Double point self-intersection surfaces of immersions

A self-transverse immersion of a smooth manifold M^{k+2} in R^{2k+2} has a double point self-intersection set which is the image of an immersion of a smooth surface, the double point self-intersection surface. We prove that this surface may have odd Euler characteristic if and only if k is congruent to 1 modulo 4 or k+1 is a power of 2. This corrects a previously published result by Andras Szucs. The method of proof is to evaluate the Stiefel-Whitney numbers of the double point self-intersection surface. By earier work of the authors these numbers can be read off from the Hurewicz image h(\alpha ) in H_{2k+2}\Omega ^{\infty }\Sigma ^{\infty }MO(k) of the element \alpha in \pi _{2k+2}\Omega ^{\infty }\Sigma ^{\infty }MO(k) corresponding to the immersion under the Pontrjagin-Thom construction.Comment: 22 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol4/paper4.abs.htm

Best interests, dementia and the Mental Capacity Act (2005)

The Mental Capacity Act (2005) is an impressive piece of legislation that deserves serious ethical attention, but much of the commentary on the Act has focussed on its legal and practical implications rather than the underlying ethical concepts. This paper examines the approach that the Act takes to best interests. The Act does not provide an account of the underlying concept of best interests. Instead it lists factors that must be considered in determining best interests, and the Code of Practice to the Act states that this list is incomplete. This paper argues that this general approach is correct, contrary to some accounts of best interests. The checklist includes items that are unhelpful. Furthermore, neither the Act nor its Code of Practice provides sufficient guidance to carers faced with difficult decisions concerning best interests. This paper suggests ways in which the checklist can be developed and discusses cases that could be used in an updated Code of Practice

Choline Acetyltransferase and Carnitine Acetyltransferase Activity in Human Spermatozoa During Capacitation

The regional distribution of ChAT activity in human spermatozoa is altered during in vitro capacitation and it correlates with the fertilizing potential of sperm. Regional immunoreactivity in human spermatozoa as assessed by fluorescent immunocytochemistry was compared with ChAT and CaAT activity determined by enzymatic methodologies. Increasing proportions of sperm exhibited ChAT immunoreactivity along the equatorial region with a concomitant decrease in ChAT reactivity in the midpiece. Also, competitive studies with unlabeled ChAT blocked the equatorial region labeling; the unlabeled CaAT blocked staining along the midpiece region of the tail, suggesting some cross-reactivity of the ChAT antiserum with the CaAT enzyme. A ChAT radioassay was used to compare regional immunoreactivity in human spermatozoa as assessed by fluorescent immunocytochemistry with ChAT and CaAT activity determined by enzymatic methodologies. Although a direct comparison was not made between the ChAT radioassay and the equatorial and midpiece/tail ChAT immunoreactivity, the two procedures appeared to not correlate. However, based on findings from the ChAT radioassay study, it was concluded that the ChAT enzyme is present within the sperm and not synthesized de novo. The regional distribution of ChAT and CaAT immunoreactivity under sperm capacitating conditions was correlated with the physiological indicators of completed capacitation, including the physiological and pharmacological induction of the acrosome reaction. A significant increase in both equatorial and midpiece/tail immunoreactivity was observed when using both caffeine and pentoxifylline. The addition of caffeine significantly increased equatorial binding, midpiece/tail binding, and the acrosome reaction rate in both washed and post swim-up samples. Although the addition of caffeine increased both equatorial binding and the acrosome reaction rate, a correlation was not observed between equatorial binding and the acrosome reaction. The potential fertility of human spermatozoa was correlated with ChAT and CaAT immunoreactivity by comparison of spermatozoa obtained from proven fertile males to spermatozoa incapable of attaining the physiological indicators of completed capacitation. A significant positive correlation was demonstrated between ChAT binding and the Hemizona Assay Index. A significant positive correlation was also demonstrated between CaAT binding and original sperm concentration, VAP, VSL, VCL, and both original and swim-up motility

Effect of Cannabinoids on Osteogenic Differentiation of Cultured Vascular Smooth Muscle Cells

Vascular calcification is strongly correlated with the clinical manifestations of atherosclerosis, heart attacks and strokes. The calcification process resembles bone formation and involves the osteogenic trans-differentiation of smooth muscles cells within the arterial wall. Cannabinoid receptors are known to modulate bone formation and are present in atherosclerotic vessels, suggesting they may also play a role in modulating calcification. Therefore, we evaluated the effects of cannabinoids on the expression of osteogenic proteins by vascular smooth muscle cells undergoing calcification

Trace Element Analysis of Rutile and Zr-in-Rutile Thermometry for Southern Appalachian Pelitic Schists

Over the past decade, geochronology studies in the southern Appalachians have focused on zircon, monazite, and mica ages to confirm the occurrence of a major Taconic event (~460‐450 Ma) affecting the Western and Central Blue Ridge, followed by a younger NeoAcadian (~360‐345 Ma) event affecting the Eastern Blue Ridge and Piedmont. Peak conditions of granulite facies metamorphism are estimated at ~850°C (garnet‐biotite) and 7‐9 kbar (GASP) for sillimanite schists at Winding Stair Gap (WSG), but thermobarometric studies of metasedimentary rocks in the region are limited and consequently Pressure‐Temperature‐time‐Deformation (P‐T‐t‐D) paths are poorly understood. Many details of the orogenic processes in the region remain unanswered, such as the depth of burial, rates of burial, cooling, and exhumation of various terranes, and variation of ages along strike. Rutile provides a robust, high‐temperature U‐Pb geochronometer that forms during metamorphic reactions and is a key phase for applying several thermobarometers in the determination of P‐T conditions. This study focuses on electron microprobe analysis of rutile‐bearing metapelitic schists in the Blue Ridge to obtain major and some trace element data and the generation of temperature constraints for the orogen. Initial sampling indicates that rutile‐bearing schists are somewhat sparse across the orogen, but have been confirmed in the Great Smoky Group of the Western Blue Ridge as well as in the Cartoogechaye and Cowrock terranes of the Central Blue Ridge, all of which were metamorphosed to high grades during the Taconic Orogeny. Rutile is found in both kyanite‐ and sillimanitegrade rocks, primarily as a matrix phase associated with biotite. Common assemblages in these rocks include garnet, biotite, muscovite, quartz, opaques, plagioclase, ±kyanite, ±sillimanite, and ±staurolite. Zirconium‐in‐rutile thermometry performed on the samples generated varying results based on sample location. The thin sections from the Western Blue Ridge were consistent with one another and comparable to previously published temperature estimates of ~600°C, indicating method consistency. However, the samples of Shooting Creek schist from near the Appalachian Trail generated temperatures that were lower than expected, especially since the rutile grains exist as inclusions in the garnet and should represent an earlier, higher‐temperature assemblage. Finally, the temperatures for rocks near Winding Stair Gap were much lower than the published peak condition estimates for the area, possibly supporting similar findings from Chen et al. (2007) that temperature estimates may be consistently too low at extreme temperatures and/or pressures due to thermometer resetting

Energetic particle observations at the subsolar magnetopause

International audienceThe pitch-angle distributions (PAD) of energetic particles are examined as the ISEE-1 satellite crosses the Earth's magnetopause near the subsolar point. The investigation focuses on the possible existence of a particular type of distribution that would be associated with a source of energetic particles in the high-latitude magnetosphere. PADs, demonstrating broad, persistent field-aligned fluxes filling a single hemisphere (upper/northern or lower/southern), were observed just sunward of the magnetopause current layer for an extended period of many minutes. These distributions are a direct prediction of a possible source of energetic particles located in the high altitude dayside cusp and we present five examples in detail of the three-dimensional particle distributions to demonstrate their existence. From these results, other possible causes of such PADs are examined