Synthesis With Hypergraphs

Many problems related to synthesis with intelligent tutoring may be phrased as program synthesis problems using AI-style search and formal reasoning techniques. The _x000C_first two results in this dissertation focus on problem synthesis as an aspect of intelligent tutoring systems applied to STEM-based education frameworks, specifically high school geometry. Given a geometric _x000C_figure as input, our technique constructs a hypergraph representing logical deduction of facts, and then traverses the hypergraph to synthesize problems and their corresponding solutions. Using similar techniques, our third result is focused on exhaustive synthesis of molecules. This synthesis process involves bonding sets of basic, molecular `fragments\u27 according to chemical constraints to create molecules of increasing size. For each input set of fragments, synthesis results in a significant set of molecules. Due to big data constraints we give special consideration in how to construct a corresponding molecular hypergraph based on a target, template molecule. Synthesis of the target molecule in a laboratory environment then corresponds to any path in the molecular hypergraph from the set of fragments to the target molecule

Lifted Successor Generation using Query Optimization Techniques

The standard PDDL language for classical planning uses sev eral first-order features, such as schematic actions. Yet, most classical planners ground this first-order representation into a propositional one as a preprocessing step. While this simpli fies the design of other parts of the planner, in several bench- marks the grounding process causes an exponential blowup that puts otherwise solvable tasks out of reach of the planners. In this work, we take a step towards planning with lifted representations . We tackle the successor generation task, a key operation in forward-search planning, directly on the lifted representation using well-known techniques from database theory . We show how computing the variable substitutions that make an action schema applicable in a given state is essentially a query evaluation problem. Interestingly, a large number of the action schemas in the standard benchmarks result in acyclic conjunctive queries, for which query evaluation is tractable. Our empirical results show that our approach is competitive with the standard (grounded) successor generation techniques in a few domains and outperforms them on benchmarks where grounding is challenging or infeasible

The compositional and evolutionary logic of metabolism

Metabolism displays striking and robust regularities in the forms of modularity and hierarchy, whose composition may be compactly described. This renders metabolic architecture comprehensible as a system, and suggests the order in which layers of that system emerged. Metabolism also serves as the foundation in other hierarchies, at least up to cellular integration including bioenergetics and molecular replication, and trophic ecology. The recapitulation of patterns first seen in metabolism, in these higher levels, suggests metabolism as a source of causation or constraint on many forms of organization in the biosphere. We identify as modules widely reused subsets of chemicals, reactions, or functions, each with a conserved internal structure. At the small molecule substrate level, module boundaries are generally associated with the most complex reaction mechanisms and the most conserved enzymes. Cofactors form a structurally and functionally distinctive control layer over the small-molecule substrate. Complex cofactors are often used at module boundaries of the substrate level, while simpler ones participate in widely used reactions. Cofactor functions thus act as "keys" that incorporate classes of organic reactions within biochemistry. The same modules that organize the compositional diversity of metabolism are argued to have governed long-term evolution. Early evolution of core metabolism, especially carbon-fixation, appears to have required few innovations among a small number of conserved modules, to produce adaptations to simple biogeochemical changes of environment. We demonstrate these features of metabolism at several levels of hierarchy, beginning with the small-molecule substrate and network architecture, continuing with cofactors and key conserved reactions, and culminating in the aggregation of multiple diverse physical and biochemical processes in cells.Comment: 56 pages, 28 figure

Analysis of Generative Chemistries

For the modelling of chemistry we use undirected, labelled graphs as explicit models of molecules and graph transformation rules for modelling generalised chemical reactions. This is used to define artificial chemistries on the level of individual bonds and atoms, where formal graph grammars implicitly represent large spaces of chemical compounds. We use a graph rewriting formalism, rooted in category theory, called the Double Pushout approach, which directly expresses the transition state of chemical reactions. Using concurrency theory for transformation rules, we define algorithms for the composition of rewrite rules in a chemically intuitive manner that enable automatic abstraction of the level of detail in chemical pathways. Based on this rule composition we define an algorithmic framework for generation of vast reaction networks for specific spaces of a given chemistry, while still maintaining the level of detail of the model down to the atomic level. The framework also allows for computation with graphs and graph grammars, which is utilised to model non-trivial chemical systems. The graph generation relies on graph isomorphism testing, and we review the general individualisation-refinement paradigm used in the state-of-the-art algorithms for graph canonicalisation, isomorphism testing, and automorphism discovery. We present a model for chemical pathways based on a generalisation of network flows from ordinary directed graphs to directed hypergraphs. The model allows for reasoning about the flow of individual molecules in general pathways, and the introduction of chemically motivated routing constraints. It further provides the foundation for defining specialised pathway motifs, which is illustrated by defining necessary topological constraints for both catalytic and autocatalytic pathways. We also prove that central types of pathway questions are NP-complete, even for restricted classes of reaction networks. The complete pathway model, including constraints for catalytic and autocatalytic pathways, is implemented using integer linear programming. This implementation is used in a tree search method to enumerate both optimal and near-optimal pathway solutions. The formal methods are applied to multiple chemical systems: the enzyme catalysed beta-lactamase reaction, variations of the glycolysis pathway, and the formose process. In each of these systems we use rule composition to abstract pathways and calculate traces for isotope labelled carbon atoms. The pathway model is used to automatically enumerate alternative non-oxidative glycolysis pathways, and enumerate thousands of candidates for autocatalytic pathways in the formose process

One Utility for Sustainable Communities Modelling and Optimisation of Utility–Service Provision

Utility–service provision is a process in which products such as water, electricity, food, gas are transformed by appropriate devices into services satisfying human needs such as nutrition, thermal comfort, and wants such as e.g. entertainment. Utility products required for these processes are usually delivered to households via separate infrastructures, i.e. real-world networks such as electricity grids, water distribution systems or gas distribution networks. Additionally, they can be supplemented sourced locally from natural resources, e.g. electricity can be obtained from sun or wind. The main objectives of the research are to numerically evaluate feasibility of alternative approaches to utility–service provision problems and automatically generate suggestions of such alternative approaches, using knowledge base of present and future technologies and devices. These objectives are achieved via a simulation system implemented in C# and .NET 4.0 that is composed of the following blocks: an interface to define the utility–service provision problem (problem formulation), an interface to define candidate solutions (transformation graphs), a computational engine to analyse the feasibility of transformation graphs, a heuristic search algorithm to generate transformation graphs and a XML database. The core of the proposed approach is a simulation system that carries out a feasibility study of transformation graphs. A transformation graph describes direct and indirect transformations of products into defined services or other products using various devices. The transformation graphs are represented in a form of standard directed graph where devices, product storages and services are nodes and edges represent product and service carriers. In the adapted approach each product has associated storage. The information about products, services and devices is used to create a visual representation of the content of the database - a Mastergraph. It is a directed hypergraph where services and product storages are nodes, while devices are edges spanning between. Since devices usually connect more than two nodes, a standard graph would not suffice to describe utility–service provision problem and therefore a hypergraph was chosen as a more appropriate representation of the system. Two methods for defining transformation graphs are proposed. In the first one the candidate solutions are constructed manually. Additionally, an interface to calculate shortest paths between two products or a product and a service in Mastergraph was developed to simplify the manual process. In the second method, the transformation graphs are automatically generated using heuristic search approach developed for this model. The functionalities of the proposed approach are presented through case studies. A benchmark case study based on the literature is analysed and compared with automatically generated solutions that vary in terms of energy and water delivered by the infrastructure as well as the total cost of supplying and removing products. These case studies showcase how the use of natural resources, recycling of some of the products that would normally be disposed, or simply the use of alternative devices have impact on the total cost and the amount of water and energy delivered by the infrastructure