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Articles 1 - 4 of 4
Full-Text Articles in Other Applied Mathematics
Arrangements Of N Planes Resulting In One Bounded Tetrahedral Chamber, Ava Knight
Arrangements Of N Planes Resulting In One Bounded Tetrahedral Chamber, Ava Knight
Williams Honors College, Honors Research Projects
This paper investigates the combinatorial geometry of plane arrangements in three-dimensional space, focusing on configurations that produce exactly one bounded tetrahedral chamber. We define T(n) as the number of face-combinatorial equivalence classes of arrangements of n planes in ℝ³ containing exactly one bounded tetrahedral chamber. Known values — T(3) = 0, T(4) = 1, and T(5) = 2 — are established through direct construction, while T(6) remains an open problem. This paper contributes experimental evidence toward resolving T(6) by systematically extending the two valid 5-plane arrangements and verifying, through a plane removal argument, that each yields a valid plane configuration …
Models Of Functional Redundancy In Ecological Communities, Sandra Annie Tsiorintsoa
Models Of Functional Redundancy In Ecological Communities, Sandra Annie Tsiorintsoa
All Dissertations
Functional redundancy is the number of taxa that perform a given function within a given community. In most systems, high levels of functional redundancy are important, because they contribute to ecosystem stability. However, we currently have very little understanding of why functional redundancy varies among communities. One possible factor that could affect functional redundancy is environmental complexity. Many studies show that simplified ecosystems harbor communities with lower taxon diversity. What is less clear is if this simplicity and lower taxon diversity also affects functional redundancy. To answer this question, we use metacommunity models to explore the connection between environmental complexity …
Combinatorial Optimization: Introductory Problems And Methods, Erin Brownell
Combinatorial Optimization: Introductory Problems And Methods, Erin Brownell
Honors Scholar Theses
This paper will cover some topics of combinatorial optimization, the study of finding the best possible arrangement of a set of discrete objects. These topics include the shortest path problem and network flows, which can be extended to solve more complex problems. We will also briefly cover some basics of graph theory and solving linear programming problems to give context to the reader.
Generating Minimal Pair-Wise Covering Test Suites, Luis C. Gutierrez ^, Martine Ceberio *
Generating Minimal Pair-Wise Covering Test Suites, Luis C. Gutierrez ^, Martine Ceberio *
COURI Symposium Abstracts, Spring 2012
Software is ubiquitous and needs to be reliable. Software testing therefore plays an important role in software development. Proper testing a software system informs about its quality and reliability so as to prevent unexpected behavior during system execution. One of the methods to prevent failures consists in testing a system under different input values, but when all possible input values are tested, an impractical number of test cases might result. In software testing, pair-wise testing is a combinatorial technique which uses combination of pair input values to generate test cases. Using pair-wise testing dramatically reduces the number of test cases, …