{"product_id":"a-prolegomenon-to-differential-equations-and-variational-methods-on-graphs-hardback-9781009494656","title":"A Prolegomenon to Differential Equations and Variational Methods on Graphs (Hardback) 9781009494656","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eA Prolegomenon to Differential Equations and Variational Methods on Graphs\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA bird's eye view of  theoretical developments and concrete applications that will enable newcomers to get a flavour of key results.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eYves van Gennip (Author), Jeremy Budd (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009494656, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 27 February 2025\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e100 pages\u003cbr\u003e23.5 x 16 x 1 cm, 0.282 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThe use of differential equations on graphs as a framework for the mathematical analysis of images emerged about fifteen years ago and since then it has burgeoned, and with applications also to machine learning. The authors have written a bird's eye view of theoretical developments that will enable newcomers to quickly get a flavour of key results and ideas. Additionally, they provide an substantial bibliography which will point readers to where fuller details and other directions can be explored. This title is also available as open access on Cambridge Core.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Introduction\u003cbr\u003e 2. History and literature overview\u003cbr\u003e 3. Calculus on undirected edge-weighted graphs\u003cbr\u003e 4. Directed graphs\u003cbr\u003e 5. The graph Ginzburg–Landau functional\u003cbr\u003e 6. Spectrum of the graph Laplacians\u003cbr\u003e 7. Gradient flow: Allen–Cahn\u003cbr\u003e 8. Merriman–Bence–Osher scheme\u003cbr\u003e 9. Graph curvature and mean curvature flow\u003cbr\u003e 10. Freezing of Allen–Cahn, MBO, and mean curvature flow\u003cbr\u003e 11. Multiclass extensions\u003cbr\u003e 12. Laplacian learning and Poisson learning\u003cbr\u003e 13. Conclusions\u003cbr\u003e Bibliography.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Numerical analysis [\u003ca title=\"See our other books on Numerical analysis\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Numerical%20analysis%20%5BPBKS%5D%22\"\u003ePBKS\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Brand New","offer_id":52414092738840,"sku":"9781009494656","price":46.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781009494656i.jpg?v=1784337797","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/a-prolegomenon-to-differential-equations-and-variational-methods-on-graphs-hardback-9781009494656","provider":"Freshly Printed Books","version":"1.0","type":"link"}