### Toni Guillamon

Department of Mathematics, Universitat Politècnica de Catalunya

Department of Mathematical Sciences, NJIT

Some results on estimation of synaptic conductances

In this talk we will try to give an overview of different approaches to estimate synaptic conductances from membrane potential traces of a neuron and discern between excitatory and inhibitory inputs. In neuroscience, this information can provide insights on the excitation/inhibition balance in parts of the brain. From a mathematical point of view, the purpose of this problem is to quantify the input that a multidimensional externally forced system is receiving from the only information of a single variable. It results, then, in an inverse problem and, as other estimation problems, it brings up interesting challenges for many branches of mathematics: statistics, stochastic processes, dynamical systems, Bayesian inference, optimization,... We will discuss on the influence of active ionic channels, and the necessity of both inferring conductances from single trials and providing model-free methods. We will show our proposals to overcome nonlinear effects in the subthreshold regime, as well as a proof of concept for the spiking regime. If time allows, we will also go through heuristic estimation methods. It is fair saying that I learnt about this problem at NYU some years ago, so it is a pleasure to give my feedback to this audience.