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.

Electrical activity induced by nitric oxide in canine colonic circular muscle.

Nitric oxide generates slow electrical oscillations (SEOs) in cells near the myenteric edge of the circular muscle layer, which resemble slow waves generated by interstitial cells of Cajal (ICCs) at the submucosal edge of this muscle. The properties of SEOs were studied to determine whether these events are similar to slow waves. Rapid frequency membrane potential oscillations (MPOs; 16 +/- 1 cycles/min and 9.6 +/- 0.2 mV) were recorded from control muscles near the myenteric edge. Sodium nitroprusside (0.3 microM) reduced MPOs and initiated SEOs (1.3 +/- 0.3 cycles/min and 13.4 +/- 1.4 mV amplitude). SEOs were abolished by the guanylate cyclase inhibitor 1H-[1,2,4]-oxadiazolo-[4,3-a]-quinoxaline-1-one (10 microM). MPOs were abolished by nifedipine (1 microM), whereas SEO frequency increased and the amount of depolarization decreased. BAY K 8644 (1 microM) prolonged SEOs and reduced their frequency. SEOs were abolished by Ni(2+) (0.5 mM), low Ca(2+) solution (0.1 mM Ca(2+)), cyclopiazonic acid (10 microM), and the mitochondrial uncouplers antimycin (10 microM) and carbonyl cyanide p-trifluoromethoxyphenylhydrazone (1 microM). Oligomycin (10 microM) was without effect. These effects are similar to those described for colonic slow waves. Our results suggest that nitric oxide-induced SEOs are similar in mechanism to slow waves, an activity not previously thought to be generated by myenteric pacemakers.

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.