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Mackey First Countability and Docile Locally Convex Spaces

Acta Mathematica Sinica,English Series 2011年第4期27卷 737-740页

作者： carlos bosch giral Thomas E. GILSDORF Claudia GOMEZ-WULSCHNER Departamento de Matemdticas ITAM Rio Hondo #1 Col. Progreso Tizapan Mdxico DF 01080 Mexico Department of Mathematics University of North Dakota Grand Forks ND 58202-8376 USA

We define a generalization of Mackey first countability and prove that it is equivalent to being docile. A consequence of the main result is to give a partial affirmative answer to an old question of Mackey regarding arbitrary quotients of Mackey first countable spaces. Some applications of the main result to spaces such as inductive limits are also given.

关键词： Bounded set docile space Mackey first countable inductive limit

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High interpretable machine learning classifier for early glaucoma diagnosis

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International Journal of Ophthalmology(English edition) 2021年第3期14卷 393-398页

作者： carlos Salvador Fernandez Escamez Elena Martin giral Susana Perncho Martinez Nicolas Toledano Fernandez Ophthalmology Department Hospital de FuenlabradaMadrid 28942Spain Doctorate Program in Heath Sciences Universidad Rey Juan CarlosAlcorcon 28922MadnidSpain

AIM:To develop a classifier for differentiating between healthy and early stage glaucoma eyes based on peripapillary retinal nerve fiber layer(RNFL)thicknesses measured with optical coherence tomography(OCT),using machine learning algorithms with a high ***:Ninety patients with early glaucoma and 85 healthy eyes were *** glaucoma eyes showed a visual field(VF)defect with mean deviation>-6.00 d B and characteristic glaucomatous *** thickness in every quadrant,clock-hour and average thickness were used to feed machine learning *** analysis was conducted to detect and exclude *** gradient boosting algorithms were used to calculate the importance of parameters on the classifier and to check the relation between their values and its impact on the *** with the lowest importance were excluded and a weighted decision tree analysis was applied to obtain an interpretable *** under the ROC curve(AUC),accuracy and generalization ability of the model were estimated using cross validation ***:Average and 7 clock-hour RNFL thicknesses were the parameters with the highest impor *** between parameter values and impact on classification displayed a stepped pattern for average *** tree model revealed that average thickness lower than 82μm was a high predictor for early *** scores had AUC of 0.953(95%CI:0.903-0998),with an accuracy of 89%.CONCLUSION:Gradient boosting methods provide accurate and highly interpretable classifiers to discriminate between early glaucoma and healthy *** and 7-hour RNFL thicknesses have the best discriminant power.

关键词： machine learning glaucoma diagnosis optical coherence tomography

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