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We study a one-dimensional random walk with memory. The behavior of the walker is modified with respect to the simple symmetric random walk (SSRW) only when he is at the maximum distance ever reached from his starting point (home). In this case, having the choice to move farther or to move closer, he decides with different probabilities. If the probability of a forward step is higher then the probability of a backward step, the walker is bold, otherwise he is timorous. We investigate the asymptotic properties of this bold/timorous random walk (BTRW) showing that the scaling behavior vary continuously from subdiffusive (timorous) to superdiffusive (bold). The scaling exponents are fully determined with a new mathematical approach.
Anomalous diffusion or, more generally, anomalous transport, with nonlinear dependence of the mean-squared displacement on the measurement time, is ubiquitous in nature. It has been observed in processes ranging from microscopic movement of molecules
We investigate the time evolution of the scores of the second most popular sport in world: the game of cricket. By analyzing the scores event-by-event of more than two thousand matches, we point out that the score dynamics is an anomalous diffusive p
Recent studies show that in interdependent networks a very small failure in one network may lead to catastrophic consequences. Above a critical fraction of interdependent nodes, even a single node failure can invoke cascading failures that may abrupt
We have studied the distribution of traffic flow $q$ for the Nagel-Schreckenberg model by computer simulations. We applied a large-deviation approach, which allowed us to obtain the distribution $P(q)$ over more than one hundred decades in probabilit
We investigate a stationary processs crypticity---a measure of the difference between its hidden state information and its observed information---using the causal states of computational mechanics. Here, we motivate crypticity and cryptic order as ph