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Single-case experimental design (SCED) allows for the identification of a functional relationship between a dependent and independent variable. For individuals who work as Board Certified Behavior Analysts (BCBAs), it is crucial and part of the ethics code that they can interpret SCED graphed outcomes to make data-based decisions. Visual analysis is the primary method to detect outcomes of SCED; however, research suggests graph characteristics may impact the reliability and estimation of intervention effects, specifically the ratio of the x-to-y axes. This study examined how the alteration of the data-points-per-x-to-y-ratio (DPPXYR) influences BCBA’s ability to detect a function in functional analysis multielement graphs. A primary finding was the overall low agreement in BCBAs selecting function compared to the modified visual inspection (MVI). Descriptive results showed participants had highest accuracy in detecting the function when the DPPXYR was 0.09, although the difference across manipulation was minimal. / Applied Behavioral Analysis

Every graph G = (V, E) has a dominating set S ⊆ V(G) such that any vertex not in S is adjacent to a vertex in S. We define a paired-dominating set S to be a dominating set S = {v1, v2,..., v2t-1, v2t} where M = {v1v2, v3v4, ..., v2t-1v2t} is a perfect matching in 〈S〉, the subgraph induced by S. The domination number of a graph G is the smallest cardinality of any dominating set of G, and the paired-domination number is the smallest cardinality of any paired-dominating set. Determining the domination number for grid graphs is a well-known open problem in graph theory. Not surprisingly, determining the paired-domination number for grid graphs is also a difficult problem. In this thesis, we survey past research in domination, paired-domination and grid graphs to obtain background for our study of paired-domination in grid graphs. We determine the paired-domination number for grid graphs Gr,c where r ∈ {2,3}, for infinite dimensional grid graphs, and for the complement of a grid graph.

Consider infecting a subset $A_0 \subseteq V(G)$ of the vertices of a graph $G$. Let an uninfected vertex $v \in V(G)$ become infected if $|N_G(v) \cap A_0| \geq r$, for some integer $r$. Define $A_t = A_{t-1} \cup \{v \in V(G) : |N_G(v) \cap A_{t-1}| \geq r \},$ and say that the set $A_0$ is \emph{lethal} under $r$-neighbor percolation if there exists a $t$ such that $A_t = V(G)$. For a graph $G$, let $m(G,r)$ be the size of the smallest lethal set in $G$ under $r$-neighbor percolation. The problem of determining $m(G,r)$ has been extensively studied for grids $G$ of various dimensions. We define $$m(a_1, \dots, a_d, r) = m\left (\prod_{i=1}^d [a_i], r\right )$$ for ease of notation. Famously, a lower bound of $m(a_1, \dots, a_d, d) \geq \frac{\sum_{j=1}^d \prod_{i \neq j} a_i}{d}$ is given by a beautiful argument regarding the high-dimensional ``surface area" of $G = [a_1] \times \dots \times [a_d]$. While exact values of $m(G,r)$ are known in some specific cases, general results are difficult to come by. In this thesis, we introduce a novel technique for viewing $3$-neighbor lethal sets on three-dimensional grids in terms of lethal sets in two dimensions. We also provide a strategy for recursively building up large lethal sets from existing small constructions. Using these techniques, we determine the exact size of all lethal sets under 3-neighbor percolation in three-dimensional grids $[a_1] \times [a_2] \times [a_3]$, for $a_1,a_2,a_3 \geq 11$. The problem of determining $m(n,n,3)$ is discussed by Benevides, Bermond, Lesfari and Nisse in \cite{benevides:2021}. The authors determine the exact value of $m(n,n,3)$ for even $n$, and show that, for odd $n$, $$\ceil*{\frac{n^2+2n}{3}} \leq m(n,n,3) \leq \ceil*{\frac{n^2+2n}{3}} + 1.$$ We prove that $m(n,n,3) = \ceil*{\frac{n^2+2n}{3}}$ if and only if $n = 2^k-1$, for some $k >0$. Finally, we provide a construction to prove that for $a_1,a_2,a_3 \geq 12$, bounds on the minimum lethal set on the the torus $G = C_{a_1} \square C_{a_2} \square C_{a_3}$ are given by $$2 \le m(G,3) - \frac{a_1a_2 + a_2a_3 + a_3a_1 -2(a_1+a_2+a_3)}{3} \le 3.$$ / Graduate

The positional Burrows-Wheeler transform (PBWT) is a foundational data structure for representing haplotype matches of biobank scale. Once the PBWT panel of a set of haplotypes are constructed, efficient algorithms are available for “All vs. All” positional substring matching, finding exact matches of substrings in pre-aligned strings, for haplotypes within the panel, and “One vs. All” positional substring match query for an out-of-panel haplotype against all haplotypes in the panel. While the original PBWT was designed from linear reference genomes, GBWT was proposed to extend PBWT to genome graphs that allow large insertions and deletions. However, there are no GBWT algorithms for haplotype matching. In this work, we develop the efficient algorithms for “All vs. All” and “One vs. All” haplotype set-maximal and long matching algorithms for GBWT. For a GBWT containing a panel of paths P, we show algorithms similar to the matching algorithms of PBWT. Our algorithms achieves theoretically optimal time complexity to output all “All vs. All” matches in time linear to the size of the input panel (O(∑|Pi| + |out put|)), and quasilinear time to the length of the query path for “One vs. All” path match queries (O(|Q| log σ + |out put| log σ ), where σ is the maximum out- degree in the GBWT and out put is the set of discovered path matches). Under the constant σ assumption made by gPBWT and GBWT, these algorithms are in fact linear. Our algorithms open the possibilities for applications of efficient positional substring matching in pangenome references such as identical-by-descent (IBD) segment identification and genotype imputation.

This thesis consists of two papers. The first paper is a study of the structure of the k-assignment polytope, whose vertices are the m x n (0; 1)-matrices with exactly k 1:s and at most one 1 in each row and each column. This is a natural generalisation of the Birkhoff polytope and many of the known properties of the Birkhoff polytope are generalised. Two equivalent representations of the faces are given, one as (0; 1)-matrices and one as ear decompositions of bipartite graphs. These tools are used to describe properties of the polytope, especially a complete description of the cover relation in the face lattice of the polytope and an exact expression for the diameter. The second paper studies the edge-product space Є(X) for trees on X. This space is generated by the set of edge-weighted finite trees on X, and arises by multiplying the weights of edges on paths in trees. These spaces are closely connected to tree-indexed Markov processes in molecular evolutionary biology. It is known that Є(X) has a natural CW-complex structure, and a combinatorial description of the associated face poset exists which is a poset S(X) of X-forests. In this paper it is shown that the edge-product space is a regular cell complex. One important part in showing that is to conclude that all intervals [Ô, Г], Г Є S(X), have recursive coatom orderings.

We present the rich research potential at the union of multi agent reinforcement learning (MARL), game theory, and financial graphs. We demonstrate how multiple game theoretic scenarios arise in three node financial graphs with minor modifications. We highlight six scenarios used in this study. We discuss how to setup an environment for MARL training and evaluation. We first investigate individual games and demonstrate that MARL agents consistently learn Nash Equilibrium strategies. We next investigate mixed games and find again that MARL agents learn Nash Equilibrium strategies given sufficient information and incentive (e.g. prosociality). We find introducing a embedding layer in agents deep network improves learned representations and as such, learned strategies, (2) MARL agents can learn a variety of complex strategies, and (3) selfishness improves strategies’ fairness and efficiency. Next we introduce populations and find that (1) pro social members in a population influences the action profile and that (2) complex strategies present in individual scenarios no longer emerge as populations’ portfolio of strategies converge to a main diagonal. We identify two challenges that arises in populations; namely (1) identifying partner’s prosociality and (2) identifying partner’s identity. We study three information settings which supplement agents observation set and find having knowledge of partners prosociality or identity to have negligible impact on how portfolio of strategies converges. / Vi presenterar den rika forskningspotentialen vid unionen av multi-agent förstärkningslärning (MARL), spelteori och finansiella grafer. Vi demonstrerar hur flera spelteoretiska scenarier uppstår i tre nodgrafikgrafer med mindre ändringar. Vi belyser sex scenarier som används i denna studie. Vi diskuterar hur man skapar en miljö för MARL -utbildning och utvärdering. Vi undersöker först enskilda spel och visar att MARL -agenter konsekvent lär sig Nash Equilibrium -strategier. Vi undersöker sedan blandade spel och finner igen att MARL -agenter lär sig Nash Equilibrium -strategier med tillräcklig information och incitament (t.ex. prosocialitet). Vi finner att införandet av ett inbäddande lager i agenternas djupa nätverk förbättrar inlärda representationer och som sådan inlärda strategier, (2) MARL-agenter kan lära sig en mängd komplexa strategier och (3) själviskhet förbättrar strategiernas rättvisa och effektivitet. Därefter introducerar vi populationer och upptäcker att (1) pro sociala medlemmar i en befolkning påverkar åtgärdsprofilen och att (2) komplexa strategier som finns i enskilda scenarier inte längre framkommer när befolkningens portfölj av strategier konvergerar till en huvuddiagonal. Vi identifierar två utmaningar som uppstår i befolkningen; nämligen (1) identifiera partnerns prosocialitet och (2) identifiera partnerns identitet. Vi studerar tre informationsinställningar som kompletterar agents observationsuppsättning och finner att kunskap om partners prosocialitet eller identitet har en försumbar inverkan på hur portföljen av strategier konvergerar.

The use of computer aided design (CAD) tools has catalyzed the growth of IC design techniques. The rapid growth in transistor count for synchronous digital circuits has increased circuit complexity. This growing complexity of synchronous circuits has exposed design issues such as clock skew, increased power consumption, increased electromagnetic interference and worst case performance. The increasing number of challenges posed by synchronous designs has encouraged researchers to explore asynchronous design techniques as an alternative methodology. Asynchronous circuits do not use a global clock signal that is the primary cause of many design challenges faced by synchronous designers. It has also been shown in some designs that asynchronous circuits consumes less power, and exhibits better average case performance than synchronous circuits. Asynchronous design techniques, even with their various advantages over synchronous systems, are not widely accepted by logic designers. This is due to the shortcomings of asynchronous design methodologies, primarily, the limited availability of CAD tool support and the use of proprietary specification languages. To overcome the shortcomings of current asynchronous design techniques, this research uses a methodology for designing asynchronous circuits starting from clocked RTL design. This research extends the concepts of Phased Logic (PL) and marked graphs to quasi-delay insensitive gates (QDI) gates to create an asynchronous PL-QDI methodology. The PL methodology is easy to use as it maps conventional RTL designs into delay insensitive PL circuits using commercial CAD tools. Caltech?s QDI gates exhibit fast forward latency, but the use of Caltech?s methodology requires a user skilled in the pecurialities of the Caltech design methodology. This research uses best of Caltech?s QDI circuit methodology and the PL methodology to come up with a new asynchronous PL-QDI methodology. It also presents a synthesis algorithm that uses commercially available synchronous CAD tools to map clocked designs to PL-QDI systems. Results of this research show that third-party clocked RTL codes including intellectual property (IP) cores can be converted to asynchronous PL-QDI systems using the PL-QDI CAD tools presented in this research. This work shows how mature synchronous CAD tools can be used to design clockless circuits.