Teaching Mathematical Modeling of Cellular Systems with the VCell MathModel

ABSTRACT Mathematical biology has emerged as a powerful approach to describe and understand biological systems. Here, we introduce an interactive teaching tool with a practical hands-on skill session plan to introduce students to the various components of a mathematical model with 4 different mathematical approaches (i.e., ordinary differential equations, partial differential equations, stochastic differential equations, and spatial stochastic differential equations) and their advantages and disadvantages. As such, we provide a didactic summary for instructors and students interested in using VCell MathModels for mathematical modeling; this work is also valuable for mathematics-savvy users who would like to exploit fully the capabilities of the VCell software.

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MATHEMATICAL MODELING OF THE PROCESS OF DRAWING AN OPTICAL FIBER USING THE LANGEVIN EQUATION

Informatyka Automatyka Pomiary w Gospodarce i Ochronie Środowiska ◽

10.5604/01.3001.0013.2551 ◽

2019 ◽

Vol 9 (2) ◽

pp. 64-67

Author(s):

Aliya Tergeussizova

Keyword(s):

Mathematical Modeling ◽

Differential Equations ◽

Optical Fiber ◽

Automatic Control ◽

Stochastic Differential Equations ◽

Differential System ◽

Langevin Equation ◽

Pulse Frequency ◽

Dynamic Compensation

In order to design stochastic pulse frequency systems for automatic control of objects with delay, this article shows how we obtained their models in the form of stochastic differential equations. The method of dynamic compensation of objects with delay is considered. A stochastic differential system in the Langevin form is obtained.

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Stochastic Differential Equations for Power Law Behaviors

10.21236/ada577839 ◽

2012 ◽

Author(s):

Bo Jiang ◽

Roger Brockett ◽

Weibo Gong ◽

Don Towsley

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Power Law

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Constrained Stochastic Differential Equations Driven by Fractional Brownian Motions: Stationarity and Parameter Estimation Problems

10.21236/ada591767 ◽

2013 ◽

Author(s):

Chihoon Lee

Keyword(s):

Parameter Estimation ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Brownian Motions ◽

Fractional Brownian Motions ◽

Estimation Problems

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Method of Iterated Integrals for Solution of Stochastic Integrals with Applications to Monte Carlo Simulation of Stochastic Differential Equations.

SSRN Electronic Journal ◽

10.2139/ssrn.3133959 ◽

2018 ◽

Author(s):

Ahsan Amin

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Stochastic Integrals ◽

Iterated Integrals

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Science Fiction and Administrative Truths: The Short Story and Novella as Administrative Cases

Public Voices ◽

10.22140/pv.389 ◽

2017 ◽

Vol 2 (3) ◽

pp. 61

Author(s):

Nolan J. Argyle ◽

Lee M. Allen

Keyword(s):

Science Fiction ◽

Public Administration ◽

Short Story ◽

Interesting Case ◽

Organizational Complexity ◽

Professional Career ◽

Playing Field ◽

Advantages And Disadvantages ◽

Hands On

Pre-service and in-service MPA students share a common desire for hands-on, real world instruction related to their professional career goals, leading to a pedagogic discounting of fiction as an appropriate tool for analyzing and "solving" problems. However, several factors weigh heavily in favor of using science fiction short stories and novellas in the MPA classroom setting. These include the need for interesting case scenarios exploring various administrative issues; leveling the playing field between the two types of students by de-emphasizing the use of "contemporary" cases; access to literature that explores the future shock of increasing organizational complexity; and the desirability of Rorschach type materials that facilitate discussion of. values and administrative truths. The discussion proceeds by tracing the development of the case study technique, its advantages and disadvantages in the classroom, addressing the utility of "fiction" as an educational resource, and showing how the science fiction literature has matured to the point where it can be applied in all of the major sub-fields of public administration. Several outstanding examples are detailed, and a thorough bibliography is provided.

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