Monotonically normal topological vector spaces are stratifiable

We prove that for any Hausdorff topological vector space E over the field R there exists A subset of E such that E is homeomorphic to a subset of A x R and A x R is homeomorphic to a subset of E. Using this fact we prove that E is monotonically normal if and only if E is stratifiable.

Decay spectrum and decay subspace of normal operators

Let A be a self-adjoint operator on a Hilbert space. It is well known that A admits a unique decomposition into a direct sum of three self-adjoint operators A(p), A(ac) and A(sc) such that there exists an orthonormal basis of eigenvectors for the operator A(p) the operator A(ac) has purely absolutely continuous spectrum and the operator A(sc) has purely singular continuous spectrum. We show the existence of a natural further decomposition of the singular continuous component A c into a direct sum of two self-adjoint operators A(sc)(D) and A(sc)(ND). The corresponding subspaces and spectra are called decaying and purely non-decaying singular subspaces and spectra. Similar decompositions are also shown for unitary operators and for general normal operators.

A novel shrinkage technique based on the normal inverse Gaussian density model

This paper proposes a novel image denoising technique based on the normal inverse Gaussian (NIG) density model using an extended non-negative sparse coding (NNSC) algorithm proposed by us. This algorithm can converge to feature basis vectors, which behave in the locality and orientation in spatial and frequency domain. Here, we demonstrate that the NIG density provides a very good fitness to the non-negative sparse data. In the denoising process, by exploiting a NIG-based maximum a posteriori estimator (MAP) of an image corrupted by additive Gaussian noise, the noise can be reduced successfully. This shrinkage technique, also referred to as the NNSC shrinkage technique, is self-adaptive to the statistical properties of image data. This denoising method is evaluated by values of the normalized signal to noise rate (SNR). Experimental results show that the NNSC shrinkage approach is indeed efficient and effective in denoising. Otherwise, we also compare the effectiveness of the NNSC shrinkage method with methods of standard sparse coding shrinkage, wavelet-based shrinkage and the Wiener filter. The simulation results show that our method outperforms the three kinds of denoising approaches mentioned above.

The control and learning of patterns of interlimb coordination: past and present issues in normal and disordered control

The present paper provides a historical note on the evolution of the behavioral study of interlimb coordination and the reasons for its success as a field of investigation in the past decades. Whereas the original foundations for this field of science were laid down back in the seventies, it has steadily grown in the past decades and has attracted the attention of various scientific disciplines. A diversity of topics is currently being addressed and this is also expressed in the present contributions to the special issue. The main theme is centered on the brain basis of interlimb coordination. On the one hand, this pertains to the study of the control and learning of patterns of interlimb coordination in clinical groups. On the other hand, basic neural approaches are being merged together with behavioral approaches to reveal the neural basis of interlimb coordination. (C) 2002 Elsevier Science B.V. All rights reserved.

Phonological oddballs in the focus of attention elicit a normal P3b in dyslexic adults

Difficulties in phonological processing have been proposed to be the core symptom of developmental dyslexia. Phoneme awareness tasks have been shown to both index and predict individual reading ability. In a previous experiment, we observed that dyslexic adults fail to display a P3a modulation for phonological deviants within an alliterated word stream when concentrating primarily on a lexical decision task [Fosker and Thierry, 2004, Neurosci. Lett. 357, 171-174]. Here we recorded the P3b oddball response elicited by initial phonemes within streams of alliterated words and pseudo-words when participants focussed directly on detecting the oddball phonemes. Despite significant verbal screening test differences between dyslexic adults and controls, the error rates, reactions times, and main components (P2, N2, P3a, and P3b) were indistinguishable across groups. The only difference between groups was found in the NI range, where dyslexic participants failed to show the modulations induced by phonological pairings (/b/-/p/ versus /r/ /g/) in controls. In light of previous P3a differences, these results suggest an important role for attention allocation in the manifestation of phonological deficits in developmental dyslexia. (c) 2005 Elsevier B.V. All rights reserved.