We use the generating function formalism to calculate the fractal dimensions for the percolating cluster at criticality in Erdős–Rényi (ER) and random scale free (SF) networks, with degree distribution P(k)=ck−λ. We show that the chemical dimension is dl=2 for ER and SF networks with...

We analyze transport properties of a random walk on a comb structure, which serves as a model for a random walk on the backbone of a percolation cluster. It is shown that the random walk along the x axis, which is the analog of the backbone, exhibits anomalous diffusion in that 〈x2(n)〉 ∼...

It is well known that while daily price returns of financial markets are uncorrelated, their absolute values (‘volatility’) are long-term correlated. Here we provide evidence that certain subsequences of the returns themselves also exhibit long-term memory. These subsequences consist of...

We investigate the local cumulative phases at single sites of the lattice for time-dependent wave functions in the Anderson model in d=2 and 3. In addition to a local linear trend, the phases exhibit some fluctuations. We study the time correlations of these fluctuations using detrended...

Using detrended fluctuation analysis, we study the scaling properties of the volatility time series Vi=|Ti+1−Ti| of daily temperatures Ti for 10 chosen sites around the globe. We find that the volatility is long-range power-law correlated with an exponent γ close to 0.8 for all sites...

We study the Zipf plots describing the occurrence of different elements in a given group as a function of their rank. We define a “distance” between two Zipf plots characterizing the differences between the two groups. We apply the distance concept on groups of words contained in books. Our...

Many natural records exhibit long-term correlations characterized by a power-law decay of the auto-correlation function, C(s)∼s−γ, with time lag s and correlation exponent 0γ1. We study, how the presence of such correlations affects the statistics of the return intervals rq for events...

The basic assumption of common extreme value statistics is that different events in a time record are uncorrelated. In this case, the return intervals rq of events above a given threshold size q are uncorrelated and follow the Poisson distribution. In recent years there is growing evidence that...

We describe effects of the asymmetry of cycles and non-stationarity in time series on the phase synchronization method which may lead to artifacts. We develop a modified method that overcomes these effects and apply it to study parkinsonian tremor. Our results indicate that there is...

We study the reaction front for the diffusion-reaction system A + B → C with initially separated reactants. We present analytical results for the form of the front and the exponents that characterize its width and height asymptotically, which appear to hold in d ⩾ 2. We also present...