A unified wavelet-based modelling framework for non-linear system identification: the WANARX model structure

A new unified modelling framework based on the superposition of additive submodels, functional components, and wavelet decompositions is proposed for non-linear system identification. A non-linear model, which is often represented using a multivariate non-linear function, is initially decomposed into a number of functional components via the wellknown analysis of variance (ANOVA) expression, which can be viewed as a special form of the NARX (non-linear autoregressive with exogenous inputs) model for representing dynamic input–output systems. By expanding each functional component using wavelet decompositions including the regular lattice frame decomposition, wavelet series and multiresolution wavelet decompositions, the multivariate non-linear model can then be converted into a linear-in-theparameters problem, which can be solved using least-squares type methods. An efficient model structure determination approach based upon a forward orthogonal least squares (OLS) algorithm, which involves a stepwise orthogonalization of the regressors and a forward selection of the relevant model terms based on the error reduction ratio (ERR), is employed to solve the linear-in-the-parameters problem in the present study. The new modelling structure is referred to as a wavelet-based ANOVA decomposition of the NARX model or simply WANARX model, and can be applied to represent high-order and high dimensional non-linear systems

The wavelet-NARMAX representation : a hybrid model structure combining polynomial models with multiresolution wavelet decompositions

A new hybrid model structure combing polynomial models with multiresolution wavelet decompositions is introduced for nonlinear system identification. Polynomial models play an important role in approximation theory, and have been extensively used in linear and nonlinear system identification. Wavelet decompositions, in which the basis functions have the property of localization in both time and frequency, outperform many other approximation schemes and offer a flexible solution for approximating arbitrary functions. Although wavelet representations can approximate even severe nonlinearities in a given signal very well, the advantage of these representations can be lost when wavelets are used to capture linear or low-order nonlinear behaviour in a signal. In order to sufficiently utilise the global property of polynomials and the local property of wavelet representations simultaneously, in this study polynomial models and wavelet decompositions are combined together in a parallel structure to represent nonlinear input-output systems. As a special form of the NARMAX model, this hybrid model structure will be referred to as the WAvelet-NARMAX model, or simply WANARMAX. Generally, such a WANARMAX representation for an input-output system might involve a large number of basis functions and therefore a great number of model terms. Experience reveals that only a small number of these model terms are significant to the system output. A new fast orthogonal least squares algorithm, called the matching pursuit orthogonal least squares (MPOLS) algorithm, is also introduced in this study to determine which terms should be included in the final model

A study on spline quasi-interpolation based quadrature rules for the isogeometric Galerkin BEM

Two recently introduced quadrature schemes for weakly singular integrals [Calabr\`o et al. J. Comput. Appl. Math. 2018] are investigated in the context of boundary integral equations arising in the isogeometric formulation of Galerkin Boundary Element Method (BEM). In the first scheme, the regular part of the integrand is approximated by a suitable quasi--interpolation spline. In the second scheme the regular part is approximated by a product of two spline functions. The two schemes are tested and compared against other standard and novel methods available in literature to evaluate different types of integrals arising in the Galerkin formulation. Numerical tests reveal that under reasonable assumptions the second scheme convergences with the optimal order in the Galerkin method, when performing $h$-refinement, even with a small amount of quadrature nodes. The quadrature schemes are validated also in numerical examples to solve 2D Laplace problems with Dirichlet boundary conditions

The Influence of Personality Traits on Reported Adherence to Medication in Individuals with Chronic Disease: An Epidemiological Study in West Sweden

BACKGROUND: Limited research exists exploring the influence of personality on adherence behaviour. Since non-adherence is a major obstacle in treating prevalent chronic diseases the aim was to determine whether personality traits are related to reported adherence to medication in individuals with chronic disease. METHODOLOGY/PRINCIPAL FINDINGS: Individuals with chronic disease (n = 749) were identified in a random population sample of 5000 inhabitants aged 30-70 in two municipalities in West Sweden. Data on five personality traits, Neuroticism, Extraversion, Openness to experiences, Agreeableness, and Conscientiousness, and medication adherence behaviour was collected by questionnaires. Statistical analyses resulted in a negative relationship between Neuroticism and medication adherence (P < 0.001), while both Agreeableness (P < 0.001) and Conscientiousness (P < 0.001) were positively related to adherence. At high levels of Conscientiousness, low adherence was related to higher scores in Neuroticism. At high levels of Agreeableness, low adherence was related to low scores in Conscientiousness and high scores in Openness to experiences. CONCLUSIONS: This study demonstrated that multiple personality traits are of significant importance for adherence behaviour in individuals with chronic disease. The findings suggest that several personality traits may interact in influencing adherence behaviour. Personality traits could putatively be used to focus efforts to educate and support patients with high risk of low medical adherence

SV2 Mediates Entry of Tetanus Neurotoxin into Central Neurons

Tetanus neurotoxin causes the disease tetanus, which is characterized by rigid paralysis. The toxin acts by inhibiting the release of neurotransmitters from inhibitory neurons in the spinal cord that innervate motor neurons and is unique among the clostridial neurotoxins due to its ability to shuttle from the periphery to the central nervous system. Tetanus neurotoxin is thought to interact with a high affinity receptor complex that is composed of lipid and protein components; however, the identity of the protein receptor remains elusive. In the current study, we demonstrate that toxin binding, to dissociated hippocampal and spinal cord neurons, is greatly enhanced by driving synaptic vesicle exocytosis. Moreover, tetanus neurotoxin entry and subsequent cleavage of synaptobrevin II, the substrate for this toxin, was also dependent on synaptic vesicle recycling. Next, we identified the potential synaptic vesicle binding protein for the toxin and found that it corresponded to SV2; tetanus neurotoxin was unable to cleave synaptobrevin II in SV2 knockout neurons. Toxin entry into knockout neurons was rescued by infecting with viruses that express SV2A or SV2B. Tetanus toxin elicited the hyper excitability in dissociated spinal cord neurons - due to preferential loss of inhibitory transmission - that is characteristic of the disease. Surprisingly, in dissociated cortical cultures, low concentrations of the toxin preferentially acted on excitatory neurons. Further examination of the distribution of SV2A and SV2B in both spinal cord and cortical neurons revealed that SV2B is to a large extent localized to excitatory terminals, while SV2A is localized to inhibitory terminals. Therefore, the distinct effects of tetanus toxin on cortical and spinal cord neurons are not due to differential expression of SV2 isoforms. In summary, the findings reported here indicate that SV2A and SV2B mediate binding and entry of tetanus neurotoxin into central neurons