We study the size distribution of purine and pyrimidine clusters in coding and non-coding DNA sequences. We observe that the cluster-size distribution P(s) follows an exponential decay in coding sequences whereas it follows a power-law decay in non-coding sequences: P(s) ∼ s−1−μ, with a...

The behavior of the solution for an exactly solvable bistable model is analyzed. The decay processes of unstable states are discussed. The results of the scaling theory are tested. It is concluded that the scaling theory is not valid for the model even when the potential barrier is very high.

Two exactly solvable models—the double oscillator model and the associated harmonic oscillator model for which the Kramers approximation taken in the Gaussian approximation has an extra factor √π2-are discussed. A quantum mechanical derivation of the Kramers approximation without the...

A random aggregation model with influx is proposed for the formation of the non-coding DNA regions via random co-aggregation and influx of biological macromolecules such as viruses, parasite DNA, and replication segments. The constant mixing (transpositions) and influx drives the system in an...

We use q-exponential distributions, which maximize the nonextensive entropy Sq (defined as Sq≡(1−∑ipiq)/(q−1)), to study the size distributions of non-coding DNA (including introns and intergenic regions) in all human chromosomes. We show that the value of the exponent q describing the...

By using non-extensive block entropy statistics, we demonstrate analytically that the static structures of deterministic Cantor sets with fractal dimension df are characterised by a non-extensive q-exponent q=1/(df-d), for dfd (where d is the embedding dimensions of the fractal set). To...

An abstract network approach is proposed for the description of the dynamics in reactive processes. The phase space of the variables (concentrations in reactive systems) is partitioned into a finite number of segments, which constitute the nodes of the abstract network. Transitions between the...

Much of the on-going statistical analysis of DNA sequences is focused on the estimation of characteristics of coding and non-coding regions that would possibly allow discrimination of these regions. In the current approach, we concentrate specifically on genes and intergenic regions. To estimate...

The cluster formation in the cyclic (4+1)-Lattice Lotka–Volterra Model is studied by Kinetic Monte Carlo simulations on a square lattice support. At the Mean Field level this model demonstrates conservative four-dimensional oscillations which, depending on the parameters, can be chaotic or...