Mathematics Commons^™

Biocontrol Of The Emerald Ash Borer: An Adapted Nicholson-Bailey Model, Michael Kerckhove, Shuheng Chen

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Model Describing The Behavior Of Biomass, Acidity, And Viscosity As A Function Of Temperature In The Shelf Life Of Yogurt, Manuel Alvarado, Paul A. Valle, Yolocuauhtli Salazar

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Level And Gorenstein Projective Dimension, Laila Awadalla, Thomas Marley

Department of Mathematics: Faculty Publications

We investigate the relationship between the level of a bounded complex over a commutative ring with respect to the class of Gorenstein projective modules and other invariants of the complex or ring, such as projective dimension, Gorenstein projective dimension, and Krull dimension. The results build upon work done by J. Christensen [7], H. Altmann et al. [1], and Avramov et al. [4] for levels with respect to the class of finitely generated projective modules.

The concept of level in a triangulated category, first defined by Avramov, Buch- weitz, Iyengar, and Miller [4], is a measure of how many mapping cones …

Mathematical Modeling Of Breast Cancer Cell Mcf-7 Growths Due To Curcumin Treatments, Widodo Samyono, Hildana Assefa, Kana Kassa

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Covariant Ergodic Quantum Markov Semigroups Via Systems Of Imprimitivity, Radhakrishnan Balu

Journal of Stochastic Analysis

No abstract provided.

Congruences Between Coefficients Of A Class Of Eta-Quotients And Their Applications To Combinatorics, Shashika Petta Mestrige

LSU Doctoral Dissertations

Ramanujan in $1920$s discovered remarkable congruence properties of the partition function $p(n)$. Later, Watson and Atkin proved these congruences using the theory of modular forms. Atkin, Gordon, and Hughes extended these works to $k$-colored partition functions. In $2010$, Folsom-Kent-Ono and Boylan-Webb proved the congruences of $p(n)$ by studying a $\ell$-adic module associated with a certain sequence of modular functions which are related to $p(n)$.

Primary goal of this thesis is to generalize the work of Atkin, Gordon, Hughes, Folsom-Kent-Ono, and Boylan-Webb about the partition function to a larger class of partition functions. For this purpose we study a closely related …

ℂ-Motivic Modular Forms, Bogdan Gheorghe, Daniel C. Isaksen, Achim Krause, Nicolas Ricka

Mathematics Faculty Research Publications

We construct a topological model for cellular, 2-complete, stable C-motivic homotopy theory that uses no algebro-geometric foundations.We compute the Steenrod algebra in this context, and we construct a “motivic modular forms” spectrum over ℂ.

Effectiveness And Safety Of Tranexamic Acid Use In Acute Traumatic Injury In The Prehospital And In-Hospital Settings: A Systematic Review And Meta-Analysis Of Randomized Controlled Trials, Scott Rowe, Amy Liu, Israel Zagales, Muhammad Awan, Radleigh Santos, Mark Mckenney, Adel Elkbuli

Mathematics Faculty Articles

Background and Objectives:

This systematic review and meta-analysis of randomized controlled trials (RCTs) aims to assess efficacy and safety of tranexamic acid (TXA) use in acute traumatic injuries.

Methods:

PubMed and Cochrane libraries were searched for relevant RCTs published between January 2011 and January 3, 2021. Cohen’s Q Test for heterogeneous effects was used to determine the appropriateness of fixed versus random effects models.

Results:

Twenty-two studies met inclusion criteria. Meta-analysis of relative risk of mortality between treatment and placebo groups in the in-hospital, and perioperative settings was not significant. However, the risk of mortality is significantly lower in the …

Matrix Multiplier: Cramer’S Method Calculation, Haruka Kido

Electrical Engineering Student Publications

This paper is a technical report of the C++ and LabVIEW algorithms for and the underlying mathematics of The Cramer’s Method. The systemic process of the Cramer’s Method enhances the efficiency of solving matrix multiplication problems involving systems of linear equations with sets of 3 or more added or subtracted unknown variables associated with numerical coefficients. The coefficients of the system of equations generate the numbers in the matrix to be used in the replicable and formulaic computation process.

Optimal Quantization For Mixed Distributions, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability distribution by a discrete distribution. Mixed distributions are an exciting new area for optimal quantization. In this paper, we have determined the optimal sets of n -means, the n th quantization errors, and the quantization dimensions of different mixed distributions. Besides, we have discussed whether the quantization coefficients for the mixed distributions exist. The results in this paper will give a motivation and insight into more …

De Finetti’S Theorem In Categorical Probability, Tobias Fritz, Tomáš Gonda, Paolo Perrone

Journal of Stochastic Analysis

No abstract provided.

On 𝜃- -Closed Sets And 𝜃- -Continuous Functlons, Amin Hamoud Saif, Nahid Mohammed Al-Showhati

Hadhramout University Journal of Natural & Applied Sciences

In topological spaces, the class of 𝜃-closed sets and 𝜃-continuous function have been introduced by Velicko and Fomin respectively. The purpose of this paper is to introduce and study these notions in grill topological spaces by giving the new classes of 𝜃- -closed sets and 𝜃- -continuous functions in grill topological space.

Splitting-Up Technique And Cubic Spline Approximations For Solving Modified Coupled Burgers' Equations, Anwar Abdulla Bassaif

Hadhramout University Journal of Natural & Applied Sciences

In this paper, a finite difference scheme based on the splitting-up technique and cubic spline approximations is developed for solving modified coupled Burgers' equations. The accuracy and stability of the scheme have been analyzed. It is found that the scheme is of first-order accuracy in time and second-order accuracy in space direction and is unconditionally stable. The numerical results are obtained with severe/moderate gradients in the initial and boundary conditions and the steady state solutions are plotted for different values of given parameters. It is concluded that the resulting scheme produces satisfactory results, even in the case of very severe …

Under Pressure: A Case Study Of The Effects Of External Pressure On Mlb Players Using Twitter Sentiment Analysis, Jonathan Huntley

Honors Projects in Mathematics

Performance under pressure and psychological momentum are well-documented topics in sports psychology, but most research focuses on “in-game” pressure. This study views pressure more broadly to examine how the external pressure of fans, quantified using the sentiment of tweets mentioning the players, can affect how MLB players perform. Although external pressure is intangible, it can impact a player’s psyche and performance. This investigation focuses on players Chris Sale and David Price. A new process was developed leveraging the Vader package in Python that can generate tweet sentiment to compare to several performance metrics from Baseball Reference. Results proved to be …

Why Moments (And Generalized Moments) Are Used In Statistics And Why Expected Utility Is Used In Decision Making: A Possible Explanation, R. Noah Padilla, Vladik Kreinovich

Departmental Technical Reports (CS)

Among the most efficient characteristics of a probability distribution are its moments and, more generally, generalized moments. One of the most adequate numerical characteristics describing human behavior is expected utility. In both cases, the corresponding characteristic is the sum of results of applying appropriate nonlinear functions applied to individual inputs. In this paper, we provide a possible theoretical explanation of why such functions are efficient.

How Multi-View Techniques Can Help In Processing Uncertainty, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Multi-view techniques help us reconstruct a 3-D object and its properties from its 2-D (or even 1-D) projections. It turns out that similar techniques can be used in processing uncertainty -- where many problems can reduced to a similar task of reconstructing properties of a multi-D object from its 1-D projections. In this chapter, we provide an overview of these techniques.

Why Do People Become Addicted: Towards A Theoretical Explanation For Eyal's Experiment-Based Hook Model, Christopher Reyes, Vladik Kreinovich

Departmental Technical Reports (CS)

Why do people become addicted, e.g., to gambling? Experiments have shown that simple lotteries, in which we can win a small prize with a certain probability, and not addictive. However, if we add a second possibility -- of having a large prize with a small probability -- the lottery becomes highly addictive to many participants. In this paper, we provide a possible theoretical explanation for this empirical phenomenon.

Why Ovals In Eliciting Intervals?, Joshua Zamora, Vladik Kreinovich

Departmental Technical Reports (CS)

To elicit people's opinions, we usually ask them to mark their degree of satisfaction on a scale -- e.g., from 0 to 5 or from 0 to 10. Often, people are unsure about the exact degree: 7 or 8? To cover such situations, it is desirable to elicit not a single value but an interval of possible values. However, it turns out that most people are not comfortable with marking an interval. Empirically, it turned out that the best way to elicit an interval is to ask them to draw an oval whose intersection with the 0-to-10 line is the …

Decision Making Under Uncertainty: Cases When We Only Know An Upper Bound Or A Lower Bound, Toshiki Kamio, Gavin Baechle, Vladik Kreinovich

Departmental Technical Reports (CS)

In situations when we have a perfect knowledge about the outcomes of several situations, a natural idea is to select the best of these situations. For example, among different investments, we should select the one with the largest gain. In practice, however, we rarely know the exact consequences of each action. In some cases, we know the lower and upper bounds on the corresponding gain. It has been proven that in such cases, an appropriate decision is to use Hurwicz optimism-pessimism criterion. In this paper, we extend the corresponding results to the cases when we only know an upper bound …

Commonsense "And"-Operations, Javier Tellez, Wenbo Xie, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we need to estimate our degree of belief in a statement "A and B" when the only thing we know are the degrees of belief a and b in combined statements A and B. An algorithm for this estimation is known as an "and"-operation, or, for historical reasons, a t-norm. Usually, "and"-operations are selected in such a way that if one of the statements A or B is false, our degree of belief in "A and B" is 0. However, in practice, this is sometimes not the case: for example, an ideal faculty candidate must satisfy …

Fourier Transform And Other Quadratic Problems Under Interval Uncertainty, Oscar Galindo, Christopher Ibarra, Vladik Kreinovich

Departmental Technical Reports (CS)

In general, computing the range of a quadratic function on given intervals is NP-hard. Recently, a feasible algorithm was proposed for computing the range of a specific quadratic function -- square of the modulus of a Fourier coefficient. For this function, the rank of the quadratic form -- i.e., the number of nonzero eigenvalues -- is 2. In this paper, we show that this algorithm can be extended to all the cases when the rank of the quadratic form is bounded by a constant.

Why Model Order Reduction, Salvador Robles, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

Reasonably recently, a new efficient method appeared for solving complex non-linear differential equations (and systems of differential equations). In this method -- known as Model Order Reduction (MOR) -- we select several solutions, and approximate a general solution by a linear combination of the selected solutions. In this paper, we use the known explanation for efficiency of neural networks to explain the efficiency of MOR techniques.

Why Residual Neural Networks, Sofia Holguin, Vladik Kreinovich

Departmental Technical Reports (CS)

In the traditional neural networks, the outputs of each layer serve as inputs to the next layer. It is known that in many cases, it is beneficial to also allow outputs from pre-previous etc. layers as inputs. Such networks are known as residual. In this paper, we provide a possible theoretical explanation for the empirical success of residual neural networks.

How To Gauge The Quality Of A Multi-Class Classification When Ground Truth Is Known With Uncertainty, Ricardo Mendez, Osagumwenro Osaretin, Vladik Kreinovich

Departmental Technical Reports (CS)

The usual formulas for gauging the quality of a classification method assume that we know the ground truth, i.e., that for several objects, we know for sure to which class they belong. In practice, we often only know this with some degree of certainty. In this paper, we explain how to take this uncertainty into account when gauging the quality of a classification method.

Kinematic Metric Spaces Under Interval Uncertainty: Towards An Adequate Definition, Vladik Kreinovich, Olga Kosheleva, Victor Selivanov

Departmental Technical Reports (CS)

In the physical space, we define distance between the two points as the length of the shortest path connecting these points. Similarly, in space-time, for every pair of events for which the event a can causally effect the event b, we can define the longest proper time t(a,b) over all causal trajectories leading from a to b. The resulting function is known as kinematic metric. In practice, our information about all physical quantities -- including time -- comes from measurement, and measurements are never absolutely precise: the measurement result V is, in general, different from the actual (unknown) value v …

Fuzzy Logic Beyond Traditional "And"- And "Or"-Operations, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

In the traditional fuzzy logic, we can use "and"-operations (also known as t-norms) to estimate the expert's degree of confidence in a composite statement A&B based on his/her degrees of confidence d(A) and d(B) in the corresponding basic statements A and B. But what if we want to estimate the degree of confidence in A&B&C in situations when, in addition to the degrees of estimate d(A), d(B), and d(C) of the basic statements, we also know the expert's degrees of confidence in the pairs d(A&B), d(A&C), and d(B&C)? Traditional "and"-operations can provide such an estimate -- but only by ignoring …

On The Relationship Between Pain Variability And Relief In Randomized Clinical Trials, Siddharth Tiwari '22

Student Publications & Research

Previous research suggests greater baseline variability is associated with greater pain relief in those who receive a placebo. However, studies that evidence this association do not control for confounding effects (natural history and regression-to-the-mean); for this reason, we analyzed data from two randomized clinical trials (Placebo I and Placebo II, N = 134) while adjusting for confounding effects via a no-treatment group. Results agree between the two placebo groups: both placebo groups showed a negligible correlation between baseline variability and adjusted response (r sp (CI 95% ) = 0.13 (−0.09, 0.37) and 0.01 (−0.15, 0.20) for Placebo I and II, …

Different Concepts, Similar Computational Complexity: Nguyen's Results About Fuzzy And Interval Computations 35 Years Later, Hung T. Nguyen, Vladik Kreinovich

Departmental Technical Reports (CS)

When we know for sure which values are possible and which are not, we have crisp uncertainty -- of which interval uncertainty is a usual case. In practice, we are often not 100% sure about our knowledge, i.e., we have fuzzy uncertainty -- i.e., we have fuzzy knowledge, of which crisp is a particular case. Usually, general problems are more difficult to solve that most of their particular cases. It was therefore expected that processing fuzzy data is, in general, more computationally difficult than processing interval data -- and indeed, Zadeh's extension principle -- a natural formula for fuzzy computations …

Fault Detection In A Smart Electric Grid: Geometric Analysis, Hector Reyes, Dillon Trinh, Vladik Kreinovich

Departmental Technical Reports (CS)

The main idea behind a smart grid is to equip the grid with a dense lattice of sensors monitoring the state of the grid. If there is a fault, the sensors closer to the fault will detect larger deviations from the normal readings that sensors that are farther away. In this paper, we show that this fact can be used to locate the fault with high accuracy.

Why Geological Regions?, Daniela Flores, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In most practical applications, we approximate the spatial dependence by smooth functions. The main exception is geosciences, where, to describe, e.g., how the density depends on depth and/or on spatial location, geophysicists divide the area into regions on each of which the corresponding quantity is approximately constant. In this paper, we provide a possible explanation for this difference.