The cell-cell adhesion molecule E-cadherin has been shown to suppress invasive growth of epithelial cells in vitro, and loss of its expression is thought to be important in invasion and metastatic potential of epithelial tumors in vivo. We retrospectively studied the level of E-cadherin expression in 50 primary head and neck squamous-cell carcinomas (HNSCC) by immunohistochemical methods, on frozen sections, using anti-E-cadherin monoclonal antibody (MAb) 6F9. It concerned patients with different stages of carcinoma of larynx or oral cavity who had been treated with curative intention 30 months or more before. Percentages of membranous stained tumor cells were scored in 1 of 5 categories. Scores were generally low, as in 11/50 lesions < or = 5% cells were stained, and in 19/50 lesions only 6-25% cells showed membranous staining. In 9 lymph-node metastases evaluated, E-cadherin expression was in the same range as in the primary tumors. There was a significant correlation between the level of membranous E-cadherin expression in the primary tumor and the degree of differentiation. No relation was found with tumor size (pT) or regional lymph-node classification (pN). Nevertheless, 29 patients surviving> or = 30 months without evidence of disease had significantly higher levels of membranous E-cadherin expression in their primary tumors than 10 patients with unfavorable clinical course clearly related to recurrent and/or metastatic HNSCC. Moreover, this could only partially be explained by distinctions in differentiation grade between both groups. Our results suggest that membranous E-cadherin expression has prognostic importance in patients with HNSCC.

We show that there exist polynomial endomorphisms of C 2 , possessing a wandering Fatou component. These mappings are polynomial skewproducts, and can be chosen to extend holomorphically of P 2 (C). We also find real examples with wandering domains in R 2 . The proof relies on parabolic implosion techniques, and is based on an original idea of M. Lyubich.

A conjecture of Sokal [23] regarding the domain of non-vanishing for independence polynomials of graphs, states that given any natural number ∆ ≥ 3, there exists a neighborhood in C of the interval [0, (∆−1) ∆−1 (∆−2) ∆ ) on which the independence polynomial of any graph with maximum degree at most ∆ does not vanish. We show here that Sokal's Conjecture holds, as well as a multivariate version, and prove optimality for the domain of non-vanishing. An important step is to translate the setting to the language of complex dynamical systems.

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This paper studies the implications of the “zero-condition” for multiattribute utility theory. The zero-condition simplifies the measurement and derivation of the Quality Adjusted Life Year (QALY) measure commonly used in medical decision analysis. For general multiattribute utility theory, no simple condition has heretofore been found to characterize multiplicatively decomposable forms. When the zero-condition is satisfied, however, such a simple condition, “standard gamble invariance,” becomes available.

Specific product formation rates and cellular growth rates are important maximization targets in biotechnology and microbial evolution. Maximization of a specific rate (i.e. a rate expressed per unit biomass amount) requires the expression of particular metabolic pathways at optimal enzyme concentrations. In contrast to the prediction of maximal product yields, any prediction of optimal specific rates at the genome scale is currently computationally intractable, even if the kinetic properties of all enzymes are available. In the present study, we characterize maximal-specific-rate states of metabolic networks of arbitrary size and complexity, including genome-scale kinetic models. We report that optimal states are elementary flux modes, which are minimal metabolic networks operating at a thermodynamically-feasible steady state with one independent flux. Remarkably, elementary flux modes rely only on reaction stoichiometry, yet they function as the optimal states of mathematical models incorporating enzyme kinetics. Our results pave the way for the optimization of genome-scale kinetic models because they offer huge simplifications to overcome the concomitant computational problems. Database The mathematical model described here has been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at