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- Goodness-of-fit tests for neural population models: the multivariate time-rescaling theorem (2010)
- Poster Presentation from Nineteenth Annual Computational Neuroscience Meeting: CNS*2010 San Antonio, TX, USA. 24-30 July 2010 Statistical models of neural activity are at the core of the field of modern computational neuroscience. The activity of single neurons has been modeled to successfully explain dependencies of neural dynamics to its own spiking history, to external stimuli or other covariates [1]. Recently, there has been a growing interest in modeling spiking activity of a population of simultaneously recorded neurons to study the effects of correlations and functional connectivity on neural information processing (existing models include generalized linear models [2,3] or maximum-entropy approaches [4]). For point-process-based models of single neurons, the time-rescaling theorem has proven to be a useful toolbox to assess goodness-of-fit. In its univariate form, the time-rescaling theorem states that if the conditional intensity function of a point process is known, then its inter-spike intervals can be transformed or “rescaled” so that they are independent and exponentially distributed [5]. However, the theorem in its original form lacks sensitivity to detect even strong dependencies between neurons. Here, we present how the theorem can be extended to be applied to neural population models and we provide a step-by-step procedure to perform the statistical tests. We then apply both the univariate and multivariate tests to simplified toy models, but also to more complicated many-neuron models and to neuronal populations recorded in V1 of awake monkey during natural scenes stimulation. We demonstrate that important features of the population activity can only be detected using the multivariate extension of the test. ...
- SORN: a self-organizing recurrent neural network (2009)
- Understanding the dynamics of recurrent neural networks is crucial for explaining how the brain processes information. In the neocortex, a range of different plasticity mechanisms are shaping recurrent networks into effective information processing circuits that learn appropriate representations for time-varying sensory stimuli. However, it has been difficult to mimic these abilities in artificial neural network models. Here we introduce SORN, a self-organizing recurrent network. It combines three distinct forms of local plasticity to learn spatio-temporal patterns in its input while maintaining its dynamics in a healthy regime suitable for learning. The SORN learns to encode information in the form of trajectories through its high-dimensional state space reminiscent of recent biological findings on cortical coding. All three forms of plasticity are shown to be essential for the network's success. Keywords: synaptic plasticity, intrinsic plasticity, recurrent neural networks, reservoir computing, time series prediction
- Effect of the topology and delayed interactions in neuronal networks synchronization (2011)
- As important as the intrinsic properties of an individual nervous cell stands the network of neurons in which it is embedded and by virtue of which it acquires great part of its responsiveness and functionality. In this study we have explored how the topological properties and conduction delays of several classes of neural networks affect the capacity of their constituent cells to establish well-defined temporal relations among firing of their action potentials. This ability of a population of neurons to produce and maintain a millisecond-precise coordinated firing (either evoked by external stimuli or internally generated) is central to neural codes exploiting precise spike timing for the representation and communication of information. Our results, based on extensive simulations of conductance-based type of neurons in an oscillatory regime, indicate that only certain topologies of networks allow for a coordinated firing at a local and long-range scale simultaneously. Besides network architecture, axonal conduction delays are also observed to be another important factor in the generation of coherent spiking. We report that such communication latencies not only set the phase difference between the oscillatory activity of remote neural populations but determine whether the interconnected cells can set in any coherent firing at all. In this context, we have also investigated how the balance between the network synchronizing effects and the dispersive drift caused by inhomogeneities in natural firing frequencies across neurons is resolved. Finally, we show that the observed roles of conduction delays and frequency dispersion are not particular to canonical networks but experimentally measured anatomical networks such as the macaque cortical network can display the same type of behavior.
- Spike train auto-structure impacts post-synaptic firing and timing-based plasticity (2011)
- Cortical neurons are typically driven by several thousand synapses. The precise spatiotemporal pattern formed by these inputs can modulate the response of a post-synaptic cell. In this work, we explore how the temporal structure of pre-synaptic inhibitory and excitatory inputs impact the post-synaptic firing of a conductance-based integrate and fire neuron. Both the excitatory and inhibitory input was modeled by renewal gamma processes with varying shape factors for modeling regular and temporally random Poisson activity. We demonstrate that the temporal structure of mutually independent inputs affects the post-synaptic firing, while the strength of the effect depends on the firing rates of both the excitatory and inhibitory inputs. In a second step, we explore the effect of temporal structure of mutually independent inputs on a simple version of Hebbian learning, i.e., hard bound spike-timing-dependent plasticity. We explore both the equilibrium weight distribution and the speed of the transient weight dynamics for different mutually independent gamma processes. We find that both the equilibrium distribution of the synaptic weights and the speed of synaptic changes are modulated by the temporal structure of the input. Finally, we highlight that the sensitivity of both the post-synaptic firing as well as the spike-timing-dependent plasticity on the auto-structure of the input of a neuron could be used to modulate the learning rate of synaptic modification.
- Context Matters: The Illusive Simplicity of Macaque V1 Receptive Fields (2012)
- Even in V1, where neurons have well characterized classical receptive fields (CRFs), it has been difficult to deduce which features of natural scenes stimuli they actually respond to. Forward models based upon CRF stimuli have had limited success in predicting the response of V1 neurons to natural scenes. As natural scenes exhibit complex spatial and temporal correlations, this could be due to surround effects that modulate the sensitivity of the CRF. Here, instead of attempting a forward model, we quantify the importance of the natural scenes surround for awake macaque monkeys by modeling it non-parametrically. We also quantify the influence of two forms of trial to trial variability. The first is related to the neuron’s own spike history. The second is related to ongoing mean field population activity reflected by the local field potential (LFP). We find that the surround produces strong temporal modulations in the firing rate that can be both suppressive and facilitative. Further, the LFP is found to induce a precise timing in spikes, which tend to be temporally localized on sharp LFP transients in the gamma frequency range. Using the pseudo R2 as a measure of model fit, we find that during natural scene viewing the CRF dominates, accounting for 60% of the fit, but that taken collectively the surround, spike history and LFP are almost as important, accounting for 40%. However, overall only a small proportion of V1 spiking statistics could be explained (R2~5%), even when the full stimulus, spike history and LFP were taken into account. This suggests that under natural scene conditions, the dominant influence on V1 neurons is not the stimulus, nor the mean field dynamics of the LFP, but the complex, incoherent dynamics of the network in which neurons are embedded.
- Extraction of network topology from multi-electrode recordings: is there a small-world effect? (2011)
- The simultaneous recording of the activity of many neurons poses challenges for multivariate data analysis. Here, we propose a general scheme of reconstruction of the functional network from spike train recordings. Effective, causal interactions are estimated by fitting generalized linear models on the neural responses, incorporating effects of the neurons’ self-history, of input from other neurons in the recorded network and of modulation by an external stimulus. The coupling terms arising from synaptic input can be transformed by thresholding into a binary connectivity matrix which is directed. Each link between two neurons represents a causal influence from one neuron to the other, given the observation of all other neurons from the population. The resulting graph is analyzed with respect to small-world and scale-free properties using quantitative measures for directed networks. Such graph-theoretic analyses have been performed on many complex dynamic networks, including the connectivity structure between different brain areas. Only few studies have attempted to look at the structure of cortical neural networks on the level of individual neurons. Here, using multi-electrode recordings from the visual system of the awake monkey, we find that cortical networks lack scale-free behavior, but show a small, but significant small-world structure. Assuming a simple distance-dependent probabilistic wiring between neurons, we find that this connectivity structure can account for all of the networks’ observed small-world-ness. Moreover, for multi-electrode recordings the sampling of neurons is not uniform across the population. We show that the small-world-ness obtained by such a localized sub-sampling overestimates the strength of the true small-world structure of the network. This bias is likely to be present in all previous experiments based on multi-electrode recordings.
- Neural synchrony in cortical networks: history, concept and current status (2009)
- Following the discovery of context-dependent synchronization of oscillatory neuronal responses in the visual system, the role of neural synchrony in cortical networks has been expanded to provide a general mechanism for the coordination of distributed neural activity patterns. In the current paper, we present an update of the status of this hypothesis through summarizing recent results from our laboratory that suggest important new insights regarding the mechanisms, function and relevance of this phenomenon. In the first part, we present recent results derived from animal experiments and mathematical simulations that provide novel explanations and mechanisms for zero and nero-zero phase lag synchronization. In the second part, we shall discuss the role of neural synchrony for expectancy during perceptual organization and its role in conscious experience. This will be followed by evidence that indicates that in addition to supporting conscious cognition, neural synchrony is abnormal in major brain disorders, such as schizophrenia and autism spectrum disorders. We conclude this paper with suggestions for further research as well as with critical issues that need to be addressed in future studies.
- Transfer entropy - a model-free measure of effective connectivity for the neurosciences (2010)
- Understanding causal relationships, or effective connectivity, between parts of the brain is of utmost importance because a large part of the brain’s activity is thought to be internally generated and, hence, quantifying stimulus response relationships alone does not fully describe brain dynamics. Past efforts to determine effective connectivity mostly relied on model based approaches such as Granger causality or dynamic causal modeling. Transfer entropy (TE) is an alternative measure of effective connectivity based on information theory. TE does not require a model of the interaction and is inherently non-linear. We investigated the applicability of TE as a metric in a test for effective connectivity to electrophysiological data based on simulations and magnetoencephalography (MEG) recordings in a simple motor task. In particular, we demonstrate that TE improved the detectability of effective connectivity for non-linear interactions, and for sensor level MEG signals where linear methods are hampered by signal-cross-talk due to volume conduction.
- NeuroXidence: reliable and efficient analysis of an excess or deficiency of joint-spike events (2009)
- Poster presentation: We present a non-parametric and computationally-efficient method named NeuroXidence (see http://www.NeuroXidence.com ) that detects coordinated firing within a group of two or more neurons and tests whether the observed level of coordinated firing is significantly different from that expected by chance. NeuroXidence [1] considers the full auto-structure of the data, including the changes in the rate responses and the history dependencies in the spiking activity. We demonstrate that NeuroXidence can identify epochs with significant spike synchronisation even if these coincide with strong and fast rate modulations. We also show, that the method accounts for trial-by-trial variability in the rate responses and their latencies, and that it can be applied to short data windows lasting only tens of milliseconds. Based on simulated data we compare the performance of NeuroXidence with the UE-method [2,3] and the cross-correlation analysis. An application of NeuroXidence to 42 single-units (SU) recorded in area 17 of an anesthetized cat revealed significant coincident events of high complexities, involving firing of up to 8 SUs simultaneously (5 ms window). The results were highly consistent with those obtained by traditional pair-wise measures based on cross-correlation: Neuronal synchrony was strongest in stimulation conditions in which the orientation of the sinusoidal grating matched the preferred orientation of most of the SUs included in the analysis, and was the weakest when the neurons were stimulated least optimally. Interestingly, events of higher complexities showed stronger stimulus-specific modulation than pair-wise interactions. The results suggest strong evidence for stimulus specific synchronous firing and, therefore, support the temporal coding hypothesis in visual cortex. ...
- Using transfer entropy to measure the patterns of information flow though cortex : application to MEG recordings from a visual Simon task (2009)
- Poster presentation: Functional connectivity of the brain describes the network of correlated activities of different brain areas. However, correlation does not imply causality and most synchronization measures do not distinguish causal and non-causal interactions among remote brain areas, i.e. determine the effective connectivity [1]. Identification of causal interactions in brain networks is fundamental to understanding the processing of information. Attempts at unveiling signs of functional or effective connectivity from non-invasive Magneto-/Electroencephalographic (M/EEG) recordings at the sensor level are hampered by volume conduction leading to correlated sensor signals without the presence of effective connectivity. Here, we make use of the transfer entropy (TE) concept to establish effective connectivity. The formalism of TE has been proposed as a rigorous quantification of the information flow among systems in interaction and is a natural generalization of mutual information [2]. In contrast to Granger causality, TE is a non-linear measure and not influenced by volume conduction. ...
