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result(s) for
"Jakeman, E"
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Emergence of periodic behaviours from randomness
This paper discusses how periodic behaviours can arise in discrete systems where the underlying dynamics are purely random. We consider non-interacting particles moving randomly on a network of nodes forming a closed loop. The population dynamics describing the number of particles at a node is a stochastic birth-death process, augmented by particles migrating randomly to adjacent nodes. This can result in the emergence of periodic behaviours occurring because of the interaction between the dynamics of the particles and the spatial structure through which they move. The conditions for this requires the network to comprise of three or more nodes and the migration to have a preferred direction. Moreover there are three classes of equilibria for the populations at nodes that depend on the relative values of the migration and birth rates.
Journal Article
Laguerre population processes
We analyse a number of stochastic processes that give rise to first-order number statistics governed by Laguerre distributions with properties that lie between Poisson and geometric random variables. These distributions have hitherto been used to characterize the photon statistics of a coherent mixture of thermal and laser light. Here, we explore a number of discrete population processes that can lead to the same first-order statistics and correlation functions and highlight the distinguishing features that may be used to identify the relevant model from data.
Journal Article
Intrinsic and measured statistics of discrete stochastic populations
The notion that the nature of a measurement is critical to its outcome is usually associated with quantum phenomena. In this paper, we show that the observed statistical properties are also a function of the measurement technique in the case of simple classical populations. In particular, the measured and intrinsic statistics of a single population may be different, while correlation and transfer of individuals between two populations may be hidden from the observer.
Journal Article
Distinguishing population processes by external monitoring
We investigate the statistical and correlation properties of two stochastic population models that give rise to identical first-order probability densities. We assume that the processes are monitored indirectly through measurement of the rate at which individuals emigrate from the population. Formulae characterizing the integrated statistics of these counting processes are derived, and it is shown how they may be used to distinguish the population models.
Journal Article
The Great War in the Heart of Dixie
There has been much scholarship on how the U.S.as a nation reacted to World War I, but few have explored how Alabama responded.Did the state follow the federal government's lead in organizing its resources or did Alabamians devise their own solutions to unique problems they faced?How did the state's cultural institutions and government react?.
eBook
On the solution of the Bénard problem with boundaries of finite conductivity
The Bénard problem in hydrodynamic stability is formulated under conditions where the media bounding the fluid have finite thermal diffusivity. It is shown that the principle of the exchange of stabilities remains valid in this case so that instability in the fluid first sets in as stationary convection. Solutions are obtained for various values of the ratio of the thermal diffusivity of the fluid to that of the bounding media; the critical Rayleigh number at which the instability occurs is markedly reduced when this ratio is large.
Journal Article
The evolution and measurement of a population of pairs
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.
Journal Article
