In this paper we develop a new approach for the stable approximation of a minimal surface problem associated with a relaxed Dirichlet problem in the space BV(Ω) of functions of bounded variation. The problem can be reformulated as an unconstrained minimization problem of a functional J on BV(Ω) defined by J (u) = A(u) + ∫ ∂Ω |Tu − φ|, where A(u) is the “area integral” of u with respect to Ω, T ...

Numerous geometric problems in computer vision involve the solution of systems of polynomial equations. This is particularly true for so called minimal problems, but also for finding stationary points for overdetermined problems. The state-of-the-art is based on the use of numerical linear algebra on the large but sparse coefficient matrix that represents the original equations multiplied with ...

This answers affirmatively a question posed in [CM04]. In [CM99], T. H. Colding and W. P. Minicozzi II proved an analogous theorem, stating that there exists an open set of metrics on M such that there are embedded minimal tori of arbitrarily large area. This result was extended to surfaces of positive genus in [Dea03] by B. Dean. The genus zero case has remained an open problem since then, lar...

We show that any family of sets uniformly definable in an ominimal structure has an extended compression scheme of size equal to the number of parameters in the defining formula. As a consequence, the combinatorial complexity (or density) of any definable family in a structure with a o-minimal theory is bounded by the number of parameters in the defining formula. ∗Partially supported by NSF gra...

We propose and study algorithms to compute minimal models, stable models and answer sets of t-CNF theories, and normal and disjunctive t-programs. We are especially interested in algorithms with non-trivial worst-case performance bounds. The bulk of the paper is concerned with the classes of 2and 3-CNF theories, and normal and disjunctive 2and 3-programs, for which we obtain significantly stron...

In this paper, our goal is to characterize two graph classes based on the properties of minimal vertex (edge) separators. We first present a structural characterization of graphs in which every minimal vertex separator is a stable set. We show that such graphs are precisely those in which the induced subgraph, namely, a cycle with exactly one chord is forbidden. We also show that deciding maxim...

The minimal model approach to estimating insulin sensitivity (Sl) and glucose effectiveness in promoting its own disposition at basal insulin (SG) is a powerful tool that has been underutilized given its potential applications. In part, this has been due to its inability to separate insulin and glucose effects on peripheral uptake from their effects on hepatic glucose inflow. Prior enhancements...

When data sources are virtually integrated there is no common and centralized mechanism for maintaining global consistency. In consequence, it is likely that inconsistencies with respect to certain global integrity constraints (ICs) will occur. In this chapter we consider the problem of defining and computing those answers that are consistent wrt the global ICs when global queries are posed to ...

We propose a new solution concept in the roommate problem, based on “robustness” of deviations (i.e., blocking coalitions). call deviation from matching robust up to depth k, if none deviators gets worse off than at original after any sequence most k subsequent deviations. say that is stable against (for short, SaRD) no it k. As smaller imposes stronger requirement for be SaRD, we investigate e...

In this paper, a generalized mathematical model of spread of infectious disease as SIRS epidemic model is considered as a nonlinear system of differential equation. We prove that for positive initial conditions the resulting equivalence system has positive solution and under some hypothesis, this system with initial positive condition, has a positive $T$-periodic solution which is globally asym...