Sparse model identification using orthogonal forward regression with basis pursuit and D-optimality

An efficient model identification algorithm for a large class of linear-in-the-parameters models is introduced that simultaneously optimises the model approximation ability, sparsity and robustness. The derived model parameters in each forward regression step are initially estimated via the orthogonal least squares (OLS), followed by being tuned with a new gradient-descent learning algorithm based on the basis pursuit that minimises the l(1) norm of the parameter estimate vector. The model subset selection cost function includes a D-optimality design criterion that maximises the determinant of the design matrix of the subset to ensure model robustness and to enable the model selection procedure to automatically terminate at a sparse model. The proposed approach is based on the forward OLS algorithm using the modified Gram-Schmidt procedure. Both the parameter tuning procedure, based on basis pursuit, and the model selection criterion, based on the D-optimality that is effective in ensuring model robustness, are integrated with the forward regression. As a consequence the inherent computational efficiency associated with the conventional forward OLS approach is maintained in the proposed algorithm. Examples demonstrate the effectiveness of the new approach.

M-estimator, and D-optimality model construction using orthogonal forward regression

This correspondence introduces a new orthogonal forward regression (OFR) model identification algorithm using D-optimality for model structure selection and is based on an M-estimators of parameter estimates. M-estimator is a classical robust parameter estimation technique to tackle bad data conditions such as outliers. Computationally, The M-estimator can be derived using an iterative reweighted least squares (IRLS) algorithm. D-optimality is a model structure robustness criterion in experimental design to tackle ill-conditioning in model Structure. The orthogonal forward regression (OFR), often based on the modified Gram-Schmidt procedure, is an efficient method incorporating structure selection and parameter estimation simultaneously. The basic idea of the proposed approach is to incorporate an IRLS inner loop into the modified Gram-Schmidt procedure. In this manner, the OFR algorithm for parsimonious model structure determination is extended to bad data conditions with improved performance via the derivation of parameter M-estimators with inherent robustness to outliers. Numerical examples are included to demonstrate the effectiveness of the proposed algorithm.

A neurofuzzy network knowledge extraction and extended gram-Schmidt algorithm for model subspace decomposition

This paper introduces a new neurofuzzy model construction and parameter estimation algorithm from observed finite data sets, based on a Takagi and Sugeno (T-S) inference mechanism and a new extended Gram-Schmidt orthogonal decomposition algorithm, for the modeling of a priori unknown dynamical systems in the form of a set of fuzzy rules. The first contribution of the paper is the introduction of a one to one mapping between a fuzzy rule-base and a model matrix feature subspace using the T-S inference mechanism. This link enables the numerical properties associated with a rule-based matrix subspace, the relationships amongst these matrix subspaces, and the correlation between the output vector and a rule-base matrix subspace, to be investigated and extracted as rule-based knowledge to enhance model transparency. The matrix subspace spanned by a fuzzy rule is initially derived as the input regression matrix multiplied by a weighting matrix that consists of the corresponding fuzzy membership functions over the training data set. Model transparency is explored by the derivation of an equivalence between an A-optimality experimental design criterion of the weighting matrix and the average model output sensitivity to the fuzzy rule, so that rule-bases can be effectively measured by their identifiability via the A-optimality experimental design criterion. The A-optimality experimental design criterion of the weighting matrices of fuzzy rules is used to construct an initial model rule-base. An extended Gram-Schmidt algorithm is then developed to estimate the parameter vector for each rule. This new algorithm decomposes the model rule-bases via an orthogonal subspace decomposition approach, so as to enhance model transparency with the capability of interpreting the derived rule-base energy level. This new approach is computationally simpler than the conventional Gram-Schmidt algorithm for resolving high dimensional regression problems, whereby it is computationally desirable to decompose complex models into a few submodels rather than a single model with large number of input variables and the associated curse of dimensionality problem. Numerical examples are included to demonstrate the effectiveness of the proposed new algorithm.

Variability of the Atlantic thermohaline circulation described by three-dimensional empirical orthogonal functions

We describe the use of bivariate 3d empirical orthogonal functions (EOFs) in characterising low frequency variability of the Atlantic thermohaline circulation (THC) in the Hadley Centre global climate model, HadCM3. We find that the leading two modes are well correlated with an index of the meridional overturning circulation (MOC) on decadal timescales, with the leading mode alone accounting for 54% of the decadal variance. Episodes of coherent oscillations in the sub-space of the leading EOFs are identified; these episodes are of great interest for the predictability of the THC, and could indicate the existence of different regimes of natural variability. The mechanism identified for the multi-decadal variability is an internal ocean mode, dominated by changes in convection in the Nordic Seas, which lead the changes in the MOC by a few years. Variations in salinity transports from the Arctic and from the North Atlantic are the main feedbacks which control the oscillation. This mode has a weak feedback onto the atmosphere and hence a surface climatic influence. Interestingly, some of these climate impacts lead the changes in the overturning. There are also similarities to observed multi-decadal climate variability.

A new set of orthogonal patterns in weather and climate: Optimally interpolated patterns.

A new spectral-based approach is presented to find orthogonal patterns from gridded weather/climate data. The method is based on optimizing the interpolation error variance. The optimally interpolated patterns (OIP) are then given by the eigenvectors of the interpolation error covariance matrix, obtained using the cross-spectral matrix. The formulation of the approach is presented, and the application to low-dimension stochastic toy models and to various reanalyses datasets is performed. In particular, it is found that the lowest-frequency patterns correspond to largest eigenvalues, that is, variances, of the interpolation error matrix. The approach has been applied to the Northern Hemispheric (NH) and tropical sea level pressure (SLP) and to the Indian Ocean sea surface temperature (SST). Two main OIP patterns are found for the NH SLP representing respectively the North Atlantic Oscillation and the North Pacific pattern. The leading tropical SLP OIP represents the Southern Oscillation. For the Indian Ocean SST, the leading OIP pattern shows a tripole-like structure having one sign over the eastern and north- and southwestern parts and an opposite sign in the remaining parts of the basin. The pattern is also found to have a high lagged correlation with the Niño-3 index with 6-months lag.

Empirical Orthogonal Functions: The Medium is the Message

Empirical orthogonal function (EOF) analysis is a powerful tool for data compression and dimensionality reduction used broadly in meteorology and oceanography. Often in the literature, EOF modes are interpreted individually, independent of other modes. In fact, it can be shown that no such attribution can generally be made. This review demonstrates that in general individual EOF modes (i) will not correspond to individual dynamical modes, (ii) will not correspond to individual kinematic degrees of freedom, (iii) will not be statistically independent of other EOF modes, and (iv) will be strongly influenced by the nonlocal requirement that modes maximize variance over the entire domain. The goal of this review is not to argue against the use of EOF analysis in meteorology and oceanography; rather, it is to demonstrate the care that must be taken in the interpretation of individual modes in order to distinguish the medium from the message.

Osmotic upshift transiently inhibits uptake via ABC transporters in gram-negative bacteria

ATP-binding cassette transporters from several rhizobia and Salmonella enterica serovar Typhimurium, but not secondarily coupled systems, were inhibited by high concentrations (100 to 500 mM) of various osmolytes, an effect reversed by the removal of the osmolyte. ABC systems were also inactivated in isolated pea bacteroids, probably due to the obligatory use of high-osmolarity isolation media. Measurement of nutrient cycling in isolated pea bacteroids is impeded by this effect.

A family of promoter probe vectors incorporating autofluorescent and chromogenic reporter proteins for studying gene expression in Gram-negative bacteria

A series of promoter probe vectors for use in Gram-negative bacteria has been made in two broad-host-range vectors, pOT (pBBR replicon) and pJP2 (incP replicon). Reporter fusions can be made to gfpUV, gfprnut3.1, unstable gfpmut3.1 variants (LAA, LVA, AAV and ASV), gfp+, dsRed2, dsRedT3, dsRedT4, mRFP1, gusA or lacZ. The two vector families, pOT and pJP2, are compatible with one another and share the same polylinker for facile interchange of promoter regions. Vectors based on pJP2 have the advantage of being ultra-stable in the environment due to the presence of the parABCDE genes. As a confirmation of their usefulness, the dicarboxylic acid transport system promoter (dctA(p)) was cloned into a pOT (pRU1097)- and a pJP2 (pRU1156)-based vector and shown to be expressed by Rhizobium leguminosarum in infection threads of vetch. This indicates the presence of dicarboxylates at the earliest stages of nodule formation.

Some new three-level orthogonal main effects plans robust to model uncertainty

In this paper, we list some new orthogonal main effects plans for three-level designs for 4, 5 and 6 factors in IS runs and compare them with designs obtained from the existing L-18 orthogonal array. We show that these new designs have better projection properties and can provide better parameter estimates for a range of possible models. Additionally, we study designs in other smaller run-sizes when there are insufficient resources to perform an 18-run experiment. Plans for three-level designs for 4, 5 and 6 factors in 13 to 17 runs axe given. We show that the best designs here are efficient and deserve strong consideration in many practical situations.

Acute stroke predisposes to oral gram-negative bacilli - a cause of aspiration pneumonia?

Objectives: To assess any change in the oral flora in the mouths of stroke patients during the acute and rehabilitation phases and to determine whether this is related to episodes of aspiration pneumonia and clinical outcome. Materials and Methods: This observational study was carried out in hospital wards in a University teaching hospital. The subjects were patients immediately post-stroke and during the rehabilitation period, acute admissions and a group of healthy volunteers. An assessment of dentition and swallow in the presence or absence of oral aerobic gram-negative bacilli (AGNB) was correlated. Results: Of the acute stroke patients 52% had an unsafe swallow. AGNB carriage was documented in 34% of the acute stroke group. Of the 11 patients who died 55% had AGNB, 73% had an unsafe swallow and 36% had a combination of both. Conclusion: AGNB is a common finding in acute stroke patients. It is not a consequence of age or acute hospitalisation and is associated with an unsafe swallow and a higher mortality. Copyright (C) 2003 S. Karger AG, Basel.

The incidence of oral Gram-negative bacteria in patients with Parkinson's disease

Background: Parkinson's disease is a common neurodegenerative disorder that affects an increasing number of older people every year. Dysphagia is not only a common feature, but one that results in poor nutrition and an increased risk of bronchopneumonia. Previous work has suggested that the oral flora is altered in patients with oral pathology. Methods: Fifty patients were assessed to quantify the incidence of oral Gram-negative bacteria. Results: Sixteen of the patients with Parkinson's disease were found to have six different Gram-negative bacilli in their oral cavities. The 20 different Gram-negative bacteria present were Escherichia coli (n=7), Klebsiella spp. (n=3), Kluyvera spp. (n=3), Serratia spp. (n=3), Proteus spp. (n=2) and Enterobacter spp. (n=2). We found that the oral cavity of 16 (32%) of the patients with Parkinson's disease was abnormally colonised with Gram-negative bacteria and that Gram-negative bacteria were more likely to occur in those patients in whom oromuscular dysfunction was present (88% vs. 21%; p<0.05). Conclusion: Further work is required to determine the association between oral flora and the pathogenic organisms found in aspiration pneumonia as well as work on innovative treatments to reduce oral Gram-negative bacteria in those patients at particular risk of aspiration pneumonia.

Fastidiosipila sanguinis gen. nov., sp nov., a new Gram-positive, coccus-shaped organism from human blood

Phenotypic and phylogenetic studies were performed on two strains of an unidentified Gram-positive, fastidious, non-spore-forming, coccus-shaped bacterium recovered from human blood. The organism was catalase-negative and grew under strictly anaerobic conditions and in the presence of 2 and 6% O-2. Comparative 16S rRNA gene sequencing demonstrated that the unidentified bacterium was, phylogenetically, far removed from peptostreptococci and related Gram-positive coccus-shaped organisms, but exhibited a phylogenetic association with Clostridium rRNA cluster III [as defined by Collins et al, Int J Syst Bacteriol 44 (1994), 812-826]. Sequence divergence values of 15% or more were observed between the unidentified bacterium and all other recognized species within this and related rRINIA clostridial clusters. Treeing analysis showed that the unknown bacterium formed a deep line branching at the periphery of rRNA cluster III and represents a hitherto unknown genus within this supra-generic grouping. On the basis of both phylogenetic and phenotypic evidence, it is proposed that the unknown bacterium from blood be classified in a new genus, Fastidiosipila gen. nov., as Fastidiosipila sanguinis sp, nov. The type strain of Fastidiosipila sanguinis is CCUG 47711(T) (= CIP 108292(T)).