A model-based PID controller for Hammerstein systems using B-spline neural networks

In this paper, a new model-based proportional–integral–derivative (PID) tuning and controller approach is introduced for Hammerstein systems that are identified on the basis of the observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a B-spline neural network. The control signal is composed of a PID controller, together with a correction term. Both the parameters in the PID controller and the correction term are optimized on the basis of minimizing the multistep ahead prediction errors. In order to update the control signal, the multistep ahead predictions of the Hammerstein system based on B-spline neural networks and the associated Jacobian matrix are calculated using the de Boor algorithms, including both the functional and derivative recursions. Numerical examples are utilized to demonstrate the efficacy of the proposed approaches.

Assimilation of RAPID array observations into an ocean model

Experiments assimilating the RAPID dataset of deep temperature and salinity profiles at 26.5°N on the western and eastern Atlantic boundaries into a 1° global NEMO ocean model have been performed. The meridional overturning circulation (MOC) is then assessed against the transports calculated directly from observations. The best initialization found for this short period was obtained by assimilating the EN3 upper-ocean hydrography database prior to 2004, after which different methods of assimilating 5-day average RAPID profiles at the western boundary were tested. The model MOC is strengthened by ∼ 2 Sv giving closer agreement with the RAPID array transports, when the western boundary profiles are assimilated only below 900 m (the approximate depth of the Florida Straits, which are not well resolved) and when the T,S observations are spread meridionally from 10 to 35°N along the deep western boundary. The use of boundary-focused covariances has the largest impact on the assimilation results, otherwise using more conventional Gaussian covariances has a very local impact on the MOC at 26°N with strong adverse impacts on the MOC stream function at higher and lower latitudes. Even using boundary-focused covariances only enables the MOC to be strengthened for ∼ 2 years, after which the increased transport of warm waters leads to a negative feedback on water formation in the subpolar gyre which then reduces the MOC. This negative feedback can be mitigated if EN3 hydrography data continue to be assimilated along with the RAPID array boundary data. Copyright © 2012 Royal Meteorological Society and Crown in the right of Canada.

Advances in sequential data assimilation and numerical weather forecasting: an Ensemble Transform Kalman-Bucy Filter, a study on clustering in deterministic Ensemble Square Root Filters, and a test of a new time stepping scheme in an atmospheric model

This dissertation deals with aspects of sequential data assimilation (in particular ensemble Kalman filtering) and numerical weather forecasting. In the first part, the recently formulated Ensemble Kalman-Bucy (EnKBF) filter is revisited. It is shown that the previously used numerical integration scheme fails when the magnitude of the background error covariance grows beyond that of the observational error covariance in the forecast window. Therefore, we present a suitable integration scheme that handles the stiffening of the differential equations involved and doesn’t represent further computational expense. Moreover, a transform-based alternative to the EnKBF is developed: under this scheme, the operations are performed in the ensemble space instead of in the state space. Advantages of this formulation are explained. For the first time, the EnKBF is implemented in an atmospheric model. The second part of this work deals with ensemble clustering, a phenomenon that arises when performing data assimilation using of deterministic ensemble square root filters in highly nonlinear forecast models. Namely, an M-member ensemble detaches into an outlier and a cluster of M-1 members. Previous works may suggest that this issue represents a failure of EnSRFs; this work dispels that notion. It is shown that ensemble clustering can be reverted also due to nonlinear processes, in particular the alternation between nonlinear expansion and compression of the ensemble for different regions of the attractor. Some EnSRFs that use random rotations have been developed to overcome this issue; these formulations are analyzed and their advantages and disadvantages with respect to common EnSRFs are discussed. The third and last part contains the implementation of the Robert-Asselin-Williams (RAW) filter in an atmospheric model. The RAW filter is an improvement to the widely popular Robert-Asselin filter that successfully suppresses spurious computational waves while avoiding any distortion in the mean value of the function. Using statistical significance tests both at the local and field level, it is shown that the climatology of the SPEEDY model is not modified by the changed time stepping scheme; hence, no retuning of the parameterizations is required. It is found the accuracy of the medium-term forecasts is increased by using the RAW filter.

Characterisation of the intracellular-glutamate decarboxylase system (GAD): analysis of its function, transcription and role in the acid resistance of various strains of Listeria monocytogenes

The glutamate decarboxylase (GAD) system is important for the acid resistance of Listeria monocytogenes. We previously showed that under acidic conditions, glutamate (Glt)/γ-aminobutyrate (GABA) antiport is impaired in minimal media but not in rich ones, like brain heart infusion. Here we demonstrate that this behavior is more complex and it is subject to strain and medium variation. Despite the impaired Glt/GABA antiport, cells accumulate intracellular GABA (GABA(i)) as a standard response against acid in any medium, and this occurs in all strains tested. Since these systems can occur independently of one another, we refer to them as the extracellular (GAD(e)) and intracellular (GAD(i)) systems. We show here that GAD(i) contributes to acid resistance since in a ΔgadD1D2 mutant, reduced GABA(i) accumulation coincided with a 3.2-log-unit reduction in survival at pH 3.0 compared to that of wild-type strain LO28. Among 20 different strains, the GAD(i) system was found to remove 23.11% ± 18.87% of the protons removed by the overall GAD system. Furthermore, the GAD(i) system is activated at milder pH values (4.5 to 5.0) than the GAD(e) system (pH 4.0 to 4.5), suggesting that GAD(i) is the more responsive of the two and the first line of defense against acid. Through functional genomics, we found a major role for GadD2 in the function of GAD(i), while that of GadD1 was minor. Furthermore, the transcription of the gad genes in three common reference strains (10403S, LO28, and EGD-e) during an acid challenge correlated well with their relative acid sensitivity. No transcriptional upregulation of the gadT2D2 operon, which is the most important component of the GAD system, was observed, while gadD3 transcription was the highest among all gad genes in all strains. In this study, we present a revised model for the function of the GAD system and highlight the important role of GAD(i) in the acid resistance of L. monocytogenes.

Effects of fermentation products of pro- and prebiotics on trans-epithelial electrical resistance in an in vitro model of the colon

Evidence from in vivo and in vitro studies suggests that the consumption of pro- and prebiotics may inhibit colon carcinogenesis; however, the mechanisms involved have, thus far, proved elusive. There are some indications from animal studies that the effects are being exerted during the promotion stage of carcinogenesis. One feature of the promotion stage of colorectal cancer is the disruption of tight junctions, leading to a loss of integrity across the intestinal barrier. We have used the Caco-2 human adenocarcinoma cell line as a model for the intestinal epithelia. Trans-epithelial electrical resistance measurements indicate Caco-2 monolayer integrity, and we recorded changes to this integrity following exposure to the fermentation products of selected probiotics and prebiotics, in the form of nondigestible oligosaccharides (NDOs). Our results indicate that NDOs themselves exert varying, but generally minor, effects upon the strength of the tight junctions, whereas the fermentation products of probiotics and NDOs tend to raise tight junction integrity above that of the controls. This effect was bacterial species and oligosaccharide specific. Bifidobacterium Bb 12 was particularly effective, as were the fermentation products of Raftiline and Raftilose. We further investigated the ability of Raftilose fermentations to protect against the negative effects of deoxycholic acid (DCA) upon tight junction integrity. We found protection to be species dependent and dependent upon the presence of the fermentation products in the media at the same time as or after exposure to the DCA. Results suggest that the Raftilose fermentation products may prevent disruption of the intestinal epithelial barrier function during damage by tumor promoters.

Likelihood-free estimation of model evidence

Statistical methods of inference typically require the likelihood function to be computable in a reasonable amount of time. The class of “likelihood-free” methods termed Approximate Bayesian Computation (ABC) is able to eliminate this requirement, replacing the evaluation of the likelihood with simulation from it. Likelihood-free methods have gained in efficiency and popularity in the past few years, following their integration with Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) in order to better explore the parameter space. They have been applied primarily to estimating the parameters of a given model, but can also be used to compare models. Here we present novel likelihood-free approaches to model comparison, based upon the independent estimation of the evidence of each model under study. Key advantages of these approaches over previous techniques are that they allow the exploitation of MCMC or SMC algorithms for exploring the parameter space, and that they do not require a sampler able to mix between models. We validate the proposed methods using a simple exponential family problem before providing a realistic problem from human population genetics: the comparison of different demographic models based upon genetic data from the Y chromosome.

The structure of the optimal income tax in the quasi-linear model

Existing numerical characterizations of the optimal income tax have been based on a limited number of model specifications. As a result, they do not reveal which properties are general. We determine the optimal tax in the quasi-linear model under weaker assumptions than have previously been used; in particular, we remove the assumption of a lower bound on the utility of zero consumption and the need to permit negative labor incomes. A Monte Carlo analysis is then conducted in which economies are selected at random and the optimal tax function constructed. The results show that in a significant proportion of economies the marginal tax rate rises at low skills and falls at high. The average tax rate is equally likely to rise or fall with skill at low skill levels, rises in the majority of cases in the centre of the skill range, and falls at high skills. These results are consistent across all the specifications we test. We then extend the analysis to show that these results also hold for Cobb-Douglas utility.

A mechanism for Atlantic multidecadal variability in the Kiel Climate Model

Atlantic Multidecadal Variability (AMV) is investigated in a millennial control simulation with the Kiel Climate Model (KCM), a coupled atmosphere–ocean–sea ice model. An oscillatory mode with approximately 60 years period and characteristics similar to observations is identified with the aid of three-dimensional temperature and salinity joint empirical orthogonal function analysis. The mode explains 30 % of variability on centennial and shorter timescales in the upper 2,000 m of the North Atlantic. It is associated with changes in the Atlantic Meridional Overturning Circulation (AMOC) of ±1–2 Sv and Atlantic Sea Surface Temperature (SST) of ±0.2 °C. AMV in KCM results from an out-of-phase interaction between horizontal and vertical ocean circulation, coupled through Irminger Sea convection. Wintertime convection in this region is mainly controlled by salinity anomalies transported by the Subpolar Gyre (SPG). Increased (decreased) dense water formation in this region leads to a stronger (weaker) AMOC after 15 years, and this in turn leads to a weaker (stronger) SPG after another 15 years. The key role of salinity variations in the subpolar North Atlantic for AMV is confirmed in a 1,000 year long simulation with salinity restored to model climatology: No low frequency variations in convection are simulated, and the 60 year mode of variability is absent.

Prediction of visibility and aerosol within the operational Met Office unified model. I: Model formulation and variational assimilation

The formulation and performance of the Met Office visibility analysis and prediction system are described. The visibility diagnostic within the limited-area Unified Model is a function of humidity and a prognostic aerosol content. The aerosol model includes advection, industrial and general urban sources, plus boundary-layer mixing and removal by rain. The assimilation is a 3-dimensional variational scheme in which the visibility observation operator is a very nonlinear function of humidity, aerosol and temperature. A quality control scheme for visibility data is included. Visibility observations can give rise to humidity increments of significant magnitude compared with the direct impact of humidity observations. We present the results of sensitivity studies which show the contribution of different components of the system to improved skill in visibility forecasts. Visibility assimilation is most important within the first 6-12 hours of the forecast and for visibilities below 1 km, while modelling of aerosol sources and advection is important for slightly higher visibilities (1-5 km) and is still significant at longer forecast times

Model-measurement comparison of mesospheric temperature inversions, and a simple theory for their occurrence

Mesospheric temperature inversions are well established observed phenomena, yet their properties remain the subject of ongoing research. Comparisons between Rayleigh-scatter lidar temperature measurements obtained by the University of Western Ontario's Purple Crow Lidar (42.9°N, 81.4°W) and the Canadian Middle Atmosphere Model are used to quantify the statistics of inversions. In both model and measurements, inversions occur most frequently in the winter and exhibit an average amplitude of ∼10 K. The model exhibits virtually no inversions in the summer, while the measurements show a strongly reduced frequency of occurrence with an amplitude about half that in the winter. A simple theory of mesospheric inversions based on wave saturation is developed, with no adjustable parameters. It predicts that the environmental lapse rate must be less than half the adiabatic lapse rate for an inversion to form, and it predicts the ratio of the inversion amplitude and thickness as a function of environmental lapse rate. Comparison of this prediction to the actual amplitude/thickness ratio using the lidar measurements shows good agreement between theory and measurements.

A unified neurofuzzy model for classification

This work proposes a unified neurofuzzy modelling scheme. To begin with, the initial fuzzy base construction method is based on fuzzy clustering utilising a Gaussian mixture model (GMM) combined with the analysis of covariance (ANOVA) decomposition in order to obtain more compact univariate and bivariate membership functions over the subspaces of the input features. The mean and covariance of the Gaussian membership functions are found by the expectation maximisation (EM) algorithm with the merit of revealing the underlying density distribution of system inputs. The resultant set of membership functions forms the basis of the generalised fuzzy model (GFM) inference engine. The model structure and parameters of this neurofuzzy model are identified via the supervised subspace orthogonal least square (OLS) learning. Finally, instead of providing deterministic class label as model output by convention, a logistic regression model is applied to present the classifier’s output, in which the sigmoid type of logistic transfer function scales the outputs of the neurofuzzy model to the class probability. Experimental validation results are presented to demonstrate the effectiveness of the proposed neurofuzzy modelling scheme.

The du2J mouse model of ataxia and absence epilepsy has deficient cannabinoid CB1 receptor-mediated signalling

Key point summary • Cerebellar ataxias are progressive debilitating diseases with no known treatment and are associated with defective motor function and, in particular, abnormalities to Purkinje cells. • Mutant mice with deficits in Ca2+ channel auxiliary α2δ-2 subunits are used as models of cerebellar ataxia. • Our data in the du2J mouse model shows an association between the ataxic phenotype exhibited by homozygous du2J/du2J mice and increased irregularity of Purkinje cell firing. • We show that both heterozygous +/du2J and homozygous du2J/du2J mice completely lack the strong presynaptic modulation of neuronal firing by cannabinoid CB1 receptors which is exhibited by litter-matched control mice. • These results show that the du2J ataxia model is associated with deficits in CB1 receptor signalling in the cerebellar cortex, putatively linked with compromised Ca2+ channel activity due to reduced α2δ-2 subunit expression. Knowledge of such deficits may help design therapeutic agents to combat ataxias. Abstract Cerebellar ataxias are a group of progressive, debilitating diseases often associated with abnormal Purkinje cell (PC) firing and/or degeneration. Many animal models of cerebellar ataxia display abnormalities in Ca2+ channel function. The ‘ducky’ du2J mouse model of ataxia and absence epilepsy represents a clean knock-out of the auxiliary Ca2+ channel subunit, α2δ-2, and has been associated with deficient Ca2+ channel function in the cerebellar cortex. Here, we investigate effects of du2J mutation on PC layer (PCL) and granule cell (GC) layer (GCL) neuronal spiking activity and, also, inhibitory neurotransmission at interneurone-Purkinje cell(IN-PC) synapses. Increased neuronal firing irregularity was seen in the PCL and, to a less marked extent, in the GCL in du2J/du2J, but not +/du2J, mice; these data suggest that the ataxic phenotype is associated with lack of precision of PC firing, that may also impinge on GC activity and requires expression of two du2J alleles to manifest fully. du2J mutation had no clear effect on spontaneous inhibitory postsynaptic current (sIPSC) frequency at IN-PC synapses, but was associated with increased sIPSC amplitudes. du2J mutation ablated cannabinoid CB1 receptor (CB1R)-mediated modulation of spontaneous neuronal spike firing and CB1Rmediated presynaptic inhibition of synaptic transmission at IN-PC synapses in both +/du2J and du2J/du2J mutants; effects that occurred in the absence of changes in CB1R expression. These results demonstrate that the du2J ataxia model is associated with deficient CB1R signalling in the cerebellar cortex, putatively linked with compromised Ca2+ channel activity and the ataxic phenotype.

Negative blood oxygen level dependence in the rat: a model for investigating the role of suppression in neurovascular coupling

Modern neuroimaging techniques rely on neurovascular coupling to show regions of increased brain activation. However, little is known of the neurovascular coupling relationships that exist for inhibitory signals. To address this issue directly we developed a preparation to investigate the signal sources of one of these proposed inhibitory neurovascular signals, the negative blood oxygen level-dependent (BOLD) response (NBR), in rat somatosensory cortex. We found a reliable NBR measured in rat somatosensory cortex in response to unilateral electrical whisker stimulation, which was located in deeper cortical layers relative to the positive BOLD response. Separate optical measurements (two-dimensional optical imaging spectroscopy and laser Doppler flowmetry) revealed that the NBR was a result of decreased blood volume and flow and increased levels of deoxyhemoglobin. Neural activity in the NBR region, measured by multichannel electrodes, varied considerably as a function of cortical depth. There was a decrease in neuronal activity in deep cortical laminae. After cessation of whisker stimulation there was a large increase in neural activity above baseline. Both the decrease in neuronal activity and increase above baseline after stimulation cessation correlated well with the simultaneous measurement of blood flow suggesting that the NBR is related to decreases in neural activity in deep cortical layers. Interestingly, the magnitude of the neural decrease was largest in regions showing stimulus-evoked positive BOLD responses. Since a similar type of neural suppression in surround regions was associated with a negative BOLD signal, the increased levels of suppression in positive BOLD regions could importantly moderate the size of the observed BOLD response.

Nutrient-limited toxin production and the dynamics of two phytoplankton in culture media: a mathematical model

In this paper we have proposed and analyzed a simple mathematical model consisting of four variables, viz., nutrient concentration, toxin producing phytoplankton (TPP), non-toxic phytoplankton (NTP), and toxin concentration. Limitation in the concentration of the extracellular nutrient has been incorporated as an environmental stress condition for the plankton population, and the liberation of toxic chemicals has been described by a monotonic function of extracellular nutrient. The model is analyzed and simulated to reproduce the experimental findings of Graneli and Johansson [Graneli, E., Johansson, N., 2003. Increase in the production of allelopathic Prymnesium parvum cells grown under N- or P-deficient conditions. Harmful Algae 2, 135–145]. The robustness of the numerical experiments are tested by a formal parameter sensitivity analysis. As the first theoretical model consistent with the experiment of Graneli and Johansson (2003), our results demonstrate that, when nutrient-deficient conditions are favorable for the TPP population to release toxic chemicals, the TPP species control the bloom of other phytoplankton species which are non-toxic. Consistent with the observations made by Graneli and Johansson (2003), our model overcomes the limitation of not incorporating the effect of nutrient-limited toxic production in several other models developed on plankton dynamics.

Sparse model construction using coordinate descent optimization

We propose a new sparse model construction method aimed at maximizing a model’s generalisation capability for a large class of linear-in-the-parameters models. The coordinate descent optimization algorithm is employed with a modified l1- penalized least squares cost function in order to estimate a single parameter and its regularization parameter simultaneously based on the leave one out mean square error (LOOMSE). Our original contribution is to derive a closed form of optimal LOOMSE regularization parameter for a single term model, for which we show that the LOOMSE can be analytically computed without actually splitting the data set leading to a very simple parameter estimation method. We then integrate the new results within the coordinate descent optimization algorithm to update model parameters one at the time for linear-in-the-parameters models. Consequently a fully automated procedure is achieved without resort to any other validation data set for iterative model evaluation. Illustrative examples are included to demonstrate the effectiveness of the new approaches.