We briefly review some recent attempts to achieve some genuine understanding of diffusion-limited aggregation (DLA), the paradigm model for dynamical mechanisms of disorderly growth processes. We shall see that the seminal ideas of Professor Cyril Domb have influenced to a great degree many of...

We review recent developments in the study of the multifractal properties of dynamical processes in disordered systems. In particular, we discuss the multifractality of the growth probabilities of DLA clusters and of the probability density for random walks on random fractals. The results for...

We review the present status of the studies of DNA sequences using methods of statistical physics. We present evidence, based on systematic studies of the entire GenBank database, supporting the idea that the DNA sequence in genes containing noncoding regions is correlated, and that the...

We discuss the appearance of long-range power-law correlations in various systems of interest to condensed matter physicists and biophysicists, with emphasis on the recent discovery of long-range correlations in DNA sequences that contain non-coding regions.

Here we discuss recent advances in applying ideas of fractals and disordered systems to two topics of biological interest, both topics having in common the appearance of scale-free phenomena, i.e., correlations that have no characteristic length scale, typically exhibited by physical systems...

We discuss examples of complex systems composed of many interacting subsystems. We focus on those systems displaying nontrivial long-range correlations. These include the one-dimensional sequence of base pairs in DNA, the sequence of flight times of the large seabird Wandering Albatross, and the...

We discuss multiple-time scale properties of neurophysiological control mechanisms, using heart rate and gait regulation as model systems. We find that scaling exponents can be used as prognostic indicators. Furthermore, detection of more subtle degradation of scaling properties may provide a...

We introduce and develop new techniques to quantify DNA patchiness, and characteristics of their mosaic structure. These techniques, which involve calculating two functions, α(ℓ) and β(ℓ), measure correlation exponents at length scale ℓ and detect distinct characteristic patch sizes...

One challenge of biology, medicine, and economics is that the systems treated by these serious scientific disciplines have no perfect metronome in time and no perfect spatial architecture—crystalline or otherwise. Nonetheless, as if by magic, out of nothing but randomness one finds remarkably...

We consider a Lévy flyer of order α that starts from a point x0 on an interval [0,L] with absorbing boundaries. We find a closed-form expression for an arbitrary average quantity, characterizing the trajectory of the flyer, such as mean first passage time, average total path length,...