Applied Mathematics Commons^™

Fixed-Point Proximity Minimization: A Theoretical Review And Numerical Study, Daniel Weddle, Jianfeng Guo

OUR Journal: ODU Undergraduate Research Journal

This study examines the relatively recent development of a “fixed-point proximity” approach to one type of minimization problem, considers its application to image denoising, and explores convergence and divergence of the iterative algorithm beyond a (previously supplied) theoretically guaranteed convergence bound on one of the parameters (𝜆). While reviewing the fixed-point proximity approach and its application to image denoising, we aim to communicate the concepts and details in a way that will facilitate understanding for undergraduates and for scholars from other subfields. In the latter portion of our study, the numerical experiment provides thought-provoking data on the effects that parameters …

A Geometric Description Of The Set Of Stabilizing Pid Controllers, Keqin Gu, Qian Ma, Huiqing Zhou, Mahzoon Salma, Xingzi Yang

SIUE Faculty Research, Scholarship, and Creative Activity

This article developed a new method to described the set of stabilizing PID control. The method is based on D-parameterization with natural description of the set. It was found that the stability crossing surface is a ruled surface that is completely determined by a curve known as discriminant. The discriminant is divided into sectors at the cusps. Corresponding to the sectors, the stability crossing surface is divided into positive and negative patches. A systematic study is conducted to identify the regions with a fixed number of right half-plane characteristic roots. The crossing directions of characteristic roots for positive patches and …

An Enumeration Of Nested Networks, Nathan Cornelius

Williams Honors College, Honors Research Projects

Nested networks have several applications in phylogenetics and electrical circuit theory. In many cases, there may exist more than one distinct network which correctly models a given data set. This proposes a combinatorial problem to determine all possible network solutions. In this paper, we partially solve this problem by developing exponential generating functions which enumerate all 1-nested and 2-nested unicyclic networks. We also describe our procedure to directly count all 1-nested and 2-nested networks and provide all 1-nested networks with 7, 8, and 9 terminal nodes.

Design Project: Smart Headband, John Michel, Jack Durkin, Noah Lewis

Williams Honors College, Honors Research Projects

Concussion in sports is a prevalent medical issue. It can be difficult for medical professionals to diagnose concussions. With the fast pace nature of many sports, and the damaging effects of concussions, it is important that any concussion risks are assessed immediately. There is a growing trend of wearable technology that collects data such as steps and provides the wearer with in-depth information regarding their performance. The Smart Headband project created a wearable that can record impact data and provide the wearer with a detailed analysis on their risk of sustaining a concussion. The Smart Headband uses accelerometers and gyroscopes …

Obstructive Wiring Patterns To Circular Planarity In Electrical Networks, Hannah Lebo

Williams Honors College, Honors Research Projects

In order for an electrical network to be printed on a flat surface without changing the network’s input or output, it is important to consider if any wires will cross and if this problem can be avoided. If a circular network can be printed so that no wires cross, the network is said to be circular planar. In this paper, we identify a number of wiring patterns that make circular planarity impossible. We find exactly 3 wiring patterns using circular pairs with sets of two nodes, and we find exactly 78 wiring patterns using circular pairs with sets of three …

Multigrid For The Nonlinear Power Flow Equations, Enrique Pereira Batista

Mathematics Theses and Dissertations

The continuously changing structure of power systems and the inclusion of renewable
energy sources are leading to changes in the dynamics of modern power grid,
which have brought renewed attention to the solution of the AC power flow equations.
In particular, development of fast and robust solvers for the power flow problem
continues to be actively investigated. A novel multigrid technique for coarse-graining
dynamic power grid models has been developed recently. This technique uses an
algebraic multigrid (AMG) coarsening strategy applied to the weighted
graph Laplacian that arises from the power network's topology for the construction
of coarse-grain approximations to …

Under Frequency Load Shedding Scheme For Islanded Distribution System Based On Mixed Integer Linear Programming, Sohail Sarwar

Student Works (2020-2029)

In recent years, significant climate changes have pivoted the distribution system towards utilization of renewable energy, particularly through distributed generators (DGs). Although DGs offer many benefits, its integration affects the stability of the system, which could lead to blackout, when the grid is disconnected. The system frequency will drop drastically if DG’s generation capacity is less than the total load demand in the network. In order to sustain the system stability, Under Frequency Load Shedding (UFLS) is a commonly used technique to minimize the difference in load demand and power generation. However, existing load shedding techniques are lack in accurate …

Energy-Efficient Communications In Wireless Powered Cognitive Radio Networks Based On Game Theory, Fadhil Mukhlif Aswad Al-Obaidy

Student Works (2020-2029)

There are challenging and prevalent problems related to spectrum resources with the interference of battery-based devices in future wireless networks. To address such challenges, this thesis proposes a theoretical framework for designing and analyzing the distributed power control algorithms in modern 5G cognitive networks. Previous experiments have shown that game theory tools can be used as a suitable and efficient technique to build scalable, balanced, and energy efficient for the distributed power control schemes in order to use it practically in battery-based devices in wireless networks. In reality, the power control issue is constructed as a non-cooperative game for which …

Dynamic Between Biomass, Ph And Acid Lactic By Microorganisms In Fermentation Of Fresh Milk, Emmanuel Rodriguez, Aurelio Castillo, Paul A. Valle, Yolocuauhtli Salazar

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

An Adaptive Approach To Gibbs’ Phenomenon, Jannatul Ferdous Chhoa

Master's Theses

Gibbs’ Phenomenon, an unusual behavior of functions with sharp jumps, is encountered while applying the Fourier Transform on them. The resulting reconstructions have high frequency oscillations near the jumps making the reconstructions far from being accurate. To get rid of the unwanted oscillations, we used the Lanczos sigma factor to adjust the Fourier series and we came across three cases. Out of the three, two of them failed to give us the right reconstructions because either it was removing the oscillations partially but not entirely or it was completely removing them but smoothing out the jumps a little too much. …

Coding Against Stragglers In Distributed Computation Scenarios, Malihe Aliasgari

Dissertations

Data and analytics capabilities have made a leap forward in recent years. The volume of available data has grown exponentially. The huge amount of data needs to be transferred and stored with extremely high reliability. The concept of "coded computing", or a distributed computing paradigm that utilizes coding theory to smartly inject and leverage data/computation redundancy into distributed computing systems, mitigates the fundamental performance bottlenecks for running large-scale data analytics.

In this dissertation, a distributed computing framework, first for input files distributedly stored on the uplink of a cloud radio access network architecture, is studied. It focuses on that decoding …

Evaluating Driving Performance Of A Novel Behavior Planning Model On Connected Autonomous Vehicles, Keyur Shah

Honors Scholar Theses

Many current algorithms and approaches in autonomous driving attempt to solve the "trajectory generation" or "trajectory following” problems: given a target behavior (e.g. stay in the current lane at the speed limit or change lane), what trajectory should the vehicle follow, and what inputs should the driving agent apply to the throttle and brake to achieve this trajectory? In this work, we instead focus on the “behavior planning” problem—specifically, should an autonomous vehicle change lane or keep lane given the current state of the system?

In addition, current theory mainly focuses on single-vehicle systems, where vehicles do not communicate with …

Nonlinear Least Squares 3-D Geolocation Solutions Using Time Differences Of Arrival, Michael V. Bredemann

Mathematics & Statistics ETDs

This thesis uses a geometric approach to derive and solve nonlinear least squares minimization problems to geolocate a signal source in three dimensions using time differences of arrival at multiple sensor locations. There is no restriction on the maximum number of sensors used. Residual errors reach the numerical limits of machine precision. Symmetric sensor orientations are found that prevent closed form solutions of source locations lying within the null space. Maximum uncertainties in relative sensor positions and time difference of arrivals, required to locate a source within a maximum specified error, are found from these results. Examples illustrate potential requirements …

Investigating The Solution Properties Of Population Model Of Cross-Diffusion Model With Double Nonlinearity And With Variable Density, Dildora Kabilovna Muhamediyeva

Chemical Technology, Control and Management

The models of two competing populations with double nonlinear diffusion and three types of functional dependencies are considered. The first dependence corresponds to the Malthusian type, the second to the Verhühlst type (logistic population), and the third to Olli-type populations. A common element of this kind of description is the presence of a linear source. Nonlinear sinks are also present in descriptions of populations of the Verhulst and Ollie type. Suitable initial approximations for a rapidly converging iterative process are proposed. Based on a self-similar analysis and comparison of the solutions of the Cauchy problem in the domain for an …

A Computationally-Efficient Bound For The Variance Of Measuring The Orientation Of Single Molecules, Tingting Wu, Tianben Ding, Hesam Mazidi, Oumeng Zhang, Matthew D. Lew

Electrical & Systems Engineering Publications and Presentations

Modulating the polarization of excitation light, resolving the polarization of emitted fluorescence, and point spread function (PSF) engineering have been widely leveraged for measuring the orientation of single molecules. Typically, the performance of these techniques is optimized and quantified using the Cramér-Rao bound (CRB), which describes the best possible measurement variance of an unbiased estimator. However, CRB is a local measure and requires exhaustive sampling across the measurement space to fully characterize measurement precision. We develop a global variance upper bound (VUB) for fast quantification and comparison of orientation measurement techniques. Our VUB tightly bounds the diagonal elements of the …

Filtered-Dynamic-Inversion Control For Unknown Minimum-Phase Systems With Unknown Relative Degree, Sumit Suryakant Kamat

Theses and Dissertations--Mechanical and Aerospace Engineering

We present filtered-dynamic-inversion (FDI) control for unknown linear time-invariant systems that are multi-input multi-output and minimum phase with unknown-but-bounded relative degree. This FDI controller requires limited model information, specifically, knowledge of an upper bound on the relative degree and knowledge of the first nonzero Markov parameter. The FDI controller is a single-parameter high-parameter-stabilizing controller that is robust to uncertainty in the relative degree. We characterize the stability of the closed-loop system. We present numerical examples, where the FDI controller is implemented in feedback with mathematical and physical systems. The numerical examples demonstrate that the FDI controller for unknown relative degree …

The Potentials Of Faecal Sludge Treatment Using Local Conditioners In Tanzania: A Review, Doglas Benjamin1

Tanzania Journal of Engineering and Technology (TJET)

Worldwide, every day human beings generate millions of tons of Faecal Sludge (FS), which is rich in water, nutrients, energy, and organic compounds. Yet FS is not being managed in a way that permits us to derive value from its reuse, while at the same time, millions of farmers struggle with depleted soils and lack of water. In most of the developing countries, energy for cooking is mainly derived from cutting of trees, either as wood or charcoal. Resource recovery and reuse from FS can create livelihoods, enhance food security, support green economies, reduce waste and contribute to cost recovery …

Blind Algorithm Development For Peak To Average Power Ratio Reduction In Ofdm Systems Under Frequency Selective Channels, Kwame S. Ibwe

Tanzania Journal of Engineering and Technology (TJET)

One major drawback of orthogonal frequency division multiplexing (OFDM) system is peak to average power ratio (PAPR). This effect causes high power amplifier (HPA) to introduce intermodulation and out of band radiation as the signal goes through, thus degrades the performance of OFDM systems. This paper proposes blind algorithms which takes advantage of signal transformation technique and signal distortion technique. Simulation results show that at complementary cumulative distribution function (CCDF) level of 10-3, the proposed algorithm achieved 3.2 dB PAPR improvement compared to discrete Fourier transform with interleaved frequency division multiple access (DFT-IFDMA) based algorithm. The bit error rate (BER) …

Image Restoration Using Automatic Damaged Regions Detection And Machine Learning-Based Inpainting Technique, Chloe Martin-King

Computational and Data Sciences (PhD) Dissertations

In this dissertation we propose two novel image restoration schemes. The first pertains to automatic detection of damaged regions in old photographs and digital images of cracked paintings. In cases when inpainting mask generation cannot be completely automatic, our detection algorithm facilitates precise mask creation, particularly useful for images containing damage that is tedious to annotate or difficult to geometrically define. The main contribution of this dissertation is the development and utilization of a new inpainting technique, region hiding, to repair a single image by training a convolutional neural network on various transformations of that image. Region hiding is also …

Analog Implementation Of The Hodgkin-Huxley Model Neuron, Zachary D. Mobille, George H. Rutherford, Jordan Brandt-Trainer, Rosangela Follmann, Epaminondas Rosa

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Academic Skill Learning And The Problem Of Complexity I: Creational Purposeful Integrated Capability At Skill (Cpics), Martin F. Gardiner

Northeast Journal of Complex Systems (NEJCS)

Physical and mental skills are intended to achieve success at acting purposefully. As capability at any skill increases, the need to adjust details of application to complexity of context and goals will increase as well. It will become more and more important to prepare mentally for what I now term Creational Purposeful Integrated Capability at Skill (CPICS). This paper develops what I mean by CPICS. Theory concerning Complex Dynamical Systems (CDS) such as the brain and other evidence points to the likelihood that the mental operations by which our brain produces any kind of skillful behavior cannot remain constant, …

A Patterning Approach To Complexity Thinking And Understanding For Students: A Case Study, Shae L. Brown

Northeast Journal of Complex Systems (NEJCS)

Complexity thinking and understanding are vital skills for young people in these times of uncertainty and change. Such skills contribute to resilience and capacities for adaptivity and innovation. Within my teaching practice I have found students to be aware of complex dynamics, uncertainty and change, both in their lives and in the world. However, the current curriculum lacks language and process to conceptualise, articulate and develop complexity understanding. To address this problem, I developed and introduced a patterns-based design and process to a cohort of Australian secondary students. Comprising flowform patterning together with ecological metaphors, the design forms a conceptual …

Being In Uncertainties: An Inquiry-Based Model Leveraging Complexity In Teaching-Learning, Diane Rosen

Northeast Journal of Complex Systems (NEJCS)

Education is traditionally structured as a closed system, privileging result-driven methods that offer control and predictability. In recent decades this reductionist approach has been effectively challenged by interdisciplinary work in complex systems theory, revealing myriad levels of orderly disorder that make either-or, linear instruction an inadequate norm. Narrowing the broad implications of a complexity lens on education, this paper focuses on generative uncertainty in teaching-learning, a paradoxical state of epistemological and creative growth described by English poet John Keats as "the negative capability of being in uncertainties, mysteries, doubts." Opportunities to advance this potentiating capacity are especially abundant in constructivist …

Creativity As An Emergent Property Of Complex Educational System, Ceire Monahan, Mika Munakata, Ashwin Vaidya

Northeast Journal of Complex Systems (NEJCS)

The importance of creativity in education has been discussed often in the literature. While there remains no agreed-upon definition of creativity, the psychological literature points to traits of a creative person. These include the ability to think outside the box, make connections between seemingly disparate ideas, and question norms. The literature provides several examples of classroom experiments to help foster creativity in the classroom. In science and mathematics, we can start by getting students to recognize mathematics and the sciences as being creative endeavors. While these attempts are noteworthy, they are not necessarily aligned with instructional practices. In this article, …

Rethinking Educational Reforms Through A Complex Dynamical Systems Approach: Preliminary Report From An Empirical Research, Eugenia Tsiouplis, Dimitrios Stamovlasis

Northeast Journal of Complex Systems (NEJCS)

Literature on educational reforms is rich of cases where changes have been attempted, without however to attain success. Likewise the Greek education system had experienced a lot of reforms, most of which have failed to make the intended changes and they attenuated shortly after their implementation or they ceased at the stage of legislative planning. On the other hand, the traditional research have failed to develop a coherent theoretical perspective and provide satisfactory interpretations of the perpetually unsuccessful reforms. This paper is part of wider project which attempts to address the above issue following the Complex Dynamical Systems (CDS) perspective, …

Editorial Introduction To The Northeast Journal Of Complex Systems (Nejcs), Hiroki Sayama, Georgi Georgiev

Northeast Journal of Complex Systems (NEJCS)

Editorial Introduction to the Northeast Journal of Complex Systems (NEJCS)

Fractality And Power Law Distributions: Shifting Perspectives In Educational Research, Matthijs Koopmans

Northeast Journal of Complex Systems (NEJCS)

The dynamical character of education and the complexity of its constituent relationships have long been recognized, but the full appreciation of the implications of these insights for educational research is recent. Most educational research to this day tends to focus on outcomes rather than process, and rely on conventional cross-sectional designs and statistical inference methods that do not capture this complexity. This presentation focuses on two related aspects not well accommodated by conventional models, namely fractality (self-similarity, scale invariance) and power law distributions (an inverse relationship between frequency of occurrence and strength of response). Examples are presented for both phenomena …

Stability Analysis Of A More General Class Of Systems With Delay-Dependent Coefficients, Chi Jin, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu

SIUE Faculty Research, Scholarship, and Creative Activity

This paper presents a systematic method to analyse the stability of systems with single delay in which the coefficient polynomials of the characteristic equation depend on the delay. Such systems often arise in, for example, life science and engineering systems. A method to analyze such systems was presented by Beretta and Kuang in a 2002 paper, but with some very restrictive assumptions. This work extends their results to the general case with the exception of some degenerate cases. It is found that a much richer behavior is possible when the restrictive assumptions are removed. The interval of interest for the …

On Analytic Nonlinear Input-Output Systems: Expanded Global Convergence And System Interconnections, Irina M. Winter Arboleda

Electrical & Computer Engineering Theses & Dissertations

Functional series representations of nonlinear systems first appeared in engineering in the early 1950’s. One common representation of a nonlinear input-output system are Chen-Fliess series or Fliess operators. Such operators are described by functional series indexed by words over a noncommutative alphabet. They can be viewed as a noncommutative generalization of a Taylor series. A Fliess operator is said to be globally convergent when its radius of convergence is infinite, in other words, when there is no a priori upper bound on both the L1-norm of an admissible input and the length of time over which the corresponding output is …

Solutions For Fermi Questions, November 2019: Question 1: Cell Phones Make Me Boil; Question 2: Charging The Phone, Larry Weinstein

Physics Faculty Publications

Answers to the Fermi questions:

How much water can you boil with the energy stored in a cell phone battery?

How much does the electrical energy for a cell phone cost each year?