Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

Semiclassical evolution of dissipative Markovian systems

A semiclassical approximation for an evolving density operator, driven by a `closed` Hamiltonian operator and `open` Markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the Hamiltonian operator is a quadratic function and the Lindblad operators are linear functions of positions and momenta. Initially, the semiclassical formulae for the case of Hermitian Lindblad operators are reinterpreted in terms of a (real) double phase space, generated by an appropriate classical double Hamiltonian. An extra `open` term is added to the double Hamiltonian by the non-Hermitian part of the Lindblad operators in the general case of dissipative Markovian evolution. The particular case of generic Hamiltonian operators, but linear dissipative Lindblad operators, is studied in more detail. A Liouville-type equivariance still holds for the corresponding classical evolution in double phase space, but the centre subspace, which supports the Wigner function, is compressed, along with expansion of its conjugate subspace, which supports the chord function. Decoherence narrows the relevant region of double phase space to the neighbourhood of a caustic for both the Wigner function and the chord function. This difficulty is avoided by a propagator in a mixed representation, so that a further `small-chord` approximation leads to a simple generalization of the quadratic theory for evolving Wigner functions.

UNIFORM DISSIPATIVENESS, ROBUST SYNCHRONIZATION AND LOCATION OF THE ATTRACTOR OF PARAMETRIZED NONAUTONOMOUS DISCRETE SYSTEMS

In this series of papers, we study issues related to the synchronization of two coupled chaotic discrete systems arising from secured communication. The first part deals with uniform dissipativeness with respect to parameter variation via the Liapunov direct method. We obtain uniform estimates of the global attractor for a general discrete nonautonomous system, that yields a uniform invariance principle in the autonomous case. The Liapunov function is allowed to have positive derivative along solutions of the system inside a bounded set, and this reduces substantially the difficulty of constructing a Liapunov function for a given system. In particular, we develop an approach that incorporates the classical Lagrange multiplier into the Liapunov function method to naturally extend those Liapunov functions from continuous dynamical system to their discretizations, so that the corresponding uniform dispativeness results are valid when the step size of the discretization is small. Applications to the discretized Lorenz system and the discretization of a time-periodic chaotic system are given to illustrate the general results. We also show how to obtain uniform estimation of attractors for parametrized linear stable systems with nonlinear perturbation.

The log-exponentiated Weibull regression model for interval-censored data

In interval-censored survival data, the event of interest is not observed exactly but is only known to occur within some time interval. Such data appear very frequently. In this paper, we are concerned only with parametric forms, and so a location-scale regression model based on the exponentiated Weibull distribution is proposed for modeling interval-censored data. We show that the proposed log-exponentiated Weibull regression model for interval-censored data represents a parametric family of models that include other regression models that are broadly used in lifetime data analysis. Assuming the use of interval-censored data, we employ a frequentist analysis, a jackknife estimator, a parametric bootstrap and a Bayesian analysis for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Furthermore, for different parameter settings, sample sizes and censoring percentages, various simulations are performed; in addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended to a modified deviance residual in log-exponentiated Weibull regression models for interval-censored data. (C) 2009 Elsevier B.V. All rights reserved.

A linear optimization approach to the combined production planning model

Two fundamental processes usually arise in the production planning of many industries. The first one consists of deciding how many final products of each type have to be produced in each period of a planning horizon, the well-known lot sizing problem. The other process consists of cutting raw materials in stock in order to produce smaller parts used in the assembly of final products, the well-studied cutting stock problem. In this paper the decision variables of these two problems are dependent of each other in order to obtain a global optimum solution. Setups that are typically present in lot sizing problems are relaxed together with integer frequencies of cutting patterns in the cutting problem. Therefore, a large scale linear optimizations problem arises, which is exactly solved by a column generated technique. It is worth noting that this new combined problem still takes the trade-off between storage costs (for final products and the parts) and trim losses (in the cutting process). We present some sets of computational tests, analyzed over three different scenarios. These results show that, by combining the problems and using an exact method, it is possible to obtain significant gains when compared to the usual industrial practice, which solve them in sequence. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Large Changes of Static Electric Properties Induced by Hydrogen Bonding: An ab Initio Study of Linear HCN Oligomers

We report the partitioning of the interaction-induced static electronic dipole (hyper)polarizabilities for linear hydrogen cyanide complexes into contributions arising from various interaction energy terms. We analyzed the nonadditivities of the studied properties and used these data to predict the electric properties of an infinite chain. The interaction-induced static electric dipole properties and their nonadditivities were analyzed using an approach based on numerical differentiation of the interaction energy components estimated in an external electric field. These were obtained using the hybrid variational-perturbational interaction energy decomposition scheme, augmented with coupled-cluster calculations, with singles, doubles, and noniterative triples. Our results indicate that the interaction-induced dipole moments and polarizabilities are primarily electrostatic in nature; however, the composition of the interaction hyperpolarizabilities is much more complex. The overlap effects substantially quench the contributions due to electrostatic interactions, and therefore, the major components are due to the induction and exchange induction terms, as well as the intramolecular electron-correlation corrections. A particularly intriguing observation is that the interaction first hyperpolarizability in the studied systems not only is much larger than the corresponding sum of monomer properties, but also has the opposite sign. We show that this effect can be viewed as a direct consequence of hydrogen-bonding interactions that lead to a decrease of the hyperpolarizability of the proton acceptor and an increase of the hyperpolarizability of the proton donor. In the case of the first hyperpolarizability, we also observed the largest nonadditivity of interaction properties (nearly 17%) which further enhances the effects of pairwise interactions.

Fock space for fermion-like lattices and the linear Glauber model

The concept of Fock space representation is developed to deal with stochastic spin lattices written in terms of fermion operators. A density operator is introduced in order to follow in parallel the developments of the case of bosons in the literature. Some general conceptual quantities for spin lattices are then derived, including the notion of generating function and path integral via Grassmann variables. The formalism is used to derive the Liouvillian of the d-dimensional Linear Glauber dynamics in the Fock-space representation. Then the time evolution equations for the magnetization and the two-point correlation function are derived in terms of the number operator. (C) 2008 Elsevier B.V. All rights reserved.

Augmented Lagrangian methods under the constant positive linear dependence constraint qualification

Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented.

Skew-normal linear calibration: a Bayesian perspective

In this paper, we present a Bayesian approach for estimation in the skew-normal calibration model, as well as the conditional posterior distributions which are useful for implementing the Gibbs sampler. Data transformation is thus avoided by using the methodology proposed. Model fitting is implemented by proposing the asymmetric deviance information criterion, ADIC, a modification of the ordinary DIC. We also report an application of the model studied by using a real data set, related to the relationship between the resistance and the elasticity of a sample of concrete beams. Copyright (C) 2008 John Wiley & Sons, Ltd.

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem. (C) 2008 Elsevier Inc. All rights reserved.

Techno-economic Appraisal of Concentrating Solar Power Systems (CSP)

The diffusion of Concentrating Solar Power Systems (CSP) systems is currently taking place at a much slower pace than photovoltaic (PV) power systems. This is mainly because of the higher present cost of the solar thermal power plants, but also for the time that is needed in order to build them. Though economic attractiveness of different Concentrating technologies varies, still PV power dominates the market. The price of CSP is expected to drop significantly in the near future and wide spread installation of them will follow. The main aim of this project is the creation of different relevant case studies on solar thermal power generation and a comparison betwwen them. The purpose of this detailed comparison is the techno-economic appraisal of a number of CSP systems and the understanding of their behaviour under various boundary conditions. The CSP technologies which will be examined are the Parabolic Trough, the Molten Salt Power Tower, the Linear Fresnel Mirrors and the Dish Stirling. These systems will be appropriatly sized and simulated. All of the simulations aim in the optimization of the particular system. This includes two main issues. The first is the achievement of the lowest possible levelized cost of electricity and the second is the maximization of the annual energy output (kWh). The project also aims in the specification of these factors which affect more the results and more specifically, in what they contribute to the cost reduction or the power generation. Also, photovoltaic systems will be simulated under same boundary conditions to facolitate a comparison between the PV and the CSP systems. Last but not leats, there will be a determination of the system which performs better in each case study.

Likelihood prediction for generalized linear mixed models under covariate uncertainty

This paper presents the techniques of likelihood prediction for the generalized linear mixed models. Methods of likelihood prediction is explained through a series of examples; from a classical one to more complicated ones. The examples show, in simple cases, that the likelihood prediction (LP) coincides with already known best frequentist practice such as the best linear unbiased predictor. The paper outlines a way to deal with the covariate uncertainty while producing predictive inference. Using a Poisson error-in-variable generalized linear model, it has been shown that in complicated cases LP produces better results than already know methods.

Low cost BIST techniques for linear and non-linear analog circuits

With the ever increasing demands for high complexity consumer electronic products, market pressures demand faster product development and lower cost. SoCbased design can provide the required design flexibility and speed by allowing the use of IP cores. However, testing costs in the SoC environment can reach a substantial percent of the total production cost. Analog testing costs may dominate the total test cost, as testing of analog circuits usually require functional verification of the circuit and special testing procedures. For RF analog circuits commonly used in wireless applications, testing is further complicated because of the high frequencies involved. In summary, reducing analog test cost is of major importance in the electronic industry today. BIST techniques for analog circuits, though potentially able to solve the analog test cost problem, have some limitations. Some techniques are circuit dependent, requiring reconfiguration of the circuit being tested, and are generally not usable in RF circuits. In the SoC environment, as processing and memory resources are available, they could be used in the test. However, the overhead for adding additional AD and DA converters may be too costly for most systems, and analog routing of signals may not be feasible and may introduce signal distortion. In this work a simple and low cost digitizer is used instead of an ADC in order to enable analog testing strategies to be implemented in a SoC environment. Thanks to the low analog area overhead of the converter, multiple analog test points can be observed and specific analog test strategies can be enabled. As the digitizer is always connected to the analog test point, it is not necessary to include muxes and switches that would degrade the signal path. For RF analog circuits, this is specially useful, as the circuit impedance is fixed and the influence of the digitizer can be accounted for in the design phase. Thanks to the simplicity of the converter, it is able to reach higher frequencies, and enables the implementation of low cost RF test strategies. The digitizer has been applied successfully in the testing of both low frequency and RF analog circuits. Also, as testing is based on frequency-domain characteristics, nonlinear characteristics like intermodulation products can also be evaluated. Specifically, practical results were obtained for prototyped base band filters and a 100MHz mixer. The application of the converter for noise figure evaluation was also addressed, and experimental results for low frequency amplifiers using conventional opamps were obtained. The proposed method is able to enhance the testability of current mixed-signal designs, being suitable for the SoC environment used in many industrial products nowadays.

Novel catalyst systems based on Ni(II), Ti(IV), and Cr(III) complexes for oligo-and polymerization of ethylene

The complex of Brookhart Ni(α-diimine)Cl2 (1) (α-diimine = 1,4-bis(2,6- diisopropylphenyl)-acenaphthenediimine) has been characterized after impregnation on silica (S1) and MAO-modified silicas (4.0, 8.0 and 23.0 wts.% Al/SiO2 called S2, S3 and S4, respectively). The treatment of these heterogeneous systems with MAO produces some active catalysts for the polymerization of the ethylene. A high catalytic activity has been gotten while using the system supported 1/S3 (196 kg of PE/mol[Ni].h.atm; toluene, Al/Ni = 1000, 30ºC, 60 min and atmospheric pressure of ethylene). The effects of polymerization conditions have been tested with the catalyst supported in S2 and the best catalytic activity has been gotten with solvent hexane, MAO as cocatalyst, molar ratio Al/Ni of 1000 and to the temperature of 30°C (285 kg of PE/mol[Ni].h.atm). When the reaction has been driven according to the in situ methodology, the activity practically doubled and polymers showed some similar properties. Polymers products by the supported catalysts showed the absence of melting fusion, results similar to those gotten with the homogeneous systems by DSC analysis. But then, polymers gotten with the transplanted system present according to the GPC’s curves the polydispersity (MwD) varies between 1.7 and 7.0. A polyethylene blend (BPE/LPE) was prepared using the complex Ni(α-diimine)Cl2 (1) (α-diimine = 1,4-bis(2,6-diisopropylphenyl)-acenaphthenediimine) and {TpMs*}TiCl3 (2) (TpMs* = hydridobis(3-mesitylpyrazol-1-yl)(5-mesitylpyrazol-1-yl)) supported in situ on MAO-modified silica (4.0 wts. -% Al/SiO2, S2). Reactions of polymerization of ethylene have been executed in the toluene in two different temperatures (0 and 30°C), varying the molars fraction of nickel (xNi), and using MAO as external cocatalyst. To all temperatures, the activities show a linear variation tendency with xNi and indicate the absence of the effect synergic between the species of nickel and the titanium. The maximum of activity have been found at 0°C. The melting temperature for the blends of polyethylene produced at 0 °C decrease whereas xNi increases indicating a good compatibility between phases of the polyethylene gotten with the two catalysts. The melting temperature for the blends of polyethylene showed be depend on the order according to which catalysts have been supported on the MAO-modified silica. The initial immobilization of 1 on the support (2/1/S2) product of polymers with a melting temperature (Tm) lower to the one of the polymer gotten when the titanium has been supported inicially (1/2/S2). The observation of polyethylenes gotten with the two systems (2/1/S2 and 1/2/S2) by scanning electron microscopy (SEM) showed the spherical polymer formation showing that the spherical morphology of the support to been reproduced. Are described the synthesis, the characterization and the catalytic properties for the oligomerization of the ethylene of four organometallics compounds of CrIII with ligands ([bis[2-(3,5-dimethyl-1-pyrazolyl)ethyl]amine] chromium (III) chloride (3a), [bis[2-(3,5- dimethyl-l-pyrazolyl)ethyl]benzylamine] chromium (III) chloride (3b), [bis[2-(3,5-dimethyl-lpyrazolyl) ethyl]ether] chromiun(III)chloride (3c), [bis[2-(3-phenyl-lpyrazolyl) ethyl]ether]chromiun(III)chloride (3d)). In relation of the oligomerization, at exception made of the compounds 3a, all complex of the chromium showed be active after activation with MAO and the TOF gotten have one effect differentiated to those formed with CrCl3(thf)3. The coordination of a tridentate ligand on the metallic center doesn't provoke any considerable changes on the formation of the C4 and C6, but the amount of C8 are decrease and the C10 and C12+ have increased. The Polymers produced by the catalyst 3a to 3 and 20 bar of ethylene have, according to analyses by DSC, the temperatures of fusion of 133,8 and 136ºC respectively. It indicates that in the two cases the production of high density polyethylene. The molar mass, gotten by GPC, is 46647 g/mols with MwD = 2,4 (3 bar). The system 3c/MAO showed values of TOF, activity and selectivity to different α-olefins according to the pressure of ethylene uses. Himself that shown a big sensibility to the concentration of ethylene solubilized.

A comparison of test of non-linear cointegration with an application to the predictability of US interest rates using the term structure

We evaluate the forecasting performance of a number of systems models of US shortand long-term interest rates. Non-linearities, induding asymmetries in the adjustment to equilibrium, are shown to result in more accurate short horizon forecasts. We find that both long and short rates respond to disequilibria in the spread in certain circumstances, which would not be evident from linear representations or from single-equation analyses of the short-term interest rate.