From single decisions to sequential choice patterns: Extending the dynamics of value-based decision-making.

Every day, we make many value-based decisions where we weigh the value of options with other properties, e.g. their time of delivery. In the laboratory, such value-based decision-making is usually studied on a trial by trial basis and each decision is assumed to represent an isolated choice process. Real-life decisions however are usually embedded in a rich context of previous choices at different time scales. A fundamental question is therefore how the dynamics of value-based decision processes unfold on a time scale across several decisions. Indeed, findings from perceptual decision making suggest that sequential decisions patterns might also be present for vale-based decision making. Here, we use a neural-inspired attractor model as an instance of dynamic models from perceptual decision making, as such models incorporate inherent activation dynamics across decisions. We use the model to predict sequential patterns, namely oscillatory switching, perseveration and dependence of perseveration on the delay between decisions. Furthermore, we predict RT effects for specific sequences of trials. We validate the predictions in two new studies and a reanalysis of existing data from a novel decision game in which participants have to perform delay discounting decisions. Applying the validated reasoning to a well-established choice questionnaire, we illustrate and discuss that taking sequential choice patterns into account may be necessary to accurately analyse and model value-based decision processes, especially when considering differences between individuals.

A comparative study of integrated pest management strategies based on impulsive control.

The paper presents a comprehensive numerical study of mathematical models used to describe complex biological systems in the framework of integrated pest management. Our study considers two specific ecosystems that describe the application of control mechanisms based on pesticides and natural enemies, implemented in an impulsive and periodic manner, due to which the considered models belong to the class of impulsive differential equations. The present work proposes a numerical approach to study such type of models in detail, via the application of path-following (continuation) techniques for nonsmooth dynamical systems, via the novel continuation platform COCO (Dankowicz and Schilder). In this way, a detailed study focusing on the influence of selected system parameters on the effectiveness of the pest control scheme is carried out for both ecological scenarios. Furthermore, a comparative study is presented, with special emphasis on the mechanisms upon which a pest outbreak can occur in the considered ecosystems. Our study reveals that such outbreaks are determined by the presence of a branching point found during the continuation analysis. The numerical investigation concludes with an in-depth study of the state-dependent pesticide mortality considered in one of the ecological scenarios.

An SIR-Dengue transmission model with seasonal effects and impulsive control.

In recent decades, Dengue fever and its deadly complications, such as Dengue hemorrhagic fever, have become one of the major mosquito-transmitted diseases, with an estimate of 390 million cases occurring annually in over 100 tropical and subtropical countries, most of which belonging to the developing world. Empirical evidence indicates that the most effective mechanism to reduce Dengue infections is to combat the disease-carrying vector, which is often implemented via chemical pesticides to destroy mosquitoes in their adult or larval stages. The present paper considers an SIR epidemiological model describing the vector-to-host and host-to-vector transmission dynamics. The model includes pesticide control represented in terms of periodic impulsive perturbations, as well as seasonal fluctuations of the vector growth and transmission rates of the disease. The effectiveness of the control strategy is studied numerically in detail by means of path-following techniques for non-smooth dynamical systems. Special attention is given to determining the optimal timing of the pesticide applications, in such a way that the number of infections and the required amount of pesticide are minimized.

Finite-time Lyapunov exponents and metabolic control coefficients for threshold detection of stimulus-response curves.

In biochemical networks transient dynamics plays a fundamental role, since the activation of signalling pathways is determined by thresholds encountered during the transition from an initial state (e.g. an initial concentration of a certain protein) to a steady-state. These thresholds can be defined in terms of the inflection points of the stimulus-response curves associated to the activation processes in the biochemical network. In the present work, we present a rigorous discussion as to the suitability of finite-time Lyapunov exponents and metabolic control coefficients for the detection of inflection points of stimulus-response curves with sigmoidal shape.

How Inhomogeneous Site Percolation Works on Bethe Lattices: Theory and Application.

Inhomogeneous percolation, for its closer relationship with real-life, can be more useful and reasonable than homogeneous percolation to illustrate the critical phenomena and dynamical behaviour of complex networks. However, due to its intricacy, the theoretical framework of inhomogeneous percolation is far from being complete and many challenging problems are still open. In this paper, we first investigate inhomogeneous site percolation on Bethe Lattices with two occupation probabilities, and then extend the result to percolation with m occupation probabilities. The critical behaviour of this inhomogeneous percolation is shown clearly by formulating the percolation probability P∞(p) with given occupation probability p, the critical occupation probability pc = sup{p|P∞(p) = o}, and the average cluster size χ(p) where p is subject to P∞(p) = o. Moreover, using the above theory, we discuss in detail the diffusion behaviour of an infectious disease (SARS) and present specific disease-control strategies in consideration of groups with different infection probabilities.

General analysis of mathematical models for bone remodeling.

Bone remodeling is regulated by pathways controlling the interplay of osteoblasts and osteoclasts. In this work, we apply the method of generalized modeling to systematically analyse a large class of models of bone remodeling. Our analysis shows that osteoblast precursors can play an important role in the regulation of bone remodeling. Further, we find that the parameter regime most likely realized in nature lies close to bifurcation lines, marking qualitative changes in the dynamics. Although proximity to a bifurcation facilitates adaptive responses to changing external conditions, it entails the danger of losing dynamical stability. Some evidence implicates such dynamical transitions as a potential mechanism leading to forms of Paget's disease.