The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes

This paper introduces a new data structure, called simplex tree, to represent abstract simplicial complexes of any dimension. All faces of the simplicial complex are explicitly stored in a trie whose nodes are in bijection with the faces of the complex. This data structure allows to efficiently implement a large range of basic operations on simplicial complexes. We provide theoretical complexity analysis as well as detailed experimental results. We more specifically study Rips and witness complexes.     

The viscosity dependence on concentration,molecular weight and shear rate of xanthan solutions

Summary This paper concerns the viscosity dependence of Xanthan as a function of polymer concentration, shear rate and molecular weight in the ordered conformation. The different samples with various molecular weights are obtained by ultrasonication. A unique curve is obtained for the reduced specific viscosity ( ) as a function of γ · γ _r ⁻¹ for the different molecular weight samples and polymer concentrations below an overlap concentration C [η]₀⩽ 1.5. The master curve giving the relation as a function of C [η]₀ is drawn and compared with that of polystyrene in good solvent. The largest increase of in semidilute solution may be due to larger interchain interactions and to larger stiffness of the Xanthan molecule.     

Exploiting Multi-Beam Antennas for End-to-End Delay Reduction in Ad Hoc Networks

A Multi-Beam Antenna (MBA) can be defined as a set of directional radio transceivers. These transceivers are facing different directions to prevent signal interference with each other. MBA nodes have two main characteristics: the Multi-Packet Transmission (MPT) capability and the Multi-Packet Reception (MPR) capability whereby a node can transmit/receive multiple packets at the same time. In this paper, we provide an analysis of how this MPT/MPR capability can be used to reduce the end-to-end delay for delivered packets in ad hoc networks. Taking beam considerations (determination of the beam in which neighbors are located) into account, we formulate the delay reduction issue as an optimization problem that we solve. Our results show that to maximally exploit the full potential of MBAs for delay reduction, the scheduling of links has to promote the formation of star nodes and keep the formation of bridges to a minimum; all of which leads to the selection of routes that very often are not the shortest. In fact, using only the shortest routes has a negative impact on the delay. However, the optimal link scheduling comes at the expense of a higher overhead in terms of the total number of packet transmissions. Furthermore, the beamwidth has a direct and significant impact on the end-to-end delay and the computation time.     

On the abnormal exponents aν and aD in Mark Houwink type equations for wormlike chain polysaccharides

Summary The Mark Houwink exponent relating intrinsic viscosity and the molecular weight are usually much larger for polysaccharides than for synthetic polymers. In a moderate range of molecular weights, it depends directly on the stiffness of the molecules considered as worm like chains. This paper demonstrates that these exponents are predictible from the model of Yamakawa-Fujii.     

Cholesteric order in aqueous solutions of the polysaccharide Xanthan

Summary Measurements of birefringence, optical rotation and laser light diffraction show that aqueous solutions of the polyelectrolytic polysaccharide Xanthan at a concentration of 7.5 % (vol/vol) have long range order very similar to cholesteric liquid crystals. The cholesteric screw is left handed implying a rod-like conformation and right handed helicity of individual molecules. The cholesteric phase separates from a less concentrated isotropic solution and spherolites are formed.     

On the existence of two different secondary structures for the xanthan in aqueous solutions

Summary This paper gives experimental evidence for two different ordered conformations in solution for the xanthan molecules. Their hydrodynamic characteristics are quite different and their existence is controlled by experimental conditions.Laboratoire Propre du C.N.R.S., associé à l'Université Scientifique et Médicale de Grenoble, France     

Shortest paths of bounded curvature in the plane

Given two oriented points in the plane, we determine and compute the shortest paths of bounded curvature joining them. This problem has been solved recently by Dubins in the no-cusp case, and by Reeds and Shepp otherwise. We propose a new solution based on the minimum principle of Pontryagin. Our approach simplifies the proofs and makes clear the global or local nature of the results.     

On the volume change on non covalent gels in solvent-non solvent mixtures

Summary In this paper, the volume change on polysaccharide gels in non solvent mixtures is investigated. No phase transition is observed. A reversible decrease of the swelling volume is obtained directly related to the mechanical properties of the gels and to the charge parameters of the polymers. The effect of deswelling in presence of acetone or alcohol is increasing from agarose, k-carrageenan and i-carrageenan.