scholarly journals Generalized mathematical model of cancer heterogeneity

2020 ◽  
Author(s):  
Motohiko Naito
Keyword(s):  
Mathematical Modeling ◽  
Differential Equation ◽  
Mathematical Model ◽  
Stochastic Process ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stochastic Differential Equation ◽  
Cancer Growth ◽  
Cancer Heterogeneity ◽  
Growth Properties

AbstractThe number of reports on mathematical modeling related to oncology is increasing with advances in oncology. Even though the field of oncology has developed significantly over the years, oncology-related experiments remain limited in their ability to examine cancer. To overcome this limitation, in this study, a stochastic process was incorporated into conventional cancer growth properties to obtain a generalized mathematical model of cancer growth. Further, an expression for the violation of symmetry by cancer clones that leads to cancer heterogeneity was derived by solving a stochastic differential equation. Monte Carlo simulations of the solution to the derived equation validate the theories formulated in this study. These findings are expected to provide a deeper understanding of the mechanisms of cancer growth, with Monte Carlo simulation having the potential of being a useful tool for oncologists.

scholarly journals Monte-Carlo Galerkin Approximation of Fractional Stochastic Integro-Differential Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Abdallah Ali Badr ◽  
Hanan Salem El-Hoety
Keyword(s):  
Differential Equation ◽  
Stochastic Process ◽  
Monte Carlo ◽  
Stochastic Differential Equation ◽  
Galerkin Method ◽  
Existence And Uniqueness ◽  
Galerkin Approximation ◽  
Integro Differential Equation ◽  
Uniqueness Of The Solution ◽  
Time Continuum

A stochastic differential equation, SDE, describes the dynamics of a stochastic process defined on a space-time continuum. This paper reformulates the fractional stochastic integro-differential equation as a SDE. Existence and uniqueness of the solution to this equation is discussed. A numerical method for solving SDEs based on the Monte-Carlo Galerkin method is presented.

scholarly journals Calculation of Probability of the Exit of a Stochastic Process from a Band by Monte-Carlo Method: A Wiener-Hopf Factorization

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 581
Author(s):  
Beliavsky ◽  
Danilova ◽  
Ougolnitsky
Keyword(s):  
Differential Equation ◽  
Stochastic Process ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Stochastic Differential Equation ◽  
Random Partition ◽  
Numerical Examples ◽  
Girsanov Transform ◽  
The Monte Carlo Method

This paper considers a method of the calculation of probability of the exit from a band of the solution of a stochastic differential equation. The method is based on the approximation of the solution of the considered equation by a process which is received as a concatenation of Gauss processes, random partition of the interval, Girsanov transform and Wiener-Hopf factorization, and the Monte-Carlo method. The errors of approximation are estimated. The proposed method is illustrated by numerical examples.

Monte-Carlo simulation of a stochastic differential equation

2017 ◽  
Vol 19 (12) ◽  
pp. 125001 ◽  
Author(s):  
Arif ULLAH ◽  
Majid KHAN ◽  
M KAMRAN ◽  
R KHAN ◽  
Zhengmao SHENG
Keyword(s):  
Differential Equation ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stochastic Differential Equation

scholarly journals Ice Gouge Depth Determination Via an Efficient Stochastic Dynamics Technique

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Nikolaos Gazis ◽  
Ioannis A. Kougioumtzoglou ◽  
Edoardo Patelli
Keyword(s):  
Differential Equation ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stochastic Differential Equation ◽  
Path Integral ◽  
Stochastic Dynamics ◽  
Simplified Model ◽  
Preliminary Design ◽  
Depth Determination ◽  
Nonlinear Stochastic Differential Equation

A simplified model of the motion of a grounding iceberg for determining the gouge depth into the seabed is proposed. Specifically, taking into account uncertainties relating to the soil strength, a nonlinear stochastic differential equation governing the evolution of the gouge length/depth in time is derived. Further, a recently developed Wiener path integral (WPI) based approach for solving approximately the nonlinear stochastic differential equation is employed; thus, circumventing computationally demanding Monte Carlo based simulations and rendering the approach potentially useful for preliminary design applications. The accuracy/reliability of the approach is demonstrated via comparisons with pertinent Monte Carlo simulation (MCS) data.

An approximation result and Monte Carlo simulation of the adapted solution of the one-dimensional backward stochastic differential equation

2018 ◽  
Vol 26 (3) ◽  
pp. 131-142
Author(s):  
A. Sghir ◽  
D. Seghir ◽  
S. Hadiri
Keyword(s):  
Differential Equation ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stochastic Differential Equation ◽  
Backward Stochastic Differential Equation ◽  
Multidimensional Case ◽  
Reference Trajectory ◽  
Approximation Result ◽  
One Dimensional ◽  
The One

Abstract In this paper, we give an approximation result for the adapted solution of the one-dimensional backward stochastic differential equation driven by a one-dimensional Brownian motion (BSDE for short). To prove our main result, we linearize the generator of the BSDE around a deterministic nominal reference trajectory by using a Taylor series expansion. We then find an approximate linear model of the BSDE. A test of our method is given with a numerical scheme driven by the Monte Carlo simulation. We believe that our result is new and valid for the multidimensional case.

Mathematical Modeling of the λ Switch

2010 ◽  
pp. 573-603
Author(s):  
Dmitriy Laschov ◽  
Michael Margaliot
Keyword(s):  
Mathematical Modeling ◽  
Differential Equation ◽  
Mathematical Model ◽  
Gene Regulation ◽  
Equilibrium Points ◽  
Domain Of Attraction ◽  
Verbal Description ◽  
Quantitative Understanding ◽  
Living Organisms ◽  
Scientific Challenge

Gene regulation plays a central role in the development and functioning of living organisms. Developing a deeper qualitative and quantitative understanding of gene regulation is an important scientific challenge. The Lambda switch is commonly used as a paradigm of gene regulation. Verbal descriptions of the structure and functioning of the Lambda switch have appeared in biological textbooks. We apply fuzzy modeling to transform one such verbal description into a well-defined mathematical model. The resulting model is a piecewise-quadratic, second-order differential equation. It demonstrates functional fidelity with known results while being simple enough to allow a rather detailed analysis. Properties such as the number, location, and domain of attraction of equilibrium points can be studied analytically. Furthermore, the model provides a rigorous explanation for the so-called stability puzzle of the Lambda switch.

Analysis on Motion Precision Reliability of Hydraulic Support

2011 ◽  
Vol 48-49 ◽  
pp. 224-227
Author(s):  
Dong Chen Qin ◽  
Qiang Zhu ◽  
Hong Xia Wu ◽  
Zhe Feng Guo
Keyword(s):  
Mathematical Model ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Theoretical Calculation ◽  
Calculation Method ◽  
Effective Length ◽  
Future Research ◽  
Hydraulic Support ◽  
Continuous Contact ◽  
Continuous Contact Model

In order to research the motion precision reliability of hydraulic support when the influence of the bar length error and gap error is considered, the motion trace mathematical model for the top beam of hydraulic support is established, with the calculation method of motion precision reliability and the effective length of bar based on continuous contact model. Taking some type of hydraulic support as an example, its motion precision reliability is calculated and analyzed. The Monte Carlo simulation is also used to verify the model, and the T-R curve of the gap error and the reliability is plotted. The results from simulation accord with those from the theoretical calculation, which verifies the model established and can provide some valuable reference for the related future research.

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