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Strong Overall Error Analysis for the Training of Artificial Neural Networks Via Random Initializations

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Communications in Mathematics and Statistics 2024年第3期12卷 385-434页

作者： arnulf Jentzen Adrian Riekert School of Data Science and Shenzhen Research Institute of Big Data The Chinese University of Hong KongShenzhenPeople’s Republic of China Applied Mathematics:Institute for Analysis and Numerics University of MünsterMünsterGermany

Although deep learning-based approximation algorithms have been applied very successfully to numerous problems,at the moment the reasons for their performance are not entirely understood from a mathematical point of ***,estimates for the convergence of the overall error have been obtained in the situation of deep supervised learning,but with an extremely slow rate of *** this note,we partially improve on these *** specifically,we show that the depth of the neural network only needs to increase much slower in order to obtain the same rate of *** results hold in the case of an arbitrary stochastic optimization algorithm with *** initializations.

关键词： Deep learning Artificial intelligence Empirical risk minimization Optimization

Effect of excitation wavelength(blue vs near UV)and dopant concentrations on afterglow and fast decay of persistent phosphor SrAl_(2)O_(4):Eu^(2+),Dy^(3+)

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Journal of Rare Earths 2022年第7期40卷 1022-1028页

作者： Bernhard Walfort Nando Gartmann Jafar Afshani arnulf Rosspeintner Hans Hagemann LumiNova AG SwitzerlandSpeicherstrasse 60aCH-9053TeufenSwitzerland Dépt.de Chimie Physique Universitéde Genève30Quai E.AnsermetCH 1211Geneva 4Switzerland

The persistent phosphor SrAl_(2)O_(4):Eu^(2+),Dy^(3+)is the subject of numerous *** often neglected aspect is that in this phosphor,as well as in Sr_(4)Al_(14)O_(25):Eu^(2+),Dy^(3+),there are two different Sr^(2)+sites which can be occupied by the dopant Eu^(2+)ions,We first introduce a general scheme of possible energy transfers in these persistent phosphor materials including explicitly both europium ions,This scheme is used as a generic starting point to study experimentally specific *** illustrate this application with the study of the effect of excitation wavelength(444 and 382 nm)on the afterglow of differently doped SrAl_(2)O_(4):Eu^(2+),Dy^(3+)samples,as well as on the emission decay *** the same excitation intensity under 444 nm excitation,the resulting afterglow intensity is stronger than under near UV *** 382 nm,Eu^(2+)ions on both Sr^(2)+s ites in SrAl_(2)O_(4)are excited,but at room temperature the blue emission is quenched,leading to a loss of *** observed effects can further be associated with the ratio of Eu^(2+)ions and trap states which are modulated by the concentrations of Eu^(2+)and Dy^(3+)in SrAl_(2)O_(4),as well as by temperature,Increasing the nominal Dy^(3+)content from 0.1 mol%to 0.5 mol%with respect to Sr results in the doubling of the integrated afterglow intensity and confirms thus that Dy^(3+)ions are indeed involved in the trapping process,The concentration of trap states is much lower than the concentration of Eu^(2+)ions,as even with low excitation densities,a plateau of integrated afterglow intensity(corresponding to the total number of accessible traps)is *** postulate that an important fraction of excited Eu^(2+)ions can potentially transfer their energy to trap *** that all traps are filled or in a dynamical filling-depletion process under illumination(with thermal and/or optical depletion processes),for the remaining Eu^(2+)a"normal"steady-state emission is observed

关键词： Persistent phosphor Strontium aluminate Europium Forster energy transfer Rare earths

Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations

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Communications in Mathematics and Statistics 2017年第4期5卷 349-380页

作者： Weinan E Jiequn Han arnulf Jentzen Beijing Institute of Big Data Research BeijingChina Princeton University PrincetonNJUSA Peking University BeijingChina ETH Zurich ZurichSwitzerland

We study a new algorithm for solvingparabolic partial differential equations(PDEs)and backward stochastic differential equations(BSDEs)in high dimension,which is based on an analogy between the BSDE and reinforcement learning with the gradient of the solution playing the role of the policy function,and the loss function given by the error between the prescribed terminal condition and the solution of the *** policy function is then approximated by a neural network,as is done in deep reinforcement *** results using TensorFlow illustrate the efficiency and accuracy of the studied algorithm for several 100-dimensional nonlinear PDEs from physics and finance such as the Allen–Cahn equation,the Hamilton–Jacobi–Bellman equation,and a nonlinear pricing model for financial derivatives.

关键词： PDEs High dimension Backward stochastic differential equations Deep learning Control Feynman-Kac

ASSESSING HISTORICAL RELIABILITY OF THE AGENT-BASED MODEL OF THE GLOBAL ENERGY SYSTEM

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Journal of Systems Science and Systems Engineering 2016年第3期25卷 326-350页

作者： Anna Shchiptsova Jiangjiang Zhao arnulf Grubler Arkady Kryazhimski Tieju Ma International Institute for Applied Systems Analysis Laxenburg Austria East China University of Science and Technology Shanghai China School of Forestry and Environmental Studies Yale University New Haven USA Steklov Mathematical Institute Russian Academy of Sciences Moscow Russia

This study looks at the historical reliability of the agent-based model of the global energy system. We present a mathematical framework for the agent-based model calibration and sensitivity analysis based on historical observations. Simulation consistency with the historical record is measured as a distance between two vectors of data points and inference on parameter values is done from the probability distribution of this stochastic estimate. Proposed methodology is applied to the model of the global energy system. Some model properties and limitations followed from calibration results are discussed.

关键词： Agent-based modeling calibration energy system

Circulating tumor cells and their role in prostate cancer

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Asian Journal of Andrology 2019年第1期21卷 24-31页

作者： Moritz Maas Miriam Hegemann Steffen Rausch Jens Bedke arnulf Stenzl Tilman Todenhofer Department of Urology University Hospital TuebingenHoppe-Seyler-Strabe 3Tuebingen 72076Germany.

Circulating tumor cells (CTC)have become an important biomarker in patients with advanced prostate *** count has been demonstrated to be a prognostic factor for overall survival in patients with metastatic castration-resistant prostate cancer (mCRPC). In localized prostate cancer,a clear correlation between CTC counts and clinicopathological risk parameters and outcome has not been ***,the focus of research is shifting from CTC enumeration towards molecular characterization of CTC leading to the discovery of markers predicting treatment *** role of androgen receptor splice variants expressed by CTC as markers of resistance to abiraterone and enzalutamide has been assessed by various *** identification of CTC markers predicting treatment response represents a key step to guide the selection of treatment (e.g.,abiraterone/enzalutamide vs taxanes), particularly in patients with *** an alternative to CTC,the analysis of circulating tumor DNA has been shown to enable a noninvasive disease characterization having high potential to promote precision oncology.

关键词： AR-V7 biomarker cell-free DNA cfDNA circulating tumor cells ctDNA liquid biopsy prostate cancer

Pathohistological classification systems in gastric cancer:Diagnostic relevance and prognostic value

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World Journal of Gastroenterology 2014年第19期20卷 5679-5684页

作者： Felix Berlth Elfriede Bollschweiler Uta Drebber arnulf H Hoelscher Stefan Moenig Department of General Visceral and Cancer SurgeryUniversity of Cologne50937 CologneGermany Department of Pathology University of Cologne50937 CologneGermany

Several pathohistological classification systems exist for the diagnosis of gastric cancer. Many studies have investigated the correlation between the pathohistological characteristics in gastric cancer and patient characteristics, disease specific criteria and overall outcome. It is still controversial as to which classification system imparts the most reliable information, and therefore, the choice of system may vary in clinical routine. In addition to the most common classification systems, such as the Laurén and the World Health Organization (WHO) classifications, other authors have tried to characterize and classify gastric cancer based on the microscopic morphology and in reference to the clinical outcome of the patients. In more than 50 years of systematic classification of the pathohistological characteristics of gastric cancer, there is no sole classification system that is consistently used worldwide in diagnostics and research. However, several national guidelines for the treatment of gastric cancer refer to the Laurén or the WHO classifications regarding therapeutic decision-making, which underlines the importance of a reliable classification system for gastric cancer. The latest results from gastric cancer studies indicate that it might be useful to integrate DNA- and RNA-based features of gastric cancer into the classification systems to establish prognostic relevance. This article reviews the diagnostic relevance and the prognostic value of different pathohistological classification systems in gastric cancer.

关键词： Gastric cancer classification Lauré n World Health Organization classification Pathohistology

Current concepts and trends in the treatment of bone metastases in patients with advanced prostate cancer

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Asian Journal of Andrology 2019年第1期21卷 12-18页

作者： Miriam Hegemann Moritz Maas Steffen Rausch Simon Walz lens Bedke arnulf Stenzl Tilman Todenhofer Department of Urology University Hospital TuebingenTuebingen 72076Germany.

Bone metastases have a major impact on quality of life and survival of patients with advanced prostate cancer,in the last decade,the development and approval of substances inhibiting the vicious cycle of bone metastases have enabled the reduction of complications caused by bone metastases in patients with castration-resistant prostate *** drugs have raised awareness of the importance of skeletal-related events which in the meantime represent an important end point also in trials using agents not specifically designed for bone ***-generation antihormona]drugs such as enzalutamide or abiraterone have been shown to have a positive impact on the incidence of skeletal complications and therefore provide an important tool in the armamentarium used for treating bone *** such as radium-223 dichloride([^223Ra])have been demonstrated not only to reduce skeletal-related events and bone-related pain,but also to prolong overall survival,thereby being the first bone-targeting agent showing a survival *** previous studies have not provided an obvious benefit of bone-targeted lesions in castration-sensitive disease,the use of these agents is not *** oligometastatic prostate cancer,the role of local treatment of metastases using stereotactic radiation or radiosurgery is a matter of intense debates and may play an increasing role in the future.

关键词： bone metastases bone-targeting agents denosumab hormonal therapy prostate cancer radium-223 dichloride zoledronic acid

Treatment of early gastric cancer in the Western World

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World Journal of Gastroenterology 2014年第19期20卷 5672-5678页

作者： Elfriede Bollschweiler Felix Berlth Christoph Baltin Stefan Mnig arnulf H Hlscher Department of General Visceral and Cancer SurgeryUniversity of Cologne50937 CologneGermany

The incidence rate of gastric cancer is much higher in Asia than in the Western industrial *** to the different screening programs in Japan and Korea about fifty percent of treated patients had an early tumor *** contrast,European and American patients with gastric cancer had an advanced tumor ***,the experience for the various therapeutic options for gastric cancer may be different between these *** this review we tried to point out the treatment modalities in Western industrial countries for early gastric cancer.

关键词： Gastric cancer Early cancer Epidemiology Diagnosis Therapy Western World

How Are Minor Mental Health Problems Perceived by Traditional Chinese Medicine?

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Chinese Medicine 2012年第2期3卷 79-86页

作者： arnulf Kolstad Nini Gjesvik Department of Psychology Norwegian University of Science and Technology Trondheim Norway Hangzhou Normal University Hangzhou China Department of Social Work and Health Norwegian University of Science and Technology Trondheim Norway

The purpose of this study was to reach a better understanding of how minor mental health problems (MMP) are perceived in China by professionals practicing Traditional Chinese Medicine (TCM) and by well-educated people living in three urban locations. The results derive from interviews with three TCM doctors, three TCM students and eight other students. Psychological problems are separated into two different categories: “serious” and “not serious”. MMP are labelled not as disorders or illnesses but looked upon as ordinary problems in daily living or as “heart problems”. MMP seem to have less serious consequences according to the Chinese than from a modern Western perspective. “Problems of life” rather than sickness was the category that best summarized perceptions of MMP. TCM professionals’ advice to change lifestyle and most Chinese regulate by themselves less serious mental problems. Both lay people and TCM professionals associate serious problems with pathological mental function in a disease perspective. Some reasons for and consequences of these comprehensions are discussed.

关键词： China Heart Problems Minor Mental Health Problems Problems of Life Traditional Chinese Medicine