The main purpose of this paper is to prove a local Hölder regularity result for the solutions of the total variation based denoising problem assuming that the datum is locally Hölder continuous. We also prove a global estimate on the modulus of continuity of the solution in convex domains of R and some extensions of this result for the total variation minimization flow.

This paper is concerned with the numerical minimization of energy functionals in BV (Ω) (the space of bounded variation functions) involving total variation for gray-scale 1-dimensional inpainting problem. Applications are shown by finite element method and discontinuous Galerkin method for total variation minimization. We include the numerical examples which show the different recovery image b...

We study the problem of computing a planar curve, restricted to lie between two given polygonal chains, such that the integral of the square of arc-length derivative of curvature along the curve is minimized. We introduce the Minimum Variation B-spline problem which is a linearly constrained optimization problem over curves defined by Bspline functions only. An empirical investigation indicates...

Migraine is one of the most prevalent types of headache, which imposes a substantial burden on society as measured by direct and indirect costs. In the present work we review the obstacles to carrying out migraine epidemiological studies. Knowledge of the epidemiology of migraine has expanded because of the recent proliferation of large scale population-based studies using standardized case def...

Given a graph and a single watchman, the objective of the Watchman’s Walk Problem is to find a closed dominating walk of minimum length which the watchman can traverse to efficiently guard the graph. When multiple guards are available, one natural variation is to assume fixed time constraints on the monitoring of vertices and attempt to minimize the number of guards required. We find upper boun...

An effective form of the Variation Evolving Method (VEM), which originates from the continuous-time dynamics stability theory, is developed for the classic time-optimal control problem with control constraint. Within the mathematic derivation, the Pontryagin’s Minimum Principle (PMP) optimality conditions are used. Techniques including limited integrator and corner points are introduced to capt...

One of the oldest problems in evolutionary biology remains largely unsolved. Which mutations generate evolutionarily relevant phenotypic variation? What kinds of molecular changes do they entail? What are the phenotypic magnitudes, frequencies of origin, and pleiotropic effects of such mutations? How is the genome constructed to allow the observed abundance of phenotypic diversity? Historically...

Spelling issues tend to create relatively minor (though still complex) problems for corpus linguistics, information retrieval and natural language processing tasks that use ‘standard’ or modern varieties of English. For example, in corpus annotation, we have to decide how to deal with tokenisation issues such as whether (i) periods represent sentence boundaries or acronyms and (ii) apostrophes ...

It is demonstrated that the pre-dual for problems with total bounded variation regularization terms can be expressed as bilaterally constrained optimization problem. Existence of a Lagrange multiplier and an optimality system are established. This allows to utilize efficient optimization methods developed for problems with box constraints in the context of bounded variation formulations. Here, ...

Background and Motivation Theories of the cognitive architecture (Langley et al., 2009) aim to specify the constant features of the human mind. They make assumptions about the representation and organization of memory, as well as about performance and learning mechanisms that operate over its structures. They specifically do not include content that changes, whether rapidly through reasoning an...