Level Sets of the Takagi Function: Local Level Sets

The Takagi function \tau : [0, 1] \to [0, 1] is a continuous non-differentiable function constructed by Takagi in 1903. The level sets L(y) = {x : \tau(x) = y} of the Takagi function \tau(x) are studied by introducing a notion of local level set into which level sets are partitioned. Local level sets are simple to analyze, reducing questions to understanding the relation of level sets to local level sets, which is more complicated. It is known that for a "generic" full Lebesgue measure set of ordinates y, the level sets are finite sets. Here it is shown for a "generic" full Lebesgue measure set of abscissas x, the level set L(\tau(x)) is uncountable. An interesting singular monotone function is constructed, associated to local level sets, and is used to show the expected number of local level sets at a random level y is exactly 3/2.Comment: 32 pages, 2 figures, 1 table. Latest version has updated equation numbering. The final publication will soon be available at springerlink.co

Sols tropicaux : quelques expériences de gestion de la matière organique

Les systèmes actuels de production de grains, viande et lait dans la région des Cerrados présentent des problèmes croissants économiques et de production. Une des solutions pour améliorer la production, tout en maintenant ou en améliorant la qualité des sols, consiste à intégrer dans les mêmes exploitations l'élevage et la production de grains, comme la rotation de cultures annuelles et de prairies, en associant ce processus au renouvellement ou à la récupération des pâturages. Ce travail présente, au travers d'expériences conduites chez les producteurs, les possibilités offertes par cette intégration de cultures à cycles courts et de l'élevage. Ces exemples sont choisis de manière à illustrer la variabilité de sols existante (latossols de diverses textures). (Résumé d'auteur

Preferences over location-scale family

Location-scale family, Inverse problem, Non-expected utility function, Stochastic dominance, Location-scale dominance, Mean-variance rule, G11, C60, G10,

Crk Adapter Proteins Promote an Epithelial–Mesenchymal-like Transition and Are Required for HGF-mediated Cell Spreading and Breakdown of Epithelial Adherens Junctions

Activation of the Met receptor tyrosine kinase through its ligand, hepatocyte growth factor (HGF), promotes an epithelial–mesenchymal transition and cell dispersal. However, little is known about the HGF-dependent signals that regulate these events. HGF stimulation of epithelial cell colonies leads to the enhanced recruitment of the CrkII and CrkL adapter proteins to Met-dependent signaling complexes. We provide evidence that signals involving CrkII and CrkL are required for the breakdown of adherens junctions, the spreading of epithelial colonies, and the formation of lamellipodia in response to HGF. The overexpression of a CrkI SH3 domain mutant blocks these HGF-dependent events. In addition, the overexpression of CrkII or CrkL promotes lamellipodia formation, loss of adherens junctions, cell spreading, and dispersal of colonies of breast cancer epithelial cells in the absence of HGF. Stable lines of epithelial cells overexpressing CrkII show enhanced activation of Rac1 and Rap1. The Crk-dependent breakdown of adherens junctions and cell spreading is inhibited by the expression of a dominant negative mutant of Rac1 but not Rap1. These findings provide evidence that Crk adapter proteins play a critical role in the breakdown of adherens junctions and the spreading of sheets of epithelial cells