The Cop Number of the One-Cop-Moves Game on Planar Graphs

Cops and robbers is a vertex-pursuit game played on graphs. In the classical cops-and-robbers game, a set of cops and a robber occupy the vertices of the graph and move alternately along the graph's edges with perfect information about each other's positions. If a cop eventually occupies the same vertex as the robber, then the cops win; the robber wins if she can indefinitely evade capture. Aigner and Frommer established that in every connected planar graph, three cops are sufficient to capture a single robber. In this paper, we consider a recently studied variant of the cops-and-robbers game, alternately called the one-active-cop game, one-cop-moves game or the lazy-cops-and-robbers game, where at most one cop can move during any round. We show that Aigner and Frommer's result does not generalise to this game variant by constructing a connected planar graph on which a robber can indefinitely evade three cops in the one-cop-moves game. This answers a question recently raised by Sullivan, Townsend and Werzanski.Comment: 32 page

Plant RuBisCo assembly in E. coli with five chloroplast chaperones including BSD2

Plant RuBisCo, a complex of eight large and eight small subunits, catalyzes the fixation of CO2 in photosynthesis. The low catalytic efficiency of RuBisCo provides strong motivation to reengineer the enzyme with the goal of increasing crop yields. However, genetic manipulation has been hampered by the failure to express plant RuBisCo in a bacterial host. We achieved the functional expression of Arabidopsis thaliana RuBisCo in Escherichia coli by coexpressing multiple chloroplast chaperones. These include the chaperonins Cpn60/Cpn20, RuBisCo accumulation factors 1 and 2, RbcX, and bundle-sheath defective-2 (BSD2). Our structural and functional analysis revealed the role of BSD2 in stabilizing an end-state assembly intermediate of eight RuBisCo large subunits until the small subunits become available. The ability to produce plant RuBisCo recombinantly will facilitate efforts to improve the enzyme through mutagenesis

Regulation of Gdf5 expression in joint remodelling, repair and osteoarthritis

Funding: Arthritis Research UK (grants no. 20775, 19667, 20865, 21156); European Union’s Horizon 2020 research and innovation programme under Marie Sklodowska Curie grant agreement no. 642414; Medical Research Council (grant MR/L022893/1); A.H.K.R. was supported by the Wellcome Trust through the Scottish Translational Medicine and Therapeutics Initiative (grant no. WT 085664). The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.Peer reviewedPublisher PD

Design of the strut braced wing aircraft in the agile collaborative MDO framework

The paper describes the deployment of the AGILE Development Framework to investigate the Strut Braced Wing aircraft configuration. The design process consists of a multilevel multidisciplinary architecture, progressing from the initial conceptual synthesis to the physics based analysis. All the main disciplinary domains, including on board system design and cost assessment, are accounted for in the assembled workflow. Due to the specific characteristics of the Strut Braced Wing configuration, the aeroelastic analysis is the main focus of the study and it is addressed at both high and low fidelity levels. The integration of the engine-wing system is also included in the design process. All the design competences, which are hosted at the different partners, communicate via CPACS (Common Parametric Aircraft Configuration Schema) data schema. All the results generated, including the multidisciplinary design process itself, will be published and made available as part of the AGILE Overall Aircraft Design database

Effects of microRNA-146a on the proliferation and apoptosis of human osteochondrocytes by targeting TRAF6 through the NF- κB signalling pathway

MicroRNAs are important cellular mediators of mRNA degradation and translation repression, which in turn can have an impact on various processes and, if their function is perturbed, can cause disease. Here, we summarize the recent manuscript by Zhong et al. [(2017) Biosci. Rep. 37, BSR20160578], which explores microRNA-146a and how it may play an indirect yet vital role in the proliferation of osteoarthritis (OA) chondrocytes. The data presented by the authors could have important implications for future OA therapies

The haematopoietic GTPase RhoH modulates IL3 signalling through regulation of STAT activity and IL3 receptor expression

<p>Abstract</p> <p>Background</p> <p>RhoH is a constitutively active member of the family of Rho GTPases. Its expression is restricted to the haematopoietic lineage, where it serves as a positive regulator for T cell selection and mast cell function and as a negative regulator for growth-related functions in other lineages. Here, we examined the activation of signal transducer and activator of transcription (STAT) proteins in response to stimulation with interleukin 3 (IL3).</p> <p>Results</p> <p>Using the murine IL3-dependent cell line BaF3 we investigated the influence of RhoH protein expression levels on IL3-mediated cellular responses. RhoH overexpressing cells showed lower sensitivity to IL3 and decreased STAT5 activation. SiRNA-mediated repression of <it>RhoH </it>gene expression led to an increase in proliferation and STAT5 activity which correlated with an increased number of IL3 receptor α chain molecules, also known as CD123, expressed at the cell surface. Interestingly, these findings could be reproduced using human THP-1 cells as a model system for acute myeloid leukaemia, where low RhoH levels are known to be an unfavourable prognostic marker. Overexpression of RhoH on the other hand caused an induction of STAT1 activity and western blot analysis revealed that activated STAT1 is phosphorylated on Tyr701. STAT1 is known to induce apoptosis or cell cycle arrest and we detected an upregulation of cyclin-dependent kinase inhibitors (CDKI) <it>p21^Cip1</it>and <it>p27^Kip1</it>in RhoH overexpressing BaF3 cells.</p> <p>Conclusions</p> <p>We propose that RhoH functions as a negative regulator for IL3-induced signals through modulation of the JAK-STAT pathway. High levels of RhoH allow the IL3-dependent activation of STAT1 causing decreased proliferation through upregulation of <it>p21^Cip1</it>and <it>p27^Kip1</it>. Low RhoH levels on the other hand led to an upregulation of IL3-dependent cell growth, STAT5 activity and an increase of CD123 surface expression, linking RhoH to a CD123/STAT5 phenotype that has been described in AML patients.</p

Quantum Hall transitions: An exact theory based on conformal restriction

We revisit the problem of the plateau transition in the integer quantum Hall effect. Here we develop an analytical approach for this transition, based on the theory of conformal restriction. This is a mathematical theory that was recently developed within the context of the Schramm-Loewner evolution which describes the stochastic geometry of fractal curves and other stochastic geometrical fractal objects in 2D space. Observables elucidating the connection with the plateau transition include the so-called point-contact conductances (PCCs) between points on the boundary of the sample, described within the language of the Chalker-Coddington network model. We show that the disorder-averaged PCCs are characterized by classical probabilities for certain geometric objects in the plane (pictures), occurring with positive statistical weights, that satisfy the crucial restriction property with respect to changes in the shape of the sample with absorbing boundaries. Upon combining this restriction property with the expected conformal invariance at the transition point, we employ the mathematical theory of conformal restriction measures to relate the disorder-averaged PCCs to correlation functions of primary operators in a conformal field theory (of central charge $c=0$). We show how this can be used to calculate these functions in a number of geometries with various boundary conditions. Since our results employ only the conformal restriction property, they are equally applicable to a number of other critical disordered electronic systems in 2D. For most of these systems, we also predict exact values of critical exponents related to the spatial behavior of various disorder-averaged PCCs.Comment: Published versio