URLanized bistability  is the counterpart of URLanized criticality " (SOC), for systems tuning themselves to the edge of bistability of a discontinuous /first-order phase transition, rather than to the critical point of a continuous /second order one. The equations defining the  theory of SOB turn out to be very similar to a mesoscopic (Landau-Ginzburg) theory recently proposed to describe the dynamics in the cerebral cortex. This theory describes the bistable/oscillating neuronal activity of coupled mesoscopic patches of cortex, homeostatically regulated by short-term synaptic plasticity. However, the theory for cortex dynamics entails  significant differences with respect to SOB, including the lack of a (bulk) conservation law, the absence of a perfect separation of timescales between driving anddissipation and , the fact that in the former  there is a parameter that controls the overall system state (in blatant contrast with the very idea of URLanization). Here, we scrutinize --by employing a combination of analytical and computational tools-- the analogies and differences between both theories and explore whether in some limit SOB could play an important role to explain the emergence of scale-invariant neuronal avalanches observed empirically in the cortex. We conclude that  actually, in the limit of infinitely slow synaptic-dynamics, the two theories behave identically , but the separation of timescales required for the URLanization mechanism to be effective does not seem to be biologically plausible. We discuss the key differences between URLanization mechanisms with or without conservation and separated timescales, and in particular, we  scrutinize the implications of our findings in neuroscience, hopefully shedding new light into the problem of scale invariance  in cortical dynamics.
URLanized bistability (SOB) is the counterpart of URLanized criticality ' (SOC), for systems tuning themselves to the edge of bistability of a discontinuous phase transition, rather than to the critical point of a continuous one. The equations defining the mathematical theory of SOB turn out to bear strong resemblance to a (Landau-Ginzburg) theory recently proposed to analyze the dynamics of the cerebral cortex. This theory describes the neuronal activity of coupled mesoscopic patches of cortex, homeostatically regulated by short-term synaptic plasticity. The theory for cortex dynamics entails , however, some significant differences with respect to SOB, including the lack of a (bulk) conservation law, the absence of a perfect separation of timescales and , the fact that in the former , but not in the second, there is a parameter that controls the overall system state (in blatant contrast with the very idea of URLanization). Here, we scrutinize --by employing a combination of analytical and computational tools-- the analogies and differences between both theories and explore whether in some limit SOB can play an important role to explain the emergence of scale-invariant neuronal avalanches observed empirically in the cortex. We conclude that , actually, in the limit of infinitely slow synaptic-dynamics, the two theories become identical , but the timescales required for the URLanization mechanism to be effective do not seem to be biologically plausible. We discuss the key differences between URLanization mechanisms with / without conservation and with/without infinitely separated timescales. In particular, we introduce the concept of URLanized collective oscillations' and scrutinize the implications of our findings in neuroscience, shedding new light into the problems of scale invariance and oscillations in cortical dynamics.
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(SOB)
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"
'
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/first-order
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/second order
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mathematical
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be very similar to a mesoscopic
bear strong resemblance to a
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describe the dynamics in
analyze the dynamics of
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bistable/oscillating
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However, the
The
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, however, some
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between driving anddissipation and
and
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, but not in the second,
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could
can
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,
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behave identically
become identical
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separation of
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does
do
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or
/
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separated timescales, and in
with/without infinitely separated timescales. In
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introduce the concept of URLanized collective oscillations' and
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hopefully
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problem
problems
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and oscillations