Group classification of systems of diffusion equations

Group classification of a class of systems of diffusion equations is carried out. Arbitrary elements that appear in the system depend on two variables. All forms of the arbitrary elements that provide additional Lie symmetries are determined. Equivalence transformations are used to simplify the analysis. Examples of similarity reductions are presented. Copyright © 2016 John Wiley & Sons, Ltd.     

Convex Underestimation of Twice Continuously Differentiable Functions by Piecewise Quadratic Perturbation: Spline αBB Underestimators

This paper describes the construction of convex underestimators for twice continuously differentiable functions over box domains through piecewise quadratic perturbation functions. A refinement of the classical α BB convex underestimator, the underestimators derived through this approach may be significantly tighter than the classical αBB underestimator. The convex underestimator is the difference of the nonconvex function f and a smooth, piecewise quadratic, perturbation function, q. The convexity of the underestimator is guaranteed through an analysis of the eigenvalues of the Hessian of f over all subdomains of a partition of the original box domain. Smoothness properties of the piecewise quadratic perturbation function are derived in a manner analogous to that of spline construction.     

Extended Linial Hyperplane Arrangements for Root Systems and a Conjecture of Postnikov and Stanley

A hyperplane arrangement is said to satisfy the Riemann hypothesis if all roots of its characteristic polynomial have the same real part. This property was conjectured by Postnikov and Stanley for certain families of arrangements which are defined for any irreducible root system and was proved for the root system A _{n – 1}. The proof is based on an explicit formula [1, 2, 11] for the characteristic polynomial, which is of independent combinatorial significance. Here our previous derivation of this formula is simplified and extended to similar formulae for all but the exceptional root systems. The conjecture follows in these cases.     

Performance of convex underestimators in a branch-and-bound framework

The efficient determination of tight lower bounds in a branch-and-bound algorithm is crucial for the global optimization of models spanning numerous applications and fields. The global optimization method \(\alpha \)-branch-and-bound (\(\alpha \)BB, Adjiman et al. in Comput Chem Eng 22(9):1159–1179, 1998b, Comput Chem Eng 22(9):1137–1158, 1998a; Adjiman and Floudas in J Global Optim 9(1):23–40, 1996; Androulakis et al. J Global Optim 7(4):337–363, 1995; Floudas in Deterministic Global Optimization: Theory, Methods and Applications, vol. 37. Springer, Berlin, 2000; Maranas and Floudas in J Chem Phys 97(10):7667–7678, 1992, J Chem Phys 100(2):1247–1261, 1994a, J Global Optim 4(2):135–170, 1994), guarantees a global optimum with \(\epsilon \)-convergence for any \(\mathcal {C}^2\)-continuous function within a finite number of iterations via fathoming nodes of a branch-and-bound tree. We explored the performance of the \(\alpha \)BB method and a number of competing methods designed to provide tight, convex underestimators, including the piecewise (Meyer and Floudas in J Global Optim 32(2):221–258, 2005), generalized (Akrotirianakis and Floudas in J Global Optim 30(4):367–390, 2004a, J Global Optim 29(3):249–264, 2004b), and nondiagonal (Skjäl et al. in J Optim Theory Appl 154(2):462–490, 2012) \(\alpha \)BB methods, the Brauer and Rohn+E (Skjäl et al. in J Global Optim 58(3):411–427, 2014) \(\alpha \)BB methods, and the moment method (Lasserre and Thanh in J Global Optim 56(1):1–25, 2013). Using a test suite of 40 multivariate, box-constrained, nonconvex functions, the methods were compared based on the tightness of generated underestimators and the efficiency of convergence of a branch-and-bound global optimization algorithm.     

Integrated computational and experimental approach for lead optimization and design of compstatin variants with improved activity

A novel structure-activity-based combinatorial computational optimization methodology for the design of peptides that are candidates to become therapeutics is presented. This methodology has been successfully applied in the design of a 7-fold more active analogue, among other active analogues, in the case of the complement inhibitor compstatin. The main steps of the approach involve the availability of NMR-derived structural templates, combinatorial selection of sequences based on optimization of parametrized pairwise residue interaction potentials, prediction of fold stabilities using deterministic global optimization, and experimental validation with immunological activity measurements. This work is direct evidence that an integrated experimental and theoretical approach can make the engineering of compounds with enhanced immunological properties possible.     

Synthesis and Characterization of Chitosan/ Dextran-Based Hydrogels for Surgical Use

A series of hydrogels were formed from the reaction between an amine functionalized succinyl chitosan and an oxidized dextran. The properties and rate of formation of the gel were related to both the amine and aldehyde levels of the precursors. These levels could be readily changed by altering the reaction conditions, and allowed good control of the gel properties. Oxidation of the dextran with periodate was accompanied by chain scission and a large reduction in molecular weight. The gel showed excellent haemostatic properties and reduction of adhesions in animal models.     

Electrical conductivity of titanium pyrophosphate between 100 and 400 °C: effect of sintering temperature and phosphorus content

The synthesis of titanium pyrophosphate is carried out, and the material is sintered at different temperatures between 370 and 970 °C. Yttrium is added during the synthesis to act as acceptor dopant, but it is mainly present in the material in secondary phases. The conductivity is studied systematically as a function of sintering temperature, pH₂O, pO₂, and temperature (100–400 °C). Loss of phosphorus upon sintering above 580–600 °C is confirmed by energy dispersive spectroscopy and combined thermogravimetry and mass spectrometry. The conductivity decreases with increasing sintering temperature and decreasing phosphorus content. The highest conductivity is 5.3?×?10^?4 S cm^?1 at 140 °C in wet air (pH₂O?=?0.22 atm) after sintering at 370 °C. The conductivity is higher in wet atmospheres than in dry atmospheres. The proton conduction mechanism is discussed, and the conductivity is attributed to an amorphous secondary phase at the grain boundaries, associated with the presence of excess phosphorus in the samples. A contribution to the conductivity by point defects in the bulk may explain the conductivity trend in dry air and the difference in conductivity between oxidizing and reducing atmospheres at 300–390 °C. Slow loss of phosphorus by evaporation over time and changes in the distribution of the amorphous phase during testing are suggested as causes of conductivity degradation above 220 °C.     

Age-dependent dichotomous effect of superoxide dismutase Ala16Val polymorphism on oxidized LDL levels

We investigated the association between superoxide dismutase (SOD) Ala16Val polymorphism and the levels of oxidized LDL lipoprotein-C (ox-LDL-C) in two age-different Greek cohorts. Four hundred fifteen middle-aged (n=147 females: 43.2+/-13 years, n=268 males: 43.3+/-14 years) Caucasian Greek subjects consisted the middle aged cohort. One hundred seventy five elderly (n=88 females: 79.9+/-4 years; n=87 males: 80.6+/-4 years) were selected from the elderly cohort. Genotype data were obtained for all of them. Multiple linear regression analysis, stratified by gender and adjusted for age, smoking habits and body mass index as covariates, showed higher ox-LDL-C levels for the middle aged men with the Val/Val genotype, compared to the other allele (Ala/Ala and Ala/Val) carriers (65.9+/-25.7 vs. 55.7+/-20.5 mg/dl; standardized beta coefficient=0.192, P=0.012). On the contrary, elderly women with the Val/Val genotype occurred with lower ox-LDL-C levels compared to the Ala/Ala or Ala/Val genotype (74.2+/-22.1 vs. 86.5+/-26.6 mg/dl; standardized beta coefficient= -0.269, P=0.015). The same trend was also recorded in elderly men, however without reaching statistical significance (standardized beta coefficient= -0.187, P=0.077). Moreover, elderly men and women with the Ala/Ala or Ala/Val genotype presented higher triglycerides levels compared to Val/Val (women: 145.2+/-68.7 vs. 114.3+/- 34.3 mg/dl, P= 0.027; men: 147.8+/-72.4 vs. 103.7 +/-38.0 mg/dl, P=0.002). Additionally, middle aged men with the Val/Val genotype had higher HDL-C levels compared to the Ala allele carriers. The results suggest that SOD Ala16Val polymorphism is an age-dependent modulator of ox-LDL-C levels in middle-aged men and elderly women.