A 3D copepod trajectory is recorded in the laboratory, using two digital cameras. The copepod undergoes a very structured type of trajectory, with successive moves displaying intermittent amplitudes. We perform a statistical analysis of this 3D trajectory using statistical tools developed in the...

The cyto-architecture of eukaryotic cells contains self-assembled long cylinder-like structures called microtubules (MTs) which play an important role in a number of cellular activities such as cell division, motility, information processing and intracellular transport. In this paper we present...

From the generalized scheme of random walks on the comb-like structure, one can obtain the fractional Fokker–Planck equation in the domain of fractal time evolution with critical exponent β(0β⩽1). The operator method for the moments associated with the density p(x,t) is used to solve the...

We show that the platform stage of network evolution plays a principal role in the topology of resulting networks generated by short-cuts stimulated by the movements of a random walker, the mechanism of which tends to produce power-law degree distributions. To examine the numerical results, we...

For arbitrary random walks in any d-dimensional space, expansions in powers of 1/d of asphericity and prolateness parameters and moments of the inverse size ratio have been developed, which, at O(1/d3), yield very good approximations to exact values of the parameters for chains, rings, dumbbells...

We determine the geometrical properties of the most probable paths at finite temperatures T, between two points separated by a distance r, in one-dimensional lattices with positive energies of interaction εi associated with bond i. The most probable path-length tmp in a homogeneous medium...

We study the statistics of record-breaking events in daily stock prices of 366 stocks from the Standard and Poor’s 500 stock index. Both the record events in the daily stock prices themselves and the records in the daily returns are discussed. In both cases we try to describe the record...

We present a simple mechanism for generating undirected scale-free networks using random walkers, where the network growth is determined by choosing parent vertices by sequential random walks. We show that this mechanism produces scale-free networks with degree exponent γ=3 and clustering...

One of several critical issues in the development of optimal disease containment and eradication strategies is the knowledge of underlying contacts between individuals. Here we employ random search strategies to identify all possible links, representing direct or indirect interactions between...

We use a decimation procedure in order to obtain the dynamical renormalization group transformation (RGT) properties of random walk distribution in a 1+1 lattice. We obtain an equation similar to the Chapman–Kolmogorov equation. First we show the existence of invariants of the RGT, and that...