We propose a randomized polynomial time algorithm for computing nontrivial zeros of quadratic forms in 4 or more variables over Fq(t), where Fq is a finite field of odd characteristic. The algorithm is based on a suitable splitting of the form into two forms and finding a common value they both represent. We make use of an effective formula on the number of fixed degree irreducible polynomials ...

In this paper we consider Lur'e systems where a linear dynamical system is feedback interconnected to a multilayer perceptron nonlinearity, corresponding to recurrent neural networks with two hidden layers. For this class of nonlinear systems, we present suu-cient conditions for global asymptotic stability based on quadratic and Lur'e-Postnikov Lyapunov functions. Suucient conditions for dissip...

An algorithm for refining an essentially unrestricted mesh of points into a bivariate C 1 surface is given. The algorithm generalizes the construction of quadratic splines from a mesh of control points. It gives an explicit parametrization of the surface with quadratic and cubic pieces. When the mesh is regular then a quadratic spline surface is generated. Irregular input meshes with non quadri...

We give in this paper a partial classification of the consistent quadratic gauge actions that can be written in terms of s-form fields. This provides a starting point to study the uniqueness of the Yang-Mills action as a deformation of Maxwell-like theories. We also show that it is impossible to write kinetic 1-form terms that can be consistently added to other 1-form actions such as tetrad gra...

We extend the theorem of Balslev and Combes on the absence of singular continuous spectrum to a class of interactions including r~ (3/2 ̂ α < 2) local potentials. In addition, we note that the theory of sectorial operators allows a simplification of their proof and allows one to push the cuts through angles larger than the π/2 restriction employed by Balslev-Combes.

We consider a proximal operator given by a quadratic function subject to bound constraints and give an optimization algorithm using the alternating direction method of multipliers (ADMM). The algorithm is particularly efficient to solve a collection of proximal operators that share the same quadratic form, or if the quadratic program is the relaxation of a binary quadratic problem.