Kempe equivalence of colourings of cubic graphs

Given a graph G=(V,E) and a proper vertex colouring of G, a Kempe chain is a subset of V that induces a maximal connected subgraph of G in which every vertex has one of two colours. To make a Kempe change is to obtain one colouring from another by exchanging the colours of vertices in a Kempe chain. Two colourings are Kempe equivalent if each can be obtained from the other by a series of Kempe changes. A conjecture of Mohar asserts that, for k≥3, all k-colourings of connected k-regular graphs that are not complete are Kempe equivalent. We address the case k=3 by showing that all 3-colourings of a connected cubic graph G are Kempe equivalent unless G is the complete graph K4 or the triangular prism

Recognizing Graphs Close to Bipartite Graphs with an Application to Colouring Reconfiguration

We continue research into a well-studied family of problems that ask whether the vertices of a given graph can be partitioned into sets A and B, where A is an independent set and B induces a graph from some specified graph class G. We consider the case where G is the class of k-degenerate graphs. This problem is known to be polynomial-time solvable if k = 0 (recognition of bipartite graphs), but NP-complete if k = 1 (near-bipartite graphs) even for graphs of maximum degree 4. Yang and Yuan [DM, 2006] showed that the k = 1 case is polynomial-time solvable for graphs of maximum degree 3. This also follows from a result of Catlin and Lai [DM, 1995]. We study the general k ≥ 1 case for n-vertex graphs of maximum degree k + 2 We show how to find A and B in O(n) time for k = 1, and in O(n 2 ) time for k ≥ 2. Together, these results provide an algorithmic version of a result of Catlin [JCTB, 1979] and also provide an algorithmic version of a generalization of Brook’s Theorem, proved by Borodin, Kostochka and Toft [DM, 2000] and Matamala [JGT, 2007]. The results also enable us to solve an open problem of Feghali et al. [JGT, 2016]. For a given graph G and positive integer `, the vertex colouring reconfiguration graph of G has as its vertex set the set of `-colourings of G and contains an edge between each pair of colourings that differ on exactly on vertex. We complete the complexity classification of the problem of finding a path in the reconfiguration graph between two given `-colourings of a given graph of maximum degree k

The 1064-nm Nd:YAG Photobiomodulation vs. 20% Benzocaine Topical Gel in Inducing Mucosal Anesthetic Effect: A Double-Blind Randomized Clinical Trial

The periapical local anesthetic injection may be associated with fear of needles and pain administration. Dental topical anesthetic agents can help to reduce pain perception; however, adverse events can occur. To investigate the efficacy of 1064-nm photobiomodualtion (PBM) in inducing mucosal anesthesia delivered with a flat-top hand-piece compared to 20% Benzocaine topical anesthetic gel, sixty healthy patients were randomly allocated (1:1) to either 20% benzocaine topical gel + placebo laser (T group) or PBM + placebo gel (L group). The 1064-nm Nd:YAG laser was employed and is associated with a novel flat-top hand piece. The applied operational parameters were 0.5 W, 10 Hz, 100 µs pulse width, and 30 J/cm2 for one-minute single application time. The enrolled subjects were asked to assess pain intensity at the time of anesthetic injection with a Visual Analog Scale. Taking into consideration taste, undesirable numbness, and overall satisfaction, the patients were asked to rate their experiences according to a verbal rating scale. Statistical analysis showed no statistically significant difference between the T and L Groups for pain ratings (p = 0.0596). The L Group displayed significantly higher ratings than T Group for taste, undesirable numbness, and overall satisfaction (p < 0.001). The 1064-nm PBM delivered by flat-top hand piece is effective in inducing mucosal anesthesia, eliminating the adverse side-effects of the conventional topical anesthetic gel

Frontiers of antifibrotic therapy in systemic sclerosis

Although fibrosis is becoming increasingly recognized as a major cause of morbidity and mortality in modern societies, targeted anti-fibrotic therapies are still not approved for most fibrotic disorders. However, intense research over the last decade has improved our understanding of the underlying pathogenesis of fibrotic diseases. We now appreciate fibrosis as the consequence of a persistent tissue repair responses, which, in contrast to normal wound healing, fails to be effectively terminated. Profibrotic mediators released from infiltrating leukocytes, activated endothelial cells and degranulated platelets may predominantly drive fibroblast activation and collagen release in early stages, whereas endogenous activation of fibroblasts due epigenetic modifications and biomechanical or physical factors such as stiffening of the extracellular matrix and hypoxia may play pivotal role for disease progression in later stages. In the present review, we discuss novel insights into the pathogenesis of fibrotic diseases using systemic sclerosis (SSc) as example for an idiopathic, multisystem disorder. We set a strong translational focus and predominantly discuss approaches with very high potential for rapid transfer from bench-to-bedside. We highlight the molecular basis for ongoing clinical trials in SSc and also provide an outlook on upcoming trials. This article is protected by copyright. All rights reserved

A Reconfigurations Analogue of Brooks’ Theorem

Let G be a simple undirected graph on n vertices with maximum degree Δ. Brooks’ Theorem states that G has a Δ-colouring unless G is a complete graph, or a cycle with an odd number of vertices. To recolour G is to obtain a new proper colouring by changing the colour of one vertex. We show that from a k-colouring, k > Δ, a Δ-colouring of G can be obtained by a sequence of O(n 2) recolourings using only the original k colours unless G is a complete graph or a cycle with an odd number of vertices, or k = Δ + 1, G is Δ-regular and, for each vertex v in G, no two neighbours of v are coloured alike. We use this result to study the reconfiguration graph R k (G) of the k-colourings of G. The vertex set of R k (G) is the set of all possible k-colourings of G and two colourings are adjacent if they differ on exactly one vertex. It is known that if k ≤ Δ(G), then R k (G) might not be connected and it is possible that its connected components have superpolynomial diameter, if k ≥ Δ(G) + 2, then R k (G) is connected and has diameter O(n 2). We complete this structural classification by settling the missing case: if k = Δ(G) + 1, then R k (G) consists of isolated vertices and at most one further component which has diameter O(n 2). We also describe completely the computational complexity classification of the problem of deciding whether two k-colourings of a graph G of maximum degree Δ belong to the same component of R k (G) by settling the case k = Δ(G) + 1. The problem is O(n 2) time solvable for k = 3, PSPACE-complete for 4 ≤ k ≤ Δ(G), O(n) time solvable for k = Δ(G) + 1, O(1) time solvable for k ≥ Δ(G) + 2 (the answer is always yes)

TGF-β Isoform Specific Regulation of Airway Inflammation and Remodelling in a Murine Model of Asthma

The TGF-β family of mediators are thought to play important roles in the regulation of inflammation and airway remodelling in asthma. All three mammalian isoforms of TGF-β, TGF-β1–3, are expressed in the airways and TGF-β1 and -β2 are increased in asthma. However, there is little information on the specific roles of individual TGF-β isoforms. In this study we assess the roles of TGF-β1 and TGF-β2 in the regulation of allergen-induced airway inflammation and remodelling associated with asthma, using a validated murine model of ovalbumin sensitization and challenge, and isoform specific TGF-β neutralising antibodies. Antibodies to both isoforms inhibited TGF-β mediated Smad signalling. Anti-TGF-β1 and anti-TGF-β2 inhibited ovalbumin-induced sub-epithelial collagen deposition but anti-TGF-β1 also specifically regulated airway and fibroblast decorin deposition by TGF-β1. Neither antibody affected the allergen-induced increase in sub-epithelial fibroblast-like cells. Anti- TGF-β1 also specifically inhibited ovalbumin-induced increases in monocyte/macrophage recruitment. Whereas, both TGF-β1 and TGF-β2 were involved in regulating allergen-induced increases in eosinophil and lymphocyte numbers. These data show that TGF-β1 and TGF-β2 exhibit a combination of specific and shared roles in the regulation of allergen-induced airway inflammation and remodelling. They also provide evidence in support of the potential for therapeutic regulation of specific subsets of cells and extracellular matrix proteins associated with inflammation and remodelling in airway diseases such as asthma and COPD, as well as other fibroproliferative diseases

Recognizing graphs close to bipartite graphs.

We continue research into a well-studied family of problems that ask if the vertices of a graph can be partitioned into sets A and B, where A is an independent set and B induces a graph from some specified graph class G. We let G be the class of k-degenerate graphs. The problem is known to be polynomial-time solvable if k=0 (bipartite graphs) and NP-complete if k=1 (near-bipartite graphs) even for graphs of diameter 4, as shown by Yang and Yuan, who also proved polynomial-time solvability for graphs of diameter 2. We show that recognizing near-bipartite graphs of diameter 3 is NP-complete resolving their open problem. To answer another open problem, we consider graphs of maximum degree D on n vertices. We show how to find A and B in O(n) time for k=1 and D=3, and in O(n^2) time for k >= 2 and D >= 4. These results also provide an algorithmic version of a result of Catlin [JCTB, 1979] and enable us to complete the complexity classification of another problem: finding a path in the vertex colouring reconfiguration graph between two given k-colourings of a graph of bounded maximum degree

Transcriptome analysis reveals differential splicing events in IPF lung tissue

Idiopathic pulmonary fibrosis (IPF) is a complex disease in which a multitude of proteins and networks are disrupted. Interrogation of the transcriptome through RNA sequencing (RNA-Seq) enables the determination of genes whose differential expression is most significant in IPF, as well as the detection of alternative splicing events which are not easily observed with traditional microarray experiments. We sequenced messenger RNA from 8 IPF lung samples and 7 healthy controls on an Illumina HiSeq 2000, and found evidence for substantial differential gene expression and differential splicing. 873 genes were differentially expressed in IPF (FDR<5%), and 440 unique genes had significant differential splicing events in at least one exonic region (FDR<5%). We used qPCR to validate the differential exon usage in the second and third most significant exonic regions, in the genes COL6A3 (RNA-Seq adjusted pval = 7.18e-10) and POSTN (RNA-Seq adjusted pval = 2.06e-09), which encode the extracellular matrix proteins collagen alpha-3(VI) and periostin. The increased gene-level expression of periostin has been associated with IPF and its clinical progression, but its differential splicing has not been studied in the context of this disease. Our results suggest that alternative splicing of these and other genes may be involved in the pathogenesis of IPF. We have developed an interactive web application which allows users to explore the results of our RNA-Seq experiment, as well as those of two previously published microarray experiments, and we hope that this will serve as a resource for future investigations of gene regulation in IPF. © 2014 Nance et al

Sample-ready multiplex qPCR assay for detection of malaria

BACKGROUND: Microscopy and antigen detecting rapid diagnostic tests are the diagnostic tests of choice in management of clinical malaria. However, due to their limitations, the need to utilize more sensitive methods such as real-time PCR (qPCR) is evident as more studies are now utilizing molecular methods in detection of malaria. Some of the challenges that continue to limit the widespread utilization of qPCR include lack of assay standardization, assay variability, risk of contamination, and the need for cold-chain. Lyophilization of molecular assays can overcome some of these limitations and potentially enable widespread qPCR utilization. METHODS: A recently published multiplex malaria qPCR assay was lyophilized by freezing drying into Sample-Ready™ format (MMSR). MMSR assay contained all the required reagents for qPCR including primers and probes, requiring only the addition of water and sample to perform qPCR. The performance of the MMSR assay was compared to the non-freeze dried, “wet” assay. Stability studies were done by maintaining the MMSR assays at four different ambient temperatures of 4°C, room temperature (RT), 37°C and 42°C over a period of 42 days, tested at seven-day intervals. Plasmodium falciparum and Plasmodium vivax DNAs were used for analysis of the MMSR assay either as single or mixed parasites, at two different concentrations. The C(T) values and the standard deviations (SD) were used in the analysis of the assay performance. RESULTS: The limit of detection for the MMSR assay was 0.244 parasites/μL for Plasmodium spp. (PLU) and P. falciparum (FAL) assay targets compared to “wet” assay which was 0.39 and 3.13 parasites/μL for PLU and FAL assay targets, respectively. The MMSR assay performed with high efficiencies similar to those of the “wet” assay and was stable at 37°C for 42 days, with estimated shelf-life of 5 months. When used to analyse field clinical samples, MMSR assay performed with 100% sensitivity and specificity compared to the “wet” assay. CONCLUSION: The MMSR assay has the same robust performance characteristics as the “wet” assay and is highly stable. Availability of MMSR assay allows flexibility and provides an option in choosing assay for malaria diagnostics depending on the application, needs and budget