Open Access. Powered by Scholars. Published by Universities.®
- Institution
- Keyword
-
- Combinatorics (3)
- Mathematics (2)
- Optimization (2)
- AI (1)
- Academic -- UNF -- Master of Science in Mathematical Science; Dissertations (1)
-
- Academic -- UNF -- Mathematics; Finite State Automata; Regular Languages; Subword Closure; Involution Mappings; Strictly Locally Testable Languages; DNA Code Words (1)
- Algorithms (1)
- Applied Mathematics (1)
- Approximation (Mathematics) (1)
- Artificial Intelligence (1)
- BCH Codes (1)
- Balance (1)
- Bounds (1)
- CSP (1)
- Calculus of variations (1)
- Category theory (1)
- Collaborative filtering (1)
- Complexity (1)
- Computer Science (1)
- Conjecture (1)
- Cooper's Philosophy (1)
- Cosine similarity based clustering (1)
- Cyclic Codes (1)
- Data Science (1)
- Differential geometry (1)
- Dynamic graphs (1)
- EEG (1)
- Fiedler vector (1)
- Frames (1)
- Free monoid (1)
- Publication Year
Articles 1 - 16 of 16
Full-Text Articles in Other Mathematics
Signings Of Graphs And Sign-Symmetric Signed Graphs, Ahmad Asiri
Signings Of Graphs And Sign-Symmetric Signed Graphs, Ahmad Asiri
Theses and Dissertations
In this dissertation, we investigate various aspects of signed graphs, with a particular focus on signings and sign-symmetric signed graphs. We begin by examining the complete graph on six vertices with one edge deleted ($K_6$\textbackslash e) and explore the different ways of signing this graph up to switching isomorphism. We determine the frustration index (number) of these signings and investigate the existence of sign-symmetric signed graphs. We then extend our study to the $K_6$\textbackslash 2e graph and the McGee graph with exactly two negative edges. We investigate the distinct ways of signing these graphs up to switching isomorphism and demonstrate …
Finding Optimal Cayley Map Embeddings Using Genetic Algorithms, Jacob Buckelew
Finding Optimal Cayley Map Embeddings Using Genetic Algorithms, Jacob Buckelew
Honors Program Theses
Genetic algorithms are a commonly used metaheuristic search method aimed at solving complex optimization problems in a variety of fields. These types of algorithms lend themselves to problems that can incorporate stochastic elements, which allows for a wider search across a search space. However, the nature of the genetic algorithm can often cause challenges regarding time-consumption. Although the genetic algorithm may be widely applicable to various domains, it is not guaranteed that the algorithm will outperform other traditional search methods in solving problems specific to particular domains. In this paper, we test the feasibility of genetic algorithms in solving a …
Decoding Cyclic Codes Via Gröbner Bases, Eduardo Sosa
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 …
A Mathematical Analysis Of The Game Of Santorini, Carson Clyde Geissler
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.
Maximality And Applications Of Subword-Closed Languages, Rhys Davis Jones
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
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 …
Logic -> Proof -> Rest, Maxwell Taylor
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.
Vertex Weighted Spectral Clustering, Mohammad Masum
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 …
Combinatorial Polynomial Hirsch Conjecture, Sam Miller
Combinatorial Polynomial Hirsch Conjecture, Sam Miller
HMC Senior Theses
The Hirsch Conjecture states that for a d-dimensional polytope with n facets, the diameter of the graph of the polytope is at most n-d. This conjecture was disproven in 2010 by Francisco Santos Leal. However, a polynomial bound in n and d on the diameter of a polytope may still exist. Finding a polynomial bound would provide a worst-case scenario runtime for the Simplex Method of Linear Programming. However working only with polytopes in higher dimensions can prove challenging, so other approaches are welcome. There are many equivalent formulations of the Hirsch Conjecture, one of which is the …
Triple Non-Negative Matrix Factorization Technique For Sentiment Analysis And Topic Modeling, Alexander A. Waggoner
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 …
An Algorithm For The Machine Calculation Of Minimal Paths, Robert Whitinger
An Algorithm For The Machine Calculation Of Minimal Paths, Robert Whitinger
Electronic Theses and Dissertations
Problems involving the minimization of functionals date back to antiquity. The mathematics of the calculus of variations has provided a framework for the analytical solution of a limited class of such problems. This paper describes a numerical approximation technique for obtaining machine solutions to minimal path problems. It is shown that this technique is applicable not only to the common case of finding geodesics on parameterized surfaces in R3, but also to the general case of finding minimal functionals on hypersurfaces in Rn associated with an arbitrary metric.
The Apprentices' Tower Of Hanoi, Cory Bh Ball
The Apprentices' Tower Of Hanoi, Cory Bh Ball
Electronic Theses and Dissertations
The Apprentices' Tower of Hanoi is introduced in this thesis. Several bounds are found in regards to optimal algorithms which solve the puzzle. Graph theoretic properties of the associated state graphs are explored. A brief summary of other Tower of Hanoi variants is also presented.
Parameters Estimation Of Material Constitutive Models Using Optimization Algorithms, Kiswendsida Jules Kere
Parameters Estimation Of Material Constitutive Models Using Optimization Algorithms, Kiswendsida Jules Kere
Williams Honors College, Honors Research Projects
Optimization Algorithms are very useful for solving engineering problems. Indeed, optimization algorithms can be used to optimize engineering designs in terms of safety and economy. Understanding the proprieties of materials in engineering designs is very important in order to make designs safe. Materials are not really perfectly homogeneous and there are heterogeneous distributions in most materials. In this paper, Self-OPTIM which is an inverse constitutive parameter identification framework will be used to identify parameters of a linear elastic material constitutive model. Data for Self-OPTIM will be obtained using ABAQUS simulation of a dog-bone uniaxial test. Optimization Algorithms will be used …
Indefinite Knapsack Separable Quadratic Programming: Methods And Applications, Jaehwan Jeong
Indefinite Knapsack Separable Quadratic Programming: Methods And Applications, Jaehwan Jeong
Doctoral Dissertations
Quadratic programming (QP) has received significant consideration due to an extensive list of applications. Although polynomial time algorithms for the convex case have been developed, the solution of large scale QPs is challenging due to the computer memory and speed limitations. Moreover, if the QP is nonconvex or includes integer variables, the problem is NP-hard. Therefore, no known algorithm can solve such QPs efficiently. Alternatively, row-aggregation and diagonalization techniques have been developed to solve QP by a sub-problem, knapsack separable QP (KSQP), which has a separable objective function and is constrained by a single knapsack linear constraint and box constraints. …
Optimizing The Analysis Of Electroencephalographic Data By Dynamic Graphs, Mehrsasadat Golestaneh
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 …
Representations, Approximations, And Algorithms For Mathematical Speech Processing, Laura R. Suzuki
Representations, Approximations, And Algorithms For Mathematical Speech Processing, Laura R. Suzuki
Theses and Dissertations
Representing speech signals such that specific characteristics of speech are included is essential in many Air Force and DoD signal processing applications. A mathematical construct called a frame is presented which captures the important time-varying characteristic of speech. Roughly speaking, frames generalize the idea of an orthogonal basis in a Hilbert space, Specific spaces applicable to speech are L2(R) and the Hardy spaces Hp(D) for p> 1 where D is the unit disk in the complex plane. Results are given for representations in the Hardy spaces involving Carleson's inequalities (and its extensions), …