job deviated from the individually optimal policy, then the departure time of every job, including its own, would be prolonged. As a direct consequence of this property, the individually optimal policy is socially optimal in the sense that it minimizes the expected total weighted departure time of the system as a whole. We identify situations under which the individually optimal policy also minimizes the expected makespan of the system.
The probability of large queue lengths and waiting times in a heterogeneous multiserver queue I: Tight limits
Authors: Sadowsky John S. , Szpankowski Wojciech
Published: April 2006

We consider a multiserver queuing process specified by i.i.d. interarrival time, batch size and service time sequences. In the case that different servers have different service time distributions we say the system is heterogeneous. In this paper we establish conditions for the queuing process to be characterized as a geometrically Harris recurrent Markov chain, and we characterize the stationary probabilities of large queue lengths and waiting times. The queue length is asymptotically geometric and the waiting time is asymptotically exponential. Our analysis is a generalization of the well-known characterization of the GI/G/1 queue obtained using classical probabilistic techniques of exponential change of measure and renewal theory.
Superposition of Interacting Aggregated Continuous-Time Markov Chains
Authors: Ball Frank , Milne Robin K. , Tame Ian D. , Yeo Geoffrey F.
Published: April 2006

Consider a system of interacting finite Markov chains in continuous time, where each subsystem is aggregated by a common partitioning of the state space. The interaction is assumed to arise from dependence of some of the transition rates for a given subsystem at a specified time on the states of the other subsystems at that time. With two subsystem classes, labelled 0 and 1, the superposition process arising from a system counts the number of subsystems in the latter class. Key structure and results from the theory of aggregated Markov processes are summarized. These are then applied also to superposition processes. In particular, we consider invariant distributions for the level m entry process, marginal and joint distributions for sojourn-times of the superposition process at its various levels, and moments and correlation functions associated with these distributions. The distributions are obtained mainly by using matrix methods, though an approach based on point process methods and conditional probability arguments is outlined. Conditions under which an interacting aggregated Markov chain is reversible are established. The ideas are illustrated with simple examples for which numerical results are obtained using Matlab. Motivation for this study has come from stochastic modelling of the behaviour of ion channels; another application is in reliability modelling.
Poisson's equation for the recurrent M/G/1 queue
Authors: Glynn Peter W.
Published: April 2006

This paper shows how to calculate solutions to Poisson's equation for the waiting time sequence of the recurrent M/G/l queue. The solutions are used to construct martingales that permit us to study additive functionals associated with the waiting time sequence. These martingales provide asymptotic expressions, for the mean of additive functionals, that reflect dependence on the initial state of the process. In addition, we show how to explicitly calculate the scaling constants that appear in the central limit theorems for additive functionals of the waiting time sequence.
Sur Une Équation Fonctionnelle Et SES Applications: Une Extension Du Théorème De Kesten-Stigum Concernant Des Processus De Branchement
Authors: Liu Quansheng
Published: April 2006

Given a random integer N ≧ 0 and a sequence of random variables Ai ≧ 0, we define a transformation T on the class of probability measures on [0, ∞) by letting Tμ be the distribution of , where {Zi} are independent random variables with distribution μ, which are independent of N and of {Ai} as well. We obtain the optimal conditions for the functional equation μ = Tμ to have a non-trivial solution of finite mean, and we study the existence of moments of the solutions. The work unifies the corresponding theorems of Kesten-Stigum concerning the Galton-Watson process, of Biggins for branching random walks, of Kahane-Peyrière for a model of turbulence of Yaglom made precise by Mandelbrot, and of Durrett-Liggett for the study of invariant measures for certain infinite particle systems.
Some properties of a 2D arterial tree simulated by a stochastic growth model
Authors: Sandau Konrad , Kurz Haymo
Published: April 2006

The chorioallantoic membrane (CAM) of chick eggs is a well-studied embryonic organ, where the growth of blood vessels can be easily inspected in the living state, and in a quasi-two-dimensional tissue sheet. Structural and physiological knowledge about this organ was combined to define a stochastic growth process (Sandau and Kurz 1994).
A bootstrap algorithm for the isotropic random sphere
Authors: Brown Jason J.
Published: April 2006

Let be a real-valued, homogeneous, and isotropic random field indexed in . When restricted to those indices with , the Euclidean length of , equal to r (a positive constant), then the random field resides on the surface of a sphere of radius r. Using a modified stratified spherical sampling plan (Brown (1993a)) on the sphere, define to be a realization of the random process and to be the cardinality of . A bootstrap algorithm is presented and conditions for strong uniform consistency of the bootstrap cumulative distribution function of the standardized sample mean, , are given. We illustrate the bootstrap algorithm with global land-area data.
Typification of Linnaean plant names in Rosaceae
Authors: Cafferty Steve , Jarvis Charles E.
Published: April 2006

Lectotypes, neotypes and epitypes are designated by 32 specialists for 52 previously untypified Linnaean plant names belonging to the family Rosaceae. These newly proposed types support current usage of the names concerned. Earlier but ineffective or supersedable type statements are discussed.
Molecular phylogenetics of Thymelaeaceae with particular reference to African and Australian genera
Authors: van der Bank Michelle , Fay Michael F. , Chase Mark W.
Published: April 2006

Phylogenetic relationships of the African and Australian Thymelaeaceae were investigated by parsimony analysis of 41rbcLnucleotide sequences, including 27 genera and several outgroup taxa. In a second analysis, plastidtrnLintron andtrnL-Fintergenic spacer sequences for the same taxa were included as well. The results from the separate analyses produced highly congruent, although not identical, results. Lastly we combined both sequence regions in one analysis to improve resolution and support. Thymelaeaceae are monophyletic with Thymelaeoideae, Aquilarioideae, Gonystyloideae and Gilgiodaphnoideae clearly recognised.GonystylusandLethedonare grouped together, contrary to previous studies that placedLethedonin Aquilarioideae. The molecular evidence does not support monophyly of the largely African genusGnidia; at least four major lineages could be identified.Pimelea(Australian) is embedded within one of these lineages, and the others are more closely related toDrapetes(New Zealand and South America),Struthiola, PasserinaandLachnaea(all African).
Typification in the genus Rhamnus L. sectio Rhamnastrum Rouy (Rhamnaceae): R. pumilus Turra and R. alpinus L.
Authors: Baldini Riccardo M.
Published: April 2006

A neotype, LINN 262.17, is designated for Rhamnus pumilus Turra and a lectotype, Herb. Burser XXII: 14 (UPS), for R. alpinus L. The typification of these names is necessary in establishing their correct application for a revision of Rhamnus sectio Rhamnastrum Rouy.
A simplified model for the formation, movement, and dissipation of fair weather cumulus clouds
Authors: Fox Martin
Published: April 2006

Certain patches of ground are favorable to the formation of fair weather cumulus clouds. These are patches which reflect rather than absorb solar heat. As the air above these patches is warmed, it will rise and, if the humidity is sufficient, the cooling effect of higher elevation will cause formation of a cloud of the type known as the fair weather cumulus. This fact is used in the present paper to develop a stochastic model for the temporal evolution of the contribution to cloud cover by fair weather cumuli.
On a first passage problem in stochastic storage systems with total release
Authors: Ten Hoopen M. , Reuver H. A.
Published: April 2006

The deleting or delay effect which a recurrent point process exerts upon another recurrent point process (or process with stationary independent increments) is treated. The concept arises in the statistical analysis of neuronal firing patterns, but may also be useful in applications to storage systems in operations research.
Measurement of area by counting
Authors: Russell Allan M. , Josephson Nora S.
Published: April 2006

Through the use of a zone mapping transformation, geometrical probability is applied to the problem of measuring the area of a planar figure by counting the points covered when the figure is placed at random on a regular point lattice. An expression for the variance σ2 is obtained as a function of radius for the case of a circle. This expression is equivalent to a more general formula for σ2 derived earlier by Kendall and Rankin using analytical methods. Computer calculations of σ are given for two special cases and the results are compared with those predicted by alternative asymptotic formulae also due to Kendall and Rankin. Some examples of the use of zone mapping to treat asymmetric figures, not subject to analytical methods, are described.
Two inverse problems concerning the superposition of recurrent point processes
Authors: Ambartzumian R. V.
Published: April 2006

Suppose that we observe an infinite realisation of a point process Π, which is a superposition of a number of mutually independent recurrent point processes Πi, such that
Channel capacities for list codes
Authors: Ahlswede Rudolf
Published: April 2006

In the present paper we demonstrate that the concept of a list code is from a mathematical point of view a more canonical notion than the classical code concept (list size one) in that it allows a unified treatment of various coding problems. In particular we determine for small list sizes the capacities of arbitrarily varying channels.
The signal-noise problem — a solution for the case that signal and noise are Gaussian and independent
Authors: Driscoll Michael F.
Published: April 2006

A solution is obtained for the signal-noise problem X = M + Z in which M and Z are independent Gaussian processes. Conditions on the processes are given which insure that the best estimate under generalized square — error loss is the conditional mean of M given X = x. A sequence of approximators of the best estimate is also given.
Asymptotic likelihood theory for diffusion processes
Authors: Brown B. M. , Hewitt J. I.
Published: April 2006

We investigate the large-sample behaviour of maximum likelihood estimates (MLE's) of the parameters of a diffusion process, which is observed throughout continuous time. The results (limit normal distribution for the MLE and an asymptotic chi-squared likelihood ratio test) correspond exactly to classical asymptotic likelihood results, and follow easily from a central limit theorem for stochastic integrals.
Longest common subsequences of two random sequences
Authors: Chvátal Vacláv , Sankoff David
Published: April 2006

Given two random k-ary sequences of length n, what is f(n,k), the expected length of their longest common subsequence? This problem arises in the study of molecular evolution. We calculate f(n,k) for all k, where n ≦ 5, and f(n,2) where n ≦ 10. We study the limiting behaviour of n–1f(n,k) and derive upper and lower bounds on these limits for all k. Finally we estimate by Monte-Carlo methods f(100,k), f(1000,2) and f(5000,2).
Random measures and their application to motion in an incompressible fluid
Authors: Port Sidney C. , Stone Charles J.
Published: April 2006

A generalization of a theorem of Geman and Horowitz concerning random measures is obtained. Their theorem in turn is used to extend a well-known result of Lumley, which asserts that for homogeneous turbulence in an incompressible fluid the probability distributions of the Eulerian and Lagrangian velocities coincide with each other at all times.
Subfair discounted red-and-black game with a house limit
Authors: Chen Robert
Published: April 2006

A subfair discounted red-and-black game with a house limit is introduced and the optimality of the modified bold strategy is shown.
Some ratio identities for a class of skip free random walks
Authors: Pegg P. A.
Published: April 2006

We prove a ratio identity giving a transform of the distribution of the position of a two barrier random walk as a ratio of the equivalent transforms for the one barrier random walk. This ratio identity holds for skip free random walks where the increments are dependent on both the previous increment and also the position of the random walk.
Asymptotic properties of the number of replications of a paired comparison
Authors: Uppuluri V. R. R. , Blot W. J.
Published: April 2006

A discrete random variable describing the number of comparisons made in a sequence of comparisons between two opponents which terminates as soon as one opponent wins m comparisons is studied. By equating two different expressions for the mean of the variable, a closed form for the incomplete beta function with equal arguments is obtained. This expression is used in deriving asymptotic (m-large) expressions for the mean and variance. The standardized variate is shown to converge to the Gaussian distribution as m→ ∞. A result corresponding to the DeMoivre-Laplace limit theorem is proved. Finally applications are made to the genetic code problem, to Banach's Match Box Problem, and to the World Series of baseball.
An immigration super-critical branching diffusion process
Authors: Radcliffe J.
Published: April 2006

This paper is an extension of Davis (1965) by allowing immigration. Mean square convergence is proved for a random variable in a branching diffusion process allowing immigration.
An ergodic theorem for evolution in a random environment
Authors: Norman M. Frank
Published: April 2006

Let w1, w12 and w2 be the fitnesses of genotypes A1A1, A1A2 and A2A2 in an infinite diploid population, and let pn be the A1, gene frequency in the nth generation. If fitness varies independently from generation to generation, then pn is a Markov process with a continuum of states. If E[In(wi/w12)] < 0 for i = 1, 2, then there is a unique stationary probability, and the distribution of pn converges to it as n → ∞.
The law of the iterated logarithm for Brownian sheets
Authors: Park W. J.
Published: April 2006

Strassen-type law of the iterated logarithm for Brownian sheets presented by Pyke [7] is proved by using recent results of Kuelbs and Lepage [4]: the law of the iterated logarithm for Brownian motion in a Banach space and some applications are given.
The recursive estimation of a Markov chain
Authors: Blight B. J. N. , Devore J. L.
Published: April 2006

For every hth member of a two-state Markov chain the value of a random variable Y is observed where the distribution of Y is conditional on the state of the corresponding member of the chain. A recursive set of equations is derived giving the posterior probabilities for both the observed and unobserved members. The use of this recursive solution to investigate the optimality of certain simple classification rules is discussed, and a “classification by runs” is also presented.
A bound for bivariate probability of large deviations
Authors: Goldstein Matthew
Published: April 2006

Suppose (X1, Y1), (X2, Y2), …, (Xn, Yn) are independent random vectors such that a ≦ Xi ≦ b and a ≦ Yi ≦ b, i = 1, 2, …, n. An upper bound which exponentially converges to zero is derived for the probability Pr{Sx – nμx ≧ nt1;SY – nμY ≧ nt2} where Sx = Σ Xi, SY = Σ Yi,EYi = μY, EXi = μx and t1 > 0, t2 > 0. The bound is a function of the difference b — a, the correlation between Xi and Yi, μx and μY and t1 and t2.
The branching diffusion with immigration
Authors: Ivanoff B. G.
Published: April 2006

The branching diffusion with immigration is studied. Under general branching and diffusion laws, the process is shown to be mixing, according to Brillinger's definition. Brillinger's central limit theorem for spatially homogeneous mixing processes is generalized to prove that, under a renormalization transformation, the distribution of the branching diffusion with immigration converges to a completely random Gaussian random measure. In addition, the existence of a steady-state distribution is proven in the case of subcritical branching, and this distribution is shown to be mixing. Hence the steady-state random field also obeys a spatial central limit theorem.
Linear processes and bispectra
Authors: Rosenblatt M.
Published: April 2006

A linear process is generated by applying a linear filter to independent, identically distributed random variables. Only the modulus of the frequency response function can be estimated if only the linear process is observed and if the independent identically distributed random variables are Gaussian. In this case a number of distinct but related problems coalesce and the usual discussion of these problems assumes, for example, in the case of a moving average that the zeros of the polynomial given by the filter have modulus greater than one. However, if the independent identically distributed random variables are non-Gaussian, these problems become distinct and one can estimate the transfer function under appropriate conditions except for a possible linear phase shift by using higher-order spectral estimates.
Multistate reliability models
Authors: Griffith William S.
Published: April 2006

In this paper an axiomatic development of multistate systems is presented. Three types of coherence based on the strength of the relevancy axiom are studied. The strongest of these has been investigated previously by El-Neweihi, Proschan, and Sethuraman [3]. One of the weaker types of coherence permits wider applicability to real life situations without sacrificing any of the mathematical results obtained by El-Neweihi, Proschan, and Sethuraman. The concept of system performance is formalized through expected utility and the effect of component improvement on system performance is studied using a generalization of Birnbaum's reliability importance.
On the distribution of time to first system failure
Authors: Chiang Dalen T. , Niu Shun-Chen
Published: April 2006

For a maintained reliability system, i.e., components may be repaired upon failures, we prove that the distribution of time to first system failure starting with all components new is NBU under the following conditions: (a) non-repairable components have NBU uptime distributions, (b) repairable components have exponential uptime and DFR downtime distributions. This is a slight generalization of a theorem of Barlow and Proschan (1976). However, our method of proof is different from theirs. We also show that the initial up-period of the system is stochastically larger than any other system up-period. Finally, a method of finding a lower bound for the expected time until first system failure is outlined using our main result.
Maximizing the intersection density of fibre processes
Authors: Janson Svante , Kallenberg Olav
Published: April 2006

It is shown that the specific intersection density of a stationary Poisson process of cylindrical fibres in Rd, d ≧ 2, attains its maximum when the directions are uniformly distributed. This generalizes a result by R. Davidson for line processes in R2.
Optimality conditions for a Markov decision chain with unbounded costs
Authors: Robinson D. R.
Published: April 2006

It is known that when costs are unbounded satisfaction of the appropriate dynamic programming ‘optimality' equation by a policy is not sufficient to guarantee its average optimality. A ‘lowest-order potential' condition is introduced which, along with the dynamic programming equation, is sufficient to establish the optimality of the policy. Also, it is shown that under fairly general conditions, if the lowest-order potential condition is not satisfied there exists a non-memoryless policy with smaller average cost than the policy satisfying the dynamic programming equation.
On the ordered partial sums of real random variables
Authors: Takács Lajos
Published: April 2006

In 1952 Pollaczek discovered a remarkable formula for the Laplace-Stieltjes transforms of the distributions of the ordered partial sums for a sequence of independent and identically distributed real random variables. In this paper Pollaczek's result is proved in a simple way and is extended for a semi-Markov sequence of real random variables.
On the number of terminal vertices in certain random trees with an application to stemma construction in philology
Authors: Najock D. , Heyde C. C.
Published: April 2006

A fundamental task of philologists is to construct the family tree (stemma) of preserved copies of ancient manuscripts. A simple probabilistic model based on random rooted trees is proposed to assist in the identification of the number of terminal copies. The model provides the distribution of the number of terminal vertices in a random tree. An application to stemma construction is given.
Density factorizations for brownian motion, meander and the three-dimensional bessel process, and applications
Authors: Imhof J.-P.
Published: April 2006

Joint densities concerning in particular the value and time of the maximum over a fixed time interval, or the behavior over intervals determined by some first- and last-passage times, are determined for Brownian motion, the three-dimensional Bessel process and Brownian meander. Simple change of measure formulas permit easy passage from one process to the other. Examples are given.
On the transition density of a multidimensional parameter Wiener process with one barrier
Authors: Cabaña E. M.
Published: April 2006

An upper estimate of the probability density of d-parameter Wiener process with one barrier, already known for d = 2, is extended for general d.
Comparison of self-organizing linear search rules
Authors: Lam K.
Published: April 2006

Consider a file with n records denoted by R1, R2, …, Rn. At each access of a record, the file has to be searched sequentially and it is assumed that the search cost is proportional to the number of probes needed to retrieve the records. The access probabilities p1, p2, …, pn are assumed to be unknown constants and accesses are assumed to be independent. A move-forward self-organizing rule moves a record accessed in the ith position to the lith position without changing the relative ordering of other records where li, = 1, li, < i for i = 2, …, n and li+1≧li. A move-forward rule R is said to be ≦ another move-forward rule R′ if l′i≦li for all i. It is shown that when p2 = p3 = ··· = pn, R ≦ R′, implies cost R ≦ cost R′. This is a generalization of some known results. A new consequence is that the move-up-k + 1 rule is more costly than the move-up-k rule and the move-to-front rule is the most costly of all move-forward rules.
Accurate and asymptotic results for distributions of scan statistics
Authors: Gates D. J. , Westcott M.
Published: April 2006

We derive asymptotic forms for the distributions of k-point scan statistics as the interval L under study becomes infinite, while k and the window length are held fixed. In the Poisson case the intensity is also held fixed. In the uniform case the number of points N becomes infinite and N/L tends to a limit, representing a limiting intensity. These results are made explicit for k = 3, and in the Poisson case provide approximations which are typically accurate to six or seven figures, even for small L.
Inequalities with applications to percolation and reliability
Authors: Van Den Berg J. , Kesten H.
Published: April 2006

A probability measure μ on ℝn+ is defined to be strongly new better than used (SNBU) if for all increasing subsets . For n = 1 this is equivalent to being new better than used (NBU distributions play an important role in reliability theory). We derive an inequality concerning products of NBU probability measures, which has as a consequence that if μ1, μ2, ···, μn are NBU probability measures on ℝ+, then the product-measure μ = μ × μ2 × ··· × μn on ℝn+ is SNBU. A discrete analog (i.e., with N instead of ℝ+) also holds.

Applications are given to reliability and percolation. The latter are based on a new inequality for Bernoulli sequences, going in the opposite direction to the FKG–Harris inequality. The main application (3.15) gives a lower bound for the tail of the cluster size distribution for bond-percolation at the critical probability. Further applications are simplified proofs of some known results in percolation. A more general inequality (which contains the above as well as the FKG-Harris inequality) is conjectured, and connections with an inequality of Hammersley [12] and others ([17], [19] and [7]) are indicated.
Mutations, perturbations and evolutionarily stable strategies
Authors: Hines W. G. S.
Published: April 2006

The changes in diversity of competitive strategies in a Maynard Smith population model with mixed strategies are related to the changes in population mean strategy. The effects of slight mutations in strategy frequencies, and of slight perturbations of the contest payoff rules are then investigated, and found to increase and decrease diversity respectively (to a third-order approximation). A relation among mutational effects, payoff perturbation effects and stable population diversity is suggested.
Variability orderings related to coverage problems on the circle
Authors: Huffer Fred
Published: April 2006

Suppose that n arcs with random lengths having distributions F1, F2, · ··, Fn are placed uniformly and independently on a circle. This paper presents inequalities which tell how certain distributions and probabilities change as the variability of the distributions Fl, F2, ··, Fn is increased. A distribution F is considered to be more variable than G if f h(x)dF(x) ≧ h(x)dG(x) for all convex functions h.
Pseudo-conservation laws in cyclic-service systems
Authors: Boxma O. J. , Groenendijk W. P.
Published: April 2006

This paper considers single-server, multi-queue systems with cyclic service. Non-zero switch-over times of the server between consecutive queues are assumed. A stochastic decomposition for the amount of work in such systems is obtained. This decomposition allows a short derivation of a ‘pseudo-conservation law' for a weighted sum of the mean waiting times at the various queues. Thus several recently proved conservation laws are generalised and explained.
On almost sure convergence of an erosion process due to Todorovic and Gani
Authors: Puri Prem S.
Published: April 2006

The questions of almost sure convergence of the sequence Xn defined below in (1) as well as that of to a finite limit are settled here. These sequences arise in a simple stochastic model for crop erosion considered by Todorovic and Gani (1987).
Approximating last-exit probabilities of a random walk, by application to conditional queue length moments within busy periods of M/GI/1 queues
Authors: Daley D. J. , Servi L. D.
Published: April 2006

Certain last-exit and first-passage probabilities for random walks are approximated via a heuristic method suggested by a ladder variable argument. They yield satisfactory approximations of the first- and second-order moments of the queue length within a busy period of an M/D/1 queue. The approximation is applied to the wider class of random walks that arise in studying M/GI/1 queues. For gamma-distributed service times the queue length distribution is independent of the arrival rate. For other distributions where the arrival rate affects the queue length distribution, we have to use conjugate distributions in order to exploit a local central limit property. The limit underlying the approximation has the nature of a Brownian excursion.

The source of the problem lies in recent queueing inference work; the connection with Takács' interests comes from both queueing theory and the ballot theorem.
Randomly perturbed vibrations
Authors: Elshamy M.
Published: April 2006

Let uε(t, x) be the position at time t of a point x on a string, where the time variable t varies in an interval I: = [0, T], T is a fixed positive time, and the space variable x varies in an interval J. The string is performing forced vibrations and also under the influence of small stochastic perturbations of intensity ε. We consider two kinds of random perturbations, one in the form of initial white noise, and the other is a nonlinear random forcing which involves the formal derivative of a Brownian sheet. When J has finite endpoints, a Dirichlet boundary condition is imposed for the solutions of the resulting non-linear wave equation. Assuming that the initial conditions are of sufficient regularity, we analyze the deviations uε(t, x) from u0(t, x), the unperturbed position function, as the intensity of perturbation ε ↓ 0 in the uniform topology. We also discuss some continuity properties of the realization of the solutions uε(t, x).
Influence of phosphorus level and soaking of food on phosphorus availability and performance in growing-finishing pigs
Authors: Lyberg K. , Simonsson A. , Lindberg J. E.
Published: April 2006

Abstrct

The effects of 1-h soaking of a pig diet based on wheat and barley with low (4·1 g P per kg) and high (6·8 g P per kg) total phosphorus (P) content on total tract apparent digestibility and performance in growing-finishing pigs were studied in a balance and a performance trial respectively. Phosphorus bound to inositol penta- and hexaphosphate (IP5-IP6) was reduced by proportionately 0·1 in the soaked food. Soaking numerically increased the apparent digestibility of P. The digestibility of P did not differ between the dry high P and the soaked low P. Excretion of P in urine was correlated (R2= 0·84) with the intake of digestible P. The average daily weight gain, final body weight and carcass weight were lower (P< 0·001), and the energy conversion ratio was higher (P< 0·001) in the dry low P treatment than in the other treatments. Pigs on the low P diets had lower levels of inorganic P in serum (P< 0·01) and slightly higher serum Ca values (P< 0·05) and there were no effects of soaking. The density of femur was lower (P< 0·01) in both the low P treatments than in the high P treatments, and soaking of the low P diet improved (P< 0·01) femur density. In conclusion, a 1-h soaking of pig food in water appears to be sufficient to improve P availability and growth performance.
Measuring children’s participation in recreation and leisure activities: construct validation of the CAPE and PAC
Authors: King G. A. , Law M. , King S. , Hurley P. , Hanna S. , Kertoy M. , Rosenbaum P.
Published: April 2006

There is a need for psychometrically sound measures of children’s participation in recreation and leisure activities, for both clinical and research purposes. This paper provides information about the construct validity of the Children’s Assessment of Participation and Enjoyment (CAPE) and its companion measure, Preferences for Activities of Children (PAC). These measures are appropriate for children and youth with and without disabilities between the ages of 6 and 21 years. They provide information about six dimensions of participation (i.e. diversity, intensity, where, with whom, enjoyment and preference) and two categories of recreation and leisure activities: (i) formal and informal activities; and (ii) five types of activities (recreational, active physical, social, skill‐based and self‐improvement). This paper presents information about the performance of the CAPE and PAC activity type scores using data from a study involving 427 children with physical disabilities between the ages of 6 and 15 years. Intensity, enjoyment and preference scores were significantly correlated with environmental, family and child variables, in expected ways. Predictions also were supported with respect to differences in mean scores for boys vs. girls, and children in various age groups. The information substantiates the construct validity of the measures. The clinical and research utility of the measures are discussed.
Bone metabolism markers predict increase in bone mass, height and sitting height during puberty depending on the VDR Fok1 genotype
Authors: Terpstra L. , Knol D. L. , Van Coeverden S. C. , Delemarre‐van de Waal H. A.
Published: April 2006

Objectives  Longitudinal growth and bone mass accumulation are two important phenomena during puberty, resulting in attainment of peak bone mass (PBM) and final height. They are thought to be under strong genetic control, with the vitamin D receptor (VDR) gene being among the candidate genes. Bone metabolism markers are reported to be good predictors of longitudinal growth and bone mass increase. The purpose of this longitudinal study was to evaluate whether bone metabolism markers predict bone mass and height increase differently according to Fok1 VDR genotype throughout puberty in healthy adolescents.

Patients and measurements  At the start of the study 130 girls were aged 10·8 (range 8·5–12·8) years and 125 boys were aged 11·8 (range 9·4–14·6) years at the first visit. Markers of bone formation and bone resorption were measured at the first visit, as well as height and sitting height (SH), and bone mineral content (BMC) of the lumbar spine, femur, arm and total body. All measurements were repeated after 2 years.

Results  A higher BMC of the femur, distal arm and total body was found in ff boys at the first visit, which was not related to higher levels of bone metabolism markers in this group. In girls, no differences between genotypes were seen in BMC (increase). However, concentrations of markers of bone formation [alkaline phosphatase (AP), bone‐specific alkaline phosphatase (BAP), procollagen aminoterminal propeptide (PINP)] and bone resorption [type I carboxyterminal telopeptide (ICTP)] were higher in ff girls. Regression coefficients between bone metabolism markers and bone mass increase differed according to genotype and sex. A similar pattern was found for height and SH (increase), the latter as a representative of growth of the axial skeleton, mainly consisting of cancellous bone.

Conclusions  Our data suggest that the predicting capacities of bone metabolism markers on bone mass (increase), height and SH (increase) are genotype dependent. Their use as predictors of final height or PBM therefore remains questionable without knowing the genotype.