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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...

INVOLVEMENT OF THE INFERIOR FRONTAL CORTEX IN THE LEVODOPA-INDUCED DYSKINESIAS

Parkinson’s disease (PD) is one of the most prevailing neurodegenerative disorders affecting populations all over the world.  Almost from 4.1 to 4.6 million patients suffering from PD are counted across the  fifteen most crowded countries where  live the two thirds of the world population. The average age of the PD onset is 55. The incidence grows along with the age: from 20/100000 cases in the overall population to 120/100000 in the elder population above 70 years old.   This number is expected to reach 8.7 / 9.3 million in 2030. China is expected to increase from two million to five million by 2030. (E. R. Dorsey, et al.; Neurology 2007) Gender difference  in the rate of incidence of PD was reported in many epidemiological studies:  from 1.5 to 2 times higher in men than in women. In Japan, however, there is a higher incidence in women. Environmental factors are critical in determining the incidence rate of the disease. Some studies repo...

Multiple Sclerosis: Understanding the roles of B cells

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An informative video of the Roche on the roles of B cells in Multiple Sclerosis .

A Two-Layered Diffusion Model Traces the Dynamics of Information Processing in the Valuation-and-Choice Circuit of Decision Making

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A circuit of evaluation and selection of the alternatives ( see here ) is considered a reliable model in neurobiology. In this published study , valuation and choice of a decisional process during Two-Alternative Forced-Choice ( TAFC ) task are represented as a two-layered network of computational cells, where information accrual and processing progress in nonlinear diffusion dynamics.  The evolution of the response-to-stimulus map is thus modeled by two linked diffusive modules ( 2LDM ) representing the neuronal populations involved in the valuation-and-decision circuit of decision making (Figure 1). Diffusion models are naturally appropriate for describing accumulation of evidence over the time [ see here ] . This allows the computation of the response times (RTs) in valuation and choice, under the hypothesis of ex-Wald distribution. A nonlinear transfer function integrates the activities of the two layers. The input-output map based on the infomax principle makes the 2LD...

Automatic eye fixations identification based on analysis of variance and covariance

Abstract : Eye movement is the simplest and repetitive movement that enables humans to interact with the environment. The common daily activities, such as reading a book or watching television, involve this natural activity, which consists of rapidly shifting our gaze from one region to another. In clinical application, the identification of the main components of eye movement during visual exploration, such as fixations and saccades , is the objective of the analysis of eye movements: however, in patients affected by motor control disorder the identification of fixation is not banal. This work  [ download ]  presents a new fixation identification algorithm based on the analysis of variance and covariance: the main idea was to use bivariate statistical analysis to compare variance over x and y to identify fixation. We describe the new algorithm, and we compare it with the common fixations algorithm based on dispersion. To demonstrate the performance of our approach, we t...

Relationship between the modified Rankin Scale and the Barthel Index in the process of functional recovery after stroke

The modified Rankin Scale (mRS) and the Barthel Index (BI) are the most   common clinimetrical instruments for measuring disability after stroke.  This study  [ here ]   investigated the relationship between the BI and the  mRS at multiple time points after stroke.  The BI, which is a widely used instrument for longitudinal follow-up post- stroke, was used as   reference to determine the effect of time on the  sensitivity of the mRS in differentiating   functional recovery.  Methods :  Ninety-two patients with first stroke and hemispheric brain  lesion were evaluated using the BI and mRS at 10 days, 3 and 6 months.  The Kruskal-Wallis test was applied to examine median differences in BI  among the mRS levels at 10 days, 3 and 6 months with Dunn's correction  for multigroup comparison. The Mann and Whitney test was used to  compare median differences in BI scores between two a...

MULTICOLLINEARITY IN LINEAR MODELS

1. Introduction One of the fundamental assumptions of the general linear model 1) y = X β + u where u is a vector of zero-mean and uncorrelated stochastic errors,  is that the data matrix X of order n * k has rank k, that is, the explanatory variables are not linearly dependent. This is because the least squares solution 2)  b = ( X ' X ) -1 X ' y   requires the inversion of X ' X , which, however, would not be possible if the rank of X is <k (because X becomes singular). If  some or all of the explanatory variables are perfectly collinear, then  the system 1)  is said to be affected by " extreme"  multicollinearity .   Problems in the   calculation of the solution 2) can emerge even when the collinearity among the variables is not perfect. the main effects of collinearity are [ 1 ]: Lowered precision of the estimates t hat makes it difficult, if not impossible, to separate the relative influences of ...

Global cooling. The crazy winter 2013-2014

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Another wave of frost is hitting the United States. The bad weather has caused paralysis of road traffic (with at least 13 deaths from traffic accidents) and the cancellation of about 6,000 flights in the last two days. The more dramatic  situation  is reported in North Carolina, where  because snow and ice have created an immense traffic jam in both directions of  the highway , with thousands of people trapped and hundreds of abandoned cars in the middle of the roadway . Just as had happened two weeks ago near Atlanta , Georgia. Over half a million homes and businesses were left without electricity due to power outage caused by snow and ice. President Barack Obama has declared a state of natural disaster in Georgia and South Carolina, sending federal aid. And the spate of bad weather is moving to the northeast, where heavy snowfalls are expected in Boston, the capital Washington and New York. The scenario is rather catastrophic . In the capital all federal offi...

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