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article

On the asymptotics of Bessel functions in the Fresnel regime

Zhu Heitman, James Bremer, Vladimir Rokhlin, Bogdan Vioreanu, more

Applied and Computational Harmonic Analysis > 2015 > 39 > 2 > 347-356

We introduce a version of the asymptotic expansions for Bessel functions Jν(z), Yν(z) that are valid whenever |z|>ν (which is deep in the Fresnel regime), as opposed to the standard expansions that are applicable only in the Fraunhofer regime (i.e. when |z|>ν2). As expected, in the Fraunhofer regime our asymptotics reduce to the classical ones. The approach is based on the observation that Bessel's...

article

Methodologies for the modeling and simulation of biochemical networks, illustrated for signal transduction pathways: A primer

Nesma ElKalaawy, Amr Wassal, N. ElKalaawy, A. Wassal

BioSystems > 2015 > 129 > Complete > 1-18

Biochemical networks depict the chemical interactions that take place among elements of living cells. They aim to elucidate how cellular behavior and functional properties of the cell emerge from the relationships between its components, i.e. molecules. Biochemical networks are largely characterized by dynamic behavior, and exhibit high degrees of complexity. Hence, the interest in such networks is...

article

An efficient method for the numerical integration of measured variable dependent ordinary differential equations

C. Rodrigues de Azevedo, J. Peres, M. von Stosch, C.R. de Azevedo, more

Engineering Applications of Artificial Intelligence > 2015 > 38 > Complete > 24-33

The Ordinary Differential Equations (ODEs) of dynamic models that are used in process monitoring, control or optimization, are not only functions of time and states, but also of measured variables. So far two possibilities for the numerical integration of such ODEs were given: (i) a fixed step size integration schema could be applied, matching the step size to the time instances of the measurements;...

article

A new block method with variable stepsize implementation for solving third‐order differential systems

Mufutau Ajani Rufai, Bruno Carpentieri, Higinio Ramos

Mathematical Methods in the Applied Sciences > 47 > 12 > 9987 - 9999

This article presents an efficient one‐step hybrid block method (OHBM) to solve third‐order initial value problems (IVPs). The proposed method is derived using interpolation and collocation techniques of the assumed exact solution and its derivatives. The theoretical properties of the OHBM are analyzed. An embedding‐like technique is utilized and executed in an adaptive mode to improve the performance...

article

Parameter estimation and forecasting with quantified uncertainty for ordinary differential equation models using QuantDiffForecast: A MATLAB toolbox and tutorial

Gerardo Chowell, Amanda Bleichrodt, Ruiyan Luo

Statistics in Medicine > 43 > 9 > 1826 - 1848

Mathematical models based on systems of ordinary differential equations (ODEs) are frequently applied in various scientific fields to assess hypotheses, estimate key model parameters, and generate predictions about the system's state. To support their application, we present a comprehensive, easy‐to‐use, and flexible MATLAB toolbox, QuantDiffForecast, and associated tutorial to estimate parameters...

article

A kinetic model with time‐dependent proliferative/destructive rates

Marco Menale, Ana Jacinta Soares

Mathematical Methods in the Applied Sciences > 47 > 7 > 5376 - 5391

This paper presents a new kinetic model with time‐dependent proliferative/destructive parameters, where the activity variable of the system attains its values in a discrete real subset. Therefore, a system of nonautonomous nonlinear ordinary differential equations is gained, with the related Cauchy problem. A first result of local existence and uniqueness of positive and bounded solution is proved...

article

Maximum sustainable yield as a reference point in the presence of fishing effort that follows an ideal free distribution

Darren M. Gillis, Jonah Koscielny, Benjamin Blanz

Natural Resource Modeling > 37 > 1 > n/a - n/a

The concept of maximum sustainable yield (MSY), and the underlying Schaefer model, remain relevant in fisheries management today in spite of past difficulties. However, this model is often applied without the consideration of the spatial structure or dynamics of fishing activities. We expand the Schaefer model to account for multiple fishing sites and fishing activities (effort) that follow an ideal...

article

Modelling the distinct roles of epithelial and stromal androgen receptor in the regulation of prostate epithelial dynamics

Isabel L. Woodman

The FEBS Journal > 290 > 22 > 5270 - 5291

The prostate is an androgen‐responsive organ, but the complex cellular and molecular interactions that mediate these responses remain incompletely defined. Here, I synthesise the existing literature to derive a simple conceptual framework describing the androgen‐dependent regulation of prostate epithelial dynamics. In this framework, epithelial androgen receptor (AR) cell‐autonomously controls luminal...

article

An asymptotic expansion of eigenpolynomials for a class of linear differential operators

Jorge A. Borrego‐Morell

Studies in Applied Mathematics > 151 > 3 > 923 - 956

Consider an M‐th order linear differential operator,

M \geq 2

,where

ρ_{M}

is a monic complex polynomial such that

deg [ρ_{M}] = M

and

{(ρ_{k})}_{k = 0}^{M - 1}

are complex polynomials such that

deg [ρ_{k}] \leq k, 0 \leq k \leq M - 1

. It is known that the zero counting measure of its eigenpolynomials converges in the...

article

Age‐related model for estimating the symptomatic and asymptomatic transmissibility of COVID‐19 patients

Jianbin Tan, Ye Shen, Yang Ge, Leonardo Martinez, more

Biometrics > 79 > 3 > 2525 - 2536

Estimation of age‐dependent transmissibility of COVID‐19 patients is critical for effective policymaking. Although the transmissibility of symptomatic cases has been extensively studied, asymptomatic infection is understudied due to limited data. Using a dataset with reliably distinguished symptomatic and asymptomatic statuses of COVID‐19 cases, we propose an ordinary differential equation model that...

article

Nonclassical perturbation approach to a nonlinear multiparameter eigenvalue problem arising in electromagnetics

Valeria Martynova, Dmitry Valovik

Mathematical Methods in the Applied Sciences > 46 > 12 > 13205 - 13225

The paper focuses on a problem of nonlinear electromagnetic wave propagation in a plane shielded waveguide filled with nonlinear medium. We look for nonlinear eigenvalues that correspond to propagation constants of the waveguide. One of the main feature of the problem is that it has nonperturbative solutions and therefore the corresponding linearized problem cannot be used in any perturbation approach...

article

PK/PD model of 6-mercaptopurine treatment in acute leukemia

Zofia Gruba

Mathematica Applicanda > 2022 > Vol. 50, no. 2 > 303--318

In this paper we present an analysis of a mathematical model of 6-P/6-TGN dynamics during the maintenance therapy of acute lymphoblastic leukemia which was proposed in Le et al. (2018). We first discuss the model with constant treatment, comparing its properties to the case without treatment. Next, we describe the model which switches between models with constant treatment and without treatment depending...

article

CMMSE: Study of a new symmetric anomaly in the elliptic, hyperbolic, and parabolic Keplerian motion

José Antonio López Ortí, Vicente Agost Gómez, Miguel Barreda Rochera

Mathematical Methods in the Applied Sciences > 46 > 2 > 1429 - 1442

In the present work, we define a new anomaly,

Ψ

, termed semifocal anomaly. It is determined by the mean between the true anomaly,

f

, and the antifocal anomaly,

f^{'}

; Fukushima defined

f^{'}

as the angle between the periapsis and the secondary around the empty focus. In this first part of the paper, we take an approach to...

article

Global bifurcation results for some fourth‐order nonlinear eigenvalue problem with a spectral parameter in the boundary condition

Ziyatkhan S. Aliyev, Yagut N. Aliyeva

Mathematical Methods in the Applied Sciences > 46 > 1 > 1282 - 1294

This paper is devoted to the study of global bifurcation from infinity of nontrivial solutions of a nonlinear eigenvalue problem for ordinary differential equations of fourth order with a spectral parameter in the boundary condition. We prove the existence of two families of unbounded continua of nontrivial solutions to this problem, which emanate from bifurcation points in

ℝ \times {\infty}

...

article

Modeling COVID‐19: Forecasting and analyzing the dynamics of the outbreaks in Hubei and Turkey

Ibrahim Halil Aslan, Mahir Demir, Michael Morgan Wise, Suzanne Lenhart

Mathematical Methods in the Applied Sciences > 45 > 10 > 6481 - 6494

As the pandemic of Coronavirus Disease 2019 (COVID‐19) rages worldwide, accurate modeling of the dynamics thereof is essential. However, since the availability and quality of data vary dramatically from region to region, accurate modeling directly from a global perspective is difficult. Nevertheless, via local data collected by certain regions, it is possible to develop accurate local prediction tools,...

article

Characterizing the COVID‐19 dynamics with a new epidemic model: Susceptible‐exposed‐asymptomatic‐symptomatic‐active‐removed

Grace Y. Yi, Pingbo Hu, Wenqing He

Canadian Journal of Statistics > 50 > 2 > 395 - 416

The coronavirus disease 2019 (COVID‐19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS‐CoV‐2), has spread stealthily and presented a tremendous threat to the public. It is important to investigate the transmission dynamics of COVID‐19 to help understand the impact of the disease on public health and the economy. In this article, we develop a new epidemic model that utilizes a...

article

Second‐order differential equations for the power converters dynamical performance analysis

Eleonora Amoroso, Gabriele Bonanno, Giuseppina D'Aguí, Salvatore De Caro, more

Mathematical Methods in the Applied Sciences > 45 > 9 > 5573 - 5591

The paper is devoted to the study of a second‐order differential equation of type Sturm‐Liouville with coefficients sign changing, and the existence of one positive solution is obtained by requiring a specific growth of the nonlinearity. In particular, this study is useful in the analysis of the dynamical performance of a class of power converter.

article

Modeling of drug resistance: Comparison of two hypotheses for slowly proliferating tumors on the example of low‐grade gliomas

Marek Bodnar, Urszula Foryś

Mathematical Methods in the Applied Sciences > 45 > 8 > 4161 - 4184

Acquired drug resistance (ADR) syndrome is one of the most important features associated with tumor treatment and it is therefore a topic of intensive studies. We present two simple mathematical models reflecting different mechanisms of ADR with some Darwinian effects included. These effects allow bi‐directional flow between resistant and sensitive compartments, meaning that not only sensitive cells...

article

A model of tumor‐immune system interactions with healthy cells and immunotherapies

Jui‐Ling Yu, Hsiu‐Chuan Wei, Sophia R‐J Jang

Mathematical Methods in the Applied Sciences > 45 > 5 > 2852 - 2870

A mathematical model of the tumor–immune system interactions is presented. The model includes the primary cell populations involved in CD4⁺ T cells mediated regression of the tumor, that is, tumor cells, CD4⁺ T cells, anti‐tumor cytokines, CTLA‐4 molecules, and normal cells. Our study reveals that host cells together with cytokines are key features in driving tumor dynamics. The malignant tumor can...

article

Bifurcation in the evolution of certainty in a small decision‐making group by consensus

Alexandra Gheondea‐Eladi, Aurelian Gheondea

British Journal of Mathematical and Statistical Psychology > 75 > 1 > 88 - 115

In a previous paper, the evolution of certainty measured during a consensus‐based small‐group decision process was shown to oscillate to an equilibrium value for about two‐thirds of the participants in the experiment. Starting from the observation that experimental participants are split into two groups, those for whom the evolution of certainty oscillates and those for whom it does not, in this paper...

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Search results

On the asymptotics of Bessel functions in the Fresnel regime

Methodologies for the modeling and simulation of biochemical networks, illustrated for signal transduction pathways: A primer

An efficient method for the numerical integration of measured variable dependent ordinary differential equations

A new block method with variable stepsize implementation for solving third‐order differential systems

Parameter estimation and forecasting with quantified uncertainty for ordinary differential equation models using QuantDiffForecast: A MATLAB toolbox and tutorial

A kinetic model with time‐dependent proliferative/destructive rates

Maximum sustainable yield as a reference point in the presence of fishing effort that follows an ideal free distribution

Modelling the distinct roles of epithelial and stromal androgen receptor in the regulation of prostate epithelial dynamics

An asymptotic expansion of eigenpolynomials for a class of linear differential operators

Age‐related model for estimating the symptomatic and asymptomatic transmissibility of COVID‐19 patients

Nonclassical perturbation approach to a nonlinear multiparameter eigenvalue problem arising in electromagnetics

PK/PD model of 6-mercaptopurine treatment in acute leukemia

CMMSE: Study of a new symmetric anomaly in the elliptic, hyperbolic, and parabolic Keplerian motion

Global bifurcation results for some fourth‐order nonlinear eigenvalue problem with a spectral parameter in the boundary condition

Modeling COVID‐19: Forecasting and analyzing the dynamics of the outbreaks in Hubei and Turkey

Characterizing the COVID‐19 dynamics with a new epidemic model: Susceptible‐exposed‐asymptomatic‐symptomatic‐active‐removed

Second‐order differential equations for the power converters dynamical performance analysis

Modeling of drug resistance: Comparison of two hypotheses for slowly proliferating tumors on the example of low‐grade gliomas

A model of tumor‐immune system interactions with healthy cells and immunotherapies

Bifurcation in the evolution of certainty in a small decision‐making group by consensus

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