Vertex Operators, Grassmannians, and Hilbert Schemes

We describe a well-known collection of vertex operators on the infinite wedge representation as a limit of geometric correspondences on the equivariant cohomology groups of a finite-dimensional approximation of the Sato grassmannian, by cutoffs in high and low degrees. We prove that locality, the boson-fermion correspondence, and intertwining relations with the Virasoro algebra are limits of the localization expression for the composition of these operators. We then show that these operators are, almost by definition, the Hilbert scheme vertex operators defined by Okounkov and the author in \cite{CO} when the surface is $\mathbb{C}^2$ with the torus action $z\cdot (x,y) = (zx,z^{-1}y)$.Comment: 20 pages, 0 figure

Triple Self-Sorting in Constitutional Dynamic Networks: Parallel Generation of Imine-Based CuI, FeII, and ZnII Complexes

Three imine‐based metal complexes, having no overlap in terms of their compositions, have been simultaneously generated from the self‐sorting of a constitutional dynamic library (CDL) containing three amines, three aldehydes, and three metal salts. The hierarchical ordering of the stability of the three metal complexes assembled and the leveraging of the antagonistic and agonistic relationships existing between the constituents within the constitutional dynamic network corresponding to the CDL were pivotal in achieving the sorting. Examination of the process by NMR spectroscopy showed that the self‐sorting of the FeII and ZnII complexes depended on an interplay between the thermodynamic driving forces and a kinetic trap involved in their assembly. These results also exemplify the concept of “simplexity”—the fact that the output of a self‐assembling system may be simplified by increasing its initial compositional complexity—as the two complexes could self‐sort only in the presence of the third pair of organic components, those of the CuI complex

Une synthèse des modèles de représentation des connaissances à base de Graphes Conceptuels et OWL

Nous présentons et comparons deux approches de modélisation, formelles et concrètes, pour représenter et manipuler des connaissances d’un domaine. Le modèle des graphes conceptuels permet de modéliser des connaissances en terme de graphes, basés sur un support. Cette approche de modélisation est intensionnelle, est munie d’une sémantique en logique du premier ordre, et fait l’hypothèse d’un monde fermé pour ses raisonnements. Le langage OWL permet de décrire des ontologies et des faits sur le Web, suivant une approche de modélisation extensionnelle. Il possède une sémantique issue des logiques de descriptions, et fait l’hypothèse d’un monde ouvert pour ses raisonnements

Chen-Ruan cohomology of ADE singularities

We study Ruan's \textit{cohomological crepant resolution conjecture} for orbifolds with transversal ADE singularities. In the $A_n$-case we compute both the Chen-Ruan cohomology ring $H^*_{\rm CR}([Y])$ and the quantum corrected cohomology ring $H^*(Z)(q_1,...,q_n)$. The former is achieved in general, the later up to some additional, technical assumptions. We construct an explicit isomorphism between $H^*_{\rm CR}([Y])$ and $H^*(Z)(-1)$ in the $A_1$-case, verifying Ruan's conjecture. In the $A_n$-case, the family $H^*(Z)(q_1,...,q_n)$ is not defined for $q_1=...=q_n=-1$. This implies that the conjecture should be slightly modified. We propose a new conjecture in the $A_n$-case which we prove in the $A_2$-case by constructing an explicit isomorphism.Comment: This is a short version of my Ph.D. Thesis math.AG/0510528. Version 2: chapters 2,3,4 and 5 has been rewritten using the language of groupoids; a link with the classical McKay correpondence is given. International Journal of Mathematics (to appear

Ecological aspects of Langsdorffia hypogaea (Balanophoraceae) parasitism in the Pantanal wetlands.

Most studies on holoparasitic plants have focused on taxonomic or systematic issues. The objective of this study was to examine the ecological aspects of parasitism of Langsdorffia hypogaea (Balanophoraceae) in the Pantanal wetlands. Individuals of L. hypogaea were dug out by hand and the host trees were identified. Eighty-eight percent of host trees exhibited zoochory dispersal syndrome. Protium heptaphyllum and Cordiera sessilis represented 50% of the sampled trees. Both species are evergreen and are preferentially shade-tolerant species growing under the canopy of other trees. Fecal sample of collared peccaries (Pecari tajacu) had seeds from both the host tree (Protium sp.) and the parasite L. hypogaea. We therefore propose the hypothesis that P. tajacu play a role as a seed disperser and may affect root parasitism

Estrutura e distribuição espacial de Trichilia elegans A. Juss. (Meliaceae) em uma Floresta Semidecídua no Pantanal da Nhecolândia, Mato Grosso do Sul, Brasil.

Trichilia elegans A. Juss. é uma espécie com ampla distribuição, que ocorre desde a Venezuela até o Uruguai, e constitui componente comum no sub-bosque de formações estacionais. Mesmo que os primeiros estudos sobre a flora pantaneira datem de mais de um século, trabalhos voltados para a estrutura e a distribuição espacial de espécies arbóreas ocorrentes na região são ainda raros. Os objetivos do presente estudo foram identificar o padrão de distribuição espacial e a distribuição diamétrica de T. elegans e verificar se existe correlação entre o número de indivíduos jovens e o número de indivíduos adultos em uma floresta semidecídua no Pantanal da Nhecolândia. Para o levantamento, foram amostradas 50 parcelas de 200 m2 cada e inventariados os indivíduos jovens e adultos em cada uma delas. Com o intuito de identificar o padrão de distribuição espacial, foram utilizados o Índice de Morisita (IM) e a razão de variância/média (R). Foram encontrados 218 indivíduos jovens e 78 adultos. Indivíduos jovens e adultos apresentaram distribuição espacial agrupada, estando os jovens (IM = 2,32; R = 5,49) mais agrupados que os adultos (IM = 1,88; R = 2,05). O coeficiente de correlação linear encontrado (r = 0,60) demonstrou que a densidade de indivíduos jovens está altamente correlacionada com a densidade de indivíduos adultos