In this paper,we co.sider using Schur co.plements to design preco.ditioners for twofold and block tridiagonal saddle point *** type of the preco.ditioners are based on the nested(or recursive)Schur co.plement,the othe...
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In this paper,we co.sider using Schur co.plements to design preco.ditioners for twofold and block tridiagonal saddle point *** type of the preco.ditioners are based on the nested(or recursive)Schur co.plement,the other is based on an additive type Schur co.plement after permuting the original saddle point *** analyze different preco.ditioners inco.porating the exact Schur *** show that some of them will lead to positively stable preco.ditioned systems if proper signs are selected in front of the Schur *** positive-stable preco.ditioners outperform other preco.ditioners if the Schur co.plements are further approximated *** experiments for a 3-field formulation of the Biot model are provided to verify our predictions.
Aging biomarkers are a co.bination of biological parameters to(i)assess age-related changes,(ii)track the physiological aging process,and(iii)predict the transition into a pathological *** a broad spectrum of aging bi...
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Aging biomarkers are a co.bination of biological parameters to(i)assess age-related changes,(ii)track the physiological aging process,and(iii)predict the transition into a pathological *** a broad spectrum of aging biomarkers has been developed,their potential uses and limitations remain poorly *** immediate goal of biomarkers is to help us answer the following three fundamental questions in aging research:How old are we?Why do we get old?And how can we age slower?This review aims to address this ***,we summarize our current knowledge of biomarkers developed for cellular,organ,and organismal levels of aging,co.prising six pillars:physiological characteristics,medical imaging,histological features,cellular alterations,molecular changes,and secretory *** fulfill all these requisites,we propose that aging biomarkers should qualify for being specific,systemic,and clinically relevant.
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