Measures for information propagation in Boolean networks

Rämö, Pauli; Kauffman, Stuart; Kesseli, Juha; Yli‐Harja, Olli

doi:10.1016/j.physd.2006.12.005

Cited by 56 publications

(49 citation statements)

References 15 publications

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“…Importantly, avalanche size, s, distributes according to a power law, P(s) ϳ s ␣ with exponent ␣ close to Ϫ1.5, a hallmark of critical state dynamics (Plenz and Thiagarajan, 2007;Klaus et al, 2011). Both theoretical (Kinouchi and Copelli, 2006;Rämö et al, 2007;Tanaka et al, 2009) and empirical studies (Shew et al, 2009(Shew et al, , 2011 suggest that avalanches optimize various aspects of information processing in cortical networks.…”

Section: Higher-order Interactions Are Essential For Neuronal Avalancmentioning

confidence: 99%

Higher-Order Interactions Characterized in Cortical Activity

Yu¹,

Yang²,

Nakahara³

et al. 2011

J. Neurosci.

204

267

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In the cortex, the interactions among neurons give rise to transient coherent activity patterns that underlie perception, cognition, and action. Recently, it was actively debated whether the most basic interactions, i.e., the pairwise correlations between neurons or groups of neurons, suffice to explain those observed activity patterns. So far, the evidence reported is controversial. Importantly, the overall organization of neuronal interactions and the mechanisms underlying their generation, especially those of high-order interactions, have remained elusive. Here we show that higher-order interactions are required to properly account for cortical dynamics such as ongoing neuronal avalanches in the alert monkey and evoked visual responses in the anesthetized cat. A Gaussian interaction model that utilizes the observed pairwise correlations and event rates and that applies intrinsic thresholding identifies those higher-order interactions correctly, both in cortical local field potentials and spiking activities. This allows for accurate prediction of large neuronal population activities as required, e.g., in brain-machine interface paradigms. Our results demonstrate that higher-order interactions are inherent properties of cortical dynamics and suggest a simple solution to overcome the apparent formidable complexity previously thought to be intrinsic to those interactions.

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Section: Higher-order Interactions Are Essential For Neuronal Avalancmentioning

confidence: 99%

Higher-Order Interactions Characterized in Cortical Activity

Yu¹,

Yang²,

Nakahara³

et al. 2011

J. Neurosci.

204

267

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show abstract

“…1 Ribeiro et al [31] measured mutual information within random node pairs as a function of connectivity in the network, finding a maximum near the critical point. Rämö et al [30] measured the uncertainty (entropy) in the size of perturbation avalanches as a function of an order parameter, and also found a maximum near the critical point. Lizier et al [20] studied the information storage and transfer components of the computation conducted by each node in RBNs.…”

Section: Introductionmentioning

confidence: 99%

“…For example, the study of perturbation avalanches in [30] is not applicable to systems in which we cannot interfere. The measure of pairwise mutual information [31] can be imagined to be maximized for trivial short-period behavior as well as complex behavior at the critical point.…”

Section: Introductionmentioning

confidence: 99%

Fisher Information at the Edge of Chaos in Random Boolean Networks

2011

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We study the order-chaos phase transition in random Boolean networks (RBNs), which have been used as models of gene regulatory networks. In particular we seek to characterize the phase diagram in information-theoretic terms, focusing on the effect of the control parameters (activity level and connectivity). Fisher information, which measures how much system dynamics can reveal about the control parameters, offers a natural interpretation of the phase diagram in RBNs. We report that this measure is maximized near the order-chaos phase transitions in RBNs, since this is the region where the system is most sensitive to its parameters. Furthermore, we use this study of RBNs to clarify the relationship between Shannon and Fisher information measures.

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“…On the other hand it would be of interest to tackle the topic of information propagation in such Boolean networks subject to noise. This kind of work has been recently developed in the context of perturbation avalanches in Boolean networks by Rämö et al [32].…”

Section: Discussionmentioning

confidence: 99%