On the domain of singular traces

The question whether an operator belongs to the domain of some singular trace is addressed, together with the dual question whether an operator does not belong to the domain of some singular trace. We show that the answers are positive in general, namely for any (compact, infinite rank) positive operator A we exhibit two singular traces, the first being zero and the second being infinite on A. However, if we assume that the singular traces are generated by a "regular" operator, the answers change, namely such traces always vanish on trace-class, non singularly traceable operators and are always infinite on non trace-class, non singularly traceable operators. These results are achieved on a general semifinite factor, and make use of a new characterization of singular traceability (cf. math.OA/0202108).Comment: 7 pages, LaTeX. Minor corrections, to appear on the International Journal of Mathematic

Dynamics of the melatonin MT1 receptor in the rat parotid gland upon melatonin administration

Our recent ultrastructural study of human parotid glands revealed that the melatonin receptors, MT1 and MT2, are localised in the plasma cell membranes of acinar and ductal cells but also, and intriguingly, predominantly in acinar secretory granules, giving rise to the working hypothesis that secretory granules are a part of a transcytotic transport system for melatonin. To put this hypothesis to the test in rat parotid glands, anaesthetised animals were exposed to a high melatonin dose (3 mg/kg per hour), infused intravenously over two hours and aiming to stimulate a glandular melatonin-receptor-dependent intracellular transport system, if any. Thirty minutes later, the right parotids were removed. Pre-stimulation, left parotid gland tissue was removed to serve as (untreated) controls. Gland tissues were processed for the gold post-embedding technique and for western blot analysis. In untreated glands, on transmission electron microscope images, melatonin receptors displayed a distribution pattern similar to that in human parotids, i.e. here, too, the receptors were principally associated with the acinar secretory granules. In melatonin- treated glands, the number of granules associated with the MT1 receptor was twice that in untreated glands, despite the same total granule number in the two glands. Moreover, the density of gold particles showing MT1-receptor immunoreactivity associated with granules in melatonin-treated glands was 2.5 times that in untreated glands. The number of MT1 receptors associated with the granule membrane was about three times higher in melatonin-treated glands than in untreated glands, while the number of MT1 receptors inside the granules was about twice that in untreated glands. The immunoblotting of membrane-enriched samples showed that the MT1-receptor expression was about three times that of untreated glands. When it came to the MT2 receptor, no changes were observed. Melatonin itself thus exerts dynamic effects on its MT1 receptor, which may reflect an adaptive receptor-linked carrier system for melatonin, delivering - upon gland stimulation - melatonin to the saliva by exocytosis

Ultrastructural evidence of a secretory role for melatonin in the human parotid gland

In vivo animal studies show that pentagastrin, cholecystokinin and melatonin cause the secretion and synthesis of salivary proteins. Melatonin occurs in large amounts in the gut and is released into the blood on food intake. In vitro experiments suggest that pentagastrin exerts secretory activity in human salivary glands, as judged by ultrastructural changes, reflecting secretion, and an actual protein output. Currently, it is hypothesised that melatonin induces secretory exocytotic events in the human parotid gland. Human parotid tissues were exposed to a high single concentration of melatonin in vitro, processed for high resolution scanning electron microscopy and then assessed morphometrically with the emphasis on the membrane of the intercellular canaliculi, a site of protein secretion. Compared with controls and in terms of density, the melatonin-exposed parotid tissues displayed increases in protrusions (signalling anchored granules) and microbuds (signalling membrane recycling and/or vesicle secretion) and decreases in microvilli (signalling cytoskeletal re-arrangement related to exocytosis), phenomena abolished or very largely reduced by the melatonin receptor blocker, luzindole. In conclusion, acinar serous cells of parotid tissue displayed in vitro exocytotic activity to melatonin, signalling protein secretion. Whether, under physiological conditions, melatonin influences the secretion of human parotid glands remains to be explored, however

Cluster Approximation for the Farey Fraction Spin Chain

We consider the Farey fraction spin chain in an external field $h$. Utilising ideas from dynamical systems, the free energy of the model is derived by means of an effective cluster energy approximation. This approximation is valid for divergent cluster sizes, and hence appropriate for the discussion of the magnetizing transition. We calculate the phase boundaries and the scaling of the free energy. At $h=0$ we reproduce the rigorously known asymptotic temperature dependence of the free energy. For $h \ne 0$, our results are largely consistent with those found previously using mean field theory and renormalization group arguments.Comment: 17 pages, 3 figure

Genetical stability and osteogenic ability of mesenchimal stem cells on demineralized bone matrices

Journal of Osseointegration Volume 7, Issue 1, 1 March 2015, Pages 2-7 Open Access Genetical stability and osteogenic ability of mesenchimal stem cells on demineralized bone matrices (Article) Pozzuoli, A.a, Gardin, C.b, Aldegheri, R.a, Bressan, E.c, Isola, M.d, Calvo-Guirado, J.L.e, Biz, C.a, Arrigoni, P.a, Feroni, L.b, Zavan, B.b a Department of Surgical,Oncological and Gastroenterological Sciences, University of Padua, Padua, Italy b Department of Biomedical Sciences, University of Padua, Padua, Italy c Department of Neurosciences, University of Padua, Padua, Italy d Department of Animal Medicine, Production and Health (MAPS), Italy e Department of General Dentistry, Faculty of Medicine and Dentistry, University of Murcia, Murcia, Spain Hide additional affiliations View references (44) Abstract Aim: Tissue engineering is a rapidly expanding field with regard to the use of biomaterials and stem cells in the orthopedic surgery. Many experimental studies have been done to understand the best characteristics of cells, materials and laboratory methods for safe clinical applications. The aim of this study was to compare the ability of 2 different human demineralized bone matrices (DBMs), the one enriched and the other not enriched with hyaluronic acid, to stimulate in vitro the proliferation and the osteogenic differentiation of human adipose-derived stem cells (ADSCs) seeded onto an osteoconductive scaffold. Materials and Methods: ADSCs were isolated, by enzymatic digestion, from abdominal adipose tissue of 5 patients undergoing cosmetic lipoaspiration surgery. ADSCs were then seeded onto a 3D scaffold in the presence of the two different osteoinductive matrices of human demineralized bone and evaluated for proliferation and osteogenic differentiation. The safety of the methods was verified using array-Comparative Genomic Hybridization (array-CGH). Results: ADSCs were able to differentiate in osteogenic sense. Both DBMs showed the ability to induce osteogenic differentiation of the cells. Conclusion: array-CGH showed no changes at genome level, thus confirming the safety of materials and method

Lumpectomy with or without postoperative radiotherapy for breast cancer with favourable prognostic features: results of a randomized study

The aim of this trial was to study the value of adding post-operative radiotherapy to lumpectomy in a subgroup of breast cancer patients with favourable patient-, tumour-, and treatment-related prognostic features. 152 women aged over 40 with unifocal breast cancer seen in preoperative mammography were randomly assigned to lumpectomy alone (no-XRT group) or to lumpectomy followed by radiotherapy to the ipsilateral breast (50 Gy given within 5 weeks, XRT group). All cancers were required to be invasive node-negative, smaller than 2 cm in diameter and well or moderately differentiated, to contain no extensive intraductal component, to be progesterone receptor-positive, DNA diploid, have S-phase fraction ≤7 and be excised with at least 1 cm margin. During a mean follow-up time of 6.7 years, 13 (18.1%) cancers recurred locally in the no-XRT and 6 (7.5%) in the XRT group (P = 0.03). There was no difference between the groups in the ultimate breast preservation rate (95.0% vs. 94.4% in XRT and no-XRT, respectively, P = 0.88), distant metastasis-free survival (P = 0.36), or 5-year cancer-specific survival (97.1% in XRT and 98.6 in no-XRT). Radiation therapy given after lumpectomy reduces the frequency of ipsilateral breast recurrences even in women with small breast cancer with several favourable clinical and biological features. However, the breast preservation rate may not increase due to more frequent use of salvage mastectomies in patients treated with postoperative radiotherapy. © 2001 Cancer Research Campaign http://www.bjcancer.co

Frequent somatic loss of BRCA1 in breast tumours from BRCA2 germ-line mutation carriers and vice versa

Breast cancer susceptibility genes BRCA1 and BRCA2 are tumour suppressor genes the alleles of which have to be inactivated before tumour development occurs. Hereditary breast cancers linked to germ-line mutations of BRCA1 and BRCA2 genes almost invariably show allelic imbalance (AI) at the respective loci. BRCA1 and BRCA2 are believed to take part in a common pathway in maintenance of genomic integrity in cells. We carried out AI and fluorescence in situ hybridization (FISH) analyses of BRCA2 in breast tumours from germ-line BRCA1 mutation carriers and vice versa. For comparison, 14 sporadic breast tumours were also studied. 8 of the 11 (73%) informative BRCA1 mutation tumours showed AI at the BRCA2 locus. 53% of these tumours showed a copy number loss of the BRCA2 gene by FISH. 5 of the 6 (83%) informative BRCA2 mutation tumours showed AI at the BRCA1 locus. Half of the tumours (4/8) showed a physical deletion of the BRCA1 gene by FISH. Combined allelic loss of both BRCA1 and BRCA2 gene was seen in 12 of the 17 (71%) informative hereditary tumours, whereas copy number losses of both BRCA genes was seen in only 4/14 (29%) sporadic control tumours studied by FISH. In conclusion, the high prevalence of AI at BRCA1 in BRCA2 mutation tumours and vice versa suggests that somatic events occurring at the other breast cancer susceptibility gene locus may be selected in the cancer development. The mechanism resulting in AI at these loci seems more complex than a physical deletion.   http://www.bjcancer.com © 2001 Cancer Research Campaig