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Thesis (Ph.D.)--Ohio University, August, 2007. / Title from PDF t.p. Includes bibliographical references.

Thesis (M.S.)--Rochester Institute of Technology, 1994. / Typescript. Includes bibliographical references (leaf 123).

Local descriptors are increasingly used for the task of object recognition because of their perceived robustness with respect to occlusions and to global geometrical deformations. Such a descriptor--based on a set of oriented Gaussian derivative filters-- is used in our recognition system. We report here an evaluation of several techniques for orientation estimation to achieve rotation invariance of the descriptor. We also describe feature selection based on a single training image. Virtual images are generated by rotating and rescaling the image and robust features are selected. The results confirm robust performance in cluttered scenes, in the presence of partial occlusions, and when the object is embedded in different backgrounds.

En 1998, R. Gompf a défini un invariant homotopique des champs de plans orientés des 3-variétés fermées orientées. Cet invariant est défini pour les champs de plans orientés xi; de toute 3-variété fermée orientée M dont la première classe de Chern c_1(xi) est un élément de torsion de H_2(M;Z). Dans le premier chapitre de la thèse, nous définissons une extension de l’invariant de Gompf pour toutes les 3-variétés compactes orientées à bord et nous étudions ses variations lors de chirurgies lagrangiennes. Il en résulte que l’invariant de Gompf étendu peut être vu comme un invariant de type fini de degré 2.L’invariant Théta est un invariant de variétés de dimension 3 parallélisées qui provient de la partie de degré 1 du développement perturbatif de la théorie de Chern-Simons. G. Kuperberg et D. Thurston ont identifié l’invariant Théta(M,tau) d’une sphère d’homologie entière M munie d’une parallélisation tau; à lambda_cw(M) + 1/4·p_1(tau) où lambda_cw désigne la généralisation de Walker de l’invariant de Casson et p_1 est un invariant de la parallélisation définie à partir d’une première classe de Pontrjagin. C. Lescop a étendu l’invariant Théta aux sphères d’homologie rationnelle munies d’une classe d’homotopie de combings et elle a montré que pour toute sphère d’homologie rationnelle M munie d’un combing X, la formule Théta(M,[X]) = 3·lambda_cw(M) + 1/4·p_1([X]) était encore valable pour une extension ad hoc des nombres de Pontrjagin aux combings. Elle a aussi donné une formule combinatoire pour l’invariant Théta d’une sphère d’homologie rationnelle présentée par un diagramme de Heegaard et munie d’un combing associé au diagramme, et elle a démontré combinatoirement que cette formule définit un invariant homotopique des couples (M,[X]). Dans le prolongement de ce travail, le deuxième chapitre de la thèse présente une preuve combinatoire de la décomposition de cet invariant combinatoire comme 3·lambda_cw(M) + 1/4·p_1([X]). Cette preuve repose sur la théorie des invariants de type fini des sphères d’homologie rationnelle relativement aux chirurgies lagrangiennes établie par D. Moussard en 2012 / In 1998, R. Gompf defined a homotopy invariant of oriented 2-plane fields in 3-manifolds. This invariant is defined for oriented 2-plane fields xi in a closed oriented 3-manifold M when the first Chern class c_1(xi) is a torsion element of H_2(M;Z). In Chapter I, we define an extension of the Gompf invariant for all compact oriented 3-manifolds with boundary and we study its iterated variations under Lagrangian-preserving surgeries. It follows that the extended Gompf invariant has degree two for a suitable finite type invariant theory.The Theta-invariant is an invariant of parallelized 3-manifolds constructed from the degree one part of the perturbative expansion of Chern–Simons theory. G. Kuperberg and D. Thurston identified the invariant Theta(M,tau) of a rational homology 3-sphere M equipped with a parallelization tau with 3·lambda_cw(M) + 1/4·p_1(tau) where lambda_cw denotes Walker’s generalization of the Casson invariant and where p_1 is an invariant of parallelizations defined using a first Pontrjagin class. C. Lescop extended the Theta-invariant to rational homology 3-spheres equipped with a homotopy class of combings and she showed that for all rational homology 3-sphere M equipped with a combing X, the relation Theta(M,[X]) = 3·lambda_cw(M) + 1/4·p_1([X]) still holds using an ad hoc extension of the Pontrjagin numbers for combings. She also gave a combinatorial formula for the Theta-invariant of a rational homology 3-sphere represented by a Heeagaard diagram and equipped with a combing associated to the diagram, and she proved that this formula defines a homotopy invariant of the pair (M,[X]), in a combinatorial way. Following this work, Chapter II presents a combinatorial proof of the decomposition of this combinatorial invariant as 3·lambda_cw(M) + 1/4·p_1([X]). This proof relies on the finite type invariant theory for rational homology 3-spheres with respect to Lagrangian-preserving surgeries established by D. Moussard in 2012

In this expository paper we study the stationary measures of a stochastic process called nearest neighbor random walk on Z, and further we describe conditions for these measures to have the stronger property of reversibility. We consider both the cases of symmetric and non-symmetric random walk.

Dynamic invariant detection is a software analysis technique that uses traces of function entry and exit from executing programs and infers partial specifications that characterize the observed behavior. The specifications are reported as logical precondition and postcondition expressions (invariants) that relate arguments, instance variables, and results. Detectors typically generate large collections of invariants, among which most are true but few are interesting or useful. Refining this flood of invariants into a useful subset often requires manual tuning through configuration options and modification of the program under analysis. Our research asks whether we can improve dynamic invariant detection by enabling explicit abstractions to be declared and applied to a program under analysis and whether this is practical; this dissertation shows that it is indeed practical and useful. Given a concrete program we can synthesize a model program composed of functions and modules that are abstractions of selected concrete modules. When we execute the model program in parallel with its underlying concrete program and apply dynamic invariant detection, we obtain abstracted invariants that can reveal the behavior of the underlying concrete program. We developed the Alembic system to support and experiment with the above technique, enabling a practical method for steering the invariant detection process and shaping the analysis to produce more refined results than obtainable via traditional means. Alembic provides a simple language for defining abstractions and managing detection experiments; the system generates the necessary instrumentation, representation classes, and functions, freeing the analyst to focus on the expression of abstractions and detection experiments. Alembic currently leverages the invariant detection capability of Daikon, a powerful first-generation detector, to analyze synthetic traces on abstractions. However, the principles we demonstrate apply to any detector and language that observes function entry and exit. We present some applications of this technique to example problems and then evaluate Alembic on production code such as the Guava class library. Our research suggests new uses for existing detectors and enables the design and evaluation of features to inform the next generation of dynamic invariant detection systems. This dissertation includes previously unpublished co-authored material.

The trace form gives a connection between the representation ring and the space of invariant bilinear forms of a Lie algebra $L$. This thesis reviews the definition of the trace of an endomorphism of a finitely generated projective module over a commutative ring $R$. We then use this to look at the trace form of a finitely generated projective representation of a Lie algebra $L$ over $R$ and its representation ring. While doing so, we prove a few trace formulas which are useful in the theory of the Dynkin index, an invariant introduced by Dynkin in 1952 to study homomorphisms between simple Lie algebras.

Associated to a split, semisimple linear algebraic group G is a group of invariant quadratic forms, which we denote Q(G). Namely, Q(G) is the group of quadratic forms in characters of a maximal torus which are fixed with respect to the action of the Weyl group of G. We compute Q(G) for various examples of products of the special linear, special orthogonal, and symplectic groups as well as for quotients of those examples by central subgroups. Homomorphisms between these linear algebraic groups induce homomorphisms between their groups of invariant quadratic forms. Since the linear algebraic groups are semisimple, Q(G) is isomorphic to Z^n for some n, and so the induced maps can be described by a set of integers called Rost multipliers. We consider various cases of the Kronecker tensor product map between copies of the special linear, special orthogonal, and symplectic groups. We compute the Rost multipliers of the induced map in these examples, ultimately concluding that the Rost multipliers depend only on the dimensions of the underlying vector spaces.

A new approach to the identification problem of linear continuous-time time-invariant systems from input-output measurements is presented. Both parametric and nonparametric system models are considered. The new approach is based on the use of continuous-time functions, the modal functions, defined in terms of the system output, the output derivatives and the state variables under the assumption that the order n of the observable system is known a priori. The modal functions are obtained by linear filtering operations of the system output, the output derivatives and the state variables so that the modal functions are independent of the system instantaneous state. In this case, the modal functions are linear functions of the input exponential modes, and they contain none of the system exponential modes unlike the system general response which contains modes from both the system and the input. The filters parameters, the modal parameters are estimated using linear regression techniques. The modal functions and the modal parameters of the output and its derivatives are used to identify parametric input-output and state models of the system. The coefficients of the system characteristic polynomial are obtained by solving n algebraic equations formed from the estimates of the modal parameters. Estimates of the parameters associated with the system zeros are obtained by solving another set of linear algebraic equation. The system frequency response and step response are estimated using the output modal function. The impulse response is obtained by filtering the estimated step response using the output first derivative modal parameters. A new method is presented to obtain the system poles as the eigenvalues of a data matrix formed from the system free response. The coefficients of the system characteristic polynomial are obtained from the data matrix through a simple recursive equation. This method has some important advantages over the well known Prony's method. The state modal functions are used to obtain a minimum-time observer that gives the continuous-time system state as a direct function of input-output samples in n sampling intervals. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate