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 resource for signs and Feynman diagrams of the standart model

When performing a full calculation within the standard model (SM) or its extensions, it is crucial that one utilizes a consistent set of signs for the gauge couplings and gauge fields. Unfortunately, the literature is plagued with differing signs and notations. We present all SM Feynman rules, including ghosts, in a convention-independent notation, and we table the conventions in close to 40 books and reviews.

The US actuarial balance model for the pay-as-you-go system and its application to Spain

The aim of this paper is to formulate an approximation of the US actuarial balance model and apply it to the Spanish public retirement pension system under various scenarios in order to determine a consistent indicator of the system's financial state comparable to those used by the most advanced social security systems. This will enable us to answer the question as to whether there is any justification for reforming the pension system in Spain. This type of actuarial balance uses projections to show future challenges to the financial side of the pension system deriving basically from ageing, the projected increase in longevity and fluctuations in economic activity. If one is compiled periodically it can provide various indicators to help depoliticize the management of the pay-as-you-go system by bringing the planning horizons of politicians and the system itself closer together.

Decisions with multiple simultaneous goals and uncertain causal effects

A key aspect of decision-making in a disaster response scenario is the capability to evaluate multiple and simultaneously perceived goals. Current competing approaches to build decision-making agents are either mental-state based as BDI, or founded on decision-theoretic models as MDP. The BDI chooses heuristically among several goals and the MDP searches for a policy to achieve a specific goal. In this paper we develop a preferences model to decide among multiple simultaneous goals. We propose a pattern, which follows a decision-theoretic approach, to evaluate the expected causal effects of the observable and non-observable aspects that inform each decision. We focus on yes-or-no (i.e., pursue or ignore a goal) decisions and illustrate the proposal using the RoboCupRescue simulation environment.