Topological Complexity and Predictability in the Dynamics of a Tumor Growth Model with Shilnikov's Chaos

Dynamical systems modeling tumor growth have been investigated to determine the dynamics between tumor and healthy cells. Recent theoretical investigations indicate that these interactions may lead to different dynamical outcomes, in particular to homoclinic chaos. In the present study, we analyze both topological and dynamical properties of a recently characterized chaotic attractor governing the dynamics of tumor cells interacting with healthy tissue cells and effector cells of the immune system. By using the theory of symbolic dynamics, we first characterize the topological entropy and the parameter space ordering of kneading sequences from one-dimensional iterated maps identified in the dynamics, focusing on the effects of inactivation interactions between both effector and tumor cells. The previous analyses are complemented with the computation of the spectrum of Lyapunov exponents, the fractal dimension and the predictability of the chaotic attractors. Our results show that the inactivation rate of effector cells by the tumor cells has an important effect on the dynamics of the system. The increase of effector cells inactivation involves an inverse Feigenbaum (i.e. period-halving bifurcation) scenario, which results in the stabilization of the dynamics and in an increase of dynamics predictability. Our analyses also reveal that, at low inactivation rates of effector cells, tumor cells undergo strong, chaotic fluctuations, with the dynamics being highly unpredictable. Our findings are discussed in the context of tumor cells potential viability.

A model for heterogeneous networks management and Performance evaluation

In general, modern networks are analysed by taking several Key Performance Indicators (KPIs) into account, their proper balance being required in order to guarantee a desired Quality of Service (QoS), particularly, cellular wireless heterogeneous networks. A model to integrate a set of KPIs into a single one is presented, by using a Cost Function that includes these KPIs, providing for each network node a single evaluation parameter as output, and reflecting network conditions and common radio resource management strategies performance. The proposed model enables the implementation of different network management policies, by manipulating KPIs according to users' or operators' perspectives, allowing for a better QoS. Results show that different policies can in fact be established, with a different impact on the network, e.g., with median values ranging by a factor higher than two.

A Model to Evaluate Vertical Handovers on JRRM

In a heterogeneous cellular networks environment, users behaviour and network deployment configuration parameters have an impact on the overall Quality of Service. This paper proposes a new and simple model that, on the one hand, explores the users behaviour impact on the network by having mobility, multi-service usage and traffic generation profiles as inputs, and on the other, enables the network setup configuration evaluation impact on the Joint Radio Resource Management (JRRM), assessing some basic JRRM performance indicators, like Vertical Handover (VHO) probabilities, average bit rates, and number of active users, among others. VHO plays an important role in fulfilling seamless users sessions transfer when mobile terminals cross different Radio Access Technologies (RATs) boundaries. Results show that high bit rate RATs suffer and generate more influence from/on other RATs, by producing additional signalling traffic to a JRRM entity. Results also show that the VHOs probability can range from 5 up to 65%, depending on RATs cluster radius and users mobility profile.