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Close to a transition between different phases a substance can show universal behavior that is independent of the microscopic details and is characterized by power law correlations and critical exponents. In this Colloquium the concepts of criticality and universality are discussed when applied to biological systems and suggest that in some cases these systems can extract functional advantages close to criticality.

Colloquium : Criticality and dynamical scaling in living systems

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At Home In The Universe

Modularity: Understanding the Development and Evolution of Natural Complex Systems

Machine learning techniques for structural health monitoring of heritage buildings: A state-of-the-art review and case studies

Machine Learning for Cultural Heritage: A Survey

We describe a method to identify relevant subsets of variables, useful to understand the organization of a dynamical system. The variables belonging to a relevant subset should have a strong integration with the other variables of the same relevant subset, and a much weaker interaction with the other system variables. On this basis, extending previous work on neural networks, an information-theoretic measure, the dynamical cluster index, is introduced in order to identify good candidate relevant subsets. The method does not require any previous knowledge of the relationships among the system variables, but relies on observations of their values over time. We show its usefulness in several application domains, including: i random Boolean networks, where the whole network is made of different subnetworks with different topological relationships independent or interacting subnetworks; ii leader-follower dynamics, subject to noise and fluctuations; iii catalytic reaction networks in a flow reactor; iv the MAPK signaling pathway in eukaryotes. The validity of the method has been tested in cases where the data are generated by a known dynamical model and the dynamical cluster index is applied in order to uncover significant aspects of its organization; however, it is important that it can also be applied to time series coming from field data without any reference to a model. Given that it is based on relative frequencies of sets of values, the method could be applied also to cases where the data are not ordered in time. Several indications to improve the scope and effectiveness of the dynamical cluster index to analyze the organization of complex systems are finally given.

The search for candidate relevant subsets of variables in complex systems

Complex systems often show forms of organisation where a clear-cut hierarchy of levels with a well-defined direction of information flow cannot be found. In this paper we propose an information-theoretic method aimed at identifying the dynamically relevant parts of a system along with their relationships, interpreting in such a way the system’s dynamical organisation. The analysis is quite general and can be applied to many dynamical systems. We show here its application to two relevant biological examples, the case of mammalian cell cycle network and of Mitogen Activated Protein Kinase (MAPK) cascade. The result of our analysis shows that the elements of the mammalian cell cycle network act as a single compact group, whereas the MAPK system can be decomposed into two dynamically distinct parts, with asymmetric information flows.

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Exploring the organisation of complex systems through the dynamical interactions among their relevant subsets

Introduced in the mid-1970's as an intermediate step in proving a long-standing conjecture on arithmetic progressions, Szemeredi's regularity lemma has emerged over time as a fundamental tool in different branches of graph theory, combinatorics and theoretical computer science. Roughly, it states that every graph can be approximated by the union of a small number of random-like bipartite graphs called regular pairs. In other words, the result provides us a way to obtain a good description of a large graph using a small amount of data, and can be regarded as a manifestation of the all-pervading dichotomy between structure and randomness. In this paper we will provide an overview of the regularity lemma and its algorithmic aspects, and will discuss its relevance in the context of pattern recognition research.

Revealing Structure in Large Graphs: Szemer\'edi's Regularity Lemma and its Use in Pattern Recognition

The identification of emergent structures in dynamical systems is a major challenge in complex systems science. In particular, the formation of intermediate-level dynamical structures is of particular interest for what concerns biological as well as artificial systems. In this work, we present a set of measures aimed at identifying groups of elements that behave in a coherent and coordinated way and that loosely interact with the rest of the system (the so-called “relevant sets”). These measures are based on Shannon entropy, and they are an extension of a measure introduced for detecting clusters in biological neural networks. Even if our results are still preliminary, we have evidence for showing that our approach is able to identify and partially characterise the relevant sets in some artificial systems, and that this way is more powerful than usual measures based on statistical correlation. In this work, the two measures that contribute to the cluster index, previously adopted in the analysis of neural networks, i.e. integration and mutual information, are analysed separately in order to enhance the overall performance of the so-called dynamical cluster index. Although this latter variable already provides useful information about highly integrated subsystems, the analysis of the different parts of the index are extremely useful to better characterise the nature of the sub-systems.

Marco Fiorucci

Papers

Machine Learning for Cultural Heritage: A Survey

The search for candidate relevant subsets of variables in complex systems

Exploring the organisation of complex systems through the dynamical interactions among their relevant subsets

Revealing Structure in Large Graphs: Szemer\'edi's Regularity Lemma and its Use in Pattern Recognition

On some properties of information theoretical measures for the study of complex systems