Why Biological Systems Suddenly Change State: An Intuitive Guide to Freidlin–Wentzell Theory

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  Stochasticity is ubiquitous in biology and neuroscience, manifesting in various forms, including ion channel noise, synaptic variability, gene regulatory fluctuations, noisy population dynamics, and more. Many biological systems spend long periods in a stable “state” and only rarely transition to another state due to noise. For instance, a neuron typically remains inactive but may occasionally trigger a spontaneous spike. Similarly, a gene can switch from the OFF state to the ON state due to rare bursts of transcription factors. Cells can also transition out of metabolic or epigenetic states, populations might shift between different ecological equilibria, and a viral infection can fluctuate between phases of control and uncontrollability. Freidlin–Wentzell theory provides a mathematically rigorous framework to study these phenomena when noise is small but nonzero . It tells you, firstly, h ow likely rare transitions are,    secondly,   h ow fast they occ...
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SIDE EFFECTS OF THE FAILURE OF DETROIT

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The financial failure of the city of Detroit [here] will also have consequences on some European banks, exposed towards the debt contracted by the American metropolis.

 Among the banks involved there is also UBS: in 2005 the bank was handling the sale of $ 1.4 billion of municipal bonds. Operations conducted on behalf of the administration of Detroit, to enable it to finance its pension fund.

 Similar operations involving other banks - for a total of another billion dollars - and these include many institutions that already live in conditions of difficulty.
As in the case of the "bad bank" of Hypo Real Estate, which is the most exposed with $ 200 million, to Commerzbank, which owns a total of 4.5 billion euro in American local governments, or Deutsche Bank, not involved however excessively.

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