乐胖代购免代理版

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Recently, the authors developed a mathematical framework for the computation of optimal reaction coordinates of such systems that is based on learning a parameterization of a low-dimensional transition manifold in a certain function space. In this article, we enhance this approach by embedding and learning this transition manifold in a reproducing kernel Hilbert space, exploiting the favorable properties of kernel embeddings. Under mild assumptions on the kernel, the manifold structure is shown to be preserved under the embedding, and distortion bounds can be derived. This leads to a more robust and more efficient algorithm compared to the previous parameterization approaches.<\/jats:p>","DOI":"10.1007\/s00332-020-09668-z","type":"journal-article","created":{"date-parts":[[2020,12,18]],"date-time":"2020-12-18T12:03:37Z","timestamp":1608293017000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifolds"],"prefix":"10.1007","volume":"31","author":[{"given":"Andreas","family":"Bittracher","sequence":"first","affiliation":[]},{"given":"Stefan","family":"Klus","sequence":"additional","affiliation":[]},{"given":"Boumediene","family":"Hamzi","sequence":"additional","affiliation":[]},{"given":"P\u00e9ter","family":"Koltai","sequence":"additional","affiliation":[]},{"given":"Christof","family":"Sch\u00fctte","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,12,18]]},"reference":[{"issue":"6","key":"9668_CR1","doi-asserted-by":"crossref","first-page":"3026","DOI":"10.1016\/j.aim.2011.08.003","volume":"228","author":"I Abraham","year":"2011","unstructured":"Abraham, I., Bartal, Y., Neiman, O.: Advances in metric embedding theory. 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