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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. ...

- 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.

- 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.

- 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

- EEG processing with TESPAR for depth of anesthesia detection (2009)
- Poster presentation: Introduction Adequate anesthesia is crucial to the success of surgical interventions and subsequent recovery. Neuroscientists, surgeons, and engineers have sought to understand the impact of anesthetics on the information processing in the brain and to properly assess the level of anesthesia in an non-invasive manner. Studies have indicated a more reliable depth of anesthesia (DOA) detection if multiple parameters are employed. Indeed, commercial DOA monitors (BIS, Narcotrend, M-Entropy and A-line ARX) use more than one feature extraction method. Here, we propose TESPAR (Time Encoded Signal Processing And Recognition) a time domain signal processing technique novel to EEG DOA assessment that could enhance existing monitoring devices. ...

- A comparison of spike time prediction and receptive field mapping with point process generalized linear models, Wiener-Voltera kernels, and spike-triggered averaging methods (2009)
- Poster presentation: Characterizing neuronal encoding is essential for understanding information processing in the brain. Three methods are commonly used to characterize the relationship between neural spiking activity and the features of putative stimuli. These methods include: Wiener-Volterra kernel methods (WVK), the spike-triggered average (STA), and more recently, the point process generalized linear model (GLM). We compared the performance of these three approaches in estimating receptive field properties and orientation tuning of 251 V1 neurons recorded from 2 monkeys during a fixation period in response to a moving bar. The GLM consisted of two formulations of the conditional intensity function for a point process characterization of the spiking activity: one with a stimulus only component and one with the stimulus and spike history. We fit the GLMs by maximum likelihood using GLMfit in Matlab. Goodness-of-fit was assessed using cross-validation with Kolmogorov-Smirnov (KS) tests based on the time-rescaling theorem to evaluate the accuracy with which each model predicts the spiking activity of individual neurons and for each movement direction (4016 models in total, for 251 neurons and 16 different directions). The GLMs that considered spike history of up to 35 ms, accurately predicted neuronal spiking activity (95% confidence intervals for KS test) with a performance of 97.0% (3895/4016) for the training data, and 96.5% (3876/4016) for the test data. If spike history was not considered, performance dropped to 73,1% in the training and 71.3% in the testing data. In contrast, the WVF and the STA predicted spiking accurately for 24.2% and 44.5% of the test data examples respectively. The receptive field size estimates obtained from the GLM (with and without history), WVF and STA were comparable. Relative to the GLM orientation tuning was underestimated on average by a factor of 0.45 by the WVF and the STA. The main reason for using the STA and WVF approaches is their apparent simplicity. However, our analyses suggest that more accurate spike prediction as well as more credible estimates of receptive field size and orientation tuning can be computed easily using GLMs implemented in Matlab with standard functions such as GLMfit.

- Performance- and stimulus-dependent oscillations in monkey prefrontal cortex during short-term memory (2009)
- Short-term memory requires the coordination of sub-processes like encoding, retention, retrieval and comparison of stored material to subsequent input. Neuronal oscillations have an inherent time structure, can effectively coordinate synaptic integration of large neuron populations and could therefore organize and integrate distributed sub-processes in time and space. We observed field potential oscillations (14–95 Hz) in ventral prefrontal cortex of monkeys performing a visual memory task. Stimulus-selective and performance-dependent oscillations occurred simultaneously at 65–95 Hz and 14–50 Hz, the latter being phase-locked throughout memory maintenance. We propose that prefrontal oscillatory activity may be instrumental for the dynamical integration of local and global neuronal processes underlying short-term memory.

- A mechanism for achieving zero-lag long-range synchronization of neural activity (2009)
- Poster presentation: How can two distant neural assemblies synchronize their firings at zero-lag even in the presence of non-negligible delays in the transfer of information between them? Neural synchronization stands today as one of the most promising mechanisms to counterbalance the huge anatomical and functional specialization of the different brain areas. However, and albeit more evidence is being accumulated in favor of its functional role as a binding mechanism of distributed neural responses, the physical and anatomical substrate for such a dynamic and precise synchrony, especially zero-lag even in the presence of non-negligible delays, remains unclear. Here we propose a simple network motif that naturally accounts for zero-lag synchronization of spiking assemblies of neurons for a wide range of temporal delays. We demonstrate that when two distant neural assemblies do not interact directly but relaying their dynamics via a third mediating single neuron or population and eventually achieve zero-lag coherent firing. Extensive numerical simulations of populations of Hodgkin-Huxley neurons interacting in such a network are analyzed. The results show that even with axonal delays as large as 15 ms the distant neural populations can synchronize their firings at zero-lag in a millisecond precision after the exchange of a few spikes. The role of noise and a distribution of axonal delays in the synchronized dynamics of the neural populations are also studied confirming the robustness of this sync mechanism. The proposed network module is densely embedded within the complex functional architecture of the brain and especially within the reciprocal thalamocortical interactions where the role of indirect pathways mimicking direct cortico-cortical fibers has been already suggested to facilitate trans-areal cortical communication. In summary the robust neural synchronization mechanism presented here arises as a consequence of the relay and redistribution of the dynamics performed by a mediating neuronal population. In opposition to previous works, neither inhibitory, gap junctions, nor complex networks need to be invoked to provide a stable mechanism of zero-phase correlated activity of neural populations in the presence of large conduction delays.

- Auto-structure of spike trains matters for testing on synchronous activity (2009)
- 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.

- 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. ...