An artificial neural network is presented based on the idea of connections between units that are only active for a specific range of input values and zero outside that range (and so are not evaluated outside the active range). The connection function is represented by a polynomial with compact support. The finite range of activation allows for great activation sparsity in the network and means...

We study di erentiability of topological conjugacies between expanding piecewise C1+ interval maps. If these conjugacies are not C1 , then they have zero derivative almost everywhere. We obtain the result that in this case the Hausdor dimension of the set of points for which the derivative of the conjugacy does not exist lies strictly between zero and one. Using multifractal analysis and thermo...

Let G be a finite group acting on vector spaces V and W and consider a smooth G-equivariant mapping f : V → W. This paper addresses the question of the zero set near a zero x of f with isotropy subgroup G. It is known from results of Bierstone and Field on G-transversality theory that the zero set in a neighborhood of x is a stratified set. The purpose of this paper is to partially determine th...

We analyze a class of piecewise linear parabolic maps on the torus, namely those obtained by considering a linear map with double eigenvalue one and taking modulo one in each component. We show that within this two parameter family of maps, the set of noninvertible maps is open and dense. For cases where the entries in the matrix are rational we show that the maximal invariant set has positive ...

We consider a direct search approach for solving nonsmooth minimization problems where the objective function is locally Lipschitz continuous and piecewise continuously differentiable on a finite family of polyhedra. A generating set search method is proposed, which is named structured because the structure of the set of nondifferentiability near the current iterate is exploited to define the s...

We analyze a class of piecewise linear parabolic maps on the torus, namely those obtained by considering a linear map with double eigenvalue one and taking modulo one in each component. We show that within this two parameter family of maps, the set of noninvertible maps is open and dense. For cases where the entries in the matrix are rational we show that the maximal invariant set has positive ...