Other Mathematics Commons^™

Reducing Uncertainty In Sea-Level Rise Prediction: A Spatial-Variability-Aware Approach, Subhankar Ghosh, Shuai An, Arun Sharma, Jayant Gupta, Shashi Shekhar, Aneesh Subramanian

I-GUIDE Forum

Given multi-model ensemble climate projections, the goal is to accurately and reliably predict future sea-level rise while lowering the uncertainty. This problem is important because sea-level rise affects millions of people in coastal communities and beyond due to climate change's impacts on polar ice sheets and the ocean. This problem is challenging due to spatial variability and unknowns such as possible tipping points (e.g., collapse of Greenland or West Antarctic ice-shelf), climate feedback loops (e.g., clouds, permafrost thawing), future policy decisions, and human actions. Most existing climate modeling approaches use the same set of weights globally, during either regression or …

The History Of The Enigma Machine, Jenna Siobhan Parkinson

History Publications

The history of the Enigma machine begins with the invention of the rotor-based cipher machine in 1915. Various models for rotor-based cipher machines were developed somewhat simultaneously in different parts of the world. However, the first documented rotor machine was developed by Dutch naval officers in 1915. Nonetheless, the Enigma machine was officially invented following the end of World War I by Arthur Scherbius in 1918 (Faint, 2016).

Using Graph Theoretical Methods And Traceroute To Visually Represent Hidden Networks, Jordan M. Sahs

UNO Student Research and Creative Activity Fair

Within the scope of a Wide Area Network (WAN), a large geographical communication network in which a collection of networking devices communicate data to each other, an example being the spanning communication network, known as the Internet, around continents. Within WANs exists a collection of Routers that transfer network packets to other devices. An issue pertinent to WANs is their immeasurable size and density, as we are not sure of the amount, or the scope, of all the devices that exists within the network. By tracing the routes and transits of data that traverses within the WAN, we can identify …

Realtime Event Detection In Sports Sensor Data With Machine Learning, Mallory Cashman

Honors Theses and Capstones

Machine learning models can be trained to classify time series based sports motion data, without reliance on assumptions about the capabilities of the users or sensors. This can be applied to predict the count of occurrences of an event in a time period. The experiment for this research uses lacrosse data, collected in partnership with SPAITR - a UNH undergraduate startup developing motion tracking devices for lacrosse. Decision Tree and Support Vector Machine (SVM) models are trained and perform with high success rates. These models improve upon previous work in human motion event detection and can be used a reference …

Local-Global Results On Discrete Structures, Alexander Lewis Stevens

Electronic Theses and Dissertations

Local-global arguments, or those which glean global insights from local information, are central ideas in many areas of mathematics and computer science. For instance, in computer science a greedy algorithm makes locally optimal choices that are guaranteed to be consistent with a globally optimal solution. On the mathematical end, global information on Riemannian manifolds is often implied by (local) curvature lower bounds. Discrete notions of graph curvature have recently emerged, allowing ideas pioneered in Riemannian geometry to be extended to the discrete setting. Bakry- Émery curvature has been one such successful notion of curvature. In this thesis we use combinatorial …

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 …

Optimizing Networking Topologies With Shortest Path Algorithms, Jordan Sahs

UNO Student Research and Creative Activity Fair

Communication networks tend to contain redundant devices and mediums of transmission, thus the need to locate, document, and optimize networks is increasingly becoming necessary. However, many people do not know where to start the optimization progress. What is network topology? What is this “Shortest Path Problem”, and how can it be used to better my network? These questions are presented, taught, and answered within this paper. To supplement the reader’s understanding there are thirty-eight figures in the paper that are used to help convey and compartmentalize the learning process needed to grasp the materials presented in the ending sections.

In …

Group Theory Visualized Through The Rubik's Cube, Ashlyn Okamoto

University Honors Theses

In my thesis, I describe the work done to implement several Group Theory concepts in the context of the Rubik’s cube. A simulation of the cube was constructed using Processing-Java and with help from a YouTube series done by TheCodingTrain. I reflect on the struggles and difficulties that came with creating this program along with the inspiration behind the project. The concepts that are currently implemented at this time are: Identity, Associativity, Order, and Inverses. The functionality of the cube is described as it moves like a regular cube but has extra keypresses that demonstrate the concepts listed. Each concept …

Hamming Codes, Steve Mwangi, Sterling Quinn

Access*: Interdisciplinary Journal of Student Research and Scholarship

We will be looking into the application of Matrix Algebra in forming Hamming Codes. Hamming Codes are essential not just in the detection of errors, but also in the linear concurrent correction of these errors. The matrices we will use, will have entries that are binary units. Binary units are mathematically convenient, and their simplicity permits the representation of many open and closed circuits used in communication systems. The entries in the matrices will represent a message that is meant for transmission or reception, akin to the contemporary application of Hamming Codes in wireless communication. We will use Hamming (7,4) …

Role Of Influence In Complex Networks, Nur Dean

Dissertations, Theses, and Capstone Projects

Game theory is a wide ranging research area; that has attracted researchers from various fields. Scientists have been using game theory to understand the evolution of cooperation in complex networks. However, there is limited research that considers the structure and connectivity patterns in networks, which create heterogeneity among nodes. For example, due to the complex ways most networks are formed, it is common to have some highly “social” nodes, while others are highly isolated. This heterogeneity is measured through metrics referred to as “centrality” of nodes. Thus, the more “social” nodes tend to also have higher centrality.

In this thesis, …

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."

Extending Set Functors To Generalised Metric Spaces, Adriana Balan, Alexander Kurz, Jiří Velebil

Mathematics, Physics, and Computer Science Faculty Articles and Research

For a commutative quantale V, the category V-cat can be perceived as a category of generalised metric spaces and non-expanding maps. We show that any type constructor T (formalised as an endofunctor on sets) can be extended in a canonical way to a type constructor T_V on V-cat. The proof yields methods of explicitly calculating the extension in concrete examples, which cover well-known notions such as the Pompeiu-Hausdorff metric as well as new ones.

Conceptually, this allows us to to solve the same recursive domain equation X ≅ TX in different categories (such as sets and metric spaces) and …

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 …

International Students’ Expectations Of Information Literacy Instruction, Nicole Johnston, Meggan Houlihan, Jodi Neindorf

Research outputs 2014 to 2021

This paper presents the findings of a case study that investigated international university students’ expectations and experiences of information literacy across two countries. The results from this case study provide insights that can be utilized by librarians working with international students, to plan and develop their information literacy instruction classes and programs. Armed with an awareness of what international students’ expectations and experiences with information literacy programs are, librarians can develop more meaningful instruction that better meets the information needs of international students. Moving beyond the pilot survey, the researchers aim to improve the survey instrument and collaborate with librarians …

Sports Analytics With Computer Vision, Colby T. Jeffries

Senior Independent Study Theses

Computer vision in sports analytics is a relatively new development. With multi-million dollar systems like STATS’s SportVu, professional basketball teams are able to collect extremely fine-detailed data better than ever before. This concept can be scaled down to provide similar statistics collection to college and high school basketball teams. Here we investigate the creation of such a system using open-source technologies and less expensive hardware. In addition, using a similar technology, we examine basketball free throws to see whether a shooter’s form has a specific relationship to a shot’s outcome. A system that learns this relationship could be used to …

An Efficient Image Segmentation Algorithm Using Neutrosophic Graph Cut, Florentin Smarandache, Yanhui Guo, Yaman Akbulut, Abdulkadir Sengur, Rong Xia

Branch Mathematics and Statistics Faculty and Staff Publications

Segmentation is considered as an important step in image processing and computer vision applications, which divides an input image into various non-overlapping homogenous regions and helps to interpret the image more conveniently. This paper presents an efficient image segmentation algorithm using neutrosophic graph cut (NGC). An image is presented in neutrosophic set, and an indeterminacy filter is constructed using the indeterminacy value of the input image, which is defined by combining the spatial information and intensity information. The indeterminacy filter reduces the indeterminacy of the spatial and intensity information. A graph is defined on the image and the weight for …

Efficiently Representing The Integer Factorization Problem Using Binary Decision Diagrams, David Skidmore

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Let p be a prime positive integer and let α be a positive integer greater than 1. A method is given to reduce the problem of finding a nontrivial factorization of α to the problem of finding a solution to a system of modulo p polynomial congruences where each variable in the system is constrained to the set {0,...,p − 1}. In the case that p = 2 it is shown that each polynomial in the system can be represented by an ordered binary decision diagram with size less than 20.25log₂(α)³ + 16.5log₂(α)² + …

Shortest Path Problem Under Triangular Fuzzy Neutrosophic Information, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Luige Vladareanu

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we develop a new approach to deal with neutrosphic shortest path problem in a network in which each edge weight (or length) is represented as triangular fuzzy neutrosophic number. The proposed algorithm also gives the shortest path length from source node to destination node using ranking function. Finally, an illustrative example is also included to demonstrate our proposed approach.

The Document Similarity Network: A Novel Technique For Visualizing Relationships In Text Corpora, Dylan Baker

HMC Senior Theses

With the abundance of written information available online, it is useful to be able to automatically synthesize and extract meaningful information from text corpora. We present a unique method for visualizing relationships between documents in a text corpus. By using Latent Dirichlet Allocation to extract topics from the corpus, we create a graph whose nodes represent individual documents and whose edge weights indicate the distance between topic distributions in documents. These edge lengths are then scaled using multidimensional scaling techniques, such that more similar documents are clustered together. Applying this method to several datasets, we demonstrate that these graphs are …

A Novel Approach For Library Materials Acquisition Using Discrete Particle Swarm Optimization, Daniel A. Sabol

Publications and Research

The academic library materials acquisition problem is a challenge for librarian, since library cannot get enough funding from universities and the price of materials inflates greatly. In this paper, we analyze an integer mathematical model by considering the selection of acquired materials to maximize the average preference value as well as the budget execution rate under practical restrictions. The objective is to improve the Discrete Particle Swarm Optimization (DPSO) algorithm by adding a Simulate Annealing algorithm to reduce premature convergence. Furthermore, the algorithm is implemented in multiple threaded environment. The experimental results show the efficiency of this approach.

Quasivarieties And Varieties Of Ordered Algebras: Regularity And Exactness, Alexander Kurz

Engineering Faculty Articles and Research

We characterise quasivarieties and varieties of ordered algebras categorically in terms of regularity, exactness and the existence of a suitable generator. The notions of regularity and exactness need to be understood in the sense of category theory enriched over posets.

We also prove that finitary varieties of ordered algebras are cocompletions of their theories under sifted colimits (again, in the enriched sense).

Features Of Agent-Based Models, Reiko Heckel, Alexander Kurz, Edmund Chattoe-Brown

Engineering Faculty Articles and Research

The design of agent-based models (ABMs) is often ad-hoc when it comes to defining their scope. In order for the inclusion of features such as network structure, location, or dynamic change to be justified, their role in a model should be systematically analysed. We propose a mechanism to compare and assess the impact of such features. In particular we are using techniques from software engineering and semantics to support the development and assessment of ABMs, such as graph transformations as semantic representations for agent-based models, feature diagrams to identify ingredients under consideration, and extension relations between graph transformation systems to …

Foreword: Special Issue On Coalgebraic Logic, Alexander Kurz

Engineering Faculty Articles and Research

The second Dagstuhl seminar on coalgebraic logics took place from October 7-12, 2012, in the Leibniz Forschungszentrum Schloss Dagstuhl, following a successful earlier one in December 2009. From the 44 researchers who attended and the 30 talks presented, this collection highlights some of the progress that has been made in the field. We are grateful to Giuseppe Longo and his interest in a special issue in Mathematical Structures in Computer Science.

The Positivication Of Coalgebraic Logics, Fredrik Dahlqvist, Alexander Kurz

Engineering Faculty Articles and Research

We present positive coalgebraic logic in full generality, and show how to obtain a positive coalgebraic logic from a boolean one. On the model side this involves canonically computing a endofunctor T': Pos->Pos from an endofunctor T: Set->Set, in a procedure previously defined by the second author et alii called posetification. On the syntax side, it involves canonically computing a syntax-building functor L': DL->DL from a syntax-building functor L: BA->BA, in a dual procedure which we call positivication. These operations are interesting in their own right and we explicitly compute posetifications and positivications in the case …

Computation Of Shortest Path Problem In A Network With Sv-Trapezoidal Neutrosophic Numbers, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Luige Vladareanu

Branch Mathematics and Statistics Faculty and Staff Publications

In this work, a neutrosophic network method is proposed for finding the shortest path length with single valued trapezoidal neutrosophic number. The proposed algorithm gives the shortest path length using score function from source node to destination node. Here the weights of the edges are considered to be single valued trapezoidal neutrosophic number. Finally, a numerical example is used to illustrate the efficiency of the proposed approach

Multi-Type Display Calculus For Dynamic Epistemic Logic, Sabine Frittella, Giuseppe Greco, Alexander Kurz, Alessandra Palmigiano, Vlasta Sikimić

Engineering Faculty Articles and Research

In the present paper, we introduce a multi-type display calculus for dynamic epistemic logic, which we refer to as Dynamic Calculus. The displayapproach is suitable to modularly chart the space of dynamic epistemic logics on weaker-than-classical propositional base. The presence of types endows the language of the Dynamic Calculus with additional expressivity, allows for a smooth proof-theoretic treatment, and paves the way towards a general methodology for the design of proof systems for the generality of dynamic logics, and certainly beyond dynamic epistemic logic. We prove that the Dynamic Calculus adequately captures Baltag-Moss-Solecki’s dynamic epistemic logic, and enjoys Belnap-style cut …

Multi-Type Display Calculus For Propositional Dynamic Logic, Sabine Frittella, Giuseppe Greco, Alexander Kurz, Alessandra Palmigiano

Engineering Faculty Articles and Research

We introduce a multi-type display calculus for Propositional Dynamic Logic (PDL). This calculus is complete w.r.t. PDL, and enjoys Belnap-style cut-elimination and subformula property.

Tool Support For Reasoning In Display Calculi, Samuel Balco, Sabine Frittella, Giuseppe Greco, Alexander Kurz, Alessandra Palmigiano

Engineering Faculty Articles and Research

We present a tool for reasoning in and about propositional sequent calculi. One aim is to support reasoning in calculi that contain a hundred rules or more, so that even relatively small pen and paper derivations become tedious and error prone. As an example, we implement the display calculus D.EAK of dynamic epistemic logic. Second, we provide embeddings of the calculus in the theorem prover Isabelle for formalising proofs about D.EAK. As a case study we show that the solution of the muddy children puzzle is derivable for any number of muddy children. Third, there is a set of meta-tools, …

Extensions Of Functors From Set To V-Cat, Adriana Balan, Alexander Kurz, Jirí Velebil

Engineering Faculty Articles and Research

We show that for a commutative quantale V every functor Set --> V-cat has an enriched left- Kan extension. As a consequence, coalgebras over Set are subsumed by coalgebras over V-cat. Moreover, one can build functors on V-cat by equipping Set-functors with a metric.

Positive Fragments Of Coalgebraic Logics, Adriana Balan, Alexander Kurz, Jirí Velebil

Engineering Faculty Articles and Research

Positive modal logic was introduced in an influential 1995 paper of Dunn as the positive fragment of standard modal logic. His completeness result consists of an axiomatization that derives all modal formulas that are valid on all Kripke frames and are built only from atomic propositions, conjunction, disjunction, box and diamond. In this paper, we provide a coalgebraic analysis of this theorem, which not only gives a conceptual proof based on duality theory, but also generalizes Dunn's result from Kripke frames to coalgebras for weak-pullback preserving functors. To facilitate this analysis we prove a number of category theoretic results on …