Analytic measures and Bochner measurability

Let $\Sigma$ be a $\sigma$-algebra over $\Omega$, and let $M(\Sigma)$ denote the Banach space of complex measures. Consider a representation $T_t$ for $t\in\Bbb R$ acting on $M(\Sigma)$. We show that under certain, very weak hypotheses, that if for a given $\mu \in M(\Sigma)$ and all $A \in \Sigma$ the map $t \mapsto T_t \mu(A)$ is in $H^\infty(\Bbb R)$, then it follows that the map $t \mapsto T_t \mu$ is Bochner measurable. The proof is based upon the idea of the Analytic Radon Nikod\'ym Property. Straightforward applications yield a new and simpler proof of Forelli's main result concerning analytic measures ({\it Analytic and quasi-invariant measures}, Acta Math., {\bf 118} (1967), 33--59)

Transference in spaces of measures

The transference theory for Lp spaces of Calderon, Coifman, and Weiss is a powerful tool with many applications to singular integrals, ergodic theory, and spectral theory of operators. Transference methods afford a unified approach to many problems in diverse areas, which before were proved by a variety of methods. The purpose of this paper is to bring about a similar approach to the study of measures. Specifically, deep results in classical harmonic analysis and ergodic theory, due to Bochner, de Leeuw-Glicksberg, Forelli, and others, are all extensions of the classical F.&M. Riesz Theorem. We will show that all these extensions are obtainable via our new transference principle for spaces of measures.Comment: Also available at http://www.math.missouri.edu/~stephen/preprints

The Chondrocyte Channelome: A Novel Ion Channel Candidate in the Pathogenesis of Pectus Deformities

Costal cartilage is a type of rod-like hyaline cartilage connecting the ribs to the sternum. The chest wall deformities pectus excavatum (PE) and pectus carinatum (PC) involve displacement of the sternum causing a depression or protrusion of the chest. There is little knowledge about costal cartilage and pectus deformities with much of its understanding based on assumptions from articular cartilage. Chondrocytes are subjected to a constantly changing environment with fluctuations in pH and osmolarity. Ion channels detect these changes and in turn regulate proliferation, differentiation, and extracellular matrix production. Using ion channel qPCR arrays, we produced expression profiles for normal, fetal, PE-affected, and PC-affected costal chondrocytes as well as articular chondrocytes. Costal and articular chondrocytes had many commonly expressed ion channels with certain channels specific to each cartilage type. The discrepancy in ion channel expression is likely to be a reflection of the functional differences between the two cartilage types. Additionally, fetal costal chondrocytes had several other distinct ion channels possibly due to the differentiation status of the cells. In PC and PE chondrocytes, ACCN1 (ASIC2) and KCNN2 (SK2) were consistently down-regulated compared to normal costal chondrocytes. However, Western blot analysis found deceases only in ASIC2 protein levels. ASIC2 is a proton-gated ion channel involved in cell response to extracellular pH changes. Calcium monitoring revealed a delay in the formation calcium transients in PC cells when challenged with low pH which may be caused by aberrant signaling from ASIC channels. Immunofluorescent analysis of connexins found that Cx43 was present in chondrocytes with phosphorylated Cx43 localizing in and around the nucleus. Analysis of ATP release found that release is likely a connexin-mediated process, though external acidosis did not induce ATP release. Analysis of microRNAs found upregulation and down-regulation of several microRNAs in PC versus control cells, though further studies are needed to identify a possible microRNA signature for pectus deformities. Overall, we have generated a comprehensive ion channel profile for the costal chondrocytes, as well as identified a possible contributing factor for pectus deformities

Novel Architecture of Costal Cartilage and Implications in Chest Wall Deformities

Costal cartilage is a type of hyaline cartilage that forms rod-like structures that connect the ribs to the sternum. Deformation of costal cartilage is observed in the chest wall deformities, pectus excavatum and pectus carinatum. Pectus excavatum involves a sternal displacement causing a depression of the chest while pectus carinatum causes a protrusion of the chest. As costal cartilage is not a widely studied tissue, this leaves little knowledge into possible factors involved in the pathogenesis of pectus deformities. Costal cartilage in these deformities has been described as being weakened and may implicate proteoglycans which play an important role in the structure and maintenance of the extracellular matrix. This study focused on the major proteoglycans aggrecan, biglycan, and decorin. Immunohistochemistry and western blot analysis of these proteoglycans was performed on costal cartilage from patients with pectus deformities along with an age-matched control. Western blotting was also performed on normal costal cartilage from fetal, adolescent, and adult tissue to observe any changes in relation to age. We demonstrated that aggrecan forms distinct patterns of localization. Western blot analysis of biglycan and decorin indicated that these proteoglycans exist in a proform and mature form of different sizes likely based on varied N-glycanation. Both forms of biglycan and prodecorin were present in fetal. adolescent, and adult tissue while mature decorin was present in adolescent and adult tissue suggesting biglycan has a greater role in early costal cartilage development. Immunohistochemistry of biglycan and decorin showed both proteoglycans localized in the territorial matrix but not the interterritorial matrix and may be indicative of an alternative method of collagen organization or hindered visualization caused by the formation of large collagen nanostraws. Further studies will be performed to establish the functional differences of the different glycanated forms of biglycan and decorin as well as their inclusion in collagen fibrils

Proximity-Induced Superconductivity at Non-Helical Topological Insulator Interfaces

We study how non-helical spin textures at the boundary between a topological insulator (TI) and a superconductor (SC) affect the proximity-induced superconductivity of the TI interface state. We consider TIs coupled to both spin-singlet and spin-triplet SCs, and show that for the spin-triplet parent SCs the resulting order parameter induced onto the interface state sensitively depends on the symmetries which are broken at the TI-SC boundary. For chiral spin-triplet parent SCs, we find that nodal proximity-induced superconductivity emerges when there is broken twofold rotational symmetry which forces the spins of the non-helical topological states to tilt away from the interface plane. We furthermore show that the Andreev conductance of lateral heterostructures joining TI-vacuum and TI-SC interfaces yields experimental signatures of the reduced symmetries of the interface states.Comment: 5 pages, 2 figure

The blunted effect of glucose-dependent insulinotropic polypeptide in subcutaneous abdominal adipose tissue in obese subjects is partly reversed by weight loss

BACKGROUND: Glucose-dependent insulinotropic polypeptide (GIP) appears to have impaired effect on subcutaneous abdominal adipose tissue metabolism in obese subjects. The aim of the present study was to examine whether weight loss may reverse the impaired effect of GIP on subcutaneous abdominal adipose tissue in obese subjects. METHODS: Five obese males participated in a 12-week weight loss program, which consisted of caloric restriction (800 Cal day(−)(1)) followed by 4 weeks of weight-maintenance diet. Before and after weight loss, subcutaneous adipose tissue lipid metabolism was studied by conducting regional measurements of arterio-venous plasma concentrations of metabolites and blood flow (adipose tissue blood flow, ATBF) across a segment of the abdominal adipose tissue in the fasting state and during GIP infusion (1.5 pmol kg(−)(1 )min(−)(1)) in combination with a hyperinsulinemic–hyperglycemic clamp. RESULTS: After weight loss (7.5±0.8 kg), glucose tolerance and insulin sensitivity increased significantly as expected. No significant differences were seen in basal ATBF before (1.3±0.4 ml min(−1) 100 g tissue(−1)) and after weight loss (2.1±0.4 ml min(−1) 100 g tissue)(−1); however, a tendency to increase was seen. After weight loss, GIP infusion increased ATBF significantly (3.2±0.1 ml min(−1) 100 g tissue(−1)) whereas there was no increase before weight loss. Triacylglycerol (TAG) uptake did not change after weight loss. Baseline free fatty acid (FFA) and glycerol output increased significantly after weight loss, P<0.001. During the clamp period, FFA and glycerol output declined significantly, P<0.05, with no differences before and after weight loss. Weight loss increased glucose uptake and decreased FFA/glycerol ratio during the clamp period, P<0.05. CONCLUSIONS: In obese subjects, weight loss, induced by calorie restriction, improves the blunted effect of GIP on subcutaneous abdominal adipose tissue metabolism