Nonlinear Phenomena in Biology and Medicine

Nonlinear dynamics has changed our view of many biological phenomena; e.g., coexistence of consumer species competing for the same resource [1], biological pattern formation; e.g., clustering and differentiation of mesenchy-mal cells during pre-cartilage messenchymal condensation in chick limb chondrogenesis (bone patterning and formation) [2] and analysis of heart rate variability in healthy as well as diseased subjects [3] to name a few. The diversity of disciplines and successes of approaches based on non-linear dynamics, complexity theory, and systems biology in resolving a few difficult issues and answering some outstanding questions in recent years led to the idea of compiling a special volume on the subject. This special issue is dedicated to nonlinear phenomena in biology and medicine. The research papers which appear in this issue can be classified into two categories: (1) papers which discuss approaches to nonlinear time series analysis based on dynamical systems theory and (2) others which present models and their potential application to human behavior, biology and medicine. In this issue, K. Friston and F. Ao draw attention of researchers in neuroscience to the possibility that action and perception can be understood in terms of minimization of a free energy surface functional which minimizes " sensory surprise ". Free energy is an information theoretic measure that bounds the surprise on sampling data, given a gen-erative model. Authors compare two different approaches to describe agent action and prediction based on the free energy principle and optimal control reinforcement learning. In the first case, an agent's behavior is controlled by a free energy surface functional that minimizes " sensory surprise " along the trajectory in the phase space of a nonautonomous system with strong fluctuations. The mathematical definition of surprise is conditional entropy. In the last case, an agent's adaptive behavior is determined in order to maximize a reward. Epilepsy is the principal brain dysfunction which affects about 1% world population and has important public health implication. The conventional signal analysis methods such as the count of focal spike density, the frequency coherence, or spectral analyses are not reliable predictors. In this issue the paper by T. Khoa et al. describes a method based on fractal dimension as a principal tool to diagnose epilepsy. Their method combines independent component algorithm with averaging filter at the preprocessing step. The authors show that this improved method could be used to analyze EEG signals to diagnose epilepsy. B. Francesco et al. …