The active bijection in graphs, hyperplane arrangements, and oriented matroids, 1: The fully optimal basis of a bounded region

The present paper is the first in a series of four dealing with a mapping, introduced by the present authors, from orientations to spanning trees in graphs, from regions to simplices in real hyperplane arrangements, from reorientations to bases in oriented matroids (in order of increasing generality). This mapping is actually defined for ordered oriented matroids. We call it the active orientation-to-basis mapping, in reference to an extensive use of activities, a notion depending on a linear ordering, first introduced by W.T. Tutte for spanning trees in graphs. The active mapping, which preserves activities, can be considered as a bijective generalization of a polynomial identity relating two expressions–one in terms of activities of reorientations, and the other in terms of activities of bases–of the Tutte polynomial of a graph, a hyperplane arrangement or an oriented matroid. Specializations include bijective versions of well-known enumerative results related to the counting of acyclic orientations in graphs or of regions in hyperplane arrangements. Other interesting features of the active mapping are links established between linear programming and the Tutte polynomial.We consider here the bounded case of the active mapping, where bounded corresponds to bipolar orientations in the case of graphs, and refers to bounded regions in the case of real hyperplane arrangements, or of oriented matroids. In terms of activities, this is the uniactive internal case. We introduce fully optimal bases, simply defined in terms of signs, strengthening optimal bases of linear programming. An optimal basis is associated with one flat with a maximality property, whereas a fully optimal basis is equivalent to a complete flag of flats, each with a maximality property. The main results of the paper are that a bounded region has a unique fully optimal basis, and that, up to negating all signs, fully optimal bases provide a bijection between bounded regions and uniactive internal bases. In the bounded case, up to negating all signs, the active mapping is a bijection.     

Interexperimental and interindividual variations of DNA repair capacities after UV-B and UV-C irradiations of human keratinocytes and fibroblasts

DNA repair plays a central role in the cellular response to UV. In this work we have studied the response of skin cells (i.e. fibroblasts and keratinocytes) from the same or from different individuals after both ultraviolet-B (UV-B) and ultraviolet-C (UV-C) irradiations using the comet assay to characterize the specific cellular response to UV-induced DNA damage. Cells were irradiated with increasing doses of UV-B or UV-C. To study the UV dose dependency of initial steps of DNA repair, namely recognition and incision at DNA damage level, the comet assay was performed, under alkaline conditions, 60 min after UV irradiation to allow detection of DNA strand breaks. Comparative analysis of tail moment values after UV exposure of cells from the same or from different individuals showed interexperimental and interindividual variations, implying that repeated assays are necessary to characterize the individual DNA repair capacity. With increasing doses of UV in keratinocytes, a plateau was rapidly reached after irradiation, whereas in fibroblasts a linear dose-effect relationship was observed. These interindividual variations associated with cellular specificity in DNA response may be of significance in skin cell and individual susceptibility toward UV-induced carcinogenesis.     

Dynamic Amino Acid Side-Chains Grafting on Folded Peptide Backbone**

An efficient strategy for the synthesis of large libraries of conformationally defined peptides is reported, using dynamic combinatorial chemistry as a tool to graft amino acid side chains on a well-ordered 3D (3-dimension) peptide backbone. Combining rationally designed scaffolds with combinatorial side chains selection represents an alternative method to access peptide libraries for structures that are not genetically encodable. This method would allow a breakthrough for the discovery of protein mimetic for unconventional targets for which little is known.     

Enumerating symmetric directed convex polyominoes

It is shown, both analytically and bijectively, that the number of symmetric directed convex polyominoes with semiperimeter 2n+2 is equal to the central binomial coefficient .     

Parallel synthesis and yeast growth inhibition screening of succinamic acid libraries

Libraries of succinamic acid derivatives resulting from the condensation of a series of succinic acid derivatives with amines are reported as putative khafrefungin analogues. A total of 480 compounds derived from the initial condensation of 8 scaffolds with 60 different amines have been synthesized using automated technology with the help of scavenger resins. A simple acetate hydrolysis of five of the above sublibraries afforded additional 300 compounds for a total of 780 compounds. Around 55% of the library members showed purities higher than 70% (HPLC-ELS-MS) thus proving the generality of this approach. Results on growth inhibition of the yeast Saccharomyces cerevisiae in the presence of selected library members are also reported as a preliminary evaluation of the antifungal activity.     

Production Matrices and Riordan Arrays

We translate the concept of succession rule and the ECO method into matrix notation, introducing the concept of production matrix. This allows us to combine our method with other enumeration techniques using matrices, such as the method of Riordan matrices. Finally we treat the case of rational production matrices, i.e., those leading to rational generating functions. L. Ferrari and S. Rinaldi have been partially supported by MIUR project: Linguaggi formali e automi: metodi, modelli e applicazioni.     

A Mössbauer spectroscopy investigation of SrFe1−xScxO3−δ perovskites

Polycrystalline samples of oxygen deficient perovskites SrFe_1?xSc_xO_3?δ (0 ≤ x ≤ 0.5) have been synthesized by direct solid state reactions. Each compound has been stabilized with two different oxygen stoichiometries. The structural study shows, firstly, the good cationic homogeneity of the samples and, secondly, that the Sc and Fe atoms are randomly distributed over the same crystallographic site, whatever the scandium content. This implies that no anionic order is possible. A detailed Mossbauer spectroscopy study clearly shows that the substitution of scandium for iron involves an oxygen content decrease which decreases the tetravalent iron content until its total disappearance for x = 0.5. The evolutions of the isomer shift, the quadrupolar splitting and the relative intensity versus the Sc³⁺ content are depicted in the present paper.     

The oxygen deficient cubic perovskite SrFe1−xScxO3−δ (x ≤ 0.5; 0.1 ≤ δ ≤ 0.5): Structural features and physical properties

Solid state synthesis method has been used to stabilize oxygen deficient perovskite phases SrFe_1?xSc_xO_3?δ (0 ≤ x ≤ 0.5). The good homogeneity of samples is confirmed by energy dispersive spectroscopy (EDS) analysis performed with a transmission electronic microscope (TEM). By combining X-ray and electronic diffraction (ED), it is demonstrated that the cationic substitution on the B site of the perovskite induces a decrease of the oxygen content but without inducing long range ordering phenomenon. On this basis, X-ray patterns of compounds were indexed in the cubic Pm3m space group. The oxidation states of iron evidenced by Mössbauer spectroscopy, are in good agreement with the oxygen stoichiometries determined by cerimetric titration. In the SrFe_1?xSc_xO_3?δ series, the Fe³⁺/Fe⁴⁺ origin of the electronic conductivity is clearly evidenced. The limit compound SrFe_0.5Sc_0.5O_2.5 is highly resistive and characterized by a cluster glass-like behaviour. Finally, negative magnetoresistivity properties are revealed for the x = 0.1 and x = 0.2 samples, reaching ?10% around the magnetic transition temperature in a 7T magnetic field.