Adaptive nonlinear equalizer using a mixture of gaussians based on-line density estimator

This paper introduces a new adaptive nonlinear equalizer relying on a radial basis function (RBF) model, which is designed based on the minimum bit error rate (MBER) criterion, in the system setting of the intersymbol interference channel plus a co-channel interference. Our proposed algorithm is referred to as the on-line mixture of Gaussians estimator aided MBER (OMG-MBER) equalizer. Specifically, a mixture of Gaussians based probability density function (PDF) estimator is used to model the PDF of the decision variable, for which a novel on-line PDF update algorithm is derived to track the incoming data. With the aid of this novel on-line mixture of Gaussians based sample-by-sample updated PDF estimator, our adaptive nonlinear equalizer is capable of updating its equalizer’s parameters sample by sample to aim directly at minimizing the RBF nonlinear equalizer’s achievable bit error rate (BER). The proposed OMG-MBER equalizer significantly outperforms the existing on-line nonlinear MBER equalizer, known as the least bit error rate equalizer, in terms of both the convergence speed and the achievable BER, as is confirmed in our simulation study

Abnormal functional activation and maturation of fronto-striato-temporal and cerebellar regions during sustained attention in autism spectrum disorder

Objective Sustained attention problems are common in people with autism spectrum disorder (ASD) and may have significant implications for the diagnosis and management of ASD and associated comorbidities. Furthermore, ASD has been associated with atypical structural brain development. The authors used functional MRI to investigate the functional brain maturation of attention between childhood and adulthood in people with ASD. Method Using a parametrically modulated sustained attention/vigilance task, the authors examined brain activation and its linear correlation with age between childhood and adulthood in 46 healthy male adolescents and adults (ages 11–35 years) with ASD and 44 age- and IQ-matched typically developing comparison subjects. Results Relative to the comparison group, the ASD group had significantly poorer task performance and significantly lower activation in inferior prefrontal cortical, medial prefrontal cortical, striato-thalamic, and lateral cerebellar regions. A conjunction analysis of this analysis with group differences in brain-age correlations showed that the comparison group, but not the ASD group, had significantly progressively increased activation with age in these regions between childhood and adulthood, suggesting abnormal functional brain maturation in ASD. Several regions that showed both abnormal activation and functional maturation were associated with poorer task performance and clinical measures of ASD and inattention. Conclusions The results provide first evidence that abnormalities in sustained attention networks in individuals with ASD are associated with underlying abnormalities in the functional brain maturation of these networks between late childhood and adulthood.

The effect of chosen extraterrestrial solar spectrum on clear-sky atmospheric absorption and heating rates in the near infrared

The extraterrestrial solar spectrum (ESS) is an important component in near infrared (near-IR) radiative transfer calculations. However, the impact of a particular choice of the ESS in these regions has been given very little attention. A line-by-line (LBL) transfer model has been used to calculate the absorbed solar irradiance and solar heating rates in the near-IR from 2000-10000 cm−1(1-5 μm) using different ESS. For overhead sun conditions in a mid-latitude summer atmosphere, the absorbed irradiances could differ by up to about 11 Wm−2 (8.2%) while the tropospheric and stratospheric heating rates could differ by up to about 0.13 K day−1 (8.1%) and 0.19 K day−1 (7.6%). The spectral shape of the ESS also has a small but non-negligible impact on these factors in the near-IR.

Emotional and behavioural problems in children with language impairments and children with autism spectrum disorders

Background: Although it is well-established that children with language impairment (LI) and children with autism spectrum disorders (ASD) both show elevated levels of emotional and behavioural problems, the level and types of difficulties across the two groups have not previously been directly compared. Aims: To compare levels of emotional and behavioural problems in children with LI and children with ASD recruited from the same mainstream schools. Methods & Procedures: We measured teacher-reported emotional and behavioural problems using the Strengths and Difficulties Questionnaire (SDQ) in a sample of 5-to-13-year old children with LI (N=62) and children with ASD (N=42) attending mainstream school but with identified special educational needs. Outcomes & Results: Both groups showed similarly elevated levels of emotional, conduct and hyperactivity problems. The only differences between the LI and ASD groups were on subscales assessing peer problems (which were higher in the ASD group) and prosocial behaviours (which were higher in the LI group). Overall, there were few associations between emotional and behavioural problems and child characteristics, reflecting the pervasive nature of these difficulties in children with LI and children with ASD, although levels of problems were higher in children with ASD with lower language ability. However, in the ASD group only, a measure of family social economic status was associated with language ability and attenuated the association between language ability and emotional and behavioural problems. Conclusions & Implications: Children with LI and children with ASD in mainstream school show similarly elevated levels of emotional and behavioural problems, which require monitoring and may benefit from intervention. Further work is required to identify the child, family and situational factors that place children with LI and children with ASD at risk of emotional and behavioural problems, and whether these differ between the two groups. This work can then guide the application of evidence-based interventions to these children.

Translation and usability of autism screening and diagnostic tools for autism spectrum conditions in India

There is a critical need for screening and diagnostic tools (SDT) for autism spectrum conditions (ASC) in regional languages in South Asia. To address this, we translated four widely used SDT (Social Communication Disorder Checklist, Autism Spectrum Quotient, Social Communication Questionnaire, and Autism Diagnostic Observation Schedule) into Bengali and Hindi, two main regional languages (∼ 360 million speakers), and tested their usability in children with and without ASC. We found a significant difference in scores between children with ASC (n = 45 in Bengali, n = 40 in Hindi) and typically developing children (n = 43 in Bengali, n = 42 in Hindi) on all SDTs. These results demonstrate that these SDTs are usable in South Asia, and constitute an important resource for epidemiology research and clinical diagnosis in the region.

Representation errors and retrievals in linear and nonlinear data assimilation

This article shows how one can formulate the representation problem starting from Bayes’ theorem. The purpose of this article is to raise awareness of the formal solutions,so that approximations can be placed in a proper context. The representation errors appear in the likelihood, and the different possibilities for the representation of reality in model and observations are discussed, including nonlinear representation probability density functions. Specifically, the assumptions needed in the usual procedure to add a representation error covariance to the error covariance of the observations are discussed,and it is shown that, when several sub-grid observations are present, their mean still has a representation error ; socalled ‘superobbing’ does not resolve the issue. Connection is made to the off-line or on-line retrieval problem, providing a new simple proof of the equivalence of assimilating linear retrievals and original observations. Furthermore, it is shown how nonlinear retrievals can be assimilated without loss of information. Finally we discuss how errors in the observation operator model can be treated consistently in the Bayesian framework, connecting to previous work in this area.

Gut permeability in autism spectrum disorders

Objective To test whether gut permeability is increased in autism spectrum disorders (ASD) by evaluating gut permeability in a population-derived cohort of children with ASD compared with age- and intelligence quotient-matched controls without ASD but with special educational needs (SEN). Patients and Methods One hundred thirty-three children aged 10–14 years, 103 with ASD and 30 with SEN, were given an oral test dose of mannitol and lactulose and urine collected for 6 hr. Gut permeability was assessed by measuring the urine lactulose/mannitol (L/M) recovery ratio by electrospray mass spectrometry-mass spectrometry. The ASD group was subcategorized for comparison into those without (n = 83) and with (n = 20) regression. Results There was no significant difference in L/M recovery ratio (mean (95% confidence interval)) between the groups with ASD: 0.015 (0.013–0.018), and SEN: 0.014 (0.009–0.019), nor in lactulose, mannitol, or creatinine recovery. No significant differences were observed in any parameter for the regressed versus non-regressed ASD groups. Results were consistent with previously published normal ranges. Eleven children (9/103 = 8.7% ASD and 2/30 = 6.7% SEN) had L/M recovery ratio > 0.03 (the accepted normal range cut-off), of whom two (one ASD and one SEN) had more definitely pathological L/M recovery ratios > 0.04. Conclusion There is no statistically significant group difference in small intestine permeability in a population cohort-derived group of children with ASD compared with a control group with SEN. Of the two children (one ASD and one SEN) with an L/M recovery ratio of > 0.04, one had undiagnosed asymptomatic celiac disease (ASD) and the other (SEN) past extensive surgery for gastroschisis.

The experience of friendship, victimization and bullying in children with an autism spectrum disorder: associations with child characteristics and school placement

Children with an autism spectrum disorder (ASD) may be vulnerable to social isolation and bullying. We measured the friendship, fighting/bullying and victimization experiences of 10–12-year-old children with an ASD (N = 100) using parent, teacher and child self-report. Parent and teacher reports were compared to an IQ-matched group of children with special educational needs (SEN) without ASD (N = 80) and UK population data. Parents and teachers reported a lower prevalence of friendships compared to population norms and to children with SEN without an ASD. Parents but not teachers reported higher levels of victimization than the SEN group. Half of the children with an ASD reported having friendships that involved mutuality. By teacher report children with an ASD who were less socially impaired in mainstream school experienced higher levels of victimization than more socially impaired children; whereas for more socially impaired children victimization did not vary by school placement. Strategies are required to support and improve the social interaction skills of children with an ASD, to enable them to develop and maintain meaningful peer friendships and avoid victimization.

Parent-reported gastro-intestinal symptoms in children with autism spectrum disorders

The objective of this study is to investigate whether parentally-reported gastro-intestinal (GI) symptoms are increased in a population-derived sample of children with autism spectrum disorders (ASD) compared to controls. Participants included 132 children with ASD and 81 with special educational needs (SEN) but no ASD, aged 10-14 years plus 82 typically developing (TD) children. Data were collected on GI symptoms, diet, cognitive abilities, and developmental histories. Nearly half (weighted rate 46.5 %) of children with ASD had at least one individual lifetime GI symptom compared with 21.8 % of TD children and 29.2 % of those with SEN. Children with ASD had more past and current GI symptoms than TD or SEN groups although fewer current symptoms were reported in all groups compared with the past. The ASD group had significantly increased past vomiting and diarrhoea compared with the TD group and more abdominal pain than the SEN group. The ASD group had more current constipation (when defined as bowel movement less than three times per week) and soiling than either the TD or SEN groups. No association was found between GI symptoms and intellectual ability, ASD severity, ASD regression or limited or faddy diet. Parents report more GI symptoms in children with ASD than children with either SEN or TD children but the frequency of reported symptoms is greater in the past than currently in all groups.

Advances in the study of boundary value problems for nonlinear integrable PDEs

In this review I summarise some of the most significant advances of the last decade in the analysis and solution of boundary value problems for integrable partial differential equations in two independent variables. These equations arise widely in mathematical physics, and in order to model realistic applications, it is essential to consider bounded domain and inhomogeneous boundary conditions. I focus specifically on a general and widely applicable approach, usually referred to as the Unified Transform or Fokas Transform, that provides a substantial generalisation of the classical Inverse Scattering Transform. This approach preserves the conceptual efficiency and aesthetic appeal of the more classical transform approaches, but presents a distinctive and important difference. While the Inverse Scattering Transform follows the "separation of variables" philosophy, albeit in a nonlinear setting, the Unified Transform is a based on the idea of synthesis, rather than separation, of variables. I will outline the main ideas in the case of linear evolution equations, and then illustrate their generalisation to certain nonlinear cases of particular significance.

The elliptic sine-Gordon equation: a nonlinear elliptic integrable PDE

In this paper, we summarise this recent progress to underline the features specific to this nonlinear elliptic case, and we give a new classification of boundary conditions on the semistrip that satisfy a necessary condition for yielding a boundary value problem can be effectively linearised. This classification is based on formulation the equation in terms of an alternative Lax pair.

Nonlinear regional warming with increasing CO₂ concentration

When considering adaptation measures and global climate mitigation goals, stakeholders need regional-scale climate projections, including the range of plausible warming rates. To assist these stakeholders, it is important to understand whether some locations may see disproportionately high or low warming from additional forcing above targets such as 2 K (ref. 1). There is a need to narrow uncertainty2 in this nonlinear warming, which requires understanding how climate changes as forcings increase from medium to high levels. However, quantifying and understanding regional nonlinear processes is challenging. Here we show that regional-scale warming can be strongly superlinear to successive CO2 doublings, using five different climate models. Ensemble-mean warming is superlinear over most land locations. Further, the inter-model spread tends to be amplified at higher forcing levels, as nonlinearities grow—especially when considering changes per kelvin of global warming. Regional nonlinearities in surface warming arise from nonlinearities in global-mean radiative balance, the Atlantic meridional overturning circulation, surface snow/ice cover and evapotranspiration. For robust adaptation and mitigation advice, therefore, potentially avoidable climate change (the difference between business-as-usual and mitigation scenarios) and unavoidable climate change (change under strong mitigation scenarios) may need different analysis methods.

Estimating Lorenz's reference state in an ocean with a nonlinear equation of state for seawater

The study of the mechanical energy budget of the oceans using Lorenz available potential energy (APE) theory is based on knowledge of the adiabatically re-arranged Lorenz reference state of minimum potential energy. The compressible and nonlinear character of the equation of state for seawater has been thought to cause the reference state to be ill-defined, casting doubt on the usefulness of APE theory for investigating ocean energetics under realistic conditions. Using a method based on the volume frequency distribution of parcels as a function of temperature and salinity in the context of the seawater Boussinesq approximation, which we illustrate using climatological data, we show that compressibility effects are in fact minor. The reference state can be regarded as a well defined one-dimensional function of depth, which forms a surface in temperature, salinity and density space between the surface and the bottom of the ocean. For a very small proportion of water masses, this surface can be multivalued and water parcels can have up to two statically stable levels in the reference density profile, of which the shallowest is energetically more accessible. Classifying parcels from the surface to the bottom gives a different reference density profile than classifying in the opposite direction. However, this difference is negligible. We show that the reference state obtained by standard sorting methods is equivalent, though computationally more expensive, to the volume frequency distribution approach. The approach we present can be applied systematically and in a computationally efficient manner to investigate the APE budget of the ocean circulation using models or climatological data.

Nonlinear identification using orthogonal forward regression with nested optimal regularization

An efficient data based-modeling algorithm for nonlinear system identification is introduced for radial basis function (RBF) neural networks with the aim of maximizing generalization capability based on the concept of leave-one-out (LOO) cross validation. Each of the RBF kernels has its own kernel width parameter and the basic idea is to optimize the multiple pairs of regularization parameters and kernel widths, each of which is associated with a kernel, one at a time within the orthogonal forward regression (OFR) procedure. Thus, each OFR step consists of one model term selection based on the LOO mean square error (LOOMSE), followed by the optimization of the associated kernel width and regularization parameter, also based on the LOOMSE. Since like our previous state-of-the-art local regularization assisted orthogonal least squares (LROLS) algorithm, the same LOOMSE is adopted for model selection, our proposed new OFR algorithm is also capable of producing a very sparse RBF model with excellent generalization performance. Unlike our previous LROLS algorithm which requires an additional iterative loop to optimize the regularization parameters as well as an additional procedure to optimize the kernel width, the proposed new OFR algorithm optimizes both the kernel widths and regularization parameters within the single OFR procedure, and consequently the required computational complexity is dramatically reduced. Nonlinear system identification examples are included to demonstrate the effectiveness of this new approach in comparison to the well-known approaches of support vector machine and least absolute shrinkage and selection operator as well as the LROLS algorithm.

Nonlinear equalization of Hammerstein OFDM systems

A practical orthogonal frequency-division multiplexing (OFDM) system can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. In this contribution, we advocate a novel nonlinear equalization scheme for OFDM Hammerstein systems. We model the nonlinear HPA, which represents the static nonlinearity of the OFDM Hammerstein channel, by a B-spline neural network, and we develop a highly effective alternating least squares algorithm for estimating the parameters of the OFDM Hammerstein channel, including channel impulse response coefficients and the parameters of the B-spline model. Moreover, we also use another B-spline neural network to model the inversion of the HPA’s nonlinearity, and the parameters of this inverting B-spline model can easily be estimated using the standard least squares algorithm based on the pseudo training data obtained as a byproduct of the Hammerstein channel identification. Equalization of the OFDM Hammerstein channel can then be accomplished by the usual one-tap linear equalization as well as the inverse B-spline neural network model obtained. The effectiveness of our nonlinear equalization scheme for OFDM Hammerstein channels is demonstrated by simulation results.