A generative spike train model with time-structured higher order correlations

Emerging technologies are revealing the spiking activity in ever larger neural ensembles. Frequently, this spiking is far from independent, with correlations in the spike times of different cells. Understanding how such correlations impact the dynamics and function of neural ensembles remains an important open problem. Here we describe a new, generative model for correlated spike trains that can exhibit many of the features observed in data. Extending prior work in mathematical finance, this generalized thinning and shift (GTaS) model creates marginally Poisson spike trains with diverse temporal correlation structures. We give several examples which highlight the model's flexibility and utility. For instance, we use it to examine how a neural network responds to highly structured patterns of inputs. We then show that the GTaS model is analytically tractable, and derive cumulant densities of all orders in terms of model parameters. The GTaS framework can therefore be an important tool in the experimental and theoretical exploration of neural dynamics

Correlations Without Synchrony

Peaks in spike train correlograms are usually taken as indicative of spike timing synchronization between neurons. Strictly speaking, however, a peak merely indicates that the two spike trains were not independent. Two biologically plausible ways of departing from independence that are capable of generating peaks very similar to spike timing peaks are described here: covariations over trials in response latency and covariations over trials in neuronal excitability. Since peaks due to these interactions can be similar to spike timing peaks, interpreting a correlogram may be a problem with ambiguous solutions. What peak shapes do latency or excitability interactions generate? When are they similar to spike timing peaks? When can they be ruled out from having caused an observed correlogram peak? These are the questions addressed here. The previous article in this issue proposes quantitative methods to tell cases apart when latency or excitability covariations cannot be ruled out

Temporal Pattern of Online Communication Spike Trains in Spreading a Scientific Rumor: How Often, Who Interacts with Whom?

We study complex time series (spike trains) of online user communication while spreading messages about the discovery of the Higgs boson in Twitter. We focus on online social interactions among users such as retweet, mention, and reply, and construct different types of active (performing an action) and passive (receiving an action) spike trains for each user. The spike trains are analyzed by means of local variation, to quantify the temporal behavior of active and passive users, as a function of their activity and popularity. We show that the active spike trains are bursty, independently of their activation frequency. For passive spike trains, in contrast, the local variation of popular users presents uncorrelated (Poisson random) dynamics. We further characterize the correlations of the local variation in different interactions. We obtain high values of correlation, and thus consistent temporal behavior, between retweets and mentions, but only for popular users, indicating that creating online attention suggests an alignment in the dynamics of the two interactions.Comment: A statistical data analysis & data mining on Social Dynamic Behavior, 9 pages and 7 figure

Coordinated neuronal ensembles in primary auditory cortical columns.

The synchronous activity of groups of neurons is increasingly thought to be important in cortical information processing and transmission. However, most studies of processing in the primary auditory cortex (AI) have viewed neurons as independent filters; little is known about how coordinated AI neuronal activity is expressed throughout cortical columns and how it might enhance the processing of auditory information. To address this, we recorded from populations of neurons in AI cortical columns of anesthetized rats and, using dimensionality reduction techniques, identified multiple coordinated neuronal ensembles (cNEs), which are groups of neurons with reliable synchronous activity. We show that cNEs reflect local network configurations with enhanced information encoding properties that cannot be accounted for by stimulus-driven synchronization alone. Furthermore, similar cNEs were identified in both spontaneous and evoked activity, indicating that columnar cNEs are stable functional constructs that may represent principal units of information processing in AI

Surrogate time series

Before we apply nonlinear techniques, for example those inspired by chaos theory, to dynamical phenomena occurring in nature, it is necessary to first ask if the use of such advanced techniques is justified "by the data". While many processes in nature seem very unlikely a priori to be linear, the possible nonlinear nature might not be evident in specific aspects of their dynamics. The method of surrogate data has become a very popular tool to address such a question. However, while it was meant to provide a statistically rigorous, foolproof framework, some limitations and caveats have shown up in its practical use. In this paper, recent efforts to understand the caveats, avoid the pitfalls, and to overcome some of the limitations, are reviewed and augmented by new material. In particular, we will discuss specific as well as more general approaches to constrained randomisation, providing a full range of examples. New algorithms will be introduced for unevenly sampled and multivariate data and for surrogate spike trains. The main limitation, which lies in the interpretability of the test results, will be illustrated through instructive case studies. We will also discuss some implementational aspects of the realisation of these methods in the TISEAN (http://www.mpipks-dresden.mpg.de/~tisean) software package.Comment: 28 pages, 23 figures, software at http://www.mpipks-dresden.mpg.de/~tisea

Motif Statistics and Spike Correlations in Neuronal Networks

Motifs are patterns of subgraphs of complex networks. We studied the impact of such patterns of connectivity on the level of correlated, or synchronized, spiking activity among pairs of cells in a recurrent network model of integrate and fire neurons. For a range of network architectures, we find that the pairwise correlation coefficients, averaged across the network, can be closely approximated using only three statistics of network connectivity. These are the overall network connection probability and the frequencies of two second-order motifs: diverging motifs, in which one cell provides input to two others, and chain motifs, in which two cells are connected via a third intermediary cell. Specifically, the prevalence of diverging and chain motifs tends to increase correlation. Our method is based on linear response theory, which enables us to express spiking statistics using linear algebra, and a resumming technique, which extrapolates from second order motifs to predict the overall effect of coupling on network correlation. Our motif-based results seek to isolate the effect of network architecture perturbatively from a known network state

New statistical methods to derive functional connectivity from multiple spike trains

Analysis of functional connectivity of simultaneously recorded multiple spike trains is one of the major issues in the neuroscience. The progress of the statistical methods to the analysis of functional connectivity of multiple spike trains is relatively slow. In this thesis two statistical techniques are presented to the analysis of functional connectivity of multiple spike trains. The first method is known as the modified correlation grid (MCG). This method is based on the calculation of cross-correlation function of all possible pair-wise spike trains. The second technique is known as the Cox method. This method is based on the modulated renewal process (MRP). The original paper on the application of the Cox method (Borisyuk et al., 1985) to neuroscience data was used to analyse only pairs and triplets of spike trains. This method is further developed in this thesis to support simultaneously recorded of any possible set of multiple spike trains. A probabilistic model is developed to test the Cox method. This probabilistic model is based on the MRP. Due to the common probabilistic basis of the probabilistic model and the Cox method, the probabilistic model is a convenient technique to test the Cox method. A new technique based on a pair-wise analysis of Cox method known as the Cox metric is presented to find the groups of coupled spike trains. Another new technique known as motif analysis is introduced which is useful in identifying interconnections among the spike trains. This technique is based on the triplet-wise analysis of the Cox method. All these methods are applied to several sets of spike trains generated by the Enhanced Leaky and Integrate Fire (ELIF) model. The results suggest that these methods are successful for analysing functional connectivity of simultaneously recorded multiple spike trains. These methods are also applied to an experimental data recorded from cat’s visual cortex. The connection matrix derived from the experimental data by the Cox method is further applied to the graph theoretical methods