27 papers · ranked by Valyu relevance
Süleyman Cengizci, Mehmet Tarık Atay, Aytekin Eryılmaz
This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid…
Lida Ahmadi, Mark Daniel Ward
Patterns within strings enable us to extract vital information regarding a string’s randomness. Understanding whether a string is random (Showing no to little repetition in patterns) or periodic (showing repetitions in patterns) are described by a value that is called the kth Subword Complexity of the character string.…
Jacob M. Jepson, Nabil T. Fadai, Reuben D. O’Dea
We derive a multiphase, moving boundary model to represent the development of tissue in vitro in a porous tissue engineering scaffold. We consider a cell, extra-cellular liquid and a rigid scaffold phase, and adopt Darcy’s law to relate the velocity of the cell and liquid phases to their respective pressures. Cell-cell…
Carl M. Bender, Carlo Heissenberg
The aim of this short series of lectures is to cover a few selected topics in the theory of perturbation series and their summation. The issue of extracting sensible information from a formal power series arises quite naturally in physics: it is often impossible, when tackling a given (hard) problem, to obtain an exact…
Justin Eilertsen, Wylie Stroberg, Santiago Schnell
A theoretical analysis is performed on the nonlinear ordinary differential equations that govern the dynamics of a coupled enzyme catalyzed reaction. The assay consists of a non-observable reaction and an indicator (observable) reaction, where the product of the first reaction is the enzyme for the second. Both…
José M. Rodríguez, R. Taboada-Vázquez
In this paper we study the behavior of an incompressible viscous fluid moving between two very close surfaces also in motion. Using the asymptotic expansion method we formally justify two models, a lubrication model and a shallow water model, depending on the boundary conditions imposed. Finally, we discuss under what…
Benjamin C. Haller, Philipp W. Messer
The McDonald–Kreitman (MK) test is a widely used method for quantifying the role of positive selection in molecular evolution. One key shortcoming of this test lies in its sensitivity to the presence of slightly deleterious mutations, which can severely bias its estimates. An asymptotic version of the MK test was…
Leonardo Silva Vianna, Alexandre Leopoldo Gonçalves, João Artur Souza, Mohamed R. Abonazel
'Mohamed R. Abonazel'] The existence of large volumes of data has considerably alleviated concerns regarding the availability of sufficient data instances for machine learning experiments. Nevertheless, in certain contexts, addressing limited data availability may demand distinct strategies and efforts. Analyzing…
Carl M. Bender, Andreas Fring, Javad Komijani
This paper presents a detailed asymptotic study of the nonlinear differential equation y 0 (x) = cos[πxy(x)] subject to the initial condition y(0) = a. Although the differential equation is nonlinear, the solutions to this initial-value problem bear a striking resemblance to solutions to the time-independent…
Anatoly N. Kochubei, Daniel Soskin
1.1. In analysis of complex-valued functions on the field Qp of p-adic numbers (or, more generally, on a non-Archimedean local field), the basic operator is Vladimirov's fractional differentiation operator Dα , α > 0, defined via the Fourier transform or, for wider classes of functions, as a hypersingular integral…
C. Charlier, M. Duits, A. B. J. Kuijlaars, J. Lenells
We study a one-parameter family of probability measures on lozenge tilings of large regular hexagons that interpolates between the uniform measure on all possible tilings and a particular fully frozen tiling. The description of the asymptotic behavior can be separated into two regimes: the low and the high temperature…
Anton V. Sinitskiy
This paper extends our previous work on the simplest model of a nervous system by providing an asymptotic analysis of the evolutionarily optimal solution in this model. Building on the formalism and principles established earlier, we derive an asymptotic solution to the Fokker-Planck-Kolmogorov equation for a given…
Dave Cliff
I present a replication and, to some extent, a refutation of key results published by Zhong, Zhang, Li, Dai, & Yang in their 2022 paper “Species coexistence in spatial cyclic game of five species” (Chaos, Solitons and Fractals, 156: 111806), where ecosystem species coexistence was explored via simulation studies of the…
Alan E. Lindsay, Andrew. J. Bernoff, Adrián Navarro Hernández
An essential ability of many cell types is to detect stimuli in the form of shallow chemical gradients. Such cues may indicate the direction that new growth should occur, or the location of a mate. Amplification of these faint signals is due to intra cellular mechanisms while the cue itself is generated by the noisy…
Nathaniel S. Barlow, C. R. Stanton, Nicole Hill, Steven J. Weinstein + 1 more
'A. G. Cio'] A compact and accurate solution method is provided for problems whose infinite power series solution diverges and/or whose series coefficients are only known up to a finite order. The method only requires that either the power series solution or some truncation of the power series solution be available and…
Henrik L. Pedersen
This equation can be written as P(x, mp(x)) = p, where P is a normalized incomplete gamma function. See [5, 8.2.4]. The asymptotic behaviour at infinity of the quantiles in the gamma distribution was investigated in the papers [7] and [4] (and for the beta distribution in [8]). We complement this by an investigation at…
Emine Atıcı Endes, Neslihan Nesliye Pelen
Atherosclerotic plaques are fatty deposits in arterial walls and a major cause of heart attacks and strokes. Macrophage proliferation triggers plaque growth and instability, but the specific conditions that convert stable plaques into unstable ones remain unclear. To provide insight into the conditions for this…
Stephane Mottin, Grigory Panasenko, S. Sivaji Ganesh, Giuseppe Chirico
'Giuseppe Chirico'] In biophotonics, the light absorption in a tissue is usually modeled by the Helmholtz equation with two constant parameters, the scattering coefficient and the absorption coefficient. This classic approximation of “haemoglobin diluted everywhere” (constant absorption coefficient) corresponds to the…
Faruk Abi-Khuzam
For \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\alpha>\beta-1>0$\end{document} α > β − 1 > 0, we obtain two-sided inequalities for the…
Authors not listed
A method has been introduced to derive the solution of the time-independent Schrodinger equation for the simple harmonic oscillator. A trial solution has been chosen as the product of the divergent part of the approximate asymptomatic solution of the Schrodinger equation and an unknown function. By inserting this trial…
Justin Eilertsen, Santiago Schnell
As a case study, we consider a coupled (or auxiliary) enzyme assay of two reactions obeying the Michaelis-Menten mechanism. The coupled reaction consists of a single-substrate, single-enzyme non-observable reaction followed by another single-substrate, single-enzyme observable reaction (indicator reaction). In this…
Thomas Lugrin, A. C. Davison, Jonathan A. Tawn
Models for extreme values are generally derived from limit results, which are meant to be good enough approximations when applied to finite samples. Depending on the speed of convergence of the process underlying the data, these approximations may fail to represent subasymptotic features present in the data, and thus…
Justin Eilertsen, Santiago Schnell
As a case study, we consider a coupled enzyme assay of sequential enzyme reactions obeying the Michaelis--Menten reaction mechanism. The sequential reaction consists of a single-substrate, single-enzyme non-observable reaction followed by another single-substrate, single-enzyme observable reaction (indicator reaction).…
Authors not listed
How to accelerate a reaction has been a critical question in physical organic chemistry, eliciting multiple models describing the interplay between kinetics and thermodynamic driving forces. However, existing models often come with inevitable limitations: valid only within finite thermodynamic ranges, rely on heavy…
Lukas Roth, Hans-Peter Piepho, Andreas Hund
Temperature is a main driver of plant growth and development. New phenotyping tools enable quantifying the temperature response of hundreds of genotypes. Yet, particularly for field-derived data, the process of temperature response modelling bears potential flaws and pitfalls with regard to the interpretation of…
Justin Eilertsen, Wylie Stroberg, Santiago Schnell
A theoretical analysis is performed on the nonlinear ordinary differential equations that govern the dynamics of a reaction mechanism of zymogen activation. The reaction consists of a primary non-observable zymogen activation reaction that it is coupled to an indicator (observable) reaction. The product of the first…
Beenish, Maria Samreen, Fehaid Salem Alshammari, Angelo Marcelo Tusset
'Angelo Marcelo Tusset'] This research explores the dynamical properties and solutions of actin filaments, which serve as electrical conduits for ion transport along their lengths. Utilizing the Lie symmetry approach, we identify symmetry reductions that simplify the governing equation by lowering its dimensionality.…