How strong are correlations in strongly recurrent neuronal networks?

Cross-correlations in the activity in neural networks are commonly used to characterize their dynamical states and their anatomical and functional organizations. Yet, how these latter network features affect the spatiotemporal structure of the correlations in recurrent networks is not fully understood. Here, we develop a general theory for the emergence of correlated neuronal activity from the dynamics in strongly recurrent networks consisting of several populations of binary neurons. We apply this theory to the case in which the connectivity depends on the anatomical or functional distance between the neurons. We establish the architectural conditions under which the system settles into a dynamical state where correlations are strong, highly robust and spatially modulated. We show that such strong correlations arise if the network exhibits an effective feedforward structure. We establish how this feedforward structure determines the way correlations scale with the network size and the degree of the connectivity. In networks lacking an effective feedforward structure correlations are extremely small and only weakly depend on the number of connections per neuron. Our work shows how strong correlations can be consistent with highly irregular activity in recurrent networks, two key features of neuronal dynamics in the central nervous system

Auto-structure of spike trains matters for testing on synchronous activity

Poster presentation: Coordinated neuronal activity across many neurons, i.e. synchronous or spatiotemporal pattern, had been believed to be a major component of neuronal activity. However, the discussion if coordinated activity really exists remained heated and controversial. A major uncertainty was that many analysis approaches either ignored the auto-structure of the spiking activity, assumed a very simplified model (poissonian firing), or changed the auto-structure by spike jittering. We studied whether a statistical inference that tests whether coordinated activity is occurring beyond chance can be made false if one ignores or changes the real auto-structure of recorded data. To this end, we investigated the distribution of coincident spikes in mutually independent spike-trains modeled as renewal processes. We considered Gamma processes with different shape parameters as well as renewal processes in which the ISI distribution is log-normal. For Gamma processes of integer order, we calculated the mean number of coincident spikes, as well as the Fano factor of the coincidences, analytically. We determined how these measures depend on the bin width and also investigated how they depend on the firing rate, and on rate difference between the neurons. We used Monte-Carlo simulations to estimate the whole distribution for these parameters and also for other values of gamma. Moreover, we considered the effect of dithering for both of these processes and saw that while dithering does not change the average number of coincidences, it does change the shape of the coincidence distribution. Our major findings are: 1) the width of the coincidence count distribution depends very critically and in a non-trivial way on the detailed properties of the inter-spike interval distribution, 2) the dependencies of the Fano factor on the coefficient of variation of the ISI distribution are complex and mostly non-monotonic. Moreover, the Fano factor depends on the very detailed properties of the individual point processes, and cannot be predicted by the CV alone. Hence, given a recorded data set, the estimated value of CV of the ISI distribution is not sufficient to predict the Fano factor of the coincidence count distribution, and 3) spike jittering, even if it is as small as a fraction of the expected ISI, can falsify the inference on coordinated firing. In most of the tested cases and especially for complex synchronous and spatiotemporal pattern across many neurons, spike jittering increased the likelihood of false positive finding very strongly. Last, we discuss a procedure [1] that considers the complete auto-structure of each individual spike-train for testing whether synchrony firing occurs at chance and therefore overcomes the danger of an increased level of false positives

Construct validity of the Developmental Test of Visual-Motor Integration 6th Edition (Beery VMI-6) in Western Australian primary-school children

AIM: The construct validity of the 6th edition of the Developmental Test of Visual-Motor Integration (Beery VMI-6), is yet to be tested for a Western Australian population. This study aimed to use a combination of factor analysis and correlational tests to provide preliminary evidence for the construct validity of the Beery VMI-6 when administered to a Western Australian population of 6-10 year old children. METHOD: This pilot study utilised a quantitative non-experimental exploratory design. Convenience sampling was used to recruit 91 children (aged 6-10 years old) from two schools in the northern suburbs of Perth. Administration of the Beery VMI-6 adhered to the assessment manual guidelines. In addition, informal observations were made, and a Parent Questionnaire and Teacher Checklist were instrumented. Data was stored and analysed using SPSS 22. As the data was normally distributed, parametric analysis was used, with a paired t-test for the factor analysis and Pearson’s for the correlational tests. Principal Components Analysis and orthogonal Varimax rotation were used for the factor analysis. RESULTS: The factor analysis extracted two factors with eigenvalues exceeding 1.5, accounting for 33.106% of the total variance. Nine items loaded significantly on factor 1 and eight loaded significantly on factor 2. Correlational tests exposed that three out of five construct validity hypotheses from the Beery VMI-6 manual were justified for this population, however all significant correlations were of weak to low strength. CONCLUSION: For this population, the Beery VMI-6 is bidimensional with factor complexity. It therefore does not measure the single homogenous construct of visual-motor integration as the manual suggests, but instead measures two discrete constructs. Considering the results of the factor analysis and the mixed results of the correlational tests, the construct validity of the Beery VMI-6 does not meet the demands expected of a standardised assessment for the Western Australian population. It is therefore recommended that Occupational Therapists are cautious when using the Beery VMI-6 within this population, and that they add to the assessment by using clinical reasoning and observation

An augmented moment method for stochastic ensembles with delayed couplings: II. FitzHugh-Nagumo model

Dynamics of FitzHugh-Nagumo (FN) neuron ensembles with time-delayed couplings subject to white noises, has been studied by using both direct simulations and a semi-analytical augmented moment method (AMM) which has been proposed in a recent paper [H. Hasegawa, E-print: cond-mat/0311021]. For $N$-unit FN neuron ensembles, AMM transforms original $2N$-dimensional {\it stochastic} delay differential equations (SDDEs) to infinite-dimensional {\it deterministic} DEs for means and correlation functions of local and global variables. Infinite-order recursive DEs are terminated at the finite level $m$ in the level-$m$ AMM (AMM$m$), yielding $8(m+1)$-dimensional deterministic DEs. When a single spike is applied, the oscillation may be induced if parameters of coupling strength, delay, noise intensity and/or ensemble size are appropriate. Effects of these parameters on the emergence of the oscillation and on the synchronization in FN neuron ensembles have been studied. The synchronization shows the {\it fluctuation-induced} enhancement at the transition between non-oscillating and oscillating states. Results calculated by AMM5 are in fairly good agreement with those obtained by direct simulations.Comment: 15 pages, 3 figures; changed the title with correcting typos, accepted in Phys. Rev. E with some change

Emergent Orientation Selectivity from Random Networks in Mouse Visual Cortex

The connectivity principles underlying the emergence of orientation selectivity in primary visual cortex (V1) of mammals lacking an orientation map (such as rodents and lagomorphs) are poorly understood. We present a computational model in which random connectivity gives rise to orientation selectivity that matches experimental observations. The model predicts that mouse V1 neurons should exhibit intricate receptive fields in the two-dimensional frequency domain, causing a shift in orientation preferences with spatial frequency. We find evidence for these features in mouse V1 using calcium imaging and intracellular whole-cell recordings. Pattadkal et al. show that orientation selectivity can emerge from random connectivity, and offer a distinct perspective for how computations occur in the neocortex. They propose that a random convergence of inputs can provide signals for orientation preference in contrast with the dominant model that requires a precise arrangement.Fil: Pattadkal, Jagruti J.. University of Texas at Austin; Estados UnidosFil: Mato, German. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: van Vreeswijk, Carl. Centre National de la Recherche Scientifique; FranciaFil: Priebe, Nicholas J.. University of Texas at Austin; Estados UnidosFil: Hansel, David. Centre National de la Recherche Scientifique; Franci

Pulvinar thalamic nucleus allows for asynchronous spike propagation through the cortex

We create two multilayered feedforward networks composed of excitatoryand inhibitory integrate-and-fire neurons in the balanced state toinvestigate the role of cortico-pulvino-cortical connections. Thefirst network consists of ten feedforward levels where a Poisson spiketrain with varying firing rate is applied as an input in layerone. Although the balanced state partially avoids spikesynchronization during the transmission, the average firing-rate in the last layer either decays or saturates depending on the feedforwardpathway gain. The last layer activity is almost independent of the inputeven for a carefully chosen intermediate gain. Adding connectionsto the feedforward pathway by a nine areas Pulvinar structure improves the firing-rate propagation to become almost linear amonglayers. Incoming strong pulvinar spikes balance the low feedforwardgain to have a unit input-output relation in the last layer. Pulvinarneurons evoke a bimodal activity depending on the magnitude input: synchronized spike bursts between 20-80 Hz and an asynchronous activityfor very both low and high frequency inputs. In the first regime, spikes of last feedforward layer neurons areasynchronous with weak, low frequency, oscillations in the rate. Here,the uncorrelated incoming feedforward pathway washes out thesynchronized thalamic bursts. In the second regime, spikes in the wholenetwork are asynchronous. As the number of cortical layers increases,long-range pulvinar connections can link directly two or morecortical stages avoiding their either saturation or gradual activityfalling. The Pulvinar acts as a shortcut that supplies theinput-output firing-rate relationship of two separated cortical areaswithout changing the strength of connections in the feedforwardpathway

The Role of Pulvinar in the Transmission of Information in the Visual Hierarchy

Visual receptive field (RF) attributes in visual cortex of primates have been explained mainly from cortical connections: visual RFs progress from simple to complex through cortico-cortical pathways from lower to higher levels in the visual hierarchy. This feedforward flow of information is paired with top-down processes through the feedback pathway. Although the hierarchical organization explains the spatial properties of RFs, is unclear how a non-linear transmission of activity through the visual hierarchy can yield smooth contrast response functions in all level of the hierarchy. Depending on the gain, non-linear transfer functions create either a bimodal response to contrast, or no contrast dependence of the response in the highest level of the hierarchy. One possible mechanism to regulate this transmission of visual contrast information from low to high level involves an external component that shortcuts the flow of information through the hierarchy. A candidate for this shortcut is the Pulvinar nucleus of the thalamus. To investigate representation of stimulus contrast a hierarchical model network of ten cortical areas is examined. In each level of the network, the activity from the previous layer is integrated and then non-linearly transmitted to the next level. The arrangement of interactions creates a gradient from simple to complex RFs of increasing size as one moves from lower to higher cortical levels. The visual input is modeled as a Gaussian random input, whose width codes for the contrast. This input is applied to the first area. The output activity ratio among different contrast values is analyzed for the last level to observe sensitivity to a contrast and contrast invariant tuning. For a purely cortical system, the output of the last area can be approximately contrast invariant, but the sensitivity to contrast is poor. To account for an alternative visual processing pathway, non-reciprocal connections from and to a parallel pulvinar like structure of nine areas is coupled to the system. Compared to the pure feedforward model, cortico-pulvino-cortical output presents much more sensitivity to contrast and has a similar level of contrast invariance of the tuning

Stability of Spatio-Temporal Structures in a Lattice Model of Pulse-Coupled Oscillators

We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By studying the intrinsic dynamics of each member of the population and their mutual interactions we observe the emergence of either spatio-temporal structures or synchronized regimes. We perform a linear stability analysis of these structures.Comment: 15 pages, 2 PostScript available upon request at [email protected], Accepted in Physica