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Biochemical systems have important practical applications, in particular to understanding critical intra-cellular processes. Often biochemical kinetic models represent cellular processes as systems of chemical reactions, traditionally modeled by the deterministic reaction rate equations. In the cellular environment, many biological processes are inherently stochastic. The stochastic fluctuations due to the presence of some low molecular populations may have a great impact on the biochemical system behavior. Then, stochastic models are required for an accurate description of the system dynamics. An important stochastic model of biochemical kinetics is the Chemical Langevin Equation. In this work, we provide a numerical method for approximating the solution of the Chemical Langevin Equation, namely the derivative-free Milstein scheme. The method is compared with the widely used strategy for this class of problems, the Milstein method. As opposed to the Milstein scheme, the proposed strategy has the advantage that it does not require the calculation of exact derivatives, while having the same strong order of accuracy as the Milstein scheme. Therefore it may be used for an automatic simulation of the numerical solution of the Chemical Langevin Equation. The tests on several models of practical interest show that our method performs very well.
This paper deals with the doctrine of transubstantial change advocated by Mulla Sadra in which substances as well as accidents are thought to be in constant and gradual change. Against Aristotle’s doctrine of accidental change, Mulla Sadra argues that no stable ground can bring about change and since substance is renewable it cannot carry identity of a changing existent. Here we investigate whether identity is possible or not. If it is possible then what becomes a ground for establishing identity of changing substances.
Central to Aristotle’s metaphysics is the question of individuality. The
individuality of each substance is explained in relation to “matter” because the “form” is universal.
Avicenna, as one of the Aristotelian Neoplatonist philosophers, is not content
with this explanation and proposes to establish individuality on other grounds.
In this paper, I argue that in his perspective it is not the “matter” which determines individuality but rather the
principle of existence.