Path coupling using stopping times and counting independent sets and colorings in hypergraphs

We analyse the mixing time of Markov chains using path coupling with stopping times. We apply this approach to two hypergraph problems. We show that the Glauber dynamics for independent sets in a hypergraph mixes rapidly as long as the maximum degree Δ of a vertex and the minimum size m of an edge satisfy m ≥ 2Δ + 1. We also show that the Glauber dynamics for proper q‐colorings of a hypergraph mixes rapidly if m ≥ 4 and q > Δ, and if m = 3 and q ≥ 1.65Δ. We give related results on the hardness of exact and approximate counting for both problems. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Weakly Pseudocompact Frames

We define the notion of weak pseudocompactness for frames and present several characterizations. Among them are characterizations in terms of strong inclusions, uniformities and cozero bases. Noteworthy is the fact that these internal characterizations are not translated from characterizations of weakly pseudocompact spaces.      

Embeddings of root systems I: Root systems over commutative rings

This paper gives examples of embeddings of root systems of Coxeter groups, including sporadic embeddings of standard real root systems in other standard real root systems, and, for a general Coxeter group, an embedding of its universal symmetric root system over commutative rings into the standard real root system of a simply laced Coxeter group.     

Evaluation of Raman probe for oesophageal cancer diagnostics

Early detection of (pre-)cancerous changes improves prognosis, therefore in the UK patients at high risk of developing gastrointestinal cancers are enrolled on endoscopic surveillance programmes or the Bowel Cancer Screening Programme. The current gold standard technique for the detection of pre-cancerous changes in the gastrointestinal tract is histopathological analysis of biopsy tissue collected at endoscopy. This relies upon subjective assessment of morphological changes within the excised tissue samples and poor targeting of pre-malignant lesions. Raman spectroscopy offers a number of potential advantages for in vivo assessment of tissue at endoscopy. The performance of a custom built Raman probe as a biopsy targeting tool has been evaluated using excised biopsy material. Multivariate classification models have been used to demonstrate the likely ability of a miniature, confocal, fibre optic Raman probe to be used as an optical biopsy tool at endoscopy to provide spectral information in clinically practicable timescales. This technique could facilitate improved targeting of excisional biopsy with associated clinical benefits.     

Raman spectroscopy--a new method for the intra-operative assessment of axillary lymph nodes

Sentinel Lymph Node Biopsy has become the standard surgical procedure for the sampling of axillary lymph nodes in breast cancer. Intra operative node assessment is currently not offered to the majority of patients but would allow definitive axillary surgery to take place immediately. This would confer benefits both to the patient and to the healthcare system. Our experimental study aims to demonstrate that a Raman spectroscopy probe device could overcome many of the disadvantages of current intra-operative analysis techniques. 38 axillary lymph nodes, 25 negative and 13 positive from 20 patients undergoing breast surgery for invasive breast cancer were assessed using a commercially available Raman spectroscopy probe. Spectra were assessed using principal component fed linear discriminant analysis trained by the histopathology results. Leave one node out cross validation achieved a sensitivity of up to 92% and a specificity of up to 100% in differentiating between normal and metastatic lymph nodes.