Generating and analyzing spatial social networks

In this paper, we propose a class of models for generating spatial versions of three classic networks: Erdös-Rényi (ER), Watts-Strogatz (WS), and Barabási-Albert (BA). We assume that nodes have geographical coordinates, are uniformly distributed over an m × m Cartesian space, and long-distance connections are penalized. Our computational results show higher clustering coefficient, assortativity, and transitivity in all three spatial networks, and imperfect power law degree distribution in the BA network. Furthermore, we analyze a special case with geographically clustered coordinates, resembling real human communities, in which points are clustered over k centers. Comparison between the uniformly and geographically clustered versions of the proposed spatial networks show an increase in values of the clustering coefficient, assortativity, and transitivity, and a lognormal degree distribution for spatially clustered ER, taller degree distribution and higher average path length for spatially clustered WS, and higher clustering coefficient and transitivity for the spatially clustered BA networks.     

Pseudo–almost‐periodic solutions for delayed differential equations with integrable dichotomies and bi–almost‐periodic Green functions

Using the existence of integrable bi–almost‐periodic Green functions of linear homogeneous differential equations and the contraction fixed point, we are able to prove the existence of almost and pseudo–almost‐periodic mild solutions under quite general hypotheses for the differential equation with constant delay in a Banach space X, where τ>0 is a fixed constant. The results extend the corresponding ones in the case of exponential dichotomy. Some examples illustrate the importance of the concepts.     

A note on the transformation from companion to jordan canonical form for multivariable systems

Summary An algorithm for the transformation of generalized Companion forms for multivariable linear systems to Jordan form is considered.The procedure is based on a preliminary transformation to the corresponding maximum length chains canonical form (MLCGCF) and on knowledge of the eigenvalues and their multiplicity.

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Sommario Viene presentato un algoritmo per la trasformazione della matrice dinamica di sistemi lineari a più variabili di ingresso-uscita da forma companion generalizzata in forma di Jordan.Il procedimento è basato su una trasformazione preliminare in forma canonica a catene di massima lunghezza (MLCGCF) e sulla conoscenza degli autovalori e della loro multeplicità.

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This work was supported by CNR (Italian Council of Researches).     

TDDFT modeling of the CO‐photolysis of Fe2(S2C3H6)(CO)6, a model of the [FeFe]‐hydrogenase catalytic site

Upon irradiation with ultraviolet wavelengths, Fe₂(S₂C₃H₆)(CO)₆, a simple model of the [FeFe]‐hydrogenase active site, undergoes CO dissociation to form the unsaturated Fe₂(S₂C₃H₆)(CO)₅ species and successively a solvent adduct at the vacant coordination site. In the present work, the CO‐photolysis of Fe₂(S₂C₃H₆)(CO)₆ was investigated by density functional theory (DFT) and time‐dependent DFT (TDDFT). Trans Fe₂(S₂C₃H₆)(CO)₅ form and the corresponding trans heptane or acetonitrile solvent adducts are the lowest energy ground state forms. CO dissociation barriers computed for the lowest triplet state are roughly halved with respect to those for the ground state suggesting that some low‐lying excited potential energy surface (PES) could be loosely bound with respect to Fe? C bond cleavage. The TDDFT excited state PESs and geometry optimizations for the excited states likely involved in the CO‐photolysis suggest that the Fe? S bond elongation and the partial isomerization toward the rotated form could take place simultaneously, favoring the trans CO photodissociation. © 2014 Wiley Periodicals, Inc.     

Compatible blends of biorelated polyesters through catalytic transesterification in the melt

The transesterification during the melt blending of polylactide (PLA) and poly(butylene adipate-co-terephthalate) (PBAT) was investigated in presence of Ti(OBu)₄ as a catalyst. Both the effect of catalyst concentration and reaction duration was considered. The process was studied by analyzing the molecular weight of the polyesters by size exclusion chromatography (SEC). The rheological, thermal and morphological properties of the blends were investigated by melt flow rate, DSC and SEM analyses, respectively. Evidences about the formation of PBAT-PLA copolymers were obtained and discussed. The tensile properties of compression moulded films were also determined and correlated to the structure and phase morphology development of the blends. In particular, the use of Ti(OBu)₄ resulted in the improvement of compatibility. Moreover, the decrease in stiffness and the increase in elongation at break with the increase of mixing time was observed, in good agreement with the improved compatibility of the modified blend.     

Water-dispersible sugar-coated iron oxide nanoparticles. An evaluation of their relaxometric and magnetic hyperthermia properties

Synthesis of functionalized magnetic nanoparticles (NPs) for biomedical applications represents a current challenge. In this paper we present the synthesis and characterization of water-dispersible sugar-coated iron oxide NPs specifically designed as magnetic fluid hyperthermia heat mediators and negative contrast agents for magnetic resonance imaging. In particular, the influence of the inorganic core size was investigated. To this end, iron oxide NPs with average size in the range of 4-35 nm were prepared by thermal decomposition of molecular precursors and then coated with organic ligands bearing a phosphonate group on one side and rhamnose, mannose, or ribose moieties on the other side. In this way a strong anchorage of the organic ligand on the inorganic surface was simply realized by ligand exchange, due to covalent bonding between the Fe(3+) atom and the phosphonate group. These synthesized nanoobjects can be fully dispersed in water forming colloids that are stable over very long periods. Mannose, ribose, and rhamnose were chosen to test the versatility of the method and also because these carbohydrates, in particular rhamnose, which is a substrate of skin lectin, confer targeting properties to the nanosystems. The magnetic, hyperthermal, and relaxometric properties of all the synthesized samples were investigated. Iron oxide NPs of ca. 16-18 nm were found to represent an efficient bifunctional targeting system for theranostic applications, as they have very good transverse relaxivity (three times larger than the best currently available commercial products) and large heat release upon application of radio frequency (RF) electromagnetic radiation with amplitude and frequency close to the human tolerance limit. The results have been rationalized on the basis of the magnetic properties of the investigated samples.     

Phase diagram of the uniaxial and biaxial soft-core Gay-Berne model

Classical molecular dynamics simulations have been used to explore the phase diagrams for a family of attractive-repulsive soft-core Gay-Berne models [R. Berardi, C. Zannoni, J. S. Lintuvuori, and M. R. Wilson, J. Chem. Phys. 131, 174107 (2009)] and determine the effect of particle softness, i.e., of a moderately repulsive short-range interaction, on the order parameters and phase behaviour of model systems of uniaxial and biaxial ellipsoidal particles. We have found that isotropic, uniaxial, and biaxial nematic and smectic phases are obtained for the model. Extensive calculations of the nematic region of the phase diagram show that endowing mesogenic particles with such soft repulsive interactions affect the stability range of the nematic phases, and in the case of phase biaxiality it also shifts it to lower temperatures. For colloidal particles, stabilised by surface functionalisation, (e.g., with polymer chains), we suggest that it should be possible to tune liquid crystal behaviour to increase the range of stability of uniaxial and biaxial phases (by varying solvent quality). We calculate second virial coefficients and show that they are a useful means of characterising the change in effective softness for such systems. For thermotropic liquid crystals, the introduction of softness in the interactions between mesogens with overall biaxial shape (e.g., through appropriate conformational flexibility) could provide a pathway for the actual chemical synthesis of stable room-temperature biaxial nematics.