Higher-Order Correlations in Non-Stationary Parallel Spike Trains: Statistical Modeling and Inference

The extent to which groups of neurons exhibit higher-order correlations in their spiking activity is a controversial issue in current brain research. A major difficulty is that currently available tools for the analysis of massively parallel spike trains (N >10) for higher-order correlations typically require vast sample sizes. While multiple single-cell recordings become increasingly available, experimental approaches to investigate the role of higher-order correlations suffer from the limitations of available analysis techniques. We have recently presented a novel method for cumulant-based inference of higher-order correlations (CuBIC) that detects correlations of higher order even from relatively short data stretches of length T = 10–100 s. CuBIC employs the compound Poisson process (CPP) as a statistical model for the population spike counts, and assumes spike trains to be stationary in the analyzed data stretch. In the present study, we describe a non-stationary version of the CPP by decoupling the correlation structure from the spiking intensity of the population. This allows us to adapt CuBIC to time-varying firing rates. Numerical simulations reveal that the adaptation corrects for false positive inference of correlations in data with pure rate co-variation, while allowing for temporal variations of the firing rates has a surprisingly small effect on CuBICs sensitivity for correlations

Visualisation Studio for the analysis of massive datasets

This thesis describes the research underpinning and the development of a cross platform application for the analysis of simultaneously recorded multi-dimensional spike trains. These spike trains are believed to carry the neural code that encodes information in a biological brain. A number of statistical methods already exist to analyse the temporal relationships between the spike trains. Historically, hundreds of spike trains have been simultaneously recorded, however as a result of technological advances recording capability has increased. The analysis of thousands of simultaneously recorded spike trains is now a requirement. Effective analysis of large data sets requires software tools that fully exploit the capabilities of modern research computers and effectively manage and present large quantities of data. To be effective such software tools must; be targeted at the field under study, be engineered to exploit the full compute power of research computers and prevent information overload of the researcher despite presenting a large and complex data set. The Visualisation Studio application produced in this thesis brings together the fields of neuroscience, software engineering and information visualisation to produce a software tool that meets these criteria. A visual programming language for neuroscience is produced that allows for extensive pre-processing of spike train data prior to visualisation. The computational challenges of analysing thousands of spike trains are addressed using parallel processing to fully exploit the modern researcher’s computer hardware. In the case of the computationally intensive pairwise cross-correlation analysis the option to use a high performance compute cluster (HPC) is seamlessly provided. Finally the principles of information visualisation are applied to key visualisations in neuroscience so that the researcher can effectively manage and visually explore the resulting data sets. The final visualisations can typically represent data sets 10 times larger than previously while remaining highly interactiv

Detecting multineuronal temporal patterns in parallel spike trains

We present a non-parametric and computationally efficient method that detects spatiotemporal firing patterns and pattern sequences in parallel spike trains and tests whether the observed numbers of repeating patterns and sequences on a given timescale are significantly different from those expected by chance. The method is generally applicable and uncovers coordinated activity with arbitrary precision by comparing it to appropriate surrogate data. The analysis of coherent patterns of spatially and temporally distributed spiking activity on various timescales enables the immediate tracking of diverse qualities of coordinated firing related to neuronal state changes and information processing. We apply the method to simulated data and multineuronal recordings from rat visual cortex and show that it reliably discriminates between data sets with random pattern occurrences and with additional exactly repeating spatiotemporal patterns and pattern sequences. Multineuronal cortical spiking activity appears to be precisely coordinated and exhibits a sequential organization beyond the cell assembly concept

The Spatial Structure of Stimuli Shapes the Timescale of Correlations in Population Spiking Activity

Throughout the central nervous system, the timescale over which pairs of neural spike trains are correlated is shaped by stimulus structure and behavioral context. Such shaping is thought to underlie important changes in the neural code, but the neural circuitry responsible is largely unknown. In this study, we investigate a stimulus-induced shaping of pairwise spike train correlations in the electrosensory system of weakly electric fish. Simultaneous single unit recordings of principal electrosensory cells show that an increase in the spatial extent of stimuli increases correlations at short (~10 ms) timescales while simultaneously reducing correlations at long (~100 ms) timescales. A spiking network model of the first two stages of electrosensory processing replicates this correlation shaping, under the assumptions that spatially broad stimuli both saturate feedforward afferent input and recruit an open-loop inhibitory feedback pathway. Our model predictions are experimentally verified using both the natural heterogeneity of the electrosensory system and pharmacological blockade of descending feedback projections. For weak stimuli, linear response analysis of the spiking network shows that the reduction of long timescale correlation for spatially broad stimuli is similar to correlation cancellation mechanisms previously suggested to be operative in mammalian cortex. The mechanism for correlation shaping supports population-level filtering of irrelevant distractor stimuli, thereby enhancing the population response to relevant prey and conspecific communication inputs. © 2012 Litwin-Kumar et al

A study of dependency features of spike trains through copulas

Simultaneous recordings from many neurons hide important information and the connections characterizing the network remain generally undiscovered despite the progresses of statistical and machine learning techniques. Discerning the presence of direct links between neuron from data is still a not completely solved problem. To enlarge the number of tools for detecting the underlying network structure, we propose here the use of copulas, pursuing on a research direction we started in [1]. Here, we adapt their use to distinguish different types of connections on a very simple network. Our proposal consists in choosing suitable random intervals in pairs of spike trains determining the shapes of their copulas. We show that this approach allows to detect different types of dependencies. We illustrate the features of the proposed method on synthetic data from suitably connected networks of two or three formal neurons directly connected or influenced by the surrounding network. We show how a smart choice of pairs of random times together with the use of empirical copulas allows to discern between direct and un-direct interactions

Parameters estimation for spatio-temporal maximum entropy distributions: application to neural spike trains

We propose a numerical method to learn Maximum Entropy (MaxEnt) distributions with spatio-temporal constraints from experimental spike trains. This is an extension of two papers [10] and [4] who proposed the estimation of parameters where only spatial constraints were taken into account. The extension we propose allows to properly handle memory effects in spike statistics, for large sized neural networks.Comment: 34 pages, 33 figure

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

The Local Field Potential Reflects Surplus Spike Synchrony

The oscillatory nature of the cortical local field potential (LFP) is commonly interpreted as a reflection of synchronized network activity, but its relationship to observed transient coincident firing of neurons on the millisecond time-scale remains unclear. Here we present experimental evidence to reconcile the notions of synchrony at the level of neuronal spiking and at the mesoscopic scale. We demonstrate that only in time intervals of excess spike synchrony, coincident spikes are better entrained to the LFP than predicted by the locking of the individual spikes. This effect is enhanced in periods of large LFP amplitudes. A quantitative model explains the LFP dynamics by the orchestrated spiking activity in neuronal groups that contribute the observed surplus synchrony. From the correlation analysis, we infer that neurons participate in different constellations but contribute only a fraction of their spikes to temporally precise spike configurations, suggesting a dual coding scheme of rate and synchrony. This finding provides direct evidence for the hypothesized relation that precise spike synchrony constitutes a major temporally and spatially organized component of the LFP. Revealing that transient spike synchronization correlates not only with behavior, but with a mesoscopic brain signal corroborates its relevance in cortical processing.Comment: 45 pages, 8 figures, 3 supplemental figure