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We present a model for the interaction dynamics of lymphocytes-tumor cells population. This model reproduces all known states for the tumor. Futherly, we develop it taking into account periodical immunotheraphy treatment with cytokines alone. A detailed analysis for the evolution of tumor cells as a function of frecuency and theraphy burden applied for the… (More)

The diffusion of a walk in the presence of traps is investigated. Different diffusion regimes are obtained considering the magnitude of the fluctuations in waiting times and jump distances. A constant velocity during the jump motion is assumed to avoid the divergence of the mean squared displacement. Using the limit theorems of the theory of Lévy stable… (More)

The expression of survival factors for radiation damaged cells is currently based on probabilistic assumptions and experimentally fitted for each tumor, radiation, and conditions. Here, we show how the simplest of these radiobiological models can be derived from the maximum entropy principle of the classical Boltzmann-Gibbs expression. We extend this… (More)

- Oscar Sotolongo-Costa, Yamir Moreno-Vega, Juan J Lloveras-González, J C Antoranz
- 1994

Experiments in rupture of mercury drops have been performed recording the size distribution of the cumulative number of drops for different conditions of rupture. A transition of the distribution from log-normal to scaling behavior is shown. To describe it, a geometric probabilistic model is proposed. Consequently, the rupture can be described as a process… (More)

By using the maximum entropy principle with Tsallis entropy we obtain a fragment size distribution function which undergoes a transition to scaling. This distribution function reduces to those obtained by other authors using Shannon en-tropy. The treatment is easily generalisable to any process of fractioning with suitable constraints.

We derive a universal function for the kinetics of complex systems characterized by stretched exponential and/or power-law behaviors.This kinetic function unifies and generalizes previous theoretical attempts to describe what has been called " fractal kinetic ". The concentration evolutionary equation is formally similar to the relaxation function obtained… (More)

We show that if one uses the invariant form of the Boltzmann-Shannon continuous entropy, it is possible to obtain the generalized Pareto-Tsallis density function, using an appropriate " prior " measure m q (x) and a " Boltzman constraint " which formally is equivalent to the Tsallis q-average constraint on the random variable X. We derive the Tsallis prior… (More)

The expression of survival factors for radiation damaged cells is based on probabilistic assumptions and experimentally fitted for each tumor, radiation and conditions. Here we show how the simplest of these radiobiological models can be derived from the maximum entropy principle of the classical Boltzmann-Gibbs expression. We extend this derivation using… (More)

We model the interaction between the immune system and tumor cells including a time delay to simulate the time needed by the latter to develop a chemical and cell mediated response to the presence of the tumor. The results are compared with those of a previous paper, concluding that the delay introduces new instabilities in the system leading to an… (More)

We have derived the dipolar relaxation function for a cluster model whose volume distribution was obtained from the generalized maximum Tsallis nonextensive entropy principle. The power law exponents of the relaxation function are simply related to a global fractal parameter α and for large time to the entropy nonextensivity parameter q. For intermediate… (More)