Connections between semidefinite relaxations of the max-cut and stable set problems

We describe the links existing between a recently introduced semidefinite relaxation for the max-cut problem and the well known semidefinite relaxation for the stable set problem underlying the Lovász's theta function. It turns out that the connection between the convex bodies defining the semidefinite relaxations mimicks the connection existing between the corresponding polyhedra. We also show how the semidefinite relaxations can be combined with the classical linear relaxations in order to obtain tighter relaxations

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

A mechanistic target of rapamycin complex 1/2 (mTORC1)/V-Akt murine thymoma viral oncogene homolog 1 (AKT1)/cathepsin H axis controls filaggrin expression and processing in skin, a novel mechanism for skin barrier disruption in patients with atopic dermatitis

Background Filaggrin, which is encoded by the filaggrin gene (FLG), is an important component of the skin's barrier to the external environment, and genetic defects in FLG strongly associate with atopic dermatitis (AD). However, not all patients with AD have FLG mutations. Objective We hypothesized that these patients might possess other defects in filaggrin expression and processing contributing to barrier disruption and AD, and therefore we present novel therapeutic targets for this disease. Results We describe the relationship between the mechanistic target of rapamycin complex 1/2 protein subunit regulatory associated protein of the MTOR complex 1 (RAPTOR), the serine/threonine kinase V-Akt murine thymoma viral oncogene homolog 1 (AKT1), and the protease cathepsin H (CTSH), for which we establish a role in filaggrin expression and processing. Increased RAPTOR levels correlated with decreased filaggrin expression in patients with AD. In keratinocyte cell cultures RAPTOR upregulation or AKT1 short hairpin RNA knockdown reduced expression of the protease CTSH. Skin of CTSH-deficient mice and CTSH short hairpin RNA knockdown keratinocytes showed reduced filaggrin processing, and the mouse had both impaired skin barrier function and a mild proinflammatory phenotype. Conclusion Our findings highlight a novel and potentially treatable signaling axis controlling filaggrin expression and processing that is defective in patients with AD