On the influence of topological characteristics on robustness of complex networks

In this paper, we explore the relationship between the topological characteristics of a complex network and its robustness to sustained targeted attacks. Using synthesised scale-free, small-world and random networks, we look at a number of network measures, including assortativity, modularity, average path length, clustering coefficient, rich club profiles and scale-free exponent (where applicable) of a network, and how each of these influence the robustness of a network under targeted attacks. We use an established robustness coefficient to measure topological robustness, and consider sustained targeted attacks by order of node degree. With respect to scale-free networks, we show that assortativity, modularity and average path length have a positive correlation with network robustness, whereas clustering coefficient has a negative correlation. We did not find any correlation between scale-free exponent and robustness, or rich-club profiles and robustness. The robustness of small-world networks on the other hand, show substantial positive correlations with assortativity, modularity, clustering coefficient and average path length. In comparison, the robustness of Erdos-Renyi random networks did not have any significant correlation with any of the network properties considered. A significant observation is that high clustering decreases topological robustness in scale-free networks, yet it increases topological robustness in small-world networks. Our results highlight the importance of topological characteristics in influencing network robustness, and illustrate design strategies network designers can use to increase the robustness of scale-free and small-world networks under sustained targeted attacks

Domain-informed Language Models for Process Systems Engineering

Process systems engineering (PSE) involves a systems-level approach to solving problems in chemical engineering related to process modeling, design, control, and optimization and involves modeling interactions between various systems (and subsystems) governing the process. This requires using a combination of mathematical methods, physical intuition, and recently machine learning techniques. Recently, language models have seen tremendous advances due to new and more efficient model architectures (such as transformers), computing power, and large volumes of training data. Many of these language models could be appropriately adapted to solve several PSE-related problems. However, language models are inherently complex and are often characterized by several million parameters, which could only be trained efficiently in data-rich areas, unlike PSE. Moreover, PSE is characterized by decades of rich process knowledge that must be utilized during model training to avoid mismatch between process knowledge and data-driven language models. This thesis presents a framework for building domain-informed language models for several central problems in PSE spanning multiple scales. Specifically, the frameworks presented include molecular property prediction, forward and retrosynthesis reaction outcome prediction, chemical flowsheet representation and generation, pharmaceutical information extraction, and reaction classification. Domain knowledge is integrated with language models using custom model architectures, standard and custom-built ontologies, linguistics-inspired chemistry and process flowsheet grammar, adapted problem formulations, graph theory techniques, and so on. This thesis is intended to provide a path for future developments of domain-informed language models in process systems engineering that respect domain knowledge, but leverage their computational advantages

Maximum entropy models for financial systems

Complex systems, from financial markets to the brain, exhibit heterogeneous structures and non-stationary dynamics. These characteristics manifest themselves in the diversity of the elements in a system, and in the changing behaviour over time. Capturing and understanding this heterogeneity via appropriate models, can have important implications not only for science, but also for societal challenges like predicting the next financial crisis or developing advanced brain imaging techniques. In this thesis, we use the maximum-entropy approach to introduce a new class of statistical models, which captures part of the observed structural and/or temporal heterogeneity in the system. The models are applied to various real-world complex systems, and are used to address different problems.Theoretical Physic

A macroeconomics of social contracts

This thesis sets out the case and foundations for a new way to think about, and model, Macroeconomics. This framework aims to describe the fluctuations and differing growths of economies, not in terms of the choice and exchange of Microeconomics, but rather in terms of the enforcement relationships that allow that exchange and other cooperation between people. It first establishes just why this is necessary, with a thorough methodological critique of the way Macroeconomics is done right now. It then presents computational models of two presumably competing kinds of enforcement relationship. The first of these is the third party supervision that we are most familiar with as enforcement from every day life, and which has received some of the longest running philosophical discussion. This hierarchical model reproduces economic fluctuations, through occasional collapses of large parts of the hierarchy. To assess the scientific merit of this model on the terms of conventional Macroeconomics, I develop a compatible hypothesis testing strategy. The second kind of enforcement considered is what would commonly be called peer pressure. For this I derive a preliminary result, that would allow further development of an overarching research program