Hall conditions for edge-weighted bipartite graphs

A weighted variant of Hall's condition for the existence of matchings is shown to be equivalent to the existence of a matching in a lexicographic product. This is used to introduce characterizations of those bipartite graphs whose edges may be replicated so as to yield semiregular multigraphs or, equivalently, semiregular edge-weightings. Such bipartite graphs will be called semiregularizable. Some infinite families of semiregularizable trees are described and all semiregularizable trees on at most 11 vertices are listed. Matrix analogues of some of the results are mentioned and are shown to imply some of the known characterizations of regularizable graphs.

Is perception of upper body orientation based on the inertia tensor? Normogravity versus microgravity conditions

During lateral leg raising, a synergistic inclination of the supporting leg and trunk in the opposite direction to the leg movement is performed in order to preserve equilibrium. As first hypothesized by Pagano and Turvey (J Exp Psychol Hum Percept Perform, 1995, 21:1070-1087), the perception of limb orientation could be based on the orientation of the limb's inertia tensor. The purpose of this study was thus to explore whether the final upper body orientation (trunk inclination relative to vertical) depends on changes in the trunk inertia tensor. We imposed a loading condition, with total mass of 4 kg added to the subject's trunk in either a symmetrical or asymmetrical configuration. This changed the orientation of the trunk inertia tensor while keeping the total trunk mass constant. In order to separate any effects of the inertia tensor from the effects of gravitational torque, the experiment was carried out in normo- and microgravity. The results indicated that in normogravity the same final upper body orientation was maintained irrespective of the loading condition. In microgravity, regardless of loading conditions the same (but different from the normogravity) orientation of the upper body was achieved through different joint organizations: two joints (the hip and ankle joints of the supporting leg) in the asymmetrical loading condition, and one (hip) in the symmetrical loading condition. In order to determine whether the different orientations of the inertia tensor were perceived during the movement, the interjoint coordination was quantified by performing a principal components analysis (PCA) on the supporting and moving hips and on the supporting ankle joints. It was expected that different loading conditions would modify the principal component of the PCA. In normogravity, asymmetrical loading decreased the coupling between joints, while in microgravity a strong coupling was preserved whatever the loading condition. It was concluded that the trunk inertia tensor did not play a role during the lateral leg raising task because in spite of the absence of gravitational torque the final upper body orientation and the interjoint coupling were not influenced.

Restoration of glutathione levels in vascular smooth muscle cells exposed to high glucose conditions

Hyperglycaemia-induced oxidative stress may play a key role in the pathogenesis of diabetic vascular disease. The purpose of the present study was to determine the effects of glucose on levels of glutathione (a major intracellular antioxidant), the expression of gamma-glutamylcysteine synthetase (the rate-limiting enzyme in glutathione de novo synthesis) and DNA damage in human vascular smooth muscle cells in vitro. High glucose conditions and buthionine sulphoximine, an inhibitor of gamma-glutamylcysteine synthetase, reduced intracellular glutathione levels in vascular smooth muscle cells. This reduction was accompanied by a decrease in the mRNA expression of both subunits of gamma-glutamylcysteine synthetase as well as an increase in DNA damage. In high glucose conditions incubation of the vascular smooth muscle cells with alpha-lipoic acid and L-cystine restored glutathione levels. We suggest that the decrease in GSH levels seen in high glucose conditions is mediated by the availability of cysteine (rate-limiting substrate in de novo glutathione synthesis) and the gene expression of the gamma- glutamylcysteine synthetase enzyme. Glutathione depletion is associated with an increase in DNA damage, which can be reduced when glutathione levels are restored.

Influence of plasticizer type and storage conditions on properties of poly(methyl vinyl ether-co-maleic anhydride) bioadhesive films

Poly(methyl vinyl ether-co-maleic anhydride) formed films from aqueous formulations with characteristics that are ideal as a basis for producing a drug-containing bioadhesive delivery system when plasticized with a monohydroxyl functionalized plasticizer. Hence, films containing a novel plasticizer, tripropylene glycol methyl ether (TPME), maintained their adhesive strength and tensile properties when packaged in aluminized foil for extended periods of time. Films plasticized with commonly used polyhydric alcohols, such as the glycerol in this study, underwent an esterification reaction that led to polymer crosslinking, as shown in NMR studies. These revealed the presence of peaks in the ester/carbonyl region, suggesting that glyceride residue formation had been initiated. Given the polyfunctional nature of glycerol, progressive esterification would result in a polyester network and an accompanying profound alteration in the physical characteristics. Indeed, films became brittle over time with a loss of both the aqueous solubility and bioadhesion to porcine skin. In addition, a swelling index was measurable after 7 days, a property not seen with those films containing TPME. This change in bioadhesive strength and pliability was independent of the packaging conditions, rendering the films that contain glycerol as unsuitable as a basis for topical bioadhesive delivery of drug substances. Consequently, films containing TPME have potential as an alternative formulation strategy.