In this paper, we propose a unified primal-dual algorithm framework for two classes of problems that arise from various signal and image processing applications. We also show the connections to existing methods, in particular Bregman iteration [41] based method, such as linearized Bregman [42, 9, 10, 49] and split Bregman [31]. The convergence of the general algorithm framework is proved under ...

We introduce a new, demand-driven variant of Spector’s bar recursion in the spirit of the BerardiBezem-Coquand functional of [4]. The recursion takes place over finite partial functions u, where the control parameter φ, used in Spector’s bar recursion to terminate the computation at sequences s satisfying φ(ŝ) < |s|, now acts as a guide for deciding exactly where to make bar recursive updates, ...

Econophysics, is based on the premise that some ideas and methods from physics can be applied to economic situations. We intend to show in this paper how a physics concept such as entropy can be applied to an economic problem. In so doing, we demonstrate how information in the form of observable data and moment constraints are introduced into the method of Maximum relative Entropy (MrE). A gene...

The termination problem for affine programs over the integers was left open in [1]. For more that a decade, it has been considered and cited as a challenging open problem. To the best of our knowledge, we present here the most complete response to this issue: we show that termination for affine programs over Z is decidable under an assumption holding for almost all affine programs, except for a...

Verbs were clustered semantically on the basis of their alternation behaviour, as characterised by their syntactic subcategorisation frames extracted from maximum probability parses of a robust statistical parser, and completed by assigning WordNet classes as selectional preferences to the frame arguments. The clustering was achieved (a) iteratively by measuring the relative entropy between the...

Questions about how shifting distributions contribute to species diversification remain virtually without answer, even though rapid climate change during the Pleistocene clearly impacted genetic variation within many species. One factor that has prevented this question from being adequately addressed is the lack of precision associated with estimates of species divergence made from a single gen...

Calibration is a critical step in every molecular clock analysis but it has been the least considered. Bayesian approaches to divergence time estimation make it possible to incorporate the uncertainty in the degree to which fossil evidence approximates the true time of divergence. We explored the impact of different approaches in expressing this relationship, using arthropod phylogeny as an exa...

It is a challenge to find point wise (including inter-element boundary) divergence-free finite element bases. By identifying functions in the kernel of the divergence operator, we discover a local basis for the full divergence-free space of the C0-P1 finite element, on the union jack grid. The optimal order of approximation is shown for the P1 divergence-free finite elements on union jack grids...

In this paper, we propose and numerically investigate a family of locally divergence-free central discontinuous Galerkin methods for ideal magnetohydrodynamic (MHD) equations. The methods are based on the original central discontinuous Galerkin methods (SIAM Journal on Numerical Analysis 45 (2007) 2442-2467) for hyperbolic equations, with the use of approximating functions that are exactly dive...