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.

Milk yield, milk composition, eating behavior, and lamb performance of ewes fed diets containing soybean hulls replacing coastcross (Cynodon species) hay

The objective of this experiment was to evaluate the effects of replacing coastcross hay NDF by soybean hull (SH) NDF on the lactation performance and eating behavior of ewes and also on the performance of their lambs. Fifty-six Santa Ines lactating ewes (56.1 +/- 6.8 kg of initial BW; mean +/- SD) were penned individually and used in a randomized complete block design with 14 blocks and 4 treatments. Diets were formulated to provide similar concentrations of NDF (56%) and CP (16%). The SH NDF replaced 33 (SH33), 67 (SH67), or 100% (SH100) of the NDF contributed by coastcross hay in a 70% forage-based diet (SH0), resulting in SH inclusion rates of 0, 25, 54, and 85% of the dietary DM. Once a week, from the second to the eighth week of lactation (weaning time), ewes were separated from their lambs, stimulated by a 6-IU i.v. oxytocin injection, and hand milked to empty the udder. After 3 h, milk production was obtained after the same procedure. Quadratic effect for milk production (142.4, 179.8, 212.6, and 202.9 g/3 h) and cubic effect for DMI (2.27, 2.69, 3.25, and 3.00 kg/d) were observed as SH inclusion increased from 0 to 85% of the dietary DM. Milk fat (7.59, 7.86, 7.59, and 7.74%), protein (4.53, 4.43, 4.40, and 4.55%), and total solids (18.24, 18.54, 18.39, and 18.64%) did not differ among the 70% forage-based diet and diets with SH NDF replacing 33, 67, or 100% of the NDF. A linear increase in lactose concentration was observed with SH inclusion. Ewe BW gain during the trial showed a cubic response (0.37, 0.03, 4.80, and 2.80 kg) with SH inclusion. The preweaning ADG of lambs increased linearly, and ADG of lambs after weaning decreased linearly with SH inclusion. Final BW of lambs (2 wk after weaning) did not differ among treatments. Eating behavior observations were conducted with 44 ewes. The same facilities, experimental design, dietary treatments, and feeding management were used. Observations were visually recorded every 5 min for a 24-h period when ewes were 46 +/- 6.8 d in milk. Eating time (min/d, min/g of DMI, and min/g of NDF intake) and time expended in rumination and chewing activities (min/g of DMI and min/g of NDF intake) decreased linearly with the addition of SH in the diets. The inclusion of SH improved DMI and milk production, also reflecting on the BW of lambs at weaning. Milk performance was not affected when SH NDF replaced 100% of hay NDF.

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.

Influence of total solids contents of milk whey on the acidifying profile and viability of various lactic acid bacteria

The main objectives of the present study were (a) to study the effects of the different combinations of Lactobacillus delbrueckii subsp. bulgaricus (Lb), Lactobacillus acidophilus (La), Lactobacillus rhamnosus (Lr), and Bifidobacterium animalis subsp. lactis (BI) in co-culture with Streptococcus thermophilus (St) on the rate of acid development in milk and milk-whey mixture, and (b) the effect of the level of the total solids of the different bases on the acidification profile and viability of potential health-promoting microorganisms. The co-culture of St-Lr showed the lowest values V(max) in all bases; while the co-culture St-Bl had high t(Vmax) in milk and whey bases (12 and 10 g/100 g, respectively). Co-cultures St-La and St-Lb reached V(max) at pH 5.5, while St-Lr and St-Bl at pH 5.91. Fermentation time to reach pH 4.5 was longer when St-Lr co-culture was used, while St-Lb had the lowest value. All the products had slight development of acid during the storage period, and lowest values were observed when the St-Bl co-culture was employed. Lb, BI and St cultures had high counts at pH 4.5 in the three bases. The total solids affected the viability of Lb and La. The technological interest of these combinations is discussed in this article. (C) 2008 Swiss Society of Food Science and Technology. Published by Elsevier Ltd. AM rights reserved.

Computationally efficient solution techniques for adsorption problems involving steep gradients in bidisperse particles

A piecewise uniform fitted mesh method turns out to be sufficient for the solution of a surprisingly wide variety of singularly perturbed problems involving steep gradients. The technique is applied to a model of adsorption in bidisperse solids for which two fitted mesh techniques, a fitted-mesh finite difference method (FMFDM) and fitted mesh collocation method (FMCM) are presented. A combination (FMCMD) of FMCM and the DASSL integration package is found to be most effective in solving the problems. Numerical solutions (FMFDM and FMCMD) were found to match the analytical solution when the adsorption isotherm is linear, even under conditions involving steep gradients for which global collocation fails. In particular, FMCMD is highly efficient for macropore diffusion control or micropore diffusion control. These techniques are simple and there is no limit on the range of the parameters. The techniques can be applied to a variety of adsorption and desorption problems in bidisperse solids with non-linear isotherm and for arbitrary particle geometry.

A scheme for efficient quantum computation wtih linear optics

Quantum computers promise to increase greatly the efficiency of solving problems such as factoring large integers, combinatorial optimization and quantum physics simulation. One of the greatest challenges now is to implement the basic quantum-computational elements in a physical system and to demonstrate that they can be reliably and scalably controlled. One of the earliest proposals for quantum computation is based on implementing a quantum bit with two optical modes containing one photon. The proposal is appealing because of the ease with which photon interference can be observed. Until now, it suffered from the requirement for non-linear couplings between optical modes containing few photons. Here we show that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photo-detectors. Our methods exploit feedback from photo-detectors and are robust against errors from photon loss and detector inefficiency. The basic elements are accessible to experimental investigation with current technology.

Molecular cocrystals of carboxylic acids. XXVII - An investigation into the use of triphenylphosphine oxide cocrystals for non-linear optics: the crystal structure of the adduct of triphenylphosphine oxide with N-methylpyrrole-2-carboxylic acid

Four adducts of triphenylphosphine oxide with aromatic carboxylic acids have been synthesized and tested for second-order non-linear optical properties. These were with N-methylpyrrole-2-carboxylic acid (I), indole-2-carboxylic acid (2), 3-dimethylaminobenzoic acid (3), and thiophen-2-carboxylic acid (4). Compound (1) produced clear, colourless crystals (space group P2(1)2(1)2(1) With a 9.892(1), b 14.033(1), c 15.305(1) Angstrom, Z 4) which allowed the structure to be determined by X-ray diffraction.

Temperature and sowing date affect the linear increase of sunflower harvest index

The linearity of daily linear harvest index (HI) increase can provide a simple means to predict grain growth and yield in field crops. However, the stability of the rate of increase across genotypes and environments is uncertain. Data from three field experiments were collated to investigate the phase of linear HI increase of sunflower (Helianthus annuus L,) across environments by changing genotypes, sowing time, N level, and solar irradiation level. Linear increase in HI was similar among different genotypes, N levels, and radiation treatments (mean 0.0125 d(-1)). but significant differences occurred between sowings, The linear increase in HI was not stable at very low temperatures (down to 9 degrees C) during grain filling, due to possible limitations to biomass accumulation and translocation (mean 0.0091 d(-1)). Using the linear increase in HI to predict grain yield requires predictions of the duration from anthesis to the onset of linear HI increase (lag phase) and the cessation of linear RT increase. These studies showed that the lag phase differed, and the linear HI increase ceased when 91% of the anthesis to physiological maturity period had been completed.