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NONMONOTONE LOCAL MINIMAX METHODS FOR FINDING MULTIPLE SADDLE POINTS

Journal of Computational mathematics 2024年第3期42卷 851-884页

作者： Wei Liu Ziqing Xie Wenfan Yi South China Research center for applied mathematics and Interdisciplinary Studies South China Normal UniversityGuangzhou 510631China Key Laboratory of Computing and Stochastic mathematics(Ministry of Education) Hunan Normal UniversityChangshaHunan 410081China hunan Provincial Key Laboratory of Intelligent Information Processing and applied mathematics School of MathematicsHunan UniversityChangshaHunan 410082China

In this paper,by designing a normalized nonmonotone search strategy with the BarzilaiBorwein-type step-size,a novel local minimax method(LMM),which is a globally convergent iterative method,is proposed and analyzed to find multiple(unstable)saddle points of nonconvex functionals in Hilbert spaces.Compared to traditional LMMs with monotone search strategies,this approach,which does not require strict decrease of the objective functional value at each iterative step,is observed to converge faster with less computations.Firstly,based on a normalized iterative scheme coupled with a local peak selection that pulls the iterative point back onto the solution submanifold,by generalizing the Zhang-Hager(ZH)search strategy in the optimization theory to the LMM framework,a kind of normalized ZH-type nonmonotone step-size search strategy is introduced,and then a novel nonmonotone LMM is constructed.Its feasibility and global convergence results are rigorously carried out under the relaxation of the monotonicity for the functional at the iterative sequences.Secondly,in order to speed up the convergence of the nonmonotone LMM,a globally convergent Barzilai-Borwein-type LMM(GBBLMM)is presented by explicitly constructing the Barzilai-Borwein-type step-size as a trial step-size of the normalized ZH-type nonmonotone step-size search strategy in each iteration.Finally,the GBBLMM algorithm is implemented to find multiple unstable solutions of two classes of semilinear elliptic boundary value problems with variational structures:one is the semilinear elliptic equations with the homogeneous Dirichlet boundary condition and another is the linear elliptic equations with semilinear Neumann boundary conditions.Extensive numerical results indicate that our approach is very effective and speeds up the LMMs significantly.

关键词： Multiple saddle points Local minimax method Barzilai-Borwein gradient method Normalized nonmonotone search strategy Global convergence

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Network analysis of suicide ideation and depression-anxiety symptoms among Chinese adolescents

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General Psychiatry 2024年第2期37卷 216-223页

作者： Shuyin Xu Yumeng Ju Xiyu Wei Wenwen Ou Mohan Ma Guanyi Lv Xiaotian Zhao Yaqi Qin Yunjing Li Liang Li Mei Huang Siqi Yang Yimei Lu Yafei Chen Junwu Liu Jin Liu Bangshan Liu Yan Zhang Department of Psychiatry National Clinical Research Center for Mental Disordersand National Center for Mental DisordersThe Second Xiangya Hospital of Central South UniversityChangshaHunanChina Mental Health Institute of Central South University China National Technology Institute on Mental DisordersHunan Technology Institute of PsychiatryHunan Key Laboratory of Psychiatry and Mental HealthHunan Medical Center for Mental HealthChangshaHunanChina

Background The co-occurrence of depression and anxiety among adolescents is typically associated with suicide ideation.Aims The study aimed to investigate the symptom-level relationship between suicide ideation and the comorbidity of depression and anxiety.Methods 1501 adolescents aged 12-19 years were assessed using the Patient Health Questionnaire(PHQ-9)and the Generalized Anxiety Disorder Scale,and 716 adolescents who scored≥5 on both scales were selected as participants.Network analysis was used to identify the network structure of depressive symptoms and anxiety symptoms.Participants were categorised into either the suicide ideation or non-suicide ideation groups based on their scoring on the suicide-related item in PHQ-9.A comparison was made between the depression-anxiety symptom networks of the two groups.Results‘Restlessness’,‘sad mood’and‘trouble relaxing’were the most prominent central symptoms in the depression-anxiety symptom network,and‘restlessness’,‘nervousness’and‘reduced movement’were the bridge symptoms in this network.‘Sad mood’was found to be directly related to‘suicide ideation’with the highest variance.The network structure was significantly different in properties between the suicide ideation group and the non-suicide ideation group,with‘restlessness’and‘sad mood’exhibiting significantly higher influence in the network of the suicide ideation group than that in the non-suicide ideation group.Conclusion Restlessness and sad mood could be targeted for the intervention of depression-anxiety symptoms among adolescents with suicide ideation.

关键词： symptoms adolescent assessed

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Revealing excited states of rotational Bose-Einstein condensates

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The Innovation 2024年第1期5卷 41-48页

作者： Jianyuan Yin Zhen Huang Yongyong Cai Qiang Du Lei Zhang School of Mathematical Sciences Laboratory of Mathematics and Applied MathematicsPeking UniversityBeijing 100871China Department of mathematics National University of SingaporeSingapore 119076Singapore Department of mathematics University of CaliforniaBerkeleyBerkeleyCA 94720USA School of Mathematical Sciences Beijing Normal UniversityBeijing 100875China Department of applied Physics and applied mathematics and Data Science Institute Columbia UniversityNew YorkNY 10027USA Beijing International center for Mathematical Research Center for Quantitative BiologyCenter for Machine Learning ResearchPeking UniversityBeijing 100871China

Rotational Bose-Einstein condensates can exhibit quantized vortices as topological excitations.In this study,the ground and excited states of the rotational Bose-Einstein condensates are systematically studied by calculating the stationary points of the Gross-Pitaevskii energy functional.Various excited states and their connections at different rotational frequencies are revealed in solution landscapes constructed with the constrained high-index saddle dynamics method.Four excitation mechanisms are identified:vortex addition,rearrangement,merging,and splitting.We demonstrate changes in the ground state with increasing rotational frequencies and decipher the evolution of the stability of ground states.

关键词： method rotational excited

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p38 MAPK inhibitor SB202190 suppresses ferroptosis in the glutamate-induced retinal excitotoxicity glaucoma model

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Neural Regeneration Research 2024年第10期19卷 2299-2309页

作者： Lemeng Feng Chao Wang Cheng Zhang Wulong Zhang Weiming Zhu Ye He Zhaohua Xia Weitao Song national Clinical Research center for Geriatric Diseases Xiangya Hospital of Central South UniversityChangshaHunan ProvinceChina Eye center of Xiangya Hospital Central South UniversityChangshaHunan ProvinceChina hunan Key Laboratory of Ophthalmology ChangshaHunan ProvinceChina

Glutamate excitotoxicity has been shown to play an important role in glaucoma, and glutamate can induce ferroptosis. The p38 mitogenactivated protein kinase(MAPK) pathway inhibitor SB202190 has a potential ability to suppress ferroptosis, and its downstream targets, such as p53, have been shown to be associated with ferroptosis. However, whether ferroptosis also occurs in retinal ganglion cells in response to glutamate excitotoxicity and whether inhibition of ferroptosis reduces the loss of retinal ganglion cells induced by glutamate excitotoxicity remain unclear. This study investigated ferroptosis in a glutamate-induced glaucoma rat model and explored the effects and molecular mechanisms of SB202190 on retinal ganglion cells. A glutamate-induced excitotoxicity model in R28 cells and an N-methyl-D-aspartate-induced glaucoma model in rats were used. In vitro experiments showed that glutamate induced the accumulation of iron and lipid peroxide and morphological changes of mitochondria in R28 cells, and SB202190 inhibited these changes. Glutamate induced the levels of p-p38 MAPK/p38 MAPK and SAT1 and decreased the expression levels of ferritin light chain, SLC7A11, and GPX4. SB202190 inhibited the expression of iron death-related proteins induced by glutamate. In vivo experiments showed that SB202190 attenuated N-methyl-D-aspartate-induced damage to rat retinal ganglion cells and improved visual function. These results suggest that SB202190 can inhibit ferroptosis and protect retinal ganglion cells by regulating ferritin light chain, SAT1, and SLC7A11/Gpx4 pathways and may represent a potential retina protectant.

关键词： ferroptosis glaucoma glutamate excitotoxicity p38 MAPK retinal ganglion cell SB202190

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P-aminobenzoic acid promotes retinal regeneration through activation of Ascl1a in zebrafish

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Neural Regeneration Research 2024年第8期19卷 1849-1856页

作者： Meihui He Mingfang Xia Qian Yang Xingyi Chen Haibo Li Xiaobo Xia Eye center of Xiangya Hospital Central South UniversityChangshaHunan ProvinceChina hunan Key Laboratory of Ophthalmology ChangshaHunan ProvinceChina national Clinical Research center for Geriatric Disorders Xiangya HospitalCentral South UniversityChangshaHunan ProvinceChina

The retina of zebrafish can regenerate completely after injury.M ultiple studies have demonstrated that metabolic alte rations occur during retinal damage;however to date no study has identified a link between metabolites and retinal regeneration of zebrafish.Here,we performed an unbiased metabolome sequencing in the N-methyl-D-aspartic acid-damaged retinas of zebrafish to demonstrate the metabolomic mechanism of retinal regeneration.Among the differentially-ex pressed metabolites,we found a significant decrease in p-aminobenzoic acid in the N-methyl-D-aspartic acid-damaged retinas of zebrafish.Then,we investigated the role of p-aminobenzoic acid in retinal regeneration in adult zebrafish.Impo rtantly,p-aminobenzoic acid activated Achaetescute complex-like 1a expression,thereby promoting Müller glia reprogramming and division,as well as Müller glia-derived progenitor cell proliferation.Finally,we eliminated folic acid and inflammation as downstream effectors of PABA and demonstrated that PABA had little effect on Müller glia distribution.Taken together,these findings show that PABA contributes to retinal regeneration through activation of Achaetescute complex-like 1a expression in the N-methyl-Daspartic acid-damaged retinas of zebrafish.

关键词： Achaetescute complex-like 1a(Ascl1a) metabolomics Müller glia p-aminobenzoic acid(PABA) retina regeneration zebrafish

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Gradient-based algorithms for multi-objective bi-level optimization

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Science China mathematics 2024年第6期67卷 1419-1438页

作者： Xinmin Yang Wei Yao Haian Yin Shangzhi Zeng Jin Zhang national center for applied mathematics in Chongqing Chongqing401331China School of Mathematical Sciences Chongqing Normal UniversityChongqing401331China Department of mathematics Southern University of Science and TechnologyShenzhen518055China national center for applied mathematics Shenzhen Shenzhen518000China Department of mathematics and Statistics University of VictoriaVictoriaBCV8W 2Y2Canada

Multi-objective bi-level optimization(MOBLO)addresses nested multi-objective optimization problems common in a range of applications.However,its multi-objective and hierarchical bi-level nature makes it notably complex.Gradient-based MOBLO algorithms have recently grown in popularity,as they effectively solve crucial machine learning problems like meta-learning,neural architecture search,and reinforcement learning.Unfortunately,these algorithms depend on solving a sequence of approximation subproblems with high accuracy,resulting in adverse time and memory complexity that lowers their numerical efficiency.To address this issue,we propose a gradient-based algorithm for MOBLO,called gMOBA,which has fewer hyperparameters to tune,making it both simple and efficient.Additionally,we demonstrate the theoretical validity by accomplishing the desirable Pareto stationarity.Numerical experiments confirm the practical efficiency of the proposed method and verify the theoretical results.To accelerate the convergence of gMOBA,we introduce a beneficial L2O(learning to optimize)neural network(called L2O-gMOBA)implemented as the initialization phase of our gMOBA algorithm.Comparative results of numerical experiments are presented to illustrate the performance of L2O-gMOBA.

关键词： multi-objective bi-level optimization convergence analysis Pareto stationary learning to optimize

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Mushroom Poisoning Outbreaks—China,2023

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China CDC weekly 2024年第4期6卷 64-68,I0001-I0005页

作者： Haijiao Li Yizhe Zhang Hongshun Zhang Jing Zhou Zuohong Chen Jiaqi Liang Yu Yin Qian He Shaofeng Jiang Yutao Zhang Yuan Yuan Nan Lang Bowen Cheng Jiaju Zhong Zhongfeng Li Chengye Sun national Institute of Occupational Health and Poison Control Chinese Center for Disease Control and PreventionBeijingChina College of Life Sciences Hunan Normal UniversityChangsha CityHunan ProvinceChina

What is already known about this topic?Mushroom poisoning poses a significant food safety concern in China,with a total of 196 species identified in poisoning incidents by the end of 2022.What is added by this report?In 2023,the China CDC conducted an investigation into 505 cases of mushroom poisoning spanning 24 provincial-level administrative divisions.This investigation resulted in 1,303 patients and 16 deaths,yielding a case fatality rate of 1.23%.A total of 97 mushrooms were identified as the cause of 6 distinct clinical disease types,with 12 species newly documented as poisonous mushrooms in China.What are the implications for public health practice?Close collaboration among CDC staff,physicians,and mycologists remains crucial for the control and prevention of mushroom poisoning in the future.

关键词： prevention yielding poisoning

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CsABF3-activated CsSUT1 pathway is implicated in pre-harvest water deficit inducing sucrose accumulation in citrus fruit

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Horticultural Plant Journal 2024年第1期10卷 103-114页

作者： Xiaochuan Ma Yuanyuan Chang Feifei Li Junfeng Yang Li Ye Tie Zhou Yan Jin Ling Sheng Xiaopeng Lu College of Horticulture Hunan Agricultural UniversityChangshaHunan 410128China national center for Citrus Improvement ChangshaHunan 410128China Institute of Horticulture Hunan Academy of Agricultural ScienceChangshaHunan 410125China

Pre-harvest water deficit(PHWD)plays an important role in sugar accumulation of citrus fruit.However,the mechanism is not known well.Here,it was confirmed that PHWD promoted sucrose accumulation of citrus fruit,but had limited effect on fructose,glucose and total acid.A sucrose transporter,Cs SUT1,which localizes to the plasma membrane,was demonstrated to function in sucrose transport induced by PHWD.Compared to wild-type,Cs SUT1 overexpression in citrus calli stimulated sucrose,fructose and glucose accumulation,while its silencing in juice sacs reduced sucrose accumulation.Increased sugar accumulation in transgenic lines enhanced plant drought tolerance,and resulted in decreased electrolyte leakage,malondialdehyde and hydrogen peroxide contents,as well as increased superoxide dismutase activity and proline contents.An abscisic acid(ABA)-responsive transcription factor,Cs ABF3,was found with a same expression pattern with Cs SUT1 under PHWD.Yeast one-hybrid,electrophoretic mobility shift assay and dual-luciferase assays all revealed that Cs ABF3 directly bound with the Cs SUT1 promoter by ABA responsive elements.When Cs ABF3 was overexpressed in citrus calli,the sucrose,fructose and glucose concentration increased correspondingly.Further,transgenic studies demonstrated that Cs ABF3 could affect sucrose accumulation by regulating Cs SUT1.Overall,this study revealed a regulation of Cs ABF3 promoting Cs SUT1 expression and sucrose accumulation in response to PHWD.Our results provide a detail insight into the quality formation of citrus fruit.

关键词： Citrus Water deficit Pre-harvest Sucrose CsABF3 CsSUT1

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Normalized and self-normalized Cramér-type moderate deviations for the Euler-Maruyama scheme for the SDE

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Science China mathematics 2024年第8期67卷 1865-1880页

作者： Xiequan Fan Haijuan Hu Lihu Xu center for applied mathematics Tianjin University School of mathematics and Statistics Northeastern University at Qinhuangdao Department of mathematics Faculty of Science and TechnologyUniversity of Macau

In this paper, we establish normalized and self-normalized Cramér-type moderate deviations for the Euler-Maruyama scheme for SDE. Due to our results, Berry-Esseen's bounds and moderate deviation principles are also o... 详细信息

关键词： Euler-Maruyama scheme Cramér-type moderate deviations self-normalized sequences Berry-Esseen's bounds

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Parametric “non-nested” discriminants for multiplicities of univariate polynomials

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Science China mathematics 2024年第8期67卷 1911-1932页

作者： Hoon Hong Jing Yang Department of mathematics North Carolina State University SMS–HCIC–School of mathematics and Physics Center for Applied Mathematics of GuangxiGuangxi Minzu University

We consider the problem of complex root classification, i.e., finding the conditions on the coefficients of a univariate polynomial for all possible multiplicity structures on its complex roots. It is well known that such conditions can be written as conjunctions of several polynomial equalities and one inequality in the coefficients. Those polynomials in the coefficients are called discriminants for multiplicities. It is also known that discriminants can be obtained using repeated parametric greatest common divisors. The resulting discriminants are usually nested determinants, i.e., determinants of matrices whose entries are determinants, and so on. In this paper, we give a new type of discriminant that is not based on repeated greatest common divisors. The new discriminants are simpler in the sense that they are non-nested determinants and have smaller maximum degrees.

关键词： parametric polynomial complex roots discriminant multiplicity resultant

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