Mathematical

This article aims to provide a guide that will help healthcare professionals and clinical researchers from all fields that deal with Kaplan-Meier curves. Survival analysis methods are among the most frequently used in the medical sciences and in clinical research. Overall survival, progression free survival, time to recurrence, or any other clinically relevant parameter represented by a Kaplan-Meier curve will be discussed. We will present a practical and straightforward interpretation of these curves, setting aside intricate mathematical considerations...

Fostering equity in undergraduate science, technology, engineering, and mathematics (STEM) programs can be accomplished by incorporating learner-centered pedagogies, resulting in the closing of opportunity gaps (defined here as the difference in grades earned by minoritized and non-minoritized students). We assessed STEM courses that exhibit small and large opportunity gaps at a minority-serving, research-intensive university, and evaluated the degree to which their syllabi are learner-centered, according to a previously validated rubric...

In the article, the extreme problem of finding the optimal placement plan of 5G base stations at certain points within a linear area of finite length is set. A fundamental feature of the author's formulation of the extreme problem is that it takes into account not only the points of potential placement of base stations but also the possibility of selecting instances of stations to be placed at a specific point from a defined excess set, as well as the aspect of inseparable interaction of placed 5G base stations within the framework of SON...

Wastewater-based epidemiology is a promising public health tool that can yield a more representative view of the population than case reporting. However, only about 80% of the U.S. population is connected to public sewers, and the characteristics of populations missed by wastewater-based epidemiology are unclear. To address this gap, we used publicly available datasets to assess sewer connectivity in the U.S. by location, demographic groups, and economic groups. Data from the U.S. Census' American Housing Survey revealed that sewer connectivity was lower than average when the head of household was American Indian and Alaskan Native, White, non-Hispanic, older, and for larger households and those with higher income, but smaller geographic scales revealed local variations from this national connectivity pattern...

Analyzing and visualizing the tertiary structure and complex interactions of RNA is essential for being able to mechanistically decipher their molecular functions in vivo. Secondary structure visualization software can portray many aspects of RNA; however, these layouts are often unable to preserve topological correspondence since they do not consider tertiary interactions between different regions of an RNA molecule. Likewise, quaternary interactions between two or more interacting RNA molecules are not considered in secondary structure visualization tools...

In this paper, we study in detail the structure of the global attractor for the Lotka-Volterra system with a Volterra-Lyapunov stable structural matrix. We consider the invasion graph as recently introduced in Hofbauer and Schreiber (J Math Biol 85:54, 2022) and prove that its edges represent all the heteroclinic connections between the equilibria of the system. We also study the stability of this structure with respect to the perturbation of the problem parameters. This allows us to introduce a definition of structural stability in ecology in coherence with the classical mathematical concept where there exists a detailed geometrical structure, robust under perturbation, that governs the transient and asymptotic dynamics...

First-principles-based modelings have been extremely successful in providing crucial insights and predictions for complex biological functions and phenomena. However, they can be hard to build and expensive to simulate for complex living systems. On the other hand, modern data-driven methods thrive at modeling many types of high-dimensional and noisy data. Still, the training and interpretation of these data-driven models remain challenging. Here, we combine the two types of methods to model stochastic neuronal network oscillations...

In order to enhance the support for groundwater development and utilization, as well as pollution control and prevention in Fengtai District, Beijing, a comprehensive study was conducted based on long-term monitoring data of shallow groundwater in the eastern area of Yongding River during the dry season. The mathematical statistics, Piper diagram, Gibbs diagram, and ion ratio analysis and other methods were employed to explore the pattern of groundwater hydrochemical evolution, the formation mechanism, and sources of pollution in Fengtai District...

Ligand-binding assays (LBAs) rely on the reversible, noncovalent binding between the analyte of interest and the assay reagents, and understanding their dynamic equilibrium is key to building robust LBA methods. Although the dynamic interplay of free and bound fractions can be calculated using mathematical models, these are not routinely applied. This approach is costly in terms of both assay development time and reagents, and can result in an under-exploration of the possible parameter combinations. Therefore, we have created a user-friendly simulation tool to facilitate LBA development (the BiSim Tool)...

Atrial fibrillation (AF) poses a significant risk of stroke due to thrombus formation, which primarily occurs in the left atrial appendage (LAA). Medical image-based computational fluid dynamics (CFD) simulations can provide valuable insight into patient-specific hemodynamics and could potentially enhance personalized assessment of thrombus risk. However, the importance of accurately representing the left atrial (LA) wall dynamics has not been fully resolved. In this study, we compared four modeling scenarios; rigid walls, a generic wall motion based on a reference motion, a semi-generic wall motion based on patient-specific motion, and patient-specific wall motion based on medical images...

The field production profile over the yearly horizon is planned for a balance between economy, security, and sustainability of energy. An optimal drilling schedule is required to achieve the planned production profile with minimized drilling frequency and summation. In this study, we treat each possible production process of each well as a dependent time series and the basic unit. Then we ensemble all of them into a tensor. Based on formulated tensor calculation and Lasso regularization, a linear mathematical optimization model for well drilling schedule was developed...

This study aims to explore the characteristics of tangent hyperbolic fluid flow along a stretching sheet. The sheet has suction or injection influences and is located inside a porous medium. The research inspects the flow and heat transfer (FHT) properties, taking into account the presence of a velocity slip condition. The flow of non-Newtonian magnetohydrodynamic fluid caused by a porous stretching sheet, taking into account thermal radiation and heat generation, has a wide range of engineering applications...

BACKGROUND: Epilepsy is one of the most common serious chronic neurological disorders, which can have a serious negative impact on individuals, families and society, and even death. With the increasing application of machine learning techniques in medicine in recent years, the integration of machine learning with epilepsy has received close attention, and machine learning has the potential to provide reliable and optimal performance for clinical diagnosis, prediction, and precision medicine in epilepsy through the use of various types of mathematical algorithms, and promises to make better parallel advances...

INTRODUCTION: An essential process affecting the course of type 1 diabetes (DM1) is the appearance and duration of clinical remission. One of the most important factors promoting the occurrence of remission is physical activity, due to increased activity of antioxidants, reduces insulin resistance and improves glucose transport. Maximal oxygen capacity (VO2 max) is an objective measure of the body's aerobic capacity. To assess VO2 max, oxygen uptake should be measured directly during the exercise test...

Although epidemiological surveillance of COVID-19 has been gradually downgraded globally, the transmission of COVID-19 continues. It is critical to quantify the transmission dynamics of COVID-19 using multiple datasets including wastewater virus concentration data. Herein, we propose a comprehensive method for estimating the effective reproduction number using wastewater data. The wastewater virus concentration data, which were collected twice a week, were analyzed using daily COVID-19 incidence data obtained from Takamatsu, Japan between January 2022 and September 2022...

For thousands of years, date fruit ( Phoenix dactylifera L.) has been a popular diet in arid and semi-arid locations. It has religious importance for Muslims and is especially important during the holy month of Ramadan. The global output of date fruits has been continuously expanding, with Arab nations accounting for a sizable portion. The emphasis of this research is on two popular semi-dry Algerian date fruit types, Deglet Noor and Arechti, which are grown in the Ziban region. These fruits' physical parameters, such as size, sphericity, surface area, volumes, and density, were determined...

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Metabolic flux analysis (MFA) is a valuable tool for quantifying cellular phenotypes and to guide plant metabolic engineering. By introducing stable isotopic tracers and employing mathematical models, MFA can quantify the rates of metabolic reactions through biochemical pathways. Recent applications of isotopically nonstationary MFA (INST-MFA) to plants have elucidated nonintuitive metabolism in leaves under optimal and stress conditions, described coupled fluxes for fast-growing algae, and produced a synergistic multi-organ flux map that is a first in MFA for any biological system...

In this study we introduce an innovative mathematical and statistical framework for the analysis of motion energy dynamics in psychotherapy sessions. Our method combines motion energy dynamics with coupled linear ordinary differential equations and a measurement error model, contributing new clinical parameters to enhance psychotherapy research. Our approach transforms raw motion energy data into an interpretable account of therapist-patient interactions, providing novel insights into the dynamics of these interactions...

Machine learning (ML) methods are increasingly becoming crucial in genome-wide association studies for identifying key genetic variants or SNPs that statistical methods might overlook. Statistical methods predominantly identify SNPs with notable effect sizes by conducting association tests on individual genetic variants, one at a time, to determine their relationship with the target phenotype. These genetic variants are then used to create polygenic risk scores (PRSs), estimating an individual's genetic risk for complex diseases like cancer or cardiovascular disorders...