Mathematics Commons^™

Interpolating Between Hilbert–Samuel And Hilbert–Kunz Multiplicity, William D. Taylor

Mathematical Sciences Faculty Research

We define a function, called s-multiplicity, that interpolates between Hilbert–Samuel multiplicity and Hilbert–Kunz multiplicity by comparing powers of ideals to the Frobenius powers of ideals. The function is continuous in s, and its value is equal to Hilbert–Samuel multiplicity for small values of s and is equal to Hilbert–Kunz multiplicity for large values of s. We prove that it has an Associativity Formula generalizing the Associativity Formulas for Hilbert–Samuel and Hilbert–Kunz multiplicity. We also define a family of closures such that if two ideals have the same s-closure then they have the same s-multiplicity, and the converse holds under mild …

Additive List Coloring Of Planar Graphs With Given Girth, Axel Brandt, Sogol Jahanbekam, Jennifer Diemunsch

Faculty Publications

An additive coloring of a graph G is a labeling of the vertices of G from {1,2,...,k} such that two adjacent vertices have distinct sums of labels on their neighbors. The least integer k for which a graph G has an additive coloring is called the additive coloring number of G, denoted \luck(G). Additive coloring is also studied under the names lucky labeling and open distinguishing. In this paper, we improve the current bounds on the additive coloring number for particular classes of graphs by proving results for a list version of additive coloring. We apply the discharging method and …

Deep Learning Analysis Of Limit Order Book, Xin Xu

Arts & Sciences Graduate Student Theses and Dissertations

In this paper, we build a deep neural network for modeling spatial structure in limit order book and make prediction for future best ask or best bid price based on ideas of (Sirignano 2016). We propose an intuitive data processing method to approximate the data is non-available for us based only on level I data that is more widely available. The model is based on the idea that there is local dependence for best ask or best bid price and sizes of related orders. First we use logistic regression to prove that this approach is reasonable. To show the advantages …

A Simulation Study Of Bipower And Thresholded Realized Variations For High-Frequency Data, Zheng Xu

Arts & Sciences Graduate Student Theses and Dissertations

No abstract provided.

Algorithmic Trading With Prior Information, Xinyi Cai

Arts & Sciences Graduate Student Theses and Dissertations

Traders utilize strategies by using a mix of market and limit orders to generate profits. There are different types of traders in the market, some have prior information and can learn from changes in prices to tweak her trading strategy continuously(Informed Traders), some have no prior information but can learn(Uninformed Learners), and some have no prior information and cannot learn(Uninformed Traders). In this thesis. Alvaro C, Sebastian J and Damir K \cite{AL} proposed a model for algorithmic traders to access the impact of dynamic learning in profit and loss in 2014. The traders can employ the model to decide which …

Variable Selection Via Lasso With High-Dimensional Proteomic Data, Hongxuan Zhai

Arts & Sciences Graduate Student Theses and Dissertations

Multiclass classification with high-dimensional data is an applied topic both in statistics and machine learning. The classification procedure could be done in various ways. In this thesis, we review the theory of the Lasso procedure which provides a parameter estimator while simultaneously achieving dimension reduction due to a property of the L1 norm. Lasso with elastic net penalty and sparse group lasso are also reviewed. Our data is high-dimensional proteomic data (iTRAQ ratios) of breast cancer patients with four subtypes of breast cancer. We use the multinomial logistic regression to train our classifier and use the false classification rates obtained …

Gaps In The Saturation Spectrum Of Trees, Ronald J. Gould, Paul Horn, Michael S. Jacobson, Brent J. Thomas

Mathematics and Statistics Faculty Publications

A graph G is H-saturated if H is not a subgraph of G but the addition of any edge from the complement of G to G results in a copy of H. The minimum number of edges (the size) of an H-saturated graph on n vertices is denoted sat(n, H), while the maximum size is the well studied extremal number, ex(n, H). The saturation spectrum for a graph H is the set of sizes of H-saturated graphs between sat(n, H) and ex(n, H). In …

Non-Equilibrium Phase Transitions In Interacting Diffusions, Wael Al-Sawai

USF Tampa Graduate Theses and Dissertations

The theory of thermodynamic phase transitions has played a central role both in theoretical physics and in dynamical systems for several decades. One of its fundamental results is the classification of various physical models into equivalence classes with respect to the scaling behavior of solutions near the critical manifold. From that point of view, systems characterized by the same set of critical exponents are equivalent, regardless of how different the original physical models might be. For non-equilibrium phase transitions, the current theoretical framework is much less developed. In particular, an equivalent classification criterion is not available, thus requiring a specific …

Feasibility Of Predicting Vietnam’S Autumn Rainfall Regime Based On The Tree-Ring Record And Decadal Variability, Yan Sun, Shih-Yu (Simon) Wang, Rong Li, Brendan M. Buckley, Robert R. Gilies, Kyle G. Hansen

Mathematics and Statistics Faculty Publications

We investigate the feasibility of developing decadal prediction models for autumn rainfall ( R_A ) over Central Vietnam by utilizing a published tree-ring reconstruction of October–November (ON) rainfall derived from the earlywood width measurements from a type of Douglas-fir (Pseudotsuga sinensis). Autumn rainfall for this region accounts for a large percentage of the annual total, and is often the source of extreme flooding. Central Vietnam’s R_A along with its notable autocorrelation and significant cross-correlation with basin-wide Pacific sea surface temperature (SST) variability, to develop four discrete time-series models. The sparse autoregressive model, with Pacific SST as …

A New Finite Difference Time Domain Method To Solve Maxwell's Equations, Timothy P. Meagher

Dissertations and Theses

We have constructed a new finite-difference time-domain (FDTD) method in this project. Our new algorithm focuses on the most important and more challenging transverse electric (TE) case. In this case, the electric field is discontinuous across the interface between different dielectric media. We use an electric permittivity that stays as a constant in each medium, and magnetic permittivity that is constant in the whole domain. To handle the interface between different media, we introduce new effective permittivities that incorporates electromagnetic fields boundary conditions. That is, across the interface between two different media, the tangential component, E_r(x,y), …

Large-Scale Multiple Hypothesis Testing With Complex Data Structure, Xiaoyu Dai

Arts & Sciences Graduate Student Theses and Dissertations

In the last decade, motivated by a variety of applications in medicine, bioinformatics, genomics, brain imaging, etc., a growing amount of statistical research has been devoted to large-scale multiple testing, where thousands or even greater numbers of tests are conducted simultaneously. However, due to the complexity of real data sets, the assumptions of many existing multiple testing procedures, e.g. that tests are independent and have continuous null distributions of p-values, may not hold. This poses limitations in their performances such as low detection power and inflated false discovery rate (FDR). In this dissertation, we study how to better proceed the …

Carlson's Theorem For Different Measures, Meredith Sargent

Arts & Sciences Graduate Student Theses and Dissertations

Hedenmalm, Lindqvist, and Seip in 1997 [11] revitalized the modern study of Dirichletseries by defining the space H 2 and considering it as isometrically isomorphic to the Hardyspace of the infinite polytorus H 2 (T ∞ ). This allowed a new viewpoint to be applied toclassical theorems, including Carlson’s theorem about the integral in the mean of a Dirichletseries. Carlson’s theorem holds only for vertical lines in the right half plane, and cannot beextended to the boundary in full generality (as shown by Saksman and Seip in [14]). However,Carlson’s theorem can be shown to hold on the imaginary axis for …

Impacts Of Simultaneous Multislice Acquisition On Sensitivity And Specificity In Fmri, Benjamin B. Risk, Mary C. Kociuba, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Simultaneous multislice (SMS) imaging can be used to decrease the time between acquisition of fMRI volumes, which can increase sensitivity by facilitating the removal of higher-frequency artifacts and boosting effective sample size. The technique requires an additional processing step in which the slices are separated, or unaliased, to recover the whole brain volume. However, this may result in signal “leakage” between aliased locations, i.e., slice “leakage,” and lead to spurious activation (decreased specificity). SMS can also lead to noise amplification, which can reduce the benefits of decreased repetition time. In this study, we evaluate the original slice-GRAPPA (no leak block) …

Regulators On Higher Chow Groups, Muxi Li

Arts & Sciences Graduate Student Theses and Dissertations

There are two natural questions one can ask about the higher Chow group of number fields: One is its torsion, the other one is its relation with the homology of GLn. For the first question, based on some earlier work, the integral regulator on higher Chow complexes introduced here can put a lot of earlier result on a firm ground. For the second question, we give a counterexample to an earlier proof of the existence of linear representatives of higher Chow groups of number fields. Chapter 1 gives a general picture of the two problems we are talking about. Chapter …

Distributed Quantile Regression Analysis And A Group Variable Selection Method, Liqun Yu

Arts & Sciences Graduate Student Theses and Dissertations

This dissertation develops novel methodologies for distributed quantile regression analysisfor big data by utilizing a distributed optimization algorithm called the alternating directionmethod of multipliers (ADMM). Specifically, we first write the penalized quantile regressioninto a specific form that can be solved by the ADMM and propose numerical algorithmsfor solving the ADMM subproblems. This results in the distributed QR-ADMMalgorithm. Then, to further reduce the computational time, we formulate the penalizedquantile regression into another equivalent ADMM form in which all the subproblems haveexact closed-form solutions and hence avoid iterative numerical methods. This results in thesingle-loop QPADM algorithm that further improve on the computational …

A Comparison Of The Product Topology On Two Trees With The Tree Topology On The Concatenation Of Two Trees, Katlyn Kathleen Cox

UNLV Theses, Dissertations, Professional Papers, and Capstones

A game tree is a nonempty set of sequences, closed under subsequences (i.e., if p ∈ T

and p extends q, then q ∈ T). If T is a game tree, then there is a natural topology on [T],

the set of paths through T. In this study we consider two types of topological spaces, both

constructed from game trees. The first is constructed by taking the Cartesian product of

two game trees, T and S: [T] × [S]. The second is constructed by the concatenation of two

game trees, T and S: [T ∗ S]. The goal of our …

Bi-Directional Testing For Change Point Detection In Poisson Processes, Moinak Bhaduri

UNLV Theses, Dissertations, Professional Papers, and Capstones

Point processes often serve as a natural language to chronicle an event's temporal evolution, and significant changes in the flow, synonymous with non-stationarity, are usually triggered by assignable and frequently preventable causes, often heralding devastating ramifications. Examples include amplified restlessness of a volcano, increased frequencies of airplane crashes, hurricanes, mining mishaps, among others. Guessing these time points of changes, therefore, merits utmost care. Switching the way time traditionally propagates, we posit a new genre of bidirectional tests which, despite a frugal construct, prove to be exceedingly efficient in culling out non-stationarity under a wide spectrum of environments. A journey surveying …

Meshless Methods For Numerically Solving Boundary Value Problems Of Elliptic Type Partial Differential Equations, Minhwa Choi

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this dissertation we propose and examine numerical methods for solving the boundary value problems of partial differential equations (PDEs) by meshless methods. First we aim at getting approximate particular solutions up of a nonhomogeneous equation by radial basis methods. For instance, the collocation method by radial basis functions (RBFs) for finding particular solutions is very popular in the literature. Now the particular solutions of certain important PDEs by RBF approximation are available with the order of convergence to the exact solutions provided. Here we explore and examine the numerical performances of these particular solutions in various examples. We then …

Notes On Linear Divisible Sequences And Their Construction: A Computational Approach, Sean Trendell

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this Masters thesis, we examine linear divisible sequences. A linear divisible sequence is any sequence {an}n≥0 that can be expressed by a linear homogeneous recursion relation that is also a divisible sequence. A sequence {an}n≥0 is called a divisible sequence if it has the property that if n|m, then an|am. A sequence of numbers {an}n≥0 is called a linear homogeneous recurrence sequence of order m if it can be written in the form

an+m = p1an+m−1 + p2an+m−2 + · · · + pm−1an+1 + pman, n ≥ 0,

for some constants p1, p2, ..., pm with pm = …

Developmental Mathematics: A Quantitative Investigation Of Instructor Classification As Related To Student Success, Brittany A. Fish

Electronic Theses and Dissertations

The purpose of this quantitative study was to examine what type of predictive power exists between an instructor’s employment classification, student gender, student race, and first-generation status on a student’s academic success in developmental mathematics, as measured by final semester grades at a regionally comprehensive state university in Texas between fall 2013 and spring 2017. Data were collected from the institution under study and the sample population included 1932 unique student observations. The data collected in this study were analyzed through a binary logistic regression model to determine whether an instructor’s employment classification, student gender, student race, and first-generation status …

Using Computational Bayesian Statistics To Analyze Parameters In A Differential Equation Model, Jacob Menix

Mahurin Honors College Capstone Experience/Thesis Projects

The purpose of this project is to use Bayesian statistics to analyze values of parameters for a previously developed system of differential equations which describes the healing process of diabetic foot ulcers. The model describes the relationships between matrix metalloproteinases (MMPs), their inhibitors (TIMPs), and extracellular matrix (ECM). A Bayesian approach is used when the availability of data is sparse, as it is in this case. Delayed Rejection Adaptive Metropolis (DRAM), a MATLAB implementation of a Metropolis-Hastings algorithm, is used to estimate parameters. This approach with the individual patient data allows us to estimate and compare parameters and their pairwise …

Re-Evaluating Performance Measurement: New Mathematical Methods To Address Common Performance Measurement Challenges, Jordan David Benis

Electronic Theses and Dissertations

Performance Measurement is an essential discipline for any business. Robust and reliable performance metrics for people, processes, and technologies enable a business to identify and address deficiencies to improve performance and profitability. The complexity of modern operating environments presents real challenges to developing equitable and accurate performance metrics. This thesis explores and develops two new methods to address common challenges encountered in businesses across the world. The first method addresses the challenge of estimating the relative complexity of various tasks by utilizing the Pearson Correlation Coefficient to identify potentially over weighted and under weighted tasks. The second method addresses the …

Modeling Amateur Radio Soundings Of The Ionospheric Response To The 2017 Great American Eclipse, N. A. Frissell, J. D. Katz, S. W. Gunning, J. S. Vega, A. J. Gerrard, G. D. Earle, M. L. Moses, M. L. West, J. D. Huba, P. J. Erickson, E. S. Miller, R. B. Gerzoff, W. Liles, H. W. Silver

Department of Mathematics Faculty Scholarship and Creative Works

On 21 August 2017, a total solar eclipse traversed the continental United States and caused large-scale changes in ionospheric densities. These were detected as changes in medium- and high-frequency radio propagation by the Solar Eclipse QSO Party citizen science experiment organized by the Ham Radio Science Citizen Investigation (hamsci.org). This is the first eclipse-ionospheric study to make use of measurements from a citizen-operated, global-scale HF propagation network and develop tools for comparison to a physics-based model ionosphere. Eclipse effects were observed ±0.3 hr on 1.8 MHz, ±0.75 hr on 3.5 and 7 MHz, and ±1 hr on 14 MHz and …

Andrews Student Receives Prestigious Award-Mykhaylo M. Malakhov Awarded The Barry Goldwater Scholarship, Hannah Gallant

Andrews Agenda: Campus News

No abstract provided.

Lyapunov Functions To Caputo Fractional Neural Networks With Time-Varying Delays, Ravi P. Agarwal, Snezhana G. Hristova, Donal O'Regan

Mathematics and System Engineering Faculty Publications

One of the main properties of solutions of nonlinear Caputo fractional neural networks is stability and often the direct Lyapunov method is used to study stability properties (usually these Lyapunov functions do not depend on the time variable). In connection with the Lyapunov fractional method we present a brief overview of the most popular fractional order derivatives of Lyapunov functions among Caputo fractional delay differential equations. These derivatives are applied to various types of neural networks with variable coefficients and time-varying delays. We show that quadratic Lyapunov functions and their Caputo fractional derivatives are not applicable in some cases when …

Exploring The Use Of Predictive Analytics In Banking And Finance Decision-Making, Melanie Tummino

Honors Program Theses and Projects

Predictive analytics is a branch of advanced analytics that is composed of various statistical techniques where each contributes in making predictions about future scenarios and outcomes. Some of these techniques include machine learning, artificial intelligence, data mining, predictive modeling, logistic regression, etc., and the patterns found in the results can be used to identify risks and opportunity. Predictive analytics is often associated with meteorology and weather forecasting due to the fact there are many attributes to contribute to a response, but generally, it has many applications in existing growing or established businesses, especially when it comes to decision-making about revenue, …

Exploring The Proportion Of Prime Numbers In Quadratic Extensions Of The Integers, Jamie Nelson

Honors Program Theses and Projects

No abstract provided.

On The Toughness Of Some Johnson Solids, Sean Koval

Honors Program Theses and Projects

The Johnson solids are the 92 three-dimensional, convex solids (other than the Platonic and Archimedean solids) that can be formed with regular polygons. The purpose of this honor’s thesis work is to determine the toughness of some of the Johnson Solids and similar graphs. The Johnson solids can be broken up into classes of solids with certain characteristics. While there are only 92 Johnson solids in three dimensions, we can generate infinite classes of graphs in two dimensions with similar characteristics. We have identified some of these classes, studied the toughness of individual graphs and begun to analyze a few …

Possible Isolation Number Of A Matrix Over Nonnegative Integers, Leroy B. Beasley, Young Bae Jun, Seok-Zun Song

Mathematics and Statistics Faculty Publications

Let ℤ₊ be the semiring of all nonnegative integers and A an m × n matrix over ℤ₊. The rank of A is the smallest k such that A can be factored as an m × k matrix times a k×n matrix. The isolation number of A is the maximum number of nonzero entries in A such that no two are in any row or any column, and no two are in a 2 × 2 submatrix of all nonzero entries. We have that the isolation number of A is a lower bound of the rank of …

Golden Arm: A Probabilistic Study Of Dice Control In Craps, Donald R. Smith, Robert Scott Iii

UNLV Gaming Research & Review Journal

This paper calculates how much control a craps shooter must possess on dice outcomes to eliminate the house advantage. A golden arm is someone who has dice control (or a rhythm roller or dice influencer). There are various strategies for dice control in craps. We discuss several possibilities of dice control that would result in several different mathematical models of control. We do not assert whether dice control is possible or not (there is a lack of published evidence). However, after studying casino-legal methods described by dice-control advocates, we can see only one realistic mathematical model that describes the resulting …