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We address the general question of what is the best statistical strategy to adapt in order to search efficiently for randomly located objects ('target sites'). It is often assumed in foraging theory that the flight lengths of a forager have a characteristic scale: from this assumption gaussian, Rayleigh and other classical distributions with well-defined(More)
The study of animal foraging behaviour is of practical ecological importance, and exemplifies the wider scientific problem of optimizing search strategies. Lévy flights are random walks, the step lengths of which come from probability distributions with heavy power-law tails, such that clusters of short steps are connected by rare long steps. Lévy flights(More)
We study the role of dynamical constraints in the general problem of finding the best statistical strategy for random searching when the targets can be detected only in the limited vicinity of the searcher. We find that the optimal search strategy depends strongly on the delay time tau during which a previously visited site becomes unavailable. We also find(More)
An important application involving two-species reaction-diffusion systems relates to the problem of finding the best statistical strategy for optimizing the encounter rate between organisms. We investigate the general problem of how the encounter rate depends on whether organisms move in Lévy or Brownian random walks. By simulating a limiting generalized(More)
An important problem in physics concerns the analysis of audio time series generated by transduced acoustic phenomena. Here, we develop a new method to quantify the scaling properties of the local variance of nonstationary time series. We apply this technique to analyze audio signals obtained from selected genres of music. We find quantitative differences(More)
A classic problem in physics is the analysis of highly nonstationary time series that typically exhibit long-range correlations. Here we test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat-to-beat fluctuations in the human heart rate. We develop(More)
In this work we discuss some recent contributions to the random search problem. Our analysis includes superdiffusive Lévy processes and correlated random walks in several regimes of target site density, mobility and revisitability. We present results in the context of mean-field-like and closed-form average calculations, as well as numerical simulations. We(More)
Functional magnetic resonance imaging (fMRI) has just completed 20 years of existence. It currently serves as a research tool in a broad range of human brain studies in normal and pathological conditions, as is the case of epilepsy. To date, most fMRI studies aimed at characterizing brain activity in response to various active paradigms. More recently, a(More)
Animal searches cover a full range of possibilities from highly deterministic to apparently completely random behaviors. However, even those stochastic components of animal movement can be adaptive, since not all random distributions lead to similar success in finding targets. Here we address the general problem of optimizing encounter rates in(More)
We introduce and develop new techniques to quantify DNA patchiness, and to quantify characteristics of its mosaic structure. These techniques, which involve calculating two functions, alpha(l) and beta(l), measure correlations at length scale l and detect distinct characteristic patch sizes embedded in scale-invariant patch size distributions. Using these(More)