Seminar

Abstract: In this paper we develop a theory of weakly monotone functions on metric measure spaces. We develop some analytic properties of such functions and prove an approximation theorem for a general $N^{1,p}(X)$ function for $p>1$. We exhibit a class of functionals whose minimizers are weakly monotone which includes the $p-$energy functional and as a corollary we show that minimizers of this energy satisfy a weak maximum and weak minimum principle.

Abstract: Abstract: In this presentation, I will explore the influence of various parameters on the oscillation frequencies of neuronal networks, with a focus on a network model consisting of excitatory and inhibitory theta neurons. Central to the discussion will be the impact of adaptation currents in excitatory neurons on oscillation frequency, particularly through inducing clustered firing patterns. The talk will also introduce a discrete map to analyze and visualize the clustering behaviors and adaptation distribution within the network.

https://pitt.zoom.us/j/95537107311