Cubature formulas, geometrical designs, reproducing kernels, and Markov operators

Cubature formulas and geometrical designs are described in terms of reproducing kernels for Hilbert spaces of functions on the one hand, and Markov operators associated to orthogonal group representations on the other hand. In this way, several known results for spheres in Euclidean spaces, involving cubature formulas for polynomial functions and spherical designs, are shown to generalize to large classes of finite measure spaces $(\Omega,\sigma)$ and appropriate spaces of functions inside $L^2(\Omega,\sigma)$. The last section points out how spherical designs are related to a class of reflection groups which are (in general dense) subgroups of orthogonal groups

Construction of spherical cubature formulas using lattices

We construct cubature formulas on spheres supported by homothetic images of shells in some Euclidian lattices. Our analysis of these cubature formulas uses results from the theory of modular forms. Examples are worked out on the sphere of dimension n-1 for n=4, 8, 12, 14, 16, 20, 23, and 24, and the sizes of the cubature formulas we obtain are compared with the lower bounds given by Linear Programming

NOX enzymes: potential target for the treatment of acute lung injury

Acute lung injury (ALI) and its more severe form, acute respiratory distress syndrome (ARDS), is characterized by acute inflammation, disruption of the alveolar-capillary barrier, and in the organizing stage by alveolar pneumocytes hyperplasia and extensive lung fibrosis. The cellular and molecular mechanisms leading to the development of ALI/ARDS are not completely understood, but there is evidence that reactive oxygen species (ROS) generated by inflammatory cells as well as epithelial and endothelial cells are responsible for inflammatory response, lung damage, and abnormal repair. Among all ROS-producing enzymes, the members of NADPH oxidases (NOXs), which are widely expressed in different lung cell types, have been shown to participate in cellular processes involved in the maintenance of lung integrity. It is not surprising that change in NOXs' expression and function is involved in the development of ALI/ARDS. In this context, the use of NOX inhibitors could be a possible therapeutic perspective in the management of this syndrome. In this article, we summarize the current knowledge concerning some cellular aspects of NOXs localization and function in the lungs, consider their contribution in the development of ALI/ARDS and discuss the place of NOX inhibitors as potential therapeutical targe

Metastasis of a pleural mesothelioma to a hyperplastic stomach polyp: an increase of vimentin expression is seen during a gain in deciduoid morphology

Deciduoid mesothelioma is a rare variant of the epithelioid histotype spectrum, resembling decidua of gravid uterus. It is found in the peritoneum of young women, but also in the pleura of elderly people. Histotype plasticity from epithelioid to sarcomatoid mesothelioma may be considered as epithelial-mesenchymal transition (EMT). A full autopsy was performed and mesothelioma infiltrates were analysed by immunohistochemistry. The metastasis of an epithelioid pleural mesothelioma to a hyperplastic polyp of the stomach is presented in this autopsy case. Deciduoid morphology increased during tumour progression and metastasis. The increase in eosinophilic cytoplasm correlated with the upregulation of the intermediate filament vimentin. High expression of vimentin was found in both central and superficial periglandular regions of the polyp. High vimentin expression also can occur in epithelioid rather than sarcomatoid differentiation. Thus, although vimentin is considered to be the major EMT marker, additional pathways must regulate its expression

sCR1sLeX reduces lung allograft ischemia-reperfusion injury but does not ameliorate acute rejection

Background: Combined inhibition of complement and leukocyte adhesion by sCR1sLeX reduces lung allograft dysfunction up to 24 h. In the present study its effect on graft function and acute rejection was evaluated up to 5 days after experimental transplantation. Methods: Orthotopic single left lung transplantation was performed in 35 male rats (Brown Norway to Fischer 344) after a total ischemic time of 20 h. Two groups were assessed after 1, 3, and 5 days post-transplant, respectively (n=5 per group and time point): controls vs. recipients which received 10 mg/kg sCR1sLeX 15 min prior to reperfusion. In addition, five animals received 10 mg/kg per day sCR1sLeX for 5 days. For blood gas analysis of the graft, the contralateral lung was occluded for 5 min to assess graft function. Lung grafts were flushed, and histological grading was performed in blinded fashion according to the International Society for Heart and Lung Transplantation criteria. Results: Graft PaO2 in recipients treated with sCR1sLeX was superior on day 1 (383±118 vs. 56±15 mmHg; P≪0.0001) and day 3 (446±48 vs. 231±108 mmHg; P≪0.0001). Five days after transplantation, no difference in PaO2 was found (61±28 vs. 83±31 mmHg; P=0.59). Repeated treatment with sCR1sLeX for 5 days did not improve PaO2 (64±5 mmHg; P=0.65 vs. control; P=0.93 vs. sCR1sLeX). At any time point, there was no difference in the degree of rejection between groups. Conclusions: In this model sCR1sLeX provided marked improvement of graft function up to 3 days, but inhibition of both complement system and selectin dependent leukocyte adhesion failed to protect against acute rejectio

Pulmonary blastoma: report of five cases and identification of clinical features suggestive of the disease

Objective: Identification of clinical features suggestive of pulmonary blastoma (PB) through a retrospective comparison with cases of non-small cell lung cancer (NSCLC) operated during the same period. Methods: Between 1977 and 1999, five patients were operated for PB at Geneva University Hospital (four women and one man, aged 32-46 years - mean 36.8) versus 1913 consecutive patients (1558 men and 355 women, mean age 61.2) for primary NSCLC. In the PB subgroup (0.3%), the pulmonary tumor was single, located in an upper lobe in all but one instance, and measured between 5 and 13 cm (mean 9.6), whereas in the total NSCLC group, 27% of patients had tumors <3 cm (T1), evenly distributed in both lungs. All but one PB patients were symptomatic, compared to 45% in the NSCLC group. Results: The five patients with PB underwent curative pulmonary excisions (lobectomy in three and pneumonectomy in two) with mediastinal lymph node sampling. Pathological examination revealed extensive tumor necrosis in four, and N2 lymph node metastases in four (in the total NSCLC group, N2 disease was diagnosed in 21%). Postoperatively, three PB patients received radio- and/or chemotherapy. Four patients died between six and 30 months after the operation (mean 15), whereas 5-year survival in the NSCLC group was 32%, with a median survival of 3.7 years; the fifth patient is alive 28 months later, without any sign of recurrence. Conclusions: Compared to operated NSCLC, PB are rare, large, and symptomatic tumors; they affect younger patients and carry a worse prognosi

Primary Hyperparathyroidism: Can Parathyroid Carcinoma Be Anticipated on Clinical and Biochemical Grounds? Report of Nine Cases and Review of the Literature

Background: Parathyroid carcinoma (PC) mimics benign primary hyperparathyroidism (PHP), but the diagnosis of PC is seldom available at the time of the first operation. Because PC is plagued by recurrences usually beyond cure, one may wonder whether some of these could be prevented by more extensive resections initially, i.e., if the diagnosis of PC were available at that time. Methods: Over a 25-year period, 311 consecutive patients with PHP underwent operation in our department: 302 had benign disease (adenomas or hyperplasias), and 9 had PC. Several clinical parameters, serum calcium and parathyroid hormone (PTH) levels, and the weight of the parathyroid tumor removed were compared in both groups. Receiver operating characteristic curves and logistical regression analyses were used to distinguish PC from benign PHP. Results: Eight of 9 patients with PC had symptoms, versus 238 (79%) of 302 with benign PHP (not significant). In the PC subgroup, serum calcium and PTH levels and the tumor weights of the parathyroid glands removed were significantly higher than in the benign PHP cohort, even if these three parameters were regularly flawed by low positive predictive values (14%, 20%, and 15%, respectively). Conclusions: Serum calcium, PTH levels, and tumor weights were significantly greater in the PC subgroup, even if not invariably in a discriminatory way. However, when PTH is <4 times the upper limit of normal and tumor weight is <1.9 g, the probability of PC is ni

Delayed but Complete Response following Oral Temozolomide Treatment in Melanoma Leptomeningeal Carcinomatosis

Isolated leptomeningeal recurrence of melanoma is rare, occurring in 2% of patients with central nervous system involvement secondary to melanoma. The optimal treatment of leptomeningeal carcinomatosis (LMC) in melanoma has not yet been determined and remains a major challenge. We report a melanoma patient who presented with isolated LMC in the form of a new-onset weakness of the lower limbs, paresthesia of the left hand and foot, lumbago and headache. A lumbar puncture and spinal MRI confirmed LMC. The patient was treated with temozolomide 75 mg/m2/day on a 4 weeks on/2 weeks off schedule. After an initial transient clinical deterioration, the patient showed a complete radiological response as well as a dramatic improvement in quality of life. The encouraging clinical response reported here suggests that dose-intensified temozolomide might have significant activity in the treatment of leptomeningeal dissemination of melanoma and may be a valid treatment option for patients who have not been previously exposed to this agent. Moreover, this treatment regimen is extremely well tolerated and obviates the need for repeated intrathecal administrations of chemotherapeutic agents, which are often not well tolerated by patients who have significant co-morbidities due to their disease. As illustrated in this case, response to temozolomide may occur in a delayed manner, highlighting the importance of following temozolomide treatment long enough before determining that it is inefficient in a given patient

Diagnostic changes as a reason for the increase in papillary thyroid cancer incidence in Geneva, Switzerland

Objective: Several studies have reported upward incidence trends of papillary thyroid cancer. It is unclear whether these trends reflect a real risk increase, by some attributed to iodine supplementation, or an artificial one, due to increased diagnostic activity or changed histological criteria. This study examines if these artificial factors explain the increased papillary thyroid cancer incidence in the Swiss canton of Geneva. Methods: All thyroid carcinomas (n = 436) recorded between 1970 and 1998 at the Geneva Cancer Registry were considered. European age-adjusted incidence trends were estimated using linear regression analysis. For papillary cancers we evaluated diagnostic modalities and way of presentation (in particular microcarcinoma < 1 cm or silent carcinoma). In addition, we reviewed the histological slides of follicular carcinomas. Results: Papillary thyroid cancer incidence increased significantly from 0.7 to 1.8/100,000 for men and from 3.1 to 4.3/100,000 for women between 1970-74 and 1995-98. The proportion of microcarcinomas and silent carcinomas increased from 17% to 24% between 1970-79 and 1990-98. At histological review, follicular cancers were more often reclassified as papillary cancer for cases diagnosed between 1970 and 1979 than for cases diagnosed between 1990 and 1998 (45% vs 25%, p = n.s.). Conclusions: The increasing papillary thyroid cancer incidence seems mainly due to changes in histological diagnostic criteria and, to a lesser extent, to increased diagnostic activity. If confirmed, the results of this study indicate that fears of increasing incidence rates of papillary thyroid cancer should not prevent implementation of adequate programs of iodine supplementation in the many areas where iodine deficiency still prevail