Monoidal Supercategories And Superadjunction, 2019 University of Ottawa

#### Monoidal Supercategories And Superadjunction, Dene Lepine

*Rose-Hulman Undergraduate Mathematics Journal*

We define the notion of superadjunction in the context of supercategories. In particular, we give definitions in terms of counit-unit superadjunctions and hom-space superadjunctions, and prove that these two definitions are equivalent. These results generalize well-known statements in the non-super setting. In the super setting, they formalize some notions that have recently appeared in the literature. We conclude with a brief discussion of superadjunction in the language of string diagrams.

Strengthening Relationships Between Neural Ideals And Receptive Fields, 2019 Texas A&M University

#### Strengthening Relationships Between Neural Ideals And Receptive Fields, Angelique Morvant

*Rose-Hulman Undergraduate Mathematics Journal*

Neural codes are collections of binary vectors that represent the firing patterns of neurons. The information given by a neural code *C *can be represented by its neural ideal *J*_{C}. In turn, the polynomials in *J*_{C }can be used to determine the relationships among the receptive fields of the neurons. In a paper by Curto et al., three such relationships, known as the Type 1-3 relations, were linked to the neural ideal by three if-and-only-if statements. Later, Garcia et al. discovered the Type 4-6 relations. These new relations differed from the first three in that they were related ...

Triangle Packing On Tripartite Graphs Is Hard, 2019 University of Kansas

#### Triangle Packing On Tripartite Graphs Is Hard, Peter A. Bradshaw

*Rose-Hulman Undergraduate Mathematics Journal*

The problem of finding a maximum matching on a bipartite graph is well-understood and can be solved using the augmenting path algorithm. However, the similar problem of finding a large set of vertex-disjoint triangles on tripartite graphs has not received much attention. In this paper, we define a set of vertex-disjoint triangles as a “tratching.” The problem of finding a tratching that covers all vertices of a tripartite graph can be shown to be NP-complete using a reduction from the three-dimensional matching problem. In this paper, however, we introduce a new construction that allows us to emulate Boolean circuits using ...

Graphs, Random Walks, And The Tower Of Hanoi, 2019 Baldwin Wallace University, Berea

#### Graphs, Random Walks, And The Tower Of Hanoi, Stephanie Egler

*Rose-Hulman Undergraduate Mathematics Journal*

The Tower of Hanoi puzzle with its disks and poles is familiar to students in mathematics and computing. Typically used as a classroom example of the important phenomenon of recursion, the puzzle has also been intensively studied its own right, using graph theory, probability, and other tools. The subject of this paper is “Hanoi graphs”, that is, graphs that portray all the possible arrangements of the puzzle, together with all the possible moves from one arrangement to another. These graphs are not only fascinating in their own right, but they shed considerable light on the nature of the puzzle itself ...

Asymptotically Optimal Bounds For (T,2) Broadcast Domination On Finite Grids, 2019 Williams College

#### Asymptotically Optimal Bounds For (T,2) Broadcast Domination On Finite Grids, Timothy W. Randolph

*Rose-Hulman Undergraduate Mathematics Journal*

Let *G = (V,E)* be a graph and *t,r* be positive integers. The *signal* that a tower vertex *T* of signal strength *t* supplies to a vertex *v* is defined as *sig(T, v) = max(t − dist(T,v),0)*, where *dist(T,v)* denotes the distance between the vertices *v* and *T*. In 2015 Blessing, Insko, Johnson, and Mauretour defined a *(t, r) broadcast dominating set*, or simply a *(t, r) broadcast*, on *G* as a set *T ⊆ V* such that the sum of all signal received at each vertex *v ∈ V* from the set of towers *T ...*

New Experimental Investigations For The 3x+1 Problem: The Binary Projection Of The Collatz Map, 2019 University of California, Davis

#### New Experimental Investigations For The 3x+1 Problem: The Binary Projection Of The Collatz Map, Benjamin Bairrington, Aaron Okano

*Rose-Hulman Undergraduate Mathematics Journal*

The 3x + 1 Problem, or the Collatz Conjecture, was originally developed in the early 1930's. It has remained unsolved for over eighty years. Throughout its history, traditional methods of mathematical problem solving have only succeeded in proving heuristic properties of the mapping. Because the problem has proven to be so difficult to solve, many think it might be undecidable. In this paper we brie y follow the history of the 3x + 1 problem from its creation in the 1930's to the modern day. Its history is tied into the development of the Cosper Algorithm, which maps binary sequences ...

A Generalized Newton-Girard Identity, 2019 University of Maryland, College Park

#### A Generalized Newton-Girard Identity, Tanay Wakhare

*Rose-Hulman Undergraduate Mathematics Journal*

We present a generalization of the Newton-Girard identities, along with some applications. As an addendum, we collect many evaluations of symmetric polynomials to which these identities apply.

Unified Methods For Feature Selection In Large-Scale Genomic Studies With Censored Survival Outcomes, 2019 Temple University

#### Unified Methods For Feature Selection In Large-Scale Genomic Studies With Censored Survival Outcomes, Lauren Spirko-Burns, Karthik Devarajan

*COBRA Preprint Series*

One of the major goals in large-scale genomic studies is to identify genes with a prognostic impact on time-to-event outcomes which provide insight into the disease's process. With rapid developments in high-throughput genomic technologies in the past two decades, the scientific community is able to monitor the expression levels of tens of thousands of genes and proteins resulting in enormous data sets where the number of genomic features is far greater than the number of subjects. Methods based on univariate Cox regression are often used to select genomic features related to survival outcome; however, the Cox model assumes proportional ...

Decomposing Graphs Into Edges And Triangles, 2019 University of Warwick

#### Decomposing Graphs Into Edges And Triangles, Daniel Kral, Bernard Lidicky, Taisa L. Martins, Yanitsa Pehova

*Mathematics Publications*

We prove the following 30 year-old conjecture of Győri and Tuza: the edges of every n-vertex graph G can be decomposed into complete graphs C1,. . .,Cℓ of orders two and three such that |C1|+···+|Cℓ| ≤ (1/2+o(1))n2. This result implies the asymptotic version of the old result of Erdős, Goodman and Pósa that asserts the existence of such a decomposition with ℓ ≤ n2/4.

Analytical Wave Solutions Of The Space Time Fractional Modified Regularized Long Wave Equation Involving The Conformable Fractional Derivative, 2019 Jessore University of Science and Technology

#### Analytical Wave Solutions Of The Space Time Fractional Modified Regularized Long Wave Equation Involving The Conformable Fractional Derivative, M. Hafiz Uddin, Md. Ashrafuzzaman Khan, M. Ali Akbar, Md. Abdul Haque

*Karbala International Journal of Modern Science*

The space time fractional modified regularized long wave equation is a model equation to the gravitational water waves in the long-wave occupancy, shallow waters waves in coastal seas, the hydro-magnetic waves in cold plasma, the phonetic waves in dissident quartz and phonetic gravitational waves in contractible liquids. In nonlinear science and engineering, the mentioned equation is applied to analyze the one way tract of long waves in seas and harbors. In this study, the closed form traveling wave solutions to the above equation are evaluated due to conformable fractional derivatives through double (G'⁄G,1⁄G)-expansion method and the ...

Dissertation_Davis.Pdf, 2019 University of Kentucky

#### Dissertation_Davis.Pdf, Brian Davis

*brian davis*

Positive Solutions Of Boundary Value Dynamic Equations, 2019 Marshall University

#### Positive Solutions Of Boundary Value Dynamic Equations, Olusegun Michael Otunuga, Basant Karna, Bonita Lawrence

*Basant Karna*

In this paper, we deal with the existence of a positive solution for 2^{nd} and 3^{rd} order boundary value problem by first defining their respective Green’s function. The Green’s function is used to derive the Green’s function for the 2nth and 3nth order boundary value problem, respectively, where *n* is a positive integer. The Green’s function is also used to derive conditions for positive solution of the 2*n*th and 3*n*th order eigen value differential equation, respectively.

Enhanced Koszulity In Galois Cohomology, 2019 The University of Western Ontario

#### Enhanced Koszulity In Galois Cohomology, Marina Palaisti

*Electronic Thesis and Dissertation Repository*

Despite their central role in Galois theory, absolute Galois groups remain rather mysterious; and one of the main problems of modern Galois theory is to characterize which profinite groups are realizable as absolute Galois groups over a prescribed field. Obtaining detailed knowledge of Galois cohomology is an important step to answering this problem. In our work we study various forms of enhanced Koszulity for quadratic algebras. Each has its own importance, but the common ground is that they all imply Koszulity. Applying this to Galois cohomology, we prove that, in all known cases of finitely generated pro-$p$-groups, Galois ...

Admissible Bernoulli Correlations, 2019 University of Missouri-St. Louis

#### Admissible Bernoulli Correlations, Nevena Maric, Mark Huber

*Nevena Maric*

Prediction Of Stress Increase At Ultimate In Unbonded Tendons Using Sparse Principal Component Analysis, 2019 Utah State University

#### Prediction Of Stress Increase At Ultimate In Unbonded Tendons Using Sparse Principal Component Analysis, Eric Mckinney, Minwoo Chang, Marc Maguire, Yan Sun

*Mathematics and Statistics Faculty Publications*

While internal and external unbonded tendons are widely utilized in concrete structures, an analytical solution for the increase in unbonded tendon stress at ultimate strength, Δ𝑓𝑝𝑠, is challenging due to the lack of bond between strand and concrete. Moreover, most analysis methods do not provide high correlation due to the limited available test data. The aim of this paper is to use advanced statistical techniques to develop a solution to the unbonded strand stress increase problem, which phenomenological models by themselves have done poorly. In this paper, Principal Component Analysis (PCA), and Sparse Principal Component Analysis (SPCA) are employed on ...

Predicting Time To Dementia Using A Quantitative Template Of Disease Progression, 2019 National Institutes of Health

#### Predicting Time To Dementia Using A Quantitative Template Of Disease Progression, Murat Bilgel, Bruno Jedynak

*Bruno Jedynak*

*Introduction*: Characterization of longitudinal trajectories of biomarkers implicated in sporadic Alzheimer's disease (AD) in decades prior to clinical diagnosis is important for disease prevention and monitoring.

*Methods*: We used a multivariate Bayesian model to temporally align 1369 AD Neuroimaging Initiative participants based on the similarity of their longitudinal biomarker measures and estimated a quantitative template of the temporal evolution cerebrospinal fluid (CSF) Aβ_{1-42}, p-tau_{181p}, and t-tau, hippocampal volume, brain glucose metabolism, and cognitive measurements. We computed biomarker trajectories as a function of time to AD dementia, and predicted AD dementia onset age in a disjoint sample.

*Results ...*

Pascal's Triangle Modulo N And Its Applications To Efficient Computation Of Binomial Coefficients, 2019 University of Nebraska - Lincoln

#### Pascal's Triangle Modulo N And Its Applications To Efficient Computation Of Binomial Coefficients, Zachary Warneke

*Honors Theses, University of Nebraska-Lincoln*

In this thesis, Pascal's Triangle modulo *n* will be explored for *n* prime and *n* a prime power. Using the results from the case when *n* is prime, a novel proof of Lucas' Theorem is given. Additionally, using both the results from the exploration of Pascal's Triangle here, as well as previous results, an efficient algorithm for computation of binomial coefficients modulo *n* (*a* choose *b* mod *n*) is described, and its time complexity is analyzed and compared to naive methods. In particular, the efficient algorithm runs in *O*(*n* log(*a*)) time (as opposed to the naive ...

Drones And “Ghost Guns”: Unregulated Legal Space, 2019 Utah State University

#### Drones And “Ghost Guns”: Unregulated Legal Space, Tori Bodine

*Research on Capitol Hill*

Law enforcement agencies are fighting a two - pronged battle when it comes to emerging technologies: keeping up with new ways criminals are using technology and developing effective ways to combat these innovations, while balancing these challenges against preserving the individual liberties of law - abiding citizens. This conflict is especially apparent with regard to criminal use of commercial drones and the developing fringe market surrounding homemade untraceable firearms (“ghost guns”).

Soma-Axon Coupling Configurations That Enhance Neuronal Coincidence Detection, 2019 Swarthmore College

#### Soma-Axon Coupling Configurations That Enhance Neuronal Coincidence Detection, Joshua H. Goldwyn, M. W. H. Remme, J. Rinzel

*Mathematics & Statistics Faculty Works*

Coincidence detector neurons transmit timing information by responding preferentially to concurrent synaptic inputs. Principal cells of the medial superior olive (MSO) in the mammalian auditory brainstem are superb coincidence detectors. They encode sound source location with high temporal precision, distinguishing submillisecond timing differences among inputs. We investigate computationally how dynamic coupling between the input region (soma and dendrite) and the spike-generating output region (axon and axon initial segment) can enhance coincidence detection in MSO neurons. To do this, we formulate a two-compartment neuron model and characterize extensively coincidence detection sensitivity throughout a parameter space of coupling configurations. We focus on ...

The Duals Of *-Operator Frames For End*A(H), 2019 Nova Southeastern University

#### The Duals Of *-Operator Frames For End*A(H), Abdelkrim Bourouihiya, M. Rossafi, H. Labrigui, A. Touri

*Abdelkrim Bourouihiya*

Frames play significant role in signal and image processing, which leads to many applications in differents fields. In this paper we define the dual of ∗-operator frames and we show their propreties obtained in Hilbert *A*-modules and we establish some results.