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Feldmann, in: Twentieth Annual IEEE Applied Power Electronics Conference and Exposition, 2005. APEC 2005., 2005.","mla":"Li, R., et al. “Design and Implementation of a Hybrid Energy Supply System for Railway Vehicles.” <i>Twentieth Annual IEEE Applied Power Electronics Conference and Exposition, 2005. APEC 2005.</i>, 2005, doi:<a href=\"https://doi.org/10.1109/apec.2005.1452979\">10.1109/apec.2005.1452979</a>.","bibtex":"@inproceedings{Li_Pottharst_Frohieke_Becker_Witting_Dellnitz_Znamenshchykov_Feldmann_2005, title={Design and implementation of a hybrid energy supply system for railway vehicles}, DOI={<a href=\"https://doi.org/10.1109/apec.2005.1452979\">10.1109/apec.2005.1452979</a>}, booktitle={Twentieth Annual IEEE Applied Power Electronics Conference and Exposition, 2005. APEC 2005.}, author={Li, R. and Pottharst, A. and Frohieke, N. and Becker, J. and Witting, K. and Dellnitz, M. and Znamenshchykov, O. and Feldmann, R.}, year={2005} }","apa":"Li, R., Pottharst, A., Frohieke, N., Becker, J., Witting, K., Dellnitz, M., … Feldmann, R. (2005). Design and implementation of a hybrid energy supply system for railway vehicles. In <i>Twentieth Annual IEEE Applied Power Electronics Conference and Exposition, 2005. APEC 2005.</i> <a href=\"https://doi.org/10.1109/apec.2005.1452979\">https://doi.org/10.1109/apec.2005.1452979</a>","ieee":"R. Li <i>et al.</i>, “Design and implementation of a hybrid energy supply system for railway vehicles,” in <i>Twentieth Annual IEEE Applied Power Electronics Conference and Exposition, 2005. APEC 2005.</i>, 2005.","chicago":"Li, R., A. Pottharst, N. Frohieke, J. Becker, K. Witting, M. Dellnitz, O. Znamenshchykov, and R. 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Hestermeyer. “Covering Pareto Sets by Multilevel Subdivision Techniques.” <i>Journal of Optimization Theory and Applications</i>, 2005, 113–36. <a href=\"https://doi.org/10.1007/s10957-004-6468-7\">https://doi.org/10.1007/s10957-004-6468-7</a>.","short":"M. Dellnitz, O. Sch�tze, T. Hestermeyer, Journal of Optimization Theory and Applications (2005) 113–136.","bibtex":"@article{Dellnitz_Sch�tze_Hestermeyer_2005, title={Covering Pareto Sets by Multilevel Subdivision Techniques}, DOI={<a href=\"https://doi.org/10.1007/s10957-004-6468-7\">10.1007/s10957-004-6468-7</a>}, journal={Journal of Optimization Theory and Applications}, author={Dellnitz, M. and Sch�tze, O. and Hestermeyer, T.}, year={2005}, pages={113–136} }","mla":"Dellnitz, M., et al. “Covering Pareto Sets by Multilevel Subdivision Techniques.” <i>Journal of Optimization Theory and Applications</i>, 2005, pp. 113–36, doi:<a href=\"https://doi.org/10.1007/s10957-004-6468-7\">10.1007/s10957-004-6468-7</a>.","apa":"Dellnitz, M., Sch�tze, O., &#38; Hestermeyer, T. (2005). Covering Pareto Sets by Multilevel Subdivision Techniques. <i>Journal of Optimization Theory and Applications</i>, 113–136. <a href=\"https://doi.org/10.1007/s10957-004-6468-7\">https://doi.org/10.1007/s10957-004-6468-7</a>"},"page":"113-136","date_updated":"2022-01-06T06:52:54Z","date_created":"2020-04-16T10:31:32Z","author":[{"first_name":"M.","full_name":"Dellnitz, M.","last_name":"Dellnitz"},{"full_name":"Sch�tze, O.","last_name":"Sch�tze","first_name":"O."},{"full_name":"Hestermeyer, T.","last_name":"Hestermeyer","first_name":"T."}],"title":"Covering Pareto Sets by Multilevel Subdivision Techniques","doi":"10.1007/s10957-004-6468-7"},{"status":"public","type":"journal_article","publication":"Applied Surface Science","language":[{"iso":"eng"}],"user_id":"15701","department":[{"_id":"101"}],"_id":"16500","citation":{"apa":"Chaudhuri, I., Sertl, S., Hajnal, Z., Dellnitz, M., &#38; Frauenheim, T. (2004). Global optimization of silicon nanoclusters. <i>Applied Surface Science</i>, 108–113. <a href=\"https://doi.org/10.1016/j.apsusc.2003.11.007\">https://doi.org/10.1016/j.apsusc.2003.11.007</a>","mla":"Chaudhuri, I., et al. “Global Optimization of Silicon Nanoclusters.” <i>Applied Surface Science</i>, 2004, pp. 108–13, doi:<a href=\"https://doi.org/10.1016/j.apsusc.2003.11.007\">10.1016/j.apsusc.2003.11.007</a>.","short":"I. Chaudhuri, S. Sertl, Z. Hajnal, M. Dellnitz, T. Frauenheim, Applied Surface Science (2004) 108–113.","bibtex":"@article{Chaudhuri_Sertl_Hajnal_Dellnitz_Frauenheim_2004, title={Global optimization of silicon nanoclusters}, DOI={<a href=\"https://doi.org/10.1016/j.apsusc.2003.11.007\">10.1016/j.apsusc.2003.11.007</a>}, journal={Applied Surface Science}, author={Chaudhuri, I. and Sertl, S. and Hajnal, Z. and Dellnitz, M. and Frauenheim, Th.}, year={2004}, pages={108–113} }","ama":"Chaudhuri I, Sertl S, Hajnal Z, Dellnitz M, Frauenheim T. Global optimization of silicon nanoclusters. <i>Applied Surface Science</i>. 2004:108-113. doi:<a href=\"https://doi.org/10.1016/j.apsusc.2003.11.007\">10.1016/j.apsusc.2003.11.007</a>","ieee":"I. Chaudhuri, S. Sertl, Z. Hajnal, M. Dellnitz, and T. Frauenheim, “Global optimization of silicon nanoclusters,” <i>Applied Surface Science</i>, pp. 108–113, 2004.","chicago":"Chaudhuri, I., S. Sertl, Z. Hajnal, M. Dellnitz, and Th. 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(2004). New spectral lower bounds on the bisection width of graphs. <i>Theoretical Computer Science</i>, 155–174. <a href=\"https://doi.org/10.1016/j.tcs.2004.03.059\">https://doi.org/10.1016/j.tcs.2004.03.059</a>","bibtex":"@article{Bezrukov_Elsässer_Monien_Preis_Tillich_2004, title={New spectral lower bounds on the bisection width of graphs}, DOI={<a href=\"https://doi.org/10.1016/j.tcs.2004.03.059\">10.1016/j.tcs.2004.03.059</a>}, journal={Theoretical Computer Science}, author={Bezrukov, S. and Elsässer, R. and Monien, B. and Preis, R. and Tillich, J.-P.}, year={2004}, pages={155–174} }","short":"S. Bezrukov, R. Elsässer, B. Monien, R. Preis, J.-P. Tillich, Theoretical Computer Science (2004) 155–174.","mla":"Bezrukov, S., et al. “New Spectral Lower Bounds on the Bisection Width of Graphs.” <i>Theoretical Computer Science</i>, 2004, pp. 155–74, doi:<a href=\"https://doi.org/10.1016/j.tcs.2004.03.059\">10.1016/j.tcs.2004.03.059</a>.","ama":"Bezrukov S, Elsässer R, Monien B, Preis R, Tillich J-P. New spectral lower bounds on the bisection width of graphs. <i>Theoretical Computer Science</i>. 2004:155-174. doi:<a href=\"https://doi.org/10.1016/j.tcs.2004.03.059\">10.1016/j.tcs.2004.03.059</a>","chicago":"Bezrukov, S., R. Elsässer, B. Monien, R. Preis, and J.-P. Tillich. “New Spectral Lower Bounds on the Bisection Width of Graphs.” <i>Theoretical Computer Science</i>, 2004, 155–74. <a href=\"https://doi.org/10.1016/j.tcs.2004.03.059\">https://doi.org/10.1016/j.tcs.2004.03.059</a>.","ieee":"S. Bezrukov, R. Elsässer, B. Monien, R. Preis, and J.-P. Tillich, “New spectral lower bounds on the bisection width of graphs,” <i>Theoretical Computer Science</i>, pp. 155–174, 2004."},"year":"2004","department":[{"_id":"101"}],"user_id":"15701","_id":"16521","language":[{"iso":"eng"}],"publication":"Theoretical Computer Science","type":"journal_article","status":"public"},{"publication_status":"published","publication_identifier":{"issn":["1536-0040"]},"citation":{"ama":"Day S, Junge O, Mischaikow K. A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems. <i>SIAM Journal on Applied Dynamical Systems</i>. 2004:117-160. doi:<a href=\"https://doi.org/10.1137/030600210\">10.1137/030600210</a>","ieee":"S. Day, O. Junge, and K. Mischaikow, “A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems,” <i>SIAM Journal on Applied Dynamical Systems</i>, pp. 117–160, 2004.","chicago":"Day, S., O. Junge, and K. Mischaikow. “A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems.” <i>SIAM Journal on Applied Dynamical Systems</i>, 2004, 117–60. <a href=\"https://doi.org/10.1137/030600210\">https://doi.org/10.1137/030600210</a>.","apa":"Day, S., Junge, O., &#38; Mischaikow, K. (2004). A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems. <i>SIAM Journal on Applied Dynamical Systems</i>, 117–160. <a href=\"https://doi.org/10.1137/030600210\">https://doi.org/10.1137/030600210</a>","bibtex":"@article{Day_Junge_Mischaikow_2004, title={A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems}, DOI={<a href=\"https://doi.org/10.1137/030600210\">10.1137/030600210</a>}, journal={SIAM Journal on Applied Dynamical Systems}, author={Day, S. and Junge, O. and Mischaikow, K.}, year={2004}, pages={117–160} }","short":"S. Day, O. Junge, K. Mischaikow, SIAM Journal on Applied Dynamical Systems (2004) 117–160.","mla":"Day, S., et al. “A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems.” <i>SIAM Journal on Applied Dynamical Systems</i>, 2004, pp. 117–60, doi:<a href=\"https://doi.org/10.1137/030600210\">10.1137/030600210</a>."},"page":"117-160","year":"2004","date_created":"2020-04-15T08:17:18Z","author":[{"first_name":"S.","last_name":"Day","full_name":"Day, S."},{"last_name":"Junge","full_name":"Junge, O.","first_name":"O."},{"full_name":"Mischaikow, K.","last_name":"Mischaikow","first_name":"K."}],"date_updated":"2022-01-06T06:52:52Z","doi":"10.1137/030600210","title":"A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems","type":"journal_article","publication":"SIAM Journal on Applied Dynamical Systems","status":"public","user_id":"15701","department":[{"_id":"101"}],"_id":"16527","language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"_id":"16587","user_id":"15701","department":[{"_id":"101"}],"abstract":[{"lang":"eng","text":"<jats:p> We discuss nearest neighbor load balancing schemes on processor networks which are represented by a cartesian product of graphs and present a new optimal diffusion scheme for general graphs. In the first part of the paper, we introduce the Alternating-Direction load balancing scheme, which reduces the number of load balance iterations by a factor of 2 for cartesian products of graphs. The resulting flow is theoretically analyzed and can be very high for certain cases. Therefore, we further present the Mixed-Direction scheme which needs the same number of iterations but computes in most cases a much smaller flow. In the second part of the paper, we present a simple optimal diffusion scheme for general graphs, calculating a balancing flow which is minimal in the l<jats:sub>2</jats:sub> norm. It is based on the spectra of the graph representing the network and needs only m-1 iterations to balance the load with m being the number of distinct eigenvalues. Known optimal diffusion schemes have the same performance, however the optimal scheme presented in this paper can be implemented in a very simple manner. The number of iterations of optimal diffusion schemes is independent of the load scenario and, thus, they are practical for networks which represent graphs with known spectra. Finally, our experiments exhibit that the new optimal scheme can successfully be combined with the Alternating-Direction and Mixed-Direction schemes for efficient load balancing on product graphs. </jats:p>"}],"status":"public","type":"journal_article","publication":"Parallel Processing Letters","title":"Optimal Diffusion Schemes and Load Balancing on Product Graphs","doi":"10.1142/s0129626404001714","date_updated":"2022-01-06T06:52:52Z","author":[{"first_name":"Robert","full_name":"Elsässer, Robert","last_name":"Elsässer"},{"first_name":"Burkhard","last_name":"Monien","full_name":"Monien, Burkhard"},{"last_name":"Preis","full_name":"Preis, Robert","first_name":"Robert"},{"first_name":"Andreas","full_name":"Frommer, Andreas","last_name":"Frommer"}],"date_created":"2020-04-16T05:46:56Z","year":"2004","citation":{"apa":"Elsässer, R., Monien, B., Preis, R., &#38; Frommer, A. (2004). Optimal Diffusion Schemes and Load Balancing on Product Graphs. <i>Parallel Processing Letters</i>, 61–73. <a href=\"https://doi.org/10.1142/s0129626404001714\">https://doi.org/10.1142/s0129626404001714</a>","bibtex":"@article{Elsässer_Monien_Preis_Frommer_2004, title={Optimal Diffusion Schemes and Load Balancing on Product Graphs}, DOI={<a href=\"https://doi.org/10.1142/s0129626404001714\">10.1142/s0129626404001714</a>}, journal={Parallel Processing Letters}, author={Elsässer, Robert and Monien, Burkhard and Preis, Robert and Frommer, Andreas}, year={2004}, pages={61–73} }","mla":"Elsässer, Robert, et al. “Optimal Diffusion Schemes and Load Balancing on Product Graphs.” <i>Parallel Processing Letters</i>, 2004, pp. 61–73, doi:<a href=\"https://doi.org/10.1142/s0129626404001714\">10.1142/s0129626404001714</a>.","short":"R. Elsässer, B. Monien, R. Preis, A. Frommer, Parallel Processing Letters (2004) 61–73.","ieee":"R. Elsässer, B. Monien, R. Preis, and A. Frommer, “Optimal Diffusion Schemes and Load Balancing on Product Graphs,” <i>Parallel Processing Letters</i>, pp. 61–73, 2004.","chicago":"Elsässer, Robert, Burkhard Monien, Robert Preis, and Andreas Frommer. “Optimal Diffusion Schemes and Load Balancing on Product Graphs.” <i>Parallel Processing Letters</i>, 2004, 61–73. <a href=\"https://doi.org/10.1142/s0129626404001714\">https://doi.org/10.1142/s0129626404001714</a>.","ama":"Elsässer R, Monien B, Preis R, Frommer A. Optimal Diffusion Schemes and Load Balancing on Product Graphs. <i>Parallel Processing Letters</i>. 2004:61-73. doi:<a href=\"https://doi.org/10.1142/s0129626404001714\">10.1142/s0129626404001714</a>"},"page":"61-73","publication_status":"published","publication_identifier":{"issn":["0129-6264","1793-642X"]}},{"publication":"ESAIM: Control, Optimisation and Calculus of Variations","type":"journal_article","status":"public","_id":"16619","department":[{"_id":"101"}],"user_id":"15701","publication_identifier":{"issn":["1292-8119","1262-3377"]},"publication_status":"published","year":"2004","page":"259-270","citation":{"apa":"Junge, O., &#38; Osinga, H. M. (2004). A set oriented approach to global optimal control. <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, 259–270. <a href=\"https://doi.org/10.1051/cocv:2004006\">https://doi.org/10.1051/cocv:2004006</a>","mla":"Junge, Oliver, and Hinke M. Osinga. “A Set Oriented Approach to Global Optimal Control.” <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, 2004, pp. 259–70, doi:<a href=\"https://doi.org/10.1051/cocv:2004006\">10.1051/cocv:2004006</a>.","short":"O. Junge, H.M. Osinga, ESAIM: Control, Optimisation and Calculus of Variations (2004) 259–270.","bibtex":"@article{Junge_Osinga_2004, title={A set oriented approach to global optimal control}, DOI={<a href=\"https://doi.org/10.1051/cocv:2004006\">10.1051/cocv:2004006</a>}, journal={ESAIM: Control, Optimisation and Calculus of Variations}, author={Junge, Oliver and Osinga, Hinke M.}, year={2004}, pages={259–270} }","ama":"Junge O, Osinga HM. A set oriented approach to global optimal control. <i>ESAIM: Control, Optimisation and Calculus of Variations</i>. 2004:259-270. doi:<a href=\"https://doi.org/10.1051/cocv:2004006\">10.1051/cocv:2004006</a>","ieee":"O. Junge and H. M. Osinga, “A set oriented approach to global optimal control,” <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, pp. 259–270, 2004.","chicago":"Junge, Oliver, and Hinke M. Osinga. “A Set Oriented Approach to Global Optimal Control.” <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, 2004, 259–70. <a href=\"https://doi.org/10.1051/cocv:2004006\">https://doi.org/10.1051/cocv:2004006</a>."},"date_updated":"2022-01-06T06:52:53Z","author":[{"full_name":"Junge, Oliver","last_name":"Junge","first_name":"Oliver"},{"first_name":"Hinke M.","last_name":"Osinga","full_name":"Osinga, Hinke M."}],"date_created":"2020-04-16T08:11:16Z","title":"A set oriented approach to global optimal control","doi":"10.1051/cocv:2004006"},{"type":"conference","publication":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","status":"public","_id":"16620","user_id":"15701","department":[{"_id":"101"}],"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"isbn":["0780386825"]},"year":"2004","citation":{"mla":"Junge, O., et al. “Uncertainty in the Dynamics of Conservative Maps.” <i>2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)</i>, 2004, doi:<a href=\"https://doi.org/10.1109/cdc.2004.1430379\">10.1109/cdc.2004.1430379</a>.","bibtex":"@inproceedings{Junge_Marsden_Mezic_2004, title={Uncertainty in the dynamics of conservative maps}, DOI={<a href=\"https://doi.org/10.1109/cdc.2004.1430379\">10.1109/cdc.2004.1430379</a>}, booktitle={2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)}, author={Junge, O. and Marsden, J.E. and Mezic, I.}, year={2004} }","short":"O. Junge, J.E. Marsden, I. Mezic, in: 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. 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