Dissipative Scaling Functions in Navier-Stokes Turbulence: Experimental Tests

A recent theoretical development in the understanding of the small-scale structure of Navier-Stokes turbulence has been the proposition that the scales $\eta_n(R)$ that separate inertial from viscous behavior of many-point correlation functions depend on the order $n$ and on the typical separations $R$ of points in the correlation. This is a proposal of fundamental significance in itself but it also has implications for the inertial range scaling behaviour of various correlation functions. This dependence has never been observed directly in laboratory experiments. In order to observe it, turbulence data which both display a well-developed scaling range with clean scaling behaviour and are well-resolved in the small scales to well within the viscous range is required. We have analysed the data of the experiments performed in the laboratory of P. Tabeling of Navier-Stokes turbulence in a helium cell with counter-rotating disks, and find that this data satisfies these criteria. We have been able to find strong evidence for the existence of the predicted scaling of the viscous scale.Comment: PRL, submitted, REVTeX, 4 pages, 4 figures, included. Online (HTML) and PS versions of this and related papers available at http://lvov.weizmann.ac.il/onlinelist.htm

Implications of single-neuron gain scaling for information transmission in networks

Summary: 

Many neural systems are equipped with mechanisms to efficiently encode sensory information. To represent natural stimuli with time-varying statistical properties, neural systems should adjust their gain to the inputs' statistical distribution. Such matching of dynamic range to input statistics has been shown to maximize the information transmitted by the output spike trains (Brenner et al., 2000, Fairhall et al., 2001). Gain scaling has not only been observed as a system response property, but also in single neurons in developing somatosensory cortex stimulated with currents of different amplitude (Mease et al., 2010). While gain scaling holds for cortical neurons at the end of the first post-natal week, at birth these neurons lack this property. The observed improvement in gain scaling coincides with the disappearance of spontaneous waves of activity in cortex (Conheim et al., 2010).

We studied how single-neuron gain scaling affects the dynamics of signal transmission in networks, using the developing cortex as a model. In a one-layer feedforward network, we showed that the absence of gain control made the network relatively insensitive to uncorrelated local input fluctuations. As a result, these neurons selectively and synchronously responded to large slowly-varying correlated input--the slow build up of synaptic noise generated in pacemaker circuits which most likely triggers waves. Neurons in gain scaling networks were more sensitive to the small-scale input fluctuations, and responded asynchronously to the slow envelope. Thus, gain scaling both increases information in individual neurons about private inputs and allows the population average to encode the slow fluctuations in the input. Paradoxically, the synchronous firing that corresponds to wave propagation is associated with low information transfer. We therefore suggest that the emergence of gain scaling may help the system to increase information transmission on multiple timescales as sensory stimuli become important later in development. 

Methods:

Networks with one and two layers consisting of hundreds of model neurons were constructed. The ability of single neurons to gain scale was controlled by changing the ratio of sodium to potassium conductances in Hodgkin-Huxley neurons (Mainen et al., 1995). The response of single layer networks was studied with ramp-like stimuli with slopes that varied over several hundreds of milliseconds. Fast fluctuations were superimposed on this slowly-varying mean. Then the response to these networks was tested with continuous stimuli. Gain scaling networks captured the slow fluctuations in the inputs, while non-scaling networks simply thresholded the input. Quantifying information transmission confirmed that gain scaling neurons transmit more information about the stimulus. With the two-layer networks we simulated a cortical network where waves could spontaneously emerge, propagate and degrade, based on the gain scaling properties of the neurons in the network

Multiple timescale encoding of slowly varying whisker stimulus envelope in cortical and thalamic neurons in vivo

7 p., 5 figures and referencesAdaptive processes over many timescales endow neurons with sensitivity to stimulus changes over a similarly wide range of scales. Although spike timing of single neurons can precisely signal rapid fluctuations in their inputs, the mean firing rate can convey information about slower-varying properties of the stimulus. Here, we investigate the firing rate response to a slowly varying envelope of whisker motion in two processing stages of the rat vibrissa pathway. The whiskers of anesthetized rats were moved through a noise trajectory with an amplitude that was sinusoidally modulated at one of several frequencies. In thalamic neurons, we found that the rate response to the stimulus envelope was also sinusoidal, with an approximately frequency-independent phase advance with respect to the input. Responses in cortex were similar but with a phase shift that was about three times larger, consistent with a larger amount of rate adaptation. These response properties can be described as a linear transformation of the input for which a single parameter quantifies the phase shift as well as the degree of adaptation. These results are reproduced by a model of adapting neurons connected by synapses with short-term plasticity, showing that the observed linear response and phase lead can be built up from a network that includes a sequence of nonlinear adapting elements. Our study elucidates how slowly varying envelope information under passive stimulation is preserved and transformed through the vibrissa processing pathway.This work was supported by the following: International Human Frontier Science Program Organization shortterm fellowship (B.N.L.); Spanish Ministry of Science and Innovation Grant BFU2008-03017/BFI (M.M.), cofunded by the European Regional Development Fund; CONSOLIDER Grant CSD2007-00023; European Commission Coordination Action ENINET, Contract LSHM-CT-2005-19063; and a McKnight Scholar Award in the Neurosciences (A.L.F.)Peer reviewe

Correlation-based model of artificially induced plasticity in motor cortex by a bidirectional brain-computer interface

Experiments show that spike-triggered stimulation performed with Bidirectional Brain-Computer-Interfaces (BBCI) can artificially strengthen connections between separate neural sites in motor cortex (MC). What are the neuronal mechanisms responsible for these changes and how does targeted stimulation by a BBCI shape population-level synaptic connectivity? The present work describes a recurrent neural network model with probabilistic spiking mechanisms and plastic synapses capable of capturing both neural and synaptic activity statistics relevant to BBCI conditioning protocols. When spikes from a neuron recorded at one MC site trigger stimuli at a second target site after a fixed delay, the connections between sites are strengthened for spike-stimulus delays consistent with experimentally derived spike time dependent plasticity (STDP) rules. However, the relationship between STDP mechanisms at the level of networks, and their modification with neural implants remains poorly understood. Using our model, we successfully reproduces key experimental results and use analytical derivations, along with novel experimental data. We then derive optimal operational regimes for BBCIs, and formulate predictions concerning the efficacy of spike-triggered stimulation in different regimes of cortical activity.Comment: 35 pages, 9 figure