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Oct. 2021 King's College London Doctoral Thesis Quantitative semantics and graph theory as a framework for complex systems modeling Author: Supervisor: Ruggero Gramatica Prof. Tiziana Di Matteo A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy in Applied Mathematics Department of Mathematics December 2015 This page is intentionally left blank Published Articles I list here the peer-reviewed articles I have authored and co-authored in the course of my PhD and whose material I have used in this thesis. The articles are listed in chronological order of appearance as follows and can be reviewed in Annex 1: 1. R.Morales, T.Di Matteo, R.Gramatica and T.Aste, Dynamical General- ized Hurst Exponent as a Tool to Monitor Unstable Periods in Financial Time Series, Physica A, 391, 2012, 3180-3189. 2. Tomaso Aste, Ruggero Gramatica and T.Di Matteo, Exploring complex networks via topological embedding on surfaces, Physical Review E 86, 036109 (2012) 3. T. Aste, Ruggero Gramatica, T. Di Matteo, Random and frozen states in complex triangulations, Philosophical Magazine, Volume 92, Issue 1-3, (2012) 244-254 4. Ruggero Gramatica, T. Di Matteo, Stefano Giorgetti, Massimo Barbiani, Do- rian Bevec, Tomaso Aste, Graph Theory Enables Drug Repurposing - How a Mathematical Model Can Drive the Discovery of Hidden Mechanisms of Action, January 2014, PlosOne Volume 9, Issue 1, e84912 5. Ruggero Gramatica, Haris Dindo, T. Di Matteo, T. Aste, A quantitative se- mantic and graph theoretical approach for the analysis of financial and economic unstructured data, In preparation for 2015 - (see Chapter 6) i This page is intentionally left blank Abstract The study of Complex Systems focuses on how interactions of constituents within a system, individually or grouped into clusters, produce behavioral patterns locally or globally and how these interact with the external environment. Over the last few decades the study of Complex Systems has gone through a growing rate of interest and today, given a sufficiently big set of data, we are able to construct comprehensive models describing emerging characteristics and properties of complex phenomena transcending the different domains of physical, biological and social sciences. The use of network theory has shown, amongst others, a particular fit in describ- ing statical and dynamical correlations of complex data sets because its ability to deal not only with deterministic quantities but also with probabilistic methods. A complex system is generally an open system flexible in adapting to variable external conditions in the way that it exchanges information with environment and adjusts its internal structure in the process of self-organization. Moreover, it has been shown how real world phenomena that are represented by complex systems display inter- esting statistical properties such as power-law distributions, long-range interactions, scale invariance, criticality, multifractality and hierarchical structure. In the era of big data where effort is largely put to collect large data sets carry- ing relevant information about given phenomena to be studied and analysed, the interesting field of quantitative semantics, e.g. dealing with information expressed in natural language, is becoming more and more relevant particularly in the social sciences. However, recent studies are expanding these techniques to become a tool for structuring and organising information across a number of disparate disciplines. In this Thesis I propose a methodology that (i) extracts a structured complex data set from large corpora of descriptive language sources and efficiently exploits the power of quantitative semantics techniques to map the essence of a complex phe- nomena into a network representation, and (ii) combines such induced knowledge iii network with a graph theoretical framework utilising a number of graph theory tools to study the emerging properties of complex systems. Thus, leveraging on devel- opments in Computational Linguistics and Network Theory, the proposed approach builds a graph representation of knowledge, which is analyzed with the aim of ob- serving correlations between any two nodes or across clusters of nodes and highlights emerging properties by means of both topological structure analysis and dynamic evolution, i.e. the change in connectivity. Under this framework I will provide two real-world applications: - The first application deals with the creation of a structured network of bio- medical concepts starting from an unstructured corpus of biological text-based data set (peer reviewed articles) and next it retrieves known pathophysiologi- cal Mode of Actions by applying a stochastic random-walk measure and finds new ones by meaningfully selecting and aggregating contributions from known bio-molecular interactions. By exploiting the proposed graph-theoretic model, this approach has proven to be an innovative way to find emergent mechanism of actions aimed at drug repurposing where existing biologic compounds origi- nally intended to deal with certain pathophysiologic actions are redirected for treating other type of clinical indications. - The second application consists of a representation of a financial and economic system through a network of interacting entities and to devise a novel semantic index influenced by the topological properties of agglomerated information in a semantic graph. I have shown how it is possible to fully capture the dynamical aspects of the phenomena under investigation by identifying clusters carrying influential information and tracking them over time. By computing graph- based statistics over such clusters I turn the evolution of textual information into a mathematically well-defined, multivariate time series, where each time series encodes the evolution of particular structural, topological and semantic properties of the set of concepts previously extracted and filtered. Eventually iv an autoregressive model with vectorial exogenous inputs is defined, which lin- early mixes previous values of an index with the evolution of other time series induced by the semantic information in the graph. The methodology briefly described above concludes the contribution of my re- search work in the field of Complex Systems and it has been instrumental in successfully defining a graph-theoretical model for the study of drug repurpos- ing [1] and the construction of a framework for the analysis of financial and economic unstructured data (see chapter6). v This page is intentionally left blank Acknowledgements It had been a long term dream of mine to be able to study Applied Mathematics and gain a PhD and I would first of all like to thank Prof. William Shaw who on my first interview at King's College gave me the chance to make this a reality by approving my application as a post graduate student. He kindly reassured me that even in your 40's it is not too late to undertake a doctoral program as long as I would bring passion, commitment and sufficient background to tackle such a challenging endeavour. Next I would like to thank my supervisor Prof. Tiziana Di Matteo, she provided me with good day to day advice and a direction for my research, teaching me how to focus on innovative thinking and maintaining rigour in the investigation of adjacent domain of research. Having Dr. Tomaso Aste as adjunct supervisor was really a blessing and I appreciated his breadth of knowledge, his perspective, his strong scientific background in statistical mechanics and his sense of humour. Because of my engineering background and, more recently as an entrepreneur, it was important for me that my research was not abstract, but closely linked to the business world and I would like to thank everyone I met throughout my doctoral journey from disparate industry field for bridging the gap between the academic world and the business universe and for believing in the broad ranging applications of my work to real business problems. I would like to thank my colleagues and fellow students Dr. Raffello Morales and Nicolo' Musmeci for sharing with me the PhD experience and for being around to discuss some formal aspects of the theory of multiscaling and complex systems in general. Also, Inspiring me on my journey was my old friend and fellow mathematician Guido Previde whose shared interest in my work made him a great sounding board for ideas and he helped me to work through some of the challenges I faced with both his knowledge and his sense of humour. Last, but not least, on the academic list is Dr. Haris Dindo, who I came to know about half way through my research. As a great researcher in the field of Machine Learning and Cognitive Science he has been an invaluable help in devising new perspectives on how to tackle some challenging parts of my research.