Physical Sciences and Mathematics Commons^™

Advances In Graph-Cut Optimization: Multi-Surface Models, Label Costs, And Hierarchical Costs, Andrew T. Delong

Electronic Thesis and Dissertation Repository

Computer vision is full of problems that are elegantly expressed in terms of mathematical optimization, or energy minimization. This is particularly true of "low-level" inference problems such as cleaning up noisy signals, clustering and classifying data, or estimating 3D points from images. Energies let us state each problem as a clear, precise objective function. Minimizing the correct energy would, hypothetically, yield a good solution to the corresponding problem. Unfortunately, even for low-level problems we are confronted by energies that are computationally hard—often NP-hard—to minimize. As a consequence, a rather large portion of computer vision research is dedicated to proposing …

Solving Polynomial Systems Via Triangular Decomposition, Changbo Chen

Electronic Thesis and Dissertation Repository

Finding the solutions of a polynomial system is a fundamental problem with numerous applications in both the academic and industrial world. In this thesis, we target on computing symbolically both the real and the complex solutions of nonlinear polynomial systems with or without parameters. To this end, we improve existing algorithms for computing triangular decompositions. Based on that, we develop various new tools for solving polynomial systems and illustrate their effectiveness by applications.

We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a weakened notion of a …

Some Single And Combined Operations On Formal Languages: Algebraic Properties And Complexity, Bo Cui

Electronic Thesis and Dissertation Repository

In this thesis, we consider several research questions related to language operations in the following areas of automata and formal language theory: reversibility of operations, generalizations of (comma-free) codes, generalizations of basic operations, language equations, and state complexity.

Motivated by cryptography applications, we investigate several reversibility questions with respect to the parallel insertion and deletion operations. Among the results we obtained, the following result is of particular interest. For languages L₁, L₂ ⊆ Σ^∗, if L₂ satisfies the condition L₂ΣL₂ ∩ Σ⁺L₂Σ⁺ = ∅, then …

Workflow-Net Based Cooperative Multi-Agent Systems, Yehia T. Kotb

Electronic Thesis and Dissertation Repository

Workflow-nets are mathematical frameworks that are used to formally describe, model and implement workflows. First, we propose critical section workflow nets (abbreviated WFCSnet). This framework allows feedbacks in workflow systems while ensuring the soundness of the workflow. Feedback is generally not recommended in workflow systems as they threaten the soundness of the system. The proposed WFCSnet allows safe feedback and limits the maximum number of activities per workflow as required. A theorem for soundness of WFCSnet is presented. Serializability, Separability, Quasi-liveness and CS-Properties of WFCSnet are examined and some theorems and lemmas are proposed to mathematically formalize them. In this …

Algorithmic Contributions To The Theory Of Regular Chains, Wei Pan

Electronic Thesis and Dissertation Repository

Regular chains, introduced about twenty years ago, have emerged as one of the major

tools for solving polynomial systems symbolically. In this thesis, we focus on different

algorithmic aspects of the theory of regular chains, from theoretical questions to high-

performance implementation issues.

The inclusion test for saturated ideals is a fundamental problem in this theory.

By studying the primitivity of regular chains, we show that a regular chain generates

its saturated ideal if and only if it is primitive. As a result, a family of inclusion tests

can be detected very efficiently.

The algorithm to compute the regular GCDs …