Evolution of networks

We review the recent rapid progress in the statistical physics of evolving networks. Interest has focused mainly on the structural properties of complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of this kind have recently been created, which opens a wide field for the study of their topology, evolution, and the complex processes which occur in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of the large sizes of these networks, the distances between most of their vertices are short - a feature known as the 'small-world' effect. We discuss how growing networks self-organize into scale-free structures, and investigate the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation and disease spread on these networks. We present a number of models demonstrating the main features of evolving networks and discuss current approaches for their simulation and analytical study. Applications of the general results to particular networks in nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems of non-equilibrium physics, econophysics, evolutionary biology, and so on.     

Homomorphisms and congruences on regular semigroups with associate inverse subsemigroups

An associate inverse subsemigroup of a regular semigroup S is a subsemigroup T of S containing a least associate x* of each x ∈ S, in relation to the natural partial order ≤. In [1] the authors describe the structure of regular semigroups with an associate inverse subsemigroup, satisfying two natural conditions. In this paper we describe all *-homomorphisms and all *-congruences on such semigroups.     

Computational scheme for solving nonlinear fractional stochastic differential equations with delay

Abstract

This paper studies the numerical solution of fractional stochastic delay differential equations driven by Brownian motion. The proposed algorithm is based on linear B-spline interpolation. The convergence and the numerical performance of the method are analyzed. The technique is adopted for determining the statistical indicators of stochastic responses of fractional Langevin and Mackey-Glass models with stochastic excitations.     

Vibrational properties of Cs4W11O35 and Rb4W11O35 systems: high pressure and polarized Raman spectra

Cs₄ W₁₁O₃₅ (CW) and Rb₄ W₁₁O₃₅ (RW) belong to the class of hexagonal bronzes whose structure originates from the K_xWO₃ superconductor hexatungstate. Charge‐imbalanced tungsten bronzes are dielectric materials with rich polymorphism, ferroelectric properties and second‐harmonic generation. In this work, we report the polarized Raman spectra results for both CW and RW, as well as results of high‐pressure Raman scattering experiments (0.0–11.0 GPa) for the Cs₄ W₁₁O₃₅ system, in which we have observed two structural phase transitions at ∼4 and 7.5 GPa. We discuss these transformations and polarized Raman spectra on the basis of lattice dynamics calculation in the related system KNbW₂O₉. Polarized Raman spectra provide strong indication that the highest wavenumber modes observed in these systems originate from tungsten or oxygen vacancies. The observation of a soft‐like mode indicates that the observed phase transitions exhibit a displacive‐type behavior, thus further indicating that these transformations are likely related to reorientations of the octahedral units. The soft mode nature is discussed as well. PACS: 77.80.Bh; 78.30.Hv; 78.30.‐j. Copyright © 2010 John Wiley & Sons, Ltd.     

Temperature‐induced phase transformations in Na2WO4 and Na2MoO4 crystals

Temperature‐dependent Raman studies on Na₂WO₄and Na₂MoO₄ crystals were performed in order to obtain information on structural changes induced by temperature evolution. The stability of the cubic phase of Na₂WO₄and Na₂MoO₄crystals was assessed and our results indicate that this phase is stable in the 8–823 K and 15–773 K ranges for Na₂WO₄ and Na₂MoO₄, respectively. The crystal of Na₂WO₄ shows a phase transition occurring at 833 K. Na₂MoO₄undergoes a sequence of three phase transitions, which were observed at 783–803, 823–913 and 943–950 K. In both crystals, a strong first‐order phase transition occurs as indicated by the behavior of the Raman modes: the Raman bands split and new bands appear below 100 cm⁻¹. These transitions are connected with tilting and/or rotations of the WO₄and MoO₄ tetrahedra, which leads to a disorder at the WO₄and MoO₄ sites. Copyright © 2010 John Wiley & Sons, Ltd.     

Redaporfin Development for Photodynamic Therapy and its Combination with Glycolysis Inhibitors†

Photodynamic therapy (PDT) remains an underutilized treatment modality in oncology. Many efforts have been dedicated to the development of better photosensitizers, better formulations and delivery methods, rigorous planning of light dose distribution in tissues, mechanistic insight, improvement of treatment protocols and combinations with other therapeutic agents. Hopefully, progress in all these fields will eventually expand the use of PDT. Here we offer a brief review of our own contribution to the development of a photosensitizer for PDT – redaporfin – currently in Phase II clinical trials, and present data on its combination with two glycolysis inhibitors: 2-deoxyglucose and 3-bromopyruvate. We show that 3-bromopyruvate is more cytotoxic to a carcinoma cell line (CT26) than to a normal fibroblast (3T3) cell line, and that this selectivity is maintained in the in vitro combination with redaporfin-PDT. This combination was investigated in BALB/c mice with large subcutaneous CT26 tumors and it is shown that the cure rate in the combination is higher (33% cures) than in PDT (11% cures) or in 3-bromopyruvate (no cures) alone. The combination of redaporfin-PDT with 3-bromopyruvate illustrates the potential of combination therapies and how PDT benefits can be enhanced by systemic drugs with complementary targets.     

Polymer structure and the compensation effect of the diffusion pre-exponential factor and activation energy of a permeating solute

In the present work, the relation between the pre-exponential factor and the apparent activation energy of diffusion, ln D(0) = alpha + betaE(D), so-called compensation effect, is re-examined and critically discussed for diffusion of gases in rubbery and glassy polymers. In principle, the above equation could be derived from the enthalpy-entropy compensation in the framework of the transition state theory. However, one should consider the influence of the jump length term contained in the pre-exponential factor, which may be affected by permeating species and polymer properties. We found that parameter alpha depends on penetrant size and polymer properties, such as local chain mobility and free volume. This can be interpreted by the fact that the jump length is affected by both penetrant and polymer properties. Finally, methods for estimating the jump length are discussed.     

Simultaneous distillation-extraction of high-value volatile compounds from Cistus ladanifer L

The present paper describes a procedure to isolate volatiles from rock-rose (Cistus ladanifer L.) using simultaneous distillation-extraction (SDE). High-value volatile compounds (HVVC) were selected and the influence of the extraction conditions investigated. The effect of the solvent nature and extraction time on SDE efficiency was studied. The best performance was achieved with pentane in 1 h operation. The extraction efficiencies ranged from 65% to 85% and the repeatability varied between 4% and 6% (as a CV%).The C. ladanifer SDE extracts were analysed by headspace solid phase microextraction (HS-SPME) followed by gas chromatography with flame ionization detection (GC-FID). The HS-SPME sampling conditions such as fiber coating, temperature, ionic strength and exposure time were optimized. The best results were achieved with an 85 μm polyacrylate fiber for a 60 min headspace extraction at 40 °C with 20% (w/v) of NaCl. For optimized conditions the recovery was in average higher than 90% for all compounds and the intermediate precision ranged from 4 to 9% (as CV %). The volatiles α-pinene (22.2 mg g⁻¹ of extract), 2,2,6-trimethylcyclohexanone (6.1 mg g⁻¹ of extract), borneol (3.0 mg g⁻¹ of extract) and bornyl acetate (3.9 mg g⁻¹ of extract) were identified in the SDE extracts obtained from the fresh plant material.     

The degree of the bicanonical map of a surface with

In this note it is shown that, given a smooth minimal complex surface of general type with , , for which the bicanonical map is a morphism, the degree of is not 3. This completes our earlier results, showing that if is a minimal surface of general type with , such that is free, then the bicanonical map of can have degree 1, 2 or 4.