Numerical simulation of a binary communication channel: Comparison between a replica calculation and an exact solution

The mutual information of a single-layer perceptron with $N$ Gaussian inputs and $P$ deterministic binary outputs is studied by numerical simulations. The relevant parameters of the problem are the ratio between the number of output and input units, $\alpha = P/N$, and those describing the two-point correlations between inputs. The main motivation of this work refers to the comparison between the replica computation of the mutual information and an analytical solution valid up to $\alpha \sim O(1)$. The most relevant results are: (1) the simulation supports the validity of the analytical prediction, and (2) it also verifies a previously proposed conjecture that the replica solution interpolates well between large and small values of $\alpha$.Comment: 6 pages, 8 figures, LaTeX fil

Coordinated population activity underlying texture discrimination in rat barrel cortex

Rodents can robustly distinguish fine differences in texture using their whiskers, a capacity that depends on neuronal activity in primary somatosensory \u201cbarrel\u201d cortex. Here we explore how texture was collectively encoded by populations of three to seven neuronal clusters simultaneously recorded from barrel cortex while a rat performed a discrimination task. Each cluster corresponded to the single-unit or multiunit activity recorded at an individual electrode. To learn how the firing of different clusters combines to represent texture, we computed population activity vectors across moving time windows and extracted the signal available in the optimal linear combination of clusters. We quantified this signal using receiver operating characteristic analysis and compared it to that available in single clusters. Texture encoding was heterogeneous across neuronal clusters, and only a minority of clusters carried signals strong enough to support stimulus discrimination on their own. However, jointly recorded groups of clusters were always able to support texture discrimination at a statistically significant level, even in sessions where no individual cluster represented the stimulus. The discriminative capacity of neuronal activity was degraded when error trials were included in the data, compared to only correct trials, suggesting a link between the neuronal activity and the animal's performance. These analyses indicate that small groups of barrel cortex neurons can robustly represent texture identity through synergistic interactions, and suggest that neurons downstream to barrel cortex could extract texture identity on single trials through simple linear combination of barrel cortex responses

Interspersed distribution of selectivity to kinematic stimulus features in supragranular layers of mouse barrel cortex

Neurons in the primary sensory regions of neocortex have heterogeneous response properties. The spatial arrangement of neurons with particular response properties is a key aspect of population representations and can shed light on how local circuits are wired. Here we investigated how neurons with sensitivity to different kinematic features of whisker stimuli are distributed across local circuits in supragranular layers of the barrel cortex. Using two-photon calcium population imaging in anesthetized mice, we found that nearby neurons represent diverse kinematic features, providing a rich population representation at the local scale. Neurons interspersed in space therefore responded differently to a common stimulus kinematic feature. Conversely, neurons with similar feature selectivity were located no closer to each other than predicted by a random distribution null hypothesis. This finding relied on defining a null hypothesis that was specific for testing the spatial distribution of tuning across neurons. We also measured how neurons sensitive to specific features were distributed relative to barrel boundaries, and found no systematic organization. Our results are compatible with randomly distributed selectivity to kinematic features, with no systematic ordering superimposed upon the whisker map

Spikeling: A low-cost hardware implementation of a spiking neuron for neuroscience teaching and outreach

Understanding how neurons encode and compute information is fundamental to our study of the brain, but opportunities for hands-on experience with neurophysiological techniques on live neurons are scarce in science education. Here, we present Spikeling, an open source in silico implementation of a spiking neuron that costs £25 and mimics a wide range of neuronal behaviours for classroom education and public neuroscience outreach. Spikeling is based on an Arduino microcontroller running the computationally efficient Izhikevich model of a spiking neuron. The microcontroller is connected to input ports that simulate synaptic excitation or inhibition, to dials controlling current injection and noise levels, to a photodiode that makes Spikeling light sensitive, and to a light-emitting diode (LED) and speaker that allows spikes to be seen and heard. Output ports provide access to variables such as membrane potential for recording in experiments or digital signals that can be used to excite other connected Spikelings. These features allow for the intuitive exploration of the function of neurons and networks mimicking electrophysiological experiments. We also report our experience of using Spikeling as a teaching tool for undergraduate and graduate neuroscience education in Nigeria and the United Kingdom

Constructing seasonally adjusted data with time-varying confidence intervals

Seasonal adjustment methods transform observed time series data into estimated data, where these estimated data are constructed such that they show no or almost no seasonal variation. An advantage of model-based methods is that these can provide confidence intervals around the seasonally adjusted data. One particularly useful time series model for seasonal adjustment is the basic structural time series [BSM] model. The usual premise of the BSM is that the variance of each of the components is constant. In this paper we address the possibility that the variance of the trend component in a macro-economic time series in some way depends on the business cycle. One reason for doing so is that one can expect that there is more uncertainty in recession periods. We extend the BSM by allowing for a business-cycle dependent variance in the level equation. Next we show how this affects the confidence intervals of seasonally adjusted data. We apply our extended BSM to monthly US unemployment and we show that the estimated confidence intervals for seasonally adjusted unemployment change with past changes in the oil price

Presynaptic adenosine receptor-mediated regulation of diverse thalamocortical short-term plasticity in the mouse whisker pathway

Short-term synaptic plasticity (STP) sets the sensitivity of a synapse to incoming activity and determines the temporal patterns that it best transmits. In “driver” thalamocortical (TC) synaptic populations, STP is dominated by depression during stimulation from rest. However, during ongoing stimulation, lemniscal TC connections onto layer 4 neurons in mouse barrel cortex express variable STP. Each synapse responds to input trains with a distinct pattern of depression or facilitation around its mean steady-state response. As a result, in common with other synaptic populations, lemniscal TC synapses express diverse rather than uniform dynamics, allowing for a rich representation of temporally varying stimuli. Here, we show that this STP diversity is regulated presynaptically. Presynaptic adenosine receptors of the A1R type, but not kainate receptors (KARs), modulate STP behavior. Blocking the receptors does not eliminate diversity, indicating that diversity is related to heterogeneous expression of multiple mechanisms in the pathway from presynaptic calcium influx to neurotransmitter release

A Dynamic Model of Interactions of Ca^(2+), Calmodulin, and Catalytic Subunits of Ca^(2+)/Calmodulin-Dependent Protein Kinase II

During the acquisition of memories, influx of Ca^(2+) into the postsynaptic spine through the pores of activated N-methyl-D-aspartate-type glutamate receptors triggers processes that change the strength of excitatory synapses. The pattern of Ca^(2+) influx during the first few seconds of activity is interpreted within the Ca^(2+)-dependent signaling network such that synaptic strength is eventually either potentiated or depressed. Many of the critical signaling enzymes that control synaptic plasticity, including Ca^(2+)/calmodulin-dependent protein kinase II (CaMKII), are regulated by calmodulin, a small protein that can bind up to 4 Ca^(2+) ions. As a first step toward clarifying how the Ca^(2+)-signaling network decides between potentiation or depression, we have created a kinetic model of the interactions of Ca^(2+), calmodulin, and CaMKII that represents our best understanding of the dynamics of these interactions under conditions that resemble those in a postsynaptic spine. We constrained parameters of the model from data in the literature, or from our own measurements, and then predicted time courses of activation and autophosphorylation of CaMKII under a variety of conditions. Simulations showed that species of calmodulin with fewer than four bound Ca^(2+) play a significant role in activation of CaMKII in the physiological regime, supporting the notion that processing ofCa^(2+) signals in a spine involves competition among target enzymes for binding to unsaturated species of CaM in an environment in which the concentration of Ca^(2+) is fluctuating rapidly. Indeed, we showed that dependence of activation on the frequency of Ca^(2+) transients arises from the kinetics of interaction of fluctuating Ca^(2+) with calmodulin/CaMKII complexes. We used parameter sensitivity analysis to identify which parameters will be most beneficial to measure more carefully to improve the accuracy of predictions. This model provides a quantitative base from which to build more complex dynamic models of postsynaptic signal transduction during learning

Intrinsic gain modulation and adaptive neural coding

In many cases, the computation of a neural system can be reduced to a receptive field, or a set of linear filters, and a thresholding function, or gain curve, which determines the firing probability; this is known as a linear/nonlinear model. In some forms of sensory adaptation, these linear filters and gain curve adjust very rapidly to changes in the variance of a randomly varying driving input. An apparently similar but previously unrelated issue is the observation of gain control by background noise in cortical neurons: the slope of the firing rate vs current (f-I) curve changes with the variance of background random input. Here, we show a direct correspondence between these two observations by relating variance-dependent changes in the gain of f-I curves to characteristics of the changing empirical linear/nonlinear model obtained by sampling. In the case that the underlying system is fixed, we derive relationships relating the change of the gain with respect to both mean and variance with the receptive fields derived from reverse correlation on a white noise stimulus. Using two conductance-based model neurons that display distinct gain modulation properties through a simple change in parameters, we show that coding properties of both these models quantitatively satisfy the predicted relationships. Our results describe how both variance-dependent gain modulation and adaptive neural computation result from intrinsic nonlinearity.Comment: 24 pages, 4 figures, 1 supporting informatio

Forecasting binary longitudinal data by a functional PC-ARIMA model

In order to forecast time evolution of a binary response variable from a related continuous time series a functional logit model is proposed. The estimation of this model from discrete time observations of the predictor is solved by using functional principal component analysis and ARIMA modelling of the associated discrete time series of principal components. The proposed model is applied to forecast the risk of drought from El Niño phenomenon.Projects MTM2007-63793 from Dirección General de Investigación, Ministerio de Educación y Ciencia, Spain and P06-FQM-01470 from Consejería de Innovación Ciencia y Empresa, Junta de Andalucía, Spai