32,706 research outputs found
A Look at the Generalized Heron Problem through the Lens of Majorization-Minimization
In a recent issue of this journal, Mordukhovich et al.\ pose and solve an
interesting non-differentiable generalization of the Heron problem in the
framework of modern convex analysis. In the generalized Heron problem one is
given closed convex sets in \Real^d equipped with its Euclidean norm
and asked to find the point in the last set such that the sum of the distances
to the first sets is minimal. In later work the authors generalize the
Heron problem even further, relax its convexity assumptions, study its
theoretical properties, and pursue subgradient algorithms for solving the
convex case. Here, we revisit the original problem solely from the numerical
perspective. By exploiting the majorization-minimization (MM) principle of
computational statistics and rudimentary techniques from differential calculus,
we are able to construct a very fast algorithm for solving the Euclidean
version of the generalized Heron problem.Comment: 21 pages, 3 figure
Agents in Bioinformatics
The scope of the Technical Forum Group (TFG) on Agents in Bioinformatics (BIOAGENTS) was to inspire collaboration between the agent and bioinformatics communities with the aim of creating an opportunity to propose a different (agent-based) approach to the development of computational frameworks both for data analysis in bioinformatics and for system modelling in computational biology. During the day, the participants examined the future of research on agents in bioinformatics primarily through 12 invited talks selected to cover the most relevant topics. From the discussions, it became clear that there are many perspectives to the field, ranging from bio-conceptual languages for agent-based simulation, to the definition of bio-ontology-based declarative languages for use by information agents, and to the use of Grid agents, each of which requires further exploration. The interactions between participants encouraged the development of applications that describe a way of creating agent-based simulation models of biological systems, starting from an hypothesis and inferring new knowledge (or relations) by mining and analysing the huge amount of public biological data. In this report we summarise and reflect on the presentations and discussions
Escape rates for Gibbs measures
In this paper we study the asymptotic behaviour of the escape rate of a Gibbs measure supported on a conformal repeller through a small hole. There are additional applications to the convergence of the Hausdorff dimension of the survivor set
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