A smoothed representation (based on natural exponential and logarithmic functions) for the canonical piecewise-linear model, is presented. The result is a completely differentiable formulation that exhibits interesting properties, like preserving the parameters of the original piecewise-linear model in such a way that they can be directly inherited to the smooth model in order to determine thei...

Abstract Graphical (Linear) Algebra is a family of diagrammatic languages allowing to reason about different kinds subsets vector spaces compositionally. It has been used model various application domains, from signal-flow graphs Petri nets and electrical circuits. In this paper, we introduce the its most expressive member date: Piecewise-Linear Algebra, new language specify piecewise-linear sp...

‎‎In this article‎, ‎a new method is introduced to give approximate solution to Van der Pol equation‎. ‎The proposed method is based on the combination of two different methods‎, ‎the spectral Adomian decomposition method (SADM) and piecewise method‎, ‎called the piecewise Adomian decomposition method (PSADM)‎. ‎The numerical results obtained from the proposed method show that this method is an...

A k D tree representation of probability distribu tions is generalized to support generation of samples from conditional distributions An interpretation of the approach as a piecewise linear warping function is provided which permits a priori strati ed sample generation The representation is related to higher order spline estimators and representations via pro jection An application in glyph ba...

Fuzzy Hermite interpolation of 5th degree generalizes Lagrange interpolation by fitting a polynomial to a function f that not only interpolates f at each knot but also interpolates two number of consecutive Generalized Hukuhara derivatives of f at each knot. The provided solution for the 5th degree fuzzy Hermite interpolation problem in this paper is based on cardinal basis functions linear com...

Topology-based methods have been successfully used for the analysis and visualization of piecewise-linear functions defined on triangle meshes. This paper describes a mechanism for extending these methods to piecewise-quadratic functions defined on triangulations of surfaces. Each triangular patch is tessellated into monotone regions, so that existing algorithms for computing topological repres...