Modelos autorregressivos com valores inteiros não negativos : aplicação em séries económicas de Cabo Verde

No estudo de séries temporais, os processos estocásticos usuais assumem que as distribuições marginais são contínuas e, em geral, não são adequados para modelar séries de contagem, pois as suas características não lineares colocam alguns problemas estatísticos, principalmente na estimação dos parâmetros. Assim, investigou-se metodologias apropriadas de análise e modelação de séries com distribuições marginais discretas. Neste contexto, Al-Osh and Alzaid (1987) e McKenzie (1988) introduziram na literatura a classe dos modelos autorregressivos com valores inteiros não negativos, os processos INAR. Estes modelos têm sido frequentemente tratados em artigos científicos ao longo das últimas décadas, pois a sua importância nas aplicações em diversas áreas do conhecimento tem despertado um grande interesse no seu estudo. Neste trabalho, após uma breve revisão sobre séries temporais e os métodos clássicos para a sua análise, apresentamos os modelos autorregressivos de valores inteiros não negativos de primeira ordem INAR (1) e a sua extensão para uma ordem p, as suas propriedades e alguns métodos de estimação dos parâmetros nomeadamente, o método de Yule-Walker, o método de Mínimos Quadrados Condicionais (MQC), o método de Máxima Verosimilhança Condicional (MVC) e o método de Quase Máxima Verosimilhança (QMV). Apresentamos também um critério automático de seleção de ordem para modelos INAR, baseado no Critério de Informação de Akaike Corrigido, AICC, um dos critérios usados para determinar a ordem em modelos autorregressivos, AR. Finalmente, apresenta-se uma aplicação da metodologia dos modelos INAR em dados reais de contagem relativos aos setores dos transportes marítimos e atividades de seguros de Cabo Verde.

Simplified Mathematical Model for an Anaerobic Sequencing Batch Biofilm Reactor Treating Lipid-Rich Wastewater Subject to Rising Organic Loading Rates

This study proposes a simplified mathematical model to describe the processes occurring in an anaerobic sequencing batch biofilm reactor (ASBBR) treating lipid-rich wastewater. The reactor, subjected to rising organic loading rates, contained biomass immobilized cubic polyurethane foam matrices, and was operated at 32 degrees C +/- 2 degrees C, using 24-h batch cycles. In the adaptation period, the reactor was fed with synthetic substrate for 46 days and was operated without agitation. Whereas agitation was raised to 500 rpm, the organic loading rate (OLR) rose from 0.3 g chemical oxygen demand (COD) . L(-1) . day(-1) to 1.2 g COD . L(-1) . day(-1). The ASBBR was fed fat-rich wastewater (dairy wastewater), in an operation period lasting for 116 days, during which four operational conditions (OCs) were tested: 1.1 +/- 0.2 g COD . L(-1) . day(-1) (OC1), 4.5 +/- 0.4 g COD . L(-1) . day(-1) (OC2), 8.0 +/- 0.8 g COD . L(-1) . day(-1) (OC3), and 12.1 +/- 2.4 g COD . L(-1) . day(-1) (OC4). The bicarbonate alkalinity (BA)/COD supplementation ratio was 1:1 at OC1, 1:2 at OC2, and 1:3 at OC3 and OC4. Total COD removal efficiencies were higher than 90%, with a constant production of bicarbonate alkalinity, in all OCs tested. After the process reached stability, temporal profiles of substrate consumption were obtained. Based on these experimental data a simplified first-order model was fit, making possible the inference of kinetic parameters. A simplified mathematical model correlating soluble COD with volatile fatty acids (VFA) was also proposed, and through it the consumption rates of intermediate products as propionic and acetic acid were inferred. Results showed that the microbial consortium worked properly and high efficiencies were obtained, even with high initial substrate concentrations, which led to the accumulation of intermediate metabolites and caused low specific consumption rates.

Elastic Maier-Saupe-Zwanzig model and some properties of nematic elastomers

We introduce a simple mean-field lattice model to describe the behavior of nematic elastomers. This model combines the Maier-Saupe-Zwanzig approach to liquid crystals and an extension to lattice systems of the Warner-Terentjev theory of elasticity, with the addition of quenched random fields. We use standard techniques of statistical mechanics to obtain analytic solutions for the full range of parameters. Among other results, we show the existence of a stress-strain coexistence curve below a freezing temperature, analogous to the P-V diagram of a simple fluid, with the disorder strength playing the role of temperature. Below a critical value of disorder, the tie lines in this diagram resemble the experimental stress-strain plateau and may be interpreted as signatures of the characteristic polydomain-monodomain transition. Also, in the monodomain case, we show that random fields may soften the first-order transition between nematic and isotropic phases, provided the samples are formed in the nematic state.

A low carbohydrate diet affects autonomic modulation during heavy but not moderate exercise

The aim of this study was to examine the effects of low carbohydrate (CHO) availability on heart rate variability (HRV) responses during moderate and severe exercise intensities until exhaustion. Six healthy males (age, 26.5 +/- 6.7 years; body mass, 78.4 +/- 7.7 kg; body fat %, 11.3 +/- 4.5%; (V) over dotO(2max), 39.5 +/- 6.6 mL kg(-1) min(-1)) volunteered for this study. All tests were performed in the morning, after 8-12 h overnight fasting, at a moderate intensity corresponding to 50% of the difference between the first (LT(1)) and second (LT(2)) lactate breakpoints and at a severe intensity corresponding to 25% of the difference between the maximal power output and LT(2). Forty-eight hours before each experimental session, the subjects performed a 90-min cycling exercise followed by 5-min rest periods and subsequent 1-min cycling bouts at 125% (V) over dotO(2max) (with 1-min rest periods) until exhaustion, in order to deplete muscle glycogen. A diet providing 10% (CHO(low)) or 65% (CHO(control)) of energy as carbohydrates was consumed for the following 2 days until the experimental test. The Poicare plots (standard deviations 1 and 2: SD1 and SD2, respectively) and spectral autoregressive model (low frequency LF, and high frequency HF) were applied to obtain HRV parameters. The CHO availability had no effect on the HRV parameters or ventilation during moderate-intensity exercise. However, the SD1 and SD2 parameters were significantly higher in CHO(low) than in CHO(control), as taken at exhaustion during the severe-intensity exercise (P < 0.05). The HF and LF frequencies (ms(2)) were also significantly higher in CHO(low) than in CHO(control) (P < 0.05). In addition, ventilation measured at the 5 and 10-min was higher in CHO(low) (62.5 +/- 4.4 and 74.8 +/- 6.5 L min(-1), respectively, P < 0.05) than in CHO(control) (70.0 +/- 3.6 and 79.6 +/- 5.1 L min(-1), respectively; P < 0.05) during the severe-intensity exercise. These results suggest that the CHO availability alters the HRV parameters during severe-, but not moderate-, intensity exercise, and this was associated with an increase in ventilation volume.

A master equation model for bimolecular reaction via multi-well isomerization intermediates

A reversible linear master equation model is presented for pressure- and temperature-dependent bimolecular reactions proceeding via multiple long-lived intermediates. This kinetic treatment, which applies when the reactions are measured under pseudo-first-order conditions, facilitates accurate and efficient simulation of the time dependence of the populations of reactants, intermediate species and products. Detailed exploratory calculations have been carried out to demonstrate the capabilities of the approach, with applications to the bimolecular association reaction C3H6 + H reversible arrow C3H7 and the bimolecular chemical activation reaction C2H2 +(CH2)-C-1--> C3H3+H. The efficiency of the method can be dramatically enhanced through use of a diffusion approximation to the master equation, and a methodology for exploiting the sparse structure of the resulting rate matrix is established.

Subcycling first- and second-order generalizations of the trapezoidal rule

Subcycling algorithms which employ multiple timesteps have been previously proposed for explicit direct integration of first- and second-order systems of equations arising in finite element analysis, as well as for integration using explicit/implicit partitions of a model. The author has recently extended this work to implicit/implicit multi-timestep partitions of both first- and second-order systems. In this paper, improved algorithms for multi-timestep implicit integration are introduced, that overcome some weaknesses of those proposed previously. In particular, in the second-order case, improved stability is obtained. Some of the energy conservation properties of the Newmark family of algorithms are shown to be preserved in the new multi-timestep extensions of the Newmark method. In the first-order case, the generalized trapezoidal rule is extended to multiple timesteps, in a simple way that permits an implicit/implicit partition. Explicit special cases of the present algorithms exist. These are compared to algorithms proposed previously. (C) 1998 John Wiley & Sons, Ltd.

Marker concentration patterns of labelled leaf and stem particles in the rumen of cattle grazing bermuda grass (Cynodon dactylon) analysed by reference to a raft model

Large (>1600 mum), ingestively masticated particles of bermuda grass (Cynodon dactylon L. Pers.) leaf and stem labelled with Yb-169 and Ce-144 respectively were inserted into the rumen digesta raft of heifers grazing bermuda grass. The concentration of markers in digesta sampled from the raft and ventral rumen were monitored at regular intervals over approximately 144 h. The data from the two sampling sites were simultaneously fitted to two pool (raft and ventral rumen-reticulum) models with either reversible or sequential flow between the two pools. The sequential flow model fitted the data equally as well as the reversible flow model but the reversible flow model was used because of its greater application. The reversible flow model, hereafter called the raft model, had the following features: a relatively slow age-dependent transfer rate from the raft (means for a gamma 2 distributed rate parameter for leaf 0.0740 v. stem 0.0478 h(-1)), a very slow first order reversible flow from the ventral rumen to the raft (mean for leaf and stem 0.010 h(-1)) and a very rapid first order exit from the ventral rumen (mean of leaf and stem 0.44 h(-1)). The raft was calculated to occupy approximately 0.82 total rumen DM of the raft and ventral rumen pools. Fitting a sequential two pool model or a single exponential model individually to values from each of the two sampling sites yielded similar parameter values for both sites and faster rate parameters for leaf as compared with stem, in agreement with the raft model. These results were interpreted as indicating that the raft forms a large relatively inert pool within the rumen. Particles generated within the raft have difficulty escaping but once into the ventral rumen pool they escape quickly with a low probability of return to the raft. It was concluded that the raft model gave a good interpretation of the data and emphasized escape from and movement within the raft as important components of the residence time of leaf and stem particles within the rumen digesta of cattle.

A kinetic study of the thermally initiated free radical reactions of styrene with octanedithiol as a model for the reactions of multifunctional thiols with divinylbenzene

The kinetics of chain reactions of octanedithiol with styrene, thermally initiated with TX29B50 (a 50:50 wt% solution of TX29 diperoxy initiator in a phthalate plasticizer), have been studied over a range of initiator concentrations, a range of mixture formulations and a range of temperatures. This system has been investigated as a model system for the reactions of polyfunctional thiols with divinyl benzene. The reactions have been shown to follow first-order kinetics for both the thiol and the ene species and to be characterized by a dependence on the initiator concentration to the power of one half. The kinetic rate parameters have been shown to adhere to Arrhenius behaviour. A kinetic model for the chain reactions for this system has been proposed. (C) 2003 Society of Chemical Industry.

Fractional order modelling of fractional-order holds

Discrete time control systems require sample- and-hold circuits to perform the conversion from digital to analog. Fractional-Order Holds (FROHs) are an interpolation between the classical zero and first order holds and can be tuned to produce better system performance. However, the model of the FROH is somewhat hermetic and the design of the system becomes unnecessarily complicated. This paper addresses the modelling of the FROHs using the concepts of Fractional Calculus (FC). For this purpose, two simple fractional-order approximations are proposed whose parameters are estimated by a genetic algorithm. The results are simple to interpret, demonstrating that FC is a useful tool for the analysis of these devices.

Relationship between imatinib population pharmacokinetics and alpha-1-acid glycoprotein

Objectives: Considering the large inter-individual differences in the function of the systems involved in imatinib disposition, exposure to this drug can be expected to vary widely among patients. Among those known systems is alpha-1-acid glycoprotein (AGP), a circulating protein that strongly binds imatinib. This observational study aimed to explore the influence of plasma AGP on imatinib pharmacokinetics. Methods: A population pharmacokinetic analysis was performed using NONMEM based on 278 plasma samples from 51 oncologic patients, for whom both total imatinib and AGP plasma concentrations were measured. The influence of this biological covariate on oral clearance and volume of distribution was examined. Results: A one-compartment model with first-order absorption appropriately described the data. A hyperbolic relationship between plasma AGP levels and oral clearance, as well as volume of distribution was observed. A mechanistic approach was built up, postulating that only the unbound imatinib concentration was able to undergo first-order elimination through an unbound clearance process, and integrating the dissociation constant as a parameter in the model. This approach allowed determining an average (± SEM) free clearance of 1310 (± 172) L/h and a volume of distribution of 301 (± 23) L. By comparison, the total clearance previously determined was 14 (± 1) L/h. Free clearance was affected by body weight and pathology diagnosis. Moreover, this model provided consistent estimates of the association constant between imatinib and AGP (5.5?106 L/mol) and of the average in vivo free fraction of imatinib (1.1%). The variability observed (17% for free clearance and 66% for volume of distribution) was less than the one previously reported without considering AGP impact. AGP explained indeed about one half of the variability observed in total imatinib disposition. Conclusion: Such findings clarify in part the in vivo impact of protein binding on imatinib disposition and might raise again the question whether high levels of AGP could represent a resistance factor to imatinib. This remains however questionable, as it is not expected to affect free drug concentrations. On the other hand, would imatinib be demonstrated as a drug requiring therapeutic drug monitoring, either the measurement of free concentration or the correction of the total concentration by the actual AGP plasma levels should be considered for accurate interpretation of the results.

Intraocular penetration of penciclovir after oral administration of famciclovir: a population pharmacokinetic model.

OBJECTIVES: We developed a population model that describes the ocular penetration and pharmacokinetics of penciclovir in human aqueous humour and plasma after oral administration of famciclovir. METHODS: Fifty-three patients undergoing cataract surgery received a single oral dose of 500 mg of famciclovir prior to surgery. Concentrations of penciclovir in both plasma and aqueous humour were measured by HPLC with fluorescence detection. Concentrations in plasma and aqueous humour were fitted using a two-compartment model (NONMEM software). Inter-individual and intra-individual variabilities were quantified and the influence of demographics and physiopathological and environmental variables on penciclovir pharmacokinetics was explored. RESULTS: Drug concentrations were fitted using a two-compartment, open model with first-order transfer rates between plasma and aqueous humour compartments. Among tested covariates, creatinine clearance, co-intake of angiotensin-converting enzyme inhibitors and body weight significantly influenced penciclovir pharmacokinetics. Plasma clearance was 22.8 ± 9.1 L/h and clearance from the aqueous humour was 8.2 × 10(-5) L/h. AUCs were 25.4 ± 10.2 and 6.6 ± 1.8 μg · h/mL in plasma and aqueous humour, respectively, yielding a penetration ratio of 0.28 ± 0.06. Simulated concentrations in the aqueous humour after administration of 500 mg of famciclovir three times daily were in the range of values required for 50% growth inhibition of non-resistant strains of the herpes zoster virus family. CONCLUSIONS: Plasma and aqueous penciclovir concentrations showed significant variability that could only be partially explained by renal function, body weight and comedication. Concentrations in the aqueous humour were much lower than in plasma, suggesting that factors in the blood-aqueous humour barrier might prevent its ocular penetration or that redistribution occurs in other ocular compartments.

Application of a non isotropic turbulence model to stable atmospheric flows and dispersion over 3D topography

A non isotropic turbulence model is extended and applied to three dimensional stably stratified flows and dispersion calculations. The model is derived from the algebraic stress model (including wall proximity effects), but it retains the simplicity of the "eddy viscosity" concept of first order models. The "modified k-epsilon" is implemented in a three dimensional numerical code. Once the flow is resolved, the predicted velocity and turbulence fields are interpolated into a second grid and used to solve the concentration equation. To evaluate the model, various steady state numerical solutions are compared with small scale dispersion experiments which were conducted at the wind tunnel of Mitsubishi Heavy Industries, in Japan. Stably stratified flows and plume dispersion over three distinct idealized complex topographies (flat and hilly terrain) are studied. Vertical profiles of velocity and pollutant concentration are shown and discussed. Also, comparisons are made against the results obtained with the standard k-epsilon model.

A new model for the population pharmacokinetics of didanosine in healthy subjects

Didanosine (ddI) is a component of highly active antiretroviral therapy drug combinations, used especially in resource-limited settings and in zidovudine-resistant patients. The population pharmacokinetics of ddI was evaluated in 48 healthy volunteers enrolled in two bioequivalence studies. These data, along with a set of co-variates, were the subject of a nonlinear mixed-effect modeling analysis using the NONMEM program. A two-compartment model with first order absorption (ADVAN3 TRANS3) was fitted to the serum ddI concentration data. Final pharmacokinetic parameters, expressed as functions of the co-variates gender and creatinine clearance (CL CR), were: oral clearance (CL = 55.1 + 240 x CL CR + 16.6 L/h for males and CL = 55.1 + 240 x CL CR for females), central volume (V2 = 9.8 L), intercompartmental clearance (Q = 40.9 L/h), peripheral volume (V3 = 62.7 + 22.9 L for males and V3 = 62.7 L for females), absorption rate constant (Ka = 1.51/h), and dissolution time of the tablet (D = 0.43 h). The intraindividual (residual) variability expressed as coefficient of variation was 13.0%, whereas the interindividual variability of CL, Q, V3, Ka, and D was 20.1, 75.8, 20.6, 18.9, and 38.2%, respectively. The relatively high (>30%) interindividual variability for some of these parameters, observed under the controlled experimental settings of bioequivalence trials in healthy volunteers, may result from genetic variability of the processes involved in ddI absorption and disposition.

Early detection of metabolic and energy disorders by thermal time series stochastic complexity analysis

Maintenance of thermal homeostasis in rats fed a high-fat diet (HFD) is associated with changes in their thermal balance. The thermodynamic relationship between heat dissipation and energy storage is altered by the ingestion of high-energy diet content. Observation of thermal registers of core temperature behavior, in humans and rodents, permits identification of some characteristics of time series, such as autoreference and stationarity that fit adequately to a stochastic analysis. To identify this change, we used, for the first time, a stochastic autoregressive model, the concepts of which match those associated with physiological systems involved and applied in male HFD rats compared with their appropriate standard food intake age-matched male controls (n=7 per group). By analyzing a recorded temperature time series, we were able to identify when thermal homeostasis would be affected by a new diet. The autoregressive time series model (AR model) was used to predict the occurrence of thermal homeostasis, and this model proved to be very effective in distinguishing such a physiological disorder. Thus, we infer from the results of our study that maximum entropy distribution as a means for stochastic characterization of temperature time series registers may be established as an important and early tool to aid in the diagnosis and prevention of metabolic diseases due to their ability to detect small variations in thermal profile.

An Autoregressive Spectral Density Estimator at Frequency Zero for Nonstationarity Tests.

Many unit root and cointegration tests require an estimate of the spectral density function at frequency zero at some process. Kernel estimators based on weighted sums of autocovariances constructed using estimated residuals from an AR(1) regression are commonly used. However, it is known that with substantially correlated errors, the OLS estimate of the AR(1) parameter is severely biased. in this paper, we first show that this least squares bias induces a significant increase in the bias and mean-squared error of kernel-based estimators.