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Efficiency of the Wang–Landau Algorithm: A Simple Test Case Wang-Landau算法的效率:一个简单的测试用例
Applied mathematics research express : AMRX Pub Date : 2013-10-24 DOI: 10.1093/AMRX/ABU003
G. Fort, B. Jourdain, E. Kuhn, T. Lelièvre, G. Stoltz
{"title":"Efficiency of the Wang–Landau Algorithm: A Simple Test Case","authors":"G. Fort, B. Jourdain, E. Kuhn, T. Lelièvre, G. Stoltz","doi":"10.1093/AMRX/ABU003","DOIUrl":"https://doi.org/10.1093/AMRX/ABU003","url":null,"abstract":"We analyze the convergence properties of the Wang-Landau algorithm. This sampling method belongs to the general class of adaptive importance sampling strategies which use the free energy along a chosen reaction coordinate as a bias. Such algorithms are very helpful to enhance the sampling properties of Markov Chain Monte Carlo algorithms, when the dynamics is metastable. We prove the convergence of the Wang-Landau algorithm and an associated central limit theorem.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"82 1","pages":"275-311"},"PeriodicalIF":0.0,"publicationDate":"2013-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79679438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 15
REMARKS ON THE QUANTUM DE FINETTI THEOREM FOR BOSONIC SYSTEMS 关于玻色子系统的量子定精细定理的评述
Applied mathematics research express : AMRX Pub Date : 2013-10-08 DOI: 10.1093/AMRX/ABU006
Mathieu Lewin, P. T. Nam, N. Rougerie
{"title":"REMARKS ON THE QUANTUM DE FINETTI THEOREM FOR BOSONIC SYSTEMS","authors":"Mathieu Lewin, P. T. Nam, N. Rougerie","doi":"10.1093/AMRX/ABU006","DOIUrl":"https://doi.org/10.1093/AMRX/ABU006","url":null,"abstract":"The quantum de Finetti theorem asserts that the k-body density matrices of a N-body bosonic state approach a convex combination of Hartree states (pure tensor powers) when N is large and k fixed. In this note we review a construction due to Christandl, Mitchison, Konig and Renner valid for finite dimensional Hilbert spaces, which gives a quantitative version of the theorem. We first propose a variant of their proof that leads to a slightly improved estimate. Next we provide an alternative proof of an explicit formula due to Chiribella, which gives the density matrices of the constructed state as a function of those of the original state.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"54 1","pages":"48-63"},"PeriodicalIF":0.0,"publicationDate":"2013-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90920913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 41
Smooth Periodic Solutions of a 2×2 System of Nonlinear Hyperbolic Conservation Laws 非线性双曲型守恒律2×2系统的光滑周期解
Applied mathematics research express : AMRX Pub Date : 2013-07-12 DOI: 10.1093/AMRX/ABT006
M. Shearer
{"title":"Smooth Periodic Solutions of a 2×2 System of Nonlinear Hyperbolic Conservation Laws","authors":"M. Shearer","doi":"10.1093/AMRX/ABT006","DOIUrl":"https://doi.org/10.1093/AMRX/ABT006","url":null,"abstract":"","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"3 1","pages":"114-121"},"PeriodicalIF":0.0,"publicationDate":"2013-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86389344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Note on a 3D Haptotaxis Model of Cancer Invasion 肿瘤侵袭的三维趋向性模型研究进展
Applied mathematics research express : AMRX Pub Date : 2013-04-30 DOI: 10.1093/AMRX/ABT004
Jishan Fan, Kun Zhao
{"title":"A Note on a 3D Haptotaxis Model of Cancer Invasion","authors":"Jishan Fan, Kun Zhao","doi":"10.1093/AMRX/ABT004","DOIUrl":"https://doi.org/10.1093/AMRX/ABT004","url":null,"abstract":"","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"56 ","pages":"74-86"},"PeriodicalIF":0.0,"publicationDate":"2013-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/AMRX/ABT004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72498259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Approximate Solutions of a Stochastic Variational Inequality Modeling an Elasto-Plastic Problem with Noise 含噪声弹塑性问题随机变分不等式的近似解
Applied mathematics research express : AMRX Pub Date : 2013-03-28 DOI: 10.1093/AMRX/ABT003
Héctor Jasso-Fuentes, L. Mertz, S. Yam
{"title":"Approximate Solutions of a Stochastic Variational Inequality Modeling an Elasto-Plastic Problem with Noise","authors":"Héctor Jasso-Fuentes, L. Mertz, S. Yam","doi":"10.1093/AMRX/ABT003","DOIUrl":"https://doi.org/10.1093/AMRX/ABT003","url":null,"abstract":"","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"12 1","pages":"52-73"},"PeriodicalIF":0.0,"publicationDate":"2013-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79756642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Analysis of the Monte-Carlo Error in a Hybrid Semi-Lagrangian Scheme 混合半拉格朗日格式的蒙特卡罗误差分析
Applied mathematics research express : AMRX Pub Date : 2013-03-15 DOI: 10.1093/AMRX/ABV001
Charles-Edouard Br'ehier, E. Faou
{"title":"Analysis of the Monte-Carlo Error in a Hybrid Semi-Lagrangian Scheme","authors":"Charles-Edouard Br'ehier, E. Faou","doi":"10.1093/AMRX/ABV001","DOIUrl":"https://doi.org/10.1093/AMRX/ABV001","url":null,"abstract":"We consider Monte-Carlo discretizations of partial differential equations based on a combination of semi-lagrangian schemes and probabilistic representations of the solutions. We study the Monte-Carlo error in a simple case, and show that under an anti-CFL condition on the time-step $delta t$ and on the mesh size $delta x$ and for $N$ - the number of realizations - reasonably large, we control this error by a term of order $mathcal{O}(sqrt{delta t /N})$. We also provide some numerical experiments to confirm the error estimate, and to expose some examples of equations which can be treated by the numerical method.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"12 1","pages":"167-203"},"PeriodicalIF":0.0,"publicationDate":"2013-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90379032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Nonlinear Capacitary Problems for a General Distribution of Fibers 光纤一般分布的非线性电容问题
Applied mathematics research express : AMRX Pub Date : 2013-02-27 DOI: 10.1093/AMRX/ABT002
Michel Bellieud, C. Licht, S. Orankitjaroen
{"title":"Nonlinear Capacitary Problems for a General Distribution of Fibers","authors":"Michel Bellieud, C. Licht, S. Orankitjaroen","doi":"10.1093/AMRX/ABT002","DOIUrl":"https://doi.org/10.1093/AMRX/ABT002","url":null,"abstract":"We determine the eff ective electric properties of a composite with high contrast. The energy density is given locally in terms of a convex function of the gradient of the potential. The permittivity may take very large values in a fairly general distribution of parallel fibers of tiny cross sections. For a critical size of the cross sections, we show that a concentration of electric energy may arise in a small region of space surrounding the fi bers. This extra contribution is caused by the discrepancy between the behaviors of the potential in the matrix and in the fibers and is characterized by the density of the cross sections of the bers with respect to the cross section of the body in terms of some suitable notion of capacity. Our results extend those established in [7] in the periodic case for the p-Laplacian to a general nonlinear framework and a non-periodic distribution of fi bers.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"46 1","pages":"1-51"},"PeriodicalIF":0.0,"publicationDate":"2013-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90350795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Quasi-Static Evolution for the Armstrong-Frederick Hardening-Plasticity Model Armstrong-Frederick硬化-塑性模型的准静态演化
Applied mathematics research express : AMRX Pub Date : 2013-01-01 DOI: 10.1093/AMRX/ABT001
G. Francfort, U. Stefanelli
{"title":"Quasi-Static Evolution for the Armstrong-Frederick Hardening-Plasticity Model","authors":"G. Francfort, U. Stefanelli","doi":"10.1093/AMRX/ABT001","DOIUrl":"https://doi.org/10.1093/AMRX/ABT001","url":null,"abstract":"The Armstrong-Frederick model for nonlinear kinematic hardening is regarded as a benchmark model in contemporary elastoplasticity. This work presents an existence result to an appropriately time-rescaled evolution for that model. To do so, we have to resort to a regularization of the dependence of the convex of plasticity upon the back stress. Such a regularization process seems to be the unfortunate price one has to pay for a successful mathematical analysis.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"39 1","pages":"297-344"},"PeriodicalIF":0.0,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77954380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 23
Coherent Worst-Case Value-at-Risk with Applications to Robust Portfolio Optimization 相干最坏情况风险值在稳健投资组合优化中的应用
Applied mathematics research express : AMRX Pub Date : 2012-12-13 DOI: 10.1093/AMRX/ABS018
G. Luo
{"title":"Coherent Worst-Case Value-at-Risk with Applications to Robust Portfolio Optimization","authors":"G. Luo","doi":"10.1093/AMRX/ABS018","DOIUrl":"https://doi.org/10.1093/AMRX/ABS018","url":null,"abstract":"","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"76 1","pages":"256-276"},"PeriodicalIF":0.0,"publicationDate":"2012-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78625932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quasi-Stationary Limit and a Degenerate Landau–Lifshitz Equation of Ferromagnetism 铁磁性的准平稳极限和退化的Landau-Lifshitz方程
Applied mathematics research express : AMRX Pub Date : 2012-12-12 DOI: 10.1093/AMRX/ABS019
Wei-Qi Deng, Baisheng Yan
{"title":"Quasi-Stationary Limit and a Degenerate Landau–Lifshitz Equation of Ferromagnetism","authors":"Wei-Qi Deng, Baisheng Yan","doi":"10.1093/AMRX/ABS019","DOIUrl":"https://doi.org/10.1093/AMRX/ABS019","url":null,"abstract":"In this paper, we study a model of Landau–Lifshitz equations of ferromagnetism that does not contain the regularizing term of exchange energy. Without the exchange energy, due to the lack of certain derivative estimates and compactness, such an equation becomes degenerate and cannot be studied by the usual Galerkin method based on the elliptic equation theory. For such a degenerate model, it is known that the weak solutions can be obtained through the quasi-stationary limits of certain coupled Landau– Lifshitz–Maxwell systems as the dielectric permittivity tends to zero. In this paper, we use a simplified Landau–Lifshitz–Maxwell system with constant permittivity to present a different but more direct proof of this quasi-stationary limit result. We also establish a finite-time local L2-stability result for weak solutions of the degenerate Landau–Lifshitz equation, which yields the new uniqueness result on weak solution with bounded initial data.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"29 1","pages":"277-296"},"PeriodicalIF":0.0,"publicationDate":"2012-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86988998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
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