Mathematics Commons^™

A Browser-Based Ide For The Muzecs Platform, Omokolade Hunpatin, Casey O'Hare, Ryan Thomas, Dennis Brylow

Mathematics, Statistics and Computer Science Faculty Research and Publications

We report on a scalable, portable, and secure visual development environment for programming embedded Arduino platforms with Chromebooks in a successful secondary school computer science curriculum. Our web-based environment is part of the larger MUzECS project, an inexpensive replacement module for the Exploring Computer Science (ECS) course being widely deployed in United States high schools. Students use MUzECS to gain a deeper understanding of computing, through a set of blocks which provide appropriate abstractions for working with low-level hardware.

MUzECS improves upon the existing curriculum module by reducing the hardware cost by an order of magnitude, while still preserving the …

Unfolding Genus-2 Orthogonal Polyhedra With Linear Refinement, Mirela Damian, Erik Demaine, Robin Flatland, Joseph O'Rourke

Mathematics Sciences: Faculty Publications

We show that every orthogonal polyhedron of genus g ≤ 2 can be unfolded without overlap while using only a linear number of orthogonal cuts (parallel to the polyhedron edges). This is the first result on unfolding general orthogonal polyhedra beyond genus- 0. Our unfolding algorithm relies on the existence of at most 2 special leaves in what we call the “unfolding tree” (which ties back to the genus), so unfolding polyhedra of genus 3 and beyond requires new techniques.

Rainbow Arborescence In Random Digraphs, Deepak Bal, Patrick Bennett, Colin Cooper, Alan Frieze, Paweł Prałat

Department of Mathematics Faculty Scholarship and Creative Works

We consider the Erdős–Rényi random directed graph process, which is a stochastic process that starts with n vertices and no edges, and at each step adds one new directed edge chosen uniformly at random from the set of missing edges. Let (Formula presented.) be a graph with m edges obtained after m steps of this process. Each edge (Formula presented.) ((Formula presented.)) of (Formula presented.) independently chooses a color, taken uniformly at random from a given set of (Formula presented.) colors. We stop the process prematurely at time M when the following two events hold: (Formula presented.) has at most …

Exploring Connections Between Advanced And Secondary Mathematics, Erin E. Baldinger, Eileen Murray, Diana White, Shawn Broderick, Nicholas Wasserman

Department of Mathematics Faculty Scholarship and Creative Works

The second meeting of this Working Group continues to explore questions about the connections between abstract algebra and school mathematics. Our goal is to focus in on questions around the way in which teachers’ practice might be influenced based on their understanding of such connections. In particular, we will gather interested individuals in an effort to deepen our understanding of existing connections between abstract algebra and secondary mathematics and which of these connections are important for secondary teachers to know and understand. Moreover, we aim to further research in this area by first considering connections between abstract algebra and school …

Series Solutions Of Multi-Layer Boundary Value Problems, Amr Saad Hassan Bolbol

Theses

It is well known that differential equations (DEs) play an important role in many sciences. They are mathematical representations of many physical systems. By studying such DEs, one gains many important insights about the physical system. Solutions of DEs provide information on the physical system behavior. As many physical systems are nonlinear in nature, this naturally gives rise to nonlinear differential equations (NLDEs). Such NLDEs are, in most cases, hard or sometimes impossible to solve analytically. In such situations, we resort to numerical techniques to approximate the solutions. The purpose of this thesis is to consider nonlinear multi-layer boundary value …

Csp And “Omics” Technology Applied On Versatile And Intelligent Portable Platform For Modeling Complex Bio-Medical Data, Florentin Smarandache, Luige Vladareanu, Mihaiela Iliescu, Hongbo Wang, Feng Yongfei, Victor Vladareanu

Branch Mathematics and Statistics Faculty and Staff Publications

This paper presents relevant aspects of the idea of using the digital medicine in cancer, so that to shape a viable strategy for creating and implementing an interactive digital platform, NEO-VIP, that should be the basic support to design the strategy for integration of basic, clinical and environmental research on neoplasia progression to cancer. The two main components of the VIPRO Platform are represented by the workstation “Engineering Station” for CPS (Cyber Physical System) and “omics” technology and by the “Graphical Station” for the development of a virtual mechatronic system environment and virtual reality for system components' motion. The NEO-VIP …

Computation Of Shortest Path Problem In A Network With Sv-Trapezoidal Neutrosophic Numbers, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Luige Vladareanu

Branch Mathematics and Statistics Faculty and Staff Publications

In this work, a neutrosophic network method is proposed for finding the shortest path length with single valued trapezoidal neutrosophic number. The proposed algorithm gives the shortest path length using score function from source node to destination node. Here the weights of the edges are considered to be single valued trapezoidal neutrosophic number. Finally, a numerical example is used to illustrate the efficiency of the proposed approach

A General Elliptic Nonlinear System Of Multiple Functions With Application, Timothy Robertson, Joon Hyuk Kang

Faculty Publications

The purpose of this paper is to give a sufficient condition for the existence, nonexistence and uniqueness of positive solutions to a rather general type of elliptic system of the Dirichlet problem on a bounded domain Ω in Rn . We also investigate the effects of perturbation on the positive solutions to the system. The techniques used in this paper are upper-lower solutions, eigenvalues of operators, the maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations. This result yields an algebraically computable criterion for the positive coexistence of competing species …

Spatial Population Models With Fitness Based Dispersal, Chris Cosner

Mathematics Colloquium Series

Traditional continuous time models in spatial ecology typically describe movement in terms of linear diffusion and advection, which combine with nonlinear population dynamics to produce semi-linear parabolic equations and systems. In environments that are favorable everywhere in the sense that the local population growth rate is always positive, organisms can use linear advection and diffusion to achieve an optimal spatial distribution. (Here optimal means evolutionarily stable.) In regions where there are environmental “sinks” where the local growth rate is negative, it does not seem possible to achieve an optimal distribution via linear dispersal. It is possible for organisms using advection …

Anti-Nogo-A Immunotherapy Does Not Alter Hippocampal Neurogenesis After Stroke In Adult Rats, Timothy O'Brien, Daniel Shepherd, Gwendolyn Kartje-Tillotson, Shih-Yen Tsai, Robert G. Farrer

Mathematics and Statistics: Faculty Publications and Other Works

Ischemic stroke is a leading cause of adult disability, including cognitive impairment. Our laboratory has previously shown that treatment with function-blocking antibodies against the neurite growth inhibitory protein Nogo-A promotes functional recovery after stroke in adult and aged rats, including enhancing spatial memory performance, for which the hippocampus is critically important. Since spatial memory has been linked to hippocampal neurogenesis, we investigated whether anti-Nogo-A treatment increases hippocampal neurogenesis after stroke. Adult rats were subject to permanent middle cerebral artery occlusion followed 1 week later by 2 weeks of antibody treatment. Cellular proliferation in the dentate gyrus was quantified at the …

Fractal Analysis Of Dna Sequences, Christian G. Arias, Pedro Antonio Moreno Phd, Carlos Tellez

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Bounds On The Expected Size Of The Maximum Agreement Subtree, Colby Long, Daniel Irving Bernstein, Lam Si Tung Ho, Mike Steel, Katherine St. John, Seth Sullivant

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

General Equations For Natural Selection Under Complete Dominance, Kasthuri Kannan, Adriana Heguy

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Exploring The Space Of Rna Secondary Structures, Heather C. Smith

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Development Of Honesty In Repeated Signalling Games, Michael I. Leshowitz

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Framework For The Teaching Of Modeling For Biologists, M. Drew Lamar, Carrie Diaz Eaton

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Markov Chains On Graphical Models Of Gene Regulation, Megan Bernstein

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Territorial Movement Game, Jan Rychtar

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Genome Rearrangement: Graphs And Matrices, Jeffrey Davis

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

On The Expected Number Of Crossings In A Tanglegram, Eva Czabarka

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Designing And Mentoring In A Research Experience For Undergraduates, Alex Capaldi

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Symmetric Integer Matrices Having Integer Eigenvalues, Lei Cao, Selcuk Koyuncu

Mathematics Faculty Articles

We provide characterization of symmetric integer matrices for rank at most 2 that have integer spectrum and give some constructions for such matrices of rank 3. We also make some connection between Hanlon’s conjecture and integer eigenvalue problem.

Structure For Regular Inclusions. I, David R. Pitts

Department of Mathematics: Faculty Publications

We give general structure theory for pairs (C,D) of unital C*- algebras where D is a regular and abelian C*-subalgebra of C.

When D is maximal abelian in C, we prove existence and uniqueness of a completely positive unital map E of C into the injective envelope I(D) of D such that EjD = idD; E is a useful replacement for a conditional expectation when no expectation exists. When E is faithful, (C,D) has numerous desirable properties: e.g. the linear span of the normalizers has a unique minimal C*- norm; D norms C; and isometric isomorphisms of norm-closed subalgebras lying …

Predator-Prey Dynamics With Intraspecific Competition And An Allee Effect In The Predator Population, Anne E. Yust, Erin N. Bodine

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

On The Perfect Reconstruction Of The Structure Of Dynamic Networks, Alan Veliz-Cuba

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Spectral Graph Theory And New Stability Measures For Deterministic Gene Regulatory Networks, Fusun Akman, Devin Akman

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Extracting Biochemical Parameters From Protein Distributions Of Vascular Cells, Partha Srinivasan

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Interdisciplinary Undergraduate Research In Biofluids, Eva M. Strawbridge

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Comparing The Effects Of General And Selective Culling On Chronic Wasting Disease (Cwd) Prevalence, Elliott J. Moran

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Dem-Cfd Numerical Simulation And Experimental Validation Of Heat Transfer And Two-Component Flow In Fluidized Bed, Feihong Guo

The 8th International Conference on Physical and Numerical Simulation of Materials Processing

No abstract provided.