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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FixaTons: A collection of Human Fixations Datasets and Metrics for Scanpath Similarity

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In the last three decades, human visual attention has been a topic of great interest in various disciplines. In computer vision, many models have been proposed to predict the distribution of human fixations on a visual input. Recently, thanks to the creation of large collections of data, machine learning algorithms have obtained state-of-the-art performance on the task of saliency map estimation. On the other hand, computational models of scanpath are much less studied. Works are often only descriptive or task specific. Computational models of scanpath with general purpose are present in the literature, but are then evaluated in tasks of saliency prediction, losing therefore information about the dynamics and the behaviour. This is due to the fact that the scanpath is harder to model because it must include the description of a dynamic. In addition to the difficulty of the problem itself, two technical reasons have limited the research. The first reason is the lack of robust and uniformly used set of metrics to compare the similarity between scanpath. The second reason is the lack of sufficiently large and varied scanpath datasets. In this report we want to help in both directions. We present FixaTons, a large collection of human scanpaths (and saliency maps). It comes along with a software library for easy data usage, statistics calculation and measures for scanpaths (and saliency maps) similarity.

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