An optimal algorithm for the boundary of a cell in a union of rays

In this paper we study a cell of the subdivision induced by a union ofn half-lines (or rays) in the plane. We present two results. The first one is a novel proof of theO(n) bound on the number of edges of the boundary of such a cell, which is essentially of methodological interest. The second is an algorithm for constructing the boundary of any cell, which runs in optimal (n logn) time. A by-product of our results are the notions of skeleton and of skeletal order, which may be of interest in their own right.This work was partly supported by CEE ESPRIT Project P-940, by the Ecole Normale Supérieure, Paris, and by NSF Grant ECS-84-10902.This work was done in part while this author was visiting the Ecole Normale Supérieure, Paris, France.     

Rheological behaviour of polysaccharide aqueous solutions

Several data relative to the viscosity of water-soluble polysaccharide solutions were collected from the literature and processed by different rheological models. Some relationships between the viscosity of these polymer solutions, their molecular weight and their solution concentrations, were established and their validity checked. Thus, an accurate equation correlating the viscosity and both the shear rate and the solution concentration of different water soluble polysaccharides (xanthan, hyaluronan, carboxymethylcellulose) was deduced on the basis of Cross' model which suggests two domains in which the viscosity is constant, i.e. very low and very high shear rate ranges. Then, an expression relating the zero-shear viscosity (A) and the concentration of their solutions was proposed. Finally, an alternative equation to that of Mark–Houwink correlating the molecular weight and the intrinsic viscosity of the water-soluble polysaccharides studied in this paper was found.     

On the thermal stability of xanthan gum

The thermal stability of xanthan gum in dilute aqueous solutions at 90°C is considered. The relative viscosity as a function of ageing time is discussed, and it has been found to depend on the polymer concentration and conformation as well as on the salt content. The effectiveness of a quencher demonstrates the existence of a free-radical process in the degradation. During ageing, the molecular weight first decreases by rapid random hydrolysis of the main chain and loss of the pyruvate and acetate substituents. Later, oligomers are formed corresponding to a breakdown of both the side chain and the main chain. The identification of cellodextrins in the oligomer pool demonstrates the second effect.     

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.     

Oxidation of proteins: Basic principles and perspectives for blood proteomics

Protein oxidation mechanisms result in a wide array of modifications, from backbone cleavage or protein crosslinking to more subtle modifications such as side chain oxidations. Protein oxidation occurs as part of normal regulatory processes, as a defence mechanism against oxidative stress, or as a deleterious processes when antioxidant defences are overcome. Because blood is continually exposed to reactive oxygen and nitrogen species, blood proteomics should inherently adopt redox proteomic strategies. In this review, we recall the biochemical basis of protein oxidation, review the proteomic methodologies applied to analyse redox modifications, and highlight some physiological and in vitro responses to oxidative stress of various blood components.     

NodeTrix: a hybrid visualization of social networks

The need to visualize large social networks is growing as hardware capabilities make analyzing large networks feasible and many new data sets become available. Unfortunately, the visualizations in existing systems do not satisfactorily resolve the basic dilemma of being readable both for the global structure of the network and also for detailed analysis of local communities. To address this problem, we present NodeTrix, a hybrid representation for networks that combines the advantages of two traditional representations: node-link diagrams are used to show the global structure of a network, while arbitrary portions of the network can be shown as adjacency matrices to better support the analysis of communities. A key contribution is a set of interaction techniques. These allow analysts to create a NodeTrix visualization by dragging selections to and from node-link and matrix forms, and to flexibly manipulate the NodeTrix representation to explore the dataset and create meaningful summary visualizations of their findings. Finally, we present a case study applying NodeTrix to the analysis of the InfoVis 2004 coauthorship dataset to illustrate the capabilities of NodeTrix as both an exploration tool and an effective means of communicating results.     

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.