Branching Process Research Papers - Academia.edu (original) (raw)

The selection of entries to be included/excluded in Branch and Bound algorithms is usually done on the basis of cost values. We consider the class of Depth First Search algorithms, and we propose to use upper tolerances to guide the search for optimal solutions. In spite of the fact that it needs time to calculate tolerances, our computational experiments for Asymmetric Traveling Salesman Problems show that in most situations tolerance-based algorithms outperform cost-based algorithms. The solution time reductions are mainly caused by the fact that the branching process becomes much more effective, so that optimal solutions are found in an earlier stage of the branching process. The use of tolerances also reveals why the widely used choice for branching on a smallest cycle in assignment solutions is on average the most effective one. Moreover, it turns out that tolerance-based DFS algorithms are better in solving difficult instances than the Best First Search algorithm from Carpaneto et al. [Carpaneto, G., Dell'Amico, M., Toth, P., 1995. Exact solution of large-scale asymmetric traveling salesman problems. ACM Transactions on Mathematical Software 21 (4), 394-409].

- by
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- Modeling, Multidisciplinary, Search Algorithm, Asymmetry

In a critically self-organized model of punctuated equilibrium, boundaries determine peculiar scaling of the size distribution of evolutionary avalanches. This is derived by an inhomogeneous generalization of standard branching processes, extending previous mean field descriptions and yielding ν = 1/2 together with τ ′ = 7/4, as distribution exponent of avalanches starting from species at the ends of a food chain. For the nearest neighbor chain one obtains numerically τ ′ = 1.25 ± 0.01, and τ ′ f irst = 1.35 ± 0.01 for the first return times of activity, again distinct from bulk exponents.

- by Claudio Tebaldi
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- Physical sciences, Nearest Neighbor, Self Organization, Branching Process

The model under consideration is a catalytic branching model constructed in DF96], where the catalysts themselves su er a spatial branching mechanism. Main attention is paid to dimension d = 3: The key result is a convergence theorem towards a limit with full intensity (persistence), which in a sense is comparable with the situation for the \classical" continuous super-Brownian motion. As by-products, strong laws of large numbers are derived for the Brownian collision local time controlling the branching of reactants, and for the catalytic occupation time process. Also, the catalytic occupation measures are shown to be absolutely continuous (in space).

- by Donald Dawson
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- Statistics, Persistence, Self-similarity, Lebesgue measure

Our previous research effort has resulted in a stochastic model that provides an excellent fit to our experimental data on proliferation and differentiation of oligodendrocyte type-2 astrocyte progenitor cells at the clonal level. However, methods for estimation of model parameters and their statistical properties still remain far away from complete exploration. The main technical difficulty is that no explicit analytic expression for the joint distribution of the number of progenitor cells and oligodendrocytes, and consequently for the corresponding likelihood function, is available. In the present paper, we overcome this difficulty by using computer-intensive simulation techniques for estimation of the likelihood function. Since the output of our simulation model is essentially random, stochastic optimization methods are necessary to maximize the estimated likelihood function. We use the Kiefer–Wolfowitz procedure for this purpose. Given sufficient computing resources, the proposed estimation techniques significantly extend the spectrum of problems that become approachable. In particular, these techniques can be applied to more complex branching models of multi-type cell systems with dependent evolutions of different types of cells.

- by Margot Mayer-Pröschel
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- Stem Cells, Cell Division, Stochastic processes, Biological Sciences

A major determinant of plant architecture is the arrangement of branches around the stem, known as phyllotaxis. However, the specific form of branching conditions is not known. Here we discuss this question and suggest a branching model... more

- by V. Volpert
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- Molecular Biology, Pattern Formation, Morphogenesis, Biological Sciences
- by Anand N Vidyashankar
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- Population Size, Branching Process

Object This article describes a method for automated extraction of branching structures in three dimensional (3D) medical images. Materials and methods The algorithm recursively tracks branches and detects bifurcations by analyzing the binary connected components on the surface of a sphere that moves along the vessels. Local segmentation within the sphere is performed using a clustering algorithm based on both geometric and intensity information. It minimizes a combination of the intra-class intensity variances and of the inertia moment of the “vessel” class, which emphasizes the cylindrical structures. The algorithm was applied to 16 MRA and 12 CTA 3D images of different anatomic regions. Its capability of extracting all the branches and avoiding spurious detections was evaluated by comparing the number of extracted branches with the number of branches found by visual inspection of the datasets. Its reproducibility and sensitivity to parameter variation were also assessed. Results With a fixed parameter setting, 68 out of 286 perceptible branches were missed or partly extracted and 11 spurious branches were obtained. Increasing the weight of the geometric criterion helped in tracking the principal branches in noisy data but increased the number of missed branches. Processing time was within 5 min per dataset. Conclusion From one initial point, the algorithm extracts a vascular tree where the differences of size and of intensity between the branches are not large. Missed sub-trees can be recovered using additional starting points.

- by Eduardo Davila
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- Image Processing, 3-D Imaging, Three Dimensional Imaging, Clinical Sciences
- by Anand N Vidyashankar
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- Mathematics, Statistics, Pure Mathematics, Population Size

Correlation effects in the fluctuation of the number of particles in the process of energy branching by sequential impact ionizations are studied using an exactly soluble model of random parking on a line. The Fano factor F calculated in an uncorrelated final-state "shot-glass" model does not give an accurate answer even with the exact gap-distribution statistics. Allowing for the nearest-neighbor correlation effects gives a correction to F that brings F very close to its exact value. We discuss the implications of our results for energy resolution of semiconductor gamma detectors, where the value of F is of the essence. We argue that F is controlled by correlations in the cascade energy branching process and hence the widely used final-state model estimates are not reliable-especially in the practically relevant cases when the energy branching is terminated by competition between impact ionization and phonon emission.

- by Serge Luryi
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- Engineering, Mathematical Sciences, Physical sciences, Impact Ionization

The biological theory of adaptive dynamics proposes a description of the long-term evolution of a structured asexual population. It is based on the assumptions of large population, rare mutations and small mutation steps, that lead to a deterministic ODE describing the evolution of the dominant type, called the 'canonical equation of adaptive dynamics'. Here, in order to include the effect of stochasticity (genetic drift), we consider self-regulated randomly fluctuating populations subject to mutation, so that the number of coexisting types may fluctuate. We apply a limit of rare mutations to these populations, while keeping the population size finite. This leads to a jump process, the so-called 'trait substitution sequence', where evolution proceeds by successive invasions and fixations of mutant types. Then we apply a limit of small mutation steps (weak selection) to this jump process, that leads to a diffusion process that we call the 'canonical diffusion of adaptive dynamics', in which genetic drift is combined with directional selection driven by the gradient of the fixation probability, also interpreted as an invasion fitness. Finally, we study in detail the particular case of multitype logistic branching populations and seek explicit formulae for the invasion fitness of a mutant deviating slightly from the resident type. In particular, second-order terms of the fixation probability are products of functions of the initial mutant frequency, times functions of the initial total population size, called the invasibility coefficients of the resident by increased fertility, defence, aggressiveness, isolation, or survival.

- by Nicolas Champagnat
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- Applied Mathematics, Statistics, Genetic Drift, Population Dynamics

In this article we implement the trinomial tree of the Hull-White model, which can be easily extended to allow different assumptions about the dynamics of the short rate process. We present the Mathematica algorithm for the extended Vasicek and the Black-Karasinski model. Whenever negative interest rates are generated with a positive probability, we make use of alternative branching processes, which guarantee the positivity of interest rates. Finally we show how to price simple options such as caplets, and compare the convergence of trinomial trees with different geometries.

- by Zvi Wiener
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- Branching Process, Interest Rate

Superscalar processing is the latest in a long series of innovations aimed at producing ever-faster microprocessors. By exploiting instruction-level parallelism, superscalar processors are capable of executing more than one instruction in a clock cycle. This paper discusses the microarchitecture of superscalar processors. We begin with a discussion of the general problem solved by superscalar processors: converting an ostensibly sequential program into a more parallel one. The principles underlying this process, and the constraints that must be met, are discussed. The paper then provides a description of the specific implementation techniques used in the important phases of superscalar processing. The major phases include: i) instruction fetching and conditional branch processing, ii) the determination of data dependences involving register values, iii) the initiation, or issuing, of instructions for parallel execution, iv) the communication of data values through memory via loads and stores, and v) committing the process state in correct order so that precise interrupts can be supported. Examples of recent superscalar microprocessors, the MIPS R10000, the DEC 21164, and the AMD K5 are used to illustrate a variety of superscalar methods.

- by James Smith
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- Technology, Biomedical Engineering, Parallel Programming, Parallel Processing

1 Niche pre-emption and competitive exclusion is unsatisfactory as a sole explanation for the apparent paradox of a large number of monophyletic taxa in the Macaronesian island flora. 2 Undetected hybridizations have been proposed as an additional plausible explanation. In addition, hybrid swarm theory predicts that hybridizations between invading species would promote adaptive radiation. 3 We suggest that branching processes and coalescence offer yet another plausible explanation allowing for multiple colonizations of closely related taxa, which, because of their later local extinction or hybridization, would lead to apparent monophyly in the molecular record. 4 The cause of such widespread radiation of a few taxa has not been explained, but may involve intermediate conditions of disturbance or productivity. This proposition has, to date, only been tested in a microbial model system, but it offers a reasonable explanation for the patterns observed in the Macaronesian flora, and perhaps in other island floras worldwide.

- by David Gibson
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- Ecology, Biological Sciences, Environmental Sciences, Adaptive Radiation

We present a probabilistic approach for the study of systems with exclusions, in the regime traditionally studied via cluster-expansion methods. In this paper we focus on its application for the gases of Peierls contours found in the study of the Ising model at low temperatures, but most of the results are general. We realize the equilibrium measure as the invariant measure of a loss-network process whose existence is ensured by a subcriticality condition of a dominant branching process. In this regime, the approach yields, besides existence and uniqueness of the measure, properties such as exponential space convergence and mixing, and a central limit theorem. The loss network converges exponentially fast to the equilibrium measure, without metastable traps. This convergence is faster at low temperatures, where it leads to the proof of an asymptotic Poisson distribution of contours. Our results on the mixing properties of the measure are comparable to those obtained with \duplicated-variables expansion", used to treat systems with disorder and coupled map lattices. It works in a larger region of validity than usual cluster-expansion formalisms, and it is not tied to the analyticity of the pressure. In fact, it does not lead to any kind of expansion for the latter, and the properties of the equilibrium measure are obtained without resorting to combinatorial or complex analysis techniques.

- by Roberto Fernández
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- Statistics, Ising Model, Animal Model, Coupled Map Lattice

We give a comprehensive account of a complex systems ap- proach to large blackouts caused by cascading failure. In- stead of looking at the details of particular blackouts, we study the statistics, dynamics and risk of series of blackouts with approximate global models. North American blackout data suggests that the frequency of large blackouts is gov- erned by a power

- by David Newman and +1
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- Applied Mathematics, Power System, Risk Analysis, Chaos

In this contribution, a stochastic theory for a branching process in a neutron population with two energy levels is investigated. In particular, a variance to mean or Feynman-alpha formula is derived in this generalized scenario using the... more

- by Johan Anderson
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- Plasma Physics, Branching Process, Energy Levels, Master Equation

Secrecy graphs model the connectivity of wireless networks under secrecy constraints. Directed edges in the graph are present whenever a node can talk to another node securely in the presence of eavesdroppers. In the case of infinite networks, a critical parameter is the maximum density of eavesdroppers that can be accommodated while still guaranteeing an infinite component in the network, i.e., the percolation threshold. We focus on the case where the location of the nodes and the eavesdroppers are given by Poisson point processes. We present bounds for different types of percolation, including in-, out-and undirected percolation.

- by Amites Sarkar
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- Applied Mathematics, Graph Theory, Stochastic processes, Percolation
- by Chiara Frigerio
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- Business and Management, Reference model, Banking Industry, Organizational Design

In this paper we consider a ring of N ≥ 1 queues served by a single server in a cyclic order. After having served a queue (according to a service discipline that may vary from queue to queue), there is a switch-over period and then the... more

- by Onno Boxma
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- Stochastic Systems, Steady state, Branching Process, Levy Process

We provide the definition and a complete characterization of regular affine processes. This type of process unifies the concepts of continuousstate branching processes with immigration and Ornstein-Uhlenbeck type processes. We show, and... more

- by Darrell Duffie
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- Developing Country, Branching Process

who is best remembered for "Todd's paralysis," made many more important contributions to neurology and neuroscience, including the concept of brain electricity and electrical discharges in epilepsy. He was also a pioneering microscopist and we here review his neurohistological studies and his contributions to the application of Schwann's (1839) cell theory to the nervous system and the later neuron doctrine, as described in his textbook The Descriptive and Physiological Anatomy of the Brain, Spinal Cord and Ganglions (Todd, 1845), his Cyclopaedia of Anatomy and Physiology and his joint textbook with William Bowman The Physiological Anatomy and Physiology of Man (1845). Writing in the mid-1840s, Todd acknowledged that the "vesicles" he observed corresponded to the earlier descriptions of "globules" or "kugeln" by Valentin and which Schwann first interpreted as cell bodies. Todd was among the first to recognize that nerve cell bodies were in continuity with axons ("axis cylinders"), sometimes associated with "the white substance of Schwann" ("tubular" fibers), or sometimes without ("gelatinous" fibers). He also described continuous nerve cell branching processes, later called dendrites. He was the first to recognize the insulating properties of Schwann's "white substance" (myelin) to facilitate conduction. Influenced by his contemporary, Faraday, Todd was also the first to develop the functional concept of dynamic polarization ("nervous polarity") to explain nerve cell conduction.

- by Devin Binder
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- Cell Biology, Spinal Cord, PARALYSIS, Branching Process

Recently we proposed a model in which when a scientist writes a manuscript, he picks up several random papers, cites them and also copies a fraction of their references (cond-mat/0305150). The model was stimulated by our discovery that a majority of scientific citations are copied from the lists of references used in other papers (cond-mat/0212043). It accounted quantitatively for several properties of empirically observed distribution of citations. However, important features, such as power-law distribution of citations to papers published during the same year and the fact that the average rate of citing decreases with aging of a paper, were not accounted for by that model. Here we propose a modified model: when a scientist writes a manuscript, he picks up several random recent papers, cites them and also copies some of their references. The difference with the original model is the word recent. We solve the model using methods of the theory of branching processes, and find that it can explain the aforementioned features of citation distribution, which our original model couldn't account for. The model can also explain "sleeping beauties in science", i.e., papers that are little cited for a decade or so, and later "awake" and get a lot of citations. Although much can be understood from purely random models, we find that to obtain a good quantitative agreement with empirical citation data one must introduce Darwinian fitness parameter for the papers.

- by Vwani Roychowdhury and +1
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- Information Systems, Library and Information Studies, Sleeping Beauty, Branching Process

An architectural analysis of the root system of young oil-palm (Elaeis guineensis Jacq.) seedIings was made. In this analysis, root branching was modelled by a Markov chain (discrete-time, discrete-state space stochastic process). This study has been realized on radicles of young oil-palm seedlings which were considered as main axes which branch. We defined an elementary length unit as the smallest length between two successive lateral roots. The model was based on the analysis of a sequence of events, each event being indexed by the rank of the elementary length unit on the main axis. An event was defined as the state of the length unit, chosen between unbranched state and three branched-state categories. The branching process of the oil-palm radicle was modelled by a four-state first-order Markov chain. Consequently, the state of an elementary length unit depended only on the state of the previous one. The Markov chain was homogeneous, i.e. the transition probabiIities did not depend on the rank of the elementary length unit.

- by Christophe Jourdan
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- Stochastic Process, Biological Sciences, Environmental Sciences, State Space

We study distributions F on [0, 8) such that for some T= 8, F* 2 (x, x+T]~ 2F (x, x+T]. The case T= 8 corresponds to F being subexponential, and our analysis shows that the properties for T< 8 are, in fact, very similar to this classical case. A parallel theory is developed in the presence of densities. Applications are given to random walks, the key renewal theorem, compound Poisson process and Bellman��Harris branching processes.

- by Sergey Foss
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- Mathematics, Statistics, Pure Mathematics, Random Walk

hagen (DIKU) from November 2005 to October 2008 under the supervision of Professor David Pisinger. I would like to thank Professors Guy Desaulniers and Jacques Desrosiers whom I visited for half year in Montreal, and had the opportunity to continue working with after I returned to Denmark. Also, I would like to thank my colleagues at DIKU for a good place to work, especially Mads Jepsen, Bjørn Petersen and my supervisor David Pisinger for the many good discussions, and Mette Gamst and Laurent Flindt Muller for proof reading some chapters in this thesis. Thanks.

- by David Pisinger
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- Branch and Bound, Branching Process, Lower Bound, Shortest Path Problem

The solutions to a large class of semi-linear parabolic PDEs are given in terms of expectations of suitable functionals of a tree of branching particles. A sufficient, and in some cases necessary, condition is given for the integrability of the stochastic representation, using a companion scalar PDE. In cases where the representation fails to be integrable a sequence of pruned trees is constructed, producing a approximate stochastic representations that in some cases converge, globally in time, to the solution of the original PDE.

- by Marco Romito
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- Mathematical Physics, Statistics, Large classes, Branching Process

Mammalian lungs are branched networks containing thousands to millions of airways arrayed in intricate patterns that are crucial for respiration. How such trees are generated during development, and how the developmental patterning information is encoded, have long fascinated biologists and mathematicians. However, models have been limited by a lack of information on the normal sequence and pattern of branching events. Here we present the complete three-dimensional branching pattern and lineage of the mouse bronchial tree, reconstructed from an analysis of hundreds of developmental intermediates. The branching process is remarkably stereotyped and elegant: the tree is generated by three geometrically simple local modes of branching used in three different orders throughout the lung. We propose that each mode of branching is controlled by a genetically encoded subroutine, a series of local patterning and morphogenesis operations, which are themselves controlled by a more global master routine. We show that this hierarchical and modular programme is genetically tractable, and it is ideally suited to encoding and evolving the complex networks of the lung and other branched organs.

- by Mark Krasnow
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- Genetics, Membrane Proteins, Multidisciplinary, Nature

This paper delivers a flexible formalism for handling equilibrium ring formation. Based on graphical models of polymerization, it includes as special cases the Flory Stockmayer RAr model, the Flory AIRBg model, and Gordon's branching process formalism. When simple ring formation occurs in equireactive systems, it also includes the Jacobson-Stockmayer RA 2 and Hoeve RAj models.

- by John Spouge
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- Statistical Mechanics, Thermodynamics, Statistical Physics, Mathematical Sciences

Trees in Brownian excursions have been studied since the late 1980s. Forests in excursions of Brownian motion above its past minimum are a natural extension of this notion. In this paper we study a forest-valued Markov process which describes the growth of the Brownian forest. The key result is a composition rule for binary Galton-Watson forests with i.i.d. exponential branch lengths. We give elementary proofs of this composition rule and explain how it is intimately linked with Williams' decomposition for Brownian motion with drift.

- by Jim Pitman
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- Statistics, Brownian Motion, Branching Process, Markov Process

In this paper we study several aspects of the growth of a supercritical Galton-Watson process {Z_n:n\ge1}, and bring out some criticality phenomena determined by the Schroder constant. We develop the local limit theory of Z_n, that is, the behavior of P(Z_n=v_n) as v_n\nearrow \infty, and use this to study conditional large deviations of {Y_{Z_n}:n\ge1}, where Y_n satisfies an LDP, particularly of {Z_n^{-1}Z_{n+1}:n\ge1} conditioned on Z_n\ge v_n.

- by Anand N Vidyashankar
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- Applied Mathematics, Statistics, Large Deviations, Critical phenomena
- by Mikhail Simkin
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- Mathematical Sciences, Physical sciences, Heavy Traffic, Branching Process

In this article we obtain rates of convergence to equilibrium of marked Hawkes processes in two situations. Firstly, the stationary process is the empty process, in which case we speak of the rate of extinction. Secondly, the stationary process is the unique stationary and nontrivial marked Hawkes process, in which case we speak of the rate of installation. The first situation models small epidemics, whereas the results in the second case are useful in deriving stopping rules for simulation algorithms of Hawkes processes with random marks.

- by G. Nappo
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- Mathematics, Applied Mathematics, Stochastic Process, Statistics

Here we treat the transmission of disease through a population as a standard Galton-Watson branching process, modified to take the presence of vaccination into account. Vaccination reduces the number of secondary infections produced per infected individual. We show that introducing vaccination in a population therefore reduces the expected time to extinction of the infection. We also prove results relating the distribution of number of secondery infections with and without vaccinations.

- by Arni S.R. Srinivasa Rao
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- Branching Process
- by alison dunn
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- Genetics, Population Genetics, Reproduction, Crustacea

We consider the model of the one-dimensional cookie random walk when the initial cookie distribution is spatially uniform and the number of cookies per site is finite. We give a criterion to decide whether the limiting speed of the walk is non-zero. In particular, we show that a positive speed may be obtained for just 3 cookies per site. We also prove a result on the continuity of the speed with respect to the initial cookie distribution.

- by arvind singh
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- Probability Theory, Statistics, Law of large numbers, Random Walk

This paper is concerned with an M / G / I FCFS queue with twd types of customers, viz. (1) ordinary customers who arrive according to a Poisson process, and (2) permanent customers, who immediately return to the end of the queue after having received a service. The influence of the permanent customers on queue length and sojourn times of the Poisson customers is studied, using results from queueing theory and from the theory of branching processes. In particular it is shown, for the case that the service time distributions of the Poisson customers and all K permanent customers are negative exponential with identical means, that the queue length and sojourn time distributions of the Poisson customers are the ( K + 1 )-fold convolution of those for the case without permanent customers.

- by Onno Boxma
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- Distributed Computing, Queuing Theory, Poisson Process, Branching Process

Let (Z(t): t¿0) be a supercritical age-dependent branching process and let {Yn} be the natural martingale arising in a homogeneous branching random walk. Let Z be the almost sure limit of Z(t)=EZ(t)(t → ∞) or that of Yn (n → ∞). We study the following problems: (a) the absolute continuity of the distribution of Z and the regularity of the density function; (b) the decay rate (polynomial or exponential) of the left tail probability P(Z6x) as x → 0, and that of the characteristic function Ee itZ and its derivative as |t| → ∞; (c) the moments and decay rate (polynomial or exponential) of the right tail probability P(Z ¿ x) as x → ∞, the analyticity of the characteristic function (t) = Ee itZ and its growth rate as an entire characteristic function. The results are established for non-trivial solutions of an associated functional equation, and are therefore also applicable for other limit variables arising in age-dependent branching processes and in homogeneous branching random walks.

- by Roger Walker
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- Statistics, Density-functional theory, Stability of Functional Equation, Growth rate

In his Study of War, Q. Wright considered a model for the probability of war P "during a period of n crises", and proposed the equation P = 1-(1-p)", where p is the probability of war escalating at each individual crisis. This probability measure was formally derived recently by Cioffi-Revilla (1987), using the general theory of political reliability and an interpretation of the "n-crises problem" as a branching process. Two new, alternate solutions are presented here, one using D. Bernoulli's St. Petersburg Paradox as an analogue, the other based on the logic of conditional probabilities. Analysis shows that, while Wright's solution is robust with regard to the general overall behavior of p and n, some significant qualitative and quantitative differences emerge from the alternative solutions. In particular, P converges to 1 only in a special case (Wright's) and not generally. The "n-crises problem" arises in international politics in reference to the following situation: during a generic era of history having unspecified duration, but usually understood to mean "several years or decades", 1 two or more nations become involved in a sequence of n "crises". Though an international crisis may be defined in various ways, 2 most social scientists working in this area agree that an essential qualitative trait of an international interaction episode designated as an international "crisis" has to do with the idea that during such an episode the probability of war occurring-i.e., war breaking out between the nations involved-is distinctively greater than zero (but strictly less than 1), 0 < p < 1. 3 Some famous recent crises (e.g., the 1962 Cuban missile crisis, or the series of Berlin crises) nicely illustrate this probabilistic character of crises; the "winds of war" blow strong, and it is uncertain whether peace will result or war will break out instead. 4 Given this possibility of war occurring, the following question naturally arises: what is the probability of war, P, during a period of time (historic era) comprised of several, i.e., n crises, given that there is a probability, p, that any single, individual crisis may result in war. Such a question is called the n-crises problem, and its solution has theoretical and empirical significance, interesting to both scientists and historians. In this paper we are concerned with a class of solutions to the

- by Claudio Cioffi-Revilla
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- Philosophy, Conditional probability, Branching Process, Synthese

The probability distribution of the cascade generators in a random multiplicative cascade represents a hidden parameter which is reflected in the fine scale limiting behavior of the scaling exponents (sample moments) of a single sample cascade realization as a.s. constants. We identify a large class of cascade generators uniquely determined by these scaling exponents. For this class we provide both asymptotic consistency and confidence intervals for two different estimators of the cumulant generating function (log Laplace transform) of the cascade generator distribution. These results are derived from investigation of the convergence properties of the fine scale sample moments of a single cascade realization.

- by Ed Waymire
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- Econometrics, Martingale, Convergence, Parameter estimation

- by David Gibson
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- Ecology, Coalescent Theory, Biological Sciences, Phylogeny

A gene encoding a putative glycogen branching enzyme (SmGBE) in Streptococcus mutans was expressed in Escherichia coli and purified. The biochemical properties of the purified enzyme were examined relative to its branching specificity for amylose and starch. The activity of the approximately 75 kDa enzyme was optimal at pH 5.0, and stable up to 40°C. The enzyme predominantly transferred short maltooligosyl chains with a degree of polymerization (dp) of 6 and 7 throughout the branching process for amylose. When incubated with rice starch, the enzyme modified its optimal branch chain-length from dp 12 to 6 with large reductions in the longer chains, and simultaneously increased its branching points. The results indicate that SmGBE can make a modified starch with much shorter branches and a more branched structure than to native starch. In addition, starch retrogradation due to low temperature storage was significantly retarded along with the enzyme reaction.

- by Nguyen Huong
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- Food Chemistry, Multidisciplinary, Escherichia coli, Bacteria

This paper introduces a composite index to characterise urban expansion patterns based on four associated indices that describe the degree of compactness of urban land: nuclearity, ribbon development, leapfrogging and branching processes. Subsequently, principal component and cluster analysis are applied to build the composite index. Two baseline scenarios and three hypothetical policy alternatives, run from 2000 to 2030 using the pan-European EU-ClueScanner 1 km resolution land use model are then used to test the sensitivity and robustness of the composite index in large urban zones (LUZs).

Phylogenetic techniques are used to analyse the spread of Neolithic plant economies from the Near East to northwest Europe as a branching process from a founding ancestor. The analyses are based on a database of c. 7500 records of plant taxa from 250 sites dated to the early Neolithic of the region in which they occur, aggregated into a number of regional groups. The analysis demonstrates that a phylogenetic signal exists in the data but it is complicated by the fact that in comparison with the changes that occurred when the crop agriculture complex expanded out of the Near East, once it arrived in Europe it underwent only limited further changes. On the basis of the analysis it has been possible to identify the species losses and gains that occurred as the complex of crops and associated weeds spread and to show the influence of geographical location and cultural affinity on the pattern of losses and gains. This has led to consideration of the processes producing that history, including some reasons why the dispersal process did not produce a perfect tree phylogeny, as well as to the identification of some specific anomalies, such as the unusual nature of the Bulgarian pattern, which raise further questions for the future.

- by Sue Colledge
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- Archaeology, Geochemistry, Archaeobotany, Archaeological Science

In 1980=81 Agnati and Fuxe introduced the concept of intramembrane receptor-receptor interactions and presented the first experimental observations for their existence in crude membrane preparations. The second step was their introduction of the receptor mosaic hypothesis of the engram in 1982. The third step was their proposal that the existence of intramembrane receptor-receptor interactions made possible the integration of synaptic (WT) and extrasynaptic (VT) signals. With the discovery of the intramembrane receptor-receptor interactions with the likely formation of receptor aggregates of multiple receptors, so called receptor mosaics, the entire decoding process becomes a branched process already at the receptor level in the surface membrane. Recent developments indicate the relevance of cooperativity in intramembrane receptor-receptor interactions namely the presence of regulated cooperativity via receptor-receptor interactions in receptor mosaics (RM) built up of the same type of receptor (homo-oligomers) or of subtypes of the same receptor (RM type1). The receptor-receptor interactions will to a large extent determine the various conformational states of the receptors and their operation will be dependent on the receptor composition (stoichiometry), the spatial organization (topography) and order of receptor activation in the RM. The biochemical and functional integrative implications of the receptor-receptor interactions are outlined and longlived heteromeric receptor complexes with frozen RM in various nerve cell systems may play an essential role in learning, memory and retrieval processes. Intramembrane receptor-receptor interactions in the brain have given rise to novel strategies for treatment of Parkinson's disease (A2A and mGluR5 receptor antagonists), schizophrenia (A2A and mGluR5 agonists) and depression (galanin receptor antagonists). The A2A=D2, A2A=D3 and A2A=mGluR5 heteromers and heteromeric complexes with their possible participation in different types of RM are described in detail, especially in the cortico-striatal glutamate synapse and its extrasynaptic components, together with a postulated existence of A2A=D4 heteromers. Finally, the impact of intramembrane receptor-receptor interactions in molecular medicine is discussed outside the brain with focus on the endocrine, the cardiovascular and the immune systems.

- by Diego Guidolin and +2
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- Psychology, Neurochemistry, Signal Transduction, Sweden

- by Zaida Diaz-cabiale and +3
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- Psychology, Signal Transduction, Sweden, Learning and Memory
- by Anna Levina
- •
- Engineering, Neural Network, Recurrent Neural Network, Self-Organized Criticality

In this paper we study several aspects of the growth of a supercritical Galton-Watson process {Z n : n ≥ 1}, and bring out some criticality phenomena determined by the Schröder constant. We develop the local limit theory of Z n , that is, the behavior of P (Z n = v n) as v n ∞, and use this to study conditional large deviations of {Y Z n : n ≥ 1}, where Y n satisfies an LDP, particularly of {Z −1 n Z n+1 : n ≥ 1} conditioned on Z n ≥ v n .

- by Anand N Vidyashankar
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- Mathematics, Applied Mathematics, Statistics, Large Deviations