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Tse, Ming Fun. / Thesis submitted in: December 2001. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 142-146). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Problem Definition --- p.2 / Chapter 1.2 --- Contributions --- p.3 / Chapter 1.3 --- Thesis Outline --- p.4 / Chapter 2 --- Literature Review --- p.6 / Chapter 2.1 --- Representing Inexact Knowledge --- p.7 / Chapter 2.1.1 --- Nature of Inexact Knowledge --- p.7 / Chapter 2.1.2 --- Probability Based Reasoning --- p.8 / Chapter 2.1.3 --- Certainty Factor Algebra --- p.11 / Chapter 2.1.4 --- Fuzzy Logic --- p.13 / Chapter 2.2 --- Machine Learning Paradigms --- p.13 / Chapter 2.2.1 --- Classifications --- p.14 / Chapter 2.2.2 --- Neural Networks and Gradient Descent --- p.15 / Chapter 2.3 --- Related Learning Systems --- p.21 / Chapter 2.3.1 --- Relational Concept Learning --- p.21 / Chapter 2.3.2 --- Learning of Fuzzy Concepts --- p.24 / Chapter 2.4 --- Fuzzy Logic --- p.26 / Chapter 2.4.1 --- Fuzzy Set --- p.27 / Chapter 2.4.2 --- Basic Notations in Fuzzy Logic --- p.29 / Chapter 2.4.3 --- Basic Operations on Fuzzy Sets --- p.29 / Chapter 2.4.4 --- "Fuzzy Relations, Projection and Cylindrical Extension" --- p.31 / Chapter 2.4.5 --- Fuzzy First Order Logic and Fuzzy Prolog --- p.34 / Chapter 3 --- Knowledge Representation and Learning Algorithm --- p.43 / Chapter 3.1 --- Knowledge Representation --- p.44 / Chapter 3.1.1 --- Fuzzy First-order Logic ´ؤ A Powerful Language --- p.44 / Chapter 3.1.2 --- Literal Forms --- p.48 / Chapter 3.1.3 --- Continuous Variables --- p.50 / Chapter 3.2 --- System Architecture --- p.61 / Chapter 3.2.1 --- Data Reading --- p.61 / Chapter 3.2.2 --- Preprocessing and Postprocessing --- p.67 / Chapter 4 --- Global Evaluation of Literals --- p.71 / Chapter 4.1 --- Existing Closeness Measures between Fuzzy Sets --- p.72 / Chapter 4.2 --- The Error Function and the Normalized Error Functions --- p.75 / Chapter 4.2.1 --- The Error Function --- p.75 / Chapter 4.2.2 --- The Normalized Error Functions --- p.76 / Chapter 4.3 --- The Nodal Characteristics and the Error Peaks --- p.79 / Chapter 4.3.1 --- The Nodal Characteristics --- p.79 / Chapter 4.3.2 --- The Zero Error Line and the Error Peaks --- p.80 / Chapter 4.4 --- Quantifying the Nodal Characteristics --- p.85 / Chapter 4.4.1 --- Information Theory --- p.86 / Chapter 4.4.2 --- Applying the Information Theory --- p.88 / Chapter 4.4.3 --- Upper and Lower Bounds of CE --- p.89 / Chapter 4.4.4 --- The Whole Heuristics of FF99 --- p.93 / Chapter 4.5 --- An Example --- p.94 / Chapter 5 --- Partial Evaluation of Literals --- p.99 / Chapter 5.1 --- Importance of Covering in Inductive Learning --- p.100 / Chapter 5.1.1 --- The Divide-and-conquer Method --- p.100 / Chapter 5.1.2 --- The Covering Method --- p.101 / Chapter 5.1.3 --- Effective Pruning in Both Methods --- p.102 / Chapter 5.2 --- Fuzzification of FOIL --- p.104 / Chapter 5.2.1 --- Analysis of FOIL --- p.104 / Chapter 5.2.2 --- Requirements on System Fuzzification --- p.107 / Chapter 5.2.3 --- Possible Ways in Fuzzifing FOIL --- p.109 / Chapter 5.3 --- The α Covering Method --- p.111 / Chapter 5.3.1 --- Construction of Partitions by α-cut --- p.112 / Chapter 5.3.2 --- Adaptive-α Covering --- p.112 / Chapter 5.4 --- The Probabistic Covering Method --- p.114 / Chapter 6 --- Results and Discussions --- p.119 / Chapter 6.1 --- Experimental Results --- p.120 / Chapter 6.1.1 --- Iris Plant Database --- p.120 / Chapter 6.1.2 --- Kinship Relational Domain --- p.122 / Chapter 6.1.3 --- The Fuzzy Relation Domain --- p.129 / Chapter 6.1.4 --- Age Group Domain --- p.134 / Chapter 6.1.5 --- The NBA Domain --- p.135 / Chapter 6.2 --- Future Development Directions --- p.137 / Chapter 6.2.1 --- Speed Improvement --- p.137 / Chapter 6.2.2 --- Accuracy Improvement --- p.138 / Chapter 6.2.3 --- Others --- p.138 / Chapter 7 --- Conclusion --- p.140 / Bibliography --- p.142 / Chapter A --- C4.5 to FOIL File Format Conversion --- p.147 / Chapter B --- FF99 example --- p.150

Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Arkadi Nemirovski; Committee Co-Chair: Alexander Shapiro; Committee Co-Chair: Renato D. C. Monteiro; Committee Member: Anatoli Jouditski; Committee Member: Shabbir Ahmed. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (Ph.D.)--Tufts University, 2004. / Adviser: Roni Khardon. Submitted to the Dept. of Computer Science. Includes bibliographical references (leaves 157-161). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

Thesis (Ph.D.)--McMaster University, 2003. / Advisor: David L. Hitchcock. Includes bibliographical references (leaves 144-147). Also available via World Wide Web.

Equational reasoning with string diagrams provides an intuitive method for proving equations between morphisms in various forms of monoidal category. !-Graphs were introduced with the intention of reasoning with infinite families of string diagrams by allowing repetition of sub-diagrams. However, their combinatoric nature only allows commutative nodes. The aim of this thesis is to extend the !-graph formalism to remove the restriction of commutativity and replace the notion of equational reasoning with a natural deduction system based on first order logic. The first major contribution is the syntactic !-tensor formalism, which enriches Penrose's abstract tensor notation to allow repeated structure via !-boxes. This will allow us to work with many noncommutative theories such as bialgebras, Frobenius algebras, and Hopf algebras, which have applications in quantum information theory. A more subtle consequence of switching to !-tensors is the ability to definitionally extend a theory. We will demonstrate how noncommutativity allows us to define nodes which encapsulate entire diagrams, without inherently assuming the diagram is commutative. This is particularly useful for recursively defining arbitrary arity nodes from fixed arity nodes. For example, we can construct a !-tensor node representing the family of left associated trees of multiplications in a monoid. The ability to recursively define nodes goes hand in hand with proof by induction. This leads to the second major contribution of this thesis, which is !-Logic (!L). We extend previous attempts at equational reasoning to a fully fledged natural deduction system based on positive intuitionistic first order logic, with conjunction, implication, and universal quantification over !-boxes. The key component of !L is the principle of !-box induction. We demonstrate its application by proving how we can transition from fixed to arbitrary arity theories for monoids, antihomomorphisms, bialgebras, and various forms of Frobenius algebras. We also define a semantics for !L, which we use to prove its soundness. Finally, we reintroduce commutativity as an optional property of a morphism, along with another property called symmetry, which describes morphisms which are not affected by cyclic permutations of their edges. Implementing these notions in the !-tensor language allows us to more easily describe theories involving symmetric or commutative morphisms, which we then demonstrate for recursively defined Frobenius algebra nodes.

M.Sc. / This short dissertation is intended to give a brief account of the history and current state of affairs in the field of study called 'Zero-one Laws'. The probability of a property P on a class of finite relational structures is defined to be the limit of the sequence of fractions, of the n element structures that satisfy the property P, as n tends to infinity. A class of properties is said to have a Zero-One law if the above limit, which is usually called the asymptotic probability of the property with respect to the given class of finite structures, is either 0 or 1 for each property. The connection to the field of Mathematical Logic is given by the surprising fact that the class of properties definable by a first-order sentence has a Zero-One law with respect to the class of all finite relational structures of the common signature. We cover this result in more detail and discuss several further Zero- One laws for higher-order logics. In particular we will be interested in all those modal formulae which are 'almost surely' frame valid in the finite, i.e. those which have an asymptotic probability equal to 1 with respect to the class of all finite frames. Our goal is to find a purely logical characterization of these formulae by finding a set of axioms which describe such modal formulae absolutely. We devise a strategy and provide some Java programs to aid in this search for future research

Our work focuses on bringing the first-order reasoning closer to practicalapplications, particularly in software and hardware verification. The aim is to develop techniques that make first-order reasoners more scalablefor large problems and suitable for the applications. In pursuit of this goal the work focuses in three main directions. First, wedevelop an algorithm for an efficient pre-selection of axioms. This algorithmis already being widely used by the community and enables off-the-shelf theoremprovers to work with problems having millions of axioms that would otherwisebe overwhelming for them. Secondly, we focus on the saturation algorithm itself, and develop anew calculus for separate handling of propositional predicates. We also do anextensive research on various ways of clause splitting within the saturationalgorithm. The third main block of our work is focused on the use of saturation basedfirst-order theorem provers for software verification, particularly forgenerating invariants and computing interpolants. We base our work on theoretical results of Kovacs and Voronkov published in2009 on the CADE and FASE conferences. We develop a practical implementationwhich embraces all the extensions of the basic resolution and superposition calculus that are contained in the theorem prover Vampire. We have also developed a unique proof transforming algorithm which optimizes the computed interpolantswith respect to a user specified cost function.

An investigation of the temperature response and corresponding lesion growth resulting from in vivo interstitial laser photocoagulation was performed in order to test the applicability of Arrhenius theory. The irradiations were performed in vivo in rabbit muscle for various exposures at 1.0W using an 805 nm diode laser source coupled to an optical fibre with a pre-charred tip, thereby forcing it to function as a point heat source. Temperature responses were measured using a five-microthermocouple array along a range of radial distances from the point heat source. Each temperature profile was fitted with a curve predicted by the Weinbaum-Jiji bioheat transfer equation. The lesions were resected 48 hours after irradiation and the boundary of thermal damage resulting in necrosis was determined histologically. Numerical integration of the Arrhenius integral using temperature-time data at the lesion boundary produced corresponding activation energy and pre-exponential factor pairs (Eₐ , α) consistent with reported values for various other endpoints and tissue types. As well, theoretical predictions of the lesion growth from Arrhenius theory agreed well with experimental results. However, the thermal parameters, which are generally assumed to be constant when solving the bioheat transfer equation, were found to vary with radial distance from the source, presumably due to dependence on temperature. / Thesis / Master of Science (MS)

Hypolimnetic oxygen diffusers increase sediment oxygen demand (SOD) and, if not accounted for in design, can further exacerbate anoxic conditions. A study using extracted sediment cores, that included both field and laboratory experiments, was performed to investigate SOD kinetics in Carvin's Cove Reservoir, a eutrophic water supply reservoir for Roanoke, Virginia. A bubble-plume diffuser is used in Carvin's Cove to replenish oxygen consumed while the reservoir is thermally stratified. The applicability of zero-order, first-order, and Monod kinetics to describe transient and steady state SOD was modeled using analytical and numerical techniques. Field and laboratory experiments suggested that first-order kinetics characterize Carvin's Cove SOD. SOD calculated from field experiments reflected diffuser flow changes. Laboratory experiments using mini-diffusers to vary dissolved oxygen concentration and turbulence were conducted at 4°C and 20°C. Similar to field observations, the laboratory results followed changes in mini-diffuser flow. Kinetic-temperature relationships were also observed in the laboratory experiments. A definitive conclusion could not be made on the broad applicability of first-order kinetics to Carvin's Cove SOD due to variability within field experiments. However, in situ experiments are underway that should assist in the overall understanding of the reservoir's SOD kinetics. / Master of Science