Metastability and Eye Movements: A Dynamical‑Systems Interpretation

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  1. Why metastability is a natural language for gaze behavior The idea that perception, attention, and neural activity evolve through transiently stable states has deep roots in cognitive science and neuroscience. Concepts such as attractors , basins , noise‑induced transitions , and escape times appear in work on perceptual switching, decision‑making, and neural population dynamics (Kelso, 1995; Rabinovich et al., 2008; Deco & Jirsa, 2012). Eye movements, especially the alternation between fixations and saccades ,   fit remarkably well into this metastable picture. The Freidlin–Wentzell theory of rare events (Freidlin & Wentzell, 2012) provides a rigorous mathematical language for these intuitions. 2. Fixations as metastable states  Consider the gaze position X t as the state of a stochastic dynamical system. During a fixation the  gaze remains confined to a small region, microsaccades and noise generate small fluctuations, and the gaze tends to return...
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TWO STAGES IN DECISION-MAKING: VALUATION AND CHOICE

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Fig.1 Decision-making circuit. 
After having defined the terms of the real problem (variables and relationships among variables), the decision-maker forms possible alternative solutions (e.g., scenarios) for solving the problem (i.e., optimization). The evaluation of the alternatives may be seen as a kind of cost/benefits analsys. The solution corresponding to the the most feasible and efficient (say, the "best") input-to-output mapping will be selected. The best solution is the decision. After making the decision the decision maker should implent it. That is, the decision should be put into action (e.g., motor action). In the follow-up a control function will determine the efficacy of the actions: how far have they been from the ideal optimal target ? The answer to this question quantifies the error term. The comparison between the realization and the target triggers a learning mechanism which iteration-by-iteration will reduce the error. The procedure will stop when a given minimum desired error is reached.




Making a decision implies to solve two kind of questions, which give rise to the valuation stage of the DM and to the choice stage of DM, that is, respectively: a) the representation and learning of the value to be attributed to the alternatives and b) the criterion of selection among the weighted alternatives. Although the classical economic models were not addressed to this issue, their concern being focused on the prediction of the choices rather than on the mechanisms that generate them, in the neuroeconomics approach, none model of DM should get along without assuming the interaction of these two phases.

Hence, in front of a set of possible alternatives, any decision-maker (either the individual, at macro level, or the neural circuit, at micro level) must initially estimate their values. As before mentioned for the neural circuits involved in DM [here], the ventromedial prefrontal cortex and striatum support the valuation stage, while lateral prefrontal and parietal areas are involved in the choice. 

Kable & Glimcher (2009). The Neurobiology of decision: consensus and controversy. Neuron 63(6): 733-745.


Fig.2 the ventromedial prefrontal cortex and striatum support the valuation stage (left panel), while lateral prefrontal and parietal areas are involved in the choice (right panel).  The firing rates in those cortical areas and the dopamine release in the midbrain are expected to correspond to the weights attributed to the alternatives.



So, at a first glance, the firing rates in those cortical areas and the dopamine release in the midbrain are expected to correspond to the weights attributed to the alternatives. Indeed, the neural activity is an epiphenomenon of the valuation stage, that is, it can be considered like the measurements of some underlying size or dimension which has a specific relation with some concept  (e.g., the utility). Therefore, the valuation task implies that the values to be attributed to the alternatives should be brought at a same scale [1]. But interestingly, this “normalization” with respect to a common utility function has some implications in terms of mathematical logic and statistics.   


  1. Kable, J.W., Glimcher, P.W. (2009). The neurobiology of decision: consensus and controversy. Neuron  63, 733-745.

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