We analyze a time independent integral equation defined on a spatially extended domain which arises in the modeling of neuronal networks. In our survey, the coupling function is oscillatory and the firing rate is a smooth “heaviside-like” function. We will derive an associated fourth order ODE and establish that any bounded solution of the ODE is also a solution of the integral equation. We wil...

We consider Heterotic string theories in the DLCQ. We derive that the matrix model of the Spin(32)/Z2 Heterotic theory is the theory living on N D-strings in type I wound on a circle with no Spin(32)/Z2 Wilson line on the circle. This is an O(N) gauge theory. We rederive the matrix model for the E8 × E8 Heterotic string theory, explicitly taking care of the Wilson line around the lightlike circ...

This paper considers large discrete-time linear systems obtained from discretized partial differential equations, and controlled by a quantized law, i.e., a piecewise constant time function taking a finite set of values. We show how to generate the control by, first, applying model reduction to the original system, then using a “state-space bisection” method for synthesizing a control at the re...

Abstract. We construct a Wilson action for the Wess-Zumino model by applying the exact renormalization group perturbatively. Using neither superfields nor auxiliary fields, we construct a supersymmetric action only with complex scalar and Majorana spinor fields. We adopt the BRST (antifield) formalism to show the consistency of the construction to all orders in loop expansions. The resulting ac...