Ground-state properties of bosons in three- and two-dimensional traps

We study trapped systems of bosons at zero temperature in three and two dimensions. Conditions are fulfilled for the application of Gross-Pitaevskii theory with a positive scattering length. Series expansions for ground-state properties are obtained in both the noninteracting and the strong-coupling (Thomas-Fermi) limits. From these expansions, analytic estimates are presented in the form of two-point Pad\'e approximants. We explicitly show the approximants for the total energy per particle and the chemical potential.Comment: LaTeX, 4 pages, 3 ps figure

Bijectiveness of the Nash Map for Quasi-Ordinary Hypersurface Singularities

In this paper we give a positive answer to a question of Nash concerning the arc space of a singularity, for the class of quasi-ordinary hypersurface singularities, extending to this case previous results and techniques of Shihoko Ishii.Comment: comments and references adde

Toric embedded resolutions of quasi-ordinary hypersurface singularities

We build two embedded resolution procedures of a quasi-ordinary singularity of complex analytic hypersurface, by using toric morphisms which depend only on the characteristic monomials associated to a quasi-ordinary projection of the singularity. This result answers an open problem of Lipman in Equisingularity and simultaneous resolution of singularities, Resolution of Singularities, Progress in Mathematics No. 181, 2000, 485-503. In the first procedure the singularity is embedded as hypersurface. In the second procedure, which is inspired by a work of Goldin and Teissier for plane curves (see Resolving singularities of plane analytic branches with one toric morphism,loc. cit., pages 315-340), we re-embed the singularity in an affine space of bigger dimension in such a way that one toric morphism provides its embedded resolution. We compare both procedures and we show that they coincide under suitable hypothesis.Comment: To apear in Annales de l'Institut Fourier (Grenoble

Leptin Induces Proliferation and Notch Expression In Pancreatic Cancer

Pancreatic adenocarcinoma (PA) is an aggressive cancer. It develops in a way that causes almost no detectable symptoms, which leads to a rapid progression and a short survival rate. Researchers have discovered a link between pancreatic cancer (and other cancer types) and obesity. High levels of leptin, an appetite hormone secreted by adipocytes, have been found in obese people. Studies have shown that the absence of leptin in the body or severe leptin resistance can lead to uncontrolled eating and weight gain, hence, its connection to obesity. Consequently, our lab is analyzing the relationship between obesity and leptin and what effects they have on pancreatic cancer progression. We hypothesize that in PA cells, leptin induces proliferation, tumorigenesis, and increased levels of Notch and related molecules. These effects are reversed by our leptin antagonist linked to iron nanoparticles, IONP-LPrA2 (iron oxidized nanoparticles leptin peptide receptor antagonist). We’re mainly focused on 4 cell lines: Panc-1, MiaPaCa-2, and BxPc3 (derived from primary tumors) and AsPc-1 (from a metastatic tumor). Of the primary tumors, Panc-1 and MiaPaCa-2 are more aggressive and BxPc-3 is less aggressive. We expect results validating that leptin will induce proliferation (in Panc-1 and AsPc-1cells by MTT assay), expression of Notch and other molecules (in BxPc3 and MiaPaCa-2 cells by flow cytometry and Western Blot), and tumorsphere formation (in Panc-1). Leptin may also induce Notch expression in Panc-1 tumorspheres. In conclusion, this project will demonstrate the involvement of leptin in PA progression. Leptin\u27s effects will be abrogated by the inhibitor of leptin signaling, IONP-LPrA2

Toric Geometry and the Semple-Nash modification

This paper proposes some material towards a theory of general toric varieties without the assumption of normality. Their combinatorial description involves a fan to which is attached a set of semigroups subjected to gluing-up conditions. In particular it contains a combinatorial construction of the blowing up of a sheaf of monomial ideals on a toric variety. In the second part it is shown that over an algebraically closed base field of zero characteristic the Semple-Nash modification of a general toric variety is isomorphic to the blowing up of the sheaf of logarithmic jacobian ideals and that in any characteristic this blowing-up is an isomorphism if and only if the toric variety is non singular. In the second part we prove that orders on the lattice of monomials (toric valuations) of maximal rank are uniformized by iterated Sempla-Nash modifications.Comment: New version. Appeared in "Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales, Serie A Matematicas", October 2012 (Electronic

The Flow Fingerprinting Game

Linking two network flows that have the same source is essential in intrusion detection or in tracing anonymous connections. To improve the performance of this process, the flow can be modified (fingerprinted) to make it more distinguishable. However, an adversary located in the middle can modify the flow to impair the correlation by delaying the packets or introducing dummy traffic. We introduce a game-theoretic framework for this problem, that is used to derive the Nash Equilibrium. As obtaining the optimal adversary delays distribution is intractable, some approximations are done. We study the concrete example where these delays follow a truncated Gaussian distribution. We also compare the optimal strategies with other fingerprinting schemes. The results are useful for understanding the limits of flow correlation based on packet timings under an active attacker.Comment: Workshop on Information Forensics and Securit