Impulsive Expressions in Stochastic Simulation Algorithms

Jumps can be seen in many natural processes. Classical deterministic modeling approach explains the dynamical behavior of such systems by using impulsive differential equations. This modeling strategy assumes that the dynamical behavior of the whole system is deterministic, continuous, and it adds jumps to the state vector at certain times. Although deterministic approach is satisfactory in many cases, it is a well-known fact that stochasticity or uncertainty has crucial importance for dynamical behavior of many others. In this study, we propose to include this abrupt change in the stochastic modeling approach, beside the deterministic one. In our model, we introduce jumps to chemical master equation and use the Gillespie direct method to simulate the evolutionary system. To illustrate the idea and distinguish the differences, we present some numerically solved examples.


Functional Impulses in Exact Stochastic Simulation
Altıntan, Derya; Purutçuoğlu Gazi, Vilda; Uğur, Ömür (2015-08-20)
Jumps which are observed in many population models give rise to fluctuations in the dynamics of systems. Deterministic model which is based on the Impulsive Differential Equations (IDEs) considers these jumps as impulses and defines the dynamics of the system between successive jump times with the Ordinary Differential Equations (ODEs). From our previous studies, we have proposed a model which is the complement of IDEs in the sense that both studies consider the jumps as impulses. The main difference betwee...
Error bound and simulation algorithm for piecewise deterministic approximations of stochastic reaction systems
Ganguly, Arnab; ALTINTAN, DERYA; Koeppl, Heinz (2015-07-03)
In cellular reaction systems, events often happen at different time and abundance scales. It is possible to simulate such multi-scale processes with exact stochastic simulation algorithms, but the computational cost of these algorithms is prohibitive due to the presence of high propensity reactions. This observation motivates the development of hybrid models and simulation algorithms that combine deterministic and stochastic representation of biochemical systems. Based on the random time change model we pro...
Adsorption of H2O on double layer stepped Si(111) surface
Katırcıoğlu, Şenay (1997-03-10)
We have investigated possible water adsorption forms on stepped Si(111) surface. Calculations have been performed by using the empirical tight-binding method. Two types of adsorption model of water on single layer stepped Si(111) surface have been considered; one of them is the dissociative type (H, OH) and the other is the molecular type (H2O). The total electronic energy and TDOS calculations lead to a dissociative type of adsorption of water on stepped Si(111) surface excluding the molecular type. (C) 19...
Boundary element method formulation and its solution in forward problem of electrocardiography by using a realistic torso model
Kurt, Arda; Weber, Gerhard Wilhelm; Department of Scientific Computing (2006)
The electrical currents generated in the heart propagate to the outward direction of the body by means of conductive tissues and these currents yield a potential distribution on the body surface. This potential distribution is recorded and analyzed by a tool called electrocardiogram. It is not a problem, if this process continues normally; however, when it is distorted by some abnormalities, the results will be fatal. Electrocardiography (ECG) is the technique dealing with the acquisition and interpretation...
Inverse problems for parabolic equations
Baysal, Arzu; Çelebi, Okay; Department of Mathematics (2004)
In this thesis, we study inverse problems of restoration of the unknown function in a boundary condition, where on the boundary of the domain there is a convective heat exchange with the environment. Besides the temperature of the domain, we seek either the temperature of the environment in Problem I and II, or the coefficient of external boundary heat emission in Problem III and IV. An additional information is given, which is the overdetermination condition, either on the boundary of the domain (in Proble...
Citation Formats
D. Altintan, V. Purutçuoğlu Gazi, and Ö. Uğur, “Impulsive Expressions in Stochastic Simulation Algorithms,” INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, pp. 0–0, 2018, Accessed: 00, 2020. [Online]. Available: