Exact Solution Methods for the kk-item Quadratic Knapsack Problem

The purpose of this paper is to solve the 0-1 $k$-item quadratic knapsack problem $(kQKP)$, a problem of maximizing a quadratic function subject to two linear constraints. We propose an exact method based on semidefinite optimization. The semidefinite relaxation used in our approach includes simple rank one constraints, which can be handled efficiently by interior point methods. Furthermore, we strengthen the relaxation by polyhedral constraints and obtain approximate solutions to this semidefinite problem by applying a bundle method. We review other exact solution methods and compare all these approaches by experimenting with instances of various sizes and densities.Comment: 12 page

Mutations of the ret protooncogene in German multiple endocrine neoplasia families: Relation between genotype and phenotype.

It has been suggested that not only the position but also the nature of the mutations of the ret protooncogene strongly correlate with the clinical manifestation of the multiple endocrine neoplasm type 2 (MEN 2) syndrome. In particular, individuals with a Cys634-Arg substitution should have a greater risk of developing parathyroid disease. We, therefore, analyzed 94 unrelated families from Germany with inherited medullary thyroid carcinoma (MTC) for mutation of the ret protooncogene. In all but 1 of 59 families with MEN 2A, germline mutations in the extracellular domain of the ret protein were found. Some 81% of the MEN 2A mutations affected codon 634. Phenotype-genotype correlations suggested that the prevalence of pheochromocytoma and hyperparathyroidism is significantly higher in families with codon 634 mutations, but there was no correlation with the nature of the mutation. In all but 1 of 27 familial MTC (FMTC) families, mutations were detected in 1 of 4 cysteines in the extracellular domain of the ret protooncogene. Half of the FMTC mutations affected codon 634. Mutations outside of codon 634 occurred more often in FMTC families than in MEN 2A families. In all but 1 of 8 MEN 2B patients, de novo mutations in codon 918 were found. These data confirm the preferential localization of MEN 2-associated mutations and the correlation between disease phenotype and the position of the ret mutation, but there was no correlation between the occurrence of hyperparathyroidism or pheochromocytoma and the nature of the mutation

Metaheuristics for solving a multimodal home-healthcare scheduling problem

Abstract We present a general framework for solving a real-world multimodal home-healthcare scheduling (MHS) problem from a major Austrian home-healthcare provider. The goal of MHS is to assign home-care staff to customers and determine efficient multimodal tours while considering staff and customer satisfaction. Our approach is designed to be as problem-independent as possible, such that the resulting methods can be easily adapted to MHS setups of other home-healthcare providers. We chose a two-stage approach: in the first stage, we generate initial solutions either via constraint programming techniques or by a random procedure. During the second stage, the initial solutions are (iteratively) improved by applying one of four metaheuristics: variable neighborhood search, a memetic algorithm, scatter search and a simulated annealing hyper-heuristic. An extensive computational comparison shows that the approach is capable of solving real-world instances in reasonable time and produces valid solutions within only a few seconds

Engineering Branch-and-Cut Algorithms for the Equicut Problem

A minimum equicut of an edge-weighted graph is a partition of the nodes of the graph into two sets of equal size such hat the sum of the weights of edges joining nodes in different partitions is minimum. We compare basic linear and semidefnite relaxations for the equicut problem, and and that linear bounds are competitive with the corresponding semidefnite ones but can be computed much faster. Motivated by an application of equicut in theoretical physics, we revisit an approach by Brunetta et al. and present an enhanced branch-and-cut algorithm. Our computational results suggest that the proposed branch-andcut algorithm has a better performance than the algorithm of Brunetta et al.. Further, it is able to solve to optimality in reasonable time several instances with more than 200 nodes from the physics application

A case study of controlling crossover in a selection hyper-heuristic framework using the multidimensional knapsack problem

Hyper-heuristics are high-level methodologies for solving complex problems that operate on a search space of heuristics. In a selection hyper-heuristic framework, a heuristic is chosen from an existing set of low-level heuristics and applied to the current solution to produce a new solution at each point in the search. The use of crossover low-level heuristics is possible in an increasing number of general-purpose hyper-heuristic tools such as HyFlex and Hyperion. However, little work has been undertaken to assess how best to utilise it. Since a single-point search hyper-heuristic operates on a single candidate solution, and two candidate solutions are required for crossover, a mechanism is required to control the choice of the other solution. The frameworks we propose maintain a list of potential solutions for use in crossover. We investigate the use of such lists at two conceptual levels. First, crossover is controlled at the hyper-heuristic level where no problem-specific information is required. Second, it is controlled at the problem domain level where problem-specific information is used to produce good-quality solutions to use in crossover. A number of selection hyper-heuristics are compared using these frameworks over three benchmark libraries with varying properties for an NP-hard optimisation problem: the multidimensional 0-1 knapsack problem. It is shown that allowing crossover to be managed at the domain level outperforms managing crossover at the hyper-heuristic level in this problem domain. © 2016 Massachusetts Institute of Technolog

Live imaging of stem cell and progeny behaviour in physiological hair-follicle regeneration

Tissue development and regeneration depend on cell-cell interactions and signals that target stem cells and their immediate progeny. However, the cellular behaviours that lead to a properly regenerated tissue are not well understood. Using a new, non-invasive, intravital two-photon imaging approach we study physiological hair-follicle regeneration over time in live mice. By these means we have monitored the behaviour of epithelial stem cells and their progeny during physiological hair regeneration and addressed how the mesenchyme influences their behaviour. Consistent with earlier studies, stem cells are quiescent during the initial stages of hair regeneration, whereas the progeny are more actively dividing. Moreover, stem cell progeny divisions are spatially organized within follicles. In addition to cell divisions, coordinated cell movements of the progeny allow the rapid expansion of the hair follicle. Finally, we show the requirement of the mesenchyme for hair regeneration through targeted cell ablation and long-term tracking of live hair follicles. Thus, we have established an in vivo approach that has led to the direct observation of cellular mechanisms of growth regulation within the hair follicle and that has enabled us to precisely investigate functional requirements of hair-follicle components during the process of physiological regeneration. © 2012 Macmillan Publishers Limited. All rights reserved

Autophagy in the Thymic Epithelium Is Dispensable for the Development of Self-Tolerance in a Novel Mouse Model

The thymic epithelium plays critical roles in the positive and negative selection of T cells. Recently, it was proposed that autophagy in thymic epithelial cells is essential for the induction of T cell tolerance to self antigens and thus for the prevention of autoimmune diseases. Here we have tested this hypothesis using mouse models in which autophagy was blocked specifically in epithelial cells expressing keratin 14 (K14), including the precursor of thymic epithelial cells. While the thymic epithelial cells of mice carrying the floxed Atg7 gene (ATG7 f/f) showed a high level of autophagy, as determined by LC3 Western blot analysis and fluorescence detection of the recombinant green fluorescent protein (GFP)-LC3 reporter protein on autophagosomes, autophagy in the thymic epithelium was efficiently suppressed by deletion of the Atg7 gene using the Cre-loxP system (ATG7 f/f K14-Cre). Suppression of autophagy led to the massive accumulation of p62/sequestosome 1 (SQSTM1) in thymic epithelial cells. However, the structure of the thymic epithelium as well as the organization and the size of the thymus were not altered in mutant mice. The ratio of CD4 to CD8-positive T cells, as well as the frequency of activated (CD69+) CD4 T cells in lymphoid organs, did not differ between mice with autophagy-competent and autophagy-deficient thymic epithelium. Inflammatory infiltrating cells, potentially indicative of autoimmune reactions, were present in the liver, lung, and colon of a similar fraction of ATG7 f/f and ATG7 f/f K14-Cre mice. In contrast to previously reported mice, that had received an autophagy-deficient thymus transplant, ATG7 f/f K14-Cre mice did not suffer from autoimmunity-induced weight loss. In summary, the results of this study suggest that autophagy in the thymic epithelium is dispensable for negative selection of autoreactive T cells