Mathematics Commons^™

Identifying Requirements For The Invasion Of A Tick Species And Tick-Borne Pathogen Through Ticksim, Holly Gaff, Robyn Nadolny

Biological Sciences Faculty Publications

Ticks and tick-borne diseases have been on the move throughout the United State over the past twenty years. We use an agent-based model, TICKSIM, to identify the key parameters that determine the success of invasion of the tick and if that is successful, the success of the tick-borne pathogen. We find that if an area has competent hosts, an initial population of ten ticks is predicted to always establish a new population. The establishment of the tick-borne pathogen depends on three parameters: the initial prevalence in the ten founding ticks, the probability that a tick infects the longer-lived hosts and …

Ricean Over Gaussian Modelling In Magnitude Fmri Analysis—Added Complexity With Negligible Practical Benefits, Daniel W. Adrian, Ranjan Maitra, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

It is well known that Gaussian modelling of functional magnetic resonance imaging (fMRI) magnitude time-course data, which are truly Rice distributed, constitutes an approximation, especially at low signal-to-noise ratios (SNRs). Based on this fact, previous work has argued that Rice-based activation tests show superior performance over their Gaussian-based counterparts at low SNRs and should be preferred in spite of the attendant additional computational and estimation burden. Here, we revisit these past studies and, after identifying and removing their underlying limiting assumptions and approximations, provide a more comprehensive comparison. Our experimental evaluations using Receiver Operating Characteristic (ROC) curve methodology show that …

Recent Advances In Energy-Efficient Sensor Networks, Sheikh Iqbal Ahamed, Wei Wang, Jiman Hong

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Concept Of Sub-Independence, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Limit theorems as well as other well-known results in probability and statistics are often based on the distributions of the sums of independent random variables. The concept of sub-independence, which is weaker than that of independence, is shown to be sufficient to yield the conclusions of these theorems and results. It also provides a measure of dissociation between two random variables which is stronger than uncorrelatedness.

Undergraduate And Graduate Teaching Assistants' Perceptions Of Their Responsibilities - Factors That Help Or Hinder, Alena Moon, Hyunyi Jung, Farshid Marbouti, Kelsey Joy Rodgers, Heidi A. Diefes-Dux

Mathematics, Statistics and Computer Science Faculty Research and Publications

Effective teaching assistants (TAs) are crucial for effective student learning. This is especially true in science, technology, engineering, and mathematics (STEM) programs, where TAs are enabling large programs to transition to more student-centered learning environments. To ensure that TAs are able to support these types of learning environments, their perspectives of training, their abilities, and other work related aspects must be understood. In this paper a survey that was created based on interviews conducted with eight TAs is discussed. The survey has four primary categories of content that are critical for understanding TAs' perspectives: (1) background, (2) motivation, (3) training, …

Cross‐Campus Collaboration: A Scientometric And Network Case Study Of Publication Activity Across Two Campuses Of A Single Institution, Jeremy Birnholtz, Shion Guha, Y. Connie Yuan, Geri Gay, Caren Heller

Mathematics, Statistics and Computer Science Faculty Research and Publications

Team science and collaboration have become crucial to addressing key research questions confronting society. Institutions that are spread across multiple geographic locations face additional challenges. To better understand the nature of cross‐campus collaboration within a single institution and the effects of institutional efforts to spark collaboration, we conducted a case study of collaboration at Cornell University using scientometric and network analyses. Results suggest that cross‐campus collaboration is increasingly common, but is accounted for primarily by a relatively small number of departments and individual researchers. Specific researchers involved in many collaborative projects are identified, and their unique characteristics are described. Institutional …

Genome-Wide Associations Of Signaling Pathways In Glioblastoma Multiforme, Serdar Bozdag, Stefan Wuchty, Alexei Vazquez, Peter O. Bauer

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background: eQTL analysis is a powerful method that allows the identification of causal genomic alterations, providing an explanation of expression changes of single genes. However, genes mediate their biological roles in groups rather than in isolation, prompting us to extend the concept of eQTLs to whole gene pathways. Methods: We combined matched genomic alteration and gene expression data of glioblastoma patients and determined associations between the expression of signaling pathways and genomic copy number alterations with a non-linear machine learning approach. Results: Expectedly, over-expressed pathways were largely associated to tag-loci on chromosomes with signature alterations. Surprisingly, tag-loci that were associated …

A Proposal For A Problem-Driven Mathematics Curriculum Framework, Judith S. Zawojewski, Marta Magiera, Richard Lesh

Mathematics, Statistics and Computer Science Faculty Research and Publications

A framework for a problem-driven mathematics curriculum is proposed, grounded in the assumption that students learn mathematics while engaged in complex problem-solving activity. The framework is envisioned as a dynamic technologicallydriven multi-dimensional representation that can highlight the nature of the curriculum (e.g., revealing the relationship among modeling, conceptual, and procedural knowledge), can be used for programmatic, classroom and individual assessment, and can be easily revised to reflect ongoing changes in disciplinary knowledge development and important applications of mathematics. The discussion prompts ideas and questions for future development of the envisioned software needed to enact such a framework.

Robust Estimation Of The Correlation Matrix Of Longitudinal Data, Mehdi Maadooliat, Mohsen Pourahmadi, Jianhua Z. Huang

Mathematics, Statistics and Computer Science Faculty Research and Publications

We propose a double-robust procedure for modeling the correlation matrix of a longitudinal dataset. It is based on an alternative Cholesky decomposition of the form Σ=DLL ^⊤ D where D is a diagonal matrix proportional to the square roots of the diagonal entries of Σ and L is a unit lower-triangular matrix determining solely the correlation matrix. The first robustness is with respect to model misspecification for the innovation variances in D, and the second is robustness to outliers in the data. The latter is handled using heavy-tailed multivariate t-distributions with unknown degrees of freedom. We …

Considerations In Designing Human-Computer Interfaces For Elderly People, Drew Williams, Mohammad Arif Ul Alam, Sheikh Iqbal Ahamed, William Chu

Mathematics, Statistics and Computer Science Faculty Research and Publications

As computing devices continue to become more heavily integrated into our lives, proper design of human-computer interfaces becomes a more important topic of discussion. Efficient and useful human-computer interfaces need to take into account the abilities of the humans who will be using such interfaces, and adapt to difficulties that different users may face – such as the difficulties that elderly users must deal with. Interfaces that allow for user-specific customization, while taking into account the multiple difficulties that older users might face, can assist the elderly in properly using these newer computing devices, and in doing so possibly achieving …

The Zografos-Balakrishnan Log-Logistic Distribution: Properties And Applications, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Rssi Based Indoor Localization For Smartphone Using Fixed And Mobile Wireless Node, Md O. Gani, Casey O'Brien, Sheikh Iqbal Ahamed, Roger O. Smith

Mathematics, Statistics and Computer Science Faculty Research and Publications

Nowadays with the dispersion of wireless networks, smartphones and diverse related services, different localization techniques have been developed. Global Positioning System (GPS) has a high rate of accuracy for outdoor localization but the signal is not available inside of buildings. Also other existing methods for indoor localization have low accuracy. In addition, they use fixed infrastructure support. In this paper, we present a novel system for indoor localization, which also works well outside. We have developed a mathematical model for estimating location (distance and direction) of a mobile device using wireless technology. Our experimental results on Smartphones (Android and iOS) …

Investigating The Validity Of A Survey Intended To Gauge Mathematics Problem-Solving Disposition Along The Impulsive-Analytic Dimension, Miguel Mendoza

Open Access Theses & Dissertations

This study investigates the validity of the Likelihood-to-Act (LtA) survey developed to assess respondents' problem-solving disposition along the impulsive-analytic dimension. Sixteen pre-service teachers were strategically selected from a pool of 495 LtA survey respondents to participate in a semi-structured task-based interview approximately one hour in length. The interview consisted of three main parts: a problem solving section, a consistency section, and a classification section.

* Part 1 of the interview was developed to get interviewees to solve five open-response problems meant to elicit an impulsive response. Interviewees were also asked to verbalize their thought process in order for the researchers …

A Convex Optimization Algorithm For Sparse Representation And Applications In Classification Problems, Reinaldo Sanchez Arias

Open Access Theses & Dissertations

In pattern recognition and machine learning, a classification problem refers to finding an algorithm for assigning a given input data into one of several categories. Many natural signals are sparse or compressible in the sense that they have short representations when expressed in a suitable basis. Motivated by the recent successful development of algorithms for sparse signal recovery, we apply the selective nature of sparse representation to perform classification. Any test sample is represented in an overcomplete dictionary with the training sample as base elements. A given test sample can be expressed as a linear combination of only those training …

Generalizations Of Dirichlet Convolution, Juan Carlos Villarreal

Open Access Theses & Dissertations

The thesis reviews Dirichlet convolution of arithmetic functions and some generalizations. First, we present the main properties of the Dirichlet convolution on the set of arithmetic functions and some characterizations of prime numbers via arithmetic functions are given. Then we explore the K-convolution and the regular convolutions and finally we extend the study of Dirichlet convolution in categories. We give also an example for the evaluation of the Mobius function of a Mobius category.

Structure Borne Noise Analysis Using Helmholtz Equation Least Squares Based Forced Vibro Acoustic Components, Logesh Kumar Natarajan

Wayne State University Dissertations

This dissertation presents a structure-borne noise analysis technology that is focused on providing a cost-effective noise reduction strategy. Structure-borne sound is generated or transmitted through structural vibration; however, only a small portion of the vibration can effectively produce sound and radiate it to the far-field. Therefore, cost-effective noise reduction is reliant on identifying and suppressing the critical vibration components that are directly responsible for an undesired sound. However, current technologies cannot successfully identify these critical vibration components from the point of view of direct contribution to sound radiation and hence cannot guarantee the best cost-effective noise reduction.

The technology developed …

Machine Learning And The Perceptron Algorithm, John Travis Shrontz

Summer Community of Scholars Posters (RCEU and HCR Combined Programs)

No abstract provided.

Topological Convolution Algebras, Daniel Alpay, Guy Salomon

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we introduce a new family of topological convolution algebras of the form ⋃p∈NL2(S,μp), where S is a Borel semi-group in a locally compact group G, which carries an inequality of the type ∥f∗g∥p≤Ap,q∥f∥q∥g∥p for p>q+d where d pre-assigned, and Ap,q is a constant. We give a sufficient condition on the measures μp for such an inequality to hold. We study the functional calculus and the spectrum of the elements of these algebras, and present two examples, one in the setting of non commutative stochastic distributions, and the other related to Dirichlet series.

On Discrete Analytic Functions: Products, Rational Functions, And Reproducing Kernels, Daniel Alpay, Palle Jorgensen, Ron Seager, Dan Volok

Mathematics, Physics, and Computer Science Faculty Articles and Research

We introduce a family of discrete analytic functions, called expandable discrete analytic functions, which includes discrete analytic polynomials, and define two products in this family. The first one is defined in a way similar to the Cauchy-Kovalevskaya product of hyperholomorphic functions, and allows us to define rational discrete analytic functions. To define the second product we need a new space of entire functions which is contractively included in the Fock space. We study in this space some counterparts of Schur analysis.

Pontryagin De Branges-Rovnyak Spaces Of Slice Hyperholomorphic Functions, Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

We study reproducing kernel Hilbert and Pontryagin spaces of slice hyperholomorphic functions which are analogs of the Hilbert spaces of analytic functions introduced by de Branges and Rovnyak. In the first part of the paper we focus on the case of Hilbert spaces, and introduce in particular a version of the Hardy space. Then we define Blaschke factors and Blaschke products and we consider an interpolation problem. In the second part of the paper we turn to the case of Pontryagin spaces. We first prove some results from the theory of Pontryagin spaces in the quaternionic setting and, in particular, …