Geometry of foliations on the Wiener space and stochastic calculus of variations

Stochastic Calculus of variations deals with maps defined on the Wiener space, with finite dimensional range; within this context appears the notion of non-degenerate map, which corresponds roughly speaking to some kind of infinite dimensional ellipticity; a non-degenerate map has a smooth law; by conditioning, it generates a continuous desintegration of the Wiener measure. Infinite dimensional Stochastic Analysis and particularly SPDE theory raise the natural question of what can be done for maps with an infinite dimensional range; our approach to this problem emphasizes an intrinsic geometric aspect, replacing range by generated σ-field and its associated foliation of the Wiener space. To cite this article: H. Airault et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

The structure of 1-chloro-1-silabicyclo(2.2.2)octane as determined by gas-phase electron diffraction

The structure of 1 -chloro-1 -si labicyclo( 2.2.2 )octane is determined by gas-phase electron diffraction. The molecule is found to have a large amplitude twisting motion with a double minimum quartic potential function of the form V(φ) = V_o[1 + (φ/φ_o)⁴ - 2(φ/φ_o)²]. Least-squares analysis of the experimental data gives values of 1.4(0.8) kcal mole^? for V_o and 17.5(2.5)° for φ_o. Other structural parameters for the “quasi-C_3v” cage-like molecule include: r_g(Si-Cl) = 2.061(3) Å, r_g(Si-C) = 1.863(3) Å, r_g(C-C_av) = 1.559(2) Å, and r_g(C-H_av) = 1.098(7) Å. Several valence angles exhibit large deviations from tetrahedral values, e.g. ∠Cl-Si-C₂ = 114.6(0.2)°, ∠Si-C₂-C₃ = 105.8(0.4)°, ∠C₂-C₃-C₄ = 114.2(1.2)°, ∠C-₃-C₄-C₅ = 111.4(0.8)° and ∠C₂-Si-C₆= 103.9(0.2)°. Many of the structural features in this strained polycyclic compound. Including the nature of the quartic potential function, can be rationalized in terms of a simple molecular mechanics model. A new method for the calculation of an analytical Jacobian of the intensity function with respect to parameters of the potential function is also discussed.     

Genotyping by dynamic heating of monolayered beads on a microheated surface

A miniaturized bead-based dynamic allele-specific hybridization (DASH) approach for single-nucleotide polymorphism analysis is presented. Chips with integrated heater and temperature sensors for open-surface DNA analysis were microfabricated. Microcontact printing using a poly(dimethylsiloxane) (PDMS) stamp was employed to create monolayers of immobilized beads on the surface of the chip. This chip allows fast, well-controllable temperature ramping. The temperature distribution was homogeneous over the entire heater area. All three possible variants of an SNP site of a synthesized oligonucleotide were accurately scored using the bead-based DASH approach. Our assay has a nonoptimized temperature ramping rate of 4 degrees C-6 degrees C/min compared to earlier reported values of 2 degrees C-3 degrees C/min, thereby reducing the total analysis time by a factor of 2. Reliable DASH measurement data from areas as small as 12 x 13 microm was achieved. Our bead-based DASH approach has enabled a dramatic volume reduction and is a step towards developing a cost-effective high-throughput DASH method on arrays of single beads.     

A concept for miniaturized 3-D cell culture using an extracellular matrix gel

This paper presents a novel method to embed, anchor, and cultivate cells in a controlled 3-D flow-through microenvironment. This is realized using an etched silicon pillar flow chamber filled with extracellular matrix (ECM) gel mixed with cells. At 4 degrees C, while in liquid form, ECM gel is mixed with cells and injected into the chamber. Raising the temperature to 37 degrees C results in a gel, with cells embedded. The silicon pillars both stabilize and increase the surface to volume ratio of the gel. During polymerization the gel shrinks, thus creating channels, which enables perfusion through the chip. The pillars increase the mechanical stability of the gel permitting high surface flow rates without surface modifications. Within the structure cells were still viable and proliferating after 6 days of cultivation. Our method thus makes it possible to perform medium- to long-term cultivation of cells in a controlled 3-D environment. This concept opens possibilities to perform studies of cells in a more physiological environment compared to traditional 2-D cultures on flat substrates.     

Synthesis of (1R)-1-(4-Bromophenyl)-2,2,2-trifluoroethan-1-amine Hydrochloride through Diastereoselective Trifluoromethylation of a Chiral Sulfinimine

An efficient three-step synthesis of (1R)-1-(4-bromophenyl)-2,2,2-trifluoroethan-1-amine hydrochloride ( 1 ) starting from inexpensive and readily available starting materials was developed. The sequence features a highly diastereoselective trifluoromethylation of a chiral sulfinimine using the Rupert–Prakash reagent TMSCF₃ in combination with K₃PO₄ as an initiator. The diastereomeric purity of the resulting sulfinamide was further improved by direct precipitation of the desired diastereomer from the reaction mixture upon addition of water. The chiral auxiliary was then removed under acidic conditions, resulting in the isolation of chiral benzylamine 1 as its hydrochloride salt in 71 % overall yield and excellent purity (LC/MS: >99 % a/a; e.r.=99 : 1).