Know thy neighbour: A normative theory of synaptic depression

Synapses exhibit an extraordinary degree of short-term malleability, with release probabilities and effective synaptic strengths changing markedly over multiple timescales. From the perspective of a fixed computational operation in a network, this seems like a most unacceptable degree of added variability. We suggest an alternative theory according to which short-term synaptic plasticity plays a normatively-justifiable role. This theory starts from the commonplace observation that the spiking of a neuron is an incomplete, digital, report of the analog quantity that contains all the critical information, namely its membrane potential. We suggest that a synapse solves the inverse problem of estimating the pre-synaptic membrane potential from the spikes it receives, acting as a recursive filter. We show that the dynamics of short-term synaptic depression closely resemble those required for optimal filtering, and that they indeed support high quality estimation. Under this account, the local postsynaptic potential and the level of synaptic resources track the (scaled) mean and variance of the estimated presynaptic membrane potential. We make experimentally testable predictions for how the statistics of subthreshold membrane potential fluctuations and the form of spiking non-linearity should be related to the properties of short-term plasticity in any particular cell type.

On the existence of Zeno behavior in hybrid systems with non-isolated zeno equilibria

This paper presents proof-certificate based sufficient conditions for the existence of Zeno behavior in hybrid systems near non-isolated Zeno equilibria. To establish these conditions, we first prove sufficient conditions for Zeno behavior in a special class of hybrid systems termed first quadrant interval hybrid systems. The proof-certificate sufficient conditions are then obtained through a collection of functions that effectively "reduce" a general hybrid system to a first quadrant interval hybrid system. This paper concludes with an application of these ideas to Lagrangian hybrid systems, resulting in easily verifiable sufficient conditions for Zeno behavior. © 2008 IEEE.

Lyapunov-like conditions for the existence of zeno behavior in hybrid and lagrangian hybrid systems

Lyapunov-like conditions that utilize generalizations of energy and barrier functions certifying Zeno behavior near Zeno equilibria are presented. To better illustrate these conditions, we will study them in the context of Lagrangian hybrid systems. Through the observation that Lagrangian hybrid systems with isolated Zeno equilibria must have a onedimensional configuration space, we utilize our Lyapunov-like conditions to obtain easily verifiable necessary and sufficient conditions for the existence of Zeno behavior in systems of this form. © 2007 IEEE.

Theory of defects in amorphous semiconductors

We review the electronic structure of defects in aSi:H, aGaAs and aSi3N4, emphasising in aSi:H the doping mechanism, the evidence that its dangling bond defect has a small electron-lattice coupling and a positive correlation energy, and possible atomic mechanisms for the Staebler-Wronski effect. © 1985.