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.

Conditional transgenic expression of fibroblast growth factor 9 in the adult mouse heart reduces heart failure mortality after myocardial infarction

BACKGROUND: Fibroblast growth factor 9 (FGF9) is secreted from bone marrow cells, which have been shown to improve systolic function after myocardial infarction (MI) in a clinical trial. FGF9 promotes cardiac vascularization during embryonic development but is only weakly expressed in the adult heart. METHODS AND RESULTS: We used a tetracycline-responsive binary transgene system based on the α-myosin heavy chain promoter to test whether conditional expression of FGF9 in the adult myocardium supports adaptation after MI. In sham-operated mice, transgenic FGF9 stimulated left ventricular hypertrophy with microvessel expansion and preserved systolic and diastolic function. After coronary artery ligation, transgenic FGF9 enhanced hypertrophy of the noninfarcted left ventricular myocardium with increased microvessel density, reduced interstitial fibrosis, attenuated fetal gene expression, and improved systolic function. Heart failure mortality after MI was markedly reduced by transgenic FGF9, whereas rupture rates were not affected. Adenoviral FGF9 gene transfer after MI similarly promoted left ventricular hypertrophy with improved systolic function and reduced heart failure mortality. Mechanistically, FGF9 stimulated proliferation and network formation of endothelial cells but induced no direct hypertrophic effects in neonatal or adult rat cardiomyocytes in vitro. FGF9-stimulated endothelial cell supernatants, however, induced cardiomyocyte hypertrophy via paracrine release of bone morphogenetic protein 6. In accord with this observation, expression of bone morphogenetic protein 6 and phosphorylation of its downstream targets SMAD1/5 were increased in the myocardium of FGF9 transgenic mice. CONCLUSIONS: Conditional expression of FGF9 promotes myocardial vascularization and hypertrophy with enhanced systolic function and reduced heart failure mortality after MI. These observations suggest a previously unrecognized therapeutic potential for FGF9 after MI.

Interface dynamics in planar neural field models

Neural field models describe the coarse-grained activity of populations of interacting neurons. Because of the laminar structure of real cortical tissue they are often studied in two spatial dimensions, where they are well known to generate rich patterns of spatiotemporal activity. Such patterns have been interpreted in a variety of contexts ranging from the understanding of visual hallucinations to the generation of electroencephalographic signals. Typical patterns include localized solutions in the form of traveling spots, as well as intricate labyrinthine structures. These patterns are naturally defined by the interface between low and high states of neural activity. Here we derive the equations of motion for such interfaces and show, for a Heaviside firing rate, that the normal velocity of an interface is given in terms of a non-local Biot-Savart type interaction over the boundaries of the high activity regions. This exact, but dimensionally reduced, system of equations is solved numerically and shown to be in excellent agreement with the full nonlinear integral equation defining the neural field. We develop a linear stability analysis for the interface dynamics that allows us to understand the mechanisms of pattern formation that arise from instabilities of spots, rings, stripes and fronts. We further show how to analyze neural field models with linear adaptation currents, and determine the conditions for the dynamic instability of spots that can give rise to breathers and traveling waves.