Equivalence and Reduction of Hidden Markov Models

This report studies when and why two Hidden Markov Models (HMMs) may represent the same stochastic process. HMMs are characterized in terms of equivalence classes whose elements represent identical stochastic processes. This characterization yields polynomial time algorithms to detect equivalent HMMs. We also find fast algorithms to reduce HMMs to essentially unique and minimal canonical representations. The reduction to a canonical form leads to the definition of 'Generalized Markov Models' which are essentially HMMs without the positivity constraint on their parameters. We discuss how this generalization can yield more parsimonious representations of stochastic processes at the cost of the probabilistic interpretation of the model parameters.

Basis Reduction Algorithms and Subset Sum Problems

This thesis investigates a new approach to lattice basis reduction suggested by M. Seysen. Seysen's algorithm attempts to globally reduce a lattice basis, whereas the Lenstra, Lenstra, Lovasz (LLL) family of reduction algorithms concentrates on local reductions. We show that Seysen's algorithm is well suited for reducing certain classes of lattice bases, and often requires much less time in practice than the LLL algorithm. We also demonstrate how Seysen's algorithm for basis reduction may be applied to subset sum problems. Seysen's technique, used in combination with the LLL algorithm, and other heuristics, enables us to solve a much larger class of subset sum problems than was previously possible.

Residual Vibration Reduction in Computer Controlled Machines

Control of machines that exhibit flexibility becomes important when designers attempt to push the state of the art with faster, lighter machines. Three steps are necessary for the control of a flexible planet. First, a good model of the plant must exist. Second, a good controller must be designed. Third, inputs to the controller must be constructed using knowledge of the system dynamic response. There is a great deal of literature pertaining to modeling and control but little dealing with the shaping of system inputs. Chapter 2 examines two input shaping techniques based on frequency domain analysis. The first involves the use of the first deriviate of a gaussian exponential as a driving function template. The second, acasual filtering, involves removal of energy from the driving functions at the resonant frequencies of the system. Chapter 3 presents a linear programming technique for generating vibration-reducing driving functions for systems. Chapter 4 extends the results of the previous chapter by developing a direct solution to the new class of driving functions. A detailed analysis of the new technique is presented from five different perspectives and several extensions are presented. Chapter 5 verifies the theories of the previous two chapters with hardware experiments. Because the new technique resembles common signal filtering, chapter 6 compares the new approach to eleven standard filters. The new technique will be shown to result in less residual vibrations, have better robustness to system parameter uncertainty, and require less computation than other currently used shaping techniques.

On the correlation between microstructural changes of Ag-H-ZSM-5 catalysts and their catalytic performances in the selective catalytic reduction of NOx by methane

The silver catalyzed, selective catalytic reduction (SCR) of nitrogen oxides (NOx) by CH4, is shown to be a structure-sensitive reaction. Pretreatment has a great affect on the catalytic performances. Upon thermal treatment in inert gas stream, thermal induced changes in silver morphology lead to the formation of reduced silver species of clusters and particles. Catalysis over this catalyst indicates an initially higher activity but lower selectivity for the CH4-SCR of NOx Reaction induced restructuring of silver results in the formation of ill-defined silver oxides. This, in turn, impacts the adsorption properties and diffusivity of oxygen over silver catalyst, results in the decrease in activity but increase in selectivity of Ag-H-ZSM-5 catalyst for the CH4-SCR of NO.. (c) 2004 Elsevier B.V. All rights reserved.

Semantics-Preserving Dimensionality Reduction: Rough and Fuzzy-Rough-Based Approaches

R. Jensen and Q. Shen. Semantics-Preserving Dimensionality Reduction: Rough and Fuzzy-Rough Based Approaches. IEEE Transactions on Knowledge and Data Engineering, 16(12): 1457-1471. 2004.

Fuzzy-Rough Data Reduction with Ant Colony Optimization.

R. Jensen and Q. Shen, 'Fuzzy-Rough Data Reduction with Ant Colony Optimization,' Fuzzy Sets and Systems, vol. 149, no. 1, pp. 5-20, 2005.

Fuzzy-Rough Attribute Reduction with Application to Web Categorization.

R. Jensen and Q. Shen, 'Fuzzy-Rough Attribute Reduction with Application to Web Categorization,' Fuzzy Sets and Systems, vol. 141, no. 3, pp. 469-485, 2004.

Data Reduction with Rough Sets

R. Jensen, Q. Shen, Data Reduction with Rough Sets, In: Encyclopedia of Data Warehousing and Mining - 2nd Edition, Vol. II, 2008.

Occupational lead neurotoxicity: Improvement in behavioural effects after reduction of exposure.

To evaluate critical exposure levels and the reversibility of lead neurotoxicity a group of lead exposed foundry workers and an unexposed reference population were followed up for three years. During this period, tests designed to monitor neurobehavioural function and lead dose were administered. Evaluations of 160 workers during the first year showed dose dependent decrements in mood, visual/motor performance, memory, and verbal concept formation. Subsequently, an improvement in the hygienic conditions at the plant resulted in striking reductions in blood lead concentrations over the following two years. Attendant improvement in indices of tension (20% reduction), anger (18%), depression (26%), fatigue (27%), and confusion (13%) was observed. Performance on neurobehavioural testing generally correlated best with integrated dose estimates derived from blood lead concentrations measured periodically over the study period; zinc protoporphyrin levels were less well correlated with function. This investigation confirms the importance of compliance with workplace standards designed to lower exposures to ensure that individual blood lead concentrations remain below 50 micrograms/dl.

New Notions of Reduction and Non-Semantic Proofs of β-Strong Normalization in Typed λ-Calculi

Two new notions of reduction for terms of the λ-calculus are introduced and the question of whether a λ-term is beta-strongly normalizing is reduced to the question of whether a λ-term is merely normalizing under one of the new notions of reduction. This leads to a new way to prove beta-strong normalization for typed λ-calculi. Instead of the usual semantic proof style based on Girard's "candidats de réductibilité'', termination can be proved using a decreasing metric over a well-founded ordering in a style more common in the field of term rewriting. This new proof method is applied to the simply-typed λ-calculus and the system of intersection types.