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.

Most Popular Genre's Of Videogames To Play For Hu Students, 2023 Harrisburg University of Science and Technology

#### Most Popular Genre's Of Videogames To Play For Hu Students, Asheria Upsher, Jean Orejuela, Joshua Scott

*Harrisburg University Research Symposium: Highlighting Research, Innovation, & Creativity*

Our Poster will show the most played and favored videogame genre's according to HU students.

Reducing Uncertainty In Sea-Level Rise Prediction: A Spatial-Variability-Aware Approach, 2023 University of Minnesota - Twin Cities

#### Reducing Uncertainty In Sea-Level Rise Prediction: A Spatial-Variability-Aware Approach, Subhankar Ghosh, Shuai An, Arun Sharma, Jayant Gupta, Shashi Shekhar, Aneesh Subramanian

*I-GUIDE Forum*

Given multi-model ensemble climate projections, the goal is to accurately and reliably predict future sea-level rise while lowering the uncertainty. This problem is important because sea-level rise affects millions of people in coastal communities and beyond due to climate change's impacts on polar ice sheets and the ocean. This problem is challenging due to spatial variability and unknowns such as possible tipping points (e.g., collapse of Greenland or West Antarctic ice-shelf), climate feedback loops (e.g., clouds, permafrost thawing), future policy decisions, and human actions. Most existing climate modeling approaches use the same set of weights globally, during either regression or …

Backward Stochastic Differential Equations In A Semi-Markov Chain Model, 2023 University of Calgary, Calgary, AB, T2N 1N4, Canada

#### Backward Stochastic Differential Equations In A Semi-Markov Chain Model, Robert J. Elliott, Zhe Yang

*Journal of Stochastic Analysis*

No abstract provided.

Rigid Body Constrained Motion Optimization And Control On Lie Groups And Their Tangent Bundles, 2023 Embry-Riddle Aeronautical University

#### Rigid Body Constrained Motion Optimization And Control On Lie Groups And Their Tangent Bundles, Brennan S. Mccann

*Doctoral Dissertations and Master's Theses*

Rigid body motion requires formulations where rotational and translational motion are accounted for appropriately. Two Lie groups, the special orthogonal group SO(3) and the space of quaternions H, are commonly used to represent attitude. When considering rigid body pose, that is spacecraft position and attitude, the special Euclidean group SE(3) and the space of dual quaternions DH are frequently utilized. All these groups are Lie groups and Riemannian manifolds, and these identifications have profound implications for dynamics and controls. The trajectory optimization and optimal control problem on Riemannian manifolds presents significant opportunities for theoretical development. Riemannian optimization is an attractive …

Superoscillations And Fock Spaces, 2023 Chapman University

#### Superoscillations And Fock Spaces, Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini, Daniele C. Struppa

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

In this paper we use techniques in Fock spaces theory and compute how the Segal-Bargmann transform acts on special wave functions obtained by multiplying superoscillating sequences with normalized Hermite functions. It turns out that these special wave functions can be constructed also by computing the approximating sequence of the normalized Hermite functions. First, we start by treating the case when a superoscillating sequence is multiplied by the Gaussian function. Then, we extend these calculations to the case of normalized Hermite functions leading to interesting relations with Weyl operators. In particular, we show that the Segal-Bargmann transform maps superoscillating sequences onto …

Approaches To Assessing Nutrient Coupling In Open Ocean Datasets, 2023 Humboldt State University

#### Approaches To Assessing Nutrient Coupling In Open Ocean Datasets, James M. Moore, Claire P. Till

*IdeaFest: Interdisciplinary Journal of Creative Works and Research from Cal Poly Humboldt*

Nutrient coupling describes a process where the biogeochemical cycles of two elements are linked by being incorporated similarly into biomass. This paper uses data from the GEOTRACES GP16 cruise (Eastern Pacific Zonal Transect) to investigate the relationship between certain macronutrients generally coupled to trace elements in terms of their oceanic distributions with the notable exception of in an oxygen minimum zone: cadmium-phosphate and zinc-silicate. There are many methods applied to oceanographic data to correlate analyte concentrations; while they are often presented independently in literature, here we attempt to use them in conjunction for a more thorough interpretation. By compiling 1) …

The Mean Sum Of Squared Linking Numbers Of Random Piecewise-Linear Embeddings Of $K_N$, 2023 University of Notre Dame

#### The Mean Sum Of Squared Linking Numbers Of Random Piecewise-Linear Embeddings Of $K_N$, Yasmin Aguillon, Xingyu Cheng, Spencer Eddins, Pedro Morales

*Rose-Hulman Undergraduate Mathematics Journal*

DNA and other polymer chains in confined spaces behave like closed loops. Arsuaga et al. \cite{AB} introduced the uniform random polygon model in order to better understand such loops in confined spaces using probabilistic and knot theoretical techniques, giving some classification on the mean squared linking number of such loops. Flapan and Kozai \cite{flapan2016linking} extended these techniques to find the mean sum of squared linking numbers for random linear embeddings of complete graphs $K_n$ and found it to have order $\Theta(n(n!))$. We further these ideas by inspecting random piecewise-linear embeddings of complete graphs and give introductory-level summaries of the ideas …

On The Spectrum Of Quaquaversal Operators, 2023 The Graduate Center, City University of New York

#### On The Spectrum Of Quaquaversal Operators, Josiah Sugarman

*Dissertations, Theses, and Capstone Projects*

In 1998 Charles Radin and John Conway introduced the Quaquaversal Tiling. A three dimensional hierarchical tiling with the property that the orientations of its tiles approach a uniform distribution faster than what is possible for hierarchical tilings in two dimensions. The distribution of orientations is controlled by the spectrum of a certain Hecke operator, which we refer to as the Quaquaversal Operator. For example, by showing that the largest eigenvalue has multiplicity equal to one, Charles Radin and John Conway showed that the orientations of this tiling approach a uniform distribution. In 2008, Bourgain and Gamburd showed that this operator …

Differential Calculus: From Practice To Theory, 2023 Pennsylvania State University

#### Differential Calculus: From Practice To Theory, Eugene Boman, Robert Rogers

*Milne Open Textbooks*

*Differential Calculus: From Practice to Theory* covers all of the topics in a typical first course in differential calculus. Initially it focuses on using calculus as a problem solving tool (in conjunction with analytic geometry and trigonometry) by exploiting an informal understanding of differentials (infinitesimals). As much as possible large, interesting, and important historical problems (the motion of falling bodies and trajectories, the shape of hanging chains, the Witch of Agnesi) are used to develop key ideas. Only after skill with the computational tools of calculus has been developed is the question of rigor seriously broached. At that point, the …

Geometry In Spectral Triples: Immersions And Fermionic Fuzzy Geometries, 2023 Western University

#### Geometry In Spectral Triples: Immersions And Fermionic Fuzzy Geometries, Luuk S. Verhoeven

*Electronic Thesis and Dissertation Repository*

We investigate the metric nature of spectral triples in two ways.

Given an oriented Riemannian embedding i:X->Y of codimension 1 we construct a family of unbounded KK-cycles i!(epsilon), each of which represents the shriek class of i in KK-theory. These unbounded KK-cycles are further equipped with connections, allowing for the explicit computation of the products of i! with the spectral triple of Y at the unbounded level. In the limit epsilon to 0 the product of these unbounded KK-cycles with the canonical spectral triple for Y admits an asymptotic expansion. The divergent part of this expansion is known and …

Double Barrier Backward Doubly Stochastic Differential Equations, 2023 Pension Fund Management Division, Mitsubishi UFJ Trust and Banking Corporation, 1-4-5, Marunouchi, Chiyoda-ku, Tokyo, 100-8212, Japan

#### Double Barrier Backward Doubly Stochastic Differential Equations, Tadashi Hayashi

*Journal of Stochastic Analysis*

No abstract provided.

Symmetric Functions Algebras (Sfa) Iii: Stochastic And Constant Row Sum Matrices, 2023 Southern Illinois University, Carbondale, Illinois 62901, USA

#### Symmetric Functions Algebras (Sfa) Iii: Stochastic And Constant Row Sum Matrices, Philip Feinsilver

*Journal of Stochastic Analysis*

No abstract provided.