Three Applications Of Geometric Reasoning: Why Metastasis Is Mostly Caused By Elongated Cancer Cells? How Body Shape Affects Curiosity? Why Ring Fractures In Ice?, 2024 The University of Texas at El Paso

#### Three Applications Of Geometric Reasoning: Why Metastasis Is Mostly Caused By Elongated Cancer Cells? How Body Shape Affects Curiosity? Why Ring Fractures In Ice?, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich

*Departmental Technical Reports (CS)*

In this paper, we describe three applications of geometric reasoning to important practical problems ranging from micro- to macro-level. Specifically, we use geometric reasoning to explain why metastasis is mostly caused by elongated cancer cell, why curiosity in fish is strongly correlated with body shape, and why ring-shaped fractures appear in Antarctica.

Training Neural Networks On Interval Data: Unexpected Results And Their Explanation, 2024 The University of Texas at El Paso

#### Training Neural Networks On Interval Data: Unexpected Results And Their Explanation, Edwin Tomy George, Vladik Kreinovich, Christoph Lauter, Martine Ceberio, Luc Jaulin

*Departmental Technical Reports (CS)*

In many practically useful numerical computations, training-and-then-using a neural network turned out to be a much faster alternative than running the original computations. When we applied a similar idea to take into account interval uncertainty, we encountered two unexpected results: (1) that while for numerical computations, it is usually better to represent an interval by its midpoint and half-width, for neural networks, it is more efficient to represent an interval by its endpoints, and (2) that while usually, it is better to train a neural network on the whole data processing algorithm, in our problems, it turned out to be …

A Staged Approach Using Machine Learning And Uncertainty Quantification To Predict The Risk Of Hip Fracture, 2024 Michigan Technological University

#### A Staged Approach Using Machine Learning And Uncertainty Quantification To Predict The Risk Of Hip Fracture, Anjum Shaik, Kristoffer A. Larsen, Nancy E. Lane, Chen Zhao, Kuan Jui Su, Joyce H. Keyak, Qing Tian, Qiuying Sha, Hui Shen, Hong Wen Deng, Weihua Zhou

*Michigan Tech Publications, Part 2*

Hip fractures present a significant healthcare challenge, especially within aging populations, where they are often caused by falls. These fractures lead to substantial morbidity and mortality, emphasizing the need for timely surgical intervention. Despite advancements in medical care, hip fractures impose a significant burden on individuals and healthcare systems. This paper focuses on the prediction of hip fracture risk in older and middle-aged adults, where falls and compromised bone quality are predominant factors. The study cohort included 547 patients, with 94 experiencing hip fracture. To assess the risk of hip fracture, clinical variables and clinical variables combined with hip DXA …

Exact Solutions Of Stochastic Burgers–Korteweg De Vries Type Equation With Variable Coefficients, 2024 The University of Texas Rio Grande Valley

#### Exact Solutions Of Stochastic Burgers–Korteweg De Vries Type Equation With Variable Coefficients, Kolade Adjibi, Allan Martinez, Miguel Mascorro, Carlos Montes, Tamer Oraby, Rita Sandoval, Erwin Suazo

*School of Mathematical and Statistical Sciences Faculty Publications and Presentations*

We will present exact solutions for three variations of the stochastic Korteweg de Vries–Burgers (KdV–Burgers) equation featuring variable coefficients. In each variant, white noise exhibits spatial uniformity, and the three categories include additive, multiplicative, and advection noise. Across all cases, the coefficients are time-dependent functions. Our discovery indicates that solving certain deterministic counterparts of KdV–Burgers equations and composing the solution with a solution of stochastic differential equations leads to the exact solution of the stochastic Korteweg de Vries–Burgers (KdV–Burgers) equations.

Numerical Simulations For Fractional Differential Equations Of Higher Order And A Wright-Type Transformation, 2024 The University of Texas Rio Grande Valley

#### Numerical Simulations For Fractional Differential Equations Of Higher Order And A Wright-Type Transformation, Mariana Nacianceno, Tamer Oraby, Hansapani Rodrigo, Y. Sepulveda, Josef A. Sifuentes, Erwin Suazo, T. Stuck, J. Williams

*School of Mathematical and Statistical Sciences Faculty Publications and Presentations*

In this work, a new relationship is established between the solutions of higher order fractional differential equations and a Wright-type transformation. Solutions could be interpreted as expected values of functions in a random time process. As applications, we solve the fractional beam equation, fractional electric circuits with special functions as external sources, derive d’Alembert’s formula and show the existence of explicit solutions for a general fractional wave equation with variable coefficients. Due to this relationship, we present two methods for simulating solutions of fractional differential equations. The two approaches use the interpretation of the Caputo derivative of a function as …

Some Studies On Mathematical Morphology In Remotely Sensed Data Analysis, 2024 Indian Statistical Institute

#### Some Studies On Mathematical Morphology In Remotely Sensed Data Analysis, Geetika Barman

*Doctoral Theses*

The application of Mathematical Morphology (MM) techniques has proven to be beneficial in the extraction of shapebased and texture-based features during remote sensing image analysis. The characteristics of these techniques, such as nonlinear adaptability and comprehensive lattice structure, make them useful for contextual spatial feature analysis. Despite the advancements, there are still persistent challenges, including the curse of dimensionality, maintaining spatial correlation, and the adaptability of morphological operators in higher dimensions. The focus of this thesis is to explore the potential of MM-based methods to analyse spatial features in addressing these challenges, specifically in the context of spatialcontextual feature analysis …

Oer Textbook Review For Calculus - Openstax Calculus, 2024 Bentley University

#### Oer Textbook Review For Calculus - Openstax Calculus, Jing Hu Ph.D.

*Open Educational Resources Publications*

This OER textbook review provides a comprehensive evaluation of the "Calculus" textbook series published by OpenStax. The reviewer, Jing Hu, an adjunct lecturer at Bentley University, highlights the textbook's strengths, including its thorough coverage of essential calculus topics, accurate and well-established mathematical principles, practical relevance, and user-friendly design. The open-access nature of the resource is seen as a significant advantage, contributing to its long-term utility and accessibility for both students and educators. Overall, the review concludes that the OpenStax Calculus textbook is a high-quality, comprehensive, and freely available resource that effectively supports the learning and teaching of calculus.

A Micromagnetic Study Of Skyrmions In Thin-Film Multilayered Ferromagnetic Materials, 2024 New Jersey Institute of Technology

#### A Micromagnetic Study Of Skyrmions In Thin-Film Multilayered Ferromagnetic Materials, Nicholas J. Dubicki

*Dissertations*

Magnetic skyrmions are topologically protected, localized, nanoscale spin textures in non-centrosymmetric thin ferromagnetic materials and heterostructures. At present they are of great interest to physicists for potential applications in information technology due to their particle-like properties and stability. In a system of multiple thin ferromagnetic layers, the stray field interaction was typically treated with various simplifications and approximations. It is shown that extensive analysis of the micromagnetic equations leads to an exact representation of the stray field interaction energy in the form of layer interaction kernels, a so-called 'finite thickness' representation. This formulation reveals the competition between perpendicular magnetic anisotropy …

Graph And Group Theoretic Properties Of The Soma Cube And Somap, 2024 Rose-Hulman Institute of Technology

#### Graph And Group Theoretic Properties Of The Soma Cube And Somap, Kyle Asbury, Ben Glancy

*Mathematical Sciences Technical Reports (MSTR)*

The SOMA Cube is a puzzle toy in which seven irregularly shaped blocks must be fit together to build a cube. There are 240 distinct solutions to the SOMA Cube. One rainy afternoon, Conway and Guy created a graph of all the solutions by manually building each solution. They called their graph the SOMAP. We studied how the geometric structure of the SOMA Cube pieces informs the graph theoretic properties of the SOMAP, such as subgraphs that can or cannot appear and vertex centrality. We have also used permutation group theory to decipher notation used by Knuth in previous work …

On Blow-Up And Explicit Soliton Solutions For Coupled Variable Coefficient Nonlinear Schrödinger Equations, 2024 The University of Texas Rio Grande Valley

#### On Blow-Up And Explicit Soliton Solutions For Coupled Variable Coefficient Nonlinear Schrödinger Equations, Jose M. Escorcia, Erwin Suazo

*School of Mathematical and Statistical Sciences Faculty Publications and Presentations*

This work is concerned with the study of explicit solutions for a generalized coupled nonlinear Schrödinger equations (NLS) system with variable coefficients. Indeed, by employing similarity transformations, we show the existence of rogue wave and dark–bright soliton-like solutions for such a generalized NLS system, provided the coefficients satisfy a Riccati system. As a result of the multiparameter solution of the Riccati system, the nonlinear dynamics of the solution can be controlled. Finite-time singular solutions in the 𝐿∞ norm for the generalized coupled NLS system are presented explicitly. Finally, an n-dimensional transformation between a variable coefficient NLS coupled system and a …

New Class Function In Dual Soft Topological Space, 2024 Ministry of Education, Directorate of Educational Babylon, Hilla, Iraq,

#### New Class Function In Dual Soft Topological Space, Maryam Adnan Al-Ethary, Maryam Sabbeh Al-Rubaiea, Mohammed H. O. Ajam

*Al-Bahir Journal for Engineering and Pure Sciences*

In this paper we introduce a new class of maps in the dual Soft topological space and study some of its basic properties and relations among them, then we study and mapping.

Dynamic Optimization With Timing Risk, 2024 Reed College

#### Dynamic Optimization With Timing Risk, Erin Cottle Hunt, Frank N. Caliendo

*Economics and Finance Faculty Publications*

Timing risk refers to a situation in which the *timing* of an economically important event is unknown (risky) from the perspective of an economic decision maker. While this special class of dynamic stochastic control problems has many applications in economics, the methods used to solve them are not easily accessible within a single, comprehensive survey. We provide a survey of dynamic optimization methods under comprehensive assumptions about the nature of timing risk. We also relax the assumption of full information and summarize optimization with limited information, ambiguity, imperfect hedging, and dynamic inconsistency. Our goal is to provide a concise user …

Math Developmental Models Examined: Pass Rate, Duration For Completion, Enrollment Consistency And Racial Disparity, 2024 University of Arkansas in Little Rock

#### Math Developmental Models Examined: Pass Rate, Duration For Completion, Enrollment Consistency And Racial Disparity, Xixi Wang, Annie Childers, Lianfang Lu

*Journal of Access, Retention, and Inclusion in Higher Education*

No abstract provided.

The Bicomplex Tensor Product And A Bicomplex Choi Theorem, 2024 Chapman University

#### The Bicomplex Tensor Product And A Bicomplex Choi Theorem, Daniel Alpay, Antonino De Martino, Kamal Diki, Mihaela Vajiac

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

In this paper we extend the concept of tensor product to the bicomplex case and use it to prove the bicomplex counterpart of the classical Choi theorem in the theory of complex matrices and operators. The concept of hyperbolic tensor product is also discussed, and we link these results to the theory of quantum channels in the bicomplex and hyperbolic case.

A Second Homotopy Group For Digital Images, 2024 The University of Texas Rio Grande Valley

#### A Second Homotopy Group For Digital Images, Gregory Lupton, Oleg R. Musin, Nicholas A. Scoville, P. Christopher Staecker, Jonathan Treviño-Marroquín

*School of Mathematical and Statistical Sciences Faculty Publications and Presentations*

We define a second (higher) homotopy group for digital images. Namely, we construct a functor from digital images to abelian groups, which closely resembles the ordinary second homotopy group from algebraic topology. We illustrate that our approach can be effective by computing this (digital) second homotopy group for a digital 2-sphere.

Modeling, Analysis, Approximation, And Application Of Viscoelastic Structures And Anomalous Transport, 2024 University of South Carolina

#### Modeling, Analysis, Approximation, And Application Of Viscoelastic Structures And Anomalous Transport, Yiqun Li

*Theses and Dissertations*

(Variable-order) fractional partial differential equations are emerging as a competitive means to integer-order PDEs in characterizing the memory and hereditary properties of physical processes, e.g., anomalously diffusive transport, viscoelastic mechanics and financial mathematics, and thus have attracted widespread attention. In particular, optimal control problems governed by fractional partial differential equations are attracting increasing attentions since they are shown to provide competitive descriptions of challenging physical phenomena. Nevertheless, variable-order fractional models exhibit salient features compared with their constant-order analogues and introduce mathematical difficulties that are not typical encountered in the context of integer-order and constant-order fractional partial differential equations.

This dissertation …

Generalizations Of The Graham-Pollak Tree Theorem, 2024 University of South Carolina

#### Generalizations Of The Graham-Pollak Tree Theorem, Gabrielle Anne Tauscheck

*Theses and Dissertations*

Graham and Pollak showed in 1971 that the determinant of a tree’s distance matrix depends only on its number of vertices, and, in particular, it is always nonzero. This dissertation will generalize their result via two different directions: Steiner distance *k*-matrices and distance critical graphs. The Steiner distance of a collection of *k* vertices in a graph is the fewest number of edges in any connected subgraph containing those vertices; for *k* = 2, this reduces to the ordinary definition of graphical distance. Here, we show that the hyperdeterminant of the Steiner distance *k*-matrix is always zero if …

Representation Dimensions Of Algebraic Tori And Symmetric Ranks Of G-Lattices, 2024 University of South Carolina

#### Representation Dimensions Of Algebraic Tori And Symmetric Ranks Of G-Lattices, Jason Bailey Heath

*Theses and Dissertations*

Algebraic tori over a field k are special examples of affine group schemes over *k*, such as the multiplicative group of the field or the unit circle. Any algebraic torus can be embedded into the group of invertible *n* x *n* matrices with entries in *k* for some *n*, and the smallest such n is called the representation dimension of that torus. Representation dimensions of algebraic tori can be studied via symmetric ranks of *G*-lattices. A *G*-lattice *L* is a group isomorphic to the additive group Z^{n} for some *n*, along with an action …

Erlang-Distributed Seir Epidemic Models With Cross-Diffusion, 2024 University of South Carolina

#### Erlang-Distributed Seir Epidemic Models With Cross-Diffusion, Victoria Chebotaeva

*Theses and Dissertations*

We examine the effects of cross-diffusion dynamics in epidemiological models. Using reaction-diffusion dynamics to model the spread of infectious diseases, we focus on situations in which the movement of individuals is affected by the concentration of individuals of other categories. In particular, we present a model where susceptible individuals move away from large concentrations of infected and infectious individuals.

Our results show that accounting for this cross-diffusion dynamics leads to a noticeable effect on epidemic dynamics. It is noteworthy that this leads to a delay in the onset of epidemics and an increase in the total number of people infected. …

Global Well-Posedness Of Nonlocal Differential Equations Arising From Traffic Flow, 2024 University of South Carolina

#### Global Well-Posedness Of Nonlocal Differential Equations Arising From Traffic Flow, Thomas Joseph Hamori

*Theses and Dissertations*

Macroscopic traffic flow models describe the evolution of a function ρ(t, x), which represents the traffic density at time t and location x according to a differential equation (typically a conservation law). Numerous models have been introduced over the years which capture the phenomenon of shock formation in which the solution develops a discontinuity. This presents difficulties from the standpoint of mathematical analysis, necessitating the consideration of weak solutions. At the same time, this undesirable mathematical behavior corresponds to unsafe driving conditions on real roadways, in which the heaviness of traffic may vary abruptly and dramatically. This thesis introduces and …