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2023

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Articles 1171 - 1175 of 1175

Full-Text Articles in Mathematics

Quantization For A Set Of Discrete Distributions On The Set Of Natural Numbers, Juan Gomez, Haily Martinez, Mrinal Kanti Roychowdhury, Alexis Salazar, Daniel J. Vallez Jan 2023

Quantization For A Set Of Discrete Distributions On The Set Of Natural Numbers, Juan Gomez, Haily Martinez, Mrinal Kanti Roychowdhury, Alexis Salazar, Daniel J. Vallez

School of Mathematical & Statistical Sciences Faculty Publications

The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. In this paper, first we state and prove a theorem, and then give a conjecture. We verify the conjecture by a few examples. Assuming that the conjecture is true, for a set of discrete distributions on the set of natural numbers we have calculated the optimal sets of n-means and the nth quantization errors for all positive integers n. In addition, the quantization dimension is also calculated.

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Note On Illuminating Constant Width Bodies, Alexey Glazyrin Jan 2023

Note On Illuminating Constant Width Bodies, Alexey Glazyrin

School of Mathematical & Statistical Sciences Faculty Publications

Recently, Arman, Bondarenko, and Prymak constructed a constant width body in R n whose illumination number is exponential in n. In this note, we improve their bound by generalizing the construction. In particular, we construct a constant width body in R n whose illumination number is at least (τ + o(1))n, where τ ≈ 1.047.

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Constrained Quantization For Probability Distributions, Megha Pandey, Mrinal Kanti Roychowdhury Jan 2023

Constrained Quantization For Probability Distributions, Megha Pandey, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, for a Borel probability measure P on a Euclidean space Rk, we extend the definitions of nth unconstrained quantization error, unconstrained quantization dimension, and unconstrained quantization coefficient, which traditionally in the literature known as nth quantization error, quantization dimension, and quantization coefficient, to the definitions of nth constrained quantization error, constrained quantization dimension, and constrained quantization coefficient. The work in this paper extends the theory of quantization and opens a new area of research. In unconstrained quantization, the elements in an optimal set are the conditional expectations in their own Voronoi regions, and it is not true …

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Equity In Focus : Investigating Gender Disparities In Glioblastoma Via Propensity Score Matching, Solomon Eshun Jan 2023

Equity In Focus : Investigating Gender Disparities In Glioblastoma Via Propensity Score Matching, Solomon Eshun

School of Mathematical & Statistical Sciences Faculty Publications

Gender disparities in health outcomes have garnered significant attention, prompting investigations into their underlying causes. Glioblastoma (GBM), a devastating and highly aggressive form of brain tumor, serves as a case for such inquiries. Despite the mounting evidence on gender disparities in GBM outcomes, investigations specific at the molecular level remain scarce and often limited by confounding biases in observational studies. In this study, I aimed to investigate the gender-related differences in GBM outcomes using propensity score matching (PSM) to control for potential confounding variables. The data used was accessed from the Cancer Genome Atlas (TCGA), encompassing factors such as gender, …

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An Intertwined Cauchy––Schwarz–Type Inequality Based On A Lagrange–Type Identity, Iosif Pinelis Jan 2023

An Intertwined Cauchy––Schwarz–Type Inequality Based On A Lagrange–Type Identity, Iosif Pinelis

Michigan Tech Publications

Based on an apparently new Lagrange-type identity, a Cauchy–Schwarz-type inequality is proved. The mentioned identity is obtained by using certain “macro” variables; it is hoped that such a method can be used to prove or produce other identities and inequalities.

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