We present a general framework for carrying out perturbation analysis in Stochastic Hybrid Systems (SHS) of arbitrary structure. In particular, Infinitesimal Perturbation Analysis (IPA) is used to provide unbiased gradient estimates of performance metrics with respect to various controllable parameters. These can be combined with standard gradient-based algorithms for optimization purposes and ...

The Delaunay triangulation (DT) is one of the most common and useful triangulations of point sets P in the plane. DT is not unique when P is degenerate, specifically when it contains quadruples of co-circular points. One way to achieve uniqueness is by applying a small (or infinitesimal) perturbation to P . We consider a specific perturbation of such degenerate sets, in which the coordinates of...

A kinematically correct choice of velocity focuses subsurface offset image gathers at zero offset. Infinitesimal warping from the current image towards its focus can be approximated by a horizontal contraction. The image residual can be then taken as the difference between the warped and the original image to account for the velocity error. Least squares fitting of the effect of a velocity pert...

We present a symbolic perturbation scheme for arbitrary polynomial geometric predicates which combines the benefits of Emiris and Canny’s simple randomized linear perturbation scheme with Yap’s multiple infinitesimal scheme for general predicates. Like the randomized scheme, our method accepts black box polynomial functions as input. For nonmaliciously chosen predicates, our method is as fast a...

In a theory of quantum gravity, states can be represented as wavefunctionals that assign an amplitude to given configuration matter fields and the metric on spatial slice. These must obey set constraints consequence diffeomorphism invariance theory, most important which is known Wheeler-DeWitt equation. We study these perturbatively by expanding them leading nontrivial order in Newton's constan...

We consider a classic scheduling problem for optimally allocating a resource to multiple competing users and place it in the framework of Stochastic Flow Models (SFMs). We derive Infinitesimal Perturbation Analysis (IPA) gradient estimators for the average holding cost with respect to resource allocation parameters. These estimators are easily obtained from a sample path of the system without a...

Methods of topological analysis are inherently related to singular perturbations. For topology variation, a trial geometric object put in a test domain is examined by reducing the object size from a finite to an infinitesimal one. Based on the singular perturbation of the forward Helmholtz problem, a topology optimization approach, which is a direct one, is described for the inverse problem of ...

In this chapter, we present a sensor-based trajectory deformation process for nonholonomic robots. The method is based on infinitesimal perturbations of the input functions of the current trajectory. Input perturbation is computed in such a way that a an objective function decreases and that the trajectory initial and final configurations are kept unchanged. The method is then extended to docki...

Deformation theory of associative algebras and in particular of Poisson algebras is reviewed. The role of an “almost contraction” leading to a canonical solution of the corresponding Maurer-Cartan equation is noted. This role is reminiscent of the homotopical perturbation lemma, with the infinitesimal deformation cocycle as “initiator”. Applied to star-products, we show how Moyal’s formula can ...

The impact of various types of external potentials to the Peyrard-Bishop DNA denaturation is investigated through statistical mechanics approach. The partition function is obtained using transfer integral method, and further the stretching of hydrogen bond is calculated using time independent perturbation method. It is shown that all types of external potentials accelerate the denaturation proc...