Recent progress on univariate and multivariate polynomial and spline quasi-interpolants

Polynomial and spline quasi-interpolants (QIs) are practical and effective approximation operators. Among their remarkable properties, let us cite for example: good shape properties, easy computation and evaluation (no linear system to solve), uniform boundedness independently of the degree (polynomials) or of the partition (splines), good approximation order. We shall emphasize new results on various types of univariate and multivariate polynomial or spline QIs, depending on the nature of coefficient functionals, which can be differential, discrete or integral. We shall also present some applications of QIs to numerical methods

Modulation of induced frontocentral theta (Fm-θ) event-related (de-)synchronisation dynamics following mindfulness-based cognitive therapy in Major Depressive Disorder

Item does not contain fulltex

Biofeedback for psychiatric disorders: a systematic review

Item does not contain fulltextBiofeedback potentially provides non-invasive, effective psychophysiological interventions for psychiatric disorders. The encompassing purpose of this review was to establish how biofeedback interventions have been used to treat select psychiatric disorders [anxiety, autistic spectrum disorders, depression, dissociation, eating disorders, schizophrenia and psychoses] to date and provide a useful reference for consultation by clinicians and researchers planning to administer a biofeedback treatment. A systematic search of EMBASE, MEDLINE, PsycINFO, and WOK databases and hand searches in Applied Psychophysiology and Biofeedback, and Journal of Neurotherapy, identified 227 articles; 63 of which are included within this review. Electroencephalographic neurofeedback constituted the most investigated modality (31.7%). Anxiety disorders were the most commonly treated (68.3%). Multi-modal biofeedback appeared most effective in significantly ameliorating symptoms, suggesting that targeting more than one physiological modality for bio-regulation increases therapeutic efficacy. Overall, 80.9% of articles reported some level of clinical amelioration related to biofeedback exposure, 65.0% to a statistically significant (p < .05) level of symptom reduction based on reported standardized clinical parameters. Although the heterogeneity of the included studies warrants caution before explicit efficacy statements can be made. Further development of standardized controlled methodological protocols tailored for specific disorders and guidelines to generate comprehensive reports may contribute towards establishing the value of biofeedback interventions within mainstream psychiatry

Multi-dimensional modulations of alpha and gamma cortical dynamics following mindfulness-based cognitive therapy in Major Depressive Disorder

Item does not contain fulltextTo illuminate candidate neural working mechanisms of Mindfulness-Based Cognitive Therapy (MBCT) in the treatment of recurrent depressive disorder, parallel to the potential interplays between modulations in electro-cortical dynamics and depressive symptom severity and self-compassionate experience. Linear and nonlinear alpha and gamma EEG oscillatory dynamics were examined concomitant to an affective Go/NoGo paradigm, pre-to-post MBCT or natural wait-list, in 51 recurrent depressive patients. Specific EEG variables investigated were; (1) induced event-related (de-) synchronisation (ERD/ERS), (2) evoked power, and (3) inter-/intra-hemispheric coherence. Secondary clinical measures included depressive severity and experiences of self-compassion. MBCT significantly downregulated alpha and gamma power, reflecting increased cortical excitability. Enhanced alpha-desynchronisation/ERD was observed for negative material opposed to attenuated alpha-ERD towards positively valenced stimuli, suggesting activation of neural networks usually hypoactive in depression, related to positive emotion regulation. MBCT-related increase in left-intra-hemispheric alpha-coherence of the fronto-parietal circuit aligned with these synchronisation dynamics. Ameliorated depressive severity and increased self-compassionate experience pre-to-post MBCT correlated with alpha-ERD change. The multi-dimensional neural mechanisms of MBCT pertain to task-specific linear and non-linear neural synchronisation and connectivity network dynamics. We propose MBCT-related modulations in differing cortical oscillatory bands have discrete excitatory (enacting positive emotionality) and inhibitory (disengaging from negative material) effects, where mediation in the alpha and gamma bands relates to the former

Effects of mindfulness-based cognitive therapy on neurophysiological correlates of performance monitoring in adult attention-deficit/hyperactivity disorder

Item does not contain fulltextOBJECTIVE: To examine whether mindfulness-based cognitive therapy (MBCT) would enhance attenuated amplitudes of event-related potentials (ERPs) indexing performance monitoring biomarkers of attention-deficit/hyperactivity disorder (ADHD). METHODS: Fifty adult ADHD patients took part in a randomised controlled study investigating ERP and clinical measures pre-to-post MBCT. Twenty-six patients were randomly allocated to MBCT, 24 to a wait-list control. Main outcome measures included error processing (ERN, Pe), conflict monitoring (NoGo-N2), and inhibitory control (NoGo-P3) ERPs concomitant to a continuous performance task (CPT-X). Inattention and hyperactivity-impulsivity ADHD symptoms, psychological distress and social functioning, and mindfulness skills were also assessed. Results : MBCT was associated with increased Pe and NoGo-P3 amplitudes, coinciding with reduced 'hyperactivity/impulsivity' and 'inattention' symptomatology. Specific to the MBCT; enhanced Pe amplitudes correlated with a decrease in hyperactivity/impulsivity symptoms and increased 'act-with-awareness' mindfulness skill, whereas, enhanced P3 correlated with amelioration in inattention symptoms. CONCLUSIONS: MBCT enhanced ERP amplitudes associated with motivational saliency and error awareness, leading to improved inhibitory regulation. SIGNIFICANCE: MBCT suggests having comparable modulation on performance monitoring ERP amplitudes as pharmacological treatments. Further study and development of MBCT as a treatment for ADHD is warranted, in addition to its potential scope for clinical applicability to broader defined externalising disorders and clinical problems associated with impairments of the prefrontal cortex

Maximal Margin Classification for Metric Spaces

In this article we construct a maximal margin classification algorithm for arbitrary metric spaces. At first we show that the Support Vector Machine (SVM) is a maximal margin algorithm for the class of metric spaces where the negative squared distance is conditionally positive definite (CPD). This means that the metric space can be isometrically embedded into a Hilbert space, where one performs linear maximal margin separation. We will show that the solution only depends on the metric, but not on the kernel. Following the framework we develop for the SVM, we construct an algorithm for maximal margin classification in arbitrary metric spaces. The main difference compared with SVM is that we no longer embed isometrically into a Hilbert space, but a Banach space. We further give an estimate of the capacity of the function class involved in this algorithm via Rademacher averages. We recover an algorithm of Graepel et al. [6]

L2-approximation by the translates of a function and related attenuation factors

10.1007/BF01385736Numerische Mathematik601549-56