On Convergence of Differential Evolution Over a Class of Continuous Functions With Unique Global Optimum

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms of current interest. Since its inception in the mid 1990s, DE has been finding many successful applications in real-world optimization problems from diverse domains of science and engineering. This paper takes a first significant step toward the convergence analysis of a canonical DE (DE/rand/1/bin) algorithm. It first deduces a time-recursive relationship for the probability density function (PDF) of the trial solutions, taking into consideration the DE-type mutation, crossover, and selection mechanisms. Then, by applying the concepts of Lyapunov stability theorems, it shows that as time approaches infinity, the PDF of the trial solutions concentrates narrowly around the global optimum of the objective function, assuming the shape of a Dirac delta distribution. Asymptotic convergence behavior of the population PDF is established by constructing a Lyapunov functional based on the PDF and showing that it monotonically decreases with time. The analysis is applicable to a class of continuous and real-valued objective functions that possesses a unique global optimum (but may have multiple local optima). Theoretical results have been substantiated with relevant computer simulations.

Convergence problems in a class of model reference adaptive control systems

A class of model reference adaptive control system which make use of an augmented error signal has been introduced by Monopoli. Convergence problems in this attractive class of systems have been investigated in this paper using concepts from hyperstability theory. It is shown that the condition on the linear part of the system has to be stronger than the one given earlier. A boundedness condition on the input to the linear part of the system has been taken into account in the analysis - this condition appears to have been missed in the previous applications of hyperstability theory. Sufficient conditions for the convergence of the adaptive gain to the desired value are also given.

Class of linear time-varying discrete systems

A class of linear time-varying discrete systems is considered, and closed-form solutions are obtained in different cases. Some comments on stability are also included.

Solution of a class of surface water wave scattering problems involving non-reflecting vertical barriers

A large class of scattering problems of surface water waves by vertical barriers lead to mixed boundary value problems for Laplace equation. Specific attentions are paid, in the present article, to highlight an analytical method to handle this class of problems of surface water wave scattering, when the barriers in question are non-reflecting in nature. A new set of boundary conditions is proposed for such non-reflecting barriers and tile resulting boundary value problems are handled in the linearized theory of water waves. Three basic poblems of scattering by vertical barriers are solved. The present new theory of non-reflecting vertical barriers predict new transmission coefficients and tile solutions of tile mathematical problems turn out to be extremely simple and straight forward as compared to the solution for other types of barriers handled previously.

Features of a unique intronless cluster of class I small heat shock protein genes in tandem with box C/D snoRNA genes on chromosome 6 in tomato (Solanum lycopersicum)

Physical clustering of genes has been shown in plants; however, little is known about gene clusters that have different functions, particularly those expressed in the tomato fruit. A class I 17.6 small heat shock protein (Sl17.6 shsp) gene was cloned and used as a probe to screen a tomato (Solanum lycopersicum) genomic library. An 8.3-kb genomic fragment was isolated and its DNA sequence determined. Analysis of the genomic fragment identified intronless open reading frames of three class I shsp genes (Sl17.6, Sl20.0, and Sl20.1), the Sl17.6 gene flanked by Sl20.1 and Sl20.0, with complete 5' and 3' UTRs. Upstream of the Sl20.0 shsp, and within the shsp gene cluster, resides a box C/D snoRNA cluster made of SlsnoR12.1 and SlU24a. Characteristic C and D, and C' and D', boxes are conserved in SlsnoR12.1 and SlU24a while the upstream flanking region of SlsnoR12.1 carries TATA box 1, homol-E and homol-D box-like cis sequences, TM6 promoter, and an uncharacterized tomato EST. Molecular phylogenetic analysis revealed that this particular arrangement of shsps is conserved in tomato genome but is distinct from other species. The intronless genomic sequence is decorated with cis elements previously shown to be responsive to cues from plant hormones, dehydration, cold, heat, and MYC/MYB and WRKY71 transcription factors. Chromosomal mapping localized the tomato genomic sequence on the short arm of chromosome 6 in the introgression line (IL) 6-3. Quantitative polymerase chain reaction analysis of gene cluster members revealed differential expression during ripening of tomato fruit, and relatively different abundances in other plant parts.

Effect of addition of aluminum on the evolution of microstructure in HITPERM class Fe44Co44Zr7B4Cu1 alloy

The paper reports the effect of the addition of small amount of Al on the microstructure and properties of HITPERM class rapidly solidified Fe44Co44Zr7B4Cu1 glassy alloy. Using three dimensional atom probe measurements we present evidence for the formation of Cu clusters on annealing in the metallic glass matrix of the Al containing alloy Fe43Co43Al2Zr7B4Cu1. Such clusters are otherwise absent in the parent alloy under similar conditions. The Cu clusters provides heterogeneous nucleation sites for the formation of bcc alpha'-FeCo phase leading to an increase in number density of this nanocrystalline phase and thereby enhancing the magnetic properties. (C) 2012 Elsevier B.V. All rights reserved.

Synthesis of benzofuran based 1,3,5-substituted pyrazole derivatives: As a new class of potent antioxidants and antimicrobials-A novel accost to amend biocompatibility

In search for a new antioxidant and antimicrobial agent with improved potency, we synthesized a series of benzofuran based 1,3,5-substituted pyrazole analogues (5a-l) in five step reaction. Initially, o-alkyl derivative of salicyaldehyde readily furnish corresponding 2-acetyl benzofuran 2 in good yield, on treatment with 1,8-diaza bicyclo5.4.0]undec-7-ene (DBU) in the presence of molecular sieves. Further, aldol condensation with vanillin, Claisen-Schmidt condensation reaction with hydrazine hydrate followed by coupling of substituted anilines afforded target compounds. The structures of newly synthesized compounds were confirmed by IR, H-1 NMR, C-13 NMR, mass, elemental analysis and further screened for their antioxidant and antimicrobial activities. Among the tested compounds 5d and 5f exhibited good antioxidant property with 50% inhibitory concentration higher than that of reference while compounds 5h and 5l exhibited good antimicrobial activity at concentration 1.0 and 0.5 mg/mL compared with standard, streptomycin and fluconazole respectively. (C) 2012 Elsevier Ltd. All rights reserved.

Application of a Class of Nano fluids to improve the Loadability of Power Transformers

It is generally known that addition of conducting or insulating particles to mineral transformer oil, lowers its breakdown strength, E-d. However, if the particulates are of molecular dimensions, or nanoparticles, (NPs), as they are called, the breakdown strength is seen to increase considerably. Recent experiments by the authors on oil cooled power equipment such as transformers showed that, nanofluids comprising NPs of selected oxides of iron, such as Fe(3)o(4), called magnetite, added to transformer oil increased the breakdown voltage of the virgin oil and more importantly a remarkable enhancement in the thermal conductivity and the viscosity and hence an increased loadability of the transformer for a given top oil temperature (TOT).

Serodiagnosis of Tuberculosis in Asian Elephants (Elephas maximus) in Southern India: A Latent Class Analysis

Background: Mycobacterium tuberculosis, a causative agent of chronic tuberculosis disease, is widespread among some animal species too. There is paucity of information on the distribution, prevalence and true disease status of tuberculosis in Asian elephants (Elephas maximus). The aim of this study was to estimate the sensitivity and specificity of serological tests to diagnose M. tuberculosis infection in captive elephants in southern India while simultaneously estimating sero-prevalence. Methodology/Principal Findings: Health assessment of 600 elephants was carried out and their sera screened with a commercially available rapid serum test. Trunk wash culture of select rapid serum test positive animals yielded no animal positive for M. tuberculosis isolation. Under Indian field conditions where the true disease status is unknown, we used a latent class model to estimate the diagnostic characteristics of an existing (rapid serum test) and new (four in-house ELISA) tests. One hundred and seventy nine sera were randomly selected for screening in the five tests. Diagnostic sensitivities of the four ELISAs were 91.3-97.6% (95% Credible Interval (CI): 74.8-99.9) and diagnostic specificity were 89.6-98.5% (95% CI: 79.4-99.9) based on the model we assumed. We estimate that 53.6% (95% CI: 44.6-62.8) of the samples tested were free from infection with M. tuberculosis and 15.9% (97.5% CI: 9.8 - to 24.0) tested positive on all five tests. Conclusions/Significance: Our results provide evidence for high prevalence of asymptomatic M. tuberculosis infection in Asian elephants in a captive Indian setting. Further validation of these tests would be important in formulating area-specific effective surveillance and control measures.

Performance of a class of multi-robot deploy and search strategies based on centroidal voronoi configurations

This article considers a class of deploy and search strategies for multi-robot systems and evaluates their performance. The application framework used is deployment of a system of autonomous mobile robots equipped with required sensors in a search space to gather information. The lack of information about the search space is modelled as an uncertainty density distribution. The agents are deployed to maximise single-step search effectiveness. The centroidal Voronoi configuration, which achieves a locally optimal deployment, forms the basis for sequential deploy and search (SDS) and combined deploy and search (CDS) strategies. Completeness results are provided for both search strategies. The deployment strategy is analysed in the presence of constraints on robot speed and limit on sensor range for the convergence of trajectories with corresponding control laws responsible for the motion of robots. SDS and CDS strategies are compared with standard greedy and random search strategies on the basis of time taken to achieve reduction in the uncertainty density below a desired level. The simulation experiments reveal several important issues related to the dependence of the relative performances of the search strategies on parameters such as the number of robots, speed of robots and their sensor range limits.

Semi-supervised SVMs for classification with unknown class proportions and a small labeled dataset

In the design of practical web page classification systems one often encounters a situation in which the labeled training set is created by choosing some examples from each class; but, the class proportions in this set are not the same as those in the test distribution to which the classifier will be actually applied. The problem is made worse when the amount of training data is also small. In this paper we explore and adapt binary SVM methods that make use of unlabeled data from the test distribution, viz., Transductive SVMs (TSVMs) and expectation regularization/constraint (ER/EC) methods to deal with this situation. We empirically show that when the labeled training data is small, TSVM designed using the class ratio tuned by minimizing the loss on the labeled set yields the best performance; its performance is good even when the deviation between the class ratios of the labeled training set and the test set is quite large. When the labeled training data is sufficiently large, an unsupervised Gaussian mixture model can be used to get a very good estimate of the class ratio in the test set; also, when this estimate is used, both TSVM and EC/ER give their best possible performance, with TSVM coming out superior. The ideas in the paper can be easily extended to multi-class SVMs and MaxEnt models.