Math Research Articles

Physics Maths Engineering

Heavy-Tailed Probability Distributions: Some Examples of Their Appearance

Heavy-tailed distributions, such as Pareto's law and Lotka's law, are characterized by their propensity to produce extreme values more frequently than distributions with lighter tails, like the normal distribution. In social sciences, these distributions often describe phenomena where a small number of occurrences account for a large proportion of the effect, such as wealth distribution or scienti...
3 months ago

Physics Maths Engineering

Sequential Test of Fuzzy Hypotheses

This paper explores the problem of testing statistical hypotheses when the hypotheses are fuzzy and the data are crisp. The authors introduce new definitions for mass (density) probability functions with fuzzy parameters, as well as probabilities of type I and type II errors. They then present and prove a sequential probability ratio test for fuzzy hypotheses based on these new error definitions. ...
3 months ago

Physics Maths Engineering

Inverse problem for semilinear wave equation with strong damping

The initial-boundary and the inverse coefficient problems for the semilinear hyperbolic equation with strong damping are considered in this study. The conditions for the existence and uniqueness of solutions in Sobolev spaces to these problems have been established. The inverse problem involves determining the unknown time-dependent parameter in the right-hand side function of the equation using a...
5 months ago

Physics Maths Engineering

Regression with Ordered Predictors via Ordinal Smoothing Splines

The article "Regression with Ordered Predictors via Ordinal Smoothing Splines" by Nathaniel E. Helwig addresses the challenges of incorporating ordered categorical predictors into regression models. Traditional regression frameworks often treat ordinal predictors as either nominal (unordered) or continuous variables, which can be theoretically and computationally undesirable. This study propose...
5 months ago

Physics Maths Engineering

A Tree-Based Multiscale Regression Method

The article "A Tree-Based Multiscale Regression Method" by Haiyan Cai and Qingtang Jiang introduces a novel regression technique designed to effectively handle high-dimensional data. This method adapts to the intrinsic lower-dimensional structure of the data, mitigating the challenges posed by the "curse of dimensionality." It also offers smoother estimates in regions where the regression funct...
5 months ago

Physics Maths Engineering

CPD-Structured Multivariate Polynomial Optimization

We introduce the Tensor-Based Multivariate Optimization (TeMPO) framework for use in nonlinear optimization problems commonly encountered in signal processing, machine learning, and artificial intelligence. Within our framework, we model nonlinear relations by a multivariate polynomial that can be represented by low-rank symmetric tensors (multi-indexed arrays), making a compromise between model g...
5 months ago

Physics Maths Engineering

Three little arbitrage theorems

The authors proved three theorems about the exact solutions of a generalized or interacting Black–Scholes equation that explicitly includes arbitrage bubbles. These arbitrage bubbles can be characterized by an arbitrage number AN. The first theorem states that if AN = 0, then the solution at maturity of the interacting equation is identical to the solution of the free Black–Scholes equation wi...
5 months ago

Physics Maths Engineering

Kernel-Based Analysis of Massive Data

Dealing with massive data is a challenging task for machine learning. An important aspect of machine learning is function approximation. In the context of massive data, some of the commonly used tools for this purpose are sparsity, divide-and-conquer, and distributed learning. In this paper, we develop a very general theory of approximation by networks, which we have called eignets, to achieve loc...
5 months ago

Physics Maths Engineering

Mean-ETL Optimization in HorseRace Competition

This article explores the application of a new portfolio optimization approach called Mean-ETL (Mean-Expected Tail Loss). This method combines traditional mean return and the risk measure of expected tail loss to create more balanced portfolios that account for both returns and risks, particularly in the context of financial markets. The study demonstrates the practical implementation of Mean-E...
5 months ago

Physics Maths Engineering

Limitations of Meta-analyses of Studies With High Heterogeneity

Sabitova et al have performed an important service in compiling and summarizing 2 decades of studies on job burnout and satisfaction among physicians and dentists in middle-income countries and a few low-income countries. The authors followed a standard approach to performing a systematic review and meta-analysis to analyze studies that assessed job-related morale among physicians and dentists wor...
5 months ago

Math

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