Search results for "Hilbert"
showing 10 items of 331 documents
The factorization method for real elliptic problems
2006
The Factorization Method localizes inclusions inside a body from mea- surements on its surface. Without a priori knowing the physical parameters inside the inclusions, the points belonging to them can be characterized using the range of an auxiliary operator. The method relies on a range characterization that relates the range of the auxiliary operator to the measurements and is only known for very particular applications. In this work we develop a general framework for the method by considering sym- metric and coercive operators between abstract Hilbert spaces. We show that the important range characterization holds if the difference between the inclusions and the background medium satisfi…
On electric and magnetic problems for vector fields in anisotropic nonhomogeneous media
1983
r= 3~2, initiated by Saranen [ 131. In the above, n is the outward-drawn unit normal to the boundary and A denotes the exterior product. According to the simple models for static magnetic fields (resp. electric fields) which are governed by (0.1) (resp. (0.2)), we call (0.1) the magnetic type problem and (0.2) the electric type problem. Considering bounded smooth domains a c R3, we discussed in [ 131, by means of an appropriate Hilbert space method, the solvability and the representation of the solutions for both problems (0.1) and (0.2). Such a new approach was necessary to cover the general nonhomogeneous cases where v and E are matrix-valued functions. Here our aim is twofold. First, we …
FastEMD–CCA algorithm for unsupervised and fast removal of eyeblink artifacts from electroencephalogram
2020
Abstract Online detection and removal of eye blink (EB) artifacts from electroencephalogram (EEG) would be very useful in medical diagnosis and brain computer interface (BCI). In this work, approaches that combine unsupervised eyeblink artifact detection with empirical mode decomposition (EMD), and canonical correlation analysis (CCA), are proposed to automatically identify eyeblink artifacts and remove them in an online manner. First eyeblink artifact regions are automatically identified and an eyeblink artifact template is extracted via EMD, which incorporates an alternate interpolation technique, the Akima spline interpolation. The removal of eyeblink artifact components relies on the el…
Online detection and removal of eye blink artifacts from electroencephalogram
2021
Abstract The most prominent type of artifact contaminating electroencephalogram (EEG) signals are the eye blink (EB) artifacts, which could potentially lead to misinterpretation of the EEG signal. Online identification and elimination of eye blink artifacts are crucial in applications such a Brain-Computer Interfaces (BCI), neurofeedback, and epilepsy diagnosis. In this paper, algorithms that combine unsupervised eye blink artifact detection (eADA) with modified Empirical Mode Decomposition (FastEMD) and Canonical Correlation Analysis (CCA) are proposed, i.e., FastEMD-CCA2 and FastCCA, to automatically identify eye blink artifacts and remove them in an online setting. The average accuracy, …
Automated and Online Eye Blink Artifact Removal from Electroencephalogram
2019
Eyeblink artifacts often contaminates electroencephalogram (EEG) signals, which could potentially confound EEG's interpretation. A lot offline methods are available to remove this artifact, but an online solution is required to remove eyeblink artifacts in near real time for EEG signal to be beneficial in applications such as brain computer interface, (BCI). In this work, approaches that combines unsupervised eyeblink artifact detection with Empirical Mode Decomposition (EMD) and Canonical Correlation Analysis (CCA) are proposed to automatically identify eyeblink artifacts and remove them in an online setting. The proposed approaches are analysed and evaluated in terms of artifact removal a…
Representable and Continuous Functionals on Banach Quasi *-Algebras
2017
In the study of locally convex quasi *-algebras an important role is played by representable linear functionals; i.e., functionals which allow a GNS-construction. This paper is mainly devoted to the study of the continuity of representable functionals in Banach and Hilbert quasi *-algebras. Some other concepts related to representable functionals (full-representability, *-semisimplicity, etc) are revisited in these special cases. In particular, in the case of Hilbert quasi *-algebras, which are shown to be fully representable, the existence of a 1-1 correspondence between positive, bounded elements (defined in an appropriate way) and continuous representable functionals is proved.
MR2986428 Lebedev, Leonid P.(CL-UNC); Vorovich, Iosif I.; Cloud, Michael J. Functional analysis in mechanics. Second edition. Springer Monographs in …
2014
Grid methods and Hilbert space basis for simulations of quantum dynamics
1999
We discuss spatial grid methods adapted to the structure of Hilbert spaces, used to simulate quantum mechanical systems. We review the construction of Finite Basis Representation (FBR) and the Discrete Variable Representation (DVR). A mixed representation (pseudo-spectral method) is constructed through a quadrature relation linking both bases.
Reproducing kernel hilbert spaces regression methods for genomic assisted prediction of quantitative traits.
2008
Abstract Reproducing kernel Hilbert spaces regression procedures for prediction of total genetic value for quantitative traits, which make use of phenotypic and genomic data simultaneously, are discussed from a theoretical perspective. It is argued that a nonparametric treatment may be needed for capturing the multiple and complex interactions potentially arising in whole-genome models, i.e., those based on thousands of single-nucleotide polymorphism (SNP) markers. After a review of reproducing kernel Hilbert spaces regression, it is shown that the statistical specification admits a standard mixed-effects linear model representation, with smoothing parameters treated as variance components.…
Bergman and Bloch spaces of vector-valued functions
2003
We investigate Bergman and Bloch spaces of analytic vector-valued functions in the unit disc. We show how the Bergman projection from the Bochner-Lebesgue space Lp(, X) onto the Bergman space Bp(X) extends boundedly to the space of vector-valued measures of bounded p-variation Vp(X), using this fact to prove that the dual of Bp(X) is Bp(X*) for any complex Banach space X and 1 < p < ∞. As for p = 1 the dual is the Bloch space ℬ(X*). Furthermore we relate these spaces (via the Bergman kernel) with the classes of p-summing and positive p-summing operators, and we show in the same framework that Bp(X) is always complemented in p(X). (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)