1,720,965 research outputs found
Multivariate Bottcher equation for polynomials with non-negative coefficients
No full textWe give conditions for the multivariate Bottcher equation to have a solution, in the case where is a polynomial with non-negative coefficients. The solution is constructed from the limit of the functional iterates
Analysis of distributions in factorial experiments
No full textThe Cramer-von Mises statistic provides a useful goodness of fit test of whether a random sample has been drawn from some given null distribution. Its use in comparing several samples has also been studied, but not systematically. We show that the statistic is capable of significant generalization. In particular we consider the comparison of the distributions of observations arising from factorial experiments. Provided that observations are replicated, we show that our generalization yields a test statistic capable of decomposition like the sum of squares used in ANOVA. The statistic is calculated using ranked data rather than original observations. We give the asymptotic theory. Unlike ANOVA, the asymptotic distributional properties of the statistic can be obtained without the assumption of normality. Further, the statistic enables differences in distribution other than the mean to be detected. Because it is distribution free, Monte-Carlo sampling can be used to directly generate arbitrarily accurate critical test null values in online analysis irrespective of sample size. The statistic is thus easy to implement in practice. Its use is illustrated with an example based on a man-in-the-loop simulation trial where operators carried out self assessment of the workload that they experienced under different operating conditions
Transition probabilities for the simple random walk on the Sierpinski graph
No full textNon-Gaussian upper and lower bounds are obtained for the transition probabilities of the simple random walk on the Sierpinski graph, the pre-fractal associated with the Sierpinski gasket. They are of the same form as bounds previously obtained for the transition density of Brownian motion on the Sierpinski gasket, subject to a scale restriction. A comparison with transition density bounds for random walks on general graphs demonstrates that this restriction represents the scale at which the pre-fractal graph starts to look like the fractal gasket
Distinguishing between interference and exploitation competition for shelter in a mobile fish population.
No full textUnderstanding the functional significance of shelter for animal populations requires knowledge of the behavioural mechanisms that govern the dynamics of shelter use. Exploitation of shelters may be impeded by mutual interference, yet interference competition can be difficult to distinguish from exploitation competition. We used Bullheads (Cottus gobio) as a model system of mobile fish to investigate the effect of intraspecific competition on shelter use. A series of field experiments was conducted under controlled conditions of shelter availability and population density. For each experiment the location of each individual fish was observed over a period of 10 days. We then constructed a continuous-time Markov-chain model for the movement of fish between shelters and the open stream, which explicitly parameterised exploitation competition and interference competition for shelter, and which accounted for two different size classes of fish. By using a stochastic rather than a deterministic model, we were able to account for the distribution of fish across shelters, and not just the average occupation. Analysis of the model showed strong evidence of exploitation competition, which was highly dependent on body size, and an increased departure rate from shared shelters. Over and above exploitation, interference competition limited the ability of unsheltered fish to colonise vacant shelters at high population densities. Different formulations of the interference competition were compared using the AIC information criterion. The formulation that best fitted the observations modelled interference competition as an increasing function of average shelter occupancy, rather than population density per s
Asymptotically one-dimensional diffusion on the Sierpinski gasket and multi-type branching processes with varying environment
No full textAsymptotically one-dimensional diffusions on the Sierpinski gasket constitute a one parameter family of processes with significantly different behaviour to the Brownian motion. Due to homogenization effects they behave globally like the Brownian motion, yet locally they have a preferred direction of motion. We calculate the spectral dimension for these processes and obtain short time heat kernel estimates in the Euclidean metric. The results are derived using branching process techniques, and we give estimates for the left tail of the limiting distribution for a supercritical multi-type branching process with varying environment
Analysis of simulation factorial experiments by EDF resample statistics
No full textThe output from simulation factorial experiments can be complex and may not be amenable to standard methods of estimation like ANOVA. We consider the situation where the simulation output may not satisfy normality assumptions, but more importantly, where there may be differences in output at different factor combinations, but these are not simply differences in means. We show that EDF statistics can provide a similar but potentially more sensitive analysis to that provided by ANOVA. Moreover we show that with the use of resampling, we can generate accurate critical values for tests of hypothesis under much weaker conditions than those required for ANOVA tests. The method is illustrated with an example based on an actual simulation experiment comparing two methods of operating a production facility under different production levels
Estimating crystal growth rates using computed tomography
No full textIt has been observed that sugar crystals growing in solution exhibit Growth Rate Dispersion, that is, variation in growth rate from one crystal to the next. We consider the problem of estimating the distribution of growth rates in batch grown crystals, given only samples of their sizes at a number of fixed points in time. The problem can be expressed as a tomographic image reconstruction problem, in which we try to reconstruct the joint density of initial size and growth, from a set of marginal densities obtained by integrating the joint density in a number of different directions
Thick and thin points for random recursive fractals
No full textWe consider random recursive fractals and prove fine results about their local behaviour. We show that for a class of random recursive fractals the usual multifractal spectrum is trivial in that all points have the same local dimension. However, by examining the local behaviour of the measure at typical points in the set, we establish the size of fine fluctuations in the measure. The results are proved using a large deviation principle for a class of general branching processes which extends the known large deviation estimates for the supercritical Galton-Watson process
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