Enhancing PSO methods for global optimization

The Particle Swarm Optimization (PSO) method is a well-established technique for global optimization. During the past years several variations of the original PSO have been proposed in the relevant literature. Because of the increasing necessity in global optimization methods in almost all fields of science there is a great demand for efficient and fast implementations of relative algorithms. In this work we propose three modifications of the original PSO method in order to increase the speed and its efficiency that can be applied independently in almost every PSO variant. These modifications are: (a) a new stopping rule, (b) a similarity check and (c) a conditional application of some local search method. The proposed were tested using three popular PSO variants and a variety test functions. We have found that the application of these modifications resulted in significant gain in speed and efficiency.     

On a topological closeness of perturbed Julia sets

In the present work we expand our previous work in [1] by introducing the Julia Deviation Distance and the Julia Deviation Plot in order to study the stability of the Julia sets of noise-perturbed Mandelbrot maps. We observe a power-law behaviour of the Julia Deviation Distance of the Julia sets of a family of additive dynamic noise Mandelbrot maps from the Julia set of the Mandelbrot map as a function of the noise level. Additionally, using the above tools, we support the invariance of the Julia set of a noise-perturbed Mandelbrot map under different noise realizations.     

Extending the Newton-Kantorovich hypothesis for solving equations

The famous Newton-Kantorovich hypothesis (Kantorovich and Akilov, 1982 [3], Argyros, 2007 [2], Argyros and Hilout, 2009 [7]) has been used for a long time as a sufficient condition for the convergence of Newton’s method to a solution of an equation in connection with the Lipschitz continuity of the Fréchet-derivative of the operator involved. Here, using Lipschitz and center-Lipschitz conditions, and our new idea of recurrent functions, we show that the Newton-Kantorovich hypothesis can be weakened, under the same information. Moreover, the error bounds are tighter than the corresponding ones given by the dominating Newton-Kantorovich theorem (Argyros, 1998 [1]; [2] and [7]; Ezquerro and Hernández, 2002 [11]; [3]; Proinov 2009, 2010 [16] and [17]).Numerical examples including a nonlinear integral equation of Chandrasekhar-type (Chandrasekhar, 1960 [9]), as well as a two boundary value problem with a Green’s kernel (Argyros, 2007 [2]) are also provided in this study.     

Parsimonious representation of nonlinear dynamical systems through manifold learning: A chemotaxis case study

Nonlinear manifold learning algorithms, such as diffusion maps, have been fruitfully applied in recent years to the analysis of large and complex data sets. However, such algorithms still encounter challenges when faced with real data. One such challenge is the existence of “repeated eigendirections,” which obscures the detection of the true dimensionality of the underlying manifold and arises when several embedding coordinates parametrize the same direction in the intrinsic geometry of the data set. We propose an algorithm, based on local linear regression, to automatically detect coordinates corresponding to repeated eigendirections. We construct a more parsimonious embedding using only the eigenvectors corresponding to unique eigendirections, and we show that this reduced diffusion maps embedding induces a metric which is equivalent to the standard diffusion distance. We first demonstrate the utility and flexibility of our approach on synthetic data sets. We then apply our algorithm to data collected from a stochastic model of cellular chemotaxis, where our approach for factoring out repeated eigendirections allows us to detect changes in dynamical behavior and the underlying intrinsic system dimensionality directly from data.     

A Kantorovich-type convergence analysis of the Newton–Josephy method for solving variational inequalities

We present a Kantorovich-type semilocal convergence analysis of the Newton–Josephy method for solving a certain class of variational inequalities. By using a combination of Lipschitz and center-Lipschitz conditions, and our new idea of recurrent functions, we provide an analysis with the following advantages over the earlier works (Wang 2009, Wang and Shen, Appl Math Mech 25:1291–1297, 2004) (under the same or less computational cost): weaker sufficient convergence conditions, larger convergence domain, finer error bounds on the distances involved, and an at least as precise information on the location of the solution.     

Computing the Newton Polygon of the Implicit Equation

We consider rationally parameterized plane curves, where the polynomials in the parameterization have fixed supports and generic coefficients. We apply sparse (or toric) elimination theory in order to determine the vertex representation of the implicit equation’s Newton polygon. In particular, we consider mixed subdivisions of the input Newton polygons and regular triangulations of point sets defined by Cayley’s trick. We consider polynomial and rational parameterizations, where the latter may have the same or different denominators; the implicit polygon is shown to have, respectively, up to four, five, or six vertices.     

A study of the friedel-crafts acylation of 1-benzenesulfonyl-1H-pyrrole in the preparation of 3-aroylpyrroles

In this work, we studied the aluminum chloride catalyzed reaction of 1-benzenesulfonyl-1H-pyrrole with a series of eleven aroyl chlorides. The products formed were not isolated, but hydrolyzed to the target 3-aroylpyrroles in overall yields, usually, higher than 50%. However, in the cases with the π electron rich 1-phenyl-1H-pyrrole-3-carbonyl chloride and 1-methyl-1H-indole-3-carbonyl chloride significant C-2 substitution occured, resulting in the isolation of the corresponding 1-benzenesulfonyl-2-aroylpyrroles as the predominant or the sole products. The desired C-3 isomers were synthesized starting with 1-triisopropylsilanyl-1H-pyrrole.     

On Equilibria of the Two-fluid Model in Magnetohydrodynamics

We show how the equilibria of the two-fluid model in magnetohydrodynamics can be described by the double curl equation and through the study of this equation we study some properties of these equilibria. This revised version was published online in July 2006 with corrections to the Cover Date.     

A validated SIM GC/MS method for the simultaneous determination of dextromethorphan and its metabolites dextrorphan, 3‐methoxymorphinan and 3‐hydroxymorphinan in biological matrices and its application to in vitro CYP2D6 and CYP3A4 inhibition study

Dextromethorphan is used as a probe drug for assessing CYP2D6 and CYP3A4 activity in vivo and in vitro. A SIM GC/MS method without derivatization for the simultaneous determination of dextromethorphan and its metabolites, dextrorphan, 3‐methoxymorphinan and 3‐hydroxymorphinan, in human plasma, urine and in vitro incubation matrix was developed and validated. Calibration curves indicated good linearity with a coefficient of variation (r) better than 0.995. The lower limit of quantitation was found to be 10 ng/mL for all analytes in all matrices. Intra‐day and inter‐day precision for dextromethorphan and its metabolites was better than 9.02 and 9.91%, respectively and accuracy ranged between 91.76 and 106.27%. Recovery for dextromethorphan, its metabolites and internal standard levallorphan was greater than 72.68%. The method has been successfully applied for the in vitro inhibition of metabolism of dextromethorphan by CYP2D6 and CYP3A4 using known inhibitors of CYPs such as quinidine and verapamil. Copyright © 2009 John Wiley & Sons, Ltd.