The nature and assessment of executive function are areas of active research. Many current assessments of executive function are complex, have limited reliability and validity, and suffer from task impurity, meaning other cognitive processes may indirectly influence task performance. Additionally, measures may be culture, language, or education bound limiting their use in certain populations (Miyake, Emerson, & Friedman, 2000; Miyake, Friedman, et al., 2000; Strauss, Sherman, & Spreen, 2006; Stuss, 2007). The purpose of this project was to develop a novel set of executive function measures to address issues with current clinical measures. The new measures 1) can be used in an ERP environment, 2) use the same stimulus set to address task impurity and 3) use simpler cognitive operations of inhibition, set-shifting, and updating, identified in previous research by Miyake et al., (2000). Twenty-nine undergraduate participants at the University of South Florida were administered currently used clinical measures of executive function theorized to engage in inhibition, set-shifting, and updating and the set of the novel tasks. ERP data was collected during the administration of the novel tasks. Behaviorally, conditions theorized to engage executive function resulted in slower response reaction time than control conditions. Additionally, behavioral results indicated that performance on novel tasks were differentially related to different clinical EF tasks. ERP differences were observed between both Go/No-Go conditions (inhibition) and among N-back conditions (updating). Results suggest the novel executive function tasks are tapping into different cognitive processes and may be a viable tool for studying executive function in the future.

This study investigated the distribution of bibliographic records amongst online bibliographic databases. The topic of Fuzzy Set Theory over the period of 1965 to 1993 was chosen to provide the case study for this investigation. From the DIALOG database host, searches were conducted on 114 databases to determine the number of journal article records relating to the topic of Fuzzy Sets. Both the number of records in each database, as well as the overlap of coverage between the databases were calculated. Six counting techniques were developed to allocate records to databases based on different methods for handling records that were duplicated between databases. When duplicate records are included, the top database accounts for 19% of the records; when duplicates are removed, the top database was found to account for 37% of the records. The distribution of records in databases was found to conform to the Bradford-Zipf hyperbolic distribution. Various other analyses were undertaken including: the duplicate records themselves, the total size of the DIALOG database system over time and the density of Fuzzy Set records in databases over time. A secondary aim of this study was to perform an informetric study on the literature of Fuzzy Set Theory itself. Results obtained include an analysis of the growth of the Fuzzy Set literature, an analysis of the journals covering the topic of Fuzzy Sets, an analysis of the terminology used in describing topics related to Fuzzy Sets. Also, the Ulrich's database was used to provide a subject classification of the journals to analyse the diffusion of the topic of Fuzzy Sets into other disciplines. Apart from the discipline of mathematics, the top disciplines into which Fuzzy Sets have diffused were found to be applied physics, systems and computing. The third aim of the thesis was to refine and develop the methodology used to perform large scale informetric studies using data from a variety of online bibliographic databases. Commercially available software was used wherever possible, but where this was not possible or infeasible, custom written programs were developed to perform various steps in the methodology.

A random variable that is defined as the absorption time of an evanescent finite-state continuous-time Markov chain is said to have a phase-type distribution. A phase-type distribution is said to have a representation (α,T ) where α is the initial state probability distribution and T is the infinitesimal generator of the Markov chain. The distribution function of a phase-type distribution can be expressed in terms of this representation. The wider class of matrix-exponential distributions have distribution functions of the same form as phase-type distributions, but their representations do not need to have a simple probabilistic interpretation. This class can be equivalently defined as the class of all distributions that have rational Laplace-Stieltjes transform. There exists a one-to-one correspondence between the Laplace-Stieltjes transform of a matrix- exponential distribution and a representation (β,S) for it where S is a companion matrix. In order to use matrix-exponential distributions to fit data or approximate probability distributions the following question needs to be answered: “Given a rational Laplace-Stieltjes transform, or a pair (β,S) where S is a companion matrix, when do they correspond to a matrix-exponential distribution?” In this thesis we address this problem and demonstrate how its solution can be applied to the abovementioned fitting or approximation problem. / Thesis (Ph.D.)--School of Applied Mathematics, 2003.

The purpose of the thesis was to explore the possibilities of using a Level-Set method to design a time-optimal path planar of a subject to direction-dependent maximum velocities. A promising application for such a planning approach lies in sailboat navigation planning, because of the dynamic ocean waves, current, wind and the characteristics of a sailboat. In the thesis, we developed an IOS application to simulate such scenario as environment properties with wind, static obstacles and the sailboat mapped into direction-dependent velocities in different locations of the environment.  Considering the wind is the main power for the sailboat, a wind speed generation function was created, based on different locations. The Level-Set method is widely used in image processing because of its various advantages, for instance, the ability to deal with topology change and stability. It also can be applied in path planning, in which the process of the Level-Set method can be considered as a continuous wave front propagating with a speed from the start location. A grid-based map was used to represent the environment. While the wave front was crossing the cell on the grid, a time was recorded for every cell, following the negative gradient direction of such crossing time, and then an optimal path could be found. In addition, we used the Narrow Band method to speed up the calculation of processing the level set equation. Finally, this report gives the results of the experiments of static obstacle avoidance, wind effects and smooth path planning.

The investigation of this paper is introduced by describing an important collection of classes arising from a class which forms the domain of an abstract measure. Characterizations of the different types of classes will be formulated in order to facilitate the construction and the identification of the various classes considered.

The control of nonholonomic wheeled mobile robots (WMRs) has gained a lot of attention in the field of robotics over the past few decades as WMRs provide an increased range of motion resulting in a larger workspace. This research focuses on the application of Model Predictive Control (MPC) for real-time trajectory tracking of a nonholonomic WMR. MPC is a control strategy in which the control law is designed based on optimizing a cost function. The input and output constraints that may arise in practical situations can be directly incorporated into the control system using MPC. Computation time is the biggest hurdle in adapting MPC strategies for trajectory tracking. This research applies a non-feasible active set MPC algorithm developed in [1] which is faster than the traditional active set methods (ASMs). A discrete-time linear model of a general WMR is used for the simulation. MATLAB simulations are performed for tracking circular as well as square trajectories using the discretized WMR model and the non-feasible ASM (NF-ASM). The performance of NF-ASM is compared to two other well-known traditional algorithms, i.e. Fletcher’s ASM and MATLAB’s Quadratic Programming algorithm. It is shown that, although all these algorithms are capable of providing satisfactory trajectory tracking performance, NF-ASM is a better choice in terms of the simulation time and required number of iterations for realtime trajectory tracking of any type as long as the constraints on the inputs stay active for a long period during the simulation. / UOIT

In this thesis we study the problem of stabilizing smooth embedded submanifolds in the state space of smooth, nonlinear, autonomous, deterministic control-affine systems. Our motivation stems from a realization that important applications, such as path following and synchronization, are best understood in the set stabilization framework. Instead of directly attacking the above set stabilization problem, we seek feedback equivalence of the given control system to a normal form that facilitates control design. The process of putting a control system into the normal form of this thesis is called transverse feedback linearization. When feasible, transverse feedback linearization allows for a decomposition of the nonlinear system into a “transverse” and a “tangential” subsystem relative to the goal submanifold. The dynamics of the transverse subsystem determine whether or not the system’s state approaches the submanifold. To ease controller design, we ask that the transverse subsystem be linear time-invariant and controllable. The dynamics of the tangential subsystem determine the motion on the submanifold. The main problem considered in this work, the local transverse feedback linearization problem (LTFLP), asks: when is such a decomposition possible near a point of the goal submanifold? This problem can equivalently be viewed as that of finding a system output with a well-defined relative degree, whose zero dynamics manifold coincides with the goal submanifold. As such, LTFLP can be thought of as the inverse problem to input-output feedback linearization. We present checkable, necessary and sufficient conditions for the existence of a local coordinate and feedback transformation that puts the given system into the desired normal form. A key ingredient used in the analysis is the new notion of transverse controllability indices of a control system with respect to a set. When the goal submanifold is diffeomorphic to Euclidean space, we present sufficient conditions for feedback equivalence in a tubular neighbourhood of it. These results are used to develop a technique for solving the path following problem. When applied to this problem, transverse feedback linearization decomposes controller design into two separate stages: transversal control design and tangential control design. The transversal control inputs are used to stabilize the path, and effectively generate virtual constraints forcing the system’s output to move along the path. The tangential inputs are used to control the motion along the path. A useful feature of this twostage approach is that the motion on the set can be controlled independently of the set stabilizing control law. The effectiveness of the proposed approach is demonstrated experimentally on a magnetically levitated positioning system. Furthermore, the first satisfactory solution to a problem of longstanding interest, path following for the planar/vertical take-off and landing aircraft model to the unit circle, is presented. This solution, developed in collaboration with Luca Consolini and Mario Tosques at the University of Parma, is made possible by taking a set stabilization point of view.

Sequence alignment has become one of the most common tasks in bioinformatics. Most of the existing sequence alignment methods use general scoring schemes. But these alignments are sometimes not completely relevant because they do not necessarily provide the desired information. It would be extremely difficult, if not impossible, to include any possible objective into an algorithm. Our goal is to allow a working biologist to augment a given alignment with additional information based on their knowledge and objectives.<p></p>In this thesis, we will formally define constraints and compatible constraint sets for an alignment which require some positions of the sequences to be aligned together. Using this approach, one can align some specific segments such as domains within protein sequences by inputting constraints (the positions of the segments on the sequences), and the algorithm will automatically find an optimal alignment in which the segments are aligned together.<p></p>A necessary prerequisite of calculating an alignment is that the constraints inputted be compatible with each other, and we will develop algorithms to check this condition for both pairwise and multiple sequence alignments. The algorithms are based on a depth-first search on a graph that is converted from the constraints and the alignment. We then develop algorithms to perform pairwise and multiple sequence alignments satisfying these compatible constraints.<p></p>Using straightforward dynamic programming for pairwise sequence alignment satisfying a compatible constraint set, an optimal alignment corresponds to a path going through the dynamic programming matrix, and as we are only using single-position constraints, a constraint can be represented as a point on the matrix, so a compatible constraint set is a set of points. We try to determine a new path, rather than the original path, that achieves the highest score which goes through all the compatible constraint set points. The path is a concatenation of sub-paths, so that only the scores in the sub-matrices need to be calculated. This means the time required to get the new path decreases as the number of constraints increases, and it also varies as the positions of the points change. It can be further reduced by using the information from the original alignment, which can offer a significant speed gain.<p></p>We then use exact and progressive algorithms to find multiple sequence alignments satisfying a compatible constraint set, which are extensions of pairwise sequence alignments. With exact algorithms for three sequences, where constraints are represented as lines, we discuss a method to force the optimal path to cross the constraint lines. And with progressive algorithms, we use a set of pairwise alignments satisfying compatible constraints to construct multiple sequence alignments progressively. Because they are more complex, we leave some extensions as future work.

This thesis investigates the set stabilization problem for systems with Lie group symmetry. Initially, we examine left-invariant systems on Lie groups where the target set is a left or right coset of a closed subgroup. We broaden the scope to systems defined on smooth manifolds that are invariant under a Lie group action. Inspired by the solution of this problem for linear time-invariant systems, we show its equivalence to an equilibrium stabilization problem for a suitable quotient control system. We provide necessary and sufficient conditions for the existence of the quotient control system and analyze various properties of such a system. This theory is applied to the formation stabilization of three kinematic unicycles, the path stabilization of a particle in a gravitational field, and the conversion and temperature control of a continuously stirred tank reactor.

This thesis investigates the set stabilization problem for systems with Lie group symmetry. Initially, we examine left-invariant systems on Lie groups where the target set is a left or right coset of a closed subgroup. We broaden the scope to systems defined on smooth manifolds that are invariant under a Lie group action. Inspired by the solution of this problem for linear time-invariant systems, we show its equivalence to an equilibrium stabilization problem for a suitable quotient control system. We provide necessary and sufficient conditions for the existence of the quotient control system and analyze various properties of such a system. This theory is applied to the formation stabilization of three kinematic unicycles, the path stabilization of a particle in a gravitational field, and the conversion and temperature control of a continuously stirred tank reactor.