Another complete invariant for Steiner triple systems of order 15

In this note, the 80 non‐isomorphic triple systems on 15 points are revisited from the viewpoint of the convex hull of the characteristic vectors of their blocks. The main observation is that the numbers, of facets of these 80 polyhedra are all different, thus producing a new proof of the non‐isomorphism of these triple systems. The space dimension of these polyhedra is also discussed. Finally, we observe the large number of facets of some of these polyhedra with few vertices, in relation with the upper bound problem for combinatorial polyhedra. © 2005 Wiley Periodicals, Inc. J Combin Designs.     

An exact and polynomial distance-based algorithm to reconstruct single copy tandem duplication trees

The problem of reconstructing the duplication tree of a set of tandemly repeated sequences which are supposed to have arisen by unequal recombination, was first introduced by Fitch (1977), and has recently received a lot of attention. In this paper, we place ourselves in a distance framework and deal with the restricted problem of reconstructing single copy duplication trees. We describe an exact and polynomial distance based algorithm for solving this problem, the parsimony version of which has previously been shown to be NP-hard (like most evolutionary tree reconstruction problems). This algorithm is based on the minimum evolution principle, and thus involves selecting the shortest tree as being the correct duplication tree. After presenting the underlying mathematical concepts behind the minimum evolution principle, and some of its benefits (such as statistical consistency), we provide a new recurrence formula to estimate the tree length using ordinary least-squares, given a matrix of pairwise distances between the copies. We then show how this formula naturally forms the dynamic programming framework on which our algorithm is based, and provide an implementation in O(n³) time and O(n²) space, where n is the number of copies.     

Deglycosylation of glucose oxidase to improve biosensors and biofuel cells

We demonstrate that a more efficient redox hydrogel structure can be achieved by engineering the size and the surface charge of the bioelectrocatalyst. Deglycosylated glucose oxidase (GOx) modified electrode exhibits higher current density than native GOx, for the same molar composition of the hydrogel. This improvement is very likely due to a more efficient hydrogel structure rather than a better intrinsic electron transfer between the FAD/FADH₂ redox center and the redox mediator.     

Tetrapterosides A and B,two new oleanane‐type saponins from Tetrapleura tetraptera

From the stem bark of Tetrapleura tetraptera, two new oleanane‐type saponins, tetrapteroside A 3‐O‐{6‐O‐[(2E,6S)‐2,6‐dimethyl‐6‐hydroxyocta‐2,7‐dienoyl]‐β‐D ‐glucopyranosyl‐(1 → 2)‐β‐D ‐glucopyranosyl‐(1 → 3)‐β‐D ‐glucopyranosyl‐(1 → 4)‐[β‐D ‐glucopyranosyl‐(1 → 2)]‐β‐D ‐glucopyranosyl}‐3,27‐dihydroxyoleanolic acid (1), and tetrapteroside B 3‐O‐{ β‐D ‐glucopyranosyl‐(1 → 2)‐6‐O‐[(E)‐feruloyl]‐β‐D ‐glucopyranosyl‐(1 → 3)‐β‐D ‐glucopyranosyl‐(1 → 4)‐[β‐D ‐glucopyranosyl‐(1 → 2)]‐β‐D ‐glucopyranosyl}‐3,27‐dihydroxyoleanolic acid (2), were isolated. Further extractions from the roots led to the isolation of four known oleanane‐type saponins. Their structures were elucidated by the combination of mass spectrometry (MS), one and two‐dimensional NMR experiments. Copyright © 2009 John Wiley & Sons, Ltd.     

The critical Lazer-McKenna conjecture in low dimensions

We study a problem related to the Lazer-McKenna conjecture in the critical case. Recent results on this conjecture in this case have been obtained in dimensions n?6. We prove here that the situation is drastically different in lower dimensions.     

Controllability and asymptotic stabilization of the Camassa-Holm equation

We investigate the problems of exact controllability and asymptotic stabilization of the Camassa-Holm equation on the circle, by means of a distributed control. The results are global, and in particular the control prevents the solution from blowing up.