The Tchebyshev transforms of the first and second kind

We give an in-depth study of the Tchebyshev transforms of the first and second kind of a poset, recently discovered by Hetyei. The Tchebyshev transform (of the first kind) preserves desirable combinatorial properties, including Eulerianess (due to Hetyei) and EL-shellability. It is also a linear transformation on flag vectors. When restricted to Eulerian posets, it corresponds to the Billera, Ehrenborg and Readdy omega map of oriented matroids. One consequence is that nonnegativity of the cd-index is maintained. The Tchebyshev transform of the second kind is a Hopf algebra endomorphism on the space of quasisymmetric functions QSym. It coincides with Stembridge's peak enumerator for Eulerian posets, but differs for general posets. The complete spectrum is determined, generalizing work of Billera, Hsiao and van Willigenburg. The type B quasisymmetric function of a poset is introduced. Like Ehrenborg's classical quasisymmetric function of a poset, this map is a comodule morphism with respect to the quasisymmetric functions QSym. Similarities among the omega map, Ehrenborg's r-signed Birkhoff transform, and the Tchebyshev transforms motivate a general study of chain maps. One such occurrence, the chain map of the second kind, is a Hopf algebra endomorphism on the quasisymmetric functions QSym and is an instance of Aguiar, Bergeron and Sottile's result on the terminal object in the category of combinatorial Hopf algebras. In contrast, the chain map of the first kind is both an algebra map and a comodule endomorphism on the type B quasisymmetric functions BQSym.Comment: 33 page

Affine and toric hyperplane arrangements

We extend the Billera-Ehrenborg-Readdy map between the intersection lattice and face lattice of a central hyperplane arrangement to affine and toric hyperplane arrangements. For arrangements on the torus, we also generalize Zaslavsky's fundamental results on the number of regions.Comment: 32 pages, 4 figure

On a Generalization of Zaslavsky's Theorem for Hyperplane Arrangements

We define arrangements of codimension-1 submanifolds in a smooth manifold which generalize arrangements of hyperplanes. When these submanifolds are removed the manifold breaks up into regions, each of which is homeomorphic to an open disc. The aim of this paper is to derive formulas that count the number of regions formed by such an arrangement. We achieve this aim by generalizing Zaslavsky's theorem to this setting. We show that this number is determined by the combinatorics of the intersections of these submanifolds.Comment: version 3: The title had a typo in v2 which is now fixed. Will appear in Annals of Combinatorics. Version. 2: 19 pages, major revision in terms of style and language, some results improved, contact information updated, final versio

Multispecies virial expansions

We study the virial expansion of mixtures of countably many different types of particles. The main tool is the Lagrange–Good inversion formula, which has other applications such as counting coloured trees or studying probability generating functions in multi-type branching processes. We prove that the virial expansion converges absolutely in a domain of small densities. In addition, we establish that the virial coefficients can be expressed in terms of two-connected graphs

Phenotypic Modulation of Smooth Muscle Cells in Atherosclerosis Is Associated With Downregulation of LMOD1, SYNPO2, PDLIM7, PLN, and SYNM

OBJECTIVE: Key augmented processes in atherosclerosis have been identified, whereas less is known about downregulated pathways. Here, we applied a systems biology approach to examine suppressed molecular signatures, with the hypothesis that they may provide insight into mechanisms contributing to plaque stability. APPROACH AND RESULTS: Muscle contraction, muscle development, and actin cytoskeleton were the most downregulated pathways (false discovery rate=6.99e-21, 1.66e-6, 2.54e-10, respectively) in microarrays from human carotid plaques (n=177) versus healthy arteries (n=15). In addition to typical smooth muscle cell (SMC) markers, these pathways also encompassed cytoskeleton-related genes previously not associated with atherosclerosis. SYNPO2, SYNM, LMOD1, PDLIM7, and PLN expression positively correlated to typical SMC markers in plaques (Pearson r>0.6, P0.8, P<0.0001). By immunohistochemistry, the proteins were expressed in SMCs in normal vessels, but largely absent in human plaques and intimal hyperplasia. Subcellularly, most proteins localized to the cytoskeleton in cultured SMCs and were regulated by active enhancer histone modification H3K27ac by chromatin immunoprecipitation-sequencing. Functionally, the genes were downregulated by PDGFB (platelet-derived growth factor beta) and IFNg (interferron gamma), exposure to shear flow stress, and oxLDL (oxidized low-density lipoprotein) loading. Genetic variants in PDLIM7, PLN, and SYNPO2 loci associated with progression of carotid intima-media thickness in high-risk subjects without symptoms of cardiovascular disease (n=3378). By eQTL (expression quantitative trait locus), rs11746443 also associated with PDLIM7 expression in plaques. Mechanistically, silencing of PDLIM7 in vitro led to downregulation of SMC markers and disruption of the actin cytoskeleton, decreased cell spreading, and increased proliferation. CONCLUSIONS: We identified a panel of genes that reflect the altered phenotype of SMCs in vascular disease and could be early sensitive markers of SMC dedifferentiation

Multi-Locus Sequence Typing of Bartonella henselae Isolates from Three Continents Reveals Hypervirulent and Feline-Associated Clones

Bartonella henselae is a zoonotic pathogen and the causative agent of cat scratch disease and a variety of other disease manifestations in humans. Previous investigations have suggested that a limited subset of B. henselae isolates may be associated with human disease. In the present study, 182 human and feline B. henselae isolates from Europe, North America and Australia were analysed by multi-locus sequence typing (MLST) to detect any associations between sequence type (ST), host species and geographical distribution of the isolates. A total of 14 sequence types were detected, but over 66% (16/24) of the isolates recovered from human disease corresponded to a single genotype, ST1, and this type was detected in all three continents. In contrast, 27.2% (43/158) of the feline isolates corresponded to ST7, but this ST was not recovered from humans and was restricted to Europe. The difference in host association of STs 1 (human) and 7 (feline) was statistically significant (P≤0.001). eBURST analysis assigned the 14 STs to three clonal lineages, which contained two or more STs, and a singleton comprising ST7. These groups were broadly consistent with a neighbour-joining tree, although splits decomposition analysis was indicative of a history of recombination. These data indicate that B. henselae lineages differ in their virulence properties for humans and contribute to a better understanding of the population structure of B. henselae

Late Cenozoic tephrostratigraphy offshore the southern Central American Volcanic Arc: 2. Implications for magma production rates and subduction erosion

Pacific drill sites offshore Central America provide the unique opportunity to study the evolution of large explosive volcanism and the geotectonic evolution of the continental margin back into the Neogene. The temporal distribution of tephra layers established by tephrochonostratigraphy in Part 1 indicates a nearly continuous highly explosive eruption record for the Costa Rican and the Nicaraguan volcanic arc within the last 8 M.y. The widely distributed marine tephra layers comprise the major fraction of the respective erupted tephra volumes and masses thus providing insights into regional and temporal variations of large-magnitude explosive eruptions along the southern Central American Volcanic Arc (CAVA). We observe three pulses of enhanced explosive magmatism between 0-1 Ma at the Cordillera Central, between 1-2 Ma at the Guanacaste and at >3 Ma at the Western Nicaragua segments. Averaged over the long-term the minimum erupted magma flux (per unit arc length) is ∼0.017 g/ms. Tephra ages, constrained by Ar-Ar dating and by correlation with dated terrestrial tephras, yield time-variable accumulation rates of the intercalated pelagic sediments with four prominent phases of peak sedimentation rates that relate to tectonic processes of subduction erosion. The peak rate at >2.3 Ma near Osa particularly relates to initial Cocos Ridge subduction which began at 2.91±0.23 Ma as inferred by the 1.5 M.y. delayed appearance of the OIB geochemical signal in tephras from Barva volcano at 1.42 Ma. Subsequent tectonic re-arrangements probably involved crustal extension on the Guanacaste segment that favored the 2-1 Ma period of unusually massive rhyolite production

Duplication and Diversification of the Hypoxia-Inducible IGFBP-1 Gene in Zebrafish

Gene duplication is the primary force of new gene evolution. Deciphering whether a pair of duplicated genes has evolved divergent functions is often challenging. The zebrafish is uniquely positioned to provide insight into the process of functional gene evolution due to its amenability to genetic and experimental manipulation and because it possess a large number of duplicated genes.We report the identification and characterization of two hypoxia-inducible genes in zebrafish that are co-ortholgs of human IGF binding protein-1 (IGFBP-1). IGFBP-1 is a secreted protein that binds to IGF and modulates IGF actions in somatic growth, development, and aging. Like their human and mouse counterparts, in adult zebrafish igfbp-1a and igfbp-1b are exclusively expressed in the liver. During embryogenesis, the two genes are expressed in overlapping spatial domains but with distinct temporal patterns. While zebrafish IGFBP-1a mRNA was easily detected throughout embryogenesis, IGFBP-1b mRNA was detectable only in advanced stages. Hypoxia induces igfbp-1a expression in early embryogenesis, but induces the igfbp-1b expression later in embryogenesis. Both IGFBP-1a and -b are capable of IGF binding, but IGFBP-1b has much lower affinities for IGF-I and -II because of greater dissociation rates. Overexpression of IGFBP-1a and -1b in zebrafish embryos caused significant decreases in growth and developmental rates. When tested in cultured zebrafish embryonic cells, IGFBP-1a and -1b both inhibited IGF-1-induced cell proliferation but the activity of IGFBP-1b was significantly weaker.These results indicate subfunction partitioning of the duplicated IGFBP-1 genes at the levels of gene expression, physiological regulation, protein structure, and biological actions. The duplicated IGFBP-1 may provide additional flexibility in fine-tuning IGF signaling activities under hypoxia and other catabolic conditions

Late Cenozoic tephrostratigraphy offshore the southern Central American Volcanic Arc: 1. Tephra ages and provenance

We studied the tephra inventory of 18 deep sea drill sites from six DSDP/ODP legs (Legs 84, 138, 170, 202, 205, 206) and two IODP legs (Legs 334 and 344) offshore the southern Central American Volcanic Arc (CAVA). Eight drill sites are located on the incoming Cocos plate and ten drill sites on the continental slope of the Caribbean plate. In total we examined ∼840 ash-bearing horizons and identified ∼650 of these as primary ash beds of which 430 originated from the CAVA. Correlations of ash beds were established between marine cores and with terrestrial tephra deposits, using major and trace element glass compositions with respect to relative stratigraphic order. As a prerequisite for marine-terrestrial correlations we present a new geochemical data set for significant Neogene and Quaternary Costa Rican tephras. Moreover, new Ar/Ar ages for marine tephras have been determined and marine ash beds are also dated using the pelagic sedimentation rates. The resulting correlations and provenance analyses build a tephrochronostratigraphic framework for Costa Rica and Nicaragua that covers the last >8 Myr. We define 39 correlations of marine ash beds to specific tephra formations in Costa Rica and Nicaragua; from the 4.15 Ma Lower Sandillal Ignimbrite to the 3.5 ka Rincón de la Vieja Tephra from Costa Rica, as well as another 32 widely distributed tephra layers for which their specific region of origin along Costa Rica and Nicaragua can be constrained