Stochastic Models in Medicine and Life Sciences (IASI-CNR)

Think about it! Is it reality ‘deterministic’ or ‘stochastic’?

Maybe one of the most famous men in the battle against the “random world” as one of the truths was Einstein. He believed firmly until his death on a reality so deterministic that we could predict the future [1]. However, it is kind of fun that even his world played against him, with the famous work on Brownian Motion, one of his famous five papers [2]. Maybe if Julius Caeser had met Einstein, perhaps he would never had said that “his luck has been thrown to the dice.” This is irony maybe that the works on Brownian motion led to the current theory of stochastic differential equations, the “random” counterpart of the differential equations. 

What about the current state of the art?

“The message that keeps being repeated is that the kinetics of biological processes at the intra-cellular level are stochastic, and that cellular function cannot be properly understood without building that stochasticity into in silico models. ” [4]

 “I have reasons to expect that ‘quantum mechanics’ in ‘biological systems’ is not the only source of noise (randomness), and neither it is lack of knowledge. Those factors, mainly lack of knowledge, might be currently predominant, but it will perhaps be clear that biological systems are not so predictable as it is physical systems. It does not mean that they possess special set of laws. The matter might be boiled down to ‘flexibility’ and ‘variability’ in the cell level. The probability of finding true homogeneity in a cell population is almost zero, no matter the size. For instance, Brownian motion is significant in many real cases in biology, and it has nothing to do with quantum mechanics. “[5]

The problem of the observer in physics.

References:

[1] Clark, R. W. Einstein: the life and times. Públicado em acordos com World Publishing Company, 1971.

[2] Stachel, J (1998). Einstein’s miraculous year: five papers that changed the face of physics. Princeton University Press. New Jersey.

[3] Russell, Stuart; Norvig, Peter. Artificial Intelligence: A modern approach. Second edition. Prentice Hall Series in Artificial Intelligence: 2003.

[4] Wilkinson, DJ (2012). Stochastic modelling for systems biology. Second Edition. Chapman and Hall Book. CBC press. Online: http://www.staff.ncl.ac.uk/d.j.wilkinson/smfsb/2e/. last access: July 2014.

[5] Pires J G (2013). On the mathematical modelling in gene expression estimation. II Workshop and School on Dynamics, Transport and Control in Complex Networks  (ComplexNet), Ribeirão Preto, SP, Brazil. 21-26/October. Poster.

[6] Rome: The Rise and Fall of an Empire. Documentary.

[7] Ruffino, P R C. Uma iniciação aos sistemas dinâmicos estocásticos. Publicações Matemáticas.  IMPA, 2009.

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Jorge Pires