Droplet evaporation study applied to DNA chip manufacturing

DNA chips are potentially powerful technologies for genotyping and gene expression profiling that rely on comparative analyses of up to thousands of "spots of analysis" on a glass support. The spot quality throughout the support influences spot-to-spot variations within an array and the repeatability of data across experiments. For glass slide DNA microarrays, droplets of DNA solution are deposited on functionalized glass slides and left to react through complete evaporation of the droplet. On hydrophobic flat surfaces, different modes of droplet evaporation can be attained. Under atmospheric pressure, water droplets tend to evaporate under two main regimes. Initially, the droplet flattens with a constant contact area, and then the droplet shrinks at a constant contact angle. As a result, the diameter and morphology of thousands of spots on microarrays are not uniform. This leads to poor and unreliable data processing results. In this work, we report the evaporation of an aqueous solution under a constant contact area mode. Evaporation under reduced pressure and the effect of reagent additives to the solution have been investigated. Video microscopy and digital image analysis techniques were applied to monitor the evaporation of the droplets. A mixture of surfactants was developed to maintain a constant area regime during evaporation and to form homogeneous spots. The control of some physicochemical properties (wetting, evaporation rate) of the droplet allows the formation of well-controlled spots compatible with DNA grafting. The influence of surfactant molecules on the mechanisms of evaporation is also discussed.     

Efficient stereochemical controllers in biaryl Suzuki coupling reactions: benzylic carbinols bearing in beta-position thioether, dimethylamino, or sulfoxide groups

Highly atropo-diastereoselective Suzuki coupling between aryl halides bearing stereogenic benzylic carbinols with sulfoxide, thioether, or dimethylamino groups as efficient internal chelating ligands and 2-methoxy-1-naphthylboronic acid were performed with high yields; a palladacycle is proposed as a potential transition state. [reaction: see text]     

A limit field for orthogonal range searches in two-dimensional random point search trees

We consider the cost of general orthogonal range queries in random quadtrees. The cost of a given query is encoded into a (random) function of four variables which characterize the coordinates of two opposite corners of the query rectangle. We prove that, when suitably shifted and rescaled, the random cost function converges uniformly in probability towards a random field that is characterized as the unique solution to a distributional fixed-point equation. We also state similar results for 2-d trees. Our results imply for instance that the worst case query satisfies the same asymptotic estimates as a typical query, and thereby resolve an open question of Chanzy et al. (2001).     

Efficiently navigating a random Delaunay triangulation

Planar graph navigation is an important problem with significant implications to both point location in geometric data structures and routing in networks. However, whilst a number of algorithms and existence proofs have been proposed, very little analysis is available for the properties of the paths generated and the computational resources required to generate them under a random distribution hypothesis for the input. In this paper we analyse a new deterministic planar navigation algorithm with constant spanning ratio (w.r.t the Euclidean distance) which follows vertex adjacencies in the Delaunay triangulation. We call this strategy cone walk. We prove that given n uniform points in a smooth convex domain of unit area, and for any start point z and query point q; cone walk applied to z and q will access at most sites with complexity with probability tending to 1 as n goes to infinity. We additionally show that in this model, cone walk is ‐memoryless with high probability for any pair of start and query point in the domain, for any positive ξ. We take special care throughout to ensure our bounds are valid even when the query points are arbitrarily close to the border. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 95–136, 2016     

The continuum limit of critical random graphs

We consider the Erd?s–Rényi random graph G(n, p) inside the critical window, that is when p?=?1/n?+?λn ^?4/3, for some fixed ${\lambda \in \mathbb{R}}$ . We prove that the sequence of connected components of G(n, p), considered as metric spaces using the graph distance rescaled by n ^?1/3, converges towards a sequence of continuous compact metric spaces. The result relies on a bijection between graphs and certain marked random walks, and the theory of continuum random trees. Our result gives access to the answers to a great many questions about distances in critical random graphs. In particular, we deduce that the diameter of G(n, p) rescaled by n ^?1/3 converges in distribution to an absolutely continuous random variable with finite mean.     

Enantiopure beta-hydroxysulfoxide derivatives as novel chiral auxiliaries in asymmetric biaryl Suzuki reactions

[reaction: see text] Highly diastereoselective biaryl Suzuki coupling reactions of (1R)-1-(2-iodo or bromophenyl)-2-(R)-(4-tolylsulfinyl)-1-ethanol derivatives with various aryl- or naphthylboronic acids (or esters) were performed with high yields (up to 99%) and an excellent control of the axial chirality (up to 98% de).     

Connectivity threshold of Bluetooth graphs

We study the connectivity properties of random Bluetooth graphs that model certain “ad hoc” wireless networks. The graphs are obtained as “irrigation subgraphs” of the well‐known random geometric graph model. There are two parameters that control the model: the radius r that determines the “visible neighbors” of each vertex and the number of edges c that each vertex is allowed to send to these. The randomness comes from the underlying distribution of vertices in space and from the choices of each vertex. We prove that no connectivity can take place with high probability for a range of parameters r, c and completely characterize the connectivity threshold (in c) for values of r close the critical value for connectivity in the underlying random geometric graph.Copyright © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 44, 45–66, 2014     

Construction of the biaryl-part of vancomycin aglycon via atropo-diastereoselective Suzuki-Miyaura coupling

An atropo-diastereoselective synthesis with dr up to 98/2 towards the biaryl subunit of vancomycin based on the use of enantiopure β-hydroxysulfoxide derivatives as novel chiral auxiliary is reported.     

The distribution of height and diameter in random non‐plane binary trees

This study is dedicated to precise distributional analyses of the height of non‐plane unlabelled binary trees (“Otter trees”), when trees of a given size are taken with equal likelihood. The height of a rooted tree of size n is proved to admit a limiting theta distribution, both in a central and local sense, and obey moderate as well as large deviations estimates. The approximations obtained for height also yield the limiting distribution of the diameter of unrooted trees. The proofs rely on a precise analysis, in the complex plane and near singularities, of generating functions associated with trees of bounded height. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2012