bluuebunny/crossref_metadata_2025_split huggingface dataset:
The diffusion approximation for tandem queues in heavy traffic
Authors: Harrison J. Michael 
Published: April 2006

Consider a pair of single server queues arranged in series. (This is the simplest example of a queuing network.) In an earlier paper [2], a limit theorem was proved to justify a heavy traffic approximation for the (two-dimensional) equilibrium waiting-time distribution. Specifically the waiting-time distribution was shown to be approximated by the limit distribution F of a certain vector stochastic process Z. The process Z was defined as an explicit, but relatively complicated, transformation of vector Brownian motion, and the general problem of determining F was left unsolved.It is shown in this paper that Z is a diffusion process (continuous strong Markov process) whose state space S is the non-negative quadrant. On the interior of S, the process behaves as an ordinary vector Brownian motion, and it reflects instantaneously at each boundary surface (axis). At one axis, the reflection is normal, but at the other axis it has a tangential component as well. The generator of Z is calculated.It is shown that the limit distribution F is the solution of a first-passage problem for a certain dual diffusion process Z∗. The generator of Z∗ is calculated, and the analytical theory of Markov processes is used to derive a partial differential equation (with boundary conditions) for the density f of F. Necessary and sufficient conditions are found for f to be separable (for the limit distribution to have independent components). This extends slightly the class of explicit solutions found previously in [2]. Another special case is solved explicitly, showing that the density is not in general separable.
Trace inequalities for mixtures of Markov chains
Authors: Singer Burton , Spilerman Seymour 
Published: April 2006

In a wide variety of multi-wave panel studies in economics and sociology, comparisons between the observed transition matrices and predictions of them based on time-homogeneous Markov chains have revealed a special kind of discrepancy: the trace of the observed matrices tends to be larger than the trace of the predicted matrices. A common explanation for this discrepancy has been via mixtures of Markov chains.Specializing to mixtures of Markov semi-groups of the form
we exhibit classes of stochastic matrices M, probability measures µ and time intervals Δ such that

for k = 2, 3 and 4. These examples contradict the substantial literature which suggests — implicitly — that the above inequality should be reversed for general mixtures of Markov semi-groups.
Markovian contact processes
Authors: Mollison Denis 
Published: April 2006

Markovian contact processes(mcp's) include some of the commoner models for the spatial spread of population processes, such as the ‘simple’ and ‘general’ epidemics, percolation processes, and birth, death and migration processes. They are here set in a framework which relates them to each other, and to a particular basic model, thecontact birth process(cbp); indeed they are defined as modifications of the cbp. The immediate advantage of this is that bounds for the velocity of the cbp, which can be obtained from the linear equation describing its expected numbers (provided the contact distribution has exponentially bounded tail) apply also to general mcp's. Existence of moments (and for some processes their time-derivatives) ofSt(θ), the distance to the furthest individual in an arbitrary direction θ, can also be deduced whenever the corresponding moment of the contact distribution exists.An important subclass consists ofpopulation-monotonemcp's, for which the distributions ofStcan be shown to besubconvolutive, so that the work of Hammersley (1974) can be applied to obtain convergence theorems forSt/t; and these can be extended to convergence of the convex hull of the set of inhabited points. These results are particularly valuable because they apply to some non-linear processes, e.g. the simple epidemic. Some special results on the cbp (Section 6) emphasize the differences between linear and non-linear spatial stochastic processes.Although the paper is written throughout in terms of continuous-time processes, the results on subconvolutive distributions are actually more easily applied in the discrete-time case. (Conversely, the approach used in the accompanying paper by Biggins (pp. 62–84), which is written in terms of discrete-time processes, can be extended to deal also with continuous-time processes.)
Steinhaus's geometric location problem for random samples in the plane
Authors: Hochbaum Dorit , Steele J. Michael 
Published: April 2006

LetwhereXi, 1 ≦i≦n, are i.i.d. and uniformly distributed in [0, 1]2. It is proved thatMn∽cn1–p/2a.s. for 1 ≦p<2. This result is motivated by recent developments in the theory of algorithms and the theory of subadditive processes as well as by a well-known problem of H. Steinhaus.
Asymptotic bounds on the time to fatigue failure of bundles of fibers under local load sharing
Authors: Tierney Luke 
Published: April 2006

A fiber bundle is a parallel arrangement of fibers. Under a steady tensile load, fibers fail randomly in time in a manner that depends on how they share the applied load. The bundle fails when all its fibers have failed in a specified region.In this paper we consider the fatigue failure of such a bundle in a fiber load-sharing setting appropriate for composite materials, that is, to bundles impregnated with a flexible matrix. The bundle is actually modelled as a chain of short bundles, and local load sharing is assumed for the fibers within each short bundle. The chain of bundles fails once all the fibers in one of the short bundles have failed.Reasonable assumptions are made on the stochastic failure of individual fibers. A general framework for describing fiber bundles is developed and is used to derive the limiting distribution of the time to the first appearance of a set ofkor more adjacent failed fibers as the number of fibers in the bundle grows large. These results provide useful bounds on the distribution of the time to total bundle failure. Some implications and extensions of these results are discussed.
Prediction of level crossings for normal processes containing deterministic components
Authors: Lindgren Georg 
Published: April 2006

A level crossing predictor is a predictor process Y(t) which can be used to predict whether a specific process X(t) will cross a predetermined level or not. A natural criterion of how good a predictor is can be the probability that a crossing is detected a sufficient time ahead, and the number of times the predictor makes a false alarm.Suppose the process X(t) consists of a deterministic part A(t) which can be calculated with sufficient accuracy, and a stochastic part Xe(t) which can be predicted by some statistically based predictor An example of this is the prediction of water level near a coast, when A(t) is a sum of known tide components.The paper develops a tool to handle the detection properties of such predictor processes when used to predict level crossings for the case when A(t) is periodic or is a sum of such functions.
On the steady-state solution of the M/G/2 queue
Authors: Hokstad Per 
Published: April 2006

The asymptotic behaviour of the M/G/2 queue is studied. The difference-differential equations for the joint distribution of the number of customers present and of the remaining holding times for services in progress were obtained in Hokstad (1978a) (for M/G/m). In the present paper it is found that the general solution of these equations involves an arbitrary function.In order to decide which of the possible solutions is the answer to the queueing problem one has to consider the singularities of the Laplace transforms involved. When the service time has a rational Laplace transform, a method of obtaining the queue length distribution is outlined. For a couple of examples the explicit form of the generating function of the queue length is obtained.
The time to failure of fiber bundles subjected to random loads
Authors: Taylor Howard M. 
Published: April 2006

The effect on cable reliability of random cyclic loading such as that generated by the wave-induced rocking of ocean vessels deploying these cables is examined. A simple model yielding exact formulas is first explored. In this model, the failure time of a single fiber under a constant load is assumed to be exponentially distributed, and the random loadings are a two-state stationary Markov process. The effect of load on failure time is assumed to follow a power law breakdown rule. In this setting, exact results concerning the distribution of bundle or cable failure time, and especially the mean failure time, are obtained. Where the fluctuations in load are frequent relative to bundle life, such as may occur in long-lived cables, it is shown that randomness in load tends to decrease mean bundle life, but it is suggested that the reduction in mean life often can be restored by modestly reducing the base load on the structure or by modestly increasing the number of elements in the bundle.In later pages this simple model is extended to cover a broader range of materials and random loadings. Asymptotic distributions and mean failure times are given where fibers follow a Weibull distribution of failure time under constant load, and loads that are general non-negative stationary processes subject only to some mild condition of asymptotic independence. When the power law breakdown exponent is large, the mean time to bundle failure depends heavily on the exact form of the marginal probability distribution for the random load process and cannot be summarized by the first two moments of this distribution alone.
Asymptotic methods in reliability theory: a review
Authors: Gertsbakh I. B. 
Published: April 2006

Section 1 of this paper reviews some works related to reliability evaluation of systems without repair. The assumption that element failure rates are low enables one to obtain an expression for the main term in the asymptotic representation of system reliability function. Section 2 is devoted to repairable systems. The main index of interest in reliability is the time to the first system failure. A typical situation in reliability is that the repair time is much smaller than the element lifetime. This ‘fast repair' property leads to an interesting phenomenon, that for many renewable systems the time to system failure converges in distribution, under appropriate norming, to an exponential random variable. Some basic theorems explaining this fact are presented and a series of typical examples is considered. Special attention is paid to reviewing the works describing the exponentiality phenomenon in birth-and-death processes. Some important aspects of computing the normalizing constants are considered, among them the role played by the so-called ‘main event'. Section 2 also reviews various bounds on the deviation from exponentiality. Section 3 gives brief comments on some works and techniques related to asymptotic reliability analysis. In particular, attention is paid to the works presenting upper and lower bounds on the reliability function.A considerable part of this review is based on sources originally published in Russian.
Analysis of separable Markov-modulated rate models for information-handling systems
Authors: Stern Thomas E. , Elwalid Anwar I. 
Published: April 2006

In many communication and computer systems, information arrives to a multiplexer, switch or information processor at a rate which fluctuates randomly, often with a high degree of correlation in time. The information is buffered for service (the server typically being a communication channel or processing unit) and the service rate may also vary randomly. Accurate capture of the statistical properties of these fluctuations is facilitated by modeling the arrival and service rates as superpositions of a number of independent finite state reversible Markov processes. We call such models separable Markov-modulated rate processes (MMRP).In this work a general mathematical model for separable MMRPs is presented, focusing on Markov-modulated continuous flow models. An efficient procedure for analyzing their performance is derived. It is shown that the ‘state explosion' problem typical of systems composed of a large number of subsystems, can be circumvented because of the separability property, which permits a decomposition of the equations for the equilibrium probabilities of these systems. The decomposition technique (generalizing a method proposed by Kosten) leads to a solution of the equilibrium equations expressed as a sum of terms in Kronecker product form. A key consequence of decomposition is that the computational complexity of the problem is vastly reduced for large systems. Examples are presented to illustrate the power of the solution technique.
Insensitivity in processes with zero speeds
Authors: Taylor P. 
Published: April 2006

Many authors have discussed the equivalence of partial balance and insensitivity in in stochastic processes. When speeds are introduced into a stochastic process there arises a difficulty in proving the necessity of partial balance for insensitivity. Previous authors have overcome this difficulty by assuming that a process has the property of instantaneous attention. This property enforces the requirement that no lifetime can be created in a state in which that lifetime has zero speed.In this paper it is shown that for processes with a finite state space it is unnecessary to make this assumption provided the notion of partial balance is slightly changed. Thus we give a criterion, analogous to partial balance, which is necessary and sufficient for insensitivity even in processes which do not possess the property of instantaneous attention. When a process does have instantaneous attention this criterion is equivalent to partial balance.
Applications of generalized inverses to Markov chains
Authors: Rising William 
Published: April 2006

First it is shown that any generalized inverse of the infinitesimal generator of an irreducible Markov chain can be used to compute the exact stationary distribution and all the expected first-passage times of the chain. In the special case of a single-server queue this allows all computations to be done with upper-triangular matrices.Next it is shown that the effect of a perturbation of the infinitesimal generator on the stationary distribution and expected first-passage times can also be computed using generalized inverses. These results extend and generalize Schweitzer's [9] original work using fundamental matrices. It is then shown that any perturbation can be broken up into a series of perturbations each involving a single state.
Karyomorphology ofHeptacodium(Caprifoliaceae s.str.) and its phylogenetic implications
Authors: Zhang Zhao-Yang , Zhou Zhe-Kun , Gu Zhi-Jian 
Published: April 2006

AbstractA karyomorphological study of the speciesHeptacodium miconioidesand five species in Caprifoliaceae of presumably related genera [AbeliaandDepelta(Linnaeeae);LycesteriaandLonicera(Caprifolieae);Weigela(Diervilleae)] reveals similarities in some karyological features such as structure of interphase nuclei, chromosome size, and condensation behaviour of chromosomes during mitotic prophase. However, differences between them in chromosome base number and morphology of metaphase chromosomes have also been revealed. The chromosome number ofHeptacodium2n= 28 is unique in Caprifoliaceae, presumably having resulted from polyploidization following hybridization between two ancestral species (possibly with chromosome base numberx= 8 or 9) bearing characters of tribes Caprifolieae and Linnaeeae, respectively. The phylogenetic position ofHeptacodiumis discussed based on combination of karyomorphology and previous morphological and molecular data.
Lectotypification of Campanula barbata L. and C. cenisia L. (Campanulaceae)
Authors: Pistarino Annalaura , Forneris Giuliana , Jarvis Charlie 
Published: April 2006

AbstractThe names Campanula barbata and C. cenisia were published by Carl Linnaeus in 1759 and 1763, respectively. For both names, Linnaeus referred to material he had received from the Italian botanist Carlo Allioni, and we designate lectotypes from Allioni material preserved in LINN. For C. cenisia, it has been possible to identify the locus classicus.
Typification of the name Opephyllum martensii Schmitz (Delesseriaceae, Rhodophyta)
Authors: Wynne Michael J. 
Published: April 2006

AbstractSix slides labelled "Nitophyllum martensioides", located in the slide collection of Schmitz's red algal types in the Natural History Museum, London (BM), can be identified as Opephyllum martensii Schmitz (Schmitz & Hauptfleisch, 1897). Label data fully correspond to the protologue of O. martensii (collected by Martens from Mindanao, Philippines). This collection of six slides from a single gathering is, therefore, interpreted to be the holotype for the name Opephyllum martensii, superseding the neotype recently proposed by Lin & al. (2001).
Phenetic analyses of morphological traits in the Malesherbia humilis complex (Malesherbiaceae)
Authors: Gengler-Nowak Karla 
Published: April 2006

AbstractMalesherbia (Malesherbiaceae) is a small, xerophytic group endemic to the Peruvian and Chilean deserts and adjacent Argentina. Malesherbia humilis var. humilis, M. humilis var. propinqua, M. humilis var. parviflora, M. gabrielae, M. taltalina, and M. multiflora form a morphologically cohesive group native to Chile and Argentina characterized by a profusion of small flowers and a short, bushy habit. The difficulty in distinguishing among these taxa suggests that the taxonomic delimitations may not be meaningful. A phenetic study was conducted to determine if this complex is best treated as a large, polymorphic species or as a series of very similar yet distinguishable taxa. Sixteen morphological characters were examined on 113 operational taxonomic units (OTUs); the data were analyzed using UPGMA, PCA, and discriminant analyses. Five clusters were identified by the analyses. These clusters are distinguishable by minor characters and are geographically cohesive. Because of the minor nature of the differences found and the unreliability of most differences noted in the descriptions of the taxa, these five clusters are recognized as varieties of M. humilis. A key to the varieties and short descriptions of each are presented.
Novel visualisation techniques for working with multiple, overlapping classification hierarchies
Authors: Graham Martin , Watson Mark F. , Kennedy Jessie B. 
Published: April 2006

AbstractA Java‐based program is presented that provides a visualisation tool for display of and comparison between classification hierarchies. Taxa, or groups of taxa, can be tracked across multiple, overlapping classifications. Recognition of congruence and dissimilarity between classifications can be visually assessed through pattern matching. Software development, testing, and operation of the tool are discussed, together with potential applications. Further information (including software) is available via the Prometheus website [www.prometheusdb.org].
Stone, plant, or animal
Authors: Nicolson Dan H. 
Published: April 2006

AbstractLinnaeus organised almost everything to which he put his mind and was the first to systematically apply a binomial system to all of nature. The philosophy underlying his system of nature is that of a ladder (pyramid) leading from stones, the lowest (furthest from Man), to animals, with Man, created in the image of God, being the highest. The classification functioned like a two­dimensional map, characters of taxa being like latitude and longitude with a hierarchy of precision. It was of value in an age of discovery, although his classifications of stones and plants had short lives. The binomial system of naming, although not considered important by Linnaeus, was important in separating diagnoses/descriptions of taxa from the names of taxa. It is hoped that new philosophies will maintain the distinction between things named and their names.
Why do we name organisms? Some reminders from the past
Authors: Stevens Peter F. 
Published: April 2006

AbstractThe naming systems of Linnaeus and Bentham in particular are examined to clarify the relationships between naming and ideas of relationships. Linnaean binomials were adopted largely for practical reasons. Furthermore, Linnaeus proposed his names in the context of system, putting organisms in groups of 10. This allowed botanists of moderate capabilities to know at least the genera. Although binomials are names of taxa of the two lowest levels of a rank hierarchy, much of Linnaeus' work does not fit easily in the currently widely accepted view of Linnaeus as a hard­bitten essentialist. Neither Lamarck nor the later Bentham believed in a rank hierarchy, although to name organisms both used what is here called a flagged hierarchy: name terminations indicating only a set of inclusion relationships, not ranks of nature implied by a rank hierarchy. Bentham was clear that the adoption of a flagged hierarchy with groups of a particular size in theGenera plantarumwas to facilitate botanists' understanding of the system as a whole. Systematists like Bentham and Linnaeus managed information and presented classification systems simultaneously. I conclude that the lower level of Linnaeus' hierarchy is a special case of the noun + adjective combination that pervade folk classifications in particular and human language in general. Linking essentialism and "Linnaean" nomenclature is at best a red herring, thus few nineteenth­century botanists believed in a fully­developed rank hierarchy. Naming hierarchies are mostly such that at each level members belong to only one group, and this is at a higher level; most such hierarchies are fairly shallow. Historically, uninomials have seemed more attractive when generic limits were in flux, but suboptimal when relationships were more stable. Naming systems in general incorporate a substantial element of convention, emphasizing particular numbers of groups and groups of particular size; this facilitates comprehension and communication. Similar conventions will be needed whatever naming system is used.
How to chop up a tree
Authors: Brummitt Richard K. 
Published: April 2006

AbstractOver the past 50 years it has been pointed out with increasing frequency that our traditional Linnaean system of classification and nomenclature is incompatible with a phylogenetic system which recognises only monophyletic groups. Dividing up an evolutionary tree into mutually exclusive families, genera, and species which are all monophyletic is a logical impossibility. Darwin had emphasised that evolution is descent with modification. The rise of cladistic thinking in the last 40 years has promoted an obsession with monophyletic taxa, with classification based solely on descent at the expense of modification. Despite strong psychological pressures on a generation of biologists who have been brought up on the dogma of monophyly, the Hennigian view of classification is now increasingly seen as illogical and out­of­date. Some are therefore supporting thePhyloCode, which is based on a logical position but is impractical for general purpose classification and communication since it recognises no ranks and abandons binomials. Others still cling to the nonsensical concept of recognising families, genera, species, etc., and all being monophyletic. Linnaean classification is the optimal tool for cataloguing biodiversity and will inevitably be maintained, but this requires recognition of paraphyletic taxa and some rethinking of the practice and purposes of biological classification. Those who want a classification to recognise only monophyletic taxa should adopt an appropriate nomenclatural system such as is offered by thePhyloCode. To do otherwise will tend to lead to bad taxonomy.