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.

Beneficial effects of sub-chronic activation of glucagon-like peptide-1 (GLP-1) receptors on deterioration of glucose homeostasis and insulin secretion in aging mice

Aging is associated with an increased incidence of glucose intolerance and type 2 diabetes. Glucagon-like peptide-1 (GLP-1) is an important insulinotropic peptide secreted from the gastrointestinal tract in response to nutrient absorption. The present study was designed to assess the sub-chronic glucose regulatory effects of the potent long-acting GLP-1 receptor agonist, (Val(8))GLP-1, in aging 45-49 week old mice. Daily injection of (Val$)GLP-1 (25 nmol/kg body weight) for 12 days had no significant effect on food intake, body weight, non-fasting plasma glucose and insulin concentrations. However, after 12 days, the glycaemic response to intraperitoneal glucose was improved (P <0.05) in (Val(8))GLP-1 treated mice. In keeping with this, glucose-mediated insulin secretion was enhanced (P <0.05) and insulin sensitivity improved (P <0.05) compared to controls. These data indicate that sub-chronic activation of the GLP-1 receptor by daily treatment with (Val(8))GLP-1 counters aspects of the age-related impairment of pancreatic beta-cell function and insulin sensitivity. 2006 Elsevier Inc. All rights reserved.

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.

Nature or nurture BMI and blood pressure at 90. Findings from the Belfast Elderly longitudinal free-living aging study Belfast

Hypertension is a key risk factor for stroke, cardiovascular disease and dementia. Although the link between weight, sodium and hypertension is established in younger people, little is known about their inter-relationship in people beyond 80 years of age. Associations between blood pressure, anthropometric indices and sodium were investigated in 495 apparently healthy, community-living participants (age 90, SD 4.8; range 80–106), from the cross-sectional Belfast Elderly Longitudinal Free-living Aging STudy (BELFAST) study. In age-sex-adjusted logistic regression models, blood pressure =140/90 mmHg significantly associated with body mass index (BMI) [odds ratio (OR)?=?1.28/ kg/m2], with weight (OR?=?1.22/kg) approaching significance (P?=?0.07). In further age-sex-adjusted models, blood pressure above the 120/80 mmHg normotensive reference value significantly associated with BMI (OR?=?1.44/kg/m2), weight (OR?=?1.36/kg), skin-fold-thickness (OR?=?1.33/mm) and serum sodium (OR?=?1.37 mmol/l). In BELFAST participants over 80 years old, blood pressure =140/90 mmHg is associated with BMI, in apparently similar ways to younger groups.

Age-dependent accumulation of lipofuscin in perivascular and subretinal microglia in experimental mice

Fundus autofluorescence (AF) imaging by confocal scanning laser ophthalmoscopy has been widely used by ophthalmologists in the diagnosis/monitoring of various retinal disorders. It is believed that fundus AF is derived from lipofuscin in retinal pigment epithelial (RPE) cells; however, direct clinicopathological correlation has not been possible in humans. We examined fundus AF by confocal scanning laser ophthalmoscopy and confocal microscopy in normal C57BL/6 mice of different ages. Increasingly strong AF signals were observed with age in the neuroretina and subretinal/RPE layer by confocal scanning laser ophthalmoscopy. Unlike fundus AF detected in normal human subjects, mouse fundus AF appeared as discrete foci distributed throughout the retina. Most of the AF signals in the neuroretina were distributed around retinal vessels. Confocal microscopy of retinal and choroid/RPE flat mounts demonstrated that most of the AF signals were derived from Iba-1+ perivascular and subretinal microglia. An age-dependent accumulation of Iba-1+ microglia at the subretinal space was observed. Lipofuscin granules were detected in large numbers in subretinal microglia by electron microscopy. The number of AF+ microglia and the amount of AF granules/cell increased with age. AF granules/lipofuscin were also observed in RPE cells in mice older than 12 months, but the number of AF+ RPE cells was very low (1.48 mm-2 and 5.02 mm-2 for 12 and 24 months, respectively) compared to the number of AF+ microglial cells (20.63 mm-2 and 76.36 mm-2 for 6 and 24 months, respectively). The fluorescence emission fingerprints of AF granules in subretinal microglia were the same as those in RPE cells. Our observation suggests that perivascular and subretinal microglia are the main cells producing lipofuscin in normal aged mouse retina and are responsible for in vivo fundus AF. Microglia may play an important role in retinal aging and age-related retinal diseases.