Controlling General Polynomial Networks

Controlling General Polynomial Networks

We consider networks of massive particles connected by non-linear springs. Some particles interact with heat baths at different temperatures, which are modeled as stochastic driving forces. The structure of the network is arbitrary, but the motion of each particle is 1D. For polynomial interactions, we give sufficient conditions for Hörmander’s “bracket condition” to hold, which implies the uni...

A General Polynomial Sieve

An important component of the index calculus methods for finding discrete logarithms is the acquisition of smooth polynomial relations. Gordon and McCurley (1992) developed a sieve to aid in finding smooth Coppersmith polynomials for use in the index calculus method. We discuss their approach and some of the difficulties they found with their sieve. We present a new sieving method that can be a...

General Polynomial Time Decomposition Algorithms

We present a general decomposition algorithm that is uniformly applicable to every (suitably normalized) instance of Convex Quadratic Optimization and efficiently approaches an optimal solution. The number of iterations required to be within ε of optimality grows linearly with 1/ε and quadratically with the number m of variables. The working set selection can be performed in polynomial time. If...

Controlling Across Complex Networks

Ridge polynomial networks

This paper presents a polynomial connectionist network called ridge polynomial network (RPN) that can uniformly approximate any continuous function on a compact set in multidimensional input space R (d), with arbitrary degree of accuracy. This network provides a more efficient and regular architecture compared to ordinary higher-order feedforward networks while maintaining their fast learning p...