Complex and Adaptive Dynamical Systems: A Primer

An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and small-world networks, a generic introduction to the concepts of dynamical system theory, random Boolean networks, cellular automata and self-organized criticality, the statistical modeling of Darwinian evolution, synchronization phenomena and an introduction to the theory of cognitive systems. It inludes chapter on Graph Theory and Small-World Networks, Chaos, Bifurcations and Diffusion, Complexity and Information Theory, Random Boolean Networks, Cellular Automata and Self-Organized Criticality, Darwinian evolution, Hypercycles and Game Theory, Synchronization Phenomena and Elements of Cognitive System Theory.Comment: unformatted version of the textbook; published in Springer, Complexity Series (2008, second edition 2010

Learning in adaptive networks: analytical and computational approaches

The dynamics on networks and the dynamics of networks are usually entangled with each other in many highly connected systems, where the former means the evolution of state and the latter means the adaptation of structure. In this thesis, we will study the coupled dynamics through analytical and computational approaches, where the adaptive networks are driven by learning of various complexities. Firstly, we investigate information diffusion on networks through an adaptive voter model, where two opinions are competing for the dominance. Two types of dynamics facilitate the agreement between neighbours: one is pairwise imitation and the other is link rewiring. As the rewiring strength increases, the network of voters will transform from consensus to fragmentation. By exploring various strategies for structure adaptation and state evolution, our results suggest that network configuration is highly influenced by range-based rewiring and biased imitation. In particular, some approximation techniques are proposed to capture the dynamics analytically through moment-closure differential equations. Secondly, we study an evolutionary model under the framework of natural selection. In a structured community made up of cooperators and cheaters (or defectors), a new-born player will adopt a strategy and reorganise its neighbourhood based on social inheritance. Starting from a cooperative population, an invading cheater may spread in the population occasionally leading to the collapse of cooperation. Such a collapse unfolds rapidly with the change of external conditions, bearing the traits of a critical transition. In order to detect the risk of invasions, some indicators based on population composition and network structure are proposed to signal the fragility of communities. Through the analyses of consistency and accuracy, our results suggest possible avenues for detecting the loss of cooperation in evolving networks. Lastly, we incorporate distributed learning into adaptive agents coordination, which emerges as a consequence of rational individual behaviours. A generic framework of work-learn-adapt (WLA) is proposed to foster the success of agents organisation. To gain higher organisation performance, the division of labour is achieved by a series of events of state evolution and structure adaptation. Importantly, agents are able to adjust their states and structures through quantitative information obtained from distributed learning. The adaptive networks driven by explicit learning pave the way for a better understanding of intelligent organisations in real world

An Initial Framework Assessing the Safety of Complex Systems

Trabajo presentado en la Conference on Complex Systems, celebrada online del 7 al 11 de diciembre de 2020.Atmospheric blocking events, that is large-scale nearly stationary atmospheric pressure patterns, are often associated with extreme weather in the mid-latitudes, such as heat waves and cold spells which have significant consequences on ecosystems, human health and economy. The high impact of blocking events has motivated numerous studies. However, there is not yet a comprehensive theory explaining their onset, maintenance and decay and their numerical prediction remains a challenge. In recent years, a number of studies have successfully employed complex network descriptions of fluid transport to characterize dynamical patterns in geophysical flows. The aim of the current work is to investigate the potential of so called Lagrangian flow networks for the detection and perhaps forecasting of atmospheric blocking events. The network is constructed by associating nodes to regions of the atmosphere and establishing links based on the flux of material between these nodes during a given time interval. One can then use effective tools and metrics developed in the context of graph theory to explore the atmospheric flow properties. In particular, Ser-Giacomi et al. [1] showed how optimal paths in a Lagrangian flow network highlight distinctive circulation patterns associated with atmospheric blocking events. We extend these results by studying the behavior of selected network measures (such as degree, entropy and harmonic closeness centrality)at the onset of and during blocking situations, demonstrating their ability to trace the spatio-temporal characteristics of these events.This research was conducted as part of the CAFE (Climate Advanced Forecasting of sub-seasonal Extremes) Innovative Training Network which has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 813844

A complex systems approach to education in Switzerland

The insights gained from the study of complex systems in biological, social, and engineered systems enables us not only to observe and understand, but also to actively design systems which will be capable of successfully coping with complex and dynamically changing situations. The methods and mindset required for this approach have been applied to educational systems with their diverse levels of scale and complexity. Based on the general case made by Yaneer Bar-Yam, this paper applies the complex systems approach to the educational system in Switzerland. It confirms that the complex systems approach is valid. Indeed, many recommendations made for the general case have already been implemented in the Swiss education system. To address existing problems and difficulties, further steps are recommended. This paper contributes to the further establishment complex systems approach by shedding light on an area which concerns us all, which is a frequent topic of discussion and dispute among politicians and the public, where billions of dollars have been spent without achieving the desired results, and where it is difficult to directly derive consequences from actions taken. The analysis of the education system's different levels, their complexity and scale will clarify how such a dynamic system should be approached, and how it can be guided towards the desired performance

Statistical mechanics for biological applications: focusing on the immune system

The emergence in the last decades of a huge amount of data in many fields of biology triggered also an increase of the interest by quantitative disciplines for life sciences. Mathematics, physics and informatics have been providing quantitative models and advanced statistical tools in order to help the understanding of many biological problems. Statistical mechanics is a field that particularly contributed to quantitative biology because of its intrinsic predisposition in dealing with systems of many strongly interacting agents, noise, information processing and statistical inference. In this Thesis a collection of works at the interphase between statistical mechanics and biology is presented. In particular they are related to biological problems that can be mainly reconducted to the biology of the immune system. Beyond the unification key given by statistical mechanics of discrete systems and quantitative modeling and analysis of the immune system, the works presented here are quite diversified. The origin of this heterogeneity resides in the intent of using and learning many different techniques during the lapse of time needed for the preparation of the work reviewed in this Thesis. In fact the work presented in Chapter 3 mainly deals with statistical mechanics, networks theory and networks numerical simulations and analysis; Chapter 4 presents a mathematical physics oriented work; Chapter 5 and 6 deal with data analysis and in particular wth clinical data and amino acid sequences data sets, requiring the use of both analytical and numerical techniques. The Thesis is conceptually organized in two main parts. The first part (Chapters 1 and 2) is dedicated to the review of known results both in statistical mechanics and biology, while in the second part (Chapters 3, 4 and 6) the original works are presented together with briefs insights into the research fields in which they can be embedded. In particular, in Chapter 1 some of the most relevant models and techniques in statistical mechanics of mean field spin systems are reviewed, starting with the Ising model and then passing to the Sherrington-Kirkpatrik model for spin glasses and to the Hopfield model for attractors neural networks. The replica method is presented together with the stochastic stability method as a mathematically rigorous alternative to replicas. Chapter 2 is dedicated to a very schematic overview of the biology of the immune system. In Chapter 3, Section 3.1 is dedicated to the presentation of a mathematical phenomenological model for the study of the idiotypic network while Section 3.2 serves as a review of the statistical mechanics based models proposed by Elena 1 2 Introduction Agliari and Adriano Barra as toy models meant to underline the possible role of complex networks within the immune system. In Chapter 4 the mathematical model of an analogue neural network on a diluted graph is studied. It is shown how the problem can be mapped in a bipartite diluted spin glass. The model is rigorously solved at the replica symmetric level with the use of the stochastic stability technique and fluctuations analysis is used to study the spin glass transition of the system. A topological analysis of the network is also performed and different topological regimes are proven to emerge though the tuning of the model parameters. In Chapter 5 a model for the analysis of clinical records of testing sets of patients is presented. The model is based on a Markov chain over the space of clinical states. The machinery is applied to data concerning the insurgence of Tuberculosis and Non-Tuberculous Infections as side effects in patients treated with Tumor Necrosis Factor inhibitors. The analysis procedure is capable of capturing clinical details of the behaviors of different drugs. Lastly, Chapter 6 is dedicated to a statistical inference analysis on deep sequencing data of an antibodies repertoire with the purpose of studying the problem of antibodies affinity maturation. A partial antibodies repertoire from a HIV-1 infected donor presenting broadly neutralizing serum is used to infer a probability distribution in the space of sequences that is compared with neutralization power measurements and with the deposited crystallographic structure of a deeply matured antibody. The work is still in progress, but preliminary results are encouraging and are presented here

Statistical mechanics for biological applications: focusing on the immune system

The emergence in the last decades of a huge amount of data in many fields of biology triggered also an increase of the interest by quantitative disciplines for life sciences. Mathematics, physics and informatics have been providing quantitative models and advanced statistical tools in order to help the understanding of many biological problems. Statistical mechanics is a field that particularly contributed to quantitative biology because of its intrinsic predisposition in dealing with systems of many strongly interacting agents, noise, information processing and statistical inference. In this Thesis a collection of works at the interphase between statistical mechanics and biology is presented. In particular they are related to biological problems that can be mainly reconducted to the biology of the immune system. Beyond the unification key given by statistical mechanics of discrete systems and quantitative modeling and analysis of the immune system, the works presented here are quite diversified. The origin of this heterogeneity resides in the intent of using and learning many different techniques during the lapse of time needed for the preparation of the work reviewed in this Thesis. In fact the work presented in Chapter 3 mainly deals with statistical mechanics, networks theory and networks numerical simulations and analysis; Chapter 4 presents a mathematical physics oriented work; Chapter 5 and 6 deal with data analysis and in particular wth clinical data and amino acid sequences data sets, requiring the use of both analytical and numerical techniques. The Thesis is conceptually organized in two main parts. The first part (Chapters 1 and 2) is dedicated to the review of known results both in statistical mechanics and biology, while in the second part (Chapters 3, 4 and 6) the original works are presented together with briefs insights into the research fields in which they can be embedded. In particular, in Chapter 1 some of the most relevant models and techniques in statistical mechanics of mean field spin systems are reviewed, starting with the Ising model and then passing to the Sherrington-Kirkpatrik model for spin glasses and to the Hopfield model for attractors neural networks. The replica method is presented together with the stochastic stability method as a mathematically rigorous alternative to replicas. Chapter 2 is dedicated to a very schematic overview of the biology of the immune system. In Chapter 3, Section 3.1 is dedicated to the presentation of a mathematical phenomenological model for the study of the idiotypic network while Section 3.2 serves as a review of the statistical mechanics based models proposed by Elena 1 2 Introduction Agliari and Adriano Barra as toy models meant to underline the possible role of complex networks within the immune system. In Chapter 4 the mathematical model of an analogue neural network on a diluted graph is studied. It is shown how the problem can be mapped in a bipartite diluted spin glass. The model is rigorously solved at the replica symmetric level with the use of the stochastic stability technique and fluctuations analysis is used to study the spin glass transition of the system. A topological analysis of the network is also performed and different topological regimes are proven to emerge though the tuning of the model parameters. In Chapter 5 a model for the analysis of clinical records of testing sets of patients is presented. The model is based on a Markov chain over the space of clinical states. The machinery is applied to data concerning the insurgence of Tuberculosis and Non-Tuberculous Infections as side effects in patients treated with Tumor Necrosis Factor inhibitors. The analysis procedure is capable of capturing clinical details of the behaviors of different drugs. Lastly, Chapter 6 is dedicated to a statistical inference analysis on deep sequencing data of an antibodies repertoire with the purpose of studying the problem of antibodies affinity maturation. A partial antibodies repertoire from a HIV-1 infected donor presenting broadly neutralizing serum is used to infer a probability distribution in the space of sequences that is compared with neutralization power measurements and with the deposited crystallographic structure of a deeply matured antibody. The work is still in progress, but preliminary results are encouraging and are presented here