Armando Ciancio

HYBRID TWO SCALES MATHEMATICAL TOOLS FOR ACTIVE PARTICLES MODELLING COMPLEX SYSTEMS WITH LEARNING HIDING DYNAMICS

This paper deals with the derivation of hybrid mathematical structures to describe the behavior of large systems of active particles by ordinary differential equations with stochastic coefficients whose evolution is modelled by equations of the mathematical kinetic theory. A preliminary analysis shows how the above tools can be used to model complex systems of interest in applied sciences, with special attention to the immune competition.

Separable Transition Density in the Hybrid Model for Tumor-Immune System Competition

A hybrid model, on the competition tumor cells immune system, is studied under suitable hypotheses. The explicit form for the equations is obtained in the case where the density function of transition is expressed as the product of separable functions. A concrete application is given starting from a modified Lotka-Volterra system of equations.

Metamodeling the learning-hiding competition between tumours and the immune system: A kinematic approach

The competitive interaction between the Immune System and tumours is very complex, being non-linear and, to some extent, evolutionary. A fundamental aspect of this evolution is the asynchronous process of mutual learning of the two populations involved - the tumoural and the immune cells. In this work, to describe them, we propose a simple non-linear family of super-macroscopic models with non-monotonically time-varying coefficients. Numerical simulations of transitory phases complement the theoretical analysis.

SOME APPLICATIONS OF LINEAR RESPONSE THEORY TO MEDIA WITH MECHANICAL RELAXATION PHENOMENA

The general linear response theory it applied for study mechanical relaxations phenomena in continuous media. It is shown that phenomenological and state coefficients, in viscoanelastic media can be obtained as function of quantities which are experimentally measurable. The behaviour of the medium at low and high frequency is taking in account. Therefore, by compared the solutions of the differential equations that describe relaxation phenomena in the considered model to a relation that describe the same phenomena in linear response theory, it is possible to determine the aforementioned coefficients.

A Class of Solutions for the Hybrid Kinetic Model in the Tumor-Immune System Competition

In this paper, the hybrid kinetic models of tumor-immune system competition are studied under the assumption of pure competition. The solution of the coupled hybrid system depends on the symmetry of the state transition density which characterizes the probability of successful occurrences. Thus by defining a proper transition density function, the solutions of the hybrid system are explicitly computed and applied to a classical (realistic) model of competing populations.

Analysis of singularities by short haar wavelet transform

Wavelets give significant information on the evolution of a time series. In particular, due to their localization properties the significant local changes in observed data (both in time and in frequency) can be easily detected by a limited set of their corresponding wavelet coefficients. Some examples will be given, in the following, showing the effectiveness of this method.

Nonholonomic Geometry of Viscoanelastic Media and Experimental Confirmation

A thermodynamical model for viscoanelastic media is analyzed using the nonholonomic geometry. A 27-dimensional manifold is introduced, and the differential equations for the geodetics are determined and analytically solved. It is shown that, in this manifold, the best specific entropy is a harmonic function. In the linear case the propagation of transverse acoustic waves is studied, and the theoretical results are compared with some experimental data from a polymeric material (polyisobutylene).