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Recent years have seen a profusion of research and controversy surrounding the hypothesis that the brain may be operating at criticality. While experimental evidence supporting the presence of scale-free avalanches in neuronal activity characteristic of a critical state has been steadily accumulating, the interpretation of these data as evidence for critical brain dynamics has simultaneously been questioned (see [1,2] and references therein). From a neuroscientific point of view, the principal appeal of the criticality hypothesis is that critical dynamics have been repeatedly linked to improved information processing, including increased memory capacity, dynamic range, and computational power (see [2] and references therein). Thus far, however, the role that neuronal avalanches - whether hallmarks of criticality or not - might play in complex mental processes such as learning and memory has remained largely unexplored. In this paper, we show that scale-free cascades of neuronal activity also characterize artificial neural networks performing Hebbian learning tasks [3,4]. Our experimental framework enables us to simultaneously measure the network’s performance on the task while observing the corresponding size-distribution of neuronal assemblies. These phenomena are assessed as a function of both network topology and the degree of excitation versus inhibition. Smoothly tuning the degree of order in the network topology, we find that task-performance is optimized in the dynamical state associated with scale-free cascades of exponent 2 < α < 3 which occur in so-called ‘small-world’ networks characterized by high local clustering and short path-length. A transition to ordered, lattice-like, networks is accompanied by both the sudden onset of severely impaired performance and the loss of scale-invariance in neuronal responses. Furthermore, we find that this correlation between scale-free neuronal cascades and performance also holds true when variations in performance are achieved by altering the network’s excitatory-inhibitory balance. Performance is optimized in balanced networks, whilst excitation-dominated states are characterized by a simultaneous drop in performance and the loss of scale-invariance. This is in keeping with experimental studies in cortical slices where the application of picrotoxin, a GABA-receptor antagonist that reduces inhibitory activity, has been shown to result in the loss of power laws in local field potential recordings [5]. Finally, we note that the performance of the system is more robust to deviations from excitatory-inhibitory balance in small-world networks than in random ones. These results may provide insight into psychiatric diseases such as schizophrenia where decreased inhibitory activity [6] and a disruption of topological organization [7] have both been observed alongside the well-known cognitive impairments associated with the disease.

Table of contents A1 Functional advantages of cell-type heterogeneity in neural circuits Tatyana O. Sharpee A2 Mesoscopic modeling of propagating waves in visual cortex Alain Destexhe A3 Dynamics and biomarkers of mental disorders Mitsuo Kawato F1 Precise recruitment of spiking output at theta frequencies requires dendritic h-channels in multi-compartment models of oriens-lacunosum/moleculare hippocampal interneurons Vladislav Sekulić, Frances K. Skinner F2 Kernel methods in reconstruction of current sources from extracellular potentials for single cells and the whole brains Daniel K. Wójcik, Chaitanya Chintaluri, Dorottya Cserpán, Zoltán Somogyvári F3 The synchronized periods depend on intracellular transcriptional repression mechanisms in circadian clocks. Jae Kyoung Kim, Zachary P. Kilpatrick, Matthew R. Bennett, Kresimir Josić O1 Assessing irregularity and coordination of spiking-bursting rhythms in central pattern generators Irene Elices, David Arroyo, Rafael Levi, Francisco B. Rodriguez, Pablo Varona O2 Regulation of top-down processing by cortically-projecting parvalbumin positive neurons in basal forebrain Eunjin Hwang, Bowon Kim, Hio-Been Han, Tae Kim, James T. McKenna, Ritchie E. Brown, Robert W. McCarley, Jee Hyun Choi O3 Modeling auditory stream segregation, build-up and bistability James Rankin, Pamela Osborn Popp, John Rinzel O4 Strong competition between tonotopic neural ensembles explains pitch-related dynamics of auditory cortex evoked fields Alejandro Tabas, André Rupp, Emili Balaguer-Ballester O5 A simple model of retinal response to multi-electrode stimulation Matias I. Maturana, David B. Grayden, Shaun L. Cloherty, Tatiana Kameneva, Michael R. Ibbotson, Hamish Meffin O6 Noise correlations in V4 area correlate with behavioral performance in visual discrimination task Veronika Koren, Timm Lochmann, Valentin Dragoi, Klaus Obermayer O7 Input-location dependent gain modulation in cerebellar nucleus neurons Maria Psarrou, Maria Schilstra, Neil Davey, Benjamin Torben-Nielsen, Volker Steuber O8 Analytic solution of cable energy function for cortical axons and dendrites Huiwen Ju, Jiao Yu, Michael L. Hines, Liang Chen, Yuguo Yu O9 C. elegans interactome: interactive visualization of Caenorhabditis elegans worm neuronal network Jimin Kim, Will Leahy, Eli Shlizerman O10 Is the model any good? Objective criteria for computational neuroscience model selection Justas Birgiolas, Richard C. Gerkin, Sharon M. Crook O11 Cooperation and competition of gamma oscillation mechanisms Atthaphon Viriyopase, Raoul-Martin Memmesheimer, Stan Gielen O12 A discrete structure of the brain waves Yuri Dabaghian, Justin DeVito, Luca Perotti O13 Direction-specific silencing of the Drosophila gaze stabilization system Anmo J. Kim, Lisa M. Fenk, Cheng Lyu, Gaby Maimon O14 What does the fruit fly think about values? A model of olfactory associative learning Chang Zhao, Yves Widmer, Simon Sprecher,Walter Senn O15 Effects of ionic diffusion on power spectra of local field potentials (LFP) Geir Halnes, Tuomo Mäki-Marttunen, Daniel Keller, Klas H. Pettersen,Ole A. Andreassen, Gaute T. Einevoll O16 Large-scale cortical models towards understanding relationship between brain structure abnormalities and cognitive deficits Yasunori Yamada O17 Spatial coarse-graining the brain: origin of minicolumns Moira L. Steyn-Ross, D. Alistair Steyn-Ross O18 Modeling large-scale cortical networks with laminar structure Jorge F. 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