Reconstructing initial data using observers: error analysis of the semi-discrete and fully discrete approximations

A new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in Ramdani et al. (Automatica 46(10), 1616-1625, 2010 ). Based on the concept of observers (also called Luenberger observers), this algorithm covers a large class of abstract evolution PDE's. In this paper, we are concerned with the convergence analysis of this algorithm. More precisely, we provide a complete numerical analysis for semi-discrete (in space) and fully discrete approximations derived using finite elements in space and an implicit Euler method in time. The analysis is carried out for abstract Schrödinger and wave conservative systems with bounded observation (locally distributed)

Period- and mirror-maps for the quartic K3

We study in detail mirror symmetry for the quartic K3 surface in P3 and the mirror family obtained by the orbifold construction. As explained by Aspinwall and Morrison, mirror symmetry for K3 surfaces can be entirely described in terms of Hodge structures. (1) We give an explicit computation of the Hodge structures and period maps for these families of K3 surfaces. (2) We identify a mirror map, i.e. an isomorphism between the complex and symplectic deformation parameters, and explicit isomorphisms between the Hodge structures at these points. (3) We show compatibility of our mirror map with the one defined by Morrison near the point of maximal unipotent monodromy. Our results rely on earlier work by Narumiyah-Shiga, Dolgachev and Nagura-Sugiyama.Comment: 29 pages, 3 figure

Poisson Structures on Smooth 4–Manifolds

We show that every closed oriented smooth 4-manifold admits a complete singular Poisson structure in each homotopy class of maps to the 2-sphere. The rank of this structure is 2 outside a small singularity set, which consists of finitely many circles and isolated points. The Poisson bivector has rank 0 on the singularities, where we give its local form explicitly.Comment: v3: 17pgs. We shortened, and streamlined, both the proof and the exposition. The main result now follows from a formula used by Damianou-Petalidou, attributed to Flaschka-Rati

Single Cell Analytics for NanoBiology

Anselmetti D, Griemla N, Hellmich W, et al. Single Cell Analytics for NanoBiology. NanoBiotechnology. 2005;1(3):267-270

Interaction of biomolecules sequentially deposited at the same location using a microcantilever-based spotter

International audienceA microspotting tool, consisting of an array of micromachined silicon cantilevers with integrated microfluidic channels is introduced. This spotter, called Bioplume, is able to address on active surfaces and in a time-contact controlled manner picoliter of liquid solutions, leading to arrays of 5 to 20-μm diameter spots. In this paper, this device is used for the successive addressing of liquid solutions at the same location. Prior to exploit this principle in a biological context, it is demonstrated that: (1) a simple wash in water of the microcantilevers is enough to reduce by >96% the cross-contamination between the successive spotted solutions, and (2) the spatial resolution of the Bioplume spotter is high enough to deposit biomolecules at the same location. The methodology is validated through the immobilization of a 35mer oligonucleotide probe on an activated glass slide, showing specific hybridization only with the complementary strand spotted on top of the probe using the same microcantilevers. Similarly, this methodology is also used for the interaction of a protein with its antibody. Finally, a specifically developed external microfluidics cartridge is utilized to allow parallel deposition of three different biomolecules in a single run