Established non-union of an operatively managed trans-scaphoid perilunate fracture dislocation progressing to spontaneous union

Perilunate dislocations and fracture dislocations represent uncommon and unusual injuries that are often missed at initial presentation and diagnosed late in up to 25% of cases. Prompt open reduction, carpal stabilisation and ligamentous repair is required to reduce the risk of complications. We report a case of an established scaphoid non-union in an operatively managed perilunate fracture dislocation that spontaneously united almost 2 years after the initial injury, just before a planned revision scaphoid fixation with bone grafting. This case highlights the importance of initial clinical assessment together with appropriate radiographs and follow-up of these injuries post-operatively, especially when complications such as non-union arise

Approximate probabilistic verification of hybrid systems

Hybrid systems whose mode dynamics are governed by non-linear ordinary differential equations (ODEs) are often a natural model for biological processes. However such models are difficult to analyze. To address this, we develop a probabilistic analysis method by approximating the mode transitions as stochastic events. We assume that the probability of making a mode transition is proportional to the measure of the set of pairs of time points and value states at which the mode transition is enabled. To ensure a sound mathematical basis, we impose a natural continuity property on the non-linear ODEs. We also assume that the states of the system are observed at discrete time points but that the mode transitions may take place at any time between two successive discrete time points. This leads to a discrete time Markov chain as a probabilistic approximation of the hybrid system. We then show that for BLTL (bounded linear time temporal logic) specifications the hybrid system meets a specification iff its Markov chain approximation meets the same specification with probability $1$. Based on this, we formulate a sequential hypothesis testing procedure for verifying -approximately- that the Markov chain meets a BLTL specification with high probability. Our case studies on cardiac cell dynamics and the circadian rhythm indicate that our scheme can be applied in a number of realistic settings

Building development and roads: implications for the distribution of stone curlews across the Brecks

Background: Substantial new housing and infrastructure development planned within England has the potential to conflict with the nature conservation interests of protected sites. The Breckland area of eastern England (the Brecks) is designated as a Special Protection Area for a number of bird species, including the stone curlew (for which it holds more than 60% of the UK total population). We explore the effect of buildings and roads on the spatial distribution of stone curlew nests across the Brecks in order to inform strategic development plans to avoid adverse effects on such European protected sites. Methodology: Using data across all years (and subsets of years) over the period 1988 – 2006 but restricted to habitat areas of arable land with suitable soils, we assessed nest density in relation to the distances to nearest settlements and to major roads. Measures of the local density of nearby buildings, roads and traffic levels were assessed using normal kernel distance-weighting functions. Quasi-Poisson generalised linear mixed models allowing for spatial auto-correlation were fitted. Results: Significantly lower densities of stone curlew nests were found at distances up to 1500m from settlements, and distances up to 1000m or more from major (trunk) roads. The best fitting models involved optimally distance-weighted variables for the extent of nearby buildings and the trunk road traffic levels. Significance : The results and predictions from this study of past data suggests there is cause for concern that future housing development and associated road infrastructure within the Breckland area could have negative impacts on the nesting stone curlew population. Given the strict legal protection afforded to the SPA the planning and conservation bodies have subsequently agreed precautionary restrictions on building development within the distances identified and used the modelling predictions to agree mitigation measures for proposed trunk road developments

Star Routing: Between Vehicle Routing and Vertex Cover

We consider an optimization problem posed by an actual newspaper company, which consists of computing a minimum length route for a delivery truck, such that the driver only stops at street crossings, each time delivering copies to all customers adjacent to the crossing. This can be modeled as an abstract problem that takes an unweighted simple graph $G = (V, E)$ and a subset of edges $X$ and asks for a shortest cycle, not necessarily simple, such that every edge of $X$ has an endpoint in the cycle. We show that the decision version of the problem is strongly NP-complete, even if $G$ is a grid graph. Regarding approximate solutions, we show that the general case of the problem is APX-hard, and thus no PTAS is possible unless P $=$ NP. Despite the hardness of approximation, we show that given any $\alpha$-approximation algorithm for metric TSP, we can build a $3\alpha$-approximation algorithm for our optimization problem, yielding a concrete $9/2$-approximation algorithm. The grid case is of particular importance, because it models a city map or some part of it. A usual scenario is having some neighborhood full of customers, which translates as an instance of the abstract problem where almost every edge of $G$ is in $X$. We model this property as $|E - X| = o(|E|)$, and for these instances we give a $(3/2 + \varepsilon)$-approximation algorithm, for any $\varepsilon > 0$, provided that the grid is sufficiently big.Comment: Accepted to the 12th Annual International Conference on Combinatorial Optimization and Applications (COCOA'18

Characterising the phenotypic diversity of Papilio dardanus wing patterns using an extensive museum collection

The history of 20th Century evolutionary biology can be followed through the study of mimetic butterflies. From the initial findings of discontinuous polymorphism through the debates regarding the evolution of mimicry and the step-size of evolutionary change, to the studies on supergene evolution and molecular characterisation of butterfly genomes, mimetic butterflies have been at the heart of evolutionary thought for over 100 years. During this time, few species have received as much attention and in-depth study as Papilio dardanus. To assist all aspects of mimicry research, we present a complete data-derived overview of the extent of polymorphism within this species. Using historical samples permanently held by the NHM London, we document the extent of phenotypic variation and characterise the diversity present in each of the subspecies and how it varies across Africa. We also demonstrate an association between “imperfect” mimetic forms and the transitional race formed in the area where Eastern and Western African populations meet around Lake Victoria. We present a novel portal for access to this collection, www.mimeticbutterflies.org, allowing remote access to this unique repository. It is hoped that this online resource can act as a nucleus for the sharing and dissemination of other collections databases and imagery connected with mimetic butterflies

Redox linked flavin sites in extracellular decaheme proteins involved in microbe-mineral electron transfer

Extracellular microbe-mineral electron transfer is a major driving force for the oxidation of organic carbon in many subsurface environments. Extracellular multi-heme cytochromes of the Shewenella genus play a major role in this process but the mechanism of electron exchange at the interface between cytochrome and acceptor is widely debated. The 1.8 Å x-ray crystal structure of the decaheme MtrC revealed a highly conserved CX8C disulfide that, when substituted for AX8A, severely compromised the ability of S. oneidensis to grow under aerobic conditions. Reductive cleavage of the disulfide in the presence of flavin mononucleotide (FMN) resulted in the reversible formation of a stable flavocytochrome. Similar results were also observed with other decaheme cytochromes, OmcA, MtrF and UndA. The data suggest that these decaheme cytochromes can transition between highly reactive flavocytochromes or less reactive cytochromes, and that this transition is controlled by a redox active disulfide that responds to the presence of oxygen