Matthias Walter

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Given an undirected graph, the non-empty subgraph polytope is the convex hull of the characteristic vectors of pairs (F, S) where S is a non-empty subset of nodes and F is a subset of the edges with both endnodes in S. We obtain a strong relationship between the non-empty subgraph polytope and the spanning forest polytope. We further show that these(More)
Preface During my internship at the IBM T.J. Watson Research Center in fall 2010 I studied recent papers that may be suitable for an implementation for CPLEX, one of the state-of-the-art optimization suites. The main topic was cutting planes because an implementation was relatively easy to create without requiring specific (and secret) internal information.(More)
Recognizing the growing importance of scientific benchmarking in water distribution, we provide a comprehensive survey of the available literature. We begin with a discussion about the (limited) use of benchmarking in the regulation of UK water utilities, and then extend the analysis to regulated water sectors in other countries. We find no clear impact of(More)
OBJECTIVE To investigate clinical efficacy and incidence of complications regarding intrathecal baclofen (ITB) therapy in children. METHODS Retrospective medical chart review of 15 paediatric patients with congenital brain injuries who underwent ITB implantation for treatment of severe spasticity between 2003 and 2009. RESULTS Compared to the(More)
INTRODUCTION Lower urinary tract symptoms (LUTS) are highly prevalent, cause an enormous economic burden on healthcare systems and significantly impair the quality of life (QoL) of affected patients. The dependence of the LUT on complex central neuronal circuits makes it unique in comparison to other visceral functions, such as the gastrointestinal tract,(More)
We show that the independence polytope of every regular matroid has an extended formulation of size quadratic in the size of its ground set. This generalizes a similar statement for (co-)graphic matroids, which is a simple consequence of Martin's [9] extended formulation for the spanning-tree polytope. In our construction, we make use of Seymour's(More)
We introduce the simple extension complexity of a polytope P as the smallest number of facets of any simple (i.e., non-degenerate in the sense of linear programming) polytope which can be projected onto P. We devise a combinatorial method to establish lower bounds on the simple extension complexity and show for several polytopes that they have large simple(More)
BACKGROUND The control of the lower urinary tract is a complex, multilevel process involving both the peripheral and central nervous system. Due to lesions of the neuraxis, most spinal cord injury patients suffer from neurogenic lower urinary tract dysfunction, which may jeopardise upper urinary tract function and has a negative impact on health-related(More)