Dirac operators and spectral triples for some fractal sets built on curves

We construct spectral triples and, in particular, Dirac operators, for the algebra of continuous functions on certain compact metric spaces. The triples are countable sums of triples where each summand is based on a curve in the space. Several fractals, like a finitely summable infinite tree and the Sierpinski gasket, fit naturally within our framework. In these cases, we show that our spectral triples do describe the geodesic distance and the Minkowski dimension as well as, more generally, the complex fractal dimensions of the space. Furthermore, in the case of the Sierpinski gasket, the associated Dixmier-type trace coincides with the normalized Hausdorff measure of dimension $\log 3/ \log 2$.Comment: 48 pages, 4 figures. Elementary proofs omitted. To appear in Adv. Mat

Endomorphisms of quantized Weyl algebras

Belov-Kanel and Kontsevich conjectured that the group of automorphisms of the n'th Weyl algebra and the group of polynomial symplectomorphisms of C^2 are canonically isomorphic. We discuss how this conjecture can be approached by means of (second) quantized Weyl algebras at roots of unity

Parental socioeconomic position and midlife allostatic load:a study of potential mediators

Abstract Background The mechanisms underlying the association of parental socioeconomic position with later life allostatic load remain unclear. The present study aims to examine potential pathways underlying this association: personality, social relations, intelligence and education. Methods The study comprised 361 members of the Copenhagen Perinatal Cohort who participated in two subsequent follow-ups: the Prenatal Development Project (mean age 27 years) and the Copenhagen Aging and Midlife Biobank study (mean age 50 years). Allostatic load was based on 14 biomarkers representing the inflammatory, metabolic and cardiovascular system measured at midlife. Information on potential mediators was collected in young adulthood, and their role in the association of parental socioeconomic position with midlife allostatic load were examined in linear regression path analyses. Results Parental socioeconomic position at one year was inversely associated with midlife allostatic load (β = − 0.238, p < .001). No mediation effects were found for personality or social relations. In a model including intelligence and education, a significant indirect effect was found for education (β = − 0.151, p < .001). A significant direct effect remained (β = − 0.111, p = .040). Conclusions Parental socioeconomic position was inversely associated with allostatic load in midlife. Results suggest that part of this association was mediated by education. A better understanding of the non-cognitive pathways related to education is an important prerequisite for the development of effective intervention strategies

Deficient maturation of aspects of attention and executive functions in early onset schizophrenia

The few existing long-term, neuropsychological follow-up studies of early onset schizophrenia (EOS) patients have reported relative stability in some cognitive functions but abnormal developmental trajectories in verbal memory, set shifting, aspects of attention, and speed of information processing throughout late adolescence into early adulthood. The current 5-year follow-up study compared the development of specific cognitive functions in EOS patients (N = 17) from the time of first-episode to chronic phase with that of healthy controls (N = 38) and secondarily to patients with other early onset, non-organic, non-affective psychoses (EOP) (N = 11). Speed of processing of executive functions, set shifting, and attention improved significantly in the healthy controls and reflected continuous functional maturation during late adolescence and early adulthood. The developmental progression of attention and set shifting but not speed of processing of executive functions was significantly subnormal in EOS patients. Other specific cognitive functions that had attained functional maturity in the healthy controls before or around the time of the baseline assessment showed normal development in EOS patients during the follow-up period, indicating stable cognitive deficits. These results suggest post-onset developmental deficits in two out of the three aspects of attention and executive functions that have protracted maturational trajectories and that overlap the age of onset of EOS. No significant difference in the development of any specific cognitive function was found between the EOS and EOP group

Distribution of the aquaporin CHIP in secretory and resorptive epithelia and capillary endothelia

The existence of water-selective channels has been postulated to explain the high water permeability of erythrocytes and certain epithelial cells. The aquaporin CHIP (channel-forming integral membrane protein of 28 kDa), a molecular water channel, is abundant in erythrocytes and water-permeable segments of the nephron. To determine whether CHIP may mediate transmembrane water movement in other water-permeable epithelia, membranes of multiple organs were studied by immunoblotting, immunohistochemistry, and immunoelectron microscopy using affinity-purified anti-CHIP IgG. The apical membrane of the choroid plexus epithelium was densely stained, implying a role for CHIP in the secretion of cerebrospinal fluid. In the eye, CHIP was abundant in apical and basolateral domains of ciliary epithelium, the site of aqueous humor secretion, and also in lens epithelium and corneal endothelium. CHIP was detected in membranes of hepatic bile ducts and water-resorptive epithelium of gall bladder, suggesting a role in bile secretion and concentration. CHIP was not detected in glandular epithelium of mammary, salivary, or lacrimal glands, suggesting the existence of other water-channel isoforms. CHIP was also not detected within the epithelium of the gastrointestinal mucosa. CHIP was abundant in membranes of intestinal lacteals and continuous capillaries in diverse tissues, including cardiac and skeletal muscle, thus providing a molecular explanation for the known water permeability of certain lymphatics and capillary beds. These studies underscore the hypothesis that CHIP plays a major role in transcellular water movement throughout the body

Extensions and degenerations of spectral triples

For a unital C*-algebra A, which is equipped with a spectral triple and an extension T of A by the compacts, we construct a family of spectral triples associated to T and depending on the two positive parameters (s,t). Using Rieffel's notation of quantum Gromov-Hausdorff distance between compact quantum metric spaces it is possible to define a metric on this family of spectral triples, and we show that the distance between a pair of spectral triples varies continuously with respect to the parameters. It turns out that a spectral triple associated to the unitarization of the algebra of compact operators is obtained under the limit - in this metric - for (s,1) -> (0, 1), while the basic spectral triple, associated to A, is obtained from this family under a sort of a dual limiting process for (1, t) -> (1, 0). We show that our constructions will provide families of spectral triples for the unitarized compacts and for the Podles sphere. In the case of the compacts we investigate to which extent our proposed spectral triple satisfies Connes' 7 axioms for noncommutative geometry.Comment: 40 pages. Addedd in ver. 2: Examples for the compacts and the Podle`s sphere plus comments on the relations to matricial quantum metrics. In ver.3 the word "deformations" in the original title has changed to "degenerations" and some illustrative remarks on this aspect are adde