A novel approach based on recurrent neural networks applied to nonlinear systems optimization

This paper presents an efficient approach based on recurrent neural network for solving nonlinear optimization. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid subspace technique. These parameters guarantee the convergence of the network to the equilibrium points that represent an optimal feasible solution. The main advantage of the developed network is that it treats optimization and constraint terms in different stages with no interference with each other. Moreover, the proposed approach does not require specification of penalty and weighting parameters for its initialization. A study of the modified Hopfield model is also developed to analyze its stability and convergence. Simulation results are provided to demonstrate the performance of the proposed neural network.     

Synchronization Analysis of Coupled Noncoherent Oscillators

We present two different approaches to detect and quantify phase synchronization in the case of coupled non-phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the R?ssler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators.     

Crystalline structure of polyamide 12 as revealed by solid‐state 13C NMR and synchrotron WAXS and SAXS

The crystalline structure of polyamide‐12 (PA12) was studied by solid‐state ¹³C nuclear magnetic resonance (NMR) as well as by synchrotron wide‐ and small‐angle X‐ray scattering (WAXS and SAXS). Isotropic and oriented PA12 showed different NMR spectra ascribed to γ‐ and γ′‐crystalline modifications, respectively. On the basis of the position of the first diffraction peak, the isotropic γ‐form and the oriented γ′‐form were shown to be with hexagonal crystalline lattice at room temperature. When heated, the two PA12 polymorphs demonstrated different behaviors. Above 140 °C, the isotropic γ‐PA12 partially transformed into α‐modification. No such transition was observed with the oriented γ′‐PA12 phase even after annealing at temperatures close to melting. A γ′–γ transition was observed here only after isotropization by melting point. Various structural parameters were extracted from the WAXS and SAXS patterns and analyzed as a function of temperature and orientation: the degree of crystallinity, the d‐spacings, the Bragg's long spacings, the average thicknesses of the crystalline (l_c) and amorphous (l_a) phases, and the linear crystallinity x_cl within the lamellar stacks. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3720–3733, 2005     

Reaction kinetics and pathway of hydrothermal decomposition of aspartic acid

The kinetics and pathway of hydrothermal decomposition of aspartic acid were studied using a continuous‐flow tubular reactor. The reaction was carried out in the temperature range of 200–260°C and at a pressure of 20 MPa. Deamination was the primary reaction, indicated by the presence of significant amount of ammonia, fumaric acid, or maleic acid in the products. Other reaction products were pyruvic acid, malic acid, and traces of succinic and lactic acid. Traces of alanine were also detected, showing the possibility of decomposing high‐molecular weight amino acids to obtain simple amino acids such as glycine or alanine. Results on the effect of reaction parameters demonstrated that decomposition of aspartic acid is highly temperature dependent under hydrothermal conditions. For a slight temperature difference of 60°C (from 200 to 260°C), the first‐order reaction rate constants of 0.003 significantly increased to 0.231 s^?1. The activation energy was 144 kJ/mol, as calculated by the Arrhenius equation. No significant effect was exhibited by other reaction parameters such as pH and pressure. The results are useful in controlling the hydrolysis of proteinaceous materials toward high yield of aspartic acid under hydrothermal conditions. © 2007 Wiley Periodicals, Inc. 39: 175–180, 2007     

Analysis of a demodulation system for Fiber Bragg Grating sensors using two fixed filters

The analysis of a demodulation system for Fiber Bragg Grating sensors based on two fixed spectral filters has been carried out both theoretically and experimentally. Different system configurations were analyzed by modifying the spectral position of the filters as well as the optical power-level of the signal reaching the two photo-detectors. Measurements with integration times that varied from 0.01 to 1 s have been compared with the low-frequency limit predicted for long-term operation. Comparisons between simulated and experimental results show good agreement, and extrapolations indicate that it should be possible to achieve an operating spectrum range of the order of 7 nm, with uncertainties equivalent to less than 2 pm in measurements of the sensor peak position.     

Operator stable laws: Series representations and domains of normal attraction

LetX,X ₁,X ₂,... be i.i.d. random vectors in ^d. The limit laws that can arise by suitable affine normalizations of the partial sums,S _n=X ₁+...+X _n, are calledoperator-stable laws. These laws are a natural extension to ^d of the stable laws on. Thegeneralized domain of attraction of [GDOA()] is comprised of all random vectorsX whose partial sums can be affinely normalized to converge to . If the linear part of the affine transformation is restricted to take the formn ^–B for some exponent operatorB naturally associated to thenX is in thegeneralized domain of normal attraction of [GDONA()]. This paper extends the theory of operator-stable laws and their domains of attraction and normal attraction.