An optimally evolved connective ratio of neural networks that maximizes the occurrence of synchronized bursting behavior

<p>Abstract</p> <p>Background</p> <p>Synchronized bursting activity (SBA) is a remarkable dynamical behavior in both <it>ex vivo </it>and <it>in vivo </it>neural networks. Investigations of the underlying structural characteristics associated with SBA are crucial to understanding the system-level regulatory mechanism of neural network behaviors.</p> <p>Results</p> <p>In this study, artificial pulsed neural networks were established using spike response models to capture fundamental dynamics of large scale <it>ex vivo </it>cortical networks. Network simulations with synaptic parameter perturbations showed the following two findings. (i) In a network with an excitatory ratio (ER) of 80-90%, its connective ratio (CR) was within a range of 10-30% when the occurrence of SBA reached the highest expectation. This result was consistent with the experimental observation in <it>ex vivo </it>neuronal networks, which were reported to possess a matured inhibitory synaptic ratio of 10-20% and a CR of 10-30%. (ii) No SBA occurred when a network does not contain any all-positive-interaction feedback loop (APFL) motif. In a neural network containing APFLs, the number of APFLs presented an optimal range corresponding to the maximal occurrence of SBA, which was very similar to the optimal CR.</p> <p>Conclusions</p> <p>In a neural network, the evolutionarily selected CR (10-30%) optimizes the occurrence of SBA, and APFL serves a pivotal network motif required to maximize the occurrence of SBA.</p

Dirac series of E7(−5)E_{7(-5)}

Using the sharpened Helgason-Johnson bound, this paper classifies all the irreducible unitary representations with non-zero Dirac cohomology of $E_{7(-5)}$. As an application, we find that the cancellation between the even part and the odd part of the Dirac cohomology continues to happen for certain unitary representations of $E_{7(-5)}$. Assuming the infinitesimal character being integral, we further improve the Helgason-Johnson bound for $E_{7(-5)}$. This should help people to understand (part of) the unitary dual of this group.Comment: 25 pages. arXiv admin note: text overlap with arXiv:2204.0790