Complex Systems Science: Dreams of Universality, Reality of Interdisciplinarity

Using a large database (~ 215 000 records) of relevant articles, we empirically study the "complex systems" field and its claims to find universal principles applying to systems in general. The study of references shared by the papers allows us to obtain a global point of view on the structure of this highly interdisciplinary field. We show that its overall coherence does not arise from a universal theory but instead from computational techniques and fruitful adaptations of the idea of self-organization to specific systems. We also find that communication between different disciplines goes through specific "trading zones", ie sub-communities that create an interface around specific tools (a DNA microchip) or concepts (a network).Comment: Journal of the American Society for Information Science and Technology (2012) 10.1002/asi.2264

Chaotic Time Series Analysis in Economics: Balance and Perspectives

To show that a mathematical model exhibits chaotic behaviour does not prove that chaos is also present in the corresponding data. To convincingly show that a system behaves chaotically, chaos has to be identified directly from the data. From an empirical point of view, it is difficult to distinguish between fluctuations provoked by random shocks and endogenous fluctuations determined by the nonlinear nature of the relation between economic aggregates. For this purpose, chaos tests test are developed to investigate the basic features of chaotic phenomena: nonlinearity, fractal attractor, and sensitivity to initial conditions. The aim of the paper is not to review the large body of work concerning nonlinear time series analysis in economics, about which much has been written, but rather to focus on the new techniques developed to detect chaotic behaviours in the data. More specifically, our attention will be devoted to reviewing the results reached by the application of these techniques to economic and financial time series and to understand why chaos theory, after a period of growing interest, appears now not to be such an interesting and promising research area.Economic dynamics, nonlinearity, tests for chaos, chaos

Mathematical modelling and brain dynamical networks

In this thesis, we study the dynamics of the Hindmarsh-Rose (HR) model which studies the spike-bursting behaviour of the membrane potential of a single neuron. We study the stability of the HR system and compute its Lyapunov exponents (LEs). We consider coupled general sections of the HR system to create an undirected brain dynamical network (BDN) of Nn neurons. Then, we study the concepts of upper bound of mutual information rate (MIR) and synchronisation measure and their dependence on the values of electrical and chemical couplings. We analyse the dynamics of neurons in various regions of parameter space plots for two elementary examples of 3 neurons with two different types of electrical and chemical couplings. We plot the upper bound Ic and the order parameter rho (the measure of synchronisation) and the two largest Lyapunov exponents LE1 and LE2 versus the chemical coupling gn and electrical coupling gl. We show that, even for small number of neurons, the dynamics of the system depends on the number of neurons and the type of coupling strength between them. Finally, we evolve a network of Hindmarsh-Rose neurons by increasing the entropy of the system. In particular, we choose the Kolmogorov-Sinai entropy: HKS (Pesin identity) as the evolution rule. First, we compute the HKS for a network of 4 HR neurons connected simultaneously by two undirected electrical and two undirected chemical links. We get different entropies with the use of different values for both the chemical and electrical couplings. If the entropy of the system is positive, the dynamics of the system is chaotic and if it is close to zero, the trajectory of the system converges to one of the fixed points and loses energy. Then, we evolve a network of 6 clusters of 10 neurons each. Neurons in each cluster are connected only by electrical links and their connections form small-world networks. The six clusters connect to each other only by chemical links. We compare between the combined effect of chemical and electrical couplings with the two concepts, the information flow capacity Ic and HKS in evolving the BDNs and show results that the brain networks might evolve based on the principle of the maximisation of their entropies

Dynamic Data Assimilation

Data assimilation is a process of fusing data with a model for the singular purpose of estimating unknown variables. It can be used, for example, to predict the evolution of the atmosphere at a given point and time. This book examines data assimilation methods including Kalman filtering, artificial intelligence, neural networks, machine learning, and cognitive computing

Mind out of matter: topics in the physical foundations of consciousness and cognition

This dissertation begins with an exploration of a brand of dual aspect monism and some problems deriving from the distinction between a first person and third person point of view. I continue with an outline of one way in which the conscious experience of the subject might arise from organisational properties of a material substrate. With this picture to hand, I first examine theoretical features at the level of brain organisation which may be required to support conscious experience and then discuss what bearing some actual attributes of biological brains might have on such experience. I conclude the first half of the dissertation with comments on information processing and with artificial neural networks meant to display simple varieties of the organisational features initially described abstractly.While the first half begins with a view of conscious experience and infers downwards in the organisational hierarchy to explore neural features suggested by the view, attention in the second half shifts towards analysing low level dynamical features of material substrates and inferring upwards to possible effects on experience. There is particular emphasis on clarifying the role of chaotic dynamics, and I discuss relationships between levels of description of a cognitive system and comment on issues of complexity, computability, and predictability before returning to the topic of representation which earlier played a central part in isolating features of brain organisation which may underlie conscious experience.Some themes run throughout the dissertation, including an emphasis on understanding experience from both the first person and the third person points of view and on analysing the latter at different levels of description. Other themes include a sustained effort to integrate the picture offered here with existing empirical data and to situate current problems in the philosophy of mind within the new framework, as well as an appeal to tools from mathematics, computer science, and cognitive science to complement the more standard philosophical repertoire