Complexity in Physics and Chemistry

We present an artificial creative system that autonomously keeps producing various spatial patterns using evolutionary swarm systems and an automated object harvesting mechanism.

Stochastic processes are ubiquitous throughout the quantitative sciences and their study is of great interest across disciplinary boundaries. The complexity of stochastic process has been related to the minimal amount of memory about its past which one requires in order to predict its future [1]. Recent studies have shown that quantum hidden Markov models can further reduce this memory requirement [2].

We study the scaling of the density of iterates of the logistic map at a representative set of dynamical regimes: From the periodic motion at superstable orbits of the period-doubling route to chaos and its corresponding, aperiodic, accumulation point; to the chaotic motion at Misiurewicz points along the band-splitting chaotic cascade.

Complex computations typically occur via the composition of modular units, such as the universal logic gates found in logical circuits. The benefit of modular information processing, in contrast to globally integrated information processing, is that complex global information processing is more easily and flexibly implemented via a series of simpler, localized information processing operations that only control and change local degrees of freedom.

Complex stochastic processes describe a rich and diverse range of phenomena: natural systems such as weather, geophysical, and biological processes; and societal constructs such as financial markets and traffic networks. The essential nature of these systems necessitates our ability to track and forecast their behaviour, a task for which we generally turn to large-scale simulations. Such simulations are resource intensive, requiring extreme amounts of memory, limiting the precision to which these complex systems can be studied.

According to the classical definition, the chemical kinetics is a discipline that studies molecular compounds and the changes they undergo when reacting with each other. In the most complex cases, it is convenient to represent reaction kinetics with a reaction network -- a bipartite graph in which nodes represent reactions and species, whereas directed edges represent the participation of a species in respective reactions. A reaction network can be processed to obtain a system of non-linear differential equations, the so called zero-dimensional model.

Network theory has been a groundbreaking research field in science for the last 20 years, conceivably the only one that could glue together disparate and even contrasting disciplines such as physics, economy, biology or sociology. A network materialises the complex interactions between the composing entities of large systems, it thus defines the natural and structural backbone for describing complex systems, which dynamics is unavoidably bound to the network properties.

Since Self-Organised Criticality (SOC) was introduced in 1987, both the nature of the self- organisation and the criticality remains controversial. Recent observations on rain precipitation and brain activity suggest that real systems display a dynamics that is similar to the one observed in SOC systems, making a better understanding of such systems more urgent.

How to identify an upcoming transition in a time series from different dynamical systems continues to be an open research issue. In various fields of physical science such as environment, economics, neuroscience and engineering, abrupt transitions can occur unexpectedly and are difficult to manage during the temporal evolution of the dynamic system. In this study we address the problem using the degree centrality measure from the complex network analysis of time series.

Random matrices are formidable tools to build simple models of networked complex systems composed of large assemblies of interacting entities, being them proteins, neurons or individuals. The central idea consists in modeling the adjacency matrix of a complex network by a random matrix drawn from a certain ensemble.