Greedy algorithm and symmetric matroids

Symmetric matroids are set systems which are obtained, in some sense, by a weakening of the structure of a matroid. These set systems are characterized by a greedy algorithm and they are suitable for dealing with autodual properties of matroids. Applications are given to the eulerian tours of 4-regular graphs and the theory ofg-matroids.     

Electron energy loss spectrometry mapping

Among electron beam microanalytical techniques, electron energy loss spectrometry (EELS) offers unique advantages in terms of information content, sensitivity, limits of detection. This paper describes new methods and tools for acquiring families of spectra over many pixels on the specimen, i.e. spectrumimages, and for processing them. Applications in different fields of research, both in materials science and in life sciences, demonstrate the potential impact of the technique for characterizing nano-sized structures.     

Reducing prime graphs and recognizing circle graphs

We prove a reduction theorem for prime (simple) graphs in Cunningham’s sense. Roughly speaking this theorem says that every prime (simple) graph of ordern>5 “contains” a smaller prime graph of ordern−1. As an application we give a polynomial algorithm for recognizing circle graphs.     

Transforming trees by successive local complementations

A local complementation of a simple graph G at a vertex v consists in replacing the subgraph induced by G on the neighborhood of v by the complementary graph. Two graphs are locally equivalent if they are related by a sequence of local complementations. H. M. Mulder conjectured that any two locally equivalent trees are isomorphic. We prove this conjecture and we characterize those graphs that are locally equivalent to trees.     

Generalisation of the Eyring–Kramers Transition Rate Formula to Irreversible Diffusion Processes

In the small noise regime, the average transition time between metastable states of a reversible diffusion process is described at the logarithmic scale by Arrhenius’ law. The Eyring–Kramers formula classically provides a subexponential prefactor to this large deviation estimate. For irreversible diffusion processes, the equivalent of Arrhenius’ law is given by the Freidlin–Wentzell theory. In this paper, we compute the associated prefactor and thereby generalise the Eyring–Kramers formula to irreversible diffusion processes. In our formula, the role of the potential is played by Freidlin–Wentzell’s quasipotential, and a correction depending on the non-Gibbsianness of the system along the minimum action paths is highlighted. Our study assumes some properties for the vector field: (1) attractors are isolated points, (2) the dynamics restricted to basin of attraction boundaries are attracted to single points (which are saddle-points of the vector field). We moreover assume that the minimum action paths that connect attractors to adjacent saddle-points (the instantons) have generic properties that are summarised in the conclusion. At a technical level, our derivation combines an exact computation for the first-order WKB expansion around the instanton and an exact computation of the first-order match asymptotics expansion close to the saddle-point. While the results are exact once a formal expansion is assumed, the validity of these asymptotic expansions remains to be proven.     

Phage display of enzymes and in vitro selection for catalytic activity

Despite recent progress, our understanding of enzymes remains limited: the prediction of the changes that should be introduced to alter their properties or catalytic activities in an expected direction remains difficult. An alternative to rational design is selection of mutants endowed with the anticipated properties from a large collection of possible solutions generated by random mutagenesis. We describe here a new technique of in vitro selection of genes on the basis of the catalytic activity of the encoded enzymes. The gene coding for the enzyme to be engineered is cloned into the genome of a filamentous phage, whereas the enzyme itself is displayed on its surface, creating a phage enzyme. A bifunctional organic label containing a suicide inhibitor of the enzyme and a ligand with high affinity for an immobilized receptor are constructed. On incubation of a mixture of phage enzymes, those phages showing an activity on the inhibitor under the conditions of the experiment are labeled. These phages can be recovered by affinity chromatography. The design of the label and the factors controlling the selectivity of the selection are analyzed. The advantages of the technique and its scope in terms of the enzymes that can be engineered are discussed.     

An efficient algorithm to recognize locally equivalent graphs

To locally complement a simple graphF at one of its verticesv is to replace the subgraph induced byF onn(v)={w:vw is an edge ofF} by the complementary subgraph. Graphs related by a sequence of local complementations are said to be locally equivalent. We associate a system of equations with unknowns inGF(2) to any pair of graphs {F, F}, so thatF is locally equivalent toF if and only if the system has a solution. The equations are either linear and homogenous or bilinear, and we find a solution, if any, in polynomial time.With partial support of P. R. C. Mathématiques et Informatique.     

Performance of capillary columns for high-temperature gas chromatography

The developments in stationary-phase synthesis and capillary column technology have opened new perspectives in the analysis of high-molecular-weight compounds (600 daltons) and thermolabile organic compounds by high-temperature-high-resolution gas chromatography. This branch of high-resolution gas chromatography deals with analysis performed up to 390 degrees C oven temperature (with some applications going up to 420 degrees C and even a few applications to 450 degrees C maximum). The technique has been applied to many different fields of science (e.g., organic geochemistry, environmental chemistry, archeology, and natural product research). Apolar and medium-polar gum phases can now be operated at temperatures from 400 to 480 degrees C, but these higher temperatures are seldom used because of the thermostability of the material used to make the capillary tubing. This paper shows the performance of nine commercial high-temperature columns when used in routine applications.