Spontaneous neuronal activity is a ubiquitous feature of cortex. Its spatiotemporal organization reflects past input and modulates future network output. Here we study whether a particular type of spontaneous activity is generated by a network that is optimized for input processing. Neuronal avalanches are a type of spontaneous activity observed in superficial cortical layers in vitro and in vivo with statistical properties expected from a network operating at "criticality." Theory predicts that criticality and, therefore, neuronal avalanches are optimal for input processing, but until now, this has not been tested in experiments. Here, we use cortex slice cultures grown on planar microelectrode arrays to demonstrate that cortical networks that generate neuronal avalanches benefit from a maximized dynamic range, i.e., the ability to respond to the greatest range of stimuli. By changing the ratio of excitation and inhibition in the cultures, we derive a network tuning curve for stimulus processing as a function of distance from criticality in agreement with predictions from our simulations. Our findings suggest that in the cortex, (1) balanced excitation and inhibition establishes criticality, which maximizes the range of inputs that can be processed, and (2) spontaneous activity and input processing are unified in the context of critical phenomena.

The repertoire of neural activity patterns that a cortical network can produce constrains the ability of the network to transfer and process information. Here, we measured activity patterns obtained from multisite local field potential recordings in cortex cultures, urethaneanesthetized rats, and awake macaque monkeys. First, we quantified the information capacity of the pattern repertoire of ongoing and stimulus-evoked activity using Shannon entropy. Next, we quantified the efficacy of information transmission between stimulus and response using mutual information. By systematically changing the ratio of excitation/inhibition (E/I) in vitro and in a network model, we discovered that both information capacity and information transmission are maximized at a particular intermediate E/I, at which ongoing activity emerges as neuronal avalanches. Next, we used our in vitro and model results to correctly predict in vivo information capacity and interactions between neuronal groups during ongoing activity. Close agreement between our experiments and model suggest that neuronal avalanches and peak information capacity arise because of criticality and are general properties of cortical networks with balanced E/I.

Synchronization is of central importance in power distribution, telecommunication, neuronal and biological networks. Many networks are observed to produce patterns of synchronized clusters, but it has been difficult to predict these clusters or understand the conditions under which they form. Here we present a new framework and develop techniques for the analysis of network dynamics that shows the connection between network symmetries and cluster formation. The connection between symmetries and cluster synchronization is experimentally confirmed in the context of real networks with heterogeneities and noise using an electrooptic network. We experimentally observe and theoretically predict a surprising phenomenon in which some clusters lose synchrony without disturbing the others. Our analysis shows that such behaviour will occur in a wide variety of networks and node dynamics. The results could guide the design of new power grid systems or lead to new understanding of the dynamical behaviour of networks ranging from neural to social.

Networks of nonlocally coupled phase oscillators 1 can support chimera states in which identical oscillators evolve into distinct groups that exhibit coexisting synchronous and incoherent behaviours despite homogeneous coupling 2-6 . Similar nonlocal coupling topologies implemented in networks of chaotic iterated maps also yield dynamical states exhibiting coexisting spatial domains of coherence and incoherence 7,8 . In these discrete-time systems, the phase is not a continuous variable, so these states are generalized chimeras with respect to a broader notion of incoherence. Chimeras continue to be the subject of intense theoretical investigation, but have yet to be realized experimentally 6,9-16 . Here we show that these chimeras can be realized in experiments using a liquid-crystal spatial light modulator to achieve optical nonlinearity in a spatially extended iterated map system. We study the coherenceincoherence transition that gives rise to these chimera states through experiment, theory and simulation.Our system is an experimental realization of a coupled-map lattice (CML), a class of systems that has received sustained theoretical interest for the past three decades. Although the dynamics and statistical physics of CML systems have been theoretically explored, very few (if any) experimental realizations exist [17][18][19][20][21][22] . In our experiments, we create CML dynamics by using a liquid-crystal spatial light modulator (SLM) to control the polarization properties of an optical wavefront. We may electronically introduce any desired coupling topology including nearest neighbour, nonlocal, small world and scale free. In this work, we impose periodic boundary conditions for both onedimensional (1D) and 2D nonlocally coupled maps. Thus, we have developed a powerful experimental technique to observe the parallel evolution of the dynamics of arrays of coupled maps numbering up to thousands or more depending on the goals of the experiment. Figure 1 shows the experimental set-up of the optical CML. Polarization optics create a nonlinear relationship between the spatially dependent phase shift applied by the SLM and the intensity of the light falling on the camera: I (φ) = (1 − cos(φ))/2. The operation of the experimental apparatus is described in the Methods. Both the SLM and the camera frames are partitioned into an M ×M array of square regions. These regions correspond to nodes in the network of coupled maps. Time evolution of the network is achieved by iteratively updating the phase applied by each region of the SLM in a way that depends on the intensity measured by the camera.We present results for two different coupling schemes shown schematically in Fig. 1b,c. In the 1D configuration, the elements in the array are arranged as a ring with periodic boundary conditions. The site highlighted in white is updated based on the sites indicated in blue. As the elements are coupled diffusively to their neighbours within a range R in either one or two dimensions with periodic boundary conditions, the coupling...

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