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

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

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

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

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

Valproic Acid Induces Hair Regeneration in Murine Model and Activates Alkaline Phosphatase Activity in Human Dermal Papilla Cells

Alopecia is the common hair loss problem that can affect many people. However, current therapies for treatment of alopecia are limited by low efficacy and potentially undesirable side effects. We have identified a new function for valproic acid (VPA), a GSK3β inhibitor that activates the Wnt/β-catenin pathway, to promote hair re-growth in vitro and in vivo.Topical application of VPA to male C3H mice critically stimulated hair re-growth and induced terminally differentiated epidermal markers such as filaggrin and loricrin, and the dermal papilla marker alkaline phosphatase (ALP). VPA induced ALP in human dermal papilla cells by up-regulating the Wnt/β-catenin pathway, whereas minoxidil (MNX), a drug commonly used to treat alopecia, did not significantly affect the Wnt/β-catenin pathway. VPA analogs and other GSK3β inhibitors that activate the Wnt/β-catenin pathway such as 4-phenyl butyric acid, LiCl, and BeCl(2) also exhibited hair growth-promoting activities in vivo. Importantly, VPA, but not MNX, successfully stimulate hair growth in the wounds of C3H mice.Our findings indicate that small molecules that activate the Wnt/β-catenin pathway, such as VPA, can potentially be developed as drugs to stimulate hair re-growth