We study the multifractal (MF) properties of the set of growth probabilities {pi} for 3D off-lattice diffusion-limited aggregation (DLA). We find that: (i) the {pi} display MF scaling for all moments-in contrast to 2D DLA, where one observes a “phase transition” in the MF spectrum for...

We discuss recent findings suggesting that an inverse square probability density distribution P(ℓ)∼ℓ−2 of step lengths ℓ leads to an optimal random search strategy for organisms that can search efficiently for randomly located objects that can only be detected in the limited vicinity...

Recently it has been shown that the most efficient strategy for searching randomly located objects, when the sites are randomly distributed and can be revisited any number of times, leads to a power law distribution P(ℓ)=ℓ−μ of the flights ℓ, with μ=2. We show analytically that the...

We review the general search problem of how to find randomly located objects that can only be detected in the limited vicinity of a forager, and discuss its quantitative description using the theory of random walks. We illustrate Lévy flight foraging by comparison to Brownian random walks and...

Asymptotic forms for the expected number of distinct sites visited by an n-step random walk, being calculable for many random walks, have been used in a number of analyses of physical models. We describe three recent extensions of the problem, the first replacing the single random walker by...

We model the power-law stability in distribution of returns for S&P500 index by the GARCH process which we use to account for the long memory in the variance correlations. Precisely, we analyze the distributions corresponding to temporal aggregation of the GARCH process, i.e., the sum of n GARCH...

We investigate how simultaneously recorded long-range power-law correlated multivariate signals cross-correlate. To this end we introduce a two-component ARFIMA stochastic process and a two-component FIARCH process to generate coupled fractal signals with long-range power-law correlations which...

We report some recent attempts to understand the dynamics of complex physiologic fluctuations by adapting and extending concepts and methods developed very recently in statistical physics. We first review recent progress using wavelet-based multifractal analysis, magnitude and sign decomposition...

We record and analyze the noise experienced by a tracer particle in a one-dimensional system of particles interacting with hard-core interactions. We find that the correlations of the noise are long-range, with an algebraic decay in time.