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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The U.S. GDP Growth Accelerates in Second Quarter, doesn't it ?

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The Bureau of Economic Analysis (BEA) asserts [here]: 
"Real gross domestic product (GDP) increased 1.7 percent in the second quarter of 2013 after increasing 1.1 percent in the first quarter, according to the “advance” estimate released today [July 31, 2013] by the Bureau of Economic Analysis (BEA)." 
One would say that the reported growth of the annualized estimate of the U.S. GDP (+1.7%) outperforms the expected result. 

 We recall that the official GDP is calculated at constant prices, i.e, by applying a deflator to the current values. 

 In practice, it takes account of the specific rate of inflation in the components of GDP. Obviously the lower the GDP deflator the higher the GDP.

 Well, the deflator used by the BEA for the second quarter was a tiny +0.71% whilst in the first quarter it was +1.7% and in the last 14 quarters, the U.S. GDP deflator was +1.75% on average.

 It sounds a bit odd !

 If the GDP deflator were what the market was expecting (i.e., +1.6%), the U.S. GDP would grow in the second quarter only by 0.8% annualized (i.e., just a faint +0.2% quarter-on-quarter). 

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