bluuebunny/crossref_metadata_2025_split huggingface dataset:
Evacuation of a Yule process with immigration
Authors: Brown Mark , Ross Sheldon , Shorrock Richard 
Published: July 2016

Individuals arrive at a geographical area that is initially empty, in accordance with a pure birth process with birth parameters λj
= jλ + θ, j ≧ 0. Due to contamination, this geographical area is unsafe for its population and at some fixed time T in the future everyone in the area will be evacuated and no further immigration will be allowed.
Suppose now than an intermediate evacuation time τ, 0 ≦ τ ≦ T, at which time everyone present in the area would be evacuated, is to be chosen. The area would then again fill up with individuals between times τ and T, and, at T, the final evacuation would be made and the area would be permanently sealed off. The problem is to choose τ so as to minimise the total expected cost incurred by time T, where a cost g(x) is incurred for each individual that spends a time x in the area.
Some results on regular variation for distributions in queueing and fluctuation theory
Authors: Cohen J. W. 
Published: July 2016

For the distribution functions of the stationary actual waiting time and of the stationary virtual waiting time of the GI/G/l queueing system it is shown that the tails vary regularly at infinity if and only if the tail of the service time distribution varies regularly at infinity.
For sn
the sum of n i.i.d. variables xi, i = 1, …, n it is shown that if E {x
1} &lt; 0 then the distribution of sup, s
1
s
2, …] has a regularly varying tail at + ∞ if the tail of the distribution of x
1 varies regularly at infinity and conversely, moreover varies regularly at + ∞.
In the appendix a lemma and its proof are given providing necessary and sufficient conditions for regular variation of the tail of a compound Poisson distribution.
A population birth-and-mutation process, I: explicit distributions for the number of mutants in an old culture of bacteria
Authors: Mandelbrot Benoit 
Published: July 2016

Luria and Delbrück (1943) have observed that, in old cultures of bacteria that have mutated at random, the distribution of the number of mutants is extremely long-tailed. In this note, this distribution will be derived (for the first time) exactly and explicitly. The rates of mutation will be allowed to be either positive or infinitesimal, and the rate of growth for mutants will be allowed to be either equal, greater or smaller than for non-mutants. Under the realistic limit condition of a very low mutation rate, the number of mutants is shown to be a stable-Lévy (sometimes called “Pareto Lévy”) random variable, of maximum skewnessß, whose exponentαis essentially the ratio of the growth rates of non-mutants and of mutants. Thus, the probability of the number of mutants exceeding the very large valuemis proportional tom–α–1(a behavior sometimes referred to as “asymptotically Paretian” or “hyperbolic”). The unequal growth rate casesα≠ 1 are solved for the first time. In theα= 1 case, a result of Lea and Coulson is rederived, interpreted, and generalized. Various paradoxes involving divergent moments that were encountered in earlier approaches are either absent or fully explainable.The mathematical techniques used being standard, they will not be described in detail, so this note will be primarily a collection of results. However, the justification for deriving them lies in their use in biology, and the mathematically unexperienced biologists may be unfamiliar with the tools used. They may wish for more details of calculations, more explanations and Figures. To satisfy their needs, a report available from the author upon request has been prepared. It will be referred to as Part II.
The limiting properties of population distributions with particular application to manpower planning
Authors: Woodward Mark 
Published: July 2016

A model for predicting expected-value population distributions is developed, assuming that all movements are Markovian and time-homogeneous. Each individual is classified by the amount of time he has spent in the population and by which of a number of classes, of an unspecified nature, he inhabits. The limiting properties of the population distribution are derived, and, in particular, conditions for convergence to a stable distribution are given.
Some discussion of the relevance of the theory to practical applications is given, primarily to manpower planning when recruitment occurs purely to maintain a specified overall population size.
On a Markovian queue with weakly correlated interarrival times
Authors: Latouche Guy 
Published: July 2016

A queueing system with exponential service and correlated arrivals is analysed. Each interarrival time is exponentially distributed. The parameter of the interarrival time distribution depends on the parameter for the preceding arrival, according to a Markov chain. The parameters of the interarrival time distributions are chosen to be equal to a common value plus a factor ofε, where ε is a small number. Successive arrivals are then weakly correlated.
The stability condition is found and it is shown that the system has a stationary probability vector of matrix-geometric form. Furthermore, it is shown that the stationary probabilities for the number of customers in the system, are analytic functions ofε, for sufficiently smallε, and depend more on the variability in the interarrival time distribution, than on the correlations.
Transient behaviour of queueing networks
Authors: Harrison P. G. 
Published: July 2016

In most contemporary queueing network analysis, the assumption is made that a network is in a state of equilibrium. That is, the network's state space probabilities are assumed to be time independent. It is therefore important to be able to quantify precisely when this assumption is valid. Furthermore there are also situations in which it is desirable to model the transient behaviour of networks which occur in practice, such as computer and communication systems. For example, the immediate effects of component failure or instantaneous alteration of system status may be predicted.
In this paper an iterative solution is derived to the time-dependent Kolmogorov equations of queueing networks, and is shown to be convergent. From the solution, modelling of transient situations becomes possible and the time periods during which the equilibrium assumption can and should not be made may be identified; for example in terms of a time constant which is easily computed to a first-order approximation.
On strong mixing and Leadbetter's D condition
Authors: Chernick Michael R. 
Published: July 2016

Strong mixing is a condition which is often assumed to prove limit theorems for strictly stationary processes. Leadbetter's conditionD(un) is used to prove limit theorems for maxima of stationary processes.A sufficient condition for strong mixing to hold is given for the case where the process satisfies apth-order Markov property. This condition can be easy to check for whenpis small. This point is illustrated by two examples of first-order autoregressive processes.The conditionD(un) is shown to hold for any stationary Markov process.
Super-extremal processes and the argmax process
Authors: Resnick Sidney I. , Roy Rishin 
Published: July 2016

In this paper, we develop the probabilistic foundations of the dynamic continuous choice problem. The underlying choice set is a compact metric space E such as the unit interval or the unit square. At each time point t, utilities for alternatives are given by a random function . To achieve a model of dynamic continuous choice, the theory of classical vector-valued extremal processes is extended to super-extremal processes
Y
= {Yt, t &gt; 0}. At any t &gt; 0, Y

t
is a random upper semicontinuous function on a locally compact, separable, metric space E. General path properties of Y are discussed and it is shown that Y is Markov with state-space US(E). For each t &gt; 0, Y

t
is associated.
For a compact metric E, we consider the argmax process M = {Mt, t &gt; 0}, where . In the dynamic continuous choice application, the argmax process M represents the evolution of the set of random utility maximizing alternatives. M is a closed set-valued random process, and its path properties are investigated.
Convergence rates for M/G/1 queues and ruin problems with heavy tails
Authors: Asmussen Søren , Teugels Jozef L. 
Published: July 2016

The time-dependent virtual waiting time in a M/G/1 queue converges to a proper limit when the traffic intensity is less than one. In this paper we give precise rates on the speed of this convergence when the service time distribution has a heavy regularly varying tail.
The result also applies to the classical ruin problem. We obtain the exact rate of convergence for the ruin probability after time t for the case where claims arrive according to a Poisson process and claim sizes are heavy tailed.
Our result supplements similar theorems on exponential convergence rates for relaxation times in queueing theory and ruin probabilities in risk theory.
Stochastic vector difference equations with stationary coefficients
Authors: Glasserman Paul , Yao David D. 
Published: July 2016

We give a unified presentation of stability results for stochastic vector difference equations based on various choices of binary operations and , assuming that are stationary and ergodic. In the scalar case, under standard addition and multiplication, the key condition for stability is
E
[log |A
0|] &lt; 0. In the generalizations, the condition takes the form γ&lt; 0, where γis the limit of a subadditive process associated with . Under this and mild additional conditions, the process has a unique finite stationary distribution to which it converges from all initial conditions.
The variants of standard matrix algebra we consider replace the operations + and × with (max, +), (max,×), (min, +), or (min,×). In each case, the appropriate stability condition parallels that for the standard recursions, involving certain subadditive limits. Since these limits are difficult to evaluate, we provide bounds, thus giving alternative, computable conditions for stability.
Asymptotic probabilities in a critical age-dependent branching process
Authors: Weiner Howard J. 
Published: July 2016

Let Z(t) denote the number of cells alive at time t in a critical Bellman-Harris age-dependent branching process, that is, where the mean number of offspring per parent is one. A comparison method is used to show for k ≧ 1, and a high-order moment condition on G(t), where G(t) is the cell lifetime distribution, that lim
t→∞
t
2
P[Z(t) = k] = ak
&gt; 0, where {ak
} are constants.
The method is also applied to the total progeny in the critical process.
On a best-choice problem by dependent criteria
Authors: Gnedin Alexander V. 
Published: July 2016

We study the problem of maximizing the probability of stopping at an object which is best in at least one of a given set of criteria, using only stopping rules based on the knowledge of whether the current object is relatively best in each of the criteria. The asymptotic results for the case of independent criteria are shown to hold in certain cases where the componentwise maxima are, pairwise, either asymptotically independent or asymptotically full dependent.An example of the former is a random sample from a bivariate correlated normal distribution; thus our results settle a question posed recently by T. S. Ferguson.
On random genetic drift in a subdivided population
Authors: Pollak Edward 
Published: July 2016

SummaryGenerations are assumed to be non-overlapping. We consider a haploid population divided intoKparts, each of which containNadults in any generation. These are obtained by a random sampling of the offspring of the previous generation. We assume that the probability of an adult offspring of an individual in one subpopulation being in some other subpopulation is the same small positive number, no matter what two subpopulations are considered.If the population initially has individuals of two types, A and a, it is of interest to study approximations, if n is large, to(1)the rate at which A or a is lost between generations n-1 and n,(2)the probability that A and a are still present in generation n,(3)the joint distribution of frequencies of A in the subpopulations.A solution is given for the first problem. It is found that if the mean number of migrants per generation from one subpopulation to another is at least as large as 1, the population behaves almost as if it were not subdivided. But if this number is considerably less that 1, then the rate at which one or the other gene is lost is slower than in an undivided population. The other two problems are discussed for K = 2.
The maximum in critical Galton–Watson and birth and death processes
Authors: Kämmerle K. , Schuh H.-J. 
Published: July 2016

In this paper recent results by Weiner [10] on Mn
:= max{Z
0, · ··, Zn
} are strengthened and generalized, where (Zn
)
n
is a critical Galton–Watson branching process with finite and positive offspring variance and Z
0 ≡ 1. It is shown that

Explicit asymptotic bounds are given for with . If (Zn
)
n
has a linear fractional offspring distribution, it can be embedded in a critical birth and death process (Ẑ t
)
t
. Using martingale methods one obtains thereof.
These results generalize to the case Z
0 ≡ k.
Fitting hidden semi-Markov models to breakpoint rainfall data
Authors: Sansom John , Thomson Peter 
Published: July 2016

The paper proposes a hidden semi-Markov model for breakpoint rainfall data that consist of both the times at which rain-rate changes and the steady rates between such changes. The model builds on and extends the seminal work of Ferguson (1980) on variable duration models for speech. For the rainfall data the observations are modelled as mixtures of log-normal distributions within unobserved states where the states evolve in time according to a semi-Markov process. For the latter, parametric forms need to be specified for the state transition probabilities and dwell-time distributions.
Recursions for constructing the likelihood are developed and the EM algorithm used to fit the parameters of the model. The choice of dwell-time distribution is discussed with a mixture of distributions over disjoint domains providing a flexible alternative. The methods are also extended to deal with censored data. An application of the model to a large-scale bivariate dataset of breakpoint rainfall measurements at Wellington, New Zealand, is discussed.
The general N server finite queue
Authors: Kapadia Asha Seth 
Published: July 2016

Kingman (1962) studied the effect of queue discipline on the mean and variance of the waiting time. He made no assumptions regarding the stochastic nature of the input and the service distributions, except that the input and service processes are independent of each other. When the following two conditions hold:

(a)
no server sits idle while there are customers waiting to be served;

(b)
the busy period is finite with probability one (i.e., the queue empties infinitely often with probability one);

he has shown that the mean waiting time is independent of the queue discipline and the variance of the waiting time is a minimum when the customers are served in order of their arrival. Conditions (a) and (b) will henceforward be called Kingman conditions and a queueing system satisfying Kingman conditions will be referred to in the text as a Kingman queue.
Avalanches of electrons in a gas
Authors: Steutel F. W. 
Published: July 2016

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 parameterp, 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 currentC(t) produced by the moving electrons, as a function of time.
On the distribution of records in a finite sequence of observations, with an application to a road traffic problem
Authors: Haghighi-Talab Dariush , Wright Christopher 
Published: July 2016

Probability distributions relating to the number and positions of lower records in a finite sequence of observations are obtained by methods involving the permutation of ranks. Some new results, and results of earlier authors, are expressed in a form thought to be useful for direct practical applications.
Expressions are also given for the distribution of the length of a ‘record run’, which consists of the observations following and including a given record either up to the next record, or, if a further record does not occur, up to the end of the sequence of observations. This quantity, whose distribution is closely related to that of the inter-record time, has a direct and simple application to road traffic leaving a signal which has been confirmed by experimental observation.
Brain connectome modularity in weight-restored anorexia nervosa and body dysmorphic disorder
Authors: Zhang A. , Leow A. , Zhan L. , GadElkarim J. , Moody T. , Khalsa S. , Strober M. , Feusner J. D. 
Published: July 2016

BackgroundAnorexia nervosa (AN) and body dysmorphic disorder (BDD) frequently co-occur, and have several overlapping phenomenological features. Little is known about their shared neurobiology. The aim of the study was to compare modular organization of brain structural connectivity.MethodWe acquired diffusion-weighted magnetic resonance imaging data on unmedicated individuals with BDD (n= 29), weight-restored AN (n= 24) and healthy controls (HC) (n= 31). We constructed connectivity matrices using whole-brain white matter tractography, and compared modular structures across groups.ResultsAN showed abnormal modularity involving frontal, basal ganglia and posterior cingulate nodes. There was a trend in BDD for similar abnormalities, but no significant differences compared with AN. In AN, poor insight correlated with longer path length in right caudal anterior cingulate and right posterior cingulate.ConclusionsAbnormal network organization patterns in AN, partially shared with BDD, may have implications for understanding integration between reward and habit/ritual formation, as well as conflict monitoring/error detection.
Materials—Metallic and Non-Metallic
Authors: Megson N. J. L. 
Published: July 2016

With increasing speeds of aircraft, problems arise over materials of construction, partly through kinetic heating effects which cause temperature rises and partly through rain erosion effects. Additionally, account has to be taken of a required life of 30,000 hours which is much longer than that over which most materials are normally evaluated.For speeds of Mach 2.2, the maximum temperature attained will be of the order of 130°C, while for Mach 2.7 the corresponding temperature will be 200°C or higher. For the lower speed, it is probable that aluminium alloys will be satisfactory, although it must be emphasised that no information is yet available on the long-term behaviour of materials at the elevated temperatures likely to be experienced. Test programmes are in hand, but these will necessarily take considerable time for their completion. For speeds of Mach 2.7 or above, steel or titanium alloys will be required, but here again the necessary evaluation for long periods at high temperature has yet to be completed.
The Royal Aeronautical Society The First Fifty Years
Authors: Laurence Pritchard J. 
Published: July 2016

Thomas Moy's declaration at the 1873 Meeting of the Society, that he and his partner Shill were constructing a large-scale model of a flying machine, roused considerable interest. Twelve months later, at the Meeting held on 15th May 1874, he said:“We have not got on so fast as we had hoped. Various difficulties had arisen which had to be mastered one by one as they cropped up. As their machine was only a working model, the aeroplane required to be made of some light material. Some time ago I was trying to get thin steel rolled and corrugated but I was unable to get anything suitable. I next tried a fine kind of brown holland for our wing sails, but found this would not take the curves kindly, but got into wrinkles. I am now making use of thin pine lathes nicely planed and fitted so as to form a sectional screw surface, and I think they would answer very well, and would form the nearest approach to a perfect screw that can be obtained.”
Liquid Atomisation
Authors: Fraser R. P. 
Published: July 2016

The process of atomisation is of primary importance in several branches of engineering, such as in the combustion of liquid fuels, in the chemical industry, in operations involving drying, evaporation, absorption, and so on, in fire-fighting and the production and dissipation of fogs and in agriculture.In agriculture, the spraying of small drops is employed in the dissemination of insecticides, herbicides, etc., for the purpose of crop protection, and the spraying of large drops is used for overhead irrigation.Since the advent of the atomiser, a hundred years ago, the engineer has been in advance of theory in his practice of atomisation. For lack of fundamental data he has had to rely upon laborious hit and miss experiments to obtain a design suitable to a particular requirement. Thus the atomiser has been a fruitful avenue for the inventor. Its small size and apparent simplicity has, however, deceived many into the belief that the problem is simple. Research over the last thirty years has proved this to be anything but true, and even now our knowledge is still extremely limited.
The Pressure Registered by a Very Small Static Hole
Authors: Jackson J. D. 
Published: July 2016

Static pressure in a moving fluid is usually measured by means of a static hole either in a probe or on the wall of a duct. Such a hole creates a disturbance in the flow and thus has some error associated with it. The determination of the magnitude of this error has been attempted by several investigators and the procedure adopted in each case has been as follows :The pressure in a region of sensibly constant static pressure was registered using holes of various diameter and a curve of pressure versus hole size plotted. The true static pressure was then obtained by extrapolating this curve to zero hole size, and the errors for the various holes were found. This procedure involves the assumption that, as the hole size tends to zero, the pressure registered tends to the true value. It is usually argued that this must be so because the disturbance caused by the static hole is progressively reduced as the hole size is reduced. Obviously, the validity, or otherwise, of the argument is of fundamental importance in the estimation of static hole error, and a somewhat more rigorous justification of the use of the extrapolation procedure is attempted in what follows.
Part I: Instrument Flight Developments
Authors: Mitchell Harry W. 
Published: July 2016

SummaryHelicopters have reached a state of mechanical reliability today comparable to that of the aeroplane. Rotary wing aircraft have been severely limited performancewise, however, by the fixed wing type of instrumentation commonly used. It has been impossible to operate helicopters throughout their complete flight regime in their normal operational areas during instrument flight conditions. This paper defines the problem, the approach taken by Bell Helicopter Company, the flight test programmes and results, and the future for helicopter instrument flight operations in both populated and remote areas using information sensors and displays designed expressly for VTOL machines.