Mathematics Commons^™

Leveraging Model Flexibility And Deep Structure: Non-Parametric And Deep Models For Computer Vision Processes With Applications To Deep Model Compression, Anthony D. Rhodes

Dissertations and Theses

My dissertation presents several new algorithms incorporating non-parametric and deep learning approaches for computer vision and related tasks, including object localization, object tracking and model compression. With respect to object localization, I introduce a method to perform active localization by modeling spatial and other relationships between objects in a coherent "visual situation" using a set of probability distributions. I further refine this approach with the Multipole Density Estimation with Importance Clustering (MIC-Situate) algorithm. Next, I formulate active, "situation" object search as a Bayesian optimization problem using Gaussian Processes. Using my Gaussian Process Context Situation Learning (GP-CL) algorithm, I demonstrate improved …

Absence Of Remotely Triggered Large Earthquakes: A Geometric Explanation, Laxman Bokati, Aaron A. Velasco, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that seismic waves from a large earthquake can trigger earthquakes in distant locations. Some of the triggered earthquakes are strong themselves. Interestingly, strong triggered earthquakes only happen within a reasonably small distance (less than 1000 km) from the original earthquake. Even catastrophic earthquakes do not trigger any strong earthquakes beyond this distance. In this paper, we provide a possible geometric explanation for this phenomenon.

The Two Types Of Society: Computationally Revealing Recurrent Social Formations And Their Evolutionary Trajectories, Lux Miranda

Undergraduate Honors Capstone Projects

Comparative social science has a long history of attempts to classify societies and cultures in terms of shared characteristics. However, only recently has it become feasible to conduct quantitative analysis of large historical datasets to mathematically approach the study of social complexity and classify shared societal characteristics. Such methods have the potential to identify recurrent social formations in human societies and contribute to social evolutionary theory. However, in order to achieve this potential, repeated studies are needed to assess the robustness of results to changing methods and data sets. Using an improved derivative of the Seshat: Global History Databank, we …

Novel Inference Methods For Generalized Linear Models Using Shrinkage Priors And Data Augmentation., Arinjita Bhattacharyya

Electronic Theses and Dissertations

Generalized linear models have broad applications in biostatistics and sociology. In a regression setup, the main target is to find a relevant set of predictors out of a large collection of covariates. Sparsity is the assumption that only a few of these covariates in a regression setup have a meaningful correlation with an outcome variate of interest. Sparsity is incorporated by regularizing the irrelevant slopes towards zero without changing the relevant predictors and keeping the resulting inferences intact. Frequentist variable selection and sparsity are addressed by popular techniques like Lasso, Elastic Net. Bayesian penalized regression can tackle the curse of …

Volume 12, Haleigh James, Hannah Meyls, Hope Irvin, Megan E. Hlavaty, Samara L. Gall, Austin J. Funk, Karyn Keane, Sarah Ghali, Antonio Harvey, Andrew Jones, Rachel Hazelwood, Madison Schmitz, Marija Venta, Haley Tebo, Jeremiah Gilmer, Bridget Dunn, Benjamin Sullivan, Mckenzie Johnson

Incite: The Journal of Undergraduate Scholarship

Introduction, Dr. Roger A. Byrne, Dean

From the Editor, Dr. Larissa "Kat" Tracy

From the Designers, Rachel English, Rachel Hanson

Immortality in the Mortal World: Otherworldly Intervention in "Lanval" and "The Wife of Bath's Tale" by Haleigh James

Analysis of Phenolic Compounds in Moroccan Olive Oils by HPLC by Hannah Meyls

Art by Hope Irvin

The Effects of Cell Phone Use on Gameplay Enjoyment and Frustration by Megan E. Hlavaty, Samara L. Gall, and Austin J. Funk

Care, No Matter What: Planned Parenthood's Use of Organizational Rhetoric to Expand its Reputation by Karyn Keane

Analysis of Petroleum Products for …

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 …

Reliability Improvement On Feasibility Study For Selection Of Infrastructure Projects Using Data Mining And Machine Learning, Xi Hu

Theses and Dissertations

With the progressive development of infrastructure construction, conventional analytical methods such as correlation index, quantifying factors, and peer review are no longer satisfactory in support for decision-making of implementing an infrastructure project in the age of big data. This study proposes using a mathematical model named Fuzzy-Neural Comprehensive Evaluation Model (FNCEM) to improve the reliability of the feasibility study of infrastructure projects by using data mining and machine learning. Specifically, the data collection on time-series data, including traffic videos (278 Gigabytes) and historical weather data, uses transportation cameras and online searching, respectively. Meanwhile, the researcher sent out a questionnaire for …

Simulation Environment For Object Manipulation With Soft Robots In Shared Autonomy, Devin Hunter, Fabio Stroppa, Allison Okamura

Showcase of Osprey Advancements in Research and Scholarship (SOARS)

The robots of today have grown to be of much more significant use than their predecessors. Robots are now being used in industries outside of the factory setting which can be seen primarily in the medical, transportation, and social fields. With robots taking on all of these new roles within our society, the establishment of robust human-robot collaboration is crucial in order for robots to be able to successfully complete desired tasks without becoming a hinderance to nearby humans. We explored this concept by implementing a shared-autonomy algorithm named MBSA (Motion Based Smart Assistance) to a soft robot simulation and …

Preparing For The Future: The Effects Of Financial Literacy On Financial Planning For Young Professionals, Tanay Singh

Senior Theses

Purpose – Many people between the age of 20 and 34 have not considered planning financially for the future in any significant capacity and in doing so, they limit their potential savings. The purpose of this study is to examine what financial expectations are for people in the early stages of their career and determine if improving financial literacy and revealing financial realities helps to produce more accurate or realistic expectations. Ultimately, the goal is to better prepare participants in the study for the working world and increased responsibilities outside of the college/university environment by getting them to start thinking …

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 …

Underwater Gesture Recognition Using Classical Computer Vision And Deep Learning Techniques, Mygel Andrei M. Martija, Jakov Ivan S. Dumbrique, Prospero C. Naval Jr.

Mathematics Faculty Publications

Underwater Gesture Recognition is a challenging task since conditions which are normally not an issue in gesture recognition on land must be considered. Such issues include low visibility, low contrast, and unequal spectral propagation. In this work, we explore the underwater gesture recognition problem by taking on the recently released Cognitive Autonomous Diving Buddy Underwater Gestures dataset. The contributions of this paper are as follows: (1) Use traditional computer vision techniques along with classical machine learning to perform gesture recognition on the CADDY dataset; (2) Apply deep learning using a convolutional neural network to solve the same problem; (3) Perform …

Approximation And Computational Complexity Of Some Hammock Variations Of The Poset Cover Problem, Ivy Ordanel, Proceso L. Fernandez Jr, Richelle Ann B. Juayong, Henry N. Adorna

Department of Information Systems & Computer Science Faculty Publications

The Hammock(⏟𝟐, 𝟐 , … , 𝟐 / 𝒌 )-Poset Cover Problem is a variation of the Poset Cover Problem with the same input – set {𝑳_𝟏, 𝑳_𝟐, … , 𝑳_𝒎} of linear orders over the set {𝟏, 𝟐, … ,𝒏}, but the solution is restricted to a set of simple hammock(𝟐⏟, 𝟐 , … , 𝟐 / 𝒌 ) posets. The problem is NP-Hard when 𝒌 ≥ 𝟑 but is in 𝑷 when 𝒌 = 𝟏. The computational complexity of the problem when 𝒌 = 𝟐 is not yet known. In this paper, …

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 …

A Description Of A Humans Knowledge Using Artificial Intelligence, Dj Price

Mahurin Honors College Capstone Experience/Thesis Projects

There currently does not exist a way to easily view the relationships between a collection of written items (e.g. sports articles, diary entries, research papers). In recent years, novel machine learning methods have been developed which are very good at extracting semantic relationships from large numbers of documents. One of them is the (unsupervised) machine learning model Doc2Vec which constructs vectors for documents. The research project detailed in this paper uses this and other already existing algorithms to analyze the relationship between pieces of text. We set forth a broader ambition for this project before discussing the use and need …

The Mathematics, Computer Science, And Data Science Student Research Showcase, Seton Hall University

Petersheim Academic Exposition

No abstract provided.

Petersheim Academic Exposition 2020 Math & Computer Science Abstracts, Seton Hall University

Petersheim Academic Exposition

No abstract provided.

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 Cool Brisk Walk Through Discrete Mathematics, Stephen Davies

Computer Science Articles

A Cool Brisk Walk Through Discrete Mathematics - and its companion site "allthemath" - are completely-and-forever-free-and-open-source educational materials dedicated to the mathematics that budding computer science practitioners actually need to know. They feature the fun and addictive teaching of award-winning lecturer Dr. Stephen Davies of the University of Mary Washington in Fredericksburg, Virginia!

Psu At Clef-2020 Arqmath Track: Unsupervised Re-Ranking Using Pretraining, Shaurya Rohatgi, Jian Wu, C. Lee Giles

Computer Science Faculty Publications

This paper elaborates on our submission to the ARQMath track at CLEF 2020. Our primary run for the main Task-1: Question Answering uses a two-stage retrieval technique in which the first stage is a fusion of traditional BM25 scoring and tf-idf with cosine similarity-based retrieval while the second stage is a finer re-ranking technique using contextualized embeddings. For the re-ranking we use a pre-trained robertabase model (110 million parameters) to make the language model more math-aware. Our approach achieves a higher NDCG0 score than the baseline, while our MAP and P@10 scores are competitive, performing better than the best submission …

Multiplicative Noise Removal: Nonlocal Low-Rank Model And It's Proximal Alternating Reweighted Minimization Algorithm, Xiaoxia Liu, Jian Lu, Lixin Shen, Chen Xu, Yuesheng Xu

Mathematics & Statistics Faculty Publications

The goal of this paper is to develop a novel numerical method for efficient multiplicative noise removal. The nonlocal self-similarity of natural images implies that the matrices formed by their nonlocal similar patches are low-rank. By exploiting this low-rank prior with application to multiplicative noise removal, we propose a nonlocal low-rank model for this task and develop a proximal alternating reweighted minimization (PARM) algorithm to solve the optimization problem resulting from the model. Specifically, we utilize a generalized nonconvex surrogate of the rank function to regularize the patch matrices and develop a new nonlocal low-rank model, which is a nonconvex …

Remark On Artificial Intelligence, Humanoid And Terminator Scenario: A Neutrosophic Way To Futurology, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This article is an update of our previous article in this SGJ journal, titled: On Gödel's Incompleteness Theorem, Artificial Intelligence & Human Mind [7]. We provide some commentary on the latest developments around AI, humanoid robotics, and future scenario. Basically, we argue that a more thoughtful approach to the future is "technorealism."

A Computational Study Of Binary Linear And Quadratic Programming And Solvers, William Cody Mackelfresh

Graduate Research Theses & Dissertations

In this thesis we study and compare computational capability of two solvers, Gurobi and BiqCrunch, and their capabilities to solve various binary quadratic and linear programming problems. We review two types of programming models for three types of combinatorial optimization problems, namely Max-Cut, Max Independent Set, and Max-$k$-Cluster. We also review the Reformulation-Linearization Technique (RLT) and Semidefinite Programming (SDP) approaches for solving these models, go over the software and hardware used to solve these problems, and finally review the numerical results obtained by solving the problems.

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 …

Biasing Medial Axis Rapidly-Exploring Random Trees With Safe Hyperspheres, David Qin

Honors Theses

Motion planning is a challenging and widely researched problem in robotics. Motion planning algorithms aim to not only nd unobstructed paths, but also to construct paths with certain qualities, such as maximally avoiding obstacles to improve path safety. One such solution is a Rapidly-Exploring Random Tree (RRT) variant called Medial Axis RRT that generates the safest possible paths, but does so slowly. This paper introduces a RRT variant called Medial Axis Ball RRT (MABallRRT) that uses the concept of clearance -- a robot's distance from its nearest obstacle -- to efficiently construct a roadmap with safe paths. The safety of …

Fast Medial Axis Sampling For Use In Motion Planning, Hanglin Zhou

Honors Theses

Motion planning is a difficult but important problem in robotics. Research has tended toward approximations and randomized algorithms, like sampling-based planning. Probabilistic RoadMaps (PRMs) are one common sampling-based planning approach, but they lack safety guarantees. One main approach, Medial Axis PRM (MAPRM) addressed this deficiency by generating robot configurations as far away from the obstacles as possible, but it introduced an extensive computational burden. We present two techniques, Medial Axis Bridge and Medial Axis Spherical Step, to reduce the computational cost of sampling in MAPRM and additionally propose recycling previously computed clearance information to reduce the cost of connection in …

Computer-Assisted Coloring-Graph Generation And Structural Analysis, Wesley Su

Honors Theses

Graphs are a well studied construction in discrete math, with one of the most common areas of study being graph coloring. The graph coloring problem asks for a color to be assigned to each vertex in a graph such that no two adjacent vertices share a color. An assignment of k colors that meets these criteria is called a k-coloring. The coloring graph Ck(G) is defined as the graph where every vertex represents a valid k-coloring of graph G and edges exist between colorings that di↵er by one vertex. We call graph G the base graph of the k-coloring graph …

Artificial Neural Network Models For Pattern Discovery From Ecg Time Series, Mehakpreet Kaur

College of Graduate Studies: Theses & Dissertations

Artificial Neural Network (ANN) models have recently become de facto models for deep learning with a wide range of applications spanning from scientific fields such as computer vision, physics, biology, medicine to social life (suggesting preferred movies, shopping lists, etc.). Due to advancements in computer technology and the increased practice of Artificial Intelligence (AI) in medicine and biological research, ANNs have been extensively applied not only to provide quick information about diseases, but also to make diagnostics accurate and cost-effective. We propose an ANN-based model to analyze a patient's electrocardiogram (ECG) data and produce accurate diagnostics regarding possible heart diseases …

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 …