bluuebunny/crossref_metadata_2025 huggingface dataset:
Calculating exit times for series Jackson networks
Authors: Massey William A.
Published: April 2006

We define a new family of special functions that we call lattice Bessel functions. They are indexed by the N-dimensional integer lattice such that they reduce to modified Bessel functions when N = 1, and the exponential function when N = 0. The transition probabilities for an M/M/1 queue going from one state to another before becoming idle (exiting at 0) can be solved in terms of modified Bessel functions. In this paper, we use lattice Bessel functions to solve the analogous problem involving the exit time from the interior of the positive orthant of the N-dimensional lattice for a series Jackson network with N nodes. These special functions allow us to derive asymptotic expansions for the taboo transition probabilities, as well as for the tail of the exit-time distribution.
On limiting behavior of ordinary and conditional first-passage times for a class of birth-death processes
Authors: Sumita U.
Published: April 2006

Let N(t) be a birth-death process on 𝒩= {0, 1, 2, ·· ·} governed by the transition rates λn > 0 (n ≧ 0) and μn > 0 (n ≧ 1) where λn → λ > 0 and μn → μ > 0 as n → ∞ and ρ = λ/μ. Let Tmn be the first-passage time of N(t) from m to n and define It is shown that, when converges in distribution to TBP(μ,λ) as n → ∞ where TΒΡ (μ,λ) is the server busy period of an M/M/1 queueing system with arrival rate μ and service rate λ. Correspondingly T0n/E[T0n] converges to 1 with probability 1 as n →∞. Of related interest is the conditional first-passage time mTrn of N(t) from r to n given no visit to m where m < r < n. As we shall see, the conditional first-passage time of N(t) can be viewed as an ordinary first-passage time of a modified birth-death process M(t) governed by where are generated from λn and μn. Furthermore it is shown that for and while for and This enables one to establish the relation between the limiting behavior of the ordinary first-passage times and that of the conditional first-passage times.
Learning algorithms for Markov decision processes
Authors: Kurano Masami
Published: April 2006

This study is concerned with finite Markov decision processes whose dynamics and reward structure are unknown but the state is observable exactly.

We establish a learning algorithm which yields an optimal policy and construct an adaptive policy which is optimal under the average expected reward criterion.
On the probability that a random point is the jth nearest neighbour to its own kth nearest neighbour
Authors: Henze Norbert
Published: April 2006

In a homogeneous Poisson process in Rd, consider an arbitrary point X and let Y be its kth nearest neighbour. Denote by Rk the rank of X in the proximity order defined by Y, i.e., Rk = j if X is the jth nearest neighbour to Y. A representation for Rk in terms of a sum of independent random variables is obtained, and the limiting distribution of Rk, as k →∞, is shown to be normal. This result generalizes to mixtures of Poisson processes.
On higher-dimensional analogues of the arc-sine law
Authors: Bingham N. H. , Doney R. A.
Published: April 2006

The arc-sine laws form one of the cornerstones of classical one-dimensional fluctuation theory. In higher dimensions, knowledge of fluctuation theory remains a great deal less complete. Motivated by this, we consider higher-dimensional analogues of the classical arc-sine laws.
On the maximum of gaussian fourier series emerging in the analysis of random vibrations
Authors: Orsingher Enzo
Published: April 2006

In this paper we study the maximum of Gaussian Fourier series emerging in the analysis of random vibrations of a finite string. Evaluating the distribution of the maximal displacement corresponds to the analysis of the maximum for the related Gaussian Fourier series with independent coefficients.

When vibrations are triggered by an initial white noise disturbance (where the instantaneous form of the vibrating string is composed of three processes pieced together) we give upper bounds for the maximal displacement.

In the last section we consider forced vibrations at special instants where the instantaneous form of the vibrating string has the structure of a Brownian bridge. This enables us to give the exact distribution of the maximum for the related sine series.
Time series regression with unequally spaced data
Authors: Jones Richard H.
Published: April 2006

Regression analysis with stationary errors is extended to the case when observations are not equally spaced. The errors are modelled as either a discrete-time ARMA process with missing observations, or as a continuous-time autoregression with observational error observed at arbitrary times. Using a state-space representation, a Kalman filter is used to calculate the exact likelihood. The linear regression coefficients are separated out of the likelihood so non-linear optimization is required only with respect to the parameters modelling the error structure.
A note on the multitype Markov branching process
Authors: Gadag V. G.
Published: April 2006

We consider a supercritical, p-dimensional Markov branching process (MBP). Based on the finite and the infinite lines of descent of particles of this p-dimensional MBP, we construct an associated 2p-dimensional process. We show that such a process is a 2p-dimensional, supercritical MBP. This 2p-dimensional process retains the branching property when conditioned on the sets of extinction and non-extinction. Asymptotic results and central limit theorems for the associated process and the original process are established by using the results of Gadag and Rajarshi (1987).
Some remarks on Brownian motion with drift
Authors: Doney R. A. , Grey D. R.
Published: April 2006

Certain limit theorems due to Berman involve the total time spent by Brownian motion with positive drift below an independent exponentially distributed level. Imhof has calculated the density function and shown that this random variable has two interesting probabilistic properties. We give sample path arguments which explain these two facts.
On passage and conditional passage times for Markov chains in continuous time
Authors: Kijima Masaaki
Published: April 2006

Let X(t) be a temporally homogeneous irreducible Markov chain in continuous time defined on . For k < i < j, let H = {k + 1, ···, j − 1} and let kTij (jTik) be the upward (downward) conditional first-passage time of X(t) from i to j(k) given no visit to . These conditional passage times are studied through first-passage times of a modified chain HX(t) constructed by making the set of states absorbing. It will be shown that the densities of kTij and jTik for any birth-death process are unimodal and the modes kmij (jmik) of the unimodal densities are non-increasing (non-decreasing) with respect to i. Some distribution properties of kTij and jTik for a time-reversible Markov chain are presented. Symmetry among kTij, jTik, and is also discussed, where , and are conditional passage times of the reversed process of X(t).
Avalanches of electrons in a gas
Authors: Steutel F. W.
Published: April 2006

The motion of electrons through a gas of particles is modelled as a two-state process: an electron is alternatingly moving and being held captive by a non-moving particle, during exponentially distributed periods.

The model contains a parameter p, the probability that collision of an electron with a gas particle does not lead to its capture but produces an extra electron.

The quantity of interest is the current C(t) produced by the moving electrons, as a function of time.
Stochastic monotonicity properties of multiserver queues with impatient customers
Authors: Bhattacharya Partha P. , Ephremides Anthony
Published: April 2006

We consider multiserver queues in which a customer is lost whenever its waiting time is larger than its (possibly random) deadline. For such systems, the number of (successful) departures and the number of customers lost over a time interval are the performance measures of interest. We show that these quantities are (stochastically) monotone functions of the arrival, service and deadline processes.
Estimation of the density in a stationary Boolean model
Authors: Schmitt Michel
Published: April 2006

A new and practically tractable formula for estimating the intensity of the underlying Poisson process of a Boolean model is given, assuming only almost sure boundedness of the primary grain.
Some results involving the maximum of Brownian motion
Authors: Doney R. A.
Published: April 2006

If X is a Brownian motion with drift and γ = inf{t > 0: Mt = t} we derive the joint density of the triple {U, γ, Δ}, where and Δ= γ —Xγ. In the case δ = 0 it follows easily from this that Δ has an Exp(2) distribution and this in turn implies the rather surprising result that if τ= inf{t > 0: Xt = Mt = t}, then Pr{τ = 0} = 0 and . We also derive various other distributional results involving the pair (X, M), including for example the distribution of ; in particular we show that, in case δ. = 1, when Pr{0 < τ < ∞} = 1, the ratio τ+/τ has the arc-sine distribution.
Some characterizations of the exponential and geometric distributions arising in a queueing system with an unreliable server
Authors: Huang Wen-Jang , Shoung Jyh-Ming
Published: April 2006

In this article, we generalize results by Dimitrov and Khalil (1990), Khalil et al. (1991), and van Harn and Steutel (1991) and obtain some characterizations of the exponential and geometric laws.
Processes with associated increments
Authors: Glasserman Paul
Published: April 2006

We derive conditions under which the increments of a vector process are associated — i.e. under which all pairs of increasing functions of the increments are positively correlated. The process itself is associated if it is generated by a family of associated and monotone kernels. We show that the increments are associated if the kernels are associated and, in a suitable sense, convex. In the Markov case, we note a connection between associated increments and temporal stochastic convexity.

Our analysis is motivated by a question in variance reduction: assuming that a normalized process and its normalized compensator converge to the same value, which is the better estimator of that limit? Under some additional hypotheses we show that, for processes with conditionally associated increments, the compensator has smaller asymptotic variance.
On a decomposition result for a class of vacation queueing systems
Authors: Loris-Teghem Jacqueline
Published: April 2006

We consider a single-server infinite-capacity queueing sysem with Poisson arrivals of customer groups of random size and a general service time distribution, the server of which applies a general exhaustive service vacation policy. We are concerned with the steady-state distribution of the actual waiting time of a customer arriving while the server is active.
Slepian models for non-stationary Gaussian processes
Authors: Gadrich Tamar , Adler Robert J.
Published: April 2006

We give explicit expressions for the Slepian model process of non-stationary Gaussian processes following level crossings and local maxima. We also include a detailed analysis of the high-level case.
AB percolation on bond-decorated graphs
Authors: Appel Martin J. B. , Wierman John C.
Published: April 2006

It is known [8] that a certain class of bond-decorated graphs exhibits multiple AB percolation phase transitions. Sufficient conditions are given under which the corresponding AB percolation critical probabilities may be identified as points of intersection of the graph of a certain polynomial with the boundary of the percolative region of an associated two-parameter bond-site percolation model on the underlying undecorated graph. The main result of the article is used to prove that the graphs in [8] exhibit multiple AB percolation critical probabilities. The possibility of identifying AB percolation critical exponents with corresponding limits for the bond-site model is discussed.
On rate conservation for non-stationary processes
Authors: Mazumdar Ravi , Kannurpatti Raghavan , Rosenberg Catherine
Published: April 2006

This paper extends the rate conservation principle to cadlag processes whose jumps form a non-stationary point process with a time-dependent intensity. It is shown that this is a direct consequence of path integration and the strong law of large numbers for local martingales. When specialized to mean rates a non-stationary version of Miyazawa's result is obtained which is recovered in the stationary case. Some applications of the result are also given.
On a characterization of the exponential distribution
Authors: Van Harn K. , Steutel F. W.
Published: April 2006

The characterization of the exponential distribution as given by Dimitrov and Khalil (1990) is improved by substantially weakening the conditions.
A note on extended uniformization for non-exponential stochastic networks
Authors: Van Dijk Nico M.
Published: April 2006

The standard uniformization technique for continuous-time Markov chains is generalized to non-exponential stochastic networks.
Multivariate imperfect repair
Authors: Sheu Shey-Huei , Griffith William S.
Published: April 2006

We consider models of systems of components with dependent life-lengths having certain multivariate distributions. Upon failure, components are repaired. Two types of repair are possible. After perfect repair, a unit has the same life distribution as a new item. After imperfect repair, a unit has the life distribution of an item which is of the same age but has never failed. Different sources of failure are distinguished and affect the probabilities of perfect and imperfect repair.
Burn-in and mixed populations
Authors: Block Henry W. , Mi Jie , Savits Thomas H.
Published: April 2006

Burn-in is a procedure used for eliminating weak components in a mixed population. In this paper we focus on general mixed populations. Three types of results are established. First, it is shown that any mixed population displays a type of monotonicity property which is appropriate for burn-in. Second, it is shown that if, asymptotically, components have constant failure rates, then the mixed population will also asymptotically have a constant failure rate and this will correspond to the rate of the strongest subpopulation of the mixture. Finally, it is shown for a reasonable cost function, that if one mixture distribution dominates another in a strong sense, the resulting mixture of the dominant distribution will have larger optimal burn-in time.
On zero-avoiding transition probabilities of an r-node tandem queue: a combinatorial approach
Authors: Böhm Walter , Jain J. L. , Mohanty S. G.
Published: April 2006

In this paper we present a simple combinatorial approach for the derivation of zero-avoiding transition probabilities in a Markovian r-node series Jackson network. The method we propose offers two advantages: first, it is conceptually simple because it is based on transition counts between the nodes and does not require a tensor representation of the network. Second, the method provides us with a very efficient technique for numerical computation of zero-avoiding transition probabilities.
A general risk process and its properties
Authors: Scheike Thomas H.
Published: April 2006

We construct a risk process, where the law of the next jump time or jump size can depend on the past through earlier jump times and jump sizes. Some distributional properties of this process are established. The compensator is found and some martingale properties are discussed.
Equivalence of two descriptions of the ages of alleles
Authors: Ethier S. N.
Published: April 2006

It is shown that the two descriptions of the ages of alleles corresponding to the two formulations of the stationary infinitely-many-neutral-alleles diffusion model discussed by Ethier (1990a) are equivalent.
The M/G/1 processor sharing queue as the almost sure limit of feedback queues
Authors: Resing J. A. C. , Hooghiemstra G. , Keane M. S.
Published: April 2006

In the paper a probabilistic coupling between the M/G/1 processor sharing queue and the M/M/1 feedback queue, with general feedback probabilities, is established. This coupling is then used to prove the almost sure convergence of sojourn times in the feedback model to sojourn times in the M/G/1 processor sharing queue. Using the theory of regenerative processes it follows that for stable queues the stationary distribution of the sojourn time in the feedback model converges in law to the corresponding distribution in the processor sharing model. The results do not depend on Poisson arrival times, but are also valid for general arrival processes.
The number of extreme points in the convex hull of a random sample
Authors: Aldous David J. , Fristedt Bert , Griffin Philip S. , Pruitt William E.
Published: April 2006

Let {Xk} be an i.i.d. sequence taking values in ℝ2 with the radial and spherical components independent and the radial component having a distribution with slowly varying tail. The number of extreme points in the convex hull of {X1, · ··, Xn} is shown to have a limiting distribution which is obtained explicitly. Precise information about the mean and variance of the limit distribution is obtained.
A class of bandit problems yielding myopic optimal strategies
Authors: Banks Jeffrey S. , Sundaram Rangarajan K.
Published: April 2006

We consider the class of bandit problems in which each of the n ≧ 2 independent arms generates rewards according to one of the same two reward distributions, and discounting is geometric over an infinite horizon. We show that the dynamic allocation index of Gittins and Jones (1974) in this context is strictly increasing in the probability that an arm is the better of the two distributions. It follows as an immediate consequence that myopic strategies are the uniquely optimal strategies in this class of bandit problems, regardless of the value of the discount parameter or the shape of the reward distributions. Some implications of this result for bandits with Bernoulli reward distributions are given.
Work-modulated queues with applications to storage processes
Authors: Browne Sid , Sigman Karl
Published: April 2006

We study two FIFO single-server queueing models in which both the arrival and service processes are modulated by the amount of work in the system. In the first model, the nth customer's service time, Sn, depends upon their delay, Dn, in a general Markovian way and the arrival process is a non-stationary Poisson process (NSPP) modulated by work, that is, with an intensity that is a general deterministic function g of work in system V(t). Some examples are provided. In our second model, the arrivals once again form a work-modulated NSPP, but, each customer brings a job consisting of an amount of work to be processed that is i.i.d. and the service rate is a general deterministic function r of work. This model can be viewed as a storage (dam) model (Brockwell et al. (1982)), but, unlike previous related literature, (where the input is assumed work-independent and stationary), we allow a work-modulated NSPP. Our approach involves an elementary use of Foster's criterion (via Tweedie (1976)) and in addition to obtaining new results, we obtain new and simplified proofs of stability for some known models. Using further criteria of Tweedie, we establish sufficient conditions for the steady-state distribution of customer delay and sojourn time to have finite moments.
A queueing network analysis of dynamic reconfigurability in a hierarchical information network
Authors: Bhat U. Narayan , Nance Richard E.
Published: April 2006

Hierarchical information networks are important in applications where the information management must support an existing tree-structured organization. Embedded computer-communication systems in military applications, with a dominant hierarchical command structure, are the most prominent examples. Also typical of such applications is the variability in message demand (both sources and intensity) depending on the external conditions encountered by the encapsulating system (the system supported by the embedded computer-communication system). Using a queueing network model for a hierarchical information network, we compare the effect of limited dynamic reconfiguration on expected transmission delays. The limited reconfigurability takes the form of apex transition among a proper subset of the communication nodes designated as the apex candidate set. Each apex candidate can assume the ultimate position under designated conditions. This network architecture is called a dynamic hierarchy. The model includes N + 1 nodes (0, …, N) with 0 identifying the apex node. We assume that message processing at each node is described by an M/M/1 model (single server with Poisson arrivals and exponential service times). Further message transfers among the nodes are served by communication links which also behave as M/M/1 queues.

Two distinctive features characterize the queueing network model:

1. The assignment of a set of weights to the nodes dependent on the hierarchical level reflects the increasing importance of information as it is transferred to higher levels.

2. The dynamic hierarchy requires a communications protocol that partitions the analysis of network delay into three periods: regular operation, reconfiguration, and adjustment. Characterization of the performance of the dynamic hierarchy entails the description of message transmission delay as a composite of the three periods.
On a class of two-dimensional nearest-neighbour random walks
Authors: Cohen J. W.
Published: April 2006

For positive recurrent nearest-neighbour, semi-homogeneous random walks on the lattice {0, 1, 2, …} X {0, 1, 2, …} the bivariate generating function of the stationary distribution is analysed for the case where one-step transitions to the north, north-east and east at interior points of the state space all have zero probability. It is shown that this generating function can be represented by meromorphic functions. The construction of this representation is exposed for a variety of one-step transition vectors at the boundary points of the state space.
Estimation of cause-effect relationship under noise
Authors: Prékopa András
Published: April 2006

Events that occur consecutively or simultaneously cause some other event as effect. The latter can be observed with noise, and the problem is to estimate the weights of the causes in the realization of the effect.
Value iteration in a class of average controlled Markov chains with unbounded costs: necessary and sufficient conditions for pointwise convergence
Authors: Cavazos-Cadena Rolando , Fernández-Gaucherand Emmanuel
Published: April 2006

This work concerns controlled Markov chains with denumerable state space, (possibly) unbounded cost function, and an expected average cost criterion. Under a Lyapunov function condition, together with mild continuity-compactness assumptions, a simple necessary and sufficient criterion is given so that the relative value functions and differential costs produced by the value iteration scheme converge pointwise to the solution of the optimality equation; this criterion is applied to obtain convergence results when the cost function is bounded below or bounded above.
Two chain-transformations and their applications to quantiles
Authors: Bertoin J. , Chaumont L. , Yor M.
Published: April 2006

We describe two chain-transformations which explain and extend identities for order statistics and quantiles proved by Wendel, Port and, more recently, by Dassios.
Understanding the Wiener–Hopf factorization for the simple random walk
Authors: Kennedy Joanne
Published: April 2006

We give a sample path proof of the well-known Wiener–Hopf identity F = G– + G+ – G– ∗G+ which relates the ladder-height distributions G– and G+ of a simple random walk to the step distribution F. Unlike previous approaches this direct proof is both simple and intuitive.
A reversibility relationship for two Markovian time series models by stationary exponential tailed distribution
Authors: Littlejohn R. P.
Published: April 2006

The continuous autoregressive and minification stationary non-negative time series models discussed by Chernick et al. (1988) are generalized to model marginal distributions which have atoms of mass at zero. The reversibility theorem relating these processes with exponential marginal distributions is extended to the case where the marginal distribution has exponential tail.
On heavy traffic approximations for transient characteristics of M/M/∞ queues
Authors: Guillemin Fabrice M. , Mazumdar Ravi R. , Simonian Alain D.
Published: April 2006

In this paper, transient characteristics related to excursions of the occupation process of M/M/∞ queues are studied, when the excursion level is large and close to the mean offered load. We show that the classical diffusion approximation by an Ornstein–Uhlenbeck (OU) process captures well the average values of the transient variables considered, while the asymptotic distributions of these variables depart from those corresponding to the OU process. They exhibit, however, equivalent tail behaviour at infinity and numerical evidence shows that they are amazingly close to each other over the whole half-line.
Large deviations for departures from a shared buffer
Authors: O'connell Neil
Published: April 2006

In this paper we describe how the joint large deviation properties of traffic streams are altered when the traffic passes through a shared buffer according to a FCFS service policy with stochastic service capacity. We also consider the stationary case, proving large deviation principles for the state of the system in equilibrium and for departures from an equilibrium system.
The geometric convergence rate of a Lindley random walk
Authors: Lund Robert B.
Published: April 2006

Let {Xn} be the Lindley random walk on [0,∞) defined by . Here, {An} is a sequence of independent and identically distributed random variables. When for some r > 1, {Xn} converges at a geometric rate in total variation to an invariant distribution π; i.e. there exists s > 1 such that for every initial state . In this communication we supply a short proof and some extensions of a large deviations result initially due to Veraverbeke and Teugels (1975, 1976): the largest s satisfying the above relationship is and satisfies φ ‘(r0) = 0.
Random perturbations of recursive sequences with an application to an epidemic model
Authors: Viaud Daniel Pierre Loti
Published: April 2006

We investigate the asymptotic sample path behaviour of a randomly perturbed discrete-time dynamical system. We consider the case where the trajectories of the non-perturbed dynamical system are attracted by a finite number of limit sets and characterize a case where this property remains valid for the perturbed dynamical system when the perturbation converges to zero. For this purpose, no further assumptions on the perturbation are needed and our main condition applies to the limit sets of the non-perturbed dynamical system. When the limit sets reduce to limit points we show that this main condition is more general than the usual assumption of the existence of a Lyapunov function for the non-perturbed dynamical system. An application to an epidemic model is given to illustrate our results.
A matrix equation approach to solving recurrence relations in two-dimensional random walks
Authors: Miller James W.
Published: April 2006

The purpose of this paper is to provide explicit formulas for a variety of probabilistic quantities associated with anasymmetric random walk on a finite rectangular lattice with absorbing barriers.Quantities of interest include probabilities that a walker will exit the lattice onto some particular set of boundary states, the expected duration of the walk, and the expected number of visits to one state given a start in another. These quantities are shown to satisfy two-dimensional recurrence relations that are very similar in structure. In each case, the recurrence relations may be represented by matrix equations of the formX=AX+XB+C, whereAandBare tridiagonal Toeplitz matrices. The spectral properties ofAandBare investigated and used to provide solutions to this matrix equation. The solutions to the matrix equations then lead to solutions for the recurrence relations in very general cases.
Weak convergence of conditioned birth-death processes in discrete time
Authors: Schrijner Pauline , Van Doorn Erik A.
Published: April 2006

We consider a discrete-time birth-death process on the non-negative integers with −1 as an absorbing state and study the limiting behaviour as n → ∞ of the process conditioned on non-absorption until time n. By proving that a condition recently proposed by Martinez and Vares is vacuously true, we establish that the conditioned process is always weakly convergent when all self-transition probabilities are zero. In the aperiodic case we obtain a necessary and sufficient condition for weak convergence.
On wald-type optimal stopping for Brownian motion
Authors: Graversen S. E. , Peškir G.
Published: April 2006

The solution is presented to all optimal stopping problems of the form supτE(G(|Β τ |) – cτ), where is standard Brownian motion and the supremum is taken over all stopping times τ for B with finite expectation, while the map G : ℝ+ → ℝ satisfies for some being given and fixed. The optimal stopping time is shown to be the hitting time by the reflecting Brownian motion of the set of all (approximate) maximum points of the map . The method of proof relies upon Wald's identity for Brownian motion and simple real analysis arguments. A simple proof of the Dubins–Jacka–Schwarz–Shepp–Shiryaev (square root of two) maximal inequality for randomly stopped Brownian motion is given as an application.
On allocation of spares at component level versus system level
Authors: Singh Harshinder , Singh R. S.
Published: April 2006

Design engineers are well aware that a system where active spare allocation is made at the component level has a lifetime stochastically larger than the corresponding system where active spare allocation is made at the system level. In view of the importance of hazard rate ordering in reliability and survival analysis, Boland and El-Neweihi (1995) recently investigated this principle in hazard rate ordering and demonstrated that it does not hold in general. They showed that for a 2-out-of-n system with independent and identical components and spares, active spare allocation at the component level is superior to active spare allocation at the system level. They conjectured that such a principle holds in general for a k-out-of-n system when components and spares are independent and identical. We prove that for a k-out-of-n system where components and spares have independent and identical life distributions active spare allocation at the component level is superior to active spare allocation at the system level in likelihood ratio ordering. This is stronger than hazard rate ordering, thus establishing the conjecture of Boland and El-Neweihi (1995).
The evolution and measurement of a population of pairs
Authors: Jakeman Eric , Phayre Sean , Renshaw Eric
Published: April 2006

The statistical properties of a population of immigrant pairs of individuals subject to loss through emigration are calculated. Exact analytical results are obtained which exhibit characteristic even–odd effects. The population is monitored externally by counting the number of emigrants leaving in a fixed time interval. The integrated statistics for this process are evaluated and it is shown that under certain conditions only even numbers of individuals will be observed.
A monotonicity result for a single-server loss system
Authors: Chao Xiuli , Dai Liyi
Published: April 2006

We consider a family of M(t)/M(t)/1/1 loss systems with arrival and service intensities (λt (c), μt (c)) = (λct, μct), where (λt, μt) are governed by an irreducible Markov process with infinitesimal generator Q = (qij)m × m such that (λt, μt) = (λi, μi) when the Markov process is in state i. Based on matrix analysis we show that the blocking probability is decreasing in c in the interval [0, c∗], where c∗ = 1/maxi Σj≠iqij/(λi + μi). Two special cases are studied for which the result can be extended to all c. These results support Ross's conjecture that a more regular arrival (and service) process leads to a smaller blocking probability.
A strong law and a central limit theorem for controlled Galton-Watson processes
Authors: Viaud Daniel Pierre Loti
Published: April 2006

Through the study of a simple embedded martingale we obtain an extension of the Kesten–Stigum theorem and prove a central limit theorem for controlled Galton-Watson processes.
ABpercolation on plane triangulations is unimodal
Authors: Appel Martin J. B.
Published: April 2006

Let ℱ be a countable plane triangulation embedded in ℝ2in such a way that no bounded region contains more than finitely many vertices, and letPpbe Bernoulli (p) product measure on the vertex set of ℱ. LetEbe the event that a fixed vertex belongs to an infinite path whose vertices alternate states sequentially. It is shown that theAB percolation probability function θΑΒ(p) =Pp(E) is non-decreasing inpfor 0 ≦p≦ ½. By symmetry,θAΒ(p) is therefore unimodal on [0, 1]. This result partially verifies a conjecture due to Halley and stands in contrast to the examples of Łuczak and Wierman.
An unreliable server characterization of the exponential distribution
Authors: Galambos Janos , Hagwood Charles
Published: April 2006

Consider a workstation with one server, performing jobs with a service time, Y, having distribution function, G(t). Assume that the station is unreliable, in that it occasionally breaks down. The station is instantaneously repaired, and the server restarts the uncompleted job from the beginning. Let T denote the time it takes to complete each job. If G(t) is exponential with parameter A, then because of the lack-of-memory property of the exponential, P (T > t) = Ḡ(t) =exp(−γt), irrespective of when and how the failures occur. This property also characterizes the exponential distribution.
A sample path analysis of the delay in the M/G/C system
Authors: Seshadri Sridhar
Published: April 2006

Using sample path analysis we show that under the same load the mean delay in queue in the M/G/2 system is smaller than that in the corresponding M/G/1 system, when the service time has either the DMRL or NBU property and the service discipline is FCFS. The proof technique uses a new device that equalizes the work in a two server system with that in a single sterver system. Other interesting quantities such as the average difference in work between the two servers in the GI/G/2 system and an exact alternate derivation of the mean delay in the M/M/2 system from sample path analysis are presented. For the same load, we also show that the mean delay in the M/G/C system with general service time distribution is smaller than that in the M/G/1 system when the traffic intensity is less than 1/c.
A new approach to the G/G/1 queue with generalized setup time and exhaustive service
Authors: Li Huan , Zhu Yixin
Published: April 2006

We consider a class of G/G/1 queueing models with independent generalized setup time and exhaustive service. It is shown that a variety of single-server queueing systems with service interruption are special cases of our model. We give a simple computational scheme for the moments of the stationary waiting time and sojourn time. Our numerical investigations indicate that the algorithm is quite accurate and fast in general. For the M/G/1 case, we are able to derive a recursive formula for the moments of the stationary waiting time, which includes the Takács formula as a special case. It immediately results in the stochastic decompòsition property which can be found in the literature.
Continuity and convergence of the percolation function in continuum percolation
Authors: Sarkar Anish
Published: April 2006

We consider a percolation model on the d-dimensional Euclidean space which consists of spheres centred at the points of a Poisson point process of intensity ?. The radii of the spheres are random and are chosen independently and identically according to a distribution of a positive random variable. We show that the percolation function is continuous everywhere except perhaps at the critical point. Further, we show that the percolation functions converge to the appropriate percolation function except at the critical point when the radius random variables are uniformly bounded and converge weakly to another bounded random variable.
Monotonicity results for MR/GI/1 queues
Authors: Bäuerle Nicole
Published: April 2006

This paper considers queues with a Markov renewal arrival process and a particular transition matrix for the underlying Markov chain. We study the effect that the transition matrix has on the waiting time of the nth customer as well as on the stationary waiting time. The main theorem generalizes results of Szekli et al. (1994a) and partly confirms their conjecture. In this context we show the importance of a new stochastic ordering concept.
Cryo‐Immunogold Electron Microscopy
Authors: Peters Peter J. , Bos Erik , Griekspoor Alexander
Published: April 2006

This unit describes subcellular localization of proteins/antigens using high‐resolution cryo‐immunogold electron microscopy, which allows study of topological biochemistry at the ultrastructural level. This is the most sensitive procedure for immunodetection of antigens on ultrathin sections prepared from chemically fixed cells or tissues, because aldehyde fixation is the only denaturation step. The omission of harsh organic solvents (such as those used for plastic embedding) ensures better preservation of protein antigenicity. Support protocols describe how to embed fixed material in gelatin, cryosection, and mount the sections on Formvar‐coated grids. This unit is accompanied by eleven videos that illustrate many of the procedures used in this unit.
Matches
Authors: Cox Michael
Published: April 2006

The article contains sections titled:

1.

Introduction

2.

History

3.

The Matchmaking Process

3.1.

Splint Manufacture

3.2.

Outer‐Box Making

3.3.

Inner‐Box Making

3.4.

Composition Making

3.5.

Match Assembly Line

4.

Raw Materials

5.

Head Composition

6.

Friction Surfaces

7.

The Chemistry of Matches

8.

Match Testing

9.

Match Standards

10.

Quality Assurance

11.

Safety and Handling
Metals, Surface Treatment
Authors: Kunst Helmut , Haase Brigitte , Malloy James C. , Wittel Klaus , Nestler Montia C. , Nicoll Andrew R. , Erning Ulrich , Rauscher Gerhard
Published: April 2006

The article contains sections titled:

1.

Introduction

2.

Cleaning

2.1.

Cleaning in Aqueous and Nonaqueous Solvents

2.1.1.

Cleaning and Degreasing in Aqueous Media

2.1.2.

Cleaning Agents Based on Organic Solvents

2.1.3.

Cleaning Process Technology

2.2.

Cleaning and Pickling with Salt Baths

2.2.1.

Bath Composition and Properties

2.2.2.

Descaling of Metals

2.2.3.

Casting Cleaning

2.2.4.

Coatings Removal

3.

Phosphating

3.1.

Chemistry

3.2.

Methods of Application

3.3.

Uses of Phosphate Coatings

4.

Case Hardening of Ferrous Metals

4.1.

Case Hardening without Chemical Reaction via Phase Boundary

4.1.1.

Flame Hardening

4.1.2.

Induction Hardening

4.1.3.

Laser Hardening

4.1.4.

Electron Beam Hardening

4.2.

Thermochemical Treatment

4.2.1.

Gas Carburizing

4.2.1.1.

Principles

4.2.1.2.

Properties of Carburized Components

4.2.1.3.

Carburizing Methods

4.2.2.

Nitriding and Nitrocarburizing

4.2.2.1.

Principles

4.2.2.2.

Properties of Nitrided and Nitrocarburized Components

4.2.2.3.

Nitriding and Nitrocarburizing Methods

4.2.3.

Boriding

4.2.3.1.

Principles

4.2.3.2.

Boriding Methods

4.2.4.

Other Thermochemical Processes

5.

Thermal Spraying

5.1.

Methods of Thermal Spraying

5.1.1.

Flame Spraying

5.1.2.

Electric Arc Spraying

5.1.3.

Plasma Spraying

5.1.4.

High‐Velocity Oxy – Fuel Spraying (HVOF)

5.2.

Properties of Thermally Sprayed Coatings

5.3.

Materials

5.3.1.

Spray Coating Materials

5.3.2.

Base Materials

5.4.

Applications

6.

Coloring

7.

Acknowledgement
Chemometrics
Authors: Henrion René , Henrion Günther
Published: April 2006

The article provides an introduction to some of the basic concepts and methods in chemometrics. The first part is devoted to classical univariate statistics with emphasis on estimation and comparison of statistical parameters from one or several measurement series and its application to measurements from chemistry. The second part presents special techniques of data evaluation in analytical chemistry such as calibration, signal processing, and characterizations of analytical procedures. The third and last part introduces modern concepts of multivariate statistics (including multiway data analysis) with applications to chemometrical data sets. Numerical examples serve as illustrations for the presented methods.

The article contains sections titled:

1.

Introduction

2.

Measurements and Statistical Distributions

2.1.

Measurements

2.2.

Statistical Distributions

2.3.

Estimates

2.4.

Accuracy and Precision

3.

Statistical Tests

3.1.

General Procedure

3.2.

Tests on Parameters of One or Two Measurement Series

3.3.

Outliers, Trend and Nonparametric Tests

4.

Comparison of Several Measurement Series

4.1.

Homogeneity of Variances

4.2.

Equality of Expected Values

5.

Regression and Calibration

5.1.

Regression Analysis

5.2.

Calibration

6.

Characterization of Analytical Procedures

7.

Signal Processing

7.1.

Fourier Transform

7.2.

Data Smoothing

7.3.

Signal Resolution

8.

Basic Concepts of Multivariate Methods

8.1.

Objects, Variables, and Data Sets

8.2.

Correlation and Distance Matrices

8.3.

Data Scaling

9.

Factorial Methods

9.1.

Principal Components Analysis

9.2.

Factor Analysis

10.

Classification Methods

10.1.

Cluster Analysis

10.2.

Supervised Classification

11.

Multivariate Regression

11.1.

Multiple Linear Regression

11.2.

Latent Variable Regression

12.

Multidimensional Arrays
Linking geomorphic character, behaviour and condition to fluvial biodiversity: implications for river management
Authors: Chessman Bruce C. , Fryirs Kirstie A. , Brierley Gary J.
Published: April 2006

The River Styles® framework is a geomorphic approach to the classification of river types, assessment of the physical condition of rivers, and planning of physical rehabilitation. However, the linkages between River Styles and aquatic biodiversity conservation are still only weakly developed.

In this study, 41 sites in the Bega River basin in New South Wales, Australia, were classified according to River Style and geomorphic condition, and surveyed for four biological assemblages: diatoms, aquatic and semi‐aquatic macrophytes, aquatic macroinvertebrates and fish.

Each assemblage differed significantly among River Styles. However, in the case of diatoms and fish, these differences could be accounted for by geographic clustering of sites in the same River Style, and a tendency for River Styles to occupy particular altitudinal zones and sizes of streams. This result was attributed to the overriding influences of water quality on diatoms and of altitude‐related variation in water temperature and distance from the ocean on fish. For macrophytes and macroinvertebrates, geomorphic river type appeared to exert a direct influence, probably via variation in physical habitat characteristics.

Geomorphic condition, judged as good, moderate or poor by reference to the inferred natural condition of each River Style, was also significantly associated with differences in biological assemblages other than fish. Twice as many taxa appeared to favour sites in good geomorphic condition as favoured sites in poor condition. Many of the taxa associated with sites in poor condition are alien taxa introduced to Australia since European settlement.

These findings imply that protection of reaches that are in good geomorphic condition is likely to be critical for the maintenance of indigenous biodiversity, and that rehabilitation of geomorphic condition can assist in the rehabilitation of native riverine biota.

Copyright © 2006 John Wiley & Sons, Ltd.
Three‐year mortality in diabetic patients treated with different combinations of insulin secretagogues and metformin
Authors: Monami Matteo , Luzzi Chiara , Lamanna Caterina , Chiasserini Veronica , Addante Filomena , Desideri Carla Maria , Masotti Giulio , Marchionni Niccolò , Mannucci Edoardo
Published: April 2006

Background

Several studies have shown an increase of mortality in diabetic patients treated with combinations of sulphonylureas and biguanides. Comparisons between different insulin secretagogues in combination with metformin with respect to all‐cause mortality have not been reported so far.

Methods

An observational cohort study was performed on a consecutive series of 2002 outpatients with type 2 diabetes mellitus. Of these patients, 696 (34.8%) were receiving combinations of insulin secretagogues and biguanides at enrolment. Three‐year mortality was assessed through research in the City of Florence Registry Office.

Results

During follow‐up, 295 deaths were recorded. Among patients on combined secretagogue and biguanide treatment, glibenclamide was associated with a significantly higher yearly mortality (8.7%) than repaglinide (3.1%; p = 0.002), gliclazide (2.1%; p = 0.001), and glimepiride (0.4%; p < 0.0001). After adjusting for potential confounders (including age; duration of diabetes; Body Mass Index (BMI); lipid profile; HbA1c; insulin treatment; metformin doses; Charlson co‐morbidity score; CCS), mortality remained significantly higher in patients treated with combinations of glibenclamide and metformin when compared to those treated with different insulin secretagogues (OR with 95% CI: 2.09 [1.07;4.11]).

Conclusions

In the present study, sulphonylureas with greater selectivity for β‐cell receptors, such as glimepiride and gliclazide, were associated with a lower mortality when used in combination with metformin in comparison with glibenclamide. Safety of such combinations deserves further investigation. Copyright © 2006 John Wiley & Sons, Ltd.
LACK‐reactive CD4+ T cells require autocrine IL‐2 to mediate susceptibility to Leishmania major
Authors: Gumy Alain , Aseffa Abraham , Rachinel Nicolas , Breton Melanie , Otten Luc , Tacchini‐Cottier Fabienne , Röcken Martin , Doyen Noelle , Acha‐Orbea Hans , Locksley Richard M. , MacDonald H. Robson , Launois Pascal , Louis Jacques
Published: April 2006

Mice from most inbred strains are resistant to infection with Leishmania major whereas mice from BALB strains are highly susceptible. Resistance and susceptibility result from the development of Th1 or Th2 cells, respectively. In this report, we document an IL‐2 mRNA burst, preceding the reported early IL‐4 response, in draining lymph nodes of susceptible mice infected with L. major. Neutralization of IL‐2 during the first days of infection redirected Th1 cell maturation and resistance to L. major, through interference with the rapid IL‐4 transcription in Leishmania homolog of mammalian RACK1 (LACK)‐reactive CD4+ cells. A burst of IL‐2 transcripts also occurred in infected C57BL/6 mice that do not mount an early IL‐4 response. However, although the LACK protein induced IL‐2 transcripts in susceptible mice, it failed to trigger this response in resistant C57BL/6 mice. Reconstitution experiments using C.B.‐17 SCID mice and LACK‐reactive CD4+ T cells from IL‐2–/– BALB/c mice showed that triggering of the early IL‐4 response required autocrine IL‐2. Thus, in C57BL/6 mice, the inability of LACK‐reactive CD4+ T cells to express early IL‐4 mRNA transcription, important for disease progression, appears due to an incapacity of these cells to produce IL‐2.