One of the simplest and very popular techniques for pricing an option or other derivative involves constructing what is known as a binomial tree. This is a tree which represents the possible paths, that might be followed by the underlying assets price. We will view this tree as a dynamical...

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...

The empirical study of network dynamics has been limited by the lack of longitudinal data. Here we introduce a quantitative indicator of link persistence to explore the correlations between the structure of a mobile phone network and the persistence of its links. We show that persistent links...

The connection between fluid dynamics and classical statistical mechanics has motivated in the past mathematical investigations of the incompressible Navier–Stokes (NS) equations (INSE) by means of an asymptotic kinetic theory. This feature has suggested the search for possible alternative...

We show that any quasi-polynomial invariant of a quasi-polynomial dynamical system can be transformed into a quasi-polynomial invariant of a homogeneous quadratic Lotka–Volterra dynamical system. We show how this quasi-polynomial invariant can be decomposed in a simple manner. This...

We extend to general divergenceless systems the dynamical thermostatting approach to statistical ensembles proposed by Kusnezov, Bulgac and Bauer (KBB). Furthermore, a new family of dynamical systems inspired by the KBB method is introduced, and some of its properties considered.

Considering a prototypic model of a bimodal oscillator we investigate the synchronization of the internal time scales for a system with interacting fast and slow oscillatory modes. Particular emphasis is given to the transition between mode-locked and mode-unlocked chaos. It is shown that this...

We analyze some models of nonequilibrium systems proposed in the past decade which derive the laws of irreversible thermodynamics from deterministic dynamics. We find that these models do not posses the crucial property of local thermodynamic equilibrium, since they represent noninteracting...

We present an automated algorithm for inferring analytical models of closed reactive biochemical mixtures, on the basis of standard approaches borrowed from thermodynamics and kinetic theory of gases. As input, the method requires a number of steady states (i.e. an equilibria cloud in...

Maximum entropy principle does not seem to distinguish between the use of Tsallis and Renyi entropies as either of them may be used to derive similar kind of q-exponential distributions. In this paper, we address the question whether the Renyi entropy is equally suitable to describe those...