A new approach to the statistical treatment of 2D-maps in proteomics using fuzzy logic

A new approach to the statistical treatment of 2D-maps has been developed. This method is based on the use of fuzzy logic and allows to take into consideration the typical low reproducibility of 2D-maps. In this approach the signal corresponding to the presence of proteins on the 2D-maps is substituted with probability functions, centred on the signal itself. The standard deviation of the bidimensional gaussian probability function employed to blur the signal allows to assign different uncertainties to the two electrophoretic dimensions. The effect of changing the standard deviation and the digitalisation resolution are investigated.     

Solving Nonconvex Planar Location Problems by Finite Dominating Sets

It is well-known that some of the classical location problems with polyhedral gauges can be solved in polynomial time by finding a finite dominating set, i.e. a finite set of candidates guaranteed to contain at least one optimal location.In this paper it is first established that this result holds for a much larger class of problems than currently considered in the literature. The model for which this result can be proven includes, for instance, location problems with attraction and repulsion, and location-allocation problems.Next, it is shown that the approximation of general gauges by polyhedral ones in the objective function of our general model can be analyzed with regard to the subsequent error in the optimal objective value. For the approximation problem two different approaches are described, the sandwich procedure and the greedy algorithm. Both of these approaches lead - for fixed - to polynomial approximation algorithms with accuracy for solving the general model considered in this paper.     

Identically conserved currents and their charges

We examine, at a classical level, the features that distinguish dynamically conserved currents from identically conserved ones. Then we prove that, in four spacetime dimensions, the quantum charges corresponding to identically conserved currents always annihilate the vacuum state. We illustrate our discussion with several examples.     

Random marginal and random removal values

We propose two variations of the non-cooperative bargaining model for games in coalitional form, introduced by Hart and Mas-Colell (Econometrica 64:357–380, 1996a). These strategic games implement, in the limit, two new NTU-values: the random marginal and the random removal values. Their main characteristic is that they always select a unique payoff allocation in NTU-games. The random marginal value coincides with the Consistent NTU-value (Maschler and Owen in Int J Game Theory 18:389–407, 1989) for hyperplane games, and with the Shapley value for TU games (Shapley in In: Contributions to the theory of Games II. Princeton University Press, Princeton, pp 307–317, 1953). The random removal value coincides with the solidarity value (Nowak and Radzik in Int J Game Theory 23:43–48, 1994) in TU-games. In large games we show that, in the special class of market games, the random marginal value coincides with the Shapley NTU-value (Shapley in In: La Décision. Editions du CNRS, Paris, 1969), and that the random removal value coincides with the equal split value.      

Cystine as Ligand of Calcium(II) and Magnesium(II) in Two Ionic Media and at Two Different Temperatures (25 and 37 °C)

Cystine plays an important role in human physiology, it is the precursor of cysteine. Cystine is the molecular form preferred by the immunity cellules system, included macrophages. Although slightly soluble, it can be a ligand towards cations because it is a sulfur-containing amino acid. Because of the physiological importance of calcium(II) and magnesium(II), complex formation between these cations and cystine was studied potentiometrically by employing electrochemical cells involving glass electrodes. The investigation was performed at two temperatures (25 and 37) °C and in two ionic media (1.00 and 0.15 mol·dm^?3 NaCl). In both ionic media, the adoption of a constant ionic medium allows extension of the investigation to a large range of reagent concentration. As the formation of weak complexes was foreseen, the low solubility of cystine is an advantage. Experimental data can be explained in any case by assuming the formation of mononuclear complexes in the presence of both calcium(II) and magnesium(II). The relative stability constants were determined.     

CAESAR models for developmental toxicity

Background

The new REACH legislation requires assessment of a large number of chemicals in the European market for several endpoints. Developmental toxicity is one of the most difficult endpoints to assess, on account of the complexity, length and costs of experiments. Following the encouragement of QSAR (in silico) methods provided in the REACH itself, the CAESAR project has developed several models.

Results

Two QSAR models for developmental toxicity have been developed, using different statistical/mathematical methods. Both models performed well. The first makes a classification based on a random forest algorithm, while the second is based on an adaptive fuzzy partition algorithm. The first model has been implemented and inserted into the CAESAR on-line application, which is java-based software that allows everyone to freely use the models.

Conclusions

The CAESAR QSAR models have been developed with the aim to minimize false negatives in order to make them more usable for REACH. The CAESAR on-line application ensures that both industry and regulators can easily access and use the developmental toxicity model (as well as the models for the other four endpoints).