KP line solitons and Tamari lattices

The KP-II equation possesses a class of line soliton solutions which can be qualitatively described via a tropical approximation as a chain of rooted binary trees, except at "critical" events where a transition to a different rooted binary tree takes place. We prove that these correspond to maximal chains in Tamari lattices (which are poset structures on associahedra). We further derive results that allow to compute details of the evolution, including the critical events. Moreover, we present some insights into the structure of the more general line soliton solutions. All this yields a characterization of possible evolutions of line soliton patterns on a shallow fluid surface (provided that the KP-II approximation applies).Comment: 49 pages, 36 figures, second version: section 4 expande

Functional characterization of two PLP-dependent enzymes involved in capsular polysaccharide biosynthesis from campylobacter jejuni

Campylobacter jejuni is a Gram-negative, pathogenic bacterium that causes campylobacteriosis, a form of gastroenteritis. C. jejuni is the most frequent cause of food-borne illness in the world, surpassing Salmonella and E. coli. Coating the surface of C. jejuni is a layer of sugar molecules known as the capsular polysaccharide that, in C. jejuni NCTC 11168, is composed of a repeating unit of d-glycero-l-gluco-heptose, d-glucuronic acid, d-N-acetyl-galactosamine, and d-ribose. The d-glucuronic acid moiety is further amidated with either serinol or ethanolamine. It is unknown how these modifications are synthesized and attached to the polysaccharide. Here, we report the catalytic activities of two previously uncharacterized, pyridoxal phosphate (PLP)-dependent enzymes, Cj1436 and Cj1437, from C. jejuni NCTC 11168. Using a combination of mass spectrometry and nuclear magnetic resonance, we determined that Cj1436 catalyzes the decarboxylation of l-serine phosphate to ethanolamine phosphate. Cj1437 was shown to catalyze the transamination of dihydroxyacetone phosphate to (S)-serinol phosphate in the presence of l-glutamate. The probable routes to the ultimate formation of the glucuronamide substructures in the capsular polysaccharides of C. jejuni are discussed

Many non-equivalent realizations of the associahedron

Hohlweg and Lange (2007) and Santos (2004, unpublished) have found two different ways of constructing exponential families of realizations of the n-dimensional associahedron with normal vectors in {0,1,-1}^n, generalizing the constructions of Loday (2004) and Chapoton-Fomin-Zelevinsky (2002). We classify the associahedra obtained by these constructions modulo linear equivalence of their normal fans and show, in particular, that the only realization that can be obtained with both methods is the Chapoton-Fomin-Zelevinsky (2002) associahedron. For the Hohlweg-Lange associahedra our classification is a priori coarser than the classification up to isometry of normal fans, by Bergeron-Hohlweg-Lange-Thomas (2009). However, both yield the same classes. As a consequence, we get that two Hohlweg-Lange associahedra have linearly equivalent normal fans if and only if they are isometric. The Santos construction, which produces an even larger family of associahedra, appears here in print for the first time. Apart of describing it in detail we relate it with the c-cluster complexes and the denominator fans in cluster algebras of type A. A third classical construction of the associahedron, as the secondary polytope of a convex n-gon (Gelfand-Kapranov-Zelevinsky, 1990), is shown to never produce a normal fan linearly equivalent to any of the other two constructions.Comment: 30 pages, 13 figure

Long-term prognosis for 1-year relapse-free survivors of CD34 cell-selected allogeneic hematopoietic stem cell transplantation : a landmark analysis

Altres ajuts: This research was supported in part by National Institutes of Health award number P01 CA23766 and NIH/NCI Cancer Center Support Grant P30 CA008748. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.CD34 selection significantly improves GVHD-free survival in allogeneic hematopoietic cell transplantation (allo-HSCT). Specific information regarding long-term prognosis and risk factors for late mortality after CD34-selected allo-HSCT is lacking, however. We conducted a single-center landmark analysis in 276 patients alive without relapse 1 year after CD34-selected allo-HSCT for AML (n=164), ALL (n=33), or MDS (n=79). At 5 years' follow-up after the 1-year landmark (range 0.03-13 years), estimated RFS was 73% and OS 76%. The 5-year cumulative incidence of relapse and NRM were 11% and 16%, respectively. In multivariate analysis, HCT-CI score ≥ 3 correlated with marginally worse RFS (HR 1.78, 95% CI 0.97-3.28, p=0.06) and significantly worse OS (HR 2.53, 95% CI 1.26-5.08, p=0.004). Despite only 24% of patients with acute GVHD within 1 year, this also significantly correlated with worse RFS and OS, with increasing grades of acute GVHD associating with increasingly poorer survival on multivariate analysis (p<0.0001). Of 63 deaths after the landmark, GVHD accounted for 27% of deaths and was the most common cause of late mortality, followed by relapse and infection. While prognosis is excellent for patients alive without relapse 1 year after CD34-selected allo-HSCT, risks of late relapse and NRM persist, particularly due to GVHD