Mathematics Commons^™

Life After Calculus: 20 Years Later, Darren B. Glass

Math Faculty Publications

In 1996 Math Horizons interviewed a group of students at the Joint Mathematics Meetings; now, 20 years later, one of those students, Darren Glass, interviews another group of students.

Synchrony In A Boolean Network Of The L-Arabinose Operon In Escherichia Coli, Andy Jenkins, Matthew Macauley

Publications

The lactose operon in Escherichia coli was the first known gene regulatory network, and it is frequently used as a prototype for new modeling paradigms. Historically, many of these modeling frameworks use differential equations. More recently, Stigler and Veliz-Cuba proposed a Boolean network model that captures the bistability of the system and all of the biological steady states. In this paper, we model the well-known arabinose operon in E. coli with a Boolean network. This has several complex features not found in the lac operon, such as a protein that is both an activator and repressor, a DNA looping mechanism …

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.

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

Trigonometry, Ted Sundstrom, Steven Schlicker

Open Textbooks

This trigonometry textbook is different than other trigonometry books in that it is free to download, and the reader is expected to do more than read the book and is expected to study the material in the book by working out examples rather than just reading about them. So this book is not just about mathematical content but is also about the process of learning and doing mathematics. That is, this book is designed not to be just casually read but rather to be engaged.

Since this can be a difficult task, there are several features of the book designed …

The Classification Of Zp -Modules With Partial Decomposition Bases In L∞Ω, Carol Jacoby, Peter Loth

Mathematics Faculty Publications

Ulm’s Theorem presents invariants that classify countable abelian torsion groups up to isomorphism. Barwise and Eklof extended this result to the classification of arbitrary abelian torsion groups up to L∞ω-equivalence. In this paper, we extend this classification to a class of mixed Zp-modules which includes all Warfield modules and is closed under L∞ω-equivalence. The defining property of these modules is the existence of what we call a partial decomposition basis, a generalization of the concept of decomposition basis. We prove a complete classification theorem in L∞ω using invariants deduced from the classical Ulm and Warfield invariants.

Eventual Quasi-Linearity Of The Minkowski Length, Ivan Soprunov, Jenya Soprunova

Mathematics and Statistics Faculty Publications

The Minkowski length of a lattice polytope PP is a natural generalization of the lattice diameter of PP. It can be defined as the largest number of lattice segments whose Minkowski sum is contained in PP. The famous Ehrhart theorem states that the number of lattice points in the positive integer dilates tPtP of a lattice polytope PP behaves polynomially in t∈Nt∈N. In this paper we prove that for any lattice polytope PP, the Minkowski length of tPtP for t∈Nt∈N is eventually a quasi-polynomial with linear constituents. We also give a formula for the Minkowski length of coordinates boxes, degree …

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 …

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 …

On Characterizations And Infinite Divisibility Of Recently Introduced Distributions, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We present here characterizations of the most recently introduced continuous univariate distributions based on: (i) a simple relationship between two truncated moments; (ii) truncated moments of certain functions of the 1^th order statistic; (iii) truncated moments of certain functions of the n^th order statistic; (iv) truncated moment of certain function of the random variable. We like to mention that the characterization (i) which is expressed in terms of the ratio of truncated moments is stable in the sense of weak convergence. We will also point out that some …

New Classes Of Univariate Continuous Exponential Power Series Distributions, M. Ahsanullah, Gholamhossein G. Hamedani, M. Shakil, B.M. Golam Kibria, F. George

Mathematics, Statistics and Computer Science Faculty Research and Publications

Recently, many researchers have developed various classes of continuous probability distributions which can be generated via the generalized Pearson differential equation and other techniques. In this paper, motivated by the importance of the power series in probability theory and its applications, we derive some new classes of univariate exponential power series distributions for a realvalued continuous random variable, which we call exponential power series distributions. Various mathematical properties of the proposed classes of distributions are discussed. Based on these distributional properties, we have established some characterizations of these distributions as well. It is hoped that the findings of the paper …

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 …

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 …

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.