Channel noise induced stochastic facilitation in an auditory brainstem neuron model

Neuronal membrane potentials fluctuate stochastically due to conductance changes caused by random transitions between the open and close states of ion channels. Although it has previously been shown that channel noise can nontrivially affect neuronal dynamics, it is unknown whether ion-channel noise is strong enough to act as a noise source for hypothesised noise-enhanced information processing in real neuronal systems, i.e. 'stochastic facilitation.' Here, we demonstrate that biophysical models of channel noise can give rise to two kinds of recently discovered stochastic facilitation effects in a Hodgkin-Huxley-like model of auditory brainstem neurons. The first, known as slope-based stochastic resonance (SBSR), enables phasic neurons to emit action potentials that can encode the slope of inputs that vary slowly relative to key time-constants in the model. The second, known as inverse stochastic resonance (ISR), occurs in tonically firing neurons when small levels of noise inhibit tonic firing and replace it with burst-like dynamics. Consistent with previous work, we conclude that channel noise can provide significant variability in firing dynamics, even for large numbers of channels. Moreover, our results show that possible associated computational benefits may occur due to channel noise in neurons of the auditory brainstem. This holds whether the firing dynamics in the model are phasic (SBSR can occur due to channel noise) or tonic (ISR can occur due to channel noise).Comment: Published by Physical Review E, November 2013 (this version 17 pages total - 10 text, 1 refs, 6 figures/tables); Associated matlab code is available online in the ModelDB repository at http://senselab.med.yale.edu/ModelDB/ShowModel.asp?model=15148

Elastic electron scattering from CF3I

Experimental results are reported for elastic differential and integral cross sections for electrons scattering from CF3I. These measurements were made at ten incident electron energies in the range 10–50 eV, with a scattered electron angular range of 20◦–135◦. Where possible, comparison is made to the only other comprehensive experimental set of results available in the literature and to calculated cross sections from the Schwinger multichannel with pseudopotentials method. In general, quite good agreement is found between the present results and those of the earlier studies

Motif-role-fingerprints: the building-blocks of motifs, clustering-coefficients and transitivities in directed networks

Complex networks are frequently characterized by metrics for which particular subgraphs are counted. One statistic from this category, which we refer to as motif-role fingerprints, differs from global subgraph counts in that the number of subgraphs in which each node participates is counted. As with global subgraph counts, it can be important to distinguish between motif-role fingerprints that are 'structural' (induced subgraphs) and 'functional' (partial subgraphs). Here we show mathematically that a vector of all functional motif-role fingerprints can readily be obtained from an arbitrary directed adjacency matrix, and then converted to structural motif-role fingerprints by multiplying that vector by a specific invertible conversion matrix. This result demonstrates that a unique structural motif-role fingerprint exists for any given functional motif-role fingerprint. We demonstrate a similar result for the cases of functional and structural motif-fingerprints without node roles, and global subgraph counts that form the basis of standard motif analysis. We also explicitly highlight that motif-role fingerprints are elemental to several popular metrics for quantifying the subgraph structure of directed complex networks, including motif distributions, directed clustering coefficient, and transitivity. The relationships between each of these metrics and motif-role fingerprints also suggest new subtypes of directed clustering coefficients and transitivities. Our results have potential utility in analyzing directed synaptic networks constructed from neuronal connectome data, such as in terms of centrality. Other potential applications include anomaly detection in networks, identification of similar networks and identification of similar nodes within networks. Matlab code for calculating all stated metrics following calculation of functional motif-role fingerprints is provided as S1 Matlab File.Mark D. McDonnell, Ömer Nebil Yaveroğlu, Brett A. Schmerl, Nicolangelo Iannella, Lawrence M. War

Elastic electron scattering from CF 3 I

Experimental results are reported for elastic differential and integral cross sections for electrons scattering from CF3I. These measurements were made at ten incident electron energies in the range 10-50 eV, with a scattered electron angular range of 20°-135°. Where possible, comparison is made to the only other comprehensive experimental set of results available in the literature and to calculated cross sections from the Schwinger multichannel with pseudopotentials method. In general, quite good agreement is found between the present results and those of the earlier studies

Formulae for counting the three-node motif-role fingerprints.

<p>The first column depicts the 9 distinct roles on functional motifs. Each row shows each three-node motif in which the corresponding role appears (indexed by ), and the plurality with which motif-role appears within motif (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0114503#s3" target="_blank">Methods</a>). Black filled circles indicate the nodes in motif that play motif-role (see also Fig. 1). The equations shown for each role, <i>r</i>, are the entries of the functional motif-role fingerprint matrix, , where denotes the Hadamard product, is an unit column matrix, is the identity matrix, and is the matrix of reciprocal edges.</p

All 13 three-node connected motifs and all 30 three-node connected motif-roles.

<p>A directed network is assumed. The numerical label for each motif (denoted with the label <i>m</i>) is identical to that used in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0114503#pone.0114503-Milo1" target="_blank">[9]</a>. Each distinct motif-role within each motif is denoted by different colours, and the numerical label next to each node. The numerical label provided for each motif-role is represented by the label in the text and in Fig. 2, where .</p

Structural motifs and motif-roles decompose into functional motifs and motif-roles.

<p>Illustration of the difference between structural and functional motifs and motif-roles. When counting structural motifs in a network, the connectivity between each set of three nodes is considered. In this case, if the nodes form motif , then this counts as one instance of structural motif , and no instances of structural motifs or 2. However, the same subgraph provides one instance each of functional motifs , , and (see also Fig. 1 in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0114503#pone.0114503-Sporns1" target="_blank">[22]</a> for a similar illustration). Consequently, there are no more structural motifs in total than the number of combinations of three nodes. However, this is not the case for functional motifs, since the same set of three nodes can contain multiple functional motifs. The same decomposition occurs for motif-roles. In the example in this figure, a single instance of structural motif-role decomposes into one instance each of functional motif-roles , and .</p

Directed transitivities and average clustering coefficients for two directed <i>C. elegans</i> chemical synapse networks, and randomisations of those networks.

<p>Circles show each of the six directed transitivities and six directed clustering coefficient values for the <i>C. elegans</i> hermaphrodite and male networks. Dots show comparison points obtained from each of 20 degree-preserving randomizations of the two connectivity matrices. Clearly the male exhibits higher transitivity and clustering than the hermaphrodite, according to all 12 statistics, but both real networks are more transitive/clustered than corresponding null-hypothesis networks.</p

Dependencies between metrics that count three-node directed subgraphs.

<p>Arrows indicate that metrics can be derived from other metrics and numbers in brackets refer to equations in the text that mathematically describe these dependencies. The left side of the figure lists metrics that count subgraphs, while the right side shows metrics that are ratios of subgraph counts. The top half of the figure shows metrics that are node-referenced subgraph counts, while the bottom half shows metrics that are global subgraph counts.</p