On The Connection Between Σϵ(A1 ⊗ A2) And Σϵ(A1), Σϵ(A2) For Certain Specialoperators,
2024
TÜBİTAK
On The Connection Between Σϵ(A1 ⊗ A2) And Σϵ(A1), Σϵ(A2) For Certain Specialoperators, Fati̇h Yilmaz
Turkish Journal of Mathematics
In this paper, the connection between the ϵ -pseudospectrum of the tensor product operator A1 ⊗ A2 andthe ϵ -pseudospectrums of operators A1 and A2 has been investigated and some results are given about this connectionunder certain conditions.
Errata: The Product Of Distributions And Stochastic Differential Equations Arising From Powers Of Infinite Dimensional Brownian Motions,
2024
Institute for Industrial and Applied Mathematics, Chungbuk National University, Cheongju 28644, Korea
Errata: The Product Of Distributions And Stochastic Differential Equations Arising From Powers Of Infinite Dimensional Brownian Motions, Un Cig Ji, Hui-Hsiung Kuo, Hara-Yuko Mimachi, Kimiaki Saito
Journal of Stochastic Analysis
No abstract provided.
Minimal Separating Sets In Surfaces,
2024
Portland State University
Minimal Separating Sets In Surfaces, Christopher Nelson Aagaard
Dissertations and Theses
Given a connected topolgical space X, we say that L ⊆ X is a minimal separating set if removing L from X gives a disconnected surface, butremoving any proper subset of L leaves the surface connected. We classify which embeddings of topological graphs are minimal separating in an orientable surface X with genus g, and construct a computer program to compute the number of such embeddings, and the number of topological graphs which admit such an embedding for g ≤ 5.
Symmetric Laminations Of Degree D And Identity Return Triangles In Degree 3,
2024
University of Alabama at Birmingham
Symmetric Laminations Of Degree D And Identity Return Triangles In Degree 3, Thomas Sirna
All ETDs from UAB
Laminations of the unit disc were introduced by Thurston in the 1980s as a tool to study the Julia sets and the parameter spaces of complex polynomials. In general, a lamination will be the unit disc D (considered as a subset of the complex plane C, with the boundary of D denoted by S) along with a collection of chords in D that can only intersect at their endpoints on S. We call the chords of a lamination leaves. In most situations we also consider a map σd : S → S on the endpoints of the leaves defined by …
Coarse-Gridded Simulation Of The Nonlinear Schrödinger Equation With Machine Learning,
2024
Air Force Institute of Technology
Coarse-Gridded Simulation Of The Nonlinear Schrödinger Equation With Machine Learning, Benjamin F. Akers, Kristina O. F. Williams
Faculty Publications
A numerical method for evolving the nonlinear Schrödinger equation on a coarse spatial grid is developed. This trains a neural network to generate the optimal stencil weights to discretize the second derivative of solutions to the nonlinear Schrödinger equation. The neural network is embedded in a symmetric matrix to control the scheme’s eigenvalues, ensuring stability. The machine-learned method can outperform both its parent finite difference method and a Fourier spectral method. The trained scheme has the same asymptotic operation cost as its parent finite difference method after training. Unlike traditional methods, the performance depends on how close the initial data …
Meta-Analysis Of Set-Based Multiple Phenotype Association Test Based On Gwas Summary Statistics From Different Cohorts,
2024
Michigan Technological University
Meta-Analysis Of Set-Based Multiple Phenotype Association Test Based On Gwas Summary Statistics From Different Cohorts, Lirong Zhu, Shuanglin Zhang, Qiuying Sha
Michigan Tech Publications
Genome-wide association studies (GWAS) have emerged as popular tools for identifying genetic variants that are associated with complex diseases. Standard analysis of a GWAS involves assessing the association between each variant and a disease. However, this approach suffers from limited reproducibility and difficulties in detecting multi-variant and pleiotropic effects. Although joint analysis of multiple phenotypes for GWAS can identify and interpret pleiotropic loci which are essential to understand pleiotropy in diseases and complex traits, most of the multiple phenotype association tests are designed for a single variant, resulting in much lower power, especially when their effect sizes are small and …
Generalized Periodicity And Applications To Logistic Growth,
2024
Missouri University of Science and Technology
Generalized Periodicity And Applications To Logistic Growth, Martin Bohner, Jaqueline Mesquita, Sabrina Streipert
Mathematics and Statistics Faculty Research & Creative Works
Classically, a continuous function f:R→R is periodic if there exists an ω>0 such that f(t+ω)=f(t) for all t∈R. The extension of this precise definition to functions f:Z→R is straightforward. However, in the so-called quantum case, where f:qN0→R (q>1), or more general isolated time scales, a different definition of periodicity is needed. A recently introduced definition of periodicity for such general isolated time scales, including the quantum calculus, not only addressed this gap but also inspired this work. We now return to the continuous case and present the concept of ν-periodicity that connects these different formulations of periodicity for …
The Cubic-Quintic Nonlinear Schrödinger Equation With Inverse-Square Potential,
2024
Missouri University of Science and Technology
The Cubic-Quintic Nonlinear Schrödinger Equation With Inverse-Square Potential, Alex H. Ardila, Jason Murphy
Mathematics and Statistics Faculty Research & Creative Works
We consider the nonlinear Schrödinger equation in three space dimensions with a focusing cubic nonlinearity and defocusing quintic nonlinearity and in the presence of an external inverse-square potential. We establish scattering in the region of the mass-energy plane where the virial functional is guaranteed to be positive. Our result parallels the scattering result of [11] in the setting of the standard cubic-quintic NLS.
A Full Description Of All Commutative Associative Polynomial Operations On Probabilities,
2024
Czech Technical University in Prague
A Full Description Of All Commutative Associative Polynomial Operations On Probabilities, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong
Departmental Technical Reports (CS)
When two events are independent, the probability that both events occur is equal to the product p1 * p2 of the probabilities of each of these events. The probability that at least one of these events will occur is equal to p1 + p2 − p1 * p2. In both cases, we have a commutative associative polynomial operation. A natural question is: how can we describe all possible operations of this type? These operations are described in this paper.
Why Kolmolgorov-Arnold Networks (Kan) Work So Well: A Qualitative Explanation,
2024
New Mexico State University
Why Kolmolgorov-Arnold Networks (Kan) Work So Well: A Qualitative Explanation, Hung T. Nguyen, Vladik Kreinovich, Olga Kosheleva
Departmental Technical Reports (CS)
In the usual deep neural network, weights are adjusted during training, but the activation function remains the same. Lately, it was experimentally shown that if, instead of using the same activation function always, we train the activation functions as well, we get a much better results -- i.e., for the networks with the same number of parameters, we get a much better accuracy. Such networks are called Kolmogorov-Arnold networks. In this paper, we provide a general explanation of why these new networks work so well.
How To Check Continuity Based On Approximate Measurement Results,
2024
University of Latvia
How To Check Continuity Based On Approximate Measurement Results, Inese Bula, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, a reasonable conjecture is that, e.g., the dependence of some quantity on the spatial location is continuous, with an appropriate bounds on the difference between the values at nearby points. If we knew the exact values of the corresponding quantity, checking this conjecture would be very straightforward. In reality, however, measurement results are only approximations to the actual values. In this paper, we show how to check continuity based on the approximate measurement results.
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.
To Which Interdisciplinary Research Collaborations Should We Pay More Attention?,
2024
Czech Technical University in Prague
To Which Interdisciplinary Research Collaborations Should We Pay More Attention?, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong
Departmental Technical Reports (CS)
Interdisciplinary research is very important in modern science. However, such a research is not easy, it often needs support and help. Resources that can be used for such a support are limited, so we need to decide which of many possible collaborations we should support. In this paper, we provide a natural simple model of collaboration effectiveness. Based on this model, we conclude that we should support collaborations for which the vector product of the participants' knowledge vectors attains the largest values.
Why Decisions Based On The Results Of Worst-Case, Most Realistic, And Best-Case Scenarios Work Well?,
2024
Czech Technical University in Prague
Why Decisions Based On The Results Of Worst-Case, Most Realistic, And Best-Case Scenarios Work Well?, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich, Chon Van Le
Departmental Technical Reports (CS)
Often, to make an appropriate decision, people try three scenarios: the worst case, the most realistic case, and the best case. This three-scenarios approach often leads to reasonable decisions. A natural question is: why worst case and best case? These extreme cases mean that all numerous independent random factors work in the same direction: either are all stacked for or are all stacked against. Such stacking of random factors is highly improbable. So, at first glance, it would be more beneficial to use more realistic scenarios than the worst case and the best case. However, empirically, decisions based on the …
Why Green Wavelength Is Closer To Blue Than To Red And How It Is Related To Computations: Information-Based Explanation,
2024
Admiral Makarov National Shipbuilding University
Why Green Wavelength Is Closer To Blue Than To Red And How It Is Related To Computations: Information-Based Explanation, Victor L. Timchenko, Yury P. Kondratenko, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong
Departmental Technical Reports (CS)
In our previous papers, we analyzed the idea of using light signals of three basic color -- red, green, and blue -- to speed up computations, in particular fuzzy-related computations. A natural question is: why red, green, and blue? Why not select some other colors: e.g., from the wavelength viewpoint, green is much closer to blue than to green, so why not select colors whose distribution is more even? In this paper, we show that if we consider this problem from the information viewpoint, then the corresponding equal-information criterion indeed implies that the intermediate wavelength should be closer to the …
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 …
Fractional Derivative-Based Analysis Of The Heat Transfer Properties Of Fluid Flow Over A Contracting Permeable Infinite-Length Cylinder,
2024
United Arab Emirates University
Fractional Derivative-Based Analysis Of The Heat Transfer Properties Of Fluid Flow Over A Contracting Permeable Infinite-Length Cylinder, Anas Saeb Alhasan
Theses
Understanding the complex interplay between the contracting behavior of the cylinder and the fluid flow dynamics has implications for the design of porous structures for heat exchange and filtration systems. In this study, we investigate the dynamics and thermal behavior of fluid flow past a contracting permeable infinite cylinder. First, we developed a mathematical model based on the Navier-Stokes equations to describe the fluid dynamics around the contracting permeable infinite cylinder. A new simple well-behaved definition of fractional derivative called conformable fractional derivative introduced by authors Khalil et al. [3] is employed to generalize the PDE’s of momentum and energy. …
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
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 …
Limit Theorems For L-Functions In Analytic Number Theory,
2024
CUNY Graduate Center
Limit Theorems For L-Functions In Analytic Number Theory, Asher Roberts
Dissertations, Theses, and Capstone Projects
We use the method of Radziwill and Soundararajan to prove Selberg’s central limit theorem for the real part of the logarithm of the Riemann zeta function on the critical line in the multivariate case. This gives an alternate proof of a result of Bourgade. An upshot of the method is to determine a rate of convergence in the sense of the Dudley distance. This is the same rate Selberg claims using the Kolmogorov distance. We also achieve the same rate of convergence in the case of Dirichlet L-functions. Assuming the Riemann hypothesis, we improve the rate of convergence by using …
Twisted Alexander Polynomials And Ptolemy Varieties Of Knots And Surface Bundles,
2024
CUNY Graduate Center
Twisted Alexander Polynomials And Ptolemy Varieties Of Knots And Surface Bundles, Michael R. Marinelli
Dissertations, Theses, and Capstone Projects
The first focus of this dissertation is to compute Ptolemy varieties for triangulations of two infinite families of manifolds. Given an ideal triangulation of a cusped manifold, one can compute the Ptolemy variety and using it, obtain parabolic representations of the fundamental group. We compute certain obstruction classes for these manifolds, which are necessary to obtain the discrete faithful representation. This leads to our second focus of the dissertation, the twisted Alexander polynomial. The twisted Alexander polynomial (TAP) is a variation of the classical Alexander polynomial twisted by a representation of the fundamental group into a linear group. It was …
