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 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

Ultrasonic Sizing of Voids Using Area Functions

We present a simple technique for determining the size of voids by the inversion of backscattered ultrasonic signals using the area function formula. The formulation of this method is based on the Born approximation, which is a weak scattering approximation, but the method works well for voids. The area function has been widely used as a method for determining the position of the flaw centroid to assist implementation of some inversion algorithms. The method has been reported in [6]. Here, we report some further studies, and more experimental results in detail

Viral Filtration Using Carbon-Based Materials

Viral infections alone are a significant cause of morbidity and mortality worldwide and have a detrimental impact on global healthcare and socioeconomic development. The discovery of novel antiviral treatments has gained tremendous attention and support with the rising number of viral outbreaks. In this work, carbonaceous materials, including graphene nanoplatelets and graphene oxide nanosheets, were investigated for antiviral properties. The materials were characterised using scanning electron microscopy and transmission electron microscopy. Analysis showed the materials to be two-dimensional with lateral dimensions ranging between 1 - 4 µm for graphene oxide, 110 ± 0.11nm for graphene nanoplatelets. Antiviral properties were assessed against a DNA virus model microorganism at concentrations of 0.5, 1.0 and 2.0 wt/v%. Both carbonaceous nanomaterials exhibited potent antiviral properties and gave rise to a viral reduction of 100% across all concentrations tested. Graphene oxide nanosheets were then incorporated into polymeric fibres and their antiviral behaviour was examined after 3 and 24 hours. A viral reduction of ~39% was observed after 24 hours of exposure. The research presented here showcases, for the first time, the antiviral potential of several carbonaceous nanomaterials, also included in a carrier polymer. These outcomes can be translated and implemented in many fields and devices to prevent viral spread and infection

Cellular modelling of Alström syndrome in human primary dermal fibroblasts and derived cells

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Automated adaptive analysis of tagged magnetic resonance images of the mouse heart

The full potential of tagged MRI of the mouse heart for non-invasive evaluation of cardiac mechanics in transgenic animals has not been realized due to excessive user involvement with available image processing algorithms. Therefore, we developed an automated, rapid, high-resolution analysis technique, called High Density Mapping (HDM), that uses spectral correlation to efficiently quantify regional wall deformation, does not entail tracking of individual tags, and involves minimal user interaction. HDM analysis distinguishes regional mechanics in healthy and infarcted mice within 2 minutes. This new method may help promote the practical use of tagged MRI in mice and other species.published_or_final_versio

Improved model identification for non-linear systems using a random subsampling and multifold modelling (RSMM) approach

In non-linear system identification, the available observed data are conventionally partitioned into two parts: the training data that are used for model identification and the test data that are used for model performance testing. This sort of 'hold-out' or 'split-sample' data partitioning method is convenient and the associated model identification procedure is in general easy to implement. The resultant model obtained from such a once-partitioned single training dataset, however, may occasionally lack robustness and generalisation to represent future unseen data, because the performance of the identified model may be highly dependent on how the data partition is made. To overcome the drawback of the hold-out data partitioning method, this study presents a new random subsampling and multifold modelling (RSMM) approach to produce less biased or preferably unbiased models. The basic idea and the associated procedure are as follows. First, generate K training datasets (and also K validation datasets), using a K-fold random subsampling method. Secondly, detect significant model terms and identify a common model structure that fits all the K datasets using a new proposed common model selection approach, called the multiple orthogonal search algorithm. Finally, estimate and refine the model parameters for the identified common-structured model using a multifold parameter estimation method. The proposed method can produce robust models with better generalisation performance

Mental Health during the COVID-19 Crisis in Africa: A Systematic Review and Meta-Analysis.

We aim to provide a systematic review and meta-analysis of the prevalence rates of mental health symptoms among major African populations during the COVID-19 pandemic. We include articles from PubMed, Embase, Web of Science, PsycINFO, and medRxiv between 1 February 2020 and 6 February 2021, and pooled data using random-effects meta-analyses. We identify 28 studies and 32 independent samples from 12 African countries with a total of 15,071 participants. The pooled prevalence of anxiety was 37% in 27 studies, of depression was 45% in 24 studies, and of insomnia was 28% in 9 studies. The pooled prevalence rates of anxiety, depression, and insomnia in North Africa (44%, 55%, and 31%, respectively) are higher than those in Sub-Saharan Africa (31%, 30%, and 24%, respectively). We find (a) a scarcity of studies in several African countries with a high number of COVID-19 cases; (b) high heterogeneity among the studies; (c) the extent and pattern of prevalence of mental health symptoms in Africa is high and differs from elsewhere-more African adults suffer from depression rather than anxiety and insomnia during COVID 19 compared to adult populations in other countries/regions. Hence, our findings carry crucial implications and impact future research to enable evidence-based medicine in Africa

Entanglement Entropy of 3-d Conformal Gauge Theories with Many Flavors

Three-dimensional conformal field theories (CFTs) of deconfined gauge fields coupled to gapless flavors of fermionic and bosonic matter describe quantum critical points of condensed matter systems in two spatial dimensions. An important characteristic of these CFTs is the finite part of the entanglement entropy across a circle. The negative of this quantity is equal to the finite part of the free energy of the Euclidean CFT on the three-sphere, and it has been proposed to satisfy the so called F-theorem, which states that it decreases under RG flow and is stationary at RG fixed points. We calculate the three-sphere free energy of non-supersymmetric gauge theory with a large number N_F of bosonic and/or fermionic flavors to the first subleading order in 1/N_F. We also calculate the exact free energies of the analogous chiral and non-chiral {\cal N} = 2 supersymmetric theories using localization, and find agreement with the 1/N_F expansion. We analyze some RG flows of supersymmetric theories, providing further evidence for the F-theorem.Comment: 31 pages, 2 figures; v2 refs added, minor change