Applications Of Survival Estimation Under Stochastic Order To Cancer: The Three Sample Problem, 2024 St. Mary's University

#### Applications Of Survival Estimation Under Stochastic Order To Cancer: The Three Sample Problem, Sage Vantine

*Honors Program Theses and Research Projects*

Stochastic ordering of probability distributions holds various practical applications. However, in real-world scenarios, the empirical survival functions extracted from actual data often fail to meet the requirements of stochastic ordering. Consequently, we must devise methods to estimate these distribution curves in order to satisfy the constraint. In practical applications, such as the investigation of the time of death or the progression of diseases like cancer, we frequently observe that patients with one condition are expected to exhibit a higher likelihood of survival at all time points compared to those with a different condition. Nevertheless, when we attempt to fit a …

Quasistationary Distribution For The Invasion Model On A Complete Bipartite Graph, 2024 University of British Columbia, Vancouver, BC V6T 1Z4, Canada

#### Quasistationary Distribution For The Invasion Model On A Complete Bipartite Graph, Clayton Allard, Iddo Ben-Ari, Shrikant Chand, Van Hovenga, Edith Lee, Julia Shapiro

*Journal of Stochastic Analysis*

No abstract provided.

A Characterization Of The Operator Entropy In Terms Of An Isometry Property Related To Trace Norms, 2024 Meijo University, Tenpaku, Nagoya 468- 8502, Japan

#### A Characterization Of The Operator Entropy In Terms Of An Isometry Property Related To Trace Norms, Ryo Inayoshi

*Journal of Stochastic Analysis*

No abstract provided.

A Bayesian Approach For Lifetime Modeling And Prediction With Multi-Type Group-Shared Missing Covariates, 2024 Communication University of Zhejiang

#### A Bayesian Approach For Lifetime Modeling And Prediction With Multi-Type Group-Shared Missing Covariates, Hao Zeng, Xuxue Sun, Kuo Wang, Yuxin Wen, Wujun Si, Mingyang Li

*Engineering Faculty Articles and Research*

In the field of reliability engineering, covariate information shared among product units within a specific group (e.g., a manufacturing batch, an operating region), such as operating conditions and design settings, exerts substantial influence on product lifetime prediction. The covariates shared within each group may be missing due to sensing limitations and data privacy issues. The missing covariates shared within the same group commonly encompass a variety of attribute types, such as discrete types, continuous types, or mixed types. Existing studies have mainly considered single-type missing covariates at the individual level, and they have failed to thoroughly investigate the influence of …

Pseudo-Differential Operators On The Circle, Bernoulli Polynomials, 2024 University Bordeaux

#### Pseudo-Differential Operators On The Circle, Bernoulli Polynomials, Roger Gay, Ahmed Sebbar

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

We show how the classical polylogarithm function Li_{s} (z) and its relatives, the Hurwitz zeta function and the Lerch function are all of a spectral nature, and can explain many properties of the complex powers of the Laplacian on the circle and of the distribution (x +i0)^{s} .We also make a relation with a result of Keiper [Fractional Calculus and its relationship to Riemann’s zeta function, Master of Science, Ohio State University, Mathematics (1975)].

Spacetime Geometry Of Acoustics And Electromagnetism, 2024 Chapman University

#### Spacetime Geometry Of Acoustics And Electromagnetism, Lucas Burns, Tatsuya Daniel, Stephon Alexander, Justin Dressel

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

Both acoustics and electromagnetism represent measurable fields in terms of dynamical potential fields. Electromagnetic force-fields form a spacetime bivector that is represented by a dynamical energy–momentum 4-vector potential field. Acoustic pressure and velocity fields form an energy–momentum density 4-vector field that is represented by a dynamical action scalar potential field. Surprisingly, standard field theory analyses of spin angular momentum based on these traditional potential representations contradict recent experiments, which motivates a careful reassessment of both theories. We analyze extensions of both theories that use the full geometric structure of spacetime to respect essential symmetries enforced by vacuum wave propagation. The …

Two Non–*–Isomorphic *–Lie Algebra Structures On Sl(2,R) And Their Physical Origins, 2024 Università di Roma Tor Vergata, Roma I-00133, Italy

#### Two Non–*–Isomorphic *–Lie Algebra Structures On Sl(2,R) And Their Physical Origins, Luigi Accardi, Irina Ya. ArefʹEva, Yungang Lu, Igorʹ VasilʹEvich Volovich

*Journal of Stochastic Analysis*

No abstract provided.

New Effective Transformational Computational Methods, 2024 University of Maryland Eastern Shore

#### New Effective Transformational Computational Methods, Jun Zhang, Ruzong Fan, Fangyang Shen, Junyi Tu

*Publications and Research*

Mathematics serves as a fundamental intelligent theoretic basis for computation, and mathematical analysis is very useful to develop computational methods to solve various problems in science and engineering. Integral transforms such as Laplace Transform have been playing an important role in computational methods. In this paper, we will introduce Sumudu Transform in a new computational approach, in which effective computational methods will be developed and implemented. Such computational methods are straightforward to understand, but powerful to incorporate into computational science to solve different problems automatically. We will provide computational analysis and essentiality by surveying and summarizing some related recent works, …

The Frankensteinian Nature Of Mathematics, 2024 Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran

#### The Frankensteinian Nature Of Mathematics, Ali Barahmand

*Journal of Humanistic Mathematics*

Frankenstein is a story about a scientist who creates a sapient creature that gets out of control and horrifies its creator by its unexpected behavior. In this note, we show that this type of undesirable behavior can reflect a part of the nature of mathematics, and that its origin is related to the ontological question of whether mathematics is invented or discovered. Based on a review of the relationship be- tween discovery and invention, we demonstrate that mathematics has similarities and differences with both discovery and invention. In the natural sciences, new instruments have to be invented to discover new …

Covariant Anyons Via Mackey Machinery, 2024 Army Research Laboratory Adelphi, MD, 21005-5069, USA

#### Covariant Anyons Via Mackey Machinery, Radhakrishnan Balu

*Journal of Stochastic Analysis*

No abstract provided.

Nonlinear Filtering Of Classical And Quantum Spin Systems, 2024 National Academies/Air Force Research Laboratory, Wright Patterson Air Force Base, Ohio 45433 USA

#### Nonlinear Filtering Of Classical And Quantum Spin Systems, Sivaguru S. Sritharan, Saba Mudaliar

*Journal of Stochastic Analysis*

No abstract provided.

Reducing Food Scarcity: The Benefits Of Urban Farming, 2023 Brigham Young University

#### Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

*Journal of Nonprofit Innovation*

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Convolution And Autoencoders Applied To Nonlinear Differential Equations, 2023 East Tennessee State University

#### Convolution And Autoencoders Applied To Nonlinear Differential Equations, Noah Borquaye

*Electronic Theses and Dissertations*

Autoencoders, a type of artificial neural network, have gained recognition by researchers in various fields, especially machine learning due to their vast applications in data representations from inputs. Recently researchers have explored the possibility to extend the application of autoencoders to solve nonlinear differential equations. Algorithms and methods employed in an autoencoder framework include sparse identification of nonlinear dynamics (SINDy), dynamic mode decomposition (DMD), Koopman operator theory and singular value decomposition (SVD). These approaches use matrix multiplication to represent linear transformation. However, machine learning algorithms often use convolution to represent linear transformations. In our work, we modify these approaches to …

(R2054) Convergence Of Lagrange-Hermite Interpolation Using Non-Uniform Nodes On The Unit Circle, 2023 University of Lucknow

#### (R2054) Convergence Of Lagrange-Hermite Interpolation Using Non-Uniform Nodes On The Unit Circle, Swarnima Bahadur, Sameera Iqram, Varun .

*Applications and Applied Mathematics: An International Journal (AAM)*

In this research article, we brought into consideration the set of non-uniformly distributed nodes on the unit circle to investigate a Lagrange-Hermite interpolation problem. These nodes are obtained by projecting vertically the zeros of Jacobi polynomial onto the unit circle along with the boundary points of the unit circle on the real line. Explicitly representing the interpolatory polynomial as well as establishment of convergence theorem are the key highlights of this manuscript. The result proved are of interest to approximation theory.

Measuring The Lengths Of Sperm Whales Of The Northern Gulf Of Mexico By Wavelet Analysis Of Their Usual Clicks, 2023 University of New Orleans

#### Measuring The Lengths Of Sperm Whales Of The Northern Gulf Of Mexico By Wavelet Analysis Of Their Usual Clicks, George Drouant

*University of New Orleans Theses and Dissertations*

Abstract

Acoustic recordings of underwater sounds produced by marine mammals present an attractive alternative to costly and logistically complex ship based visual surveys for collecting population data for various species.

The first reported use of underwater acoustic recordings in the long-term monitoring of sperm whale populations was by Ackleh et al. (Ackleh et al., 2012). The paper describes counting sperm whale clicks at different locations to track population changes over time.

Analysis of sperm whale clicks offers additional insight into sperm whale populations. The echo location clicks (usual clicks) of sperm whales can be used to give an estimate of …

An Exposition Of The Curvature Of Warped Product Manifolds, 2023 California State University - San Bernardino

#### An Exposition Of The Curvature Of Warped Product Manifolds, Angelina Bisson

*Electronic Theses, Projects, and Dissertations*

The field of differential geometry is brimming with compelling objects, among which are warped products. These objects hold a prominent place in differential geometry and have been widely studied, as is evident in the literature. Warped products are topologically the same as the Cartesian product of two manifolds, but with distances in one of the factors in skewed. Our goal is to introduce warped product manifolds and to compute their curvature at any point. We follow recent literature and present a previously known result that classifies all flat warped products to find that there are flat examples of warped products …

Msis-Capaldi: Modelling The Winter Tick Epizootic In Moose, 2023 University of Tennessee, Knoxville

#### Msis-Capaldi: Modelling The Winter Tick Epizootic In Moose, Charlotte Beckford

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Integrating Quantitative Skills Into Biology Courses, 2023 UMBC

#### Integrating Quantitative Skills Into Biology Courses, Kathleen Hoffman, Sarah Leupen, Hannah Pie, Michelle Starz-Gaiano, Patricia Turner, Tory Williams

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Modelling Impact Of Diverse Vegetation On Crop-Pollinator Interactions, 2023 Texas Tech University

#### Modelling Impact Of Diverse Vegetation On Crop-Pollinator Interactions, Morgan N. Beetler

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

On A Stationary Random Knot, 2023 Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

#### On A Stationary Random Knot, Andrey A. Dorogovtsev

*Journal of Stochastic Analysis*

No abstract provided.