Astrocytic gliotransmission as a pathway for stable stimulation of post-synaptic spiking: Implications for working memory

The brain consists not only of neurons but also of non-neuronal cells, including astrocytes. Recent discoveries in neuroscience suggest that astrocytes directly regulate neuronal activity by releasing gliotransmitters such as glutamate. In this paper, we consider a biologically plausible mathematical model of a tripartite neuron-astrocyte network. We study the stability of the nonlinear astrocyte dynamics, as well as its role in regulating the firing rate of the post-synaptic neuron. We show that astrocytes enable storing neuronal information temporarily. Motivated by recent findings on the role of astrocytes in explaining mechanisms of working memory, we numerically verify the utility of our analysis in showing the possibility of two competing theories of persistent and sparse neuronal activity of working memory.Comment: IFAC World Congress (2023

Stochastic Stability of Discrete-time Phase-coupled Oscillators over Uncertain and Random Networks

This paper studies stochastic stability of a class of discrete-time phase-coupled oscillators. We introduce the two new notions of stochastic and ultimate stochastic phase-cohesiveness using the concepts of Harris and positive Harris recurrent Markov chains. Stochastic phase-cohesiveness of oscillators in two types of networks are studied. First, oscillators in a network with an underlying connected topology subject to both multiplicative and additive stochastic uncertainties are considered. Second, we study a special case of the former problem by assuming that the multiplicative uncertainties are governed by the Bernoulli process representing the well known Erd{\H o}s R\'enyi network

A combined nodal and uniform pricing mechanism for congestion management in distribution power networks

We present a price-based approach for congestion management in distribution power systems with renewable generations with the final goal of maximizing a social welfare function which includes net revenues of network users as well as the cost of real power losses. Particularly, we design a combined nodal and uniform pricing mechanism for maximization of the social welfare function while maintaining voltage magnitudes in a desired bound and respecting the grid's actual capacity. Storage systems are considered in order to increase/add elasticity to generations and loads. Simulation results are provided for a modified IEEE-37 bus. A scenario is numerically simulated where the excess of generation in the absence of storage and price signals leads to deviations of voltages from a desired bound. Thereafter, it is shown that the application of the price signals is effective to maintain the voltages within the desired bound while the designed social welfare function is maximized

Ternary and hybrid controllers for the rendezvous of unicycles

This paper presents the rendezvous (consensus) of the orientations and average positions of a group of unicycles. We assume that the decentralized controllers designed for consensus of the average positions take only values in the set {-1; 0; +1}. In addition, we introduce a hybrid controller to reach the consensus of the orientations. Finite-time practical consensus of the average positions is proven despite the simple ternary control laws together with asymptotic consensus of the orientations