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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)

- D Rodríguez-Pérez, Oscar Sotolongo-Grau, Ramón Espinosa Riquelme, Oscar Sotolongo-Costa, J Antonio Santos Miranda, J C Antoranz
- Mathematical medicine and biology : a journal of…
- 2007

A cytokine-based periodic immunotherapy treatment is included in a model of tumour growth with a delay. The effects of dose schedule are studied in the case of a weak immune system and a growing tumour. We find the existence of 'metastable' states (that may last for tens of years) induced by the treatment and also potentially adverse effects of the dosage… (More)

- Oscar Sotolongo-Costa, A Posadas
- Physical review letters
- 2004

A model for earthquake dynamics consisting of two rough profiles interacting via fragments filling the gap is introduced, the fragments being produced by the local breakage due to the interaction of the local plates. The irregularities of the fault planes can interact with the fragments between them to develop a mechanism for triggering earthquakes. The… (More)

- O Sotolongo-Grau, D Rodríguez-Pérez, J A Santos-Miranda, O Sotolongo-Costa, J C Antoranz
- Mathematical medicine and biology : a journal of…
- 2009

A dynamical system model for tumour-immune system interaction together with a method to mimic radiation therapy are proposed. A large population of virtual patients is simulated following an ideal radiation treatment. A characteristic parameter, the immune system-tumor efficiency ratio (ISTER) is introduced. ISTER dependence of treatment success and other… (More)

- O Sotolongo-Grau, D Rodríguez-Pérez, J C Antoranz, Oscar Sotolongo-Costa
- Physical review letters
- 2010

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)

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)

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 in… (More)

- Oscar Sotolongo-Costa, Arezky H. Rodriguez, G. J. Rodgers
- Entropy
- 2000

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 entropy. The treatment is easily generalisable to any process of fractioning with suitable constraints.

- 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)

- O Sotolongo-Costa, G J Rodgers
- Physical review. E, Statistical, nonlinear, and…
- 2003

We consider the phenomenon of Bose-Einstein condensation in a random growing directed network. The network grows by the addition of vertices and edges. At each time step the network gains a vertex with probability p and an edge with probability 1-p. The new vertex has a fitness (a,b) a,b>0, with probability f(a,b). A vertex with fitness (a,b), with… (More)