Computing Wasserstein Barycenter via operator splitting: the method of averaged marginals

The Wasserstein barycenter (WB) is an important tool for summarizing sets of probabilities. It finds applications in applied probability, clustering, image processing, etc. When the probability supports are finite and fixed, the problem of computing a WB is formulated as a linear optimization problem whose dimensions generally exceed standard solvers' capabilities. For this reason, the WB problem is often replaced with a simpler nonlinear optimization model constructed via an entropic regularization function so that specialized algorithms can be employed to compute an approximate WB efficiently. Contrary to such a widespread inexact scheme, we propose an exact approach based on the Douglas-Rachford splitting method applied directly to the WB linear optimization problem for applications requiring accurate WB. Our algorithm, which has the interesting interpretation of being built upon averaging marginals, operates series of simple (and exact) projections that can be parallelized and even randomized, making it suitable for large-scale datasets. As a result, our method achieves good performance in terms of speed while still attaining accuracy. Furthermore, the same algorithm can be applied to compute generalized barycenters of sets of measures with different total masses by allowing for mass creation and destruction upon setting an additional parameter. Our contribution to the field lies in the development of an exact and efficient algorithm for computing barycenters, enabling its wider use in practical applications. The approach's mathematical properties are examined, and the method is benchmarked against the state-of-the-art methods on several data sets from the literature

Повторные измерения толщины слоя нервных волокон с помощью оптического когерентного томографа Stratus

PURPOSE: Assessment of optic disc damage is an essential part of the ocular examination and differential diagnosis between the patient with ocular hypertension and pre-perimetric or perimetric glaucoma. The Stratus optic coherent tomograph (Carl Zeiss Meditec, Inc, Dublin, Calif) is still one of the most used optic nerve imaging technology throughout the world. Therefore, the development of methodology that enhances the utility of optic disc measurements with the Stratus OCT remains a relevant and meaningful goal. In an attempt to determine the optimal number of repeated measurements we investigated how the average of three sets of manually repeated measurements of retina nerve firer layer (RNFL) thickness would compare with a single set. METHODS: A total of 73 individuals (136 eyes) aged 55.3±15.2 years with ocular hypertensive (OHT), pre-peri-metric glaucoma or glaucoma were included in the final analysis. When the data was evaluated using a quadrant analysis we observed that 13.6% of the patients exhibited a clinically meaningful difference of 20% or more in the serial RNFL thickness measurements. RESULTS: The difference ranged from 9.3 to 32.7 microns and in 10 of the 12 quadrants the averaged measurement exceeded the initial measurement. Most of the differences demonstrated in this study occurred in the horizontal meridian and are probably a result of instinctive saccadic eye movements. A difference in the vertical meridian (superior and/or inferior quadrants) which is the more relevant meridian for changes in glaucoma was seen in only 3 patients (4.1%). CONCLUSIONS: One reliable RNFL measurement would be sufficient in most of these cases because in 95.9% of the cases the differences observed for the vertical meridian were less than 20%. Nevertheless, it is important to recognize that there can be more variability in the horizontal meridian and that in cases with visual loss encroaching on fixation serial measurements may be useful. At any rate, as with all ancillary tests, whenever a change is detected, it is wise to repeat the test to verify the results.ЦЕЛЬ. Оценка изменений в диске зрительного нерва является важной частью офтальмологического обследования и дифференциальной диагностики у пациентов с офтальмогипертензией и ранней и развитой стадиями глаукомы. Оптический когерентный томограф Stratus (Carl Zeiss Meditec, Inc, Dublin, Calif) до сих пор является одним из самых часто используемых приборов для визуализации зрительного нерва по всему миру. Поэтому разработка методологии, оптимизирующей оценку состояния диска зрительного нерва с помощью Stratus, остается важной и актуальной задачей. В попытке определить оптимальное количество последовательных измерений, мы сравнивали результаты одиночного измерения толщины слоя нервных волокон с усредненными результатами серии из трех последовательных измерений. методы. Всего в исследовании участвовало 73 пациента (136 глаз) в возрасте 55,3±15,2 года с офтальмогипертензией или диагностированной глаукомой. При анализе полученных данных по квадрантам поля зрения у 13,6% пациентов было обнаружено клинически значимое различие ≥ 20% в толщине слоя нервных волокон. РЕЗУЛЬТАТЫ. Разница в измерениях составляла от 9,3 до 32,7 мкм, и в 10 из 12 квадрантов усредненный результат трех последовательных измерений превышал результат единичного измерения. В большинстве случав различие отмечалось в горизонтальном меридиане и, вероятно, являлось результатом естественных саккадных движений. Различие в результатах по более значимому для изменений поля зрения при глаукоме вертикальному меридиану (верхние и/или нижние квадранты) наблюдалось только у 3 (4,1%) пациентов. ЗАКЛЮЧЕНИЕ. Поскольку в 95,9% случаев разница результатов по вертикальному меридиану не превышает 20%, можно сделать вывод, что в большинстве случаев достаточно одного достоверного измерения толщины слоя нервных волокон сетчатки. Тем не менее полезно помнить о большей вариабельности результатов по горизонтальному меридиану. Например, в случае со снижением зрения, затрудняющим фиксацию взгляда, может быть полезным проведение серии из нескольких исследований подряд. В любом случае при появлении изменений в результатах этого или других вспомогательных исследований наилучшей тактикой является повторение исследования для подтверждения результатов

Gridded global surface ozone metrics for atmospheric chemistry model evaluation

The concentration of ozone at the Earth's surface is measured at many locations across the globe for the purposes of air quality monitoring and atmospheric chemistry research. We have brought together all publicly available surface ozone observations from online databases from the modern era to build a consistent data set for the evaluation of chemical transport and chemistry-climate (Earth System) models for projects such as the Chemistry-Climate Model Initiative and Aer-Chem-MIP. From a total data set of approximately 6600 sites and 500 million hourly observations from 1971-2015, approximately 2200 sites and 200 million hourly observations pass screening as high-quality sites in regionally representative locations that are appropriate for use in global model evaluation. There is generally good data volume since the start of air quality monitoring networks in 1990 through 2013. Ozone observations are biased heavily toward North America and Europe with sparse coverage over the rest of the globe. This data set is made available for the purposes of model evaluation as a set of gridded metrics intended to describe the distribution of ozone concentrations on monthly and annual timescales. Metrics include the moments of the distribution, percentiles, maximum daily 8-hour average (MDA8), sum of means over 35 ppb (daily maximum 8-h; SOMO35), accumulated ozone exposure above a threshold of 40 ppbv (AOT40), and metrics related to air quality regulatory thresholds. Gridded data sets are stored as netCDF-4 files and are available to download from the British Atmospheric Data Centre (doi:10.5285/08fbe63d-fa6d-4a7a-b952-5932e3ab0452). We provide recommendations to the ozone measurement community regarding improving metadata reporting to simplify ongoing and future efforts in working with ozone data from disparate networks in a consistent manner

Definitions and outcome measures for bullous pemphigoid: Recommendations by an international panel of experts

Our scientific knowledge of bullous pemphigoid (BP) has dramatically progressed in recent years. However, despite the availability of various therapeutic options for the treatment of inflammatory diseases, only a few multicenter controlled trials have helped to define effective therapies in BP. A major obstacle in sharing multicenter-based evidences for therapeutic efforts is the lack of generally accepted definitions for the clinical evaluation of patients with BP. Common terms and end points of BP are needed so that experts in the field can accurately measure and assess disease extent, activity, severity, and therapeutic response, and thus facilitate and advance clinical trials. These recommendations from the International Pemphigoid Committee represent 2 years of collaborative efforts to attain mutually acceptable common definitions for BP and proposes a disease extent score, the BP Disease Area Index. These items should assist in the development of consistent reporting of outcomes in future BP reports and studies. © 2011 by the American Academy of Dermatology, Inc

Retroperitoneal Castleman's tumor and paraneoplastic pemphigus: report of a case and review of the literature

BACKGROUND: Castleman's disease is a rare lymphoproliferative syndrome. Its etiology and pathogenesis are unclear. The disease can be occasionally associated with a paraneoplastic pemphigus (PNP), an autoimmune mucocutaneous disorder commonly seen in neoplasms of lymphocytic origin. CASE PRESENTATION: We present a case of a 63-year old male patient who was referred for surgical treatment of a lately diagnosed retroperitoneal pelvic mass. The patient had been already treated for two years due to progressive diffuse cutaneous lesions histologically consistent with lichen ruber verucosus and pemphigus vulgaris. Intraoperatively a highly vascularized solid mass occupying the small pelvis was resected after meticulous vascular ligation and hemostasis. After surgery and following immunosuppressive treatment a clear remission of the skin lesions was observed. CONCLUSION: Castleman's tumor should be always suspected when a retroperitoneal mass is combined with PNP. In a review of the literature we found 37 additional cases. Complete surgical resection of the tumor can be curative in most of the cases

Non-classical forms of pemphigus: pemphigus herpetiformis, IgA pemphigus, paraneoplastic pemphigus and IgG/IgA pemphigus

The pemphigus group comprises the autoimmune intraepidermal blistering diseases classically divided into two major types: pemphigus vulgaris and pemphigus foliaceous. Pemphigus herpetiformis, IgA pemphigus, paraneoplastic pemphigus and IgG/IgA pemphigus are rarer forms that present some clinical, histological and immunopathological characteristics that are different from the classical types. These are reviewed in this article. Future research may help definitively to locate the position of these forms in the pemphigus group, especially with regard to pemphigus herpetiformis and the IgG/ IgA pemphigus.Universidade Federal de São Paulo (UNIFESP), Escola Paulista de Medicina (EPM) Dermatology DepartmentUniversidade Federal de São Paulo (UNIFESP), Escola Paulista de Medicina (EPM) Dermatology and Pathology DepartmentsUNIFESP, EPM, Dermatology DepartmentUNIFESP, EPM, Dermatology and Pathology DepartmentsSciEL

The Protease Inhibitor Alpha-2-Macroglobuline-Like-1 Is the p170 Antigen Recognized by Paraneoplastic Pemphigus Autoantibodies in Human

Paraneoplastic pemphigus (PNP) is a devastating autoimmune blistering disease, involving mucocutaneous and internal organs, and associated with underlying neoplasms. PNP is characterized by the production of autoantibodies targeting proteins of the plakin and cadherin families involved in maintenance of cell architecture and tissue cohesion. Nevertheless, the identity of an antigen of Mr 170,000 (p170), thought to be critical in PNP pathogenesis, has remained unknown

Research priorities in pediatric parenteral nutrition: a consensus and perspective from ESPGHAN/ESPEN/ESPR/CSPEN

Parenteral nutrition is used to treat children that cannot be fully fed by the enteral route. While the revised ESPGHAN/ESPEN/ESPR/CSPEN pediatric parenteral nutrition guidelines provide clear guidance on the use of parenteral nutrition in neonates, infants, and children based on current available evidence, they have helped to crystallize areas where research is lacking or more studies are needed in order to refine recommendations. This paper collates and discusses the research gaps identified by the authors of each section of the guidelines and considers each nutrient or group of nutrients in turn, together with aspects around delivery and organization. The 99 research priorities identified were then ranked in order of importance by clinicians and researchers working in the field using a survey methodology. The highest ranked priority was the need to understand the relationship between total energy intake, rapid catch-up growth, later metabolic function, and neurocognitive outcomes. Research into the optimal intakes of macronutrients needed in order to achieve optimal outcomes also featured prominently. Identifying research priorities in PN should enable research to be focussed on addressing key issues. Multicentre trials, better definition of exposure and outcome variables, and long-term metabolic and developmental follow-up will be key to achieving this. Impact: The recent ESPGHAN/ESPEN/ESPR/CSPEN guidelines for pediatric parenteral nutrition provided updated guidance for providing parenteral nutrition to infants and children, including recommendations for practice.However, in several areas there was a lack of evidence to guide practice, or research questions that remained unanswered. This paper summarizes the key priorities for research in pediatric parenteral nutrition, and ranks them in order of importance according to expert opinion