Higher-Order Interactions Characterized in Cortical Activity

Yu, Shan; Yang, Hongdian; Nakahara, Hiroyuki; Santos, Gustavo Sato dos; Nikolić, Danko; Plenz, Dietmar

doi:10.1523/jneurosci.3127-11.2011

Cited by 200 publications

(289 citation statements)

References 51 publications

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“…If the system is not well described by this maximum entropy distribution then we know from the work of Jaynes [18] that other information beyond pairwise relationships would need to be taken into account. Similar analyses have since been applied in neuroscience [19][20][21] However, the data to accurately estimate the needed bivariate probability distributions may not be available. To get around this some researchers have used the first two moments of the variables as constraints instead of the full bivariate distributions [26,27] -effectively using the cross-correlations as their constraints.…”

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confidence: 99%

Pairwise network information and nonlinear correlations

2016

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Reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines. The fundamental first step is to establish whether or to what extent the interactions between the units can be considered pairwise and, thus, can be modeled as an interaction network with simple links corresponding to pairwise interactions. In principle this can be determined by comparing the maximum entropy given the bivariate probability distributions to the true joint entropy. In many practical cases this is not an option since the bivariate distributions needed may not be reliably estimated, or the optimization is too computationally expensive. Here we present an approach that allows one to use mutual informations as a proxy for the bivariate probability distributions. This has the advantage of being less computationally expensive and easier to estimate. We achieve this by introducing a novel entropy maximization scheme that is based on conditioning on entropies and mutual informations. This renders our approach typically superior to other methods based on linear approximations. The advantages of the proposed method are documented using oscillator networks and a resting-state human brain network as generic relevant examples. Pairwise measures of dependence such as crosscorrelations (as measured by the Pearson correlation coefficient or covariance matrix) and mutual information are widely used to characterize the interactions within complex systems. They are a key ingredient to techniques such as principal component analysis, empirical orthogonal functions, and functional networks (networks inferred from dynamical time series) [1][2][3]. These techniques are widespread since they provide greatly simplified descriptions of complex systems, and allow for the analysis of what might otherwise be intractable problems [4]. In particular, functional networks have been widely applied in fields such as neuroscience [4,5], genetics [6], and cell physiology [7], as well as in climate research [1,8].In this paper we study how faithfully these measures alone can represent a given system. With the increasing use of functional networks this topic has received much attention recently, and many technical concerns have been brought to light dealing with the inference of these networks. Previous studies have shown that the estimates of the functional networks can be negatively affected by properties of the time series [9][10][11], as well as properties of the measure of association, e.g. crosscorrelations [12][13][14][15]. In this work however, we address a more fundamental question: How well do pairwise measurements represent a system?In principle this can be evaluated using a maximum entropy approach. The corresponding framework was first laid out in [16] and later applied in [17], where they assessed the rationale of only looking at the pairwise correlations between neurons. They examined how well the maximum entropy distribution, consistent with all the pairwise correlations described...

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confidence: 99%

Pairwise network information and nonlinear correlations

2016

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“…Furthermore, parameters correspond to local functional properties of neurons and their interactions. However, although the models exactly reproduce the pairwise correlations and individual firing, they fail to account for the full higher-order correlation and temporal structure in the activity (Ohiorhenuan et al, 2010;Yu et al, 2011), and tend to overestimate multineuron firing probabilities (Tkačik et al, 2014). Although we obtained good fits that could account for a large fraction of the correlation structure (Fig.…”

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confidence: 99%

Sloppiness in Spontaneously Active Neuronal Networks

et al. 2015

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Various plasticity mechanisms, including experience-dependent, spontaneous, as well as homeostatic ones, continuously remodel neural circuits. Yet, despite fluctuations in the properties of single neurons and synapses, the behavior and function of neuronal assemblies are generally found to be very stable over time. This raises the important question of how plasticity is coordinated across the network. To address this, we investigated the stability of network activity in cultured rat hippocampal neurons recorded with high-density multielectrode arrays over several days. We used parametric models to characterize multineuron activity patterns and analyzed their sensitivity to changes. We found that the models exhibited sloppiness, a property where the model behavior is insensitive to changes in many parameter combinations, but very sensitive to a few. The activity of neurons with sloppy parameters showed faster and larger fluctuations than the activity of a small subset of neurons associated with sensitive parameters. Furthermore, parameter sensitivity was highly correlated with firing rates. Finally, we tested our observations from cell cultures on an in vivo recording from monkey visual cortex and we confirm that spontaneous cortical activity also shows hallmarks of sloppy behavior and firing rate dependence. Our findings suggest that a small subnetwork of highly active and stable neurons supports group stability, and that this endows neuronal networks with the flexibility to continuously remodel without compromising stability and function.

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“…Such an identification could work only if it were impossible to have unconscious brains (16). A spectacular example is the ability to erase conscious experiences during general anesthesia; yet, a flash of light into the eye of an anesthetized animal is nevertheless able to evoke sensory potentials from pyramidal neurons in the primary visual cortex (21). If mind states were identical to brain states, it should be impossible to turn them on or off using anesthetics, because the brain states always remain brain states.…”

Section: Consciousness In Classical Physicsmentioning

confidence: 99%