Information Filtering and Array Algorithms for Discrete-Time Markovian Jump Linear Systems

This technical note develops information filter and array algorithms for a linear minimum mean square error estimator of discrete-time Markovian jump linear systems. A numerical example for a two-mode Markovian jump linear system, to show the advantage of using array algorithms to filter this class of systems, is provided.

Linear viscoelasticity of styrenic block copolymers-clay nanocomposites

In this work, the rheological behavior of block copolymers with different morphologies (lamellar, cylindrical, spherical, and disordered) and their clay-containing nanocomposites was studied using small amplitude oscillatory shear. The copolymers studied were one asymmetric starblock styrene-butadiene-styrene copolymer and four styrene-ethylene/butylenes-styrene copolymers with different molecular architectures, one of them being modified with maleic anhydride. The nanocomposites of those copolymers were prepared by adding organophilic clay using three different preparation techniques: melt mixing, solution casting, and a hybrid melt mixing-solution technique. The nanocomposites were characterized by X-ray diffraction and transmission electron microscopy, and their viscoelastic properties were evaluated and compared to the ones of the pure copolymers. The influence of copolymer morphology and presence of clay on the storage modulus (G`) curves was studied by the evaluation of the changes in the low frequency slope of log G` x log omega (omega: frequency) curves upon variation of temperature and clay addition. This slope may be related to the degree of liquid- or solid-like behavior of a material. It was observed that at temperatures corresponding to the ordered state, the rheological behavior of the nanocomposites depended mainly on the viscoelasticity of each type of ordered phase and the variation of the slope due to the addition of clay was small. For temperatures corresponding to the disordered state, however, the rheological behavior of the copolymer nanocomposites was dictated mostly by the degree of clay dispersion: When the clay was well dispersed, a strong solid-like behavior corresponding to large G` slope variations was observed.

Robust integration of real time optimization with linear model predictive control

Here, we study the stable integration of real time optimization (RTO) with model predictive control (MPC) in a three layer structure. The intermediate layer is a quadratic programming whose objective is to compute reachable targets to the MPC layer that lie at the minimum distance to the optimum set points that are produced by the RTO layer. The lower layer is an infinite horizon MPC with guaranteed stability with additional constraints that force the feasibility and convergence of the target calculation layer. It is also considered the case in which there is polytopic uncertainty in the steady state model considered in the target calculation. The dynamic part of the MPC model is also considered unknown but it is assumed to be represented by one of the models of a discrete set of models. The efficiency of the methods presented here is illustrated with the simulation of a low order system. (C) 2010 Elsevier Ltd. All rights reserved.

On the Filtering Problem for Continuous-Time Markov Jump Linear Systems with no Observation of the Markov Chain

We consider in this paper the optimal stationary dynamic linear filtering problem for continuous-time linear systems subject to Markovian jumps in the parameters (LSMJP) and additive noise (Wiener process). It is assumed that only an output of the system is available and therefore the values of the jump parameter are not accessible. It is a well known fact that in this setting the optimal nonlinear filter is infinite dimensional, which makes the linear filtering a natural numerically, treatable choice. The goal is to design a dynamic linear filter such that the closed loop system is mean square stable and minimizes the stationary expected value of the mean square estimation error. It is shown that an explicit analytical solution to this optimal filtering problem is obtained from the stationary solution associated to a certain Riccati equation. It is also shown that the problem can be formulated using a linear matrix inequalities (LMI) approach, which can be extended to consider convex polytopic uncertainties on the parameters of the possible modes of operation of the system and on the transition rate matrix of the Markov process. As far as the authors are aware of this is the first time that this stationary filtering problem (exact and robust versions) for LSMJP with no knowledge of the Markov jump parameters is considered in the literature. Finally, we illustrate the results with an example.

Discrete-time mean variance optimal control of linear systems with Markovian jumps and multiplicative noise

In this article, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noise under three kinds of performance criterions related to the final value of the expectation and variance of the output. In the first problem it is desired to minimise the final variance of the output subject to a restriction on its final expectation, in the second one it is desired to maximise the final expectation of the output subject to a restriction on its final variance, and in the third one it is considered a performance criterion composed by a linear combination of the final variance and expectation of the output of the system. We present explicit sufficient conditions for the existence of an optimal control strategy for these problems, generalising previous results in the literature. We conclude this article presenting a numerical example of an asset liabilities management model for pension funds with regime switching.

Non-linear modal analysis for beams subjected to axial loads: Analytical and finite-element solutions

A rigorous derivation of non-linear equations governing the dynamics of an axially loaded beam is given with a clear focus to develop robust low-dimensional models. Two important loading scenarios were considered, where a structure is subjected to a uniformly distributed axial and a thrust force. These loads are to mimic the main forces acting on an offshore riser, for which an analytical methodology has been developed and applied. In particular, non-linear normal modes (NNMs) and non-linear multi-modes (NMMs) have been constructed by using the method of multiple scales. This is to effectively analyse the transversal vibration responses by monitoring the modal responses and mode interactions. The developed analytical models have been crosschecked against the results from FEM simulation. The FEM model having 26 elements and 77 degrees-of-freedom gave similar results as the low-dimensional (one degree-of-freedom) non-linear oscillator, which was developed by constructing a so-called invariant manifold. The comparisons of the dynamical responses were made in terms of time histories, phase portraits and mode shapes. (C) 2008 Elsevier Ltd. All rights reserved.

Linear minimum mean square filter for discrete-time linear systems with Markov jumps and multiplicative noises

In this paper we obtain the linear minimum mean square estimator (LMMSE) for discrete-time linear systems subject to state and measurement multiplicative noises and Markov jumps on the parameters. It is assumed that the Markov chain is not available. By using geometric arguments we obtain a Kalman type filter conveniently implementable in a recurrence form. The stationary case is also studied and a proof for the convergence of the error covariance matrix of the LMMSE to a stationary value under the assumption of mean square stability of the system and ergodicity of the associated Markov chain is obtained. It is shown that there exists a unique positive semi-definite solution for the stationary Riccati-like filter equation and, moreover, this solution is the limit of the error covariance matrix of the LMMSE. The advantage of this scheme is that it is very easy to implement and all calculations can be performed offline. (c) 2011 Elsevier Ltd. All rights reserved.

Double generalized linear model for tissue culture proportion data: a Bayesian perspective

Joint generalized linear models and double generalized linear models (DGLMs) were designed to model outcomes for which the variability can be explained using factors and/or covariates. When such factors operate, the usual normal regression models, which inherently exhibit constant variance, will under-represent variation in the data and hence may lead to erroneous inferences. For count and proportion data, such noise factors can generate a so-called overdispersion effect, and the use of binomial and Poisson models underestimates the variability and, consequently, incorrectly indicate significant effects. In this manuscript, we propose a DGLM from a Bayesian perspective, focusing on the case of proportion data, where the overdispersion can be modeled using a random effect that depends on some noise factors. The posterior joint density function was sampled using Monte Carlo Markov Chain algorithms, allowing inferences over the model parameters. An application to a data set on apple tissue culture is presented, for which it is shown that the Bayesian approach is quite feasible, even when limited prior information is available, thereby generating valuable insight for the researcher about its experimental results.

ECONOMICAL OCCUPATION OF AGRICULTURAL AREA OF PIRACICABA (SAO PAULO STATE, BRAZIL), INCLUDING RISK THROUGH LINEAR PROGRAMMING

The economic occupation of an area of 500 ha for Piracicaba was studied with the irrigated cultures of maize, tomato, sugarcane and beans, having used models of deterministic linear programming and linear programming including risk for the Target-Motad model, where two situations had been analyzed. In the deterministic model the area was the restrictive factor and the water was not restrictive for none of the tested situations. For the first situation the gotten maximum income was of R$ 1,883,372.87 and for the second situation it was of R$ 1,821,772.40. In the model including risk a producer that accepts risk can in the first situation get the maximum income of R$ 1,883,372. 87 with a minimum risk of R$ 350 year(-1), and in the second situation R$ 1,821,772.40 with a minimum risk of R$ 40 year(-1). Already a producer averse to the risk can get in the first situation a maximum income of R$ 1,775,974.81 with null risk and for the second situation R$ 1.707.706, 26 with null risk, both without water restriction. These results stand out the importance of the inclusion of the risk in supplying alternative occupations to the producer, allowing to a producer taking of decision considered the risk aversion and the pretension of income.

Endophytic Colonization of Potato (Solanum tuberosum L.) by a Novel Competent Bacterial Endophyte, Pseudomonas putida Strain P9, and Its Effect on Associated Bacterial Communities

Pseudomonas putida strain P9 is a novel competent endophyte from potato. P9 causes cultivar-dependent suppression of Phytophthora infestans. Colonization of the rhizoplane and endosphere of potato plants by P9 and its rifampin-resistant derivative P9R was studied. The purposes of this work were to follow the fate of P9 inside growing potato plants and to establish its effect on associated microbial communities. The effects of P9 and P9R inoculation were studied in two separate experiments. The roots of transplants of three different cultivars of potato were dipped in suspensions of P9 or P9R cells, and the plants were planted in soil. The fate of both strains was followed by examining colony growth and by performing PCR-denaturing gradient gel electrophoresis (PCR-DGGE). Colonies of both strains were recovered from rhizoplane and endosphere samples of all three cultivars at two growth stages. A conspicuous band, representing P9 and P9R, was found in all Pseudomonas PCR-DGGE fingerprints for treated plants. The numbers of P9R CFU and the P9R-specific band intensities for the different replicate samples were positively correlated, as determined by linear regression analysis. The effects of plant growth stage, genotype, and the presence of P9R on associated microbial communities were examined by multivariate and unweighted-pair group method with arithmetic mean cluster analyses of PCR-DGGE fingerprints. The presence of strain P9R had an effect on bacterial groups identified as Pseudomonas azotoformans, Pseudomonas veronii, and Pseudomonas syringae. In conclusion, strain P9 is an avid colonizer of potato plants, competing with microbial populations indigenous to the potato phytosphere. Bacterization with a biocontrol agent has an important and previously unexplored effect on plant-associated communities.

Chemical composition of whole body and carcass of Bos indicus and tropically adapted Bos taurus breeds

Relationships between the chemical composition of the 9th- to 11th-rib section and the chemical composition of the carcass and empty body were evaluated for Bos indicus (108 Nellore and 36 Guzerah; GuS) and tropically adapted Bos taurus (56 Caracu; CaS) bulls, averaging 20 to 24 mo of age at slaughter. Nellore cattle were represented by 56 animals from the selected herd (NeS) and 52 animals from the control herd (NeC). The CaS and GuS bulls were from selected herds. Selected herds were based on 20 yr of selection for postweaning BW. Carcass composition was obtained after grinding, homogenizing, sampling, and analyzing soft tissue and bones. Similarly, empty body composition was obtained after grinding, homogenizing, sampling, analyzing, and combining blood, hide, head + feet, viscera, and carcass. Bulls were separated into 2 groups. Group 1 was composed of 36 NeS, 36 NeC, 36 CaS, and 36 GuS bulls and had water, ether extract (EE), protein, and ash chemically determined in the 9th- to 11th-rib section and in the carcass. Group 2 was composed of 20 NeS, 16 NeC, and 20 CaS bulls and water, EE, protein, and ash were determined in the 9th-to 11th-rib section, carcass, and empty body. Linear regressions were developed between the carcass and the 9th-to 11th-rib section compositions for group 1 and between carcass and empty body compositions for group 2. The 9th-to 11th-rib section percentages of water (RWt) and EE (RF) predicted the percentages of carcass water (CWt) and carcass fat (CF) with high precision: CWt, % = 29.0806 + 0.4873 x RWt, % (r(2) = 0.813, SE = 1.06) and CF, % = 10.4037 + 0.5179 x RF, % (r(2) = 0.863, SE = 1.26), respectively. Linear regressions between percentage of CWt and CF and empty body water (EBWt) and empty body fat (EBF) were also predicted with high precision: EBWt, % = -9.6821 + 1.1626 x CWt, % (r(2) = 0.878, SE = 1.43) and EBF, % = 0.3739 + 1.0386 x CF, % (r(2) = 0.982, SE = 0.65), respectively. Chemical composition of the 9th-to 11th-rib section precisely estimated carcass percentages of water and EE. These regressions can accurately predict carcass and empty body compositions for Nellore, Guzerah, and Caracu breeds.

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models

The objective of the present study was to estimate milk yield genetic parameters applying random regression models and parametric correlation functions combined with a variance function to model animal permanent environmental effects. A total of 152,145 test-day milk yields from 7,317 first lactations of Holstein cows belonging to herds located in the southeastern region of Brazil were analyzed. Test-day milk yields were divided into 44 weekly classes of days in milk. Contemporary groups were defined by herd-test-day comprising a total of 2,539 classes. The model included direct additive genetic, permanent environmental, and residual random effects. The following fixed effects were considered: contemporary group, age of cow at calving (linear and quadratic regressions), and the population average lactation curve modeled by fourth-order orthogonal Legendre polynomial. Additive genetic effects were modeled by random regression on orthogonal Legendre polynomials of days in milk, whereas permanent environmental effects were estimated using a stationary or nonstationary parametric correlation function combined with a variance function of different orders. The structure of residual variances was modeled using a step function containing 6 variance classes. The genetic parameter estimates obtained with the model using a stationary correlation function associated with a variance function to model permanent environmental effects were similar to those obtained with models employing orthogonal Legendre polynomials for the same effect. A model using a sixth-order polynomial for additive effects and a stationary parametric correlation function associated with a seventh-order variance function to model permanent environmental effects would be sufficient for data fitting.

Random regression models to estimate test-day milk yield genetic parameters Holstein cows in Southeastern Brazil

A total of 152,145 weekly test-day milk yield records from 7317 first lactations of Holstein cows distributed in 93 herds in southeastern Brazil were analyzed. Test-day milk yields were classified into 44 weekly classes of DIM. The contemporary groups were defined as herd-year-week of test-day. The model included direct additive genetic, permanent environmental and residual effects as random and fixed effects of contemporary group and age of cow at calving as covariable, linear and quadratic effects. Mean trends were modeled by a cubic regression on orthogonal polynomials of DIM. Additive genetic and permanent environmental random effects were estimated by random regression on orthogonal Legendre polynomials. Residual variances were modeled using third to seventh-order variance functions or a step function with 1, 6,13,17 and 44 variance classes. Results from Akaike`s and Schwarz`s Bayesian information criterion suggested that a model considering a 7th-order Legendre polynomial for additive effect, a 12th-order polynomial for permanent environment effect and a step function with 6 classes for residual variances, fitted best. However, a parsimonious model, with a 6th-order Legendre polynomial for additive effects and a 7th-order polynomial for permanent environmental effects, yielded very similar genetic parameter estimates. (C) 2008 Elsevier B.V. All rights reserved.

Cow/calf preweaning efficiency of Nellore and Bos taurus x Bos indicus crosses

The objectives of this study were to determine if percentage Bos taurus (0 or 50%) of the cow had an effect on ME requirements and milk production, and to compare cow/calf efficiency among 3 mating systems. Metabolizable energy requirements were estimated during a feeding trial that encompassed a gestation and lactation feeding trial for each of 2 groups of cows. Cows were 0 or 50% Bos taurus ( 100 or 50% Nellore) breed type: Nellore cows (NL; n = 10) mated to Nellore bulls, NL cows ( n = 9) mated to Angus bulls, Angus x Nellore (ANL; n = 10) and Simmental x Nellore (SNL; n = 10) cows mated to Canchim (5/ 8 Charolais 3/ 8 Zebu) bulls. Cows were individually fed a total mixed diet that contained 11.3% CP and 2.23 Mcal of ME/kg of DM. At 14-d intervals, cows and calves were weighed and the amount of DM was adjusted to keep shrunk BW and BCS of cows constant. Beginning at 38 d of age, corn silage was available to calves ad libitum. Milk production at 42, 98, 126, and 180 d postpartum was measured using the weigh-suckle-weigh technique. At 190 d of age, calves were slaughtered and body composition estimated using 9-10-11th-rib section to obtain energy deposition. Regression of BW change on daily ME intake (MEI) was used to estimate MEI at zero BW change. Increase in percentage Bos taurus had a significant effect on daily ME requirements (Mcal/d) during pregnancy (P < 0.01) and lactation (P < 0.01). Percentage Bos taurus had a positive linear effect on maintenance requirements of pregnant (P = 0.07) and lactating (P < 0.01) cows; during pregnancy, the ME requirements were 91 and 86% of those in lactation (131 +/- 3.5 vs. 145 +/- 3.4 Mcal.kg(-0.75).d(-1)) for the 0 and 50% B. taurus groups, respectively. The 50% B. taurus cows, ANL and SNL, suckling crossbred calves had greater total MEI (4,319 +/- 61 Mcal; P < 0.01) than 0% B. taurus cows suckling NL (3,484 +/- 86 Mcal) or ANL calves (3,600 +/- 91 Mcal). The 0% B. taurus cows suckling ANL calves were more efficient (45.3 +/- 1.6 g/Mcal; P = 0.03) than straightbred NL (35.1 +/- 1.5 g/Mcal) and ANL or SNL pairs (41.0 +/- 1.0 g/Mcal). Under the conditions of this study, crossbreeding improved cow/ calf efficiency and showed an advantage for cows that have lower energy requirements.

A Log-Linear Regression Model for the Beta-Weibull Distribution

We introduce the log-beta Weibull regression model based on the beta Weibull distribution (Famoye et al., 2005; Lee et al., 2007). We derive expansions for the moment generating function which do not depend on complicated functions. The new regression model represents a parametric family of models that includes as sub-models several widely known regression models that can be applied to censored survival data. We employ a frequentist analysis, a jackknife estimator, and a parametric bootstrap 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. Further, for different parameter settings, sample sizes, and censoring percentages, several 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 extended to a modified deviance residual in the proposed regression model applied to censored data. We define martingale and deviance residuals to evaluate the model assumptions. The extended regression model is very useful for the analysis of real data and could give more realistic fits than other special regression models.