Other Applied Mathematics Commons^™

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Data And Algorithmic Modeling Approaches To Count Data, Andraya Hack

Honors College Theses

Various techniques are used to create predictions based on count data. This type of data takes the form of a non-negative integers such as the number of claims an insurance policy holder may make. These predictions can allow people to prepare for likely outcomes. Thus, it is important to know how accurate the predictions are. Traditional statistical approaches for predicting count data include Poisson regression as well as negative binomial regression. Both methods also have a zero-inflated version that can be used when the data has an overabundance of zeros. Another procedure is to use computer algorithms, also known as …

Decoding Cyclic Codes Via Gröbner Bases, Eduardo Sosa

Honors Theses

In this paper, we analyze the decoding of cyclic codes. First, we introduce linear and cyclic codes, standard decoding processes, and some standard theorems in coding theory. Then, we will introduce Gr¨obner Bases, and describe their connection to the decoding of cyclic codes. Finally, we go in-depth into how we decode cyclic codes using the key equation, and how a breakthrough by A. Brinton Cooper on decoding BCH codes using Gr¨obner Bases gave rise to the search for a polynomial-time algorithm that could someday decode any cyclic code. We discuss the different approaches taken toward developing such an algorithm and …

Multi-Valued Solutions For The Equation Of Motion, Darcy-Jordan Model, As A Cauchy Problem: A Shocking Event, Chandler Shimp

Master's Theses

Shocks are physical phenomenon that occur quite often around us. In this thesis we examine the occurrence of shocks in finite amplitude acoustic waves from a numerical perspective. These waves, or jump discontinuities, yield ill-behaved solutions when solved numerically. This study takes on the challenge of finding both single- and multi-valued solutions.

The previously unsolved problem in this study is the representation of the Equation of Motion (EoM) in the form of the Darcy-Jordan model (DJM) and expressed as a dimensionless IVP Cauchy problem. Prior attempts to solve have resulted only in implicit solutions or explicit solutions with certain initial …

The “Knapsack Problem” Workbook: An Exploration Of Topics In Computer Science, Steven Cosares

Open Educational Resources

This workbook provides discussions, programming assignments, projects, and class exercises revolving around the “Knapsack Problem” (KP), which is widely a recognized model that is taught within a typical Computer Science curriculum. Throughout these discussions, we use KP to introduce or review topics found in courses covering topics in Discrete Mathematics, Mathematical Programming, Data Structures, Algorithms, Computational Complexity, etc. Because of the broad range of subjects discussed, this workbook and the accompanying spreadsheet files might be used as part of some CS capstone experience. Otherwise, we recommend that individual sections be used, as needed, for exercises relevant to a course in …

Machine Learning With Topological Data Analysis, Ephraim Robert Love

Doctoral Dissertations

Topological Data Analysis (TDA) is a relatively new focus in the fields of statistics and machine learning. Methods of exploiting the geometry of data, such as clustering, have proven theoretically and empirically invaluable. TDA provides a general framework within which to study topological invariants (shapes) of data, which are more robust to noise and can recover information on higher dimensional features than immediately apparent in the data. A common tool for conducting TDA is persistence homology, which measures the significance of these invariants. Persistence homology has prominent realizations in methods of data visualization, statistics and machine learning. Extending ML with …

Scaling Up Exact Neural Network Compression By Relu Stability, Thiago Serra, Xin Yu, Abhinav Kumar, Srikumar Ramalingam

Faculty Conference Papers and Presentations

We can compress a rectifier network while exactly preserving its underlying functionality with respect to a given input domain if some of its neurons are stable. However, current approaches to determine the stability of neurons with Rectified Linear Unit (ReLU) activations require solving or finding a good approximation to multiple discrete optimization problems. In this work, we introduce an algorithm based on solving a single optimization problem to identify all stable neurons. Our approach is on median 183 times faster than the state-of-art method on CIFAR-10, which allows us to explore exact compression on deeper (5 x 100) and wider …

Optimal Construction Of A Layer-Ordered Heap And Its Applications, Jake Pennington

Graduate Student Theses, Dissertations, & Professional Papers

The layer-ordered heap (LOH) is a simple data structure used in algorithms that perform optimal top-$k$ on $X+Y$, algorithms with the best known runtime for top-$k$ on $X_1+X_2+\cdots+X_m$, and the fastest method in practice for computing the most abundant isotopologue peaks in a chemical compound. In the analysis of these algorithms, the rank, $\alpha$, has been treated as a constant and $n$, the size of the array, has been treated as the sole parameter. Here, we explore the algorithmic complexity of LOH construction with $\alpha$ as a parameter, introduce a few algorithms for constructing LOHs, analyze their complexity in both …

Storage Management Strategy In Mobile Phones For Photo Crowdsensing, En Wang, Zhengdao Qu, Xinyao Liang, Xiangyu Meng, Yongjian Yang, Dawei Li, Weibin Meng

Department of Computer Science Faculty Scholarship and Creative Works

In mobile crowdsensing, some users jointly finish a sensing task through the sensors equipped in their intelligent terminals. In particular, the photo crowdsensing based on Mobile Edge Computing (MEC) collects pictures for some specific targets or events and uploads them to nearby edge servers, which leads to richer data content and more efficient data storage compared with the common mobile crowdsensing; hence, it has attracted an important amount of attention recently. However, the mobile users prefer uploading the photos through Wifi APs (PoIs) rather than cellular networks. Therefore, photos stored in mobile phones are exchanged among users, in order to …

Triple Non-Negative Matrix Factorization Technique For Sentiment Analysis And Topic Modeling, Alexander A. Waggoner

CMC Senior Theses

Topic modeling refers to the process of algorithmically sorting documents into categories based on some common relationship between the documents. This common relationship between the documents is considered the “topic” of the documents. Sentiment analysis refers to the process of algorithmically sorting a document into a positive or negative category depending whether this document expresses a positive or negative opinion on its respective topic. In this paper, I consider the open problem of document classification into a topic category, as well as a sentiment category. This has a direct application to the retail industry where companies may want to scour …

Network Analytics For The Mirna Regulome And Mirna-Disease Interactions, Joseph Jayakar Nalluri

Theses and Dissertations

miRNAs are non-coding RNAs of approx. 22 nucleotides in length that inhibit gene expression at the post-transcriptional level. By virtue of this gene regulation mechanism, miRNAs play a critical role in several biological processes and patho-physiological conditions, including cancers. miRNA behavior is a result of a multi-level complex interaction network involving miRNA-mRNA, TF-miRNA-gene, and miRNA-chemical interactions; hence the precise patterns through which a miRNA regulates a certain disease(s) are still elusive. Herein, I have developed an integrative genomics methods/pipeline to (i) build a miRNA regulomics and data analytics repository, (ii) create/model these interactions into networks and use optimization techniques, motif …

Network Inference Driven Drug Discovery, Gergely Zahoránszky-Kőhalmi, Tudor I. Oprea Md, Phd, Cristian G. Bologa Phd, Subramani Mani Md, Phd, Oleg Ursu Phd

Biomedical Sciences ETDs

The application of rational drug design principles in the era of network-pharmacology requires the investigation of drug-target and target-target interactions in order to design new drugs. The presented research was aimed at developing novel computational methods that enable the efficient analysis of complex biomedical data and to promote the hypothesis generation in the context of translational research. The three chapters of the Dissertation relate to various segments of drug discovery and development process.

The first chapter introduces the integrated predictive drug discovery platform „SmartGraph”. The novel collaborative-filtering based algorithm „Target Based Recommender (TBR)” was developed in the framework of this …

Optimizing The Mix Of Games And Their Locations On The Casino Floor, Jason D. Fiege, Anastasia D. Baran

International Conference on Gambling & Risk Taking

We present a mathematical framework and computational approach that aims to optimize the mix and locations of slot machine types and denominations, plus other games to maximize the overall performance of the gaming floor. This problem belongs to a larger class of spatial resource optimization problems, concerned with optimizing the allocation and spatial distribution of finite resources, subject to various constraints. We introduce a powerful multi-objective evolutionary optimization and data-modelling platform, developed by the presenter since 2002, and show how this software can be used for casino floor optimization. We begin by extending a linear formulation of the casino floor …

Stationary And Time-Dependent Optimization Of The Casino Floor Slot Machine Mix, Anastasia D. Baran, Jason D. Fiege

International Conference on Gambling & Risk Taking

Modeling and optimizing the performance of a mix of slot machines on a gaming floor can be addressed at various levels of coarseness, and may or may not consider time-dependent trends. For example, a model might consider only time-averaged, aggregate data for all machines of a given type; time-dependent aggregate data; time-averaged data for individual machines; or fully time dependent data for individual machines. Fine-grained, time-dependent data for individual machines offers the most potential for detailed analysis and improvements to the casino floor performance, but also suffers the greatest amount of statistical noise. We present a theoretical analysis of single …

Variance Of Clusterings On Graphs, Thomas Vlado Mulc

Mathematical Sciences Technical Reports (MSTR)

Graphs that represent data often have structures or characteristics that can represent some relationships in the data. One of these structures is clusters or community structures. Most clustering algorithms for graphs are deterministic, which means they will output the same clustering each time. We investigated a few stochastic algorithms, and look into the consistency of their clusterings.

Algorithms To Compute Characteristic Classes, Martin Helmer

Electronic Thesis and Dissertation Repository

In this thesis we develop several new algorithms to compute characteristics classes in a variety of settings. In addition to algorithms for the computation of the Euler characteristic, a classical topological invariant, we also give algorithms to compute the Segre class and Chern-Schwartz-MacPherson (CSM) class. These invariants can in turn be used to compute other common invariants such as the Chern-Fulton class (or the Chern class in smooth cases).

We begin with subschemes of a projective space over an algebraically closed field of characteristic zero. In this setting we give effective algorithms to compute the CSM class, Segre class and …

Optimizing The Analysis Of Electroencephalographic Data By Dynamic Graphs, Mehrsasadat Golestaneh

Electronic Thesis and Dissertation Repository

The brain’s underlying functional connectivity has been recently studied using tools offered by graph theory and network theory. Although the primary research focus in this area has so far been mostly on static graphs, the complex and dynamic nature of the brain’s underlying mechanism has initiated the usage of dynamic graphs, providing groundwork for time sensi- tive and finer investigations. Studying the topological reconfiguration of these dynamic graphs is done by exploiting a pool of graph metrics, which describe the network’s characteristics at different scales. However, considering the vast amount of data generated by neuroimaging tools, heavy computation load and …

Construction Algorithms For Expander Graphs, Vlad S. Burca

Senior Theses and Projects

Graphs are mathematical objects that are comprised of nodes and edges that connect them. In computer science they are used to model concepts that exhibit network behaviors, such as social networks, communication paths or computer networks. In practice, it is desired that these graphs retain two main properties: sparseness and high connectivity. This is equivalent to having relatively short distances between two nodes but with an overall small number of edges. These graphs are called expander graphs and the main motivation behind studying them is the efficient network structure that they can produce due to their properties. We are specifically …

Fast Monte Carlo Algorithms For Computing A Low-Rank Approximation To A Matrix, Vlad S. Burca

Senior Theses and Projects

Many of today's applications deal with big quantities of data; from DNA analysis algorithms, to image processing and movie recommendation algorithms. Most of these systems store the data in very large matrices. In order to perform analysis on the collected data, these big matrices have to be stored in the RAM (random-access memory) of the computing system. But this is a very expensive process since RAM is a scarce computational resource. Ideally, one would like to be able to store most of the data matrices on the memory disk (hard disk drive) while loading only the necessary parts of the …

Fast Algorithms For Analyzing Partially Ranked Data, Matthew Mcdermott

HMC Senior Theses

Imagine your local creamery administers a survey asking their patrons to choose their five favorite ice cream flavors. Any data collected by this survey would be an example of partially ranked data, as the set of all possible flavors is only ranked into subsets of the chosen flavors and the non-chosen flavors. If the creamery asks you to help analyze this data, what approaches could you take? One approach is to use the natural symmetries of the underlying data space to decompose any data set into smaller parts that can be more easily understood. In this work, I describe …

A Cauchy Problem For Some Local Fractional Abstract Differential Equation With Fractal Conditions, Yang Xiaojun, Zhong Weiping, Gao Feng

Xiao-Jun Yang

Fractional calculus is an important method for mathematics and engineering [1-24]. In this paper, we review the existence and uniqueness of solutions to the Cauchy problem for the local fractional differential equation with fractal conditions \[ D^\alpha x\left( t \right)=f\left( {t,x\left( t \right)} \right),t\in \left[ {0,T} \right], x\left( {t_0 } \right)=x_0 , \] where $0<\alpha \le 1$ in a generalized Banach space. We use some new tools from Local Fractional Functional Analysis [25, 26] to obtain the results.

The Discrete Yang-Fourier Transforms In Fractal Space, Yang Xiao-Jun

Xiao-Jun Yang

The Yang-Fourier transform (YFT) in fractal space is a generation of Fourier transform based on the local fractional calculus. The discrete Yang-Fourier transform (DYFT) is a specific kind of the approximation of discrete transform, used in Yang-Fourier transform in fractal space. This paper points out new standard forms of discrete Yang-Fourier transforms (DYFT) of fractal signals, and both properties and theorems are investigated in detail.

Expression Of Generalized Newton Iteration Method Via Generalized Local Fractional Taylor Series, Yang Xiao-Jun

Xiao-Jun Yang

Local fractional derivative and integrals are revealed as one of useful tools to deal with everywhere continuous but nowhere differentiable functions in fractal areas ranging from fundamental science to engineering. In this paper, a generalized Newton iteration method derived from the generalized local fractional Taylor series with the local fractional derivatives is reviewed. Operators on real line numbers on a fractal space are induced from Cantor set to fractional set. Existence for a generalized fixed point on generalized metric spaces may take place.

The Zero-Mass Renormalization Group Differential Equations And Limit Cycles In Non-Smooth Initial Value Problems, Yang Xiaojun

Xiao-Jun Yang

In the present paper, using the equation transform in fractal space, we point out the zero-mass renormalization group equations. Under limit cycles in the non-smooth initial value, we devote to the analytical technique of the local fractional Fourier series for treating zero-mass renormalization group equations, and investigate local fractional Fourier series solutions.

A Novel Approach To Processing Fractal Dynamical Systems Using The Yang-Fourier Transforms, Yang Xiaojun

Xiao-Jun Yang

In the present paper, local fractional continuous non-differentiable functions in fractal space are investigated, and the control method for processing dynamic systems in fractal space are proposed using the Yang-Fourier transform based on the local fractional calculus. Two illustrative paradigms for control problems in fractal space are given to elaborate the accuracy and reliable results.

Theory And Applications Of Local Fractional Fourier Analysis, Yang Xiaojun

Xiao-Jun Yang

Local fractional Fourier analysis is a generalized Fourier analysis in fractal space. The local fractional calculus is one of useful tools to process the local fractional continuously non-differentiable functions (fractal functions). Based on the local fractional derivative and integration, the present work is devoted to the theory and applications of local fractional Fourier analysis in generalized Hilbert space. We investigate the local fractional Fourier series, the Yang-Fourier transform, the generalized Yang-Fourier transform, the discrete Yang-Fourier transform and fast Yang-Fourier transform.

Heat Transfer In Discontinuous Media, Yang Xiaojun

Xiao-Jun Yang

From the fractal geometry point of view, the interpretations of local fractional derivative and local fractional integration are pointed out in this paper. It is devoted to heat transfer in discontinuous media derived from local fractional derivative. We investigate the Fourier law and heat conduction equation (also local fractional instantaneous heat conduct equation) in fractal orthogonal system based on cantor set, and extent them. These fractional differential equations are described in local fractional derivative sense. The results are efficiently developed in discontinuous media.

A Short Note On Local Fractional Calculus Of Function Of One Variable, Yang Xiaojun

Xiao-Jun Yang

Local fractional calculus (LFC) handles everywhere continuous but nowhere differentiable functions in fractal space. This note investigates the theory of local fractional derivative and integral of function of one variable. We first introduce the theory of local fractional continuity of function and history of local fractional calculus. We then consider the basic theory of local fractional derivative and integral, containing the local fractional Rolle’s theorem, L’Hospital’s rule, mean value theorem, anti-differentiation and related theorems, integration by parts and Taylor’ theorem. Finally, we study the efficient application of local fractional derivative to local fractional extreme value of non-differentiable functions, and give …

A New Successive Approximation To Non-Homogeneous Local Fractional Volterra Equation, Yang Xiaojun

Xiao-Jun Yang

A new successive approximation approach to the non-homogeneous local fractional Valterra equation derived from local fractional calculus is proposed in this paper. The Valterra equation is described in local fractional integral operator. The theory of local fractional derivative and integration is one of useful tools to handle the fractal and continuously non-differentiable functions, was successfully applied in engineering problem. We investigate an efficient example of handling a non-homogeneous local fractional Valterra equation.

Advanced Local Fractional Calculus And Its Applications, Yang Xiaojun

Xiao-Jun Yang

This book is the first international book to study theory and applications of local fractional calculus (LFC). It is an invitation both to the interested scientists and the engineers. It presents a thorough introduction to the recent results of local fractional calculus. It is also devoted to the application of advanced local fractional calculus on the mathematics science and engineering problems. The author focuses on multivariable local fractional calculus providing the general framework. It leads to new challenging insights and surprising correlations between fractal and fractional calculus. Keywords: Fractals - Mathematical complexity book - Local fractional calculus- Local fractional partial …