Colourings of cubic graphs inducing isomorphic monochromatic subgraphs

A $k$-bisection of a bridgeless cubic graph $G$ is a $2$-colouring of its vertex set such that the colour classes have the same cardinality and all connected components in the two subgraphs induced by the colour classes (monochromatic components in what follows) have order at most $k$. Ban and Linial conjectured that every bridgeless cubic graph admits a $2$-bisection except for the Petersen graph. A similar problem for the edge set of cubic graphs has been studied: Wormald conjectured that every cubic graph $G$ with $|E(G)| \equiv 0 \pmod 2$ has a $2$-edge colouring such that the two monochromatic subgraphs are isomorphic linear forests (i.e. a forest whose components are paths). Finally, Ando conjectured that every cubic graph admits a bisection such that the two induced monochromatic subgraphs are isomorphic. In this paper, we give a detailed insight into the conjectures of Ban-Linial and Wormald and provide evidence of a strong relation of both of them with Ando's conjecture. Furthermore, we also give computational and theoretical evidence in their support. As a result, we pose some open problems stronger than the above mentioned conjectures. Moreover, we prove Ban-Linial's conjecture for cubic cycle permutation graphs. As a by-product of studying $2$-edge colourings of cubic graphs having linear forests as monochromatic components, we also give a negative answer to a problem posed by Jackson and Wormald about certain decompositions of cubic graphs into linear forests.Comment: 33 pages; submitted for publicatio

Ab interno trabecular bypass surgery with Trabectome for open angle glaucoma

BACKGROUND: Glaucoma is the leading cause of irreversible blindness. Minimally invasive surgical techniques, such as ab interno trabecular bypass surgery, have been introduced to prevent glaucoma progressing. OBJECTIVES: The main objective was to assess the results at two years of ab interno trabecular bypass surgery with Trabectome for open angle glaucoma in comparison to conventional medical, laser, or surgical treatment in terms of efficacy and safety. A secondary objective was to examine the effects of Trabectome surgery in people who have concomitant phacoemulsification in comparison to those who do not have concomitant phacoemulsification. SEARCH METHODS: We searched CENTRAL (which contains the Cochrane Eyes and Vision Trials Register) (2016, Issue 4), Ovid MEDLINE, Ovid MEDLINE In-Process and Other Non-Indexed Citations, Ovid MEDLINE Daily, Ovid OLDMEDLINE (January 1946 to May 2016), EMBASE (January 1980 to May 2016), the ISRCTN registry (www.isrctn.com/editAdvancedSearch), ClinicalTrials.gov (www.clinicaltrials.gov), and the World Health Organization (WHO) International Clinical Trials Registry Platform (ICTRP) (www.who.int/ictrp/search/en). We did not use any date or language restrictions in the electronic searches for trials. We last searched the electronic databases on 12 May 2016. SELECTION CRITERIA: We included only randomised controlled trials (RCTs) of ab interno trabecular bypass surgery with Trabectome. DATA COLLECTION AND ANALYSIS: We planned to have two review authors independently extract data from reports of included studies using a data collection form. MAIN RESULTS: One randomised controlled trial identified from ClinicalTrials.gov, NCT00901108, met the criteria for inclusion. This study has subsequently been terminated. The ClinicalTrials.gov record indicates that the investigators plan to complete 12 months of follow-up and analysis on 19 participants already recruited into the trial. AUTHORS' CONCLUSIONS: There is currently no high-quality evidence for the outcomes of ab interno trabecular bypass surgery with Trabectome for open angle glaucoma. Properly designed RCTs are needed to assess the long-term efficacy and safety of this technique

An algorithm for counting circuits: application to real-world and random graphs

We introduce an algorithm which estimates the number of circuits in a graph as a function of their length. This approach provides analytical results for the typical entropy of circuits in sparse random graphs. When applied to real-world networks, it allows to estimate exponentially large numbers of circuits in polynomial time. We illustrate the method by studying a graph of the Internet structure.Comment: 7 pages, 3 figures, minor corrections, accepted versio

Introducing the student designer to the role of emotion in design

Products satisfy needs beyond the functional. These needs may include aspirations, emotions, cultural and social needs. It is crucial that designers are equipped to deal with the emotional domain of products and users. Carlson (1997) considered emotion to be short term waves of feeling arising without conscious effort, whereas mood, is defined as a longer termed state with less intensity. The authors’ working definition of the ‘emotional domain’ is the range of states of mind (which may influence the body) and which are influenced by internal and external stimuli. These effects tend to be transient although an individual will have a tendency towards a particular state, such as melancholy, happiness, calmness and so on. But even here various stimuli can cause a significant swing in state of mind. But this is a highly individual effect for example, one person may find the new iMac computer delightful and cheerful, where as others, may find it irritating and repulsive

Self-organization of collaboration networks

We study collaboration networks in terms of evolving, self-organizing bipartite graph models. We propose a model of a growing network, which combines preferential edge attachment with the bipartite structure, generic for collaboration networks. The model depends exclusively on basic properties of the network, such as the total number of collaborators and acts of collaboration, the mean size of collaborations, etc. The simplest model defined within this framework already allows us to describe many of the main topological characteristics (degree distribution, clustering coefficient, etc.) of one-mode projections of several real collaboration networks, without parameter fitting. We explain the observed dependence of the local clustering on degree and the degree--degree correlations in terms of the ``aging'' of collaborators and their physical impossibility to participate in an unlimited number of collaborations.Comment: 10 pages, 8 figure

Efficacy of Repeat Selective Laser Trabeculoplasty in Medication-Naïve Open Angle Glaucoma and Ocular Hypertension during the LiGHT Trial

PURPOSE: To determine the efficacy of repeat selective laser trabeculoplasty (SLT) in medication-naïve open angle glaucoma (OAG) and ocular hypertensive (OHT) patients requiring repeat treatment for early to medium-term failure during the Laser in Glaucoma and Ocular Hypertension (LiGHT) trial. // DESIGN: Post-hoc analysis of SLT treatment arm of a multicentre prospective randomised-controlled-trial. // PARTICIPANTS: Treatment-naïve OAG or OHT requiring repeat 360-degree SLT within 18 months. Re-treatment was triggered by pre-defined IOP and disease-progression criteria (using objective individualised target IOPs) // METHODS: After SLT at baseline, patients were followed for a minimum of 18 months after second (‘repeat’) SLT. A mixed model analysis was performed with the eye as the unit of analysis, with crossed random-effects to adjust for correlation between fellow eyes and repeated measures within eyes. Kaplan-Meier curves plot the duration of effect. // OUTCOME MEASURES: Initial (‘early’) IOP lowering at 2-months and duration of effect following initial and Repeat SLT. // RESULTS: 115 eyes of 90 patients received Repeat SLT during first 18 months of the trial. Pre-treatment IOP prior to Initial SLT was significantly higher than that prior to pre-retreatment IOP of Repeat SLT (mean difference: 3.4, 95% confidence interval (CI) 2.6 to 4.3, mmHg; p<0.001). Absolute IOP reduction at 2-months was greater following Initial, compared to Repeat, SLT (mean difference: 1.0, 95% CI 0.2 to 1.8, mmHg; p=0.02). Adjusted absolute IOP reduction at 2-months (adjusting for IOP prior to initial or repeat laser) was greater following Repeat SLT (adjusted mean difference: -1.1, 95% CI -1.7 to -0.5, mmHg; p=0.001). 34 eyes were ‘early failures’ (retreated 2-months after Initial SLT) vs 81 ‘later failures’ (retreatment beyond 2-months following Initial SLT). No significant difference in early absolute IOP reduction at 2-months following Repeat SLT was noted between ‘early’ vs ‘later’ failures’ (mean difference: 0.3, 95% CI, -1.1 to 1.8,mmHg; p=0.655). Repeat SLT maintained drop-free IOP control in 67% of 115 eyes at 18 months, with no clinically-relevant adverse events. // CONCLUSION: These exploratory analyses demonstrate Repeat SLT can maintain IOP at or below Target IOP in medication-naive OAG and OHT eyes requiring retreatment with atleast an equivalent duration of effect to initial laser

Finding long cycles in graphs

We analyze the problem of discovering long cycles inside a graph. We propose and test two algorithms for this task. The first one is based on recent advances in statistical mechanics and relies on a message passing procedure. The second follows a more standard Monte Carlo Markov Chain strategy. Special attention is devoted to Hamiltonian cycles of (non-regular) random graphs of minimal connectivity equal to three

Laser in Glaucoma and Ocular Hypertension (LiGHT) Trial. A multicentre, randomised controlled trial: design and methodology

PURPOSE: The Laser in Glaucoma and Ocular Hypertension (LiGHT) Trial aims to establish whether initial treatment with selective laser trabeculoplasty (SLT) is superior to initial treatment with topical medication for primary open-angle glaucoma (POAG) or ocular hypertension (OHT). DESIGN: The LiGHT Trial is a prospective, unmasked, multicentre, pragmatic, randomised controlled trial. 718 previously untreated patients with POAG or OHT were recruited at six collaborating centres in the UK between 2012 and 2014. The trial comprises two treatment arms: initial SLT followed by conventional medical therapy as required, and medical therapy without laser therapy. Randomisation was provided online by a web-based randomisation service. Participants will be monitored for 3 years, according to routine clinical practice. The target intraocular pressure (IOP) was set at baseline according to an algorithm, based on disease severity and lifetime risk of loss of vision at recruitment, and subsequently adjusted on the basis of IOP control, optic disc and visual field. The primary outcome measure is health-related quality of life (HRQL) (EQ-5D five-level). Secondary outcomes are treatment pathway cost and cost-effectiveness, Glaucoma Utility Index, Glaucoma Symptom Scale, Glaucoma Quality of Life, objective measures of pathway effectiveness, visual function and safety profiles and concordance. A single main analysis will be performed at the end of the trial on an intention-to-treat basis. CONCLUSIONS: The LiGHT Trial is a multicentre, pragmatic, randomised clinical trial that will provide valuable data on the relative HRQL, clinical effectiveness and cost-effectiveness of SLT and topical IOP-lowering medication. TRIAL REGISTRATION NUMBER: ISRCTN32038223, Pre-results

Introducing the student designer to the role of emotion in design

This is a conference paper.Products satisfy needs beyond the functional. These needs may include aspirations, emotions, cultural and social needs. It is crucial that designers are equipped to deal with the emotional domain of products and users. Carlson (1997) considered emotion to be short term waves of feeling arising without conscious effort, whereas mood, is defined as a longer termed state with less intensity. The authors’ working definition of the ‘emotional domain’ is the range of states of mind (which may influence the body) and which are influenced by internal and external stimuli. These effects tend to be transient although an individual will have a tendency towards a particular state, such as melancholy, happiness, calmness and so on. But even here various stimuli can cause a significant swing in state of mind. But this is a highly individual effect for example, one person may find the new iMac computer delightful and cheerful, where as others, may find it irritating and repulsive

Circuits in random graphs: from local trees to global loops

We compute the number of circuits and of loops with multiple crossings in random regular graphs. We discuss the importance of this issue for the validity of the cavity approach. On the one side we obtain analytic results for the infinite volume limit in agreement with existing exact results. On the other side we implement a counting algorithm, enumerate circuits at finite N and draw some general conclusions about the finite N behavior of the circuits.Comment: submitted to JSTA