Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.

Assessment of plasma chitotriosidase activity, CCL18/PARC concentration and NP-C suspicion index in the diagnosis of Niemann-Pick disease type C: A prospective observational study

Background: Niemann-Pick disease type C (NP-C) is a rare, autosomal recessive neurodegenerative disease caused by mutations in either the NPC1 or NPC2 genes. The diagnosis of NP-C remains challenging due to the non-specific, heterogeneous nature of signs/symptoms. This study assessed the utility of plasma chitotriosidase (ChT) and Chemokine (C-C motif) ligand 18 (CCL18)/pulmonary and activation-regulated chemokine (PARC) in conjunction with the NP-C suspicion index (NP-C SI) for guiding confirmatory laboratory testing in patients with suspected NP-C. Methods: In a prospective observational cohort study, incorporating a retrospective determination of NP-C SI scores, two different diagnostic approaches were applied in two separate groups of unrelated patients from 51 Spanish medical centers (n = 118 in both groups). From Jan 2010 to Apr 2012 (Period 1), patients with =2 clinical signs/symptoms of NP-C were considered ''suspected NP-C'' cases, and NPC1/NPC2 sequencing, plasma chitotriosidase (ChT), CCL18/PARC and sphingomyelinase levels were assessed. Based on findings in Period 1, plasma ChT and CCL18/PARC, and NP-C SI prediction scores were determined in a second group of patients between May 2012 and Apr 2014 (Period 2), and NPC1 and NPC2 were sequenced only in those with elevated ChT and/or elevated CCL18/PARC and/or NP-C SI =70. Filipin staining and 7-ketocholesterol (7-KC) measurements were performed in all patients with NP-C gene mutations, where possible. Results: In total across Periods 1 and 2, 10/236 (4%) patients had a confirmed diagnosis o NP-C based on gene sequencing (5/118 4.2%] in each Period): all of these patients had two causal NPC1 mutations. Single mutant NPC1 alleles were detected in 8/236 (3%) patients, overall. Positive filipin staining results comprised three classical and five variant biochemical phenotypes. No NPC2 mutations were detected. All patients with NPC1 mutations had high ChT activity, high CCL18/PARC concentrations and/or NP-C SI scores =70. Plasma 7-KC was higher than control cut-off values in all patients with two NPC1 mutations, and in the majority of patients with single mutations. Family studies identified three further NP-C patients. Conclusion: This approach may be very useful for laboratories that do not have mass spectrometry facilities and therefore, they cannot use other NP-C biomarkers for diagnosis

The challenge of habitat modelling for threatened low density species using heterogeneous data : the case of Cuvier’s beaked whales in the Mediterranean

We are grateful to the ACCOBAMS Secretariat for their support in this work, including a small grant for the analysis.The Mediterranean population of Cuvieŕs beaked whale (Ziphius cavirostris), a deep-diving cetacean, is genetically distinct from the Atlantic, and subject to a number of conservation threats, in particular underwater noise. It is also cryptic at the surface and relatively rare, so obtain robust knowledge on distribution and abundance presents unique challenges. Here we use multiplatform and multiyear survey data to analyse the distribution and abundance of this species across the Mediterranean Sea. We use a novel approach combining heterogeneous data gathered with different methods to obtain a single density index for the region. A total of 594,996 km of survey effort and 507 sightings of Cuvier’s beaked whales, from 1990 to 2016, were pooled together from 24 different sources. Data were divided into twelve major groups according to platform height, speed and sea state. Both availability bias and effective strip width were calculated from the sightings with available perpendicular distance data. This was extrapolated to the rest of the sightings for each of the twelve groups. Habitat preference models were fitted into a GAM framework using counts of groups as a response variable with the effective searched area as an offset. Depth, coefficient of variation of depth, longitude and marine regions (as defined by the International Hydrographic Organization) were identified as important predictors. Predicted abundance of groups per grid cell were multiplied by mean group size to obtain a prediction of the abundance of animals. A total abundance of 5799 (CV = 24.0%) animals was estimated for the whole Mediterranean basin. The Alborán Sea, Ligurian Sea, Hellenic Trench, southern Adriatic Sea and eastern Ionian Sea were identified as being the main hot spots in the region. It is important to urge that the relevant stakeholders incorporate this information in the planning and execution of high risk activities in these high-risk areas.PostprintPeer reviewe

Global surveillance of cancer survival 1995-2009: analysis of individual data for 25,676,887 patients from 279 population-based registries in 67 countries (CONCORD-2)

BACKGROUND: Worldwide data for cancer survival are scarce. We aimed to initiate worldwide surveillance of cancer survival by central analysis of population-based registry data, as a metric of the effectiveness of health systems, and to inform global policy on cancer control. METHODS: Individual tumour records were submitted by 279 population-based cancer registries in 67 countries for 25·7 million adults (age 15-99 years) and 75,000 children (age 0-14 years) diagnosed with cancer during 1995-2009 and followed up to Dec 31, 2009, or later. We looked at cancers of the stomach, colon, rectum, liver, lung, breast (women), cervix, ovary, and prostate in adults, and adult and childhood leukaemia. Standardised quality control procedures were applied; errors were corrected by the registry concerned. We estimated 5-year net survival, adjusted for background mortality in every country or region by age (single year), sex, and calendar year, and by race or ethnic origin in some countries. Estimates were age-standardised with the International Cancer Survival Standard weights. FINDINGS: 5-year survival from colon, rectal, and breast cancers has increased steadily in most developed countries. For patients diagnosed during 2005-09, survival for colon and rectal cancer reached 60% or more in 22 countries around the world; for breast cancer, 5-year survival rose to 85% or higher in 17 countries worldwide. Liver and lung cancer remain lethal in all nations: for both cancers, 5-year survival is below 20% everywhere in Europe, in the range 15-19% in North America, and as low as 7-9% in Mongolia and Thailand. Striking rises in 5-year survival from prostate cancer have occurred in many countries: survival rose by 10-20% between 1995-99 and 2005-09 in 22 countries in South America, Asia, and Europe, but survival still varies widely around the world, from less than 60% in Bulgaria and Thailand to 95% or more in Brazil, Puerto Rico, and the USA. For cervical cancer, national estimates of 5-year survival range from less than 50% to more than 70%; regional variations are much wider, and improvements between 1995-99 and 2005-09 have generally been slight. For women diagnosed with ovarian cancer in 2005-09, 5-year survival was 40% or higher only in Ecuador, the USA, and 17 countries in Asia and Europe. 5-year survival for stomach cancer in 2005-09 was high (54-58%) in Japan and South Korea, compared with less than 40% in other countries. By contrast, 5-year survival from adult leukaemia in Japan and South Korea (18-23%) is lower than in most other countries. 5-year survival from childhood acute lymphoblastic leukaemia is less than 60% in several countries, but as high as 90% in Canada and four European countries, which suggests major deficiencies in the management of a largely curable disease. INTERPRETATION: International comparison of survival trends reveals very wide differences that are likely to be attributable to differences in access to early diagnosis and optimum treatment. Continuous worldwide surveillance of cancer survival should become an indispensable source of information for cancer patients and researchers and a stimulus for politicians to improve health policy and health-care systems

Updated precision measurement of the average lifetime of B hadrons

The measurement of the average lifetime of B hadrons using inclusively reconstructed secondary vertices has been updated using both an improved processing of previous data and additional statistics from new data. This has reduced the statistical and systematic uncertainties and gives \tau_{\mathrm{B}} = 1.582 \pm 0.011\ \mathrm{(stat.)} \pm 0.027\ \mathrm{(syst.)}\ \mathrm{ps.} Combining this result with the previous result based on charged particle impact parameter distributions yields \tau_{\mathrm{B}} = 1.575 \pm 0.010\ \mathrm{(stat.)} \pm 0.026\ \mathrm{(syst.)}\ \mathrm{ps.

Limits on the production of scalar leptoquarks from Z (0) decays at LEP

A search has been made for pairs and for single production of scalar leptoquarks of the first and second generations using a data sample of 392000 Z0 decays from the DELPHI detector at LEP 1. No signal was found and limits on the leptoquark mass, production cross section and branching ratio were set. A mass limit at 95% confidence level of 45.5 GeV/c2 was obtained for leptoquark pair production. The search for the production of a single leptoquark probed the mass region above this limit and its results exclude first and second generation leptoquarks D0 with masses below 65 GeV/c2 and 73 GeV/c2 respectively, at 95% confidence level, assuming that the D0lq Yukawa coupling alpha(lambda) is equal to the electromagnetic one. An upper limit is also given on the coupling alpha(lambda) as a function of the leptoquark mass m(D0)