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.

Evidence for a thermally reversing window in bulk Ge–Te–Si glasses revealed by alternating differential scanning calorimetry

Experiments on Ge15Te85− x Si x glasses (2 ≤ x ≤ 12) using alternating differential scanning calorimetry (ADSC) indicate that these glasses exhibit one glass transition and two crystallization reactions upon heating. The glass transition temperature has been found to increase almost linearly with silicon content, in the entire composition tie-line. The first crystallization temperature (T c1) exhibits an increase with silicon content for x < 5; T c1 remains almost a constant in the composition range 5 < x ≤ 10 and it increases comparatively more sharply with silicon content thereafter. The specific heat change (ΔC p) is found to decrease with an increase in silicon content, exhibiting a minimum at x = 5 (average coordination number, r = 2.4); a continuous increase is seen in ΔC p with silicon concentration above x = 5. The effects seen in the variation with composition of T c1 and ΔC p at x = 5, are the specific signatures of the mean-field stiffness threshold at r = 2.4. Furthermore, a broad trough is seen in the enthalpy change (ΔH NR), which is indicative of a thermally reversing window in Ge15Te85− x Si x glasses in the composition range 2 ≤ x ≤ 6 (2.34 ≤ r ≤ 2.42).

Estimation of Series Capacitance of a Transformer Winding Based on Frequency-Response Data: An Indirect Measurement Approach

A novel procedure to determine the series capacitance of a transformer winding, based on frequency-response measurements, is reported. It is based on converting the measured driving-point impedance magnitude response into a rational function and thereafter exploiting the ratio of a specific coefficient in the numerator and denominator polynomial, which leads to the direct estimation of series capacitance. The theoretical formulations are derived for a mutually coupled ladder-network model, followed by sample calculations. The results obtained are accurate and its feasibility is demonstrated by experiments on model-coil and on actual, single, isolated transformer windings (layered, continuous disc, and interleaved disc). The authors believe that the proposed method is the closest one can get to indirectly measuring series capacitance.

Differential Reaction Kinetics, Cleavage Complex Formation, and Nonamer Binding Domain Dependence Dictate the Structure-Specific and Sequence-Specific Nuclease Activity of RAGs

During V(D)J recombination, RAG (recombination-activating gene) complex cleaves DNA based on sequence specificity. Besides its physiological function, RAG has been shown to act as a structure-specific nuclease. Recently, we showed that the presence of cytosine within the single-stranded region of heteroduplex DNA is important when RAGs cleave on DNA structures. In the present study, we report that heteroduplex DNA containing a bubble region can be cleaved efficiently when present along with a recombination signal sequence (RSS) in cis or trans configuration. The sequence of the bubble region influences RAG cleavage at RSS when present in cis. We also find that the kinetics of RAG cleavage differs between RSS and bubble, wherein RSS cleavage reaches maximum efficiency faster than bubble cleavage. In addition, unlike RSS, RAG cleavage at bubbles does not lead to cleavage complex formation. Finally, we show that the ``nonamer binding region,'' which regulates RAG cleavage on RSS, is not important during RAG activity in non-B DNA structures. Therefore, in the current study, we identify the possible mechanism by which RAG cleavage is regulated when it acts as a structure-specific nuclease. (C) 2011 Elsevier Ltd. All rights reserved.

A computational procedure to generate difference equations from differential equations

In this paper we have developed methods to compute maps from differential equations. We take two examples. First is the case of the harmonic oscillator and the second is the case of Duffing's equation. First we convert these equations to a canonical form. This is slightly nontrivial for the Duffing's equation. Then we show a method to extend these differential equations. In the second case, symbolic algebra needs to be used. Once the extensions are accomplished, various maps are generated. The Poincare sections are seen as a special case of such generated maps. Other applications are also discussed.

Insights into differential modulation of receptor function by hinge region using novel agonistic lutropin receptor and inverse agonistic thyrotropin receptor antibodies

We report two antibodies, scFv 13B1 and MAb PD1.37, against the hinge regions of LHR and TSHR, respectively, which have similar epitopes but different effects on receptor function. While neither of them affected hormone binding, with marginal effects on hormone response, scFv 13B1 stimulated LHR in a dose-dependent manner, whereas MAb PD1.37 acted as an inverse agonist of TSHR. Moreover, PD1.37 could decrease the basal activity of hinge region CAMs, but had varied effects on those present in ECLs, whereas 13B1 was refractory to any CAMs in LHR. Using truncation mutants and peptide phage display, we compared the differential roles of the hinge region cysteine box-2/3 as well as the exoloops in the activation of these two homologus receptors. (C) 2012 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.

Enhancement of circular differential deflection of light in an optically active medium

In this letter, we investigate the circular differential deflection of a light beam refracted at the interface of an optically active medium. We show that the difference between the angles of deviation of the two circularly polarized components of the transmitted beam is enhanced manyfold near total internal reflection, which suggests a simple way of increasing the limit of detection of chiro-optical measurements. (C) 2012 Optical Society of America

Differential Diffractive Reflectance Modulation Sensing

We fabricated a reflectance based sensor which relies on the diffraction pattern generated from a bio-microarray where an underlying thin film structure enhances the diffracted intensity from molecular layers. The zero order diffraction represents the background signal and the higher orders represent the phase difference between the array elements and the background. By taking the differential ratio of the first and zero order diffraction signals we get a quantitative measure of molecular binding while simultaneously rejecting common mode fluctuations. We improved the signal-to-noise ratio by an order of magnitude with this ratiometric approach compared to conventional single channel detection. In addition, we use a lithography based approach for fabricating microarrays which results in spot sizes as small as 5 micron diameter unlike the 100 micron spots from inkjet printing and is therefore capable of a high degree of multiplexing. We will describe the real-time measurement of adsorption of charged polymers and bulk refractometry using this technique. The lack of moving parts for point scanning of the microarray and the differential ratiometric measurements using diffracted orders from the same probe beam allows us to make real-time measurements in spite of noise arising from thermal or mechanical fluctuations in the fluid sample above the sensor surface. Further, the lack of moving parts leads to considerable simplification in the readout hardware permitting the use of this technique in compact point of care sensors.

Quantum capacitance in bilayer graphene nanoribbon

We address a physically based analytical model of quantum capacitance (C-Q) in a bilayer graphene nanoribbon (BGN) under the application of an external longitudinal static bias. We demonstrate that as the gap (Delta) about the Dirac point increases, a phenomenological population inversion of the carriers in the two sets of subbands occurs. This results in a periodic and composite oscillatory behavior in the C-Q with the channel potential, which also decreases with increase in Delta. We also study the quantum size effects on the C-Q, which signatures heavy spatial oscillations due to the occurrence of van Hove singularities in the total density-of-states function of both the sets of subbands. All the mathematical results as derived in this paper converge to the corresponding well-known solution of graphene under certain limiting conditions and this compatibility is an indirect test of our theoretical formalism. (C) 2012 Elsevier By. All rights reserved.

SPLIT-STEP FORWARD MILSTEIN METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS

In this paper, we consider the problem of computing numerical solutions for stochastic differential equations (SDEs) of Ito form. A fully explicit method, the split-step forward Milstein (SSFM) method, is constructed for solving SDEs. It is proved that the SSFM method is convergent with strong order gamma = 1 in the mean-square sense. The analysis of stability shows that the mean-square stability properties of the method proposed in this paper are an improvement on the mean-square stability properties of the Milstein method and three stage Milstein methods.

Zero-Sum Risk-Sensitive Stochastic Differential Games

We study zero-sum risk-sensitive stochastic differential games on the infinite horizon with discounted and ergodic payoff criteria. Under certain assumptions, we establish the existence of values and saddle-point equilibria. We obtain our results by studying the corresponding Hamilton-Jacobi-Isaacs equations. Finally, we show that the value of the ergodic payoff criterion is a constant multiple of the maximal eigenvalue of the generators of the associated nonlinear semigroups.

Existence of Value in Stochastic Differential Games of Mixed Type

In this article, we address stochastic differential games of mixed type with both control and stopping times. Under standard assumptions, we show that the value of the game can be characterized as the unique viscosity solution of corresponding Hamilton-Jacobi-Isaacs (HJI) variational inequalities.

Equal channel angular pressing processing routes and associated structure modification: a differential scanning calorimetry and X-ray line profile analysis

The effectiveness of different routes of equal channel angular pressing (A, B-c, and C) is studied for commercially pure copper. The stored energy and the activation energy of recrystallization for the deformed samples were quantified using differential scanning calorimetry and X-ray diffraction line profile analysis. Results of the study revealed that the dislocation density and the stored energy are higher in the case of route B-c deformed sample. The activation energy for recrystallization is lower for route B-c. (C) 2012 International Centre for Diffraction Data doi:10.1017/S0885715612000310]