Abstract. We develop a calculus for nonlocal operators that mimics Gauss’ theorem and the Green’s identities of the classical vector calculus. The operators we define do not involve the derivatives. We then apply the nonlocal calculus to define variational formulations of nonlocal “boundaryvalue” problems that mimic the Dirichlet and Neumann problems for second-order scalar elliptic partial dif...

This paper introduces a robust mathematical formalism for the definition of deliberative agents implemented using a case-based reasoning system. The concept behind deliberative agents is introduced and the case-based reasoning model is described using this analytical formalism. Variational calculus is used during the reasoning process to identify the problem solution. The agent may use variatio...

A self-consistent scheme based on the calculus of infinitesimal transformations that describes model based interpolation (MBI hereafter) of high dimensional data, constrained to lie on a nonlinear manifold, is expressed as a dynamical system. The variational formulation derived for a single cluster is extended to the case of finite mixture models (FMM hereafter). The suggested formulation is sh...

Variational analysis has been recognized as a rapidly growing and fruitful area in mathematics concerning mainly the study of optimization and equilibrium problems, while also applying perturbation ideas and variational principles to a broad class of problems and situations that may be not of a variational nature. It can be viewed as a modern outgrowth of the classical calculus of variations, o...

We begin by analyzing, using basic physics considerations, under what conditions it becomes energetically favorable to use aggressive regenerative braking reach a lower speed over “coasting” where one relies solely on air drag slow down. then proceed reformulate the question as an optimization problem find velocity profile that maximizes battery charge. Making simplifying assumption battery-cha...

The calculus of local variational differential operators introduced by B. L. Voronov, I. V. Tyutin, and Sh. S. Shakhverdiev is studied in the context of jet super space geometry. In a coordinate-free way, we relate these operators to variational multivectors, for which we introduce and compute the variational Poisson and Schouten brackets by means of a unifying algebraic scheme. We give a geome...

Variation is ubiquitous in software. Many applications can benefit from making this variation explicit, then manipulating and computing with it directly—a technique we call “variational programming”. This idea has been independently discovered in several application domains, such as efficiently analyzing and verifying software product lines, combining bounded and symbolic model-checking, and co...