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Brain Performance versus Phase Transitions.

Torres JJ, Marro J - Sci Rep (2015)

Bottom Line: Analyzing to what extent a weak signal endures in noisy environments, we identify the underlying mechanisms, and it results a description of how the excitability associated to (non-equilibrium) phase changes and criticality optimizes the processing of the signal.Our setting is a network of integrate-and-fire nodes in which connections are heterogeneous with rapid time-varying intensities mimicking fatigue and potentiation.Emergence then becomes quite robust against wiring topology modification--in fact, we considered from a fully connected network to the Homo sapiens connectome--showing the essential role of synaptic flickering on computations.

View Article: PubMed Central - PubMed

Affiliation: Institute Carlos I for Theoretical and Computational Physics, Granada, E-18071, Spain.

ABSTRACT
We here illustrate how a well-founded study of the brain may originate in assuming analogies with phase-transition phenomena. Analyzing to what extent a weak signal endures in noisy environments, we identify the underlying mechanisms, and it results a description of how the excitability associated to (non-equilibrium) phase changes and criticality optimizes the processing of the signal. Our setting is a network of integrate-and-fire nodes in which connections are heterogeneous with rapid time-varying intensities mimicking fatigue and potentiation. Emergence then becomes quite robust against wiring topology modification--in fact, we considered from a fully connected network to the Homo sapiens connectome--showing the essential role of synaptic flickering on computations. We also suggest how to experimentally disclose significant changes during actual brain operation.

No MeSH data available.


Related in: MedlinePlus

The lower panel shows plots of the variation with D (pA) of the input/output correlation C for different intensities d of the (weak) input signal.The main graph in this panel is, from top to bottom, for d = 20, 10, 5, 1 and 0.1. The last two ones are hardly to distinguish in this scale, and we show in the inset the same for d = 0 (black) and 0.1 (blue). The upper panel shows, for d = 20 pA, with different colors as indicated, how the (normalized) sum of the maximum values of all the overlaps varies with D. The parameters used here are the ones in Fig. 2, which shows a schematic representation of the upper panel here but in the absence of signal, i.e., for d = 0. These plots are based on 30 series of independent MC simulations involving 400 neurons and 6 memories (including negative ones).
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f6: The lower panel shows plots of the variation with D (pA) of the input/output correlation C for different intensities d of the (weak) input signal.The main graph in this panel is, from top to bottom, for d = 20, 10, 5, 1 and 0.1. The last two ones are hardly to distinguish in this scale, and we show in the inset the same for d = 0 (black) and 0.1 (blue). The upper panel shows, for d = 20 pA, with different colors as indicated, how the (normalized) sum of the maximum values of all the overlaps varies with D. The parameters used here are the ones in Fig. 2, which shows a schematic representation of the upper panel here but in the absence of signal, i.e., for d = 0. These plots are based on 30 series of independent MC simulations involving 400 neurons and 6 memories (including negative ones).

Mentions: Note that the horizontal axis in Fig. 2 is logarithmic so that the regions have a relatively much larger extension as one moves to the right, that is, IV and V correspond to a wide range of D while the regions holding the phases I and II are rather narrow. Also noticeable is that, even though somewhat hidden by finite-size effects in actual simulations, close inspection of series such as the ones in Figs 3, 4, 5 clearly indicates that the transitions I→II→III→IV are rather sharp, showing rapid changes of qualitative behavior, thus resembling the situation which is familiar from (equilibrium) discontinuous, first-order phase transitions. On the contrary, the transition IV→V is smoother, as it is also suggested by a rather continuous change of color in the top panel in Fig. 6, and it rather resembles a continuous, second-order phase transition instead. Further remarkable, on the other hand, is that the dashed lines in Fig. 2 do not locate modifications of the main global order but of the synchronization prototype. That is, the memory phase changes from synchronous to asynchronous as III→III’ and the synchronization degree decreases abruptly while roaming as IV→IV’. In any case, these transitions correspond to certainly significant changes of behavior which are clearly revealed by our “order parameter” C(D) so that one should probably term them also as (non-equilibrium) orthodox phase transitions30.


Brain Performance versus Phase Transitions.

Torres JJ, Marro J - Sci Rep (2015)

The lower panel shows plots of the variation with D (pA) of the input/output correlation C for different intensities d of the (weak) input signal.The main graph in this panel is, from top to bottom, for d = 20, 10, 5, 1 and 0.1. The last two ones are hardly to distinguish in this scale, and we show in the inset the same for d = 0 (black) and 0.1 (blue). The upper panel shows, for d = 20 pA, with different colors as indicated, how the (normalized) sum of the maximum values of all the overlaps varies with D. The parameters used here are the ones in Fig. 2, which shows a schematic representation of the upper panel here but in the absence of signal, i.e., for d = 0. These plots are based on 30 series of independent MC simulations involving 400 neurons and 6 memories (including negative ones).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4507401&req=5

f6: The lower panel shows plots of the variation with D (pA) of the input/output correlation C for different intensities d of the (weak) input signal.The main graph in this panel is, from top to bottom, for d = 20, 10, 5, 1 and 0.1. The last two ones are hardly to distinguish in this scale, and we show in the inset the same for d = 0 (black) and 0.1 (blue). The upper panel shows, for d = 20 pA, with different colors as indicated, how the (normalized) sum of the maximum values of all the overlaps varies with D. The parameters used here are the ones in Fig. 2, which shows a schematic representation of the upper panel here but in the absence of signal, i.e., for d = 0. These plots are based on 30 series of independent MC simulations involving 400 neurons and 6 memories (including negative ones).
Mentions: Note that the horizontal axis in Fig. 2 is logarithmic so that the regions have a relatively much larger extension as one moves to the right, that is, IV and V correspond to a wide range of D while the regions holding the phases I and II are rather narrow. Also noticeable is that, even though somewhat hidden by finite-size effects in actual simulations, close inspection of series such as the ones in Figs 3, 4, 5 clearly indicates that the transitions I→II→III→IV are rather sharp, showing rapid changes of qualitative behavior, thus resembling the situation which is familiar from (equilibrium) discontinuous, first-order phase transitions. On the contrary, the transition IV→V is smoother, as it is also suggested by a rather continuous change of color in the top panel in Fig. 6, and it rather resembles a continuous, second-order phase transition instead. Further remarkable, on the other hand, is that the dashed lines in Fig. 2 do not locate modifications of the main global order but of the synchronization prototype. That is, the memory phase changes from synchronous to asynchronous as III→III’ and the synchronization degree decreases abruptly while roaming as IV→IV’. In any case, these transitions correspond to certainly significant changes of behavior which are clearly revealed by our “order parameter” C(D) so that one should probably term them also as (non-equilibrium) orthodox phase transitions30.

Bottom Line: Analyzing to what extent a weak signal endures in noisy environments, we identify the underlying mechanisms, and it results a description of how the excitability associated to (non-equilibrium) phase changes and criticality optimizes the processing of the signal.Our setting is a network of integrate-and-fire nodes in which connections are heterogeneous with rapid time-varying intensities mimicking fatigue and potentiation.Emergence then becomes quite robust against wiring topology modification--in fact, we considered from a fully connected network to the Homo sapiens connectome--showing the essential role of synaptic flickering on computations.

View Article: PubMed Central - PubMed

Affiliation: Institute Carlos I for Theoretical and Computational Physics, Granada, E-18071, Spain.

ABSTRACT
We here illustrate how a well-founded study of the brain may originate in assuming analogies with phase-transition phenomena. Analyzing to what extent a weak signal endures in noisy environments, we identify the underlying mechanisms, and it results a description of how the excitability associated to (non-equilibrium) phase changes and criticality optimizes the processing of the signal. Our setting is a network of integrate-and-fire nodes in which connections are heterogeneous with rapid time-varying intensities mimicking fatigue and potentiation. Emergence then becomes quite robust against wiring topology modification--in fact, we considered from a fully connected network to the Homo sapiens connectome--showing the essential role of synaptic flickering on computations. We also suggest how to experimentally disclose significant changes during actual brain operation.

No MeSH data available.


Related in: MedlinePlus