Automated detection of block falls in the north polar region of Mars

We developed a change detection method for the identification of ice block falls using NASA's HiRISE images of the north polar scarps on Mars. Our method is based on a Support Vector Machine (SVM), trained using Histograms of Oriented Gradients (HOG), and on blob detection. The SVM detects potential new blocks between a set of images; the blob detection, then, confirms the identification of a block inside the area indicated by the SVM and derives the shape of the block. The results from the automatic analysis were compared with block statistics from visual inspection. We tested our method in 6 areas consisting of 1000x1000 pixels, where several hundreds of blocks were identified. The results for the given test areas produced a true positive rate of ~75% for blocks with sizes larger than 0.7 m (i.e., approx. 3 times the available ground pixel size) and a false discovery rate of ~8.5%. Using blob detection we also recover the size of each block within 3 pixels of their actual size

Three-Field Modelling of Nonlinear Nonsmooth Boundary Value Problems and Stability of Differential Mixed Variational Inequalities

The purpose of this paper is twofold. Firstly we consider nonlinear nonsmooth elliptic boundary value problems, and also related parabolic initial boundary value problems that model in a simplified way steady-state unilateral contact with Tresca friction in solid mechanics, respectively, stem from nonlinear transient heat conduction with unilateral boundary conditions. Here a recent duality approach, that augments the classical Babuška-Brezzi saddle point formulation for mixed variational problems to twofold saddle point formulations, is extended to the nonsmooth problems under consideration. This approach leads to variational inequalities of mixed form for three coupled fields as unknowns and to related differential mixed variational inequalities in the time-dependent case. Secondly we are concerned with the stability of the solution set of a general class of differential mixed variational inequalities. Here we present a novel upper set convergence result with respect to perturbations in the data, including perturbations of the associated nonlinear maps, the nonsmooth convex functionals, and the convex constraint set. We employ epiconvergence for the convergence of the functionals and Mosco convergence for set convergence. We impose weak convergence assumptions on the perturbed maps using the monotonicity method of Browder and Minty

Hadronic Parity Violation: a New View through the Looking Glass

Studies of the strangeness changing hadronic weak interaction have produced a number of puzzles that have so far evaded a complete explanation within the Standard Model. Their origin may lie either in dynamics peculiar to weak interactions involving strange quarks or in more general aspects of the interplay between strong and weak interactions. In principle, studies of the strangeness conserving hadronic weak interaction using parity violating hadronic and nuclear observables provide a complementary window on this question. However, progress in this direction has been hampered by the lack of a suitable theoretical framework for interpreting hadronic parity violation measurements in a model-independent way. Recent work involving effective field theory ideas has led to the formulation of such a framework while motivating the development of a number of new hadronic parity violation experiments in few-body systems. In this article, we review these recent developments and discuss the prospects and opportunities for further experimental and theoretical progress.Comment: Manuscript submitted to Annual Reviews of Nuclear and Particle Scienc

A strongly convergent combined relaxation method in hilbert spaces

We consider a combined relaxation method for variational inequalities in a Hilbert space setting. Methods of this class are known to solve finite-dimensional variational inequalities under mild monotonicity type assumptions, whereas in Hilbert space strong monotonicity is the standard assumption for strong convergence. Here, we relax this condition and show strong convergence of such a method, when strong monotonicity holds only on a subspace of finite co-dimension. Thus, the method applies to semi-coercive unilateral boundary value problems in mathematical physics. © 2014 Copyright Taylor & Francis Group, LLC