The Rock-Paper-Scissors game.

<p>(A) The payoff matrix. Each matrix element is the payoff of the row player X's action in competition with the column player Y's action. (B) The cyclic (non-transitive) dominance relationship among the three candidate actions: Rock () beats Scissors (), beats Paper (), and in turn beats .</p

Optimal CT strategy of unit memory length.

<p>The optimal values of both players' expected payoff per round and are shown in the upper panel (in units of NE payoff ) for each fixed value of , while the optimal values of the CT strategy's choice probabilities , and are shown in the lower panel. When the NE mixed strategy is better for player X than the CT strategy.</p

Optimal memoryless CT strategy.

<p>The optimal values of both players' expected payoff per round and are shown in the upper panel (in units of NE payoff ) for each fixed value of , while the optimal values of the CT strategy's choice probabilities , and are shown in the lower panel. When the NE mixed strategy is better for player X than the CT strategy.</p

Optimal CT strategy of finite memory length.

<p>The optimal values of both players' expected payoff per round and are shown in the upper panel (in units of NE payoff ) for each fixed value of , while the minimal memory length of the CT strategy is shown in the lower panel.</p

Co-emergence of multi-scale cortical activities of irregular firing, oscillations and avalanches achieves cost-efficient information capacity

<div><p>The brain is highly energy consuming, therefore is under strong selective pressure to achieve cost-efficiency in both cortical connectivities and activities. However, cost-efficiency as a design principle for cortical activities has been rarely studied. Especially it is not clear how cost-efficiency is related to ubiquitously observed multi-scale properties: irregular firing, oscillations and neuronal avalanches. Here we demonstrate that these prominent properties can be simultaneously observed in a generic, biologically plausible neural circuit model that captures excitation-inhibition balance and realistic dynamics of synaptic conductance. Their co-emergence achieves minimal energy cost as well as maximal energy efficiency on information capacity, when neuronal firing are coordinated and shaped by moderate synchrony to reduce otherwise redundant spikes, and the dynamical clusterings are maintained in the form of neuronal avalanches. Such cost-efficient neural dynamics can be employed as a foundation for further efficient information processing under energy constraint.</p></div

Co-existence of multi-scale cortical activities at moderately synchronized states.

<p>(A) Average pairwise 1-ms synchrony between excitatory neurons (E—E Synchrony); (B) Average CV (standard deviation/mean) of the inter-spike intervals (ISIs) over the excitatory population; (C) Power spectra of population activity for 3 different parameter sets indicated in (F); (D) Peak frequency; (E) Peak power. (F) Avalanche size distributions for 3 different parameter sets. (G) Distance of avalanche size distribution from the best-fitted power-law distribution; (H) ISI CV (red), distance from power-law (black) and peak power (blue) <i>vs</i>. E—E Synchrony, showing the co-existence of irregular firing, synchronized oscillations and neuronal avalanches at moderately synchronized states. (A, B, D, E, G) in the parameter space (<i>τ</i>_{<i>d</i>_<i>e</i>}, <i>τ</i>_{<i>d</i>_<i>i</i>}) (unit: ms).</p

Definition of spatiotemporal spike patterns.

<p>(A) Examples of cross-correlogram between neuron pairs for various parameter sets (<i>τ</i>_{<i>d</i>_<i>e</i>}, <i>τ</i>_{<i>d</i>_<i>i</i>}) show that spike coincidence happens within 20-ms windows; the average firing rate of one neuron is plotted relative to the time at which the other neuron spikes, averaged over 2000 pairs of randomly selected excitatory neurons. Black, blue, red points are the respective subcritical, critical supercritical cases as exampled in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005384#pcbi.1005384.g002" target="_blank">Fig 2</a>. Three more cases around the critical region are shown as green points. (B) Schematics of mapping spiking patterns of 10 randomly selected neurons into binary strings; black, patterns without any spike; blue, binary patterns with spikes.</p

Multi-scale dynamics of E-I balanced network with various synchrony degree.

<p>Left panel: asynchronous state (<i>τ_{d_e}</i> = 6 ms, <i>τ_{d_i}</i> = 6 ms); Middle panel: moderately synchronized state (<i>τ_{d_e}</i> = 4 ms, <i>τ_{d_i}</i> = 10 ms); Right panel: highly synchronized state (<i>τ_{d_e}</i> = 2 ms, <i>τ_{d_i}</i> = 14 ms). (A, C, E) Time series of membrane potential, input conductances, and input currents of a randomly selected neuron. (B, D, F) Network activity. Top, raster plot of a subset 500 neurons (Exc 400 (blue), Inh 100 (red)); bottom, the average excitatory and inhibitory population activity in 1-ms bins; inset, autocorrelation (AC) of the excitatory population activity. Middle and right panels show that the population rhythm is mainly determined by inhibitory decay time <i>τ_{d_i}</i>, and the delayed negative feedback from inhibitory population suppresses the firing of the excitatory population, leaving a window for integration, whose size controls the burst of individual activities (C, E).</p

Spiking neuron number distribution.

<p>Probability distributions of the activated neuron number for the selected states, indicated in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005384#pcbi.1005384.g006" target="_blank">Fig 6A and 6B</a> with the corresponding symbols. <i>n</i> = 40 for all patterns. The distribution in the critical region is close to the experimental data [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005384#pcbi.1005384.ref048" target="_blank">48</a>] (red).</p

Probability of empty patterns.

<p>Dependence of the probability <i>p</i>₀ of empty patterns on the number of spiking neurons <i>m</i>_<i>n</i> for and the subcritical state in our simulations at various sample size <i>n</i>. Dashed line represents the ideal case with all neurons firing randomly. Parameter set (<i>τ</i>_{<i>d</i>_<i>e</i>}, <i>τ</i>_{<i>d</i>_<i>i</i>}) is indicated by the triangle in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005384#pcbi.1005384.g006" target="_blank">Fig 6A and 6B</a>.</p