@article{16527, author = {{Day, S. and Junge, O. and Mischaikow, K.}}, issn = {{1536-0040}}, journal = {{SIAM Journal on Applied Dynamical Systems}}, pages = {{117--160}}, title = {{{A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems}}}, doi = {{10.1137/030600210}}, year = {{2004}}, } @article{16587, abstract = {{ 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 l2 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. }}, author = {{Elsässer, Robert and Monien, Burkhard and Preis, Robert and Frommer, Andreas}}, issn = {{0129-6264}}, journal = {{Parallel Processing Letters}}, pages = {{61--73}}, title = {{{Optimal Diffusion Schemes and Load Balancing on Product Graphs}}}, doi = {{10.1142/s0129626404001714}}, year = {{2004}}, } @article{16619, author = {{Junge, Oliver and Osinga, Hinke M.}}, issn = {{1292-8119}}, journal = {{ESAIM: Control, Optimisation and Calculus of Variations}}, pages = {{259--270}}, title = {{{A set oriented approach to global optimal control}}}, doi = {{10.1051/cocv:2004006}}, year = {{2004}}, } @inproceedings{16620, author = {{Junge, O. and Marsden, J.E. and Mezic, I.}}, booktitle = {{2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)}}, isbn = {{0780386825}}, title = {{{Uncertainty in the dynamics of conservative maps}}}, doi = {{10.1109/cdc.2004.1430379}}, year = {{2004}}, } @article{16498, author = {{Aston, P. J. and Dellnitz, M.}}, issn = {{1364-5021}}, journal = {{Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences}}, pages = {{2933--2955}}, title = {{{Computation of the dominant Lyapunov exponent via spatial integration using matrix norms}}}, doi = {{10.1098/rspa.2003.1143}}, year = {{2003}}, } @inbook{16543, author = {{Dellnitz, Michael and Preis, Robert}}, booktitle = {{Lecture Notes in Computer Science}}, isbn = {{9783540405542}}, issn = {{0302-9743}}, title = {{{Congestion and Almost Invariant Sets in Dynamical Systems}}}, doi = {{10.1007/3-540-45084-x_8}}, year = {{2003}}, } @article{16600, author = {{Froyland, Gary and Dellnitz, Michael}}, issn = {{1064-8275}}, journal = {{SIAM Journal on Scientific Computing}}, pages = {{1839--1863}}, title = {{{Detecting and Locating Near-Optimal Almost-Invariant Sets and Cycles}}}, doi = {{10.1137/s106482750238911x}}, year = {{2003}}, } @inbook{16664, author = {{Schütze, Oliver}}, booktitle = {{Lecture Notes in Computer Science}}, isbn = {{9783540018698}}, issn = {{0302-9743}}, title = {{{A New Data Structure for the Nondominance Problem in Multi-objective Optimization}}}, doi = {{10.1007/3-540-36970-8_36}}, year = {{2003}}, } @inbook{16665, author = {{Schütze, Oliver and Mostaghim, Sanaz and Dellnitz, Michael and Teich, Jürgen}}, booktitle = {{Lecture Notes in Computer Science}}, isbn = {{9783540018698}}, issn = {{0302-9743}}, title = {{{Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques}}}, doi = {{10.1007/3-540-36970-8_9}}, year = {{2003}}, } @article{34896, abstract = {{We apply class field theory to the computation of the minimal discriminants for certain solvable groups. In particular, we apply our techniques to small Frobenius groups and all imprimitive degree 8 groups such that the corresponding fields have only a degree 2 and no degree 4 subfield.}}, author = {{Fieker, Claus and Klüners, Jürgen}}, issn = {{0022-314X}}, journal = {{Journal of Number Theory}}, keywords = {{Algebra and Number Theory}}, number = {{2}}, pages = {{318--337}}, publisher = {{Elsevier BV}}, title = {{{Minimal discriminants for fields with small Frobenius groups as Galois groups}}}, doi = {{10.1016/s0022-314x(02)00071-9}}, volume = {{99}}, year = {{2003}}, } @inbook{16538, author = {{Dellnitz, Michael and Junge, Oliver}}, booktitle = {{Handbook of Dynamical Systems}}, isbn = {{9780444501684}}, issn = {{1874-575X}}, title = {{{Set Oriented Numerical Methods for Dynamical Systems}}}, doi = {{10.1016/s1874-575x(02)80026-1}}, year = {{2002}}, } @article{16556, author = {{Dellnitz, M.}}, issn = {{0272-4979}}, journal = {{IMA Journal of Numerical Analysis}}, pages = {{167--185}}, title = {{{Finding zeros by multilevel subdivision techniques}}}, doi = {{10.1093/imanum/22.2.167}}, year = {{2002}}, } @article{16586, author = {{Elsässer, Robert and Monien, Burkhard and Preis, Robert}}, issn = {{1432-4350}}, journal = {{Theory of Computing Systems}}, pages = {{305--320}}, title = {{{Diffusion Schemes for Load Balancing on Heterogeneous Networks}}}, doi = {{10.1007/s00224-002-1056-4}}, year = {{2002}}, } @article{35954, abstract = {{Let {\ASIE K}\,/{\small \ℚ}({\ASIE t \!}) be a finite extension. We describe algorithms for computing subfields and automorphisms of {\ASIE K}\,/{\small \ℚ}({\ASIE t }\!). As an application we give an algorithm for finding decompositions of rational functions in {\small \ℚ(α)}. We also present an algorithm which decides if an extension {\ASIE L}\,/{\small \ℚ}({\ASIE t \!}) is a subfield of {\ASIE K}. In case [{\ASIE K : \;}{\small\ℚ}({\ASIE t \!})] = [{\ASIE L : \;}{\small \ℚ}({\ASIE t \!})] we obtain a {\small \ℚ}({\ASIE t \!})-isomorphism test. Furthermore, we describe an algorithm which computes subfields of the normal closure of {\ASIE K}\,/{\small \ℚ}({\ASIE t \!}).}}, author = {{Klüners, Jürgen}}, journal = {{Experiment. Math. }}, keywords = {{algorithms, decompositions, Galois groups, subfields}}, number = {{2}}, pages = {{171--181}}, publisher = {{Elsevier BV}}, title = {{{Algorithms for function fields}}}, volume = {{11}}, year = {{2002}}, } @inbook{16555, author = {{Dellnitz, Michael and Froyland, Gary and Junge, Oliver}}, booktitle = {{Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems}}, isbn = {{9783642625244}}, title = {{{The Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical Systems}}}, doi = {{10.1007/978-3-642-56589-2_7}}, year = {{2001}}, } @inbook{16598, author = {{Froyland, Gary}}, booktitle = {{Nonlinear Dynamics and Statistics}}, isbn = {{9781461266488}}, title = {{{Extracting Dynamical Behavior via Markov Models}}}, doi = {{10.1007/978-1-4612-0177-9_12}}, year = {{2001}}, } @article{16601, author = {{Froyland, Gary and Junge, Oliver and Ochs, Gunter}}, issn = {{0167-2789}}, journal = {{Physica D: Nonlinear Phenomena}}, pages = {{68--84}}, title = {{{Rigorous computation of topological entropy with respect to a finite partition}}}, doi = {{10.1016/s0167-2789(01)00216-0}}, year = {{2001}}, } @article{16617, author = {{Junge, Oliver}}, issn = {{1468-9367}}, journal = {{Dynamical Systems}}, pages = {{213--222}}, title = {{{An adaptive subdivision technique for the approximation of attractors and invariant measures: proof of convergence}}}, doi = {{10.1080/14689360109696233}}, year = {{2001}}, } @article{34897, abstract = {{This paper announces the creation of a database for number fields. It describes the contents and the methods of access, indicates the origin of the polynomials, and formulates the aims of this collection of fields.}}, author = {{Klüners, Jürgen and Malle, Gunter}}, issn = {{1461-1570}}, journal = {{LMS Journal of Computation and Mathematics}}, keywords = {{Computational Theory and Mathematics, General Mathematics}}, pages = {{182--196}}, publisher = {{Wiley}}, title = {{{A Database for Field Extensions of the Rationals}}}, doi = {{10.1112/s1461157000000851}}, volume = {{4}}, year = {{2001}}, } @inbook{16513, author = {{Aston, P. J. and Dellnitz, M.}}, booktitle = {{Equadiff 99}}, isbn = {{9789810243593}}, title = {{{The Computation of Lyapunov Exponents via Spatial Integration Using Vector Norms}}}, doi = {{10.1142/9789812792617_0196}}, year = {{2000}}, }