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# On anti-portfolio effects in science and technology with application
to reaction kinetics chemical synthesis and molecular biology.

### Marcel O Vlad,
Alexandru Dan Corlan,
Vlad T Popa,
John Ross,

### Proc Natl Acad Sci U S A :-, 2007

## ABSTRACT

The portfolio effect is the increase of the stability of a system
to random fluctuations with the increase of the number of random
state variables due to spreading the risk among these variables;
many examples exist in various areas of science and technology. We
report the existence of an opposite effect the decrease of stability
to random fluctuations due to an increase of the number of random
state variables. For successive industrial or biochemical processes
of independent random efficiencies the stability of the total efficiency
decreases with the increase of the number of processes. Depending
on the variables considered the same process may display both a
portfolio as well as an anti-portfolio behavior. In disordered kinetics
the activation energy of a reaction or transport process is the result
of a sum of random components. Although the total activation energy
displays a portfolio effect the rate coefficient displays an anti-portfolio
effect. For random-channel kinetics the stability of the total rate
coefficient increases with the average number of reaction pathways
whereas the stability of the survival function has an opposite behavior:
it decreases exponentially with the increase of the average number
of reaction pathways (anti-portfolio effect). In molecular biology
the total rate of a nucleotide substitution displays a portfolio
effect whereas the probability that no substitutions occur displays
an anti-portfolio effect resulting in faster evolutionary processes
due to fluctuations. The anti-portfolio effect emerges for products
of random variables or equations involving multiplicative convolution
products.
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