@inproceedings{11, abstract = {We report on a novel strategy to derive mean-field limits of quantum mechanical systems in which a large number of particles weakly couple to a second-quantized radiation field. The technique combines the method of counting and the coherent state approach to study the growth of the correlations among the particles and in the radiation field. As an instructional example, we derive the Schrödinger–Klein–Gordon system of equations from the Nelson model with ultraviolet cutoff and possibly massless scalar field. In particular, we prove the convergence of the reduced density matrices (of the nonrelativistic particles and the field bosons) associated with the exact time evolution to the projectors onto the solutions of the Schrödinger–Klein–Gordon equations in trace norm. Furthermore, we derive explicit bounds on the rate of convergence of the one-particle reduced density matrix of the nonrelativistic particles in Sobolev norm.}, author = {Leopold, Nikolai K and Pickl, Peter}, location = {Munich, Germany}, pages = {185 -- 214}, publisher = {Springer}, title = {{Mean-field limits of particles in interaction with quantised radiation fields}}, doi = {10.1007/978-3-030-01602-9_9}, volume = {270}, year = {2018}, } @article{1215, abstract = {Two generalizations of Itô formula to infinite-dimensional spaces are given. The first one, in Hilbert spaces, extends the classical one by taking advantage of cancellations when they occur in examples and it is applied to the case of a group generator. The second one, based on the previous one and a limit procedure, is an Itô formula in a special class of Banach spaces having a product structure with the noise in a Hilbert component; again the key point is the extension due to a cancellation. This extension to Banach spaces and in particular the specific cancellation are motivated by path-dependent Itô calculus.}, author = {Flandoli, Franco and Russo, Francesco and Zanco, Giovanni A}, journal = {Journal of Theoretical Probability}, number = {2}, pages = {789--826}, publisher = {Springer}, title = {{Infinite-dimensional calculus under weak spatial regularity of the processes}}, doi = {10.1007/s10959-016-0724-2}, volume = {31}, year = {2018}, } @inproceedings{185, abstract = {We resolve in the affirmative conjectures of A. Skopenkov and Repovš (1998), and M. Skopenkov (2003) generalizing the classical Hanani-Tutte theorem to the setting of approximating maps of graphs on 2-dimensional surfaces by embeddings. Our proof of this result is constructive and almost immediately implies an efficient algorithm for testing whether a given piecewise linear map of a graph in a surface is approximable by an embedding. More precisely, an instance of this problem consists of (i) a graph G whose vertices are partitioned into clusters and whose inter-cluster edges are partitioned into bundles, and (ii) a region R of a 2-dimensional compact surface M given as the union of a set of pairwise disjoint discs corresponding to the clusters and a set of pairwise disjoint "pipes" corresponding to the bundles, connecting certain pairs of these discs. We are to decide whether G can be embedded inside M so that the vertices in every cluster are drawn in the corresponding disc, the edges in every bundle pass only through its corresponding pipe, and every edge crosses the boundary of each disc at most once.}, author = {Fulek, Radoslav and Kynčl, Jan}, isbn = {978-3-95977-066-8}, location = {Budapest, Hungary}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Hanani-Tutte for approximating maps of graphs}}, doi = {10.4230/LIPIcs.SoCG.2018.39}, volume = {99}, year = {2018}, } @inproceedings{188, abstract = {Smallest enclosing spheres of finite point sets are central to methods in topological data analysis. Focusing on Bregman divergences to measure dissimilarity, we prove bounds on the location of the center of a smallest enclosing sphere. These bounds depend on the range of radii for which Bregman balls are convex.}, author = {Edelsbrunner, Herbert and Virk, Ziga and Wagner, Hubert}, location = {Budapest, Hungary}, pages = {35:1 -- 35:13}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Smallest enclosing spheres and Chernoff points in Bregman geometry}}, doi = {10.4230/LIPIcs.SoCG.2018.35}, volume = {99}, year = {2018}, } @article{306, abstract = {A cornerstone of statistical inference, the maximum entropy framework is being increasingly applied to construct descriptive and predictive models of biological systems, especially complex biological networks, from large experimental data sets. Both its broad applicability and the success it obtained in different contexts hinge upon its conceptual simplicity and mathematical soundness. Here we try to concisely review the basic elements of the maximum entropy principle, starting from the notion of ‘entropy’, and describe its usefulness for the analysis of biological systems. As examples, we focus specifically on the problem of reconstructing gene interaction networks from expression data and on recent work attempting to expand our system-level understanding of bacterial metabolism. Finally, we highlight some extensions and potential limitations of the maximum entropy approach, and point to more recent developments that are likely to play a key role in the upcoming challenges of extracting structures and information from increasingly rich, high-throughput biological data.}, author = {De Martino, Andrea and De Martino, Daniele}, journal = {Heliyon}, number = {4}, publisher = {Elsevier}, title = {{An introduction to the maximum entropy approach and its application to inference problems in biology}}, doi = {10.1016/j.heliyon.2018.e00596}, volume = {4}, year = {2018}, }