Unification modulo the theory of Boolean algebras has been investigated by several autors. Nevertheless, the exact complexity of the decision problem for unification with constants and general unification was not known. In this research note, we show that the decision problem is complete for unification with constants and PSPACE-complete for general unification. In contrast, the decision problem for elementary unification (where the terms to be unified contain only symbols of the signature of Boolean algebras) is 'only' NP-complete.

Completely digital workflows for the fabrication of implant-supported removable restorations are not yet common in clinical dental practice. The aim of the current case report is to illustrate a reliable and comfortable workflow that reasonably merges conventional and digital workflows for the CAD/CAM-fabrication of implant-supported overdentures. The 53-year old patient was supplied with a digitally processed complete denture in the upper jaw and, simultaneously, with an overdenture supported by four interforaminal implants in the lower jaw. The overdenture included a completely digitally processed and manufactured alloy framework that had been fabricated by selective laser sintering. The case report indicates that digital manufacturing processes for extensive and complex removable restorations are possible. However, as it is currently not yet possible to digitally obtain functional impressions, future developments and innovations might focus on that issue.

We study an inverse problem which seeks to image the internal conductivity map of a body by one measurement of boundary and interior data. In our study the interior data is the magnitude of the current density induced by electrodes. Access to interior measurements has been made possible since the work of M. Joy et al. in early 1990s and couples two physical principles: electromagnetics and magnetic resonance. In 2007 Nachman et al. has shown that it is possible to recover the conductivity from the magnitude of one current density field inside. The method now known as Current Density Impedance Imaging is based on solving boundary value problems for the 1-Laplacian in an appropriate Riemann metric space. We consider two types of methods: the ones based on level sets and a variational approach, which aim to solve specific boundary value problem associated with the 1-Laplacian. We will address the Cauchy and Dirichlet problems with full and partial data, and also the Complete Electrode Model (CEM). The latter model is known to describe most accurately the voltage potential distribution in a conductive body, while taking into account the transition of current from the electrode to the body. For the CEM the problem is non-unique. We characterize the non-uniqueness, and explain which additional measurements fix the solution. Multiple numerical schemes for each of the methods are implemented to demonstrate the computational feasibility.

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We analyze the complexity of finite model reasoning in the description logic ALCQI, i.e. ALC augmented with qualifying number restrictions, inverse roles, and general TBoxes. It turns out that all relevant reasoning tasks such as concept satisfiability and ABox consistency are EXPTIME-complete, regardless of whether the numbers in number restrictions are coded unarily or binarily. Thus, finite model reasoning with ALCQI is not harder than standard reasoning with ALCQI.

<p>Denote by $k_t(G)$ the number of cliques of order $t$ in a graph $G$ having $n$ vertices. Let $k_t(n) = \min\{k_t(G)+k_t(\overline{G}) \}$ where $\overline{G}$ denotes the complement of $G$. Let $c_t(n) = {k_t(n)}/{\tbinom{n}{t}}$ and $c_t$ be the limit of $c_t(n)$ for $n$ going to infinity. A 1962 conjecture of Erd\H{o}s stating that $c_t = 2^{1-\tbinom{t}{2}}$ was disproved by Thomason in 1989 for all $t\geq 4$. Tighter counterexamples have been constructed by Jagger, {\v S}{\v t}ov{\' \i}{\v c}ek and Thomason in 1996, by Thomason for $t\leq 6$ in 1997, and by Franek for $t=6$ in 2002. Further tightenings $t=6,7$ and $8$ was recently obtained by Deza, Franek, and Liu.</p> <p>We investigate the computational framework used by Deza, Franek, and Liu. In particular, we present the benefits and limitations of different parallel computer memory architectures and parallel programming models. We propose a functional decomposition approach which is implemented in C++ with POSIX thread (Pthread) libraries for multi-threading. Computational benchmarking on the parallelized framework and a performance analysis including a comparison with the original computational framework are presented.</p> / Master of Science (MSc)

In this study, I introduce the alternative-dependent focal Luce model (ADFLM), a random choice model generalizing the well-known Luce model (1959). In the ADFLM, focal alternatives are chosen more frequently relative to their utilities. I identify utilities, focal sets, and the magnitude of focal biases from choice data. Additionally, I axiomatically characterize the ADFLM by weakening the independence of irrelevant alternatives (IIA) axiom. This model can explain the well-known behavioral phenomena, the attraction and compromise effects. Furthermore, I also study the seller's profit maximization problem in the ADFLM. I also study an asymmetric dynamic patent race with a deadline under complete information. In my model, two firms decide whether to invest in RandD. The patent arrives randomly according to a Poisson process, and the large firm has a higher hazard rate than the small firm. I find the unique sub-game perfect Nash equilibrium strategy for this game. At the equilibrium, the large firm will stay longer in the race, while the small firm will quit earlier. The large firm's optimal stopping time is not affected by the competition, while the small firm's stopping time is reduced. Additionally, I find that companies will remain longer in the race if the investigation cost is lower, the winning premium is higher, the deadline is extended further, and the hazard rate is more prominent. Moreover, the market becomes more efficient with the competition since the patent is easier to realize. / Doctor of Philosophy / In this research, I study the consumer's behavior when individuals have limited cannot or do not give the same attention to each alternative available to them. In my study, I characterize the alternative-dependent focal Luce model (ADFLM), a consumer behavior model. Moreover, I solve the seller's profit maximization problem when the consumer's behavior follows the ADFLM. Meanwhile, I also study a dynamic patent race problem that occurs when firms compete for a patent with a deadline. If no firms achieve the patent, the stopping time (when the firm quits the patent race) of the large firm's (with a higher success rate every period) is not affected by the introduction of the small firm. However, the small firm quits earlier when the large firm is introduced. The competition between the two companies increases the overall probability of receiving a patent.

Thesis advisor: ROWELL S. MELNICK / This issue was brought to light when the Honorable Gina M. Raimondo left the governorship behind and assumed office on March 3, 2021, to serve as the 40th U.S. Secretary of Commerce. Many asked, what would become of the initiatives she championed during her tenure? Rhode Island Universal Pre-Kindergarten (RI-UPK) was one of her signature policy goals and this research confirms the reasons behind the push, the progress made, and the challenges ahead. This thesis further highlights how the governorship plays a central role in effecting and steering education policy. Rhode Island’s state funded Pre-K has been steadily adding more seats and even before Raimondo, it has maintained the highest quality benchmarks for over a decade according to the National Institute for Early Education Research (NIEER). Therefore, the smallest state in the nation demonstrates a bright spot in Early Childhood Education (ECE) within an otherwise regionally underperforming public school system. This is a dichotomy that beckons in-depth analysis and further explanation. I argue that RI UPK is a model for the rest of the country to follow based on its selection as the sole test site leading up to the 2020 Census. According to US Census data collectors, Rhode Island is a microcosm of the entire country, reflective of future demographic trends. Hence, a policy implementation strategy that proves either successful or unsuccessful offers valuable insights that are widely applicable across numerous states. This thesis also explains and clarifies some contradictions in the larger debate over UPK implementation as well as chronically examining its evolution in RI. After conducting an empirical comparison and evaluation of case studies, state reports, and scholarly articles, I assert that RI UPK has the potential to serve as a national model. Analyzing a segment of Madam Secretary Raimondo’s education legacy reveals that Rhode Island not only excels as a leader in providing consistent Early Childhood Education but also possesses unique characteristics that position it at the forefront of the nationwide Universal Pre-K (UPK) discussion. / Thesis (MA) — Boston College, 2024. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Political Science.

The purpose of the thesis is to study completeness of abstract spaces. In particular, we study completeness in partial metric spaces, partial metric type spaces, dislocated metric spaces, dislocated metric type spaces and symmetric spaces that are generalizations of metric spaces. It is well known that complete metric spaces have a wide range of applications. For instance, the classical Banach contraction principle is phrased in the context of complete metric spaces. Analogously, the Banach's xed point theorem and xed point results for Lipschitzian maps are discussed in this context, namely in, partial metric spaces and metric type spaces. Finally, xed point results are presented for symmetric spaces / Mathematical Sciences / Ph. D. (Mathematics)

The purpose of the thesis is to study completeness of abstract spaces. In particular, we study completeness in partial metric spaces, partial metric type spaces, dislocated metric spaces, dislocated metric type spaces and symmetric spaces that are generalizations of metric spaces. It is well known that complete metric spaces have a wide range of applications. For instance, the classical Banach contraction principle is phrased in the context of complete metric spaces. Analogously, the Banach's xed point theorem and xed point results for Lipschitzian maps are discussed in this context, namely in, partial metric spaces and metric type spaces. Finally, xed point results are presented for symmetric spaces. / Geography / Ph. D. (Mathematics)