An instrumented tracer for Lagrangian measurements in Rayleigh-B\'enard convection

We have developed novel instrumentation for making Lagrangian measurements of temperature in diverse fluid flows. A small neutrally buoyant capsule is equipped with on-board electronics which measure temperature and transmit the data via a wireless radio frequency link to a desktop computer. The device has 80 dB dynamic range, resolving milli-Kelvin changes in temperature with up to 100 ms sampling time. The capabilities of these "smart particles" are demonstrated in turbulent thermal convection in water. We measure temperature variations as the particle is advected by the convective motion, and analyse its statistics. Additional use of cameras allow us to track the particle position and to report here the first direct measurement of Lagrangian heat flux transfer in Rayleigh-B{\'e}nard convection. The device shows promise for opening new research in a broad variety of fluid systems.Comment: 14 page

Inhibition causes ceaseless dynamics in networks of excitable nodes

The collective dynamics of a network of excitable nodes changes dramatically when inhibitory nodes are introduced. We consider inhibitory nodes which may be activated just like excitatory nodes but, upon activating, decrease the probability of activation of network neighbors. We show that, although the direct effect of inhibitory nodes is to decrease activity, the collective dynamics becomes self-sustaining. We explain this counterintuitive result by defining and analyzing a "branching function" which may be thought of as an activity-dependent branching ratio. The shape of the branching function implies that for a range of global coupling parameters dynamics are self-sustaining. Within the self-sustaining region of parameter space lies a critical line along which dynamics take the form of avalanches with universal scaling of size and duration, embedded in ceaseless timeseries of activity. Our analyses, confirmed by numerical simulation, suggest that inhibition may play a counterintuitive role in excitable networks.Comment: 11 pages, 6 figure

Predicting criticality and dynamic range in complex networks: effects of topology

The collective dynamics of a network of coupled excitable systems in response to an external stimulus depends on the topology of the connections in the network. Here we develop a general theoretical approach to study the effects of network topology on dynamic range, which quantifies the range of stimulus intensities resulting in distinguishable network responses. We find that the largest eigenvalue of the weighted network adjacency matrix governs the network dynamic range. Specifically, a largest eigenvalue equal to one corresponds to a critical regime with maximum dynamic range. We gain deeper insight on the effects of network topology using a nonlinear analysis in terms of additional spectral properties of the adjacency matrix. We find that homogeneous networks can reach a higher dynamic range than those with heterogeneous topology. Our analysis, confirmed by numerical simulations, generalizes previous studies in terms of the largest eigenvalue of the adjacency matrix.Comment: 4 pages, 3 figure

Control of excitable systems is optimal near criticality

Experiments suggest that cerebral cortex gains several functional advantages by operating in a dynamical regime near the critical point of a phase transition. However, a long-standing criticism of this hypothesis is that critical dynamics are rather noisy, which might be detrimental to aspects of brain function that require precision. If the cortex does operate near criticality, how might it mitigate the noisy fluctuations? One possibility is that other parts of the brain may act to control the fluctuations and reduce cortical noise. To better understand this possibility, here we numerically and analytically study a network of binary neurons. We determine how efficacy of controlling the population firing rate depends on proximity to criticality as well as different structural properties of the network. We found that control is most effective - errors are minimal for the widest range of target firing rates - near criticality. Optimal control is slightly away from criticality for networks with heterogeneous degree distributions. Thus, while criticality is the noisiest dynamical regime, it is also the regime that is easiest to control, which may offer a way to mitigate the noise.Comment: 5 pages, 3 figure

Effects of network topology, transmission delays, and refractoriness on the response of coupled excitable systems to a stochastic stimulus

We study the effects of network topology on the response of networks of coupled discrete excitable systems to an external stochastic stimulus. We extend recent results that characterize the response in terms of spectral properties of the adjacency matrix by allowing distributions in the transmission delays and in the number of refractory states, and by developing a nonperturbative approximation to the steady state network response. We confirm our theoretical results with numerical simulations. We find that the steady state response amplitude is inversely proportional to the duration of refractoriness, which reduces the maximum attainable dynamic range. We also find that transmission delays alter the time required to reach steady state. Importantly, neither delays nor refractoriness impact the general prediction that criticality and maximum dynamic range occur when the largest eigenvalue of the adjacency matrix is unity

Tuning network dynamics from criticality to an asynchronous state.

According to many experimental observations, neurons in cerebral cortex tend to operate in an asynchronous regime, firing independently of each other. In contrast, many other experimental observations reveal cortical population firing dynamics that are relatively coordinated and occasionally synchronous. These discrepant observations have naturally led to competing hypotheses. A commonly hypothesized explanation of asynchronous firing is that excitatory and inhibitory synaptic inputs are precisely correlated, nearly canceling each other, sometimes referred to as 'balanced' excitation and inhibition. On the other hand, the 'criticality' hypothesis posits an explanation of the more coordinated state that also requires a certain balance of excitatory and inhibitory interactions. Both hypotheses claim the same qualitative mechanism-properly balanced excitation and inhibition. Thus, a natural question arises: how are asynchronous population dynamics and critical dynamics related, how do they differ? Here we propose an answer to this question based on investigation of a simple, network-level computational model. We show that the strength of inhibitory synapses relative to excitatory synapses can be tuned from weak to strong to generate a family of models that spans a continuum from critical dynamics to asynchronous dynamics. Our results demonstrate that the coordinated dynamics of criticality and asynchronous dynamics can be generated by the same neural system if excitatory and inhibitory synapses are tuned appropriately