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Granger causality is among the widely used data-driven approaches for causal analysis of time series data with applications in various areas including economics, molecular biology, and neuroscience. Two of the main challenges of this methodology are: 1) over-fitting as a result of limited data duration, and 2) correlated process noise as a confounding factor, both leading to errors in identifying the causal influences. Sparse estimation via the LASSO has successfully addressed these challenges for parameter estimation. However, the classical statistical tests for Granger causality resort to asymptotic analysis of ordinary least squares, which require long data duration to be useful and are not immune to confounding effects. In this work, we address this disconnect by introducing a LASSO-based statistic and studying its non-asymptotic properties under the assumption that the true models admit sparse autoregressive representations. We establish fundamental limits for reliable identification of Granger causal influences using the proposed LASSO-based statistic. We further characterize the false positive error probability and test power of a simple thresholding rule for identifying Granger causal effects and provide two methods to set the threshold in a data-driven fashion. We present simulation studies and application to real data to compare the performance of our proposed method to ordinary least squares and existing LASSO-based methods in detecting Granger causal influences, which corroborate our theoretical results. 

Measures of functional connectivity have played a central role in advancing our understanding of how information is transmitted and processed within the brain. Traditionally, these studies have focused on identifying redundant functional connectivity, which involves determining when activity is similar across different sites or neurons. However, recent research has highlighted the importance of also identifying synergistic connectivity—that is, connectivity that gives rise to information not contained in either site or neuron alone. Here, we measured redundant and synergistic functional connectivity between neurons in the mouse primary auditory cortex during a sound discrimination task. Specifically, we measured directed functional connectivity between neurons simultaneously recorded with calcium imaging. We used Granger Causality as a functional connectivity measure. We then used Partial Information Decomposition to quantify the amount of redundant and synergistic information about the presented sound that is carried by functionally connected or functionally unconnected pairs of neurons. We found that functionally connected pairs present proportionally more redundant information and proportionally less synergistic information about sound than unconnected pairs, suggesting that their functional connectivity is primarily redundant. Further, synergy and redundancy coexisted both when mice made correct or incorrect perceptual discriminations. However, redundancy was much higher (both in absolute terms and in proportion to the total information available in neuron pairs) in correct behavioural choices compared to incorrect ones, whereas synergy was higher in absolute terms but lower in relative terms in correct than in incorrect behavioural choices. Moreover, the proportion of redundancy reliably predicted perceptual discriminations, with the proportion of synergy adding no extra predictive power. These results suggest a crucial contribution of redundancy to correct perceptual discriminations, possibly due to the advantage it offers for information propagation, and also suggest a role of synergy in enhancing information level during correct discriminations.

 

Extracting directional connectivity in a neuronal ensemble from spiking observations is a key challenge in understanding the circuit mechanisms of brain function. Existing methods proceed in two stages, by first estimating the latent processes that govern spiking, followed by characterizing connectivity using said estimates. As such, the extracted networks in the second stage are highly sensitive to the accuracy of the estimates in the first stage. In this work, we introduce a framework to directly extract Granger causal links from spiking observations, without requiring intermediate time-domain estimation, by explicitly modeling the endogenous and exogenous latent processes that underlie spiking activity. Our proposed method integrates several techniques such as point processes, state-space modeling and Pólya-Gamma augmentation. We demonstrate the utility of our proposed approach using simulated data and application to real data from the rat brain during sleep. 

Plasticity and homeostatic mechanisms allow neural networks to maintain proper function while responding to physiological challenges. Despite previous work investigating morphological and synaptic effects of brain-derived neurotrophic factor (BDNF), the most prevalent growth factor in the central nervous system, how exposure to BDNF manifests at the network level remains unknown. Here we report that BDNF treatment affects rodent hippocampal network dynamics during development and recovery from glutamate-induced excitotoxicity in culture. Importantly, these effects are not obvious when traditional activity metrics are used, so we delve more deeply into network organization, functional analyses, and in silico simulations. We demonstrate that BDNF partially restores homeostasis by promoting recovery of weak and medium connections after injury. Imaging and computational analyses suggest these effects are caused by changes to inhibitory neurons and connections. From our in silico simulations, we find that BDNF remodels the network by indirectly strengthening weak excitatory synapses after injury. Ultimately, our findings may explain the difficulties encountered in preclinical and clinical trials with BDNF and also offer information for future trials to consider.

 

Abstract Cortical ischaemic strokes result in cognitive deficits depending on the area of the affected brain. However, we have demonstrated that difficulties with attention and processing speed can occur even with small subcortical infarcts. Symptoms appear independent of lesion location, suggesting they arise from generalized disruption of cognitive networks. Longitudinal studies evaluating directional measures of functional connectivity in this population are lacking. We evaluated six patients with minor stroke exhibiting cognitive impairment 6–8 weeks post-infarct and four age-similar controls. Resting-state magnetoencephalography data were collected. Clinical and imaging evaluations of both groups were repeated 6- and 12 months later. Network Localized Granger Causality was used to determine differences in directional connectivity between groups and across visits, which were correlated with clinical performance. Directional connectivity patterns remained stable across visits for controls. After the stroke, inter-hemispheric connectivity between the frontoparietal cortex and the non-frontoparietal cortex significantly increased between visits 1 and 2, corresponding to uniform improvement in reaction times and cognitive scores. Initially, the majority of functional links originated from non-frontal areas contralateral to the lesion, connecting to ipsilesional brain regions. By visit 2, inter-hemispheric connections, directed from the ipsilesional to the contralesional cortex significantly increased. At visit 3, patients demonstrating continued favourable cognitive recovery showed less reliance on these inter-hemispheric connections. These changes were not observed in those without continued improvement. Our findings provide supporting evidence that the neural basis of early post-stroke cognitive dysfunction occurs at the network level, and continued recovery correlates with the evolution of inter-hemispheric connectivity. 

Neuronal activity correlations are key to understanding how populations of neurons collectively encode information. While two-photon calcium imaging has created a unique opportunity to record the activity of large populations of neurons, existing methods for inferring correlations from these data face several challenges. First, the observations of spiking activity produced by two-photon imaging are temporally blurred and noisy. Secondly, even if the spiking data were perfectly recovered via deconvolution, inferring network-level features from binary spiking data is a challenging task due to the non-linear relation of neuronal spiking to endogenous and exogenous inputs. In this work, we propose a methodology to explicitly model and directly estimate signal and noise correlations from two-photon fluorescence observations, without requiring intermediate spike deconvolution. We provide theoretical guarantees on the performance of the proposed estimator and demonstrate its utility through applications to simulated and experimentally recorded data from the mouse auditory cortex. 

Coordinated ensemble spiking activity is widely observable in neural recordings and central in the study of population codes, with hypothesized roles including robust stimulus representation, interareal communication of neural information, and learning and memory formation. Model-free measures of synchrony characterize the coherence of pairwise activity, but not higher-order interactions; this limitation is transcended by statistical models of ensemble spiking activity. However, existing model-based analyses often impose assumptions about the relevance of higher-order interactions and require multiple repeated trials in order to characterize dynamics in the correlational structure of ensemble activity. To address these shortcomings, we propose an adaptive greedy filtering algorithm based on a discretized mark point-process model of ensemble spiking and a corresponding precise statistical inference framework to identify significant coordinated higher-order spiking activity. In the course of developing the statistical inference procedures, we also show that confidence intervals can be constructed for greedily estimated parameters. We demonstrate the utility of our proposed methods on simulated neuronal assemblies. Applied to multi-electrode recordings of human cortical ensembles, our proposed methods provide new insights into the dynamics underlying localized population activity during transitions between brain states. 

Coordinated ensemble spiking activity is widely observable in neural recordings and central in the study of population codes, with hypothesized roles including robust stimulus representation, interareal communication of neural information, and learning and memory formation. Model-free measures of synchrony characterize the coherence of pairwise activity, but not higher-order interactions; this limitation is transcended by statistical models of ensemble spiking activity. However, existing model-based analyses often impose assumptions about the relevance of higher-order interactions and require multiple repeated trials in order to characterize dynamics in the correlational structure of ensemble activity. To address these shortcomings, we propose an adaptive greedy filtering algorithm based on a discretized mark point process model of ensemble spiking and a corresponding precise statistical inference framework to identify significant coordinated higher-order spiking activity. In the course of developing the statistical inference procedures, we also show that confidence intervals can be constructed for greedily estimated parameters. We demonstrate the utility of our proposed methods on simulated neuronal assemblies. Applied to multi-electrode recordings of human cortical ensembles, our proposed methods provide new insights into the dynamics underlying localized population activity during transitions between brain states.