Asymptotic Information-Theoretic Detection of Dynamical Organization in Complex Systems

The identification of emergent structures in complex dynamical systems is a formidable challenge. We propose a computationally efficient methodology to address such a challenge, based on modeling the state of the system as a set of random variables. Specifically, we present a sieving algorithm to navigate the huge space of all subsets of variables and compare them in terms of a simple index that can be computed without resorting to simulations. We obtain such a simple index by studying the asymptotic distribution of an information-theoretic measure of coordination among variables, when there is no coordination at all, which allows us to fairly compare subsets of variables having different cardinalities. We show that increasing the number of observations allows the identification of larger and larger subsets. As an example of relevant application, we make use of a paradigmatic case regarding the identification of groups in autocatalytic sets of reactions, a chemical situation related to the origin of life problem.     

Nanosize silicon nitride: characteristic of doped powders and of the related sintered materials

The paper reports on both the characteristics of ultrafine silicon nitride powder produced by plasma synthesis and the microstructure and properties of the relative sintered material. The powder, already containing yttria and alumina as sintering aids, has a bimodal particle size distribution and it is partly amorphous. The chemical composition and morphology of the particles are shown. Yttria and alumina were not found in separate particles but the elements constituting them (i.e., Y, Al, O) are either in solid solutions in the crystalline particles or dispersed within the amorphous portion of the powder. Dense materials were obtained by pressureless sintering at 1750 °C. Microstructure and composition of silicon nitride grains and of grain boundary phases are analyzed and discussed. When compared to a micro-sized Si₃N₄, nanoindentation tests clearly revealed the inverse Hall Petch relation. The nanosize Si₃N₄ shows a Young’s modulus which is almost independent on the peak load. PACS 81.05.J,M; 81.40; 81.05.Y; 81.05.J; 46.30.P     

A note on the classification of Fano manifolds of middle index

We rule out a doubtful case in the classification of Fano manifolds of middle indexMathematics Subject Classification (2000): 14J40, 14J45     

New π‐stacked benzofulvene polymer showing thermoreversible polymerization: Studies in macromolecular and aggregate structures and polymerization mechanism

The macromolecular and aggregate structures of poly[ethyl 1‐methylene‐3‐(4‐methylphenyl)‐1H‐indene‐2‐carboxylate] (poly‐ BF1 ; a new polymer based on a functionalized benzofulvene moiety showing interesting properties, i.e., thermoreversible polymerization/depolymerization behavior, high solubility in the most common organic solvents, and susceptibility to molecular manipulation) have been investigated with NMR spectroscopy, absorption and emission spectrophotometry, and transmission electron microscopy (TEM). Moreover, the polymerization mechanism has been studied to obtain further information on the polymer structure. The collected evidence is consistent in indicating for poly‐ BF1 a vinyl (1,2) polymer structure stabilized by means of aromatic stacking interactions. Furthermore, TEM studies performed on metal replicas have shown that the polymer is liable to give nanostructured aggregates. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3289–3304, 2005     

On cubic-linear polynomial mappings

In the field of the Jacobian conjecture it is well-known after Dru?kowski that from a polynomial ‘cubic-homogeneous’ mapping we can build a higher-dimensional ‘cubic-linear’ mapping and the other way round, so that one of them is invertible if and only if the other one is. We make this point clearer through the concept of ‘pairing’ and apply it to the related conjugability problem: one of the two maps is conjugable if and only if the other one is; moreover, we find simple formulas expressing the inverse or the conjugations of one in terms of the inverse or conjugations of the other. Two nontrivial examples of conjugable cubic-linear mappings are provided as an application.     

Finitely Additive Supermartingales

The concept of finitely additive supermartingales, originally due to Bochner, is revived and developed. We exploit it to study measure decompositions over filtered probability spaces and the properties of the associated Doléans-Dade measure. We obtain versions of the Doob–Meyer decomposition and, as an application, we establish a version of the Bichteler and Dellacherie theorem with no exogenous probability measure. I am indebted to an anonymous referee for several helping suggestions.     

Dye-sensitized photooxygenation of furanosyl furans: synthesis of a new pyridazine C-nucleoside

The dye-sensitized photooxygenation of furanosyl furans easily affords C- or O-glycosides with cis-alpha,beta-unsaturated 1,4-dioxo aglycones. The reaction, performed on a ribofuranosyl furan, provides a useful new entry to a novel pyridazine C-nucleoside that can be achieved through a simple one-pot procedure.     

Stereochemistry of cercosporin

The absolute configuration of the asymmetric carbons and the axial chirality of the natural mold metabolite cercosporin (from $\text{Cercospora sp}$.) have been established on the basis of X-ray analysis and chemical reactions. The results confirm the inherent dissymmetry of the perylenequinone ring, the twisting of which gives rise to the diastereoisomer isocercosporin. The energy barrier for the conversion of cercosporin into isocercosporin has been evaluated.