Theory and Algorithms Commons^™

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 …

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 …

Randomized Algorithms And How Society Uses Them Everyday, Rosaley Milano

Undergraduate Honors Thesis Projects

Randomness is an interesting and very beneficial phenomenon. In computer science randomness facilitates great advances in efficiency but topics like randomized algorithms aren’t taught until someone enters graduate school. This paper provides undergraduates as well as people unacquainted with computer science an opportunity to explore the topic of randomness by guiding them from essential topics all the way through the graduate level topic of randomized algorithms. Topics like what an algorithm is, how they are represented and the history that brought them into existence bring the reader up to speed before diving deeper into randomized algorithms. A discussion of complexity …

Designing Fractal Line Pied-De-Poules: A Case Study In Algorithmic Design Mediating Between Culture And Fractal Mathematics, Loe M.G. Feijs

Journal of Humanistic Mathematics

Millions of people own and wear pied-de-poule (houndstooth) garments. The pattern has an intriguing basic figure and a typical set of symmetries. The origin of the pattern lies in a specific type of weaving. In this article I apply computational techniques to modernize this ancient decorative pattern. In particular I describe a way to enrich pied-de-poule with a fractal structure.

Although a first fractal line pied-de-poule was shown at Bridges 2015, a number of fundamental questions still remained. The following questions are addressed in this article: Does the original pied-de-poule appear as a limit case when the fractal structure is …

Gröbner Bases And Systems Of Polynomial Equations, Rachel Holmes

All Graduate Theses, Dissertations, and Other Capstone Projects

This paper will explore the use and construction of Gröbner bases through Buchberger's algorithm. Specifically, applications of such bases for solving systems of polynomial equations will be discussed. Furthermore, we relate many concepts in commutative algebra to ideas in computational algebraic geometry.

A Mathematical Analysis Of The Game Of Santorini, Carson Clyde Geissler

Senior Independent Study Theses

Santorini is a two player combinatorial board game. Santorini bears resemblance to the graph theory game of Geography, a game of moving and deleting vertices on a graph. We explore Santorini with game theory, complexity theory, and artificial intelligence. We present David Lichtenstein’s proof that Geography is PSPACE-hard and adapt the proof for generalized forms of Santorini. Last, we discuss the development of an AI built for a software implementation of Santorini and present a number of improvements to that AI.

Invariance And Invertibility In Deep Neural Networks, Han Zhang

Theses and Dissertations

Machine learning is concerned with computer systems that learn from data instead of being explicitly programmed to solve a particular task. One of the main approaches behind recent advances in machine learning involves neural networks with a large number of layers, often referred to as deep learning. In this dissertation, we study how to equip deep neural networks with two useful properties: invariance and invertibility. The first part of our work is focused on constructing neural networks that are invariant to certain transformations in the input, that is, some outputs of the network stay the same even if the input …

Maximality And Applications Of Subword-Closed Languages, Rhys Davis Jones

UNF Graduate Theses and Dissertations

Characterizing languages D that are maximal with the property that D^* ⊆ S^⊗ is an important problem in formal language theory with applications to coding theory and DNA codewords. Given a finite set of words of a fixed length S, the constraint, we consider its subword closure, S^⊗, the set of words whose subwords of that fixed length are all in the constraint. We investigate these maximal languages and present characterizations for them. These characterizations use strongly connected components of deterministic finite automata and lead to polynomial time algorithms for generating such languages. We prove that …

Hybrid Recommender Systems Via Spectral Learning And A Random Forest, Alyssa Williams

Electronic Theses and Dissertations

We demonstrate spectral learning can be combined with a random forest classifier to produce a hybrid recommender system capable of incorporating meta information. Spectral learning is supervised learning in which data is in the form of one or more networks. Responses are predicted from features obtained from the eigenvector decomposition of matrix representations of the networks. Spectral learning is based on the highest weight eigenvectors of natural Markov chain representations. A random forest is an ensemble technique for supervised learning whose internal predictive model can be interpreted as a nearest neighbor network. A hybrid recommender can be constructed by first …

Testing Isomorphism Of Graded Algebras, Peter A. Brooksbank, James B. Wilson, Eamonn A. O'Brien

Faculty Journal Articles

We present a new algorithm to decide isomorphism between finite graded algebras. For a broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the order of the input algebras. We introduce heuristics that often dramatically improve the performance of the algorithm and report on an implementation in Magma.

Some Theoretical Links Between Shortest Path Filters And Minimum Spanning Tree Filters, Sravan Danda, Aditya Challa, B. S.Daya Sagar, Laurent Najman

Journal Articles

Edge-aware filtering is an important pre-processing step in many computer vision applications. In the literature, there exist several versions of collaborative edge-aware filters based on spanning trees and shortest path heuristics which work well in practice. For instance, tree filter (TF) which is recently proposed based on a minimum spanning tree (MST) heuristic yields promising results in many filtering applications. However, links between the tree-based filters and shortest path-based filters are faintly explored. In this article, we introduce an edge-aware generalization of the TF termed as UMST filter based on a subgraph generated by edges of all MSTs. The major …

Pascal's Triangle Modulo N And Its Applications To Efficient Computation Of Binomial Coefficients, Zachary Warneke

Honors Program: Senior Projects (Public)

In this thesis, Pascal's Triangle modulo n will be explored for n prime and n a prime power. Using the results from the case when n is prime, a novel proof of Lucas' Theorem is given. Additionally, using both the results from the exploration of Pascal's Triangle here, as well as previous results, an efficient algorithm for computation of binomial coefficients modulo n (a choose b mod n) is described, and its time complexity is analyzed and compared to naive methods. In particular, the efficient algorithm runs in O(n log(a)) time (as opposed to …

Improving Vix Futures Forecasts Using Machine Learning Methods, James Hosker, Slobodan Djurdjevic, Hieu Nguyen, Robert Slater

SMU Data Science Review

The problem of forecasting market volatility is a difficult task for most fund managers. Volatility forecasts are used for risk management, alpha (risk) trading, and the reduction of trading friction. Improving the forecasts of future market volatility assists fund managers in adding or reducing risk in their portfolios as well as in increasing hedges to protect their portfolios in anticipation of a market sell-off event. Our analysis compares three existing financial models that forecast future market volatility using the Chicago Board Options Exchange Volatility Index (VIX) to six machine/deep learning supervised regression methods. This analysis determines which models provide best …

Squared Distance Matrix Of A Weighted Tree, Ravindra B. Bapat

Journal Articles

Let T be a tree with vertex set f1;: :: ; ng such that each edge is assigned a nonzero weight. The squared distance matrix of T; denoted by is the n n matrix with (i; j)-element d(i; j)2; where d(i; j) is the sum of the weights of the edges on the (ij)-path. We obtain a formula for the determinant of A formula for 1 is also obtained, under certain conditions. The results generalize known formulas for the unweighted case.

Statistical Analysis Of Tandem Queues With Markovian Passages In Porous Mediums, Gboyega David Adepoju

Theses, Dissertations and Capstones

Queuing theory is the mathematical study of queues or waiting lines. A queue is formed whenever the demand for service exceeds the capacity to provide service at that point in time. In this thesis, the birth-and-death process is used to model the movement of customers or units into and out of a network of queues in tandem. We start with the theoretical analysis of M/M/1 queues with Poisson arrival and exponential service time with first-come first-served (FCFS) discipline and one service station. We derive the global balance equation for each network. Using both the iterative and the probability generating function, …

Modeling Stochastically Intransitive Relationships In Paired Comparison Data, Ryan Patrick Alexander Mcshane

Statistical Science Theses and Dissertations

If the Warriors beat the Rockets and the Rockets beat the Spurs, does that mean that the Warriors are better than the Spurs? Sophisticated fans would argue that the Warriors are better by the transitive property, but could Spurs fans make a legitimate argument that their team is better despite this chain of evidence?

We first explore the nature of intransitive (rock-scissors-paper) relationships with a graph theoretic approach to the method of paired comparisons framework popularized by Kendall and Smith (1940). Then, we focus on the setting where all pairs of items, teams, players, or objects have been compared to …

Revisiting The Isoperimetric Graph Partitioning Problem, Sravan Danda, Aditya Challa, B. S. Daya Sagar, Laurent Najman

Journal Articles

Isoperimetric graph partitioning, which is also known as the Cheeger cut, is NP-hard in its original form. In the literature, multiple modifications to this problem have been proposed to obtain approximation algorithms for clustering applications. In the context of image segmentation, a heuristic continuous relaxation to this problem introduced by Leo Grady and Eric L. Schwartz has yielded good quality results. This algorithm is based on solving a linear system of equations involving the Laplacian of the image graph. Furthermore, the same algorithm applied to a maximum spanning tree (MST) of the image graph was shown to produce similar results …

On Hybrid Temporal Basis Functions For Stable Numerical Solution Of Time Domain Boundary Integral Equations, Fang Q. Hu

Mathematics & Statistics Faculty Publications

Problems in unsteady aerodynamics and aeroacoustics can sometimes be formulated as integral equations, such as the boundary integral equations. Numerical discretization of integral equations in the time domain often leads to so-called March-On-in-Time (MOT) schemes. In the literature, the temporal basis functions used in MOT schemes have been largely limited to low-order shifted Lagrange basis functions. In order to evaluate the accuracy and effectiveness of the temporal basis functions, a Fourier analysis of the temporal interpolation schemes is carried out. Based on the Fourier analysis, the spectral resolutions of various temporal basis functions are quantified. It is argued that hybrid …

The Chapman Bone Algorithm: A Diagnostic Alternative For The Evaluation Of Osteoporosis, Elise Levesque, Anton Ketterer, Wajiha Memon, Cameron James, Noah Barrett, Cyril Rakovski, Frank Frisch

Mathematics, Physics, and Computer Science Faculty Articles and Research

Osteoporosis is the most common metabolic bone disease and goes largely undiagnosed throughout the world, due to the inaccessibility of DXA machines. Multivariate analyses of serum bone turnover markers were evaluated in 226 Orange County, California, residents with the intent to determine if serum osteocalcin and serum pyridinoline cross-links could be used to detect the onset of osteoporosis as effectively as a DXA scan. Descriptive analyses of the demographic and lab characteristics of the participants were performed through frequency, means and standard deviation estimations. We implemented logistic regression modeling to find the best classification algorithm for osteoporosis. All calculations and …

Multi Self-Adapting Particle Swarm Optimization Algorithm (Msapso)., Gerhard Koch

Electronic Theses and Dissertations

The performance and stability of the Particle Swarm Optimization algorithm depends on parameters that are typically tuned manually or adapted based on knowledge from empirical parameter studies. Such parameter selection is ineffectual when faced with a broad range of problem types, which often hinders the adoption of PSO to real world problems. This dissertation develops a dynamic self-optimization approach for the respective parameters (inertia weight, social and cognition). The effects of self-adaption for the optimal balance between superior performance (convergence) and the robustness (divergence) of the algorithm with regard to both simple and complex benchmark functions is investigated. This work …

Efficient Reduced Bias Genetic Algorithm For Generic Community Detection Objectives, Aditya Karnam Gururaj Rao

Theses

The problem of community structure identification has been an extensively investigated area for biology, physics, social sciences, and computer science in recent years for studying the properties of networks representing complex relationships. Most traditional methods, such as K-means and hierarchical clustering, are based on the assumption that communities have spherical configurations. Lately, Genetic Algorithms (GA) are being utilized for efficient community detection without imposing sphericity. GAs are machine learning methods which mimic natural selection and scale with the complexity of the network. However, traditional GA approaches employ a representation method that dramatically increases the solution space to be searched by …

Quantum Attacks On Modern Cryptography And Post-Quantum Cryptosystems, Zachary Marron

Senior Honors Theses

Cryptography is a critical technology in the modern computing industry, but the security of many cryptosystems relies on the difficulty of mathematical problems such as integer factorization and discrete logarithms. Large quantum computers can solve these problems efficiently, enabling the effective cryptanalysis of many common cryptosystems using such algorithms as Shor’s and Grover’s. If data integrity and security are to be preserved in the future, the algorithms that are vulnerable to quantum cryptanalytic techniques must be phased out in favor of quantum-proof cryptosystems. While quantum computer technology is still developing and is not yet capable of breaking commercial encryption, these …

Understanding Natural Keyboard Typing Using Convolutional Neural Networks On Mobile Sensor Data, Travis Siems

Computer Science and Engineering Theses and Dissertations

Mobile phones and other devices with embedded sensors are becoming increasingly ubiquitous. Audio and motion sensor data may be able to detect information that we did not think possible. Some researchers have created models that can predict computer keyboard typing from a nearby mobile device; however, certain limitations to their experiment setup and methods compelled us to be skeptical of the models’ realistic prediction capability. We investigate the possibility of understanding natural keyboard typing from mobile phones by performing a well-designed data collection experiment that encourages natural typing and interactions. This data collection helps capture realistic vulnerabilities of the security …

Gradient Estimation For Attractor Networks, Thomas Flynn

Dissertations, Theses, and Capstone Projects

It has been hypothesized that neural network models with cyclic connectivity may be more powerful than their feed-forward counterparts. This thesis investigates this hypothesis in several ways. We study the gradient estimation and optimization procedures for several variants of these networks. We show how the convergence of the gradient estimation procedures are related to the properties of the networks. Then we consider how to tune the relative rates of gradient estimation and parameter adaptation to ensure successful optimization in these models. We also derive new gradient estimators for stochastic models. First, we port the forward sensitivity analysis method to the …

Extensions Of The Morse-Hedlund Theorem, Eben Blaisdell

Honors Theses

Bi-infinite words are sequences of characters that are infinite forwards and backwards; for example "...ababababab...". The Morse-Hedlund theorem says that a bi-infinite word f repeats itself, in at most n letters, if and only if the number of distinct subwords of length n is at most n. Using the example, "...ababababab...", there are 2 subwords of length 3, namely "aba" and "bab". Since 2 is less than 3, we must have that "...ababababab..." repeats itself after at most 3 letters. In fact it does repeat itself every two letters. …

Logic -> Proof -> Rest, Maxwell Taylor

Senior Independent Study Theses

REST is a common architecture for networked applications. Applications that adhere to the REST constraints enjoy significant scaling advantages over other architectures. But REST is not a panacea for the task of building correct software. Algebraic models of computation, particularly CSP, prove useful to describe the composition of applications using REST. CSP enables us to describe and verify the behavior of RESTful systems. The descriptions of each component can be used independently to verify that a system behaves as expected. This thesis demonstrates and develops CSP methodology to verify the behavior of RESTful applications.

Optimal Layout For A Component Grid, Michael W. Ebert

Computer Science and Software Engineering

Several puzzle games include a specific type of optimization problem: given components that produce and consume different resources and a grid of squares, find the optimal way to place the components to maximize output. I developed a method to evaluate potential solutions quickly and automated the solving of the problem using a genetic algorithm.

Morphogenesis And Growth Driven By Selection Of Dynamical Properties, Yuri Cantor

Dissertations, Theses, and Capstone Projects

Organisms are understood to be complex adaptive systems that evolved to thrive in hostile environments. Though widely studied, the phenomena of organism development and growth, and their relationship to organism dynamics is not well understood. Indeed, the large number of components, their interconnectivity, and complex system interactions all obscure our ability to see, describe, and understand the functioning of biological organisms.

Here we take a synthetic and computational approach to the problem, abstracting the organism as a cellular automaton. Such systems are discrete digital models of real-world environments, making them more accessible and easier to study then their physical world …

Vertex Weighted Spectral Clustering, Mohammad Masum

Electronic Theses and Dissertations

Spectral clustering is often used to partition a data set into a specified number of clusters. Both the unweighted and the vertex-weighted approaches use eigenvectors of the Laplacian matrix of a graph. Our focus is on using vertex-weighted methods to refine clustering of observations. An eigenvector corresponding with the second smallest eigenvalue of the Laplacian matrix of a graph is called a Fiedler vector. Coefficients of a Fiedler vector are used to partition vertices of a given graph into two clusters. A vertex of a graph is classified as unassociated if the Fiedler coefficient of the vertex is close to …

An Analysis Of The Application Of Simplified Silhouette To The Evaluation Of K-Means Clustering Validity, Fei Wang, Hector-Hugo Franco-Penya, John D. Kelleher, John Pugh, Robert J. Ross

Conference papers

Silhouette is one of the most popular and effective internal measures for the evaluation of clustering validity. Simplified Silhouette is a computationally simplified version of Silhouette. However, to date Simplified Silhouette has not been systematically analysed in a specific clustering algorithm. This paper analyses the application of Simplified Silhouette to the evaluation of k-means clustering validity and compares it with the k-means Cost Function and the original Silhouette from both theoretical and empirical perspectives. The theoretical analysis shows that Simplified Silhouette has a mathematical relationship with both the k-means Cost Function and the original Silhouette, while empirically, we show that …