Inhibitory Self-connections Research Articles

Importance of self-connections for brain connectivity and spectral connectomics

Spectral analysis and neural field theory are used to investigate the role of local connections in brain connectivity matrices (CMs) that quantify connectivity between pairs of discretized brain regions. This work investigates how the common procedure of omitting such self-connections (i.e., the diagonal elements of CMs) in published studies of brain connectivity affects the properties of functional CMs (fCMs) and the mutually consistent effective CMs (eCMs) that correspond to them. It is shown that retention of self-connections in the fCM calculated from two-point activity covariances is essential for the fCM to be a true covariance matrix, to enable correct inference of the direct total eCMs from the fCM, and to ensure their compatibility with it; the deCM and teCM represent the strengths of direct connections and all connections between points, respectively. When self-connections are retained, inferred eCMs are found to have net inhibitory self-connections that represent the local inhibition needed to balance excitation via white matter fibers at longer ranges. This inference of spatially unresolved connectivity exemplifies the power of spectral connectivity methods, which also enable transformation of CMs to compact diagonal forms that allow accurate approximation of the fCM and total eCM in terms of just a few modes, rather than the full N^2 CM entries for connections between N brain regions. It is found that omission of fCM self-connections affects both local and long-range connections in eCMs, so they cannot be omitted even when studying the large-scale. Moreover, retention of local connections enables inference of subgrid short-range inhibitory connectivity. The results are verified and illustrated using the NKI-Rockland dataset from the University of Southern California Multimodal Connectivity Database. Deletion of self-connections is common in the field; this does not affect case-control studies but the present results imply that such fCMs must have self-connections restored before eCMs can be inferred from them.

Altered intrinsic and extrinsic connectivity in schizophrenia.

Schizophrenia is a disorder characterized by functional dysconnectivity among distributed brain regions. However, it is unclear how causal influences among large-scale brain networks are disrupted in schizophrenia. In this study, we used dynamic causal modeling (DCM) to assess the hypothesis that there is aberrant directed (effective) connectivity within and between three key large-scale brain networks (the dorsal attention network, the salience network and the default mode network) in schizophrenia during a working memory task. Functional MRI data during an n-back task from 40 patients with schizophrenia and 62 healthy controls were analyzed. Using hierarchical modeling of between-subject effects in DCM with Parametric Empirical Bayes, we found that intrinsic (within-region) and extrinsic (between-region) effective connectivity involving prefrontal regions were abnormal in schizophrenia. Specifically, in patients (i) inhibitory self-connections in prefrontal regions of the dorsal attention network were decreased across task conditions; (ii) extrinsic connectivity between regions of the default mode network was increased; specifically, from posterior cingulate cortex to the medial prefrontal cortex; (iii) between-network extrinsic connections involving the prefrontal cortex were altered; (iv) connections within networks and between networks were correlated with the severity of clinical symptoms and impaired cognition beyond working memory. In short, this study revealed the predominance of reduced synaptic efficacy of prefrontal efferents and afferents in the pathophysiology of schizophrenia.

Applications of the exponential ordering in the study of almost-periodic delayed Hopfield neural networks

This paper studies almost-periodic neural networks of Hopfield type described by delayed differential equations. The authors introduce an exponential ordering to analyze the long term behavior of the solutions. They prove some theorems of global convergence and deduce the stabilization role of the fast inhibitory self-connections. The proof, which in the case of the neural networks considered in this paper requires uniform stability, uses arguments of comparison of differential equations and methods of the non-autonomous monotone theory of dynamical systems. When the connections between different neurons are excitatory, improved conditions of convergence are obtained and the stabilization role of strongly positive inputs is also shown. The applicability of the results is illustrated with several numerical experiments based on two different families of neural networks.

The role of inhibitory neuron in a delayed neural network

The role of inhibitory self-connection in a second order recurrent neural network with delays has been investigated. A sufficient condition is proposed to guarantee the global asymptotical stability of the equilibrium point for the delayed neural network. The results indicate that an unstable neural network without inhibitory interconnections can be asymptotically stabilized to a unique equilibrium point via embedding inhibitory self-connections with proper strengths, and the role of inhibitory self-connections will be restricted by the magnitude of transmission delays. Two simulation examples are used to show the effectiveness of the obtained result.

Stabilizing Hopfield neural networks via inhibitory self-connections

The theory of monotone dynamical systems is employed to establish some sufficient conditions for the global attractivity of the Hopfield neural networks with finite distributed delays. The results show that self-inhibitory connections can be used to stabilize a delayed network provided the diagonal delays corresponding to the inhibitory self-connections are small enough.

Stabilization role of inhibitory self-connections in a delayed neural network

In a delayed Hopfield neural network that is strongly connected with non-inhibitory interconnections, fast and inhibitory self-connections lead to global convergence to a unique equilibrium of the network. By applying monotone dynamical systems theory and an embedding technique, we prove that this conclusion remains true without the requirement of strong connectivity or non-inhibitory interconnections.