Exploration of Chemical Space: Formal, chemical and historical aspects

Starting from the observation that substances and reactions are the central entities of chemistry, I have structured chemical knowledge into a formal space called a directed hypergraph, which arises when substances are connected by their reactions. I call this hypernet chemical space. In this thesis, I explore different levels of description of this space: its evolution over time, its curvature, and categorical models of its compositionality. The vast majority of the chemical literature focuses on investigations of particular aspects of some substances or reactions, which have been systematically recorded in comprehensive databases such as Reaxys for the last 200 years. While complexity science has made important advances in physics, biology, economics, and many other fields, it has somewhat neglected chemistry. In this work, I propose to take a global view of chemistry and to combine complexity science tools, modern data analysis techniques, and geometric and compositional theories to explore chemical space. This provides a novel view of chemistry, its history, and its current status. We argue that a large directed hypergraph, that is, a model of directed relations between sets, underlies chemical space and that a systematic study of this structure is a major challenge for chemistry. Using the Reaxys database as a proxy for chemical space, we search for large-scale changes in a directed hypergraph model of chemical knowledge and present a data-driven approach to navigate through its history and evolution. These investigations focus on the mechanistic features by which this space has been expanding: the role of synthesis and extraction in the production of new substances, patterns in the selection of starting materials, and the frequency with which reactions reach new regions of chemical space. Large-scale patterns that emerged in the last two centuries of chemical history are detected, in particular, in the growth of chemical knowledge, the use of reagents, and the synthesis of products, which reveal both conservatism and sharp transitions in the exploration of the space. Furthermore, since chemical similarity of substances arises from affinity patterns in chemical reactions, we quantify the impact of changes in the diversity of the space on the formulation of the system of chemical elements. In addition, we develop formal tools to probe the local geometry of the resulting directed hypergraph and introduce the Forman-Ricci curvature for directed and undirected hypergraphs. This notion of curvature is characterized by applying it to social and chemical networks with higher order interactions, and then used for the investigation of the structure and dynamics of chemical space. The network model of chemistry is strongly motivated by the observation that the compositional nature of chemical reactions must be captured in order to build a model of chemical reasoning. A step forward towards categorical chemistry, that is, a formalization of all the flavors of compositionality in chemistry, is taken by the construction of a categorical model of directed hypergraphs. We lifted the structure from a lineale (a poset version of a symmetric monoidal closed category) to a category of Petri nets, whose wiring is a bipartite directed graph equivalent to a directed hypergraph. The resulting construction, based on the Dialectica categories introduced by Valeria De Paiva, is a symmetric monoidal closed category with finite products and coproducts, which provides a formal way of composing smaller networks into larger in such a way that the algebraic properties of the components are preserved in the resulting network. Several sets of labels, often used in empirical data modeling, can be given the structure of a lineale, including: stoichiometric coefficients in chemical reaction networks, reaction rates, inhibitor arcs, Boolean interactions, unknown or incomplete data, and probabilities. Therefore, a wide range of empirical data types for chemical substances and reactions can be included in our model

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science

Concepts and analogies in cybernetics: Mathematical investigations of the role of analogy in concept formation and problem solving; with emphasis for conflict resolution via object and morphism eliminations

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.We address two problematic areas of cybernetics; nam. Analogical Problem Solving (APS) and Analogical Learning (AL). Both these human faculties do unquestionably require Intelligence. In addition, we point out that shifting of representations is the main unified theme underlying these two intellectual tasks. We focus our attention on the formulation and clarification of the notion of analogy, which has been loosely treated and used in the literature; and also on its role in shifting of representations. We describe analogizing situations in a new representational scheme, borrowed from mathematics and modified and extended to cater for our targets. We call it k-structure, closely resembling semantic networks and directed graphs; the main components of it are the so-called objects and morphisms. We argue and substantiate the need for such a representation scheme, by analysing what its constituents stand for and by cataloguing its virtues, the main one being its visual appeal and its mathematical clarity, and by listing its disadvantages when it is compared to other representation systems. Emphasis is also given to its descriptive power and usefulness by implementing it in a number of APS and AL situations. Besides representation issues, attention is paid to intelligence mechanisms which are involved in APS and AL. A cornerstone in APS and a fundamental theme in AL is the 'skeletization of k-structures'. APS is conceived as 'harmonization of skeletons'. The methodology we develop involves techniques which are computer implemented and extensively studied in theoretic terms via a proposed theory for extended k-structures. To name but a few: 1. 'the separation of the context of a concept from the concept itself', based on the ideas of k-opens and k-spaces; 2, 'object and morphism elimination' of a controversial nature; and 3. 'conflict or deadlock or dilemma resolution' which naturally arises in a k-structure interaction. The overall system, is then applied to capture the essence of EVANS' (1963) analogy-type problems and WINSTOM (1970) learning-type situations. In our attempt not to be too informal, we use basic notions and terminology from abstract Algebra, Topology and Category theory. We rather tend to be "non-logical" (analogical) in EVANS' and WINSTON's sense; "non-numeric", in MESAROVIC (1970) terms (we rather deal with abstract conceptual entities); "non-linguistic" (we do not touch natural language); and "non-resolution" oriented, in the sense of BLEDSOE (1977). However, we give hints sometimes about logical deductive axiomatic systems, employing First Order Predicate Calculus (FOPC); and about semiotics, by which we denote syntactic-semantic-pragmatic features of our system and issues of the problem domains it is acting upon. We believe in what we call: shift from the traditional 'Heuristic search paradigm' era to the 'Analogy-paradigm' era underlying Artificial Intelligence and Cybernetics. We justify this merely by listing a number of A. I. works, which employ, in some way or another, the concept of analogy, over the last fifteen years or so, where a noticeable peak is obvious during the last years and especially in 1977. Finally, we hope that if the proposed conceptual framework and techniques developed do not straightforwardly constitute some kind of platform for Artificial Intelligence, at least it would give some insights into and illuminate our understanding of the two most fundamental faculties the human brain is occupied with; namely problem solving and learning

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems

A framework for analyzing changes in health care lexicons and nomenclatures

Ontologies play a crucial role in current web-based biomedical applications for capturing contextual knowledge in the domain of life sciences. Many of the so-called bio-ontologies and controlled vocabularies are known to be seriously defective from both terminological and ontological perspectives, and do not sufficiently comply with the standards to be considered formai ontologies. Therefore, they are continuously evolving in order to fix the problems and provide valid knowledge. Moreover, many problems in ontology evolution often originate from incomplete knowledge about the given domain. As our knowledge improves, the related definitions in the ontologies will be altered. This problem is inadequately addressed by available tools and algorithms, mostly due to the lack of suitable knowledge representation formalisms to deal with temporal abstract notations, and the overreliance on human factors. Also most of the current approaches have been focused on changes within the internal structure of ontologies, and interactions with other existing ontologies have been widely neglected. In this research, alter revealing and classifying some of the common alterations in a number of popular biomedical ontologies, we present a novel agent-based framework, RLR (Represent, Legitimate, and Reproduce), to semi-automatically manage the evolution of bio-ontologies, with emphasis on the FungalWeb Ontology, with minimal human intervention. RLR assists and guides ontology engineers through the change management process in general, and aids in tracking and representing the changes, particularly through the use of category theory. Category theory has been used as a mathematical vehicle for modeling changes in ontologies and representing agents' interactions, independent of any specific choice of ontology language or particular implementation. We have also employed rule-based hierarchical graph transformation techniques to propose a more specific semantics for analyzing ontological changes and transformations between different versions of an ontology, as well as tracking the effects of a change in different levels of abstractions. Thus, the RLR framework enables one to manage changes in ontologies, not as standalone artifacts in isolation, but in contact with other ontologies in an openly distributed semantic web environment. The emphasis upon the generality and abstractness makes RLR more feasible in the multi-disciplinary domain of biomedical Ontology change management