Nonrepetitive Colouring via Entropy Compression

A vertex colouring of a graph is \emph{nonrepetitive} if there is no path whose first half receives the same sequence of colours as the second half. A graph is nonrepetitively $k$-choosable if given lists of at least $k$ colours at each vertex, there is a nonrepetitive colouring such that each vertex is coloured from its own list. It is known that every graph with maximum degree $\Delta$ is $c\Delta^2$-choosable, for some constant $c$. We prove this result with $c=1$ (ignoring lower order terms). We then prove that every subdivision of a graph with sufficiently many division vertices per edge is nonrepetitively 5-choosable. The proofs of both these results are based on the Moser-Tardos entropy-compression method, and a recent extension by Grytczuk, Kozik and Micek for the nonrepetitive choosability of paths. Finally, we prove that every graph with pathwidth $k$ is nonrepetitively $O(k^{2})$-colourable.Comment: v4: Minor changes made following helpful comments by the referee

Magnetic resonance imaging as a non-invasive method for the assessment of pancreatic fibrosis (MINIMAP): a comprehensive study design from the consortium for the study of chronic pancreatitis, diabetes, and pancreatic cancer

Characteristic features of chronic pancreatitis (CP) may be absent on standard imaging studies. Quantitative Magnetic Resonance Imaging (MRI) techniques such as T1 mapping, extracellular volume (ECV) fraction, diffusion-weighted imaging (DWI) with apparent diffusion coefficient map (ADC), MR elastography (MRE), and T1-weighted signal intensity ratio (SIR) have shown promise for the diagnosis and grading severity of CP. However, radiologists still use the Cambridge classification which is based on traditional ductal imaging alone. There is an urgent need to develop new diagnostic criteria that incorporate both parenchymal and ductal features of CP seen by MRI/MRCP. Designed to fulfill this clinical need, we present the MINIMAP study, which was funded in September 2018 by the National Institutes of Health. This is a comprehensive quantitative MR imaging study which will be performed at multiple institutions in well-phenotyped CP patient cohorts. We hypothesize that quantitative MRI/MRCP features can serve as valuable non-invasive imaging biomarkers to detect and grade CP. We will evaluate the role of T1 relaxometry, ECV, T1-weighted gradient echo SIR, MRE, arteriovenous enhancement ratio, ADC, pancreas volume/atrophy, pancreatic fat fraction, ductal features, and pancreatic exocrine output following secretin stimulation in the assessment of CP. We will attempt to generate a multi-parametric pancreatic tissue fibrosis (PTF) scoring system. We anticipate that a quantitative scoring system may serve as a biomarker of pancreatic fibrosis; hence this imaging technique can be used in clinical practice as well as clinical trials to evaluate the efficacy of agents which may slow the progression or reverse measures of CP

Rapid automatic segmentation of abnormal tissue in late gadolinium enhancement cardiovascular magnetic resonance images for improved management of long-standing persistent atrial fibrillation

Background: Atrial fibrillation (AF) is the most common heart rhythm disorder. In order for late Gd enhancement cardiovascular magnetic resonance (LGE CMR) to ameliorate the AF management, the ready availability of the accurate enhancement segmentation is required. However, the computer-aided segmentation of enhancement in LGE CMR of AF is still an open question. Additionally, the number of centres that have reported successful application of LGE CMR to guide clinical AF strategies remains low, while the debate on LGE CMR’s diagnostic ability for AF still holds. The aim of this study is to propose a method that reliably distinguishes enhanced (abnormal) from non-enhanced (healthy) tissue within the left atrial wall of (pre-ablation and 3 months post-ablation) LGE CMR data-sets from long-standing persistent AF patients studied at our centre. Methods: Enhancement segmentation was achieved by employing thresholds benchmarked against the statistics of the whole left atrial blood-pool (LABP). The test-set cross-validation mechanism was applied to determine the input feature representation and algorithm that best predict enhancement threshold levels. Results: Global normalized intensity threshold levels T PRE = 1 1/4 and T POST = 1 5/8 were found to segment enhancement in data-sets acquired pre-ablation and at 3 months post-ablation, respectively. The segmentation results were corroborated by using visual inspection of LGE CMR brightness levels and one endocardial bipolar voltage map. The measured extent of pre-ablation fibrosis fell within the normal range for the specific arrhythmia phenotype. 3D volume renderings of segmented post-ablation enhancement emulated the expected ablation lesion patterns. By comparing our technique with other related approaches that proposed different threshold levels (although they also relied on reference regions from within the LABP) for segmenting enhancement in LGE CMR data-sets of AF patients, we illustrated that the cut-off levels employed by other centres may not be usable for clinical studies performed in our centre. Conclusions: The proposed technique has great potential for successful employment in the AF management within our centre. It provides a highly desirable validation of the LGE CMR technique for AF studies. Inter-centre differences in the CMR acquisition protocol and image analysis strategy inevitably impede the selection of a universally optimal algorithm for segmentation of enhancement in AF studies

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India NSE Deepak Nitrite 24 Months Stock data

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COVID-19 Treatments and Vaccines developmen

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