Digital Commons Network^™

Feedforward Control Of Thermal History In Laser Powder Bed Fusion: Toward Physics-Based Optimization Of Processing Parameters, Alex Riensche, Benjamin D. Bevans, Ziyad M. Smoqi, Reza Yavari, Ajay Krishnan, Josie Gilligan, Nicholas Piercy, Kevin D. Cole, Prahalada K. Rao

Department of Mechanical and Materials Engineering: Faculty Publications

We developed and applied a model-driven feedforward control approach to mitigate thermal-induced flaw formation in laser powder bed fusion (LPBF) additive manufacturing process. The key idea was to avert heat buildup in a LPBF part before it is printed by adapting process parameters layer-by-layer based on insights from a physics-based thermal simulation model. The motivation being to replace cumbersome empirical build-and-test parameter optimization with a physics-guided strategy. The approach consisted of three steps: prediction, analysis, and correction. First, the temperature distribution of a part was predicted rapidly using a graph theory-based computational thermal model. Second, the model-derived thermal trends were …

Hip Osteoarthritis: A Novel Network Analysis Of Subchondral Trabecular Bone Structures, Mohsen Dorraki, Dzenita Muratovic, Anahita Fouladzadeh, Johan W Verjans, Andrew Allison, David M Findlay, Derek Abbott

Faculty and Staff Publications

Hip osteoarthritis (HOA) is a degenerative joint disease that leads to the progressive destruction of subchondral bone and cartilage at the hip joint. Development of effective treatments for HOA remains an open problem, primarily due to the lack of knowledge of its pathogenesis and a typically late-stage diagnosis. We describe a novel network analysis methodology for microcomputed tomography (micro-CT) images of human trabecular bone. We explored differences between the trabecular bone microstructure of femoral heads with and without HOA. Large-scale automated extraction of the network formed by trabecular bone revealed significant network properties not previously reported for bone. Profound differences …

Efficient And Scalable Triangle Centrality Algorithms In The Arkouda Framework, Joseph Thomas Patchett

Theses

Graph data structures provide a unique challenge for both analysis and algorithm development. These data structures are irregular in that memory accesses are not known a priori and accesses to these structures tend to lack locality.

Despite these challenges, graph data structures are a natural way to represent relationships between entities and to exhibit unique features about these relationships. The network created from these relationships can create unique local structures that can describe the behavior between members of these structures. Graphs can be analyzed in a number of different ways including at a high level in community detection and at …

Vertex-Magic Graphs, Karissa Massud

Honors Program Theses and Projects

In this paper, we will study magic labelings. Magic labelings were first introduced by Sedláček in 1963 [3]. At this time, the labels on the graph were only assigned to the edges. In 1970, Kotzig and Rosa defined what are now known as edge-magic total labelings, where both the vertices and the edges of the graph are labeled. Following this in 1999, MacDougall, Miller, Slamin, and Wallis introduced the idea of vertex-magic total labelings. There are many different types of magic labelings. In this paper will focus on vertex-magictotal labelings.

Proportional Component Order Network Connectivity, Nicholas Hanson, Nathan Shank, Ashley Armbruster, Jiequi Di

Communications on Number Theory and Combinatorial Theory

We introduce a new measure of network reliability related to the order of the largest component. This new connectivity measure considers a network to be operational if there is a component or order at least some fixed proportion, r, of the original order. Thus, the network is in a failure state if all components are sufficiently small. In this paper, we consider the parameters with vertex deletions as well as edge deletions for particular graph classes. We also find the minimum values of the parameter for graphs with a fixed size and order. We end with a discussion and some …

Presto : Fast And Effective Group Closeness Maximization, Baibhav L. Rajbhandari

Legacy Theses & Dissertations (2009 - 2024)

Given a graph and an integer k, the goal of group closeness maximization is to find, among all possible sets of k vertices (called seed sets), a set that has the highest group closeness centrality. Existing techniques for this NP-hard problem strive to quickly find a seed set with a high, but not necessarily the highest centrality.

Dimension And Ramsey Results In Partially Ordered Sets., Sida Wan

Electronic Theses and Dissertations

In this dissertation, there are two major parts. One is the dimension results on different classes of partially ordered sets. We developed new tools and theorems to solve the bounds on interval orders using different number of lengths. We also discussed the dimension of interval orders that have a representation with interval lengths in a certain range. We further discussed the interval dimension and semi dimension for posets. In the second part, we discussed several related results on the Ramsey theory of grids, the results involve the application of Product Ramsey Theorem and Partition Ramsey Theorem

Harmonious Labelings Via Cosets And Subcosets, Jared L. Painter, Holleigh C. Landers, Walker M. Mattox

Theory and Applications of Graphs

In [Abueida, A. and Roblee, K., More harmonious labelings of families of disjoint unions of an odd cycle and certain trees, J. Combin. Math. Combin. Comput., 115 (2020), 61-68] it is shown that the disjoint union of an odd cycle and certain paths is harmonious, and that certain starlike trees are harmonious using properties of cosets for a particular subgroup of the integers modulo m, where m is the number of edges of the graph. We expand upon these results by first exploring the numerical properties when adding values from cosets and subcosets in the integers modulo m. …

Optimization Opportunities In Human In The Loop Computational Paradigm, Dong Wei

Dissertations

An emerging trend is to leverage human capabilities in the computational loop at different capacities, ranging from tapping knowledge from a richly heterogeneous pool of knowledge resident in the general population to soliciting expert opinions. These practices are, in general, termed human-in-the-loop (HITL) computations.

A HITL process requires holistic treatment and optimization from multiple standpoints considering all stakeholders: a. applications, b. platforms, c. humans. In application-centric optimization, the factors of interest usually are latency (how long it takes for a set of tasks to finish), cost (the monetary or computational expenses incurred in the process), and quality of the completed …

Structure Of Number Theoretic Graphs, Lee Trent

Mathematical Sciences Technical Reports (MSTR)

The tools of graph theory can be used to investigate the structure
imposed on the integers by various relations. Here we investigate two
kinds of graphs. The first, a square product graph, takes for its vertices
the integers 1 through n, and draws edges between numbers whose product
is a square. The second, a square product graph, has the same vertex set,
and draws edges between numbers whose sum is a square.
We investigate the structure of these graphs. For square product
graphs, we provide a rather complete characterization of their structure as
a union of disjoint complete graphs. For …

Nessie Notation: A New Tool In Sequential Substitution Systems And Graph Theory For Summarizing Concatenations, Colton Davis

Student Research

While doing research looking for ways to categorize causal networks generated by Sequential Substitution Systems, I created a new notation to compactly summarize concatenations of integers or strings of integers, including infinite sequences of these, in the same way that sums, products, and unions of sets can be summarized. Using my method, any sequence of integers or strings of integers with a closed-form iterative pattern can be compactly summarized in just one line of mathematical notation, including graphs generated by Sequential Substitution Systems, many Primitive Pythagorean Triplets, and various Lucas sequences including the Fibonacci sequence and the sequence of square …

3-Uniform 4-Path Decompositions Of Complete 3-Uniform Hypergraphs, Rachel Mccann

Mathematical Sciences Undergraduate Honors Theses

The complete 3-uniform hypergraph of order v is denoted as K_v and consists of vertex set V with size v and edge set E, containing all 3-element subsets of V. We consider a 3-uniform hypergraph P₇, a path with vertex set {v₁, v₂, v₃, v₄, v₅, v₆, v₇} and edge set {{v₁, v₂, v₃}, {v₂, v₃, v₄}, {v₄, v₅, v₆}, {v₅, v_{6 …}

How To Guard An Art Gallery: A Simple Mathematical Problem, Natalie Petruzelli

The Review: A Journal of Undergraduate Student Research

The art gallery problem is a geometry question that seeks to find the minimum number of guards necessary to guard an art gallery based on the qualities of the museum’s shape, specifically the number of walls. Solved by Václav Chvátal in 1975, the resulting Art Gallery Theorem dictates that ⌊n/3⌋ guards are always sufficient and sometimes necessary to guard an art gallery with n walls. This theorem, along with the argument that proves it, are accessible and interesting results even to one with little to no mathematical knowledge, introducing readers to common concepts in both geometry and graph …

Minimality Of Integer Bar Visibility Graphs, Emily Dehoff

University Honors Theses

A visibility representation is an association between the set of vertices in a graph and a set of objects in the plane such that two objects have an unobstructed, positive-width line of sight between them if and only if their two associated vertices are adjacent. In this paper, we focus on integer bar visibility graphs (IBVGs), which use horizontal line segments with integer endpoints to represent the vertices of a given graph. We present results on the exact widths of IBVGs of paths, cycles, and stars, and lower bounds on trees and general graphs. In our main results, we find …

Intersection Cographs And Aesthetics, Robert Haas

Journal of Humanistic Mathematics

Cographs are complete graphs with colored lines (edges); in an intersection cograph, the points (vertices) and lines (edges) are labeled by sets, and the line between each pair of points is (or represents) their intersection. This article first presents the elementary theory of intersection cographs: 15 are possible on 4 points; constraints on the triangles and quadrilaterals; some forbidden configurations; and how, under suitable constraints, to generate the points from the lines alone. The mathematical theory is then applied to aesthetics, using set cographs to describe the experience of a person enjoying a picture (Mu Qi), poem (Dickinson), play (Shakespeare), …

Comprehensive Benefit Evaluation Of Transmission Network Projects Based On Improved Matter Element Extension Model, Yudong Tan, Ming Wen, Xianghua Li, De Zhang, Zhicai Wang, Zhengwei Jiang, Mingjuan Ling

Journal of Electric Power Science and Technology

Aiming at the ambiguity of the evaluation results in the evaluation of the investment benefits of transmission projects and the subjective errors in the weighting of evaluation indicators, this paper proposes a method for evaluating the investment benefits of transmission grid projects based on the improved matterelement extension model. Firstly, a grid project investment benefit evaluation index system is constructed under consideration of the improvement of the power grid by the project being put into operation. A graph model index weighting method based on the principle of graph theory is also proposed to reduce the subjective error of the traditional …

A Model For Leveraging Animal Movement To Understand Spatio-Temporal Disease Dynamics, Mark Q. Wilber, Anni Yang, Raoul Boughton, Kezia R. Manlove, Ryan S. Miller, Kim M. Pepin, George Wittemyer

United States Department of Agriculture Wildlife Services: Staff Publications

The ongoing explosion of fine-resolution movement data in animal systems provides a unique opportunity to empirically quantify spatial, temporal and individual variation in transmission risk and improve our ability to forecast disease outbreaks. However, we lack a generalizable model that can leverage movement data to quantify transmission risk and how it affects pathogen invasion and persistence on heterogeneous landscapes. We developed a flexible model ‘Movement-driven modelling of spatio-temporal infection risk’ (MoveSTIR) that leverages diverse data on animal movement to derive metrics of direct and indirect contact by decomposing transmission into constituent processes of contact formation and duration and pathogen deposition …

Matrix Interpretations And Tools For Investigating Even Functionals, Benjamin Stringer

Theses and Dissertations--Computer Science

Even functionals are a set of polynomials evaluated on the terms of hollow symmetric matrices. Their properties lend themselves to applications such as counting subgraph embeddings in generic (weighted or unweighted) host graphs and computing moments of binary quadratic forms, which occur in combinatorial optimization. This research focuses primarily on counting subgraph embeddings, which is traditionally accomplished with brute-force algorithms or algorithms curated for special types of graphs. Even functionals provide a method for counting subgraphs algebraically in time proportional to matrix multiplication and is not restricted to particular graph types. Counting subgraph embeddings can be accomplished by evaluating a …

Equitable Coloring Of Complete Tripartitle Graphs, Maxwell Vlam, Bailey Orehosky, Dominic Ditizio

Capstone Showcase

In this paper, we prove the Equitable Coloring Conjecture for variations of complete tripartite graphs with graphs K_n,n,n, K_n,n,2n, K_n,n,n+2, and K_n,n+2,n+4.

Environmental Socialization In College: A Survey Research And Network Analysis Of Changes In Climate-Conscious Concerns And Behaviors, Bijeta Lamichhane

Senior Independent Study Theses

Studies have established that socialization takes place in different stages of life. This study explores how political socialization occurs at The College of Wooster by examining changes in students' political identities as well as their perceptions towards a politicized issue, that is, climate change. These shifts in beliefs and concerns among students were evaluated by implementing quantitative research tools present in the Statistical Package for Social Sciences (SPSS) and constructing a similarity network using Gephi to explore similarities across students at this institution. The results revealed that students have become more liberal after joining this college. The study also found …

Local-Global Results On Discrete Structures, Alexander Lewis Stevens

Electronic Theses and Dissertations

Local-global arguments, or those which glean global insights from local information, are central ideas in many areas of mathematics and computer science. For instance, in computer science a greedy algorithm makes locally optimal choices that are guaranteed to be consistent with a globally optimal solution. On the mathematical end, global information on Riemannian manifolds is often implied by (local) curvature lower bounds. Discrete notions of graph curvature have recently emerged, allowing ideas pioneered in Riemannian geometry to be extended to the discrete setting. Bakry- Émery curvature has been one such successful notion of curvature. In this thesis we use combinatorial …