It was not until the 20th century that combinatorial design theory was studied as a formal subject. This field has many applications, for example in statistical experimental design, coding theory, authentication codes, and cryptography. Major approaches to the problem of discovering new t-designs rely on (i) the construction of large sets of t designs, (ii) using prescribed automorphism groups, (iii) recursive construction methods. In 2017 and 2018, Tran Van Trung introduced new recursive techniques to construct t – (v, k, λ) designs. These methods are of purely combinatorial nature and require using "ingredient" t-designs or resolutions whose parameters satisfy a system of non-linear equations. Even after restricting the range of parameters in this new method, the task is computationally intractable. In this work, we enhance Tran Van Trung's "Basic Construction" by a robust and efficient hybrid computational apparatus which enables us to construct hundreds of thousands of new t – (v, k, Λ) designs from previously known ingredient designs. Towards the end of the dissertation we also create a new family of 2-resolutions, which will be infinite if there are infinitely many Sophie Germain primes. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2019. / FAU Electronic Theses and Dissertations Collection

Web applications are increasingly moving business and processing logic from the server to the browser. Traditional, multiple-page request/response applications are quickly being replaced by single-page applications where complex application logic is downloaded on the initial page load and data is then subsequently fetched asynchronously via the browser's native XMLHttpRequest (XHR) object. These new generation web applications are called Rich Web Applications (RWA). Frameworks such as the Google Web Toolkit (GWT), and JavaScript model-view-controller (MVC) frameworks such as Backbone.js are facilitating this move. With this migration, testing frameworks need to follow the logic by moving analysis and test generation from the server to the client. One problem hindering the movement of testing in this domain is the adoption of semantic URLs. This paper introduces a novel approach to systematically identify variables in semantic URLs and use them as part of the test generation process. Using a sample RWA seeded with various JavaScript faults, I demonstrate in this thesis, as an empirical study, that combinatorial testing algorithms and reduction strategies also apply to new RWAs.

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.

Includes bibliography.

When triangulating a belief network we aim to obtain a junction tree of minimum state space. Searching for the optimal triangulation can be cast as a search over all the permutations of the network's vaeriables. Our approach is to embed the discrete set of permutations in a convex continuous domain D. By suitably extending the cost function over D and solving the continous nonlinear optimization task we hope to obtain a good triangulation with respect to the aformentioned cost. In this paper we introduce an upper bound to the total junction tree weight as the cost function. The appropriatedness of this choice is discussed and explored by simulations. Then we present two ways of embedding the new objective function into continuous domains and show that they perform well compared to the best known heuristic.

Thesis (M.A.)--Brigham Young University. Dept of Mathematics Education, 2006. / Includes bibliographical references (p. 65-66).

Allylboration reactions have been thoroughly utilized in organic chemistry since it was discovered that they could add in a nucleophilic fashion to aldehydes and ketones in 1964. Modification of allylboronates and the substrates that they can react with has been the focus of many research groups over the past three decades. Recent works have made use of catalysis to promote the addition of allylboronates that are generally otherwise unreactive toward various electrophiles. Chapter 2 will discuss the discovery that Brnsted acids can catalyze the addition of unreactive 2-alkoxycarbonyl allylboronates to aldehydes and that the diastereoselectivity of the reaction is determined by the electronic nature of the aldehyde. Ketones and imines are much less reactive than aldehydes towards allylboronates due to steric and electronic factors. As a result, new conditions are often required to promote the allylboration reaction of ketones and imines. Chapter 3 will briefly discuss the challenges that ketones present as substrates for allylboration reactions and show my attempts at achieving this transformation. Chapter 4 will describe imines and their associated challenges as substrates for allylboration reactions. However, once harnessed, these substrates provide easy access to -methylene -lactones when a 2-alkoxycarbonyl allylboronate is used as the allylating reagent. The modification of important or interesting molecules by making major or minor changes to a common core structure is the basis of diversity-oriented synthesis of combinatorial libraries. -Alkylidene -lactones and -alkylidene -lactams are biologically interesting compounds present in numerous natural products. Chapter 5 will discuss how the title compounds were modified by various metal-catalyzed coupling reactions to provide a diversity-oriented combinatorial library of -lactones and -lactams. Since -lactones are prevalent in many natural products, the application of 2-alkoxycarbonyl allylboronates to a target-oriented synthesis was intriguing. Unlike diversity-oriented synthesis, target oriented synthesis aims at synthesizing a single compound through any number of controlled steps, arriving at one specific product that is obtained as a pure isomer. Access to highly complex -lactones is often tedious, however, Chapter 6 will discuss how a simple, one-step allylboration reaction of a complex aldehyde with a 2-alkoxycarbonyl allylboronate can lead to a highly substituted -lactone. This -lactone can be further modified and transformed into chinensiolide B, a biologically active natural product isolated from a plant found in various locations in China.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, August 1999. / Includes bibliographical references. Also available on the Internet.

We focus on three different types of multi-party cryptographic protocols. The first is in the area of unconditionally secure signature schemes, the goal of which is to provide users the ability to electronically sign documents without the reliance on computational assumptions needed in traditional digital signatures. The second is on cooperative protocols in which users help each other maintain privacy while querying a database, called user-private information retrieval protocols. The third is concerned with the generalized Russian cards problem, in which two card players wish to communicate their hands to each other via public announcements without the third player learning the card deal. The latter two problems have close ties to the field of combinatorial designs, and properly fit within the field of combinatorial cryptography. All of these problems have a common thread, in that they are grounded in the information-theoretically secure or unconditionally secure setting.

The central thesis of this dissertation is that insight from queueing analysis can effectively guide standard (combinatorial) scheduling algorithms in dynamic environments. Scheduling is generally concerned with complex combinatorial decisions for static problems, whereas queueing theory simplifies the combinatorics and focuses on dynamic systems. We examine a queueing network with flexible servers under queueing and scheduling techniques. Based on the strengths of queueing analysis and scheduling, we develop a hybrid model that guides scheduling with results from the queueing model. In order to include setup times, we create a logic-based Benders decomposition model for a static representation of the queueing network. Our model is able to find optimal schedules up to 5 orders of magnitude faster than the only other model in the literature. A hybrid model is then developed for the dynamic problem and shown to achieve the best mean flow time while also guaranteeing maximal capacity.