[{"language":[{"iso":"eng"}],"_id":"53304","user_id":"56070","department":[{"_id":"263"}],"status":"public","type":"conference","publication":"ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","title":"Rademacher Complexity Regularization for Correlation-Based Multiview Representation Learning","doi":"10.1109/icassp48485.2024.10446173","date_updated":"2024-04-05T14:50:14Z","publisher":"IEEE","date_created":"2024-04-05T14:40:34Z","author":[{"first_name":"Maurice","full_name":"Kuschel, Maurice","id":"56070","last_name":"Kuschel"},{"first_name":"Tanuj","full_name":"Hasija, Tanuj","id":"43497","last_name":"Hasija"},{"last_name":"Marrinan","full_name":"Marrinan, Timothy","first_name":"Timothy"}],"year":"2024","citation":{"short":"M. Kuschel, T. Hasija, T. Marrinan, in: ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, 2024.","mla":"Kuschel, Maurice, et al. “Rademacher Complexity Regularization for Correlation-Based Multiview Representation Learning.” <i>ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)</i>, IEEE, 2024, doi:<a href=\"https://doi.org/10.1109/icassp48485.2024.10446173\">10.1109/icassp48485.2024.10446173</a>.","bibtex":"@inproceedings{Kuschel_Hasija_Marrinan_2024, title={Rademacher Complexity Regularization for Correlation-Based Multiview Representation Learning}, DOI={<a href=\"https://doi.org/10.1109/icassp48485.2024.10446173\">10.1109/icassp48485.2024.10446173</a>}, booktitle={ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, publisher={IEEE}, author={Kuschel, Maurice and Hasija, Tanuj and Marrinan, Timothy}, year={2024} }","apa":"Kuschel, M., Hasija, T., &#38; Marrinan, T. (2024). Rademacher Complexity Regularization for Correlation-Based Multiview Representation Learning. <i>ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)</i>. <a href=\"https://doi.org/10.1109/icassp48485.2024.10446173\">https://doi.org/10.1109/icassp48485.2024.10446173</a>","ieee":"M. Kuschel, T. Hasija, and T. Marrinan, “Rademacher Complexity Regularization for Correlation-Based Multiview Representation Learning,” 2024, doi: <a href=\"https://doi.org/10.1109/icassp48485.2024.10446173\">10.1109/icassp48485.2024.10446173</a>.","chicago":"Kuschel, Maurice, Tanuj Hasija, and Timothy Marrinan. “Rademacher Complexity Regularization for Correlation-Based Multiview Representation Learning.” In <i>ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)</i>. IEEE, 2024. <a href=\"https://doi.org/10.1109/icassp48485.2024.10446173\">https://doi.org/10.1109/icassp48485.2024.10446173</a>.","ama":"Kuschel M, Hasija T, Marrinan T. Rademacher Complexity Regularization for Correlation-Based Multiview Representation Learning. In: <i>ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)</i>. IEEE; 2024. doi:<a href=\"https://doi.org/10.1109/icassp48485.2024.10446173\">10.1109/icassp48485.2024.10446173</a>"},"publication_status":"published"},{"doi":"10.1007/s00028-024-00954-x","title":"A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects","date_created":"2024-04-07T12:29:25Z","author":[{"last_name":"Stinner","full_name":"Stinner, Christian","first_name":"Christian"},{"first_name":"Michael","full_name":"Winkler, Michael","last_name":"Winkler"}],"volume":24,"date_updated":"2024-04-07T12:36:21Z","publisher":"Springer Science and Business Media LLC","citation":{"short":"C. Stinner, M. Winkler, Journal of Evolution Equations 24 (2024).","mla":"Stinner, Christian, and Michael Winkler. “A Critical Exponent in a Quasilinear Keller–Segel System with Arbitrarily Fast Decaying Diffusivities Accounting for Volume-Filling Effects.” <i>Journal of Evolution Equations</i>, vol. 24, no. 2, 26, Springer Science and Business Media LLC, 2024, doi:<a href=\"https://doi.org/10.1007/s00028-024-00954-x\">10.1007/s00028-024-00954-x</a>.","bibtex":"@article{Stinner_Winkler_2024, title={A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects}, volume={24}, DOI={<a href=\"https://doi.org/10.1007/s00028-024-00954-x\">10.1007/s00028-024-00954-x</a>}, number={226}, journal={Journal of Evolution Equations}, publisher={Springer Science and Business Media LLC}, author={Stinner, Christian and Winkler, Michael}, year={2024} }","apa":"Stinner, C., &#38; Winkler, M. (2024). A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects. <i>Journal of Evolution Equations</i>, <i>24</i>(2), Article 26. <a href=\"https://doi.org/10.1007/s00028-024-00954-x\">https://doi.org/10.1007/s00028-024-00954-x</a>","ieee":"C. Stinner and M. Winkler, “A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects,” <i>Journal of Evolution Equations</i>, vol. 24, no. 2, Art. no. 26, 2024, doi: <a href=\"https://doi.org/10.1007/s00028-024-00954-x\">10.1007/s00028-024-00954-x</a>.","chicago":"Stinner, Christian, and Michael Winkler. “A Critical Exponent in a Quasilinear Keller–Segel System with Arbitrarily Fast Decaying Diffusivities Accounting for Volume-Filling Effects.” <i>Journal of Evolution Equations</i> 24, no. 2 (2024). <a href=\"https://doi.org/10.1007/s00028-024-00954-x\">https://doi.org/10.1007/s00028-024-00954-x</a>.","ama":"Stinner C, Winkler M. A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects. <i>Journal of Evolution Equations</i>. 2024;24(2). doi:<a href=\"https://doi.org/10.1007/s00028-024-00954-x\">10.1007/s00028-024-00954-x</a>"},"intvolume":"        24","year":"2024","issue":"2","publication_status":"published","publication_identifier":{"issn":["1424-3199","1424-3202"]},"language":[{"iso":"eng"}],"article_number":"26","keyword":["Mathematics (miscellaneous)"],"user_id":"31496","_id":"53316","status":"public","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>The quasilinear Keller–Segel system <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned} \\left\\{ \\begin{array}{l} u_t=\\nabla \\cdot (D(u)\\nabla u) - \\nabla \\cdot (S(u)\\nabla v), \\\\ v_t=\\Delta v-v+u, \\end{array}\\right. \\end{aligned}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mtable>\r\n                      <mml:mtr>\r\n                        <mml:mtd>\r\n                          <mml:mfenced>\r\n                            <mml:mrow>\r\n                              <mml:mtable>\r\n                                <mml:mtr>\r\n                                  <mml:mtd>\r\n                                    <mml:mrow>\r\n                                      <mml:msub>\r\n                                        <mml:mi>u</mml:mi>\r\n                                        <mml:mi>t</mml:mi>\r\n                                      </mml:msub>\r\n                                      <mml:mo>=</mml:mo>\r\n                                      <mml:mi>∇</mml:mi>\r\n                                      <mml:mo>·</mml:mo>\r\n                                      <mml:mrow>\r\n                                        <mml:mo>(</mml:mo>\r\n                                        <mml:mi>D</mml:mi>\r\n                                        <mml:mrow>\r\n                                          <mml:mo>(</mml:mo>\r\n                                          <mml:mi>u</mml:mi>\r\n                                          <mml:mo>)</mml:mo>\r\n                                        </mml:mrow>\r\n                                        <mml:mi>∇</mml:mi>\r\n                                        <mml:mi>u</mml:mi>\r\n                                        <mml:mo>)</mml:mo>\r\n                                      </mml:mrow>\r\n                                      <mml:mo>-</mml:mo>\r\n                                      <mml:mi>∇</mml:mi>\r\n                                      <mml:mo>·</mml:mo>\r\n                                      <mml:mrow>\r\n                                        <mml:mo>(</mml:mo>\r\n                                        <mml:mi>S</mml:mi>\r\n                                        <mml:mrow>\r\n                                          <mml:mo>(</mml:mo>\r\n                                          <mml:mi>u</mml:mi>\r\n                                          <mml:mo>)</mml:mo>\r\n                                        </mml:mrow>\r\n                                        <mml:mi>∇</mml:mi>\r\n                                        <mml:mi>v</mml:mi>\r\n                                        <mml:mo>)</mml:mo>\r\n                                      </mml:mrow>\r\n                                      <mml:mo>,</mml:mo>\r\n                                    </mml:mrow>\r\n                                  </mml:mtd>\r\n                                </mml:mtr>\r\n                                <mml:mtr>\r\n                                  <mml:mtd>\r\n                                    <mml:mrow>\r\n                                      <mml:mrow />\r\n                                      <mml:msub>\r\n                                        <mml:mi>v</mml:mi>\r\n                                        <mml:mi>t</mml:mi>\r\n                                      </mml:msub>\r\n                                      <mml:mo>=</mml:mo>\r\n                                      <mml:mi>Δ</mml:mi>\r\n                                      <mml:mi>v</mml:mi>\r\n                                      <mml:mo>-</mml:mo>\r\n                                      <mml:mi>v</mml:mi>\r\n                                      <mml:mo>+</mml:mo>\r\n                                      <mml:mi>u</mml:mi>\r\n                                      <mml:mo>,</mml:mo>\r\n                                    </mml:mrow>\r\n                                  </mml:mtd>\r\n                                </mml:mtr>\r\n                              </mml:mtable>\r\n                            </mml:mrow>\r\n                          </mml:mfenced>\r\n                        </mml:mtd>\r\n                      </mml:mtr>\r\n                    </mml:mtable>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:disp-formula>endowed with homogeneous Neumann boundary conditions is considered in a bounded domain <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Omega \\subset {\\mathbb {R}}^n$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>Ω</mml:mi>\r\n                    <mml:mo>⊂</mml:mo>\r\n                    <mml:msup>\r\n                      <mml:mrow>\r\n                        <mml:mi>R</mml:mi>\r\n                      </mml:mrow>\r\n                      <mml:mi>n</mml:mi>\r\n                    </mml:msup>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, <jats:inline-formula><jats:alternatives><jats:tex-math>$$n \\ge 3$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>n</mml:mi>\r\n                    <mml:mo>≥</mml:mo>\r\n                    <mml:mn>3</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, with smooth boundary for sufficiently regular functions <jats:italic>D</jats:italic> and <jats:italic>S</jats:italic> satisfying <jats:inline-formula><jats:alternatives><jats:tex-math>$$D&gt;0$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>D</mml:mi>\r\n                    <mml:mo>&gt;</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> on <jats:inline-formula><jats:alternatives><jats:tex-math>$$[0,\\infty )$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mo>[</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                    <mml:mo>,</mml:mo>\r\n                    <mml:mi>∞</mml:mi>\r\n                    <mml:mo>)</mml:mo>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, <jats:inline-formula><jats:alternatives><jats:tex-math>$$S&gt;0$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>S</mml:mi>\r\n                    <mml:mo>&gt;</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> on <jats:inline-formula><jats:alternatives><jats:tex-math>$$(0,\\infty )$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mo>(</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                    <mml:mo>,</mml:mo>\r\n                    <mml:mi>∞</mml:mi>\r\n                    <mml:mo>)</mml:mo>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$S(0)=0$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>S</mml:mi>\r\n                    <mml:mo>(</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                    <mml:mo>)</mml:mo>\r\n                    <mml:mo>=</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>. On the one hand, it is shown that if <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\frac{S}{D}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mfrac>\r\n                    <mml:mi>S</mml:mi>\r\n                    <mml:mi>D</mml:mi>\r\n                  </mml:mfrac>\r\n                </mml:math></jats:alternatives></jats:inline-formula> satisfies the subcritical growth condition <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned} \\frac{S(s)}{D(s)} \\le C s^\\alpha \\qquad \\text{ for } \\text{ all } s\\ge 1 \\qquad \\text{ with } \\text{ some } \\alpha &lt; \\frac{2}{n} \\end{aligned}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mtable>\r\n                      <mml:mtr>\r\n                        <mml:mtd>\r\n                          <mml:mrow>\r\n                            <mml:mfrac>\r\n                              <mml:mrow>\r\n                                <mml:mi>S</mml:mi>\r\n                                <mml:mo>(</mml:mo>\r\n                                <mml:mi>s</mml:mi>\r\n                                <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n                              <mml:mrow>\r\n                                <mml:mi>D</mml:mi>\r\n                                <mml:mo>(</mml:mo>\r\n                                <mml:mi>s</mml:mi>\r\n                                <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n                            </mml:mfrac>\r\n                            <mml:mo>≤</mml:mo>\r\n                            <mml:mi>C</mml:mi>\r\n                            <mml:msup>\r\n                              <mml:mi>s</mml:mi>\r\n                              <mml:mi>α</mml:mi>\r\n                            </mml:msup>\r\n                            <mml:mspace />\r\n                            <mml:mspace />\r\n                            <mml:mtext>for</mml:mtext>\r\n                            <mml:mspace />\r\n                            <mml:mspace />\r\n                            <mml:mtext>all</mml:mtext>\r\n                            <mml:mspace />\r\n                            <mml:mi>s</mml:mi>\r\n                            <mml:mo>≥</mml:mo>\r\n                            <mml:mn>1</mml:mn>\r\n                            <mml:mspace />\r\n                            <mml:mspace />\r\n                            <mml:mtext>with</mml:mtext>\r\n                            <mml:mspace />\r\n                            <mml:mspace />\r\n                            <mml:mtext>some</mml:mtext>\r\n                            <mml:mspace />\r\n                            <mml:mi>α</mml:mi>\r\n                            <mml:mo>&lt;</mml:mo>\r\n                            <mml:mfrac>\r\n                              <mml:mn>2</mml:mn>\r\n                              <mml:mi>n</mml:mi>\r\n                            </mml:mfrac>\r\n                          </mml:mrow>\r\n                        </mml:mtd>\r\n                      </mml:mtr>\r\n                    </mml:mtable>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:disp-formula>and <jats:inline-formula><jats:alternatives><jats:tex-math>$$C&gt;0$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>C</mml:mi>\r\n                    <mml:mo>&gt;</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, then for any sufficiently regular initial data there exists a global weak energy solution such that <jats:inline-formula><jats:alternatives><jats:tex-math>$${ \\mathrm{{ess}}} \\sup _{t&gt;0} \\Vert u(t) \\Vert _{L^p(\\Omega )}&lt;\\infty $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>ess</mml:mi>\r\n                    <mml:msub>\r\n                      <mml:mo>sup</mml:mo>\r\n                      <mml:mrow>\r\n                        <mml:mi>t</mml:mi>\r\n                        <mml:mo>&gt;</mml:mo>\r\n                        <mml:mn>0</mml:mn>\r\n                      </mml:mrow>\r\n                    </mml:msub>\r\n                    <mml:msub>\r\n                      <mml:mrow>\r\n                        <mml:mo>‖</mml:mo>\r\n                        <mml:mi>u</mml:mi>\r\n                        <mml:mrow>\r\n                          <mml:mo>(</mml:mo>\r\n                          <mml:mi>t</mml:mi>\r\n                          <mml:mo>)</mml:mo>\r\n                        </mml:mrow>\r\n                        <mml:mo>‖</mml:mo>\r\n                      </mml:mrow>\r\n                      <mml:mrow>\r\n                        <mml:msup>\r\n                          <mml:mi>L</mml:mi>\r\n                          <mml:mi>p</mml:mi>\r\n                        </mml:msup>\r\n                        <mml:mrow>\r\n                          <mml:mo>(</mml:mo>\r\n                          <mml:mi>Ω</mml:mi>\r\n                          <mml:mo>)</mml:mo>\r\n                        </mml:mrow>\r\n                      </mml:mrow>\r\n                    </mml:msub>\r\n                    <mml:mo>&lt;</mml:mo>\r\n                    <mml:mi>∞</mml:mi>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> for some <jats:inline-formula><jats:alternatives><jats:tex-math>$$p &gt; \\frac{2n}{n+2}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>p</mml:mi>\r\n                    <mml:mo>&gt;</mml:mo>\r\n                    <mml:mfrac>\r\n                      <mml:mrow>\r\n                        <mml:mn>2</mml:mn>\r\n                        <mml:mi>n</mml:mi>\r\n                      </mml:mrow>\r\n                      <mml:mrow>\r\n                        <mml:mi>n</mml:mi>\r\n                        <mml:mo>+</mml:mo>\r\n                        <mml:mn>2</mml:mn>\r\n                      </mml:mrow>\r\n                    </mml:mfrac>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>. On the other hand, if <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\frac{S}{D}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mfrac>\r\n                    <mml:mi>S</mml:mi>\r\n                    <mml:mi>D</mml:mi>\r\n                  </mml:mfrac>\r\n                </mml:math></jats:alternatives></jats:inline-formula> satisfies the supercritical growth condition <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned} \\frac{S(s)}{D(s)} \\ge c s^\\alpha \\qquad \\text{ for } \\text{ all } s\\ge 1 \\qquad \\text{ with } \\text{ some } \\alpha &gt; \\frac{2}{n} \\end{aligned}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mtable>\r\n                      <mml:mtr>\r\n                        <mml:mtd>\r\n                          <mml:mrow>\r\n                            <mml:mfrac>\r\n                              <mml:mrow>\r\n                                <mml:mi>S</mml:mi>\r\n                                <mml:mo>(</mml:mo>\r\n                                <mml:mi>s</mml:mi>\r\n                                <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n                              <mml:mrow>\r\n                                <mml:mi>D</mml:mi>\r\n                                <mml:mo>(</mml:mo>\r\n                                <mml:mi>s</mml:mi>\r\n                                <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n                            </mml:mfrac>\r\n                            <mml:mo>≥</mml:mo>\r\n                            <mml:mi>c</mml:mi>\r\n                            <mml:msup>\r\n                              <mml:mi>s</mml:mi>\r\n                              <mml:mi>α</mml:mi>\r\n                            </mml:msup>\r\n                            <mml:mspace />\r\n                            <mml:mspace />\r\n                            <mml:mtext>for</mml:mtext>\r\n                            <mml:mspace />\r\n                            <mml:mspace />\r\n                            <mml:mtext>all</mml:mtext>\r\n                            <mml:mspace />\r\n                            <mml:mi>s</mml:mi>\r\n                            <mml:mo>≥</mml:mo>\r\n                            <mml:mn>1</mml:mn>\r\n                            <mml:mspace />\r\n                            <mml:mspace />\r\n                            <mml:mtext>with</mml:mtext>\r\n                            <mml:mspace />\r\n                            <mml:mspace />\r\n                            <mml:mtext>some</mml:mtext>\r\n                            <mml:mspace />\r\n                            <mml:mi>α</mml:mi>\r\n                            <mml:mo>&gt;</mml:mo>\r\n                            <mml:mfrac>\r\n                              <mml:mn>2</mml:mn>\r\n                              <mml:mi>n</mml:mi>\r\n                            </mml:mfrac>\r\n                          </mml:mrow>\r\n                        </mml:mtd>\r\n                      </mml:mtr>\r\n                    </mml:mtable>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:disp-formula>and <jats:inline-formula><jats:alternatives><jats:tex-math>$$c&gt;0$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>c</mml:mi>\r\n                    <mml:mo>&gt;</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, then the nonexistence of a global weak energy solution having the boundedness property stated above is shown for some initial data in the radial setting. This establishes some criticality of the value <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha = \\frac{2}{n}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>α</mml:mi>\r\n                    <mml:mo>=</mml:mo>\r\n                    <mml:mfrac>\r\n                      <mml:mn>2</mml:mn>\r\n                      <mml:mi>n</mml:mi>\r\n                    </mml:mfrac>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> for <jats:inline-formula><jats:alternatives><jats:tex-math>$$n \\ge 3$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>n</mml:mi>\r\n                    <mml:mo>≥</mml:mo>\r\n                    <mml:mn>3</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, without any additional assumption on the behavior of <jats:italic>D</jats:italic>(<jats:italic>s</jats:italic>) as <jats:inline-formula><jats:alternatives><jats:tex-math>$$s \\rightarrow \\infty $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>s</mml:mi>\r\n                    <mml:mo>→</mml:mo>\r\n                    <mml:mi>∞</mml:mi>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, in particular without requiring any algebraic lower bound for <jats:italic>D</jats:italic>. When applied to the Keller–Segel system with volume-filling effect for probability distribution functions of the type <jats:inline-formula><jats:alternatives><jats:tex-math>$$Q(s) = \\exp (-s^\\beta )$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>Q</mml:mi>\r\n                    <mml:mrow>\r\n                      <mml:mo>(</mml:mo>\r\n                      <mml:mi>s</mml:mi>\r\n                      <mml:mo>)</mml:mo>\r\n                    </mml:mrow>\r\n                    <mml:mo>=</mml:mo>\r\n                    <mml:mo>exp</mml:mo>\r\n                    <mml:mrow>\r\n                      <mml:mo>(</mml:mo>\r\n                      <mml:mo>-</mml:mo>\r\n                      <mml:msup>\r\n                        <mml:mi>s</mml:mi>\r\n                        <mml:mi>β</mml:mi>\r\n                      </mml:msup>\r\n                      <mml:mo>)</mml:mo>\r\n                    </mml:mrow>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, <jats:inline-formula><jats:alternatives><jats:tex-math>$$s \\ge 0$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>s</mml:mi>\r\n                    <mml:mo>≥</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, for global solvability the exponent <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\beta = \\frac{n-2}{n}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>β</mml:mi>\r\n                    <mml:mo>=</mml:mo>\r\n                    <mml:mfrac>\r\n                      <mml:mrow>\r\n                        <mml:mi>n</mml:mi>\r\n                        <mml:mo>-</mml:mo>\r\n                        <mml:mn>2</mml:mn>\r\n                      </mml:mrow>\r\n                      <mml:mi>n</mml:mi>\r\n                    </mml:mfrac>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> is seen to be critical.\r\n</jats:p>","lang":"eng"}],"type":"journal_article","publication":"Journal of Evolution Equations"},{"status":"public","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>In a smoothly bounded two‐dimensional domain  and for a given nondecreasing positive unbounded , for each  and  the inequality\r\n<jats:disp-formula />is shown to hold for any positive  fulfilling\r\n<jats:disp-formula />This is thereafter applied to nonglobal solutions of the Keller–Segel system coupled to the incompressible Navier–Stokes equations through transport and buoyancy, and it is seen that in any such blow‐up event the corresponding population density cannot remain uniformly integrable over  near its explosion time.</jats:p>"}],"publication":"Journal of the London Mathematical Society","type":"journal_article","language":[{"iso":"eng"}],"keyword":["General Mathematics"],"user_id":"31496","_id":"53315","intvolume":"       109","citation":{"short":"Y. Wang, M. Winkler, Journal of the London Mathematical Society 109 (2024).","bibtex":"@article{Wang_Winkler_2024, title={An interpolation inequality involving $L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system}, volume={109}, DOI={<a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>}, number={3}, journal={Journal of the London Mathematical Society}, publisher={Wiley}, author={Wang, Yulan and Winkler, Michael}, year={2024} }","mla":"Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving $L\\log L$ Spaces and Application to the Characterization of Blow‐up Behavior in a Two‐dimensional Keller–Segel–Navier–Stokes System.” <i>Journal of the London Mathematical Society</i>, vol. 109, no. 3, Wiley, 2024, doi:<a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>.","apa":"Wang, Y., &#38; Winkler, M. (2024). An interpolation inequality involving $L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system. <i>Journal of the London Mathematical Society</i>, <i>109</i>(3). <a href=\"https://doi.org/10.1112/jlms.12885\">https://doi.org/10.1112/jlms.12885</a>","ieee":"Y. Wang and M. Winkler, “An interpolation inequality involving $L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system,” <i>Journal of the London Mathematical Society</i>, vol. 109, no. 3, 2024, doi: <a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>.","chicago":"Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving $L\\log L$ Spaces and Application to the Characterization of Blow‐up Behavior in a Two‐dimensional Keller–Segel–Navier–Stokes System.” <i>Journal of the London Mathematical Society</i> 109, no. 3 (2024). <a href=\"https://doi.org/10.1112/jlms.12885\">https://doi.org/10.1112/jlms.12885</a>.","ama":"Wang Y, Winkler M. An interpolation inequality involving $L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system. <i>Journal of the London Mathematical Society</i>. 2024;109(3). doi:<a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>"},"year":"2024","issue":"3","publication_identifier":{"issn":["0024-6107","1469-7750"]},"publication_status":"published","doi":"10.1112/jlms.12885","title":"An interpolation inequality involving $L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system","volume":109,"author":[{"first_name":"Yulan","full_name":"Wang, Yulan","last_name":"Wang"},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"date_created":"2024-04-07T12:27:28Z","date_updated":"2024-04-07T12:36:25Z","publisher":"Wiley"},{"status":"public","type":"journal_article","publication":"Mitteilungen des Instituts für Europäische Kulturgeschichte","language":[{"iso":"eng"}],"user_id":"42693","_id":"53375","citation":{"apa":"Voß, F. (2024). Rezension zu Anna-Victoria Bognár: Der Architekt in der Frühen Neuzeit. Ausbildung, Karrierewege, Berufsfelder (=Höfische Kultur interdisziplinär. Schriften und Materialien des Rudolfstädter Arbeitskreises. 2). Heidelberg 2020. <i>Mitteilungen Des Instituts Für Europäische Kulturgeschichte</i>.","short":"F. Voß, Mitteilungen Des Instituts Für Europäische Kulturgeschichte (2024).","mla":"Voß, Fabian. “Rezension Zu Anna-Victoria Bognár: Der Architekt in Der Frühen Neuzeit. Ausbildung, Karrierewege, Berufsfelder (=Höfische Kultur Interdisziplinär. Schriften Und Materialien Des Rudolfstädter Arbeitskreises. 2). Heidelberg 2020.” <i>Mitteilungen Des Instituts Für Europäische Kulturgeschichte</i>, 2024.","bibtex":"@article{Voß_2024, title={Rezension zu Anna-Victoria Bognár: Der Architekt in der Frühen Neuzeit. Ausbildung, Karrierewege, Berufsfelder (=Höfische Kultur interdisziplinär. Schriften und Materialien des Rudolfstädter Arbeitskreises. 2). Heidelberg 2020.}, journal={Mitteilungen des Instituts für Europäische Kulturgeschichte}, author={Voß, Fabian}, year={2024} }","chicago":"Voß, Fabian. “Rezension Zu Anna-Victoria Bognár: Der Architekt in Der Frühen Neuzeit. Ausbildung, Karrierewege, Berufsfelder (=Höfische Kultur Interdisziplinär. Schriften Und Materialien Des Rudolfstädter Arbeitskreises. 2). Heidelberg 2020.” <i>Mitteilungen Des Instituts Für Europäische Kulturgeschichte</i>, 2024.","ieee":"F. Voß, “Rezension zu Anna-Victoria Bognár: Der Architekt in der Frühen Neuzeit. Ausbildung, Karrierewege, Berufsfelder (=Höfische Kultur interdisziplinär. Schriften und Materialien des Rudolfstädter Arbeitskreises. 2). Heidelberg 2020.,” <i>Mitteilungen des Instituts für Europäische Kulturgeschichte</i>, 2024.","ama":"Voß F. Rezension zu Anna-Victoria Bognár: Der Architekt in der Frühen Neuzeit. Ausbildung, Karrierewege, Berufsfelder (=Höfische Kultur interdisziplinär. Schriften und Materialien des Rudolfstädter Arbeitskreises. 2). Heidelberg 2020. <i>Mitteilungen des Instituts für Europäische Kulturgeschichte</i>. Published online 2024."},"year":"2024","title":"Rezension zu Anna-Victoria Bognár: Der Architekt in der Frühen Neuzeit. Ausbildung, Karrierewege, Berufsfelder (=Höfische Kultur interdisziplinär. Schriften und Materialien des Rudolfstädter Arbeitskreises. 2). Heidelberg 2020.","date_created":"2024-04-09T11:55:21Z","author":[{"first_name":"Fabian","last_name":"Voß","full_name":"Voß, Fabian","id":"42693"}],"date_updated":"2024-04-09T11:58:06Z"},{"language":[{"iso":"eng"}],"title":"A Dispersion Algorithm for Robot Swarms Inside Polygonal Boundary Shapes","department":[{"_id":"34"},{"_id":"7"},{"_id":"79"}],"supervisor":[{"last_name":"Scheideler","full_name":"Scheideler, Christian","id":"20792","first_name":"Christian"}],"author":[{"full_name":"De Groote, Carsten","last_name":"De Groote","first_name":"Carsten"}],"date_created":"2024-04-09T11:35:20Z","user_id":"15578","_id":"53374","date_updated":"2024-04-09T11:35:41Z","status":"public","citation":{"bibtex":"@book{De Groote_2024, title={A Dispersion Algorithm for Robot Swarms Inside Polygonal Boundary Shapes}, author={De Groote, Carsten}, year={2024} }","mla":"De Groote, Carsten. <i>A Dispersion Algorithm for Robot Swarms Inside Polygonal Boundary Shapes</i>. 2024.","short":"C. De Groote, A Dispersion Algorithm for Robot Swarms Inside Polygonal Boundary Shapes, 2024.","apa":"De Groote, C. (2024). <i>A Dispersion Algorithm for Robot Swarms Inside Polygonal Boundary Shapes</i>.","ieee":"C. De Groote, <i>A Dispersion Algorithm for Robot Swarms Inside Polygonal Boundary Shapes</i>. 2024.","chicago":"De Groote, Carsten. <i>A Dispersion Algorithm for Robot Swarms Inside Polygonal Boundary Shapes</i>, 2024.","ama":"De Groote C. <i>A Dispersion Algorithm for Robot Swarms Inside Polygonal Boundary Shapes</i>.; 2024."},"year":"2024","type":"mastersthesis"},{"year":"2024","citation":{"ieee":"R. Doddegowda, <i>Optimal Drone Strategies For Packet Delivery</i>. 2024.","chicago":"Doddegowda, Rajesh. <i>Optimal Drone Strategies For Packet Delivery</i>, 2024.","ama":"Doddegowda R. <i>Optimal Drone Strategies For Packet Delivery</i>.; 2024.","bibtex":"@book{Doddegowda_2024, title={Optimal Drone Strategies For Packet Delivery}, author={Doddegowda, Rajesh}, year={2024} }","mla":"Doddegowda, Rajesh. <i>Optimal Drone Strategies For Packet Delivery</i>. 2024.","short":"R. Doddegowda, Optimal Drone Strategies For Packet Delivery, 2024.","apa":"Doddegowda, R. (2024). <i>Optimal Drone Strategies For Packet Delivery</i>."},"title":"Optimal Drone Strategies For Packet Delivery","date_updated":"2024-04-09T11:32:20Z","author":[{"full_name":"Doddegowda, Rajesh","last_name":"Doddegowda","first_name":"Rajesh"}],"date_created":"2024-04-09T11:31:47Z","supervisor":[{"last_name":"Scheideler","full_name":"Scheideler, Christian","id":"20792","first_name":"Christian"}],"status":"public","type":"mastersthesis","language":[{"iso":"eng"}],"_id":"53373","department":[{"_id":"34"},{"_id":"7"},{"_id":"79"}],"user_id":"15578"},{"title":"Evaluating the Implications","author":[{"last_name":"Thakur","full_name":"Thakur, Heena","first_name":"Heena"}],"supervisor":[{"last_name":"Scheideler","id":"20792","full_name":"Scheideler, Christian","first_name":"Christian"}],"date_created":"2024-04-09T11:28:39Z","date_updated":"2024-04-09T11:29:24Z","citation":{"bibtex":"@book{Thakur_2024, title={Evaluating the Implications}, author={Thakur, Heena}, year={2024} }","short":"H. Thakur, Evaluating the Implications, 2024.","mla":"Thakur, Heena. <i>Evaluating the Implications</i>. 2024.","apa":"Thakur, H. (2024). <i>Evaluating the Implications</i>.","ieee":"H. Thakur, <i>Evaluating the Implications</i>. 2024.","chicago":"Thakur, Heena. <i>Evaluating the Implications</i>, 2024.","ama":"Thakur H. <i>Evaluating the Implications</i>.; 2024."},"year":"2024","language":[{"iso":"eng"}],"user_id":"15578","department":[{"_id":"34"},{"_id":"7"},{"_id":"79"}],"_id":"53372","status":"public","type":"mastersthesis"},{"status":"public","type":"conference","language":[{"iso":"ger"}],"_id":"53394","project":[{"name":"TRR 285: TRR 285","_id":"130","grant_number":"418701707"},{"name":"TRR 285 - B: TRR 285 - Project Area B","_id":"132"},{"name":"TRR 285 – B04: TRR 285 - Subproject B04","_id":"143"}],"department":[{"_id":"143"}],"user_id":"45673","year":"2024","citation":{"ama":"Kullmer G, Weiß D, Schramm B. Weiterentwicklung des Exponentialansatzes zur Beschreibung von Rissfortschrittskurven. In: Deutscher Verband für Materialforschung und –prüfung e.V.; 2024. doi:<a href=\"https://doi.org/10.48447/BR-2024-369\">10.48447/BR-2024-369</a>","ieee":"G. Kullmer, D. Weiß, and B. Schramm, “Weiterentwicklung des Exponentialansatzes zur Beschreibung von Rissfortschrittskurven,” presented at the 56. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit , Kassel, 2024, doi: <a href=\"https://doi.org/10.48447/BR-2024-369\">10.48447/BR-2024-369</a>.","chicago":"Kullmer, Gunter, Deborah Weiß, and Britta Schramm. “Weiterentwicklung des Exponentialansatzes zur Beschreibung von Rissfortschrittskurven.” Deutscher Verband für Materialforschung und –prüfung e.V., 2024. <a href=\"https://doi.org/10.48447/BR-2024-369\">https://doi.org/10.48447/BR-2024-369</a>.","bibtex":"@inproceedings{Kullmer_Weiß_Schramm_2024, title={Weiterentwicklung des Exponentialansatzes zur Beschreibung von Rissfortschrittskurven}, DOI={<a href=\"https://doi.org/10.48447/BR-2024-369\">10.48447/BR-2024-369</a>}, publisher={Deutscher Verband für Materialforschung und –prüfung e.V.}, author={Kullmer, Gunter and Weiß, Deborah and Schramm, Britta}, year={2024} }","short":"G. Kullmer, D. Weiß, B. Schramm, in: Deutscher Verband für Materialforschung und –prüfung e.V., 2024.","mla":"Kullmer, Gunter, et al. <i>Weiterentwicklung des Exponentialansatzes zur Beschreibung von Rissfortschrittskurven</i>. Deutscher Verband für Materialforschung und –prüfung e.V., 2024, doi:<a href=\"https://doi.org/10.48447/BR-2024-369\">10.48447/BR-2024-369</a>.","apa":"Kullmer, G., Weiß, D., &#38; Schramm, B. (2024). <i>Weiterentwicklung des Exponentialansatzes zur Beschreibung von Rissfortschrittskurven</i>. 56. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit , Kassel. <a href=\"https://doi.org/10.48447/BR-2024-369\">https://doi.org/10.48447/BR-2024-369</a>"},"title":"Weiterentwicklung des Exponentialansatzes zur Beschreibung von Rissfortschrittskurven","conference":{"start_date":"2024-02-20","name":"56. Tagung des DVM-Arbeitskreises Bruchmechanik und Bauteilsicherheit ","location":"Kassel","end_date":"2024-02-21"},"doi":"10.48447/BR-2024-369","publisher":"Deutscher Verband für Materialforschung und –prüfung e.V.","date_updated":"2024-04-10T08:30:45Z","date_created":"2024-04-10T07:58:29Z","author":[{"first_name":"Gunter","full_name":"Kullmer, Gunter","id":"291","last_name":"Kullmer"},{"full_name":"Weiß, Deborah","id":"45673","last_name":"Weiß","first_name":"Deborah"},{"first_name":"Britta","full_name":"Schramm, Britta","id":"4668","last_name":"Schramm"}]},{"type":"book_chapter","publication":"Jahrbuch für Tod und Gesellschaft","editor":[{"last_name":"Benkel","full_name":"Benkel, Thorsten","first_name":"Thorsten"},{"last_name":"Meitzler","full_name":"Meitzler, Matthias","first_name":"Matthias"}],"status":"public","_id":"53397","series_title":"Jahrbuch für Tod und Gesellschaft","user_id":"47572","language":[{"iso":"ger"}],"year":"2024","citation":{"ama":"Magdeburg LM. Sterben und Tod in den Vorstellungen von Grundschulkindern. Eine qualitative Studie im Kontext von Sachunterrichtsdidaktik. In: Benkel T, Meitzler M, eds. <i>Jahrbuch für Tod und Gesellschaft</i>. Vol 3. Jahrbuch für Tod und Gesellschaft. Beltz Juventa; 2024:147-149.","chicago":"Magdeburg, Lena Maria. “Sterben und Tod in den Vorstellungen von Grundschulkindern. Eine qualitative Studie im Kontext von Sachunterrichtsdidaktik.” In <i>Jahrbuch für Tod und Gesellschaft</i>, edited by Thorsten Benkel and Matthias Meitzler, 3:147–49. Jahrbuch für Tod und Gesellschaft. Beltz Juventa, 2024.","ieee":"L. M. Magdeburg, “Sterben und Tod in den Vorstellungen von Grundschulkindern. Eine qualitative Studie im Kontext von Sachunterrichtsdidaktik,” in <i>Jahrbuch für Tod und Gesellschaft</i>, vol. 3, T. Benkel and M. Meitzler, Eds. Beltz Juventa, 2024, pp. 147–149.","bibtex":"@inbook{Magdeburg_2024, series={Jahrbuch für Tod und Gesellschaft}, title={Sterben und Tod in den Vorstellungen von Grundschulkindern. Eine qualitative Studie im Kontext von Sachunterrichtsdidaktik}, volume={3}, booktitle={Jahrbuch für Tod und Gesellschaft}, publisher={Beltz Juventa}, author={Magdeburg, Lena Maria}, editor={Benkel, Thorsten and Meitzler, Matthias}, year={2024}, pages={147–149}, collection={Jahrbuch für Tod und Gesellschaft} }","short":"L.M. Magdeburg, in: T. Benkel, M. Meitzler (Eds.), Jahrbuch für Tod und Gesellschaft, Beltz Juventa, 2024, pp. 147–149.","mla":"Magdeburg, Lena Maria. “Sterben und Tod in den Vorstellungen von Grundschulkindern. Eine qualitative Studie im Kontext von Sachunterrichtsdidaktik.” <i>Jahrbuch für Tod und Gesellschaft</i>, edited by Thorsten Benkel and Matthias Meitzler, vol. 3, Beltz Juventa, 2024, pp. 147–49.","apa":"Magdeburg, L. M. (2024). Sterben und Tod in den Vorstellungen von Grundschulkindern. Eine qualitative Studie im Kontext von Sachunterrichtsdidaktik. In T. Benkel &#38; M. Meitzler (Eds.), <i>Jahrbuch für Tod und Gesellschaft</i> (Vol. 3, pp. 147–149). Beltz Juventa."},"page":"147-149","intvolume":"         3","publisher":"Beltz Juventa","date_updated":"2024-04-10T09:37:58Z","date_created":"2024-04-10T09:34:46Z","author":[{"full_name":"Magdeburg, Lena Maria","id":"47572","last_name":"Magdeburg","first_name":"Lena Maria"}],"volume":3,"title":"Sterben und Tod in den Vorstellungen von Grundschulkindern. 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(2024). <i>Reproduktionspolitiken und Selbstbestimmung</i> (Vol. 16)."},"intvolume":"        16","year":"2024","date_created":"2024-03-27T10:28:27Z","volume":16,"date_updated":"2024-04-11T08:32:17Z","title":"Reproduktionspolitiken und Selbstbestimmung","type":"book_editor","status":"public","editor":[{"full_name":"Eremin, Oxana","last_name":"Eremin","first_name":"Oxana"},{"last_name":"Langer","full_name":"Langer, Antje","first_name":"Antje"},{"last_name":"Mattei","full_name":"Mattei, Annalisa","first_name":"Annalisa"},{"full_name":"Mahs, Claudia","last_name":"Mahs","first_name":"Claudia"}],"user_id":"27914","series_title":"GENDER. Zeitschrift für Geschlecht, Kultur und Gesellschaft ","_id":"53066","language":[{"iso":"eng"}]},{"_id":"38031","department":[{"_id":"655"}],"user_id":"47427","article_number":"101657","type":"journal_article","status":"public","date_updated":"2024-04-11T12:41:13Z","oa":"1","volume":71,"author":[{"last_name":"Philipp","full_name":"Philipp, Friedrich","first_name":"Friedrich"},{"first_name":"Manuel","full_name":"Schaller, Manuel","last_name":"Schaller"},{"first_name":"Karl","full_name":"Worthmann, Karl","last_name":"Worthmann"},{"first_name":"Sebastian","full_name":"Peitz, Sebastian","id":"47427","orcid":"0000-0002-3389-793X","last_name":"Peitz"},{"first_name":"Feliks","last_name":"Nüske","full_name":"Nüske, Feliks"}],"doi":"10.1016/j.acha.2024.101657","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2301.08637"}],"publication_status":"published","intvolume":"        71","citation":{"ama":"Philipp F, Schaller M, Worthmann K, Peitz S, Nüske F. Error bounds for kernel-based approximations of the Koopman operator. <i>Applied and Computational Harmonic Analysis </i>. 2024;71. doi:<a href=\"https://doi.org/10.1016/j.acha.2024.101657\">10.1016/j.acha.2024.101657</a>","chicago":"Philipp, Friedrich, Manuel Schaller, Karl Worthmann, Sebastian Peitz, and Feliks Nüske. “Error Bounds for Kernel-Based Approximations of the Koopman Operator.” <i>Applied and Computational Harmonic Analysis </i> 71 (2024). <a href=\"https://doi.org/10.1016/j.acha.2024.101657\">https://doi.org/10.1016/j.acha.2024.101657</a>.","ieee":"F. Philipp, M. Schaller, K. Worthmann, S. Peitz, and F. Nüske, “Error bounds for kernel-based approximations of the Koopman operator,” <i>Applied and Computational Harmonic Analysis </i>, vol. 71, Art. no. 101657, 2024, doi: <a href=\"https://doi.org/10.1016/j.acha.2024.101657\">10.1016/j.acha.2024.101657</a>.","apa":"Philipp, F., Schaller, M., Worthmann, K., Peitz, S., &#38; Nüske, F. (2024). Error bounds for kernel-based approximations of the Koopman operator. <i>Applied and Computational Harmonic Analysis </i>, <i>71</i>, Article 101657. <a href=\"https://doi.org/10.1016/j.acha.2024.101657\">https://doi.org/10.1016/j.acha.2024.101657</a>","short":"F. Philipp, M. Schaller, K. Worthmann, S. Peitz, F. Nüske, Applied and Computational Harmonic Analysis  71 (2024).","bibtex":"@article{Philipp_Schaller_Worthmann_Peitz_Nüske_2024, title={Error bounds for kernel-based approximations of the Koopman operator}, volume={71}, DOI={<a href=\"https://doi.org/10.1016/j.acha.2024.101657\">10.1016/j.acha.2024.101657</a>}, number={101657}, journal={Applied and Computational Harmonic Analysis }, publisher={Springer }, author={Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl and Peitz, Sebastian and Nüske, Feliks}, year={2024} }","mla":"Philipp, Friedrich, et al. “Error Bounds for Kernel-Based Approximations of the Koopman Operator.” <i>Applied and Computational Harmonic Analysis </i>, vol. 71, 101657, Springer , 2024, doi:<a href=\"https://doi.org/10.1016/j.acha.2024.101657\">10.1016/j.acha.2024.101657</a>."},"external_id":{"arxiv":["2301.08637"]},"language":[{"iso":"eng"}],"publication":"Applied and Computational Harmonic Analysis ","abstract":[{"text":"We consider the data-driven approximation of the Koopman operator for\r\nstochastic differential equations on reproducing kernel Hilbert spaces (RKHS).\r\nOur focus is on the estimation error if the data are collected from long-term\r\nergodic simulations. We derive both an exact expression for the variance of the\r\nkernel cross-covariance operator, measured in the Hilbert-Schmidt norm, and\r\nprobabilistic bounds for the finite-data estimation error. Moreover, we derive\r\na bound on the prediction error of observables in the RKHS using a finite\r\nMercer series expansion. Further, assuming Koopman-invariance of the RKHS, we\r\nprovide bounds on the full approximation error. Numerical experiments using the\r\nOrnstein-Uhlenbeck process illustrate our results.","lang":"eng"}],"publisher":"Springer ","date_created":"2023-01-23T07:03:39Z","title":"Error bounds for kernel-based approximations of the Koopman operator","year":"2024"},{"status":"public","publication":"European Journal of Special Needs Education","type":"journal_article","language":[{"iso":"eng"}],"department":[{"_id":"556"}],"user_id":"65969","_id":"43135","intvolume":"        39","page":"167–184","citation":{"apa":"Sharma ,  Umesh , Loreman ,  Tim , May ,  Fiona , Romano ,  Alessandra , Lozano , C. S., Avramidis ,  Elias , Woodcock ,  Stuart , Subban ,  Pearl , &#38; Kullmann, H. (2024). Measuring collective efficacy for inclusion in a global context. <i>European Journal of Special Needs Education</i>, <i>39</i>(2), 167–184. <a href=\"https://doi.org/10.1080/08856257.2023.2195075\">https://doi.org/10.1080/08856257.2023.2195075</a>","bibtex":"@article{Sharma _Loreman _May _Romano _Lozano _Avramidis _Woodcock _Subban _Kullmann_2024, title={Measuring collective efficacy for inclusion in a global context}, volume={39}, DOI={<a href=\"https://doi.org/10.1080/08856257.2023.2195075\">10.1080/08856257.2023.2195075</a>}, number={2}, journal={European Journal of Special Needs Education}, author={Sharma ,  Umesh  and Loreman ,  Tim  and May ,  Fiona  and Romano ,  Alessandra  and Lozano , Caroline Sahli and Avramidis ,  Elias  and Woodcock ,  Stuart  and Subban ,  Pearl  and Kullmann, Harry}, year={2024}, pages={167–184} }","short":"Umesh  Sharma ,  Tim  Loreman ,  Fiona  May ,  Alessandra  Romano , C.S. Lozano ,  Elias  Avramidis ,  Stuart  Woodcock ,  Pearl  Subban , H. Kullmann, European Journal of Special Needs Education 39 (2024) 167–184.","mla":"Sharma ,  Umesh , et al. “Measuring Collective Efficacy for Inclusion in a Global Context.” <i>European Journal of Special Needs Education</i>, vol. 39, no. 2, 2024, pp. 167–184, doi:<a href=\"https://doi.org/10.1080/08856257.2023.2195075\">10.1080/08856257.2023.2195075</a>.","ama":"Sharma   Umesh , Loreman   Tim , May   Fiona , et al. Measuring collective efficacy for inclusion in a global context. <i>European Journal of Special Needs Education</i>. 2024;39(2):167–184. doi:<a href=\"https://doi.org/10.1080/08856257.2023.2195075\">10.1080/08856257.2023.2195075</a>","ieee":"Umesh  Sharma  <i>et al.</i>, “Measuring collective efficacy for inclusion in a global context,” <i>European Journal of Special Needs Education</i>, vol. 39, no. 2, pp. 167–184, 2024, doi: <a href=\"https://doi.org/10.1080/08856257.2023.2195075\">10.1080/08856257.2023.2195075</a>.","chicago":"Sharma ,  Umesh ,  Tim  Loreman ,  Fiona  May ,  Alessandra  Romano , Caroline Sahli Lozano ,  Elias  Avramidis ,  Stuart  Woodcock ,  Pearl  Subban , and Harry Kullmann. “Measuring Collective Efficacy for Inclusion in a Global Context.” <i>European Journal of Special Needs Education</i> 39, no. 2 (2024): 167–184. <a href=\"https://doi.org/10.1080/08856257.2023.2195075\">https://doi.org/10.1080/08856257.2023.2195075</a>."},"year":"2024","issue":"2","doi":"10.1080/08856257.2023.2195075","title":"Measuring collective efficacy for inclusion in a global context","volume":39,"author":[{"last_name":"Sharma ","full_name":"Sharma ,  Umesh ","first_name":" Umesh "},{"last_name":"Loreman ","full_name":"Loreman ,  Tim ","first_name":" Tim "},{"last_name":"May ","full_name":"May ,  Fiona ","first_name":" Fiona "},{"last_name":"Romano ","full_name":"Romano ,  Alessandra ","first_name":" Alessandra "},{"full_name":"Lozano , Caroline Sahli","last_name":"Lozano ","first_name":"Caroline Sahli"},{"full_name":"Avramidis ,  Elias ","last_name":"Avramidis ","first_name":" Elias "},{"first_name":" Stuart ","last_name":"Woodcock ","full_name":"Woodcock ,  Stuart "},{"full_name":"Subban ,  Pearl ","last_name":"Subban ","first_name":" Pearl "},{"last_name":"Kullmann","full_name":"Kullmann, Harry","id":"77972","first_name":"Harry"}],"date_created":"2023-03-28T13:01:09Z","date_updated":"2024-04-11T13:17:29Z"},{"title":"Cuckoos United: Extending Cuckoo Filters for Message Dissemination in Vehicular Networks","date_updated":"2024-04-11T18:29:47Z","date_created":"2024-04-11T18:26:09Z","author":[{"first_name":"Touhid Hossain","last_name":"Pritom","full_name":"Pritom, Touhid Hossain"},{"last_name":"Welzel","full_name":"Welzel, Simon","first_name":"Simon"},{"last_name":"Klingler","full_name":"Klingler, Florian","first_name":"Florian"}],"year":"2024","place":"Big Island, HI","citation":{"apa":"Pritom, T. H., Welzel, S., &#38; Klingler, F. (2024). Cuckoos United: Extending Cuckoo Filters for Message Dissemination in Vehicular Networks. <i>11th IEEE International Conference on Computing, Networking and Communications (ICNC 2024)</i>.","short":"T.H. Pritom, S. Welzel, F. 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Klingler, “Cuckoos United: Extending Cuckoo Filters for Message Dissemination in Vehicular Networks,” 2024.","chicago":"Pritom, Touhid Hossain, Simon Welzel, and Florian Klingler. “Cuckoos United: Extending Cuckoo Filters for Message Dissemination in Vehicular Networks.” In <i>11th IEEE International Conference on Computing, Networking and Communications (ICNC 2024)</i>. Big Island, HI, 2024.","ama":"Pritom TH, Welzel S, Klingler F. Cuckoos United: Extending Cuckoo Filters for Message Dissemination in Vehicular Networks. In: <i>11th IEEE International Conference on Computing, Networking and Communications (ICNC 2024)</i>. ; 2024."},"language":[{"iso":"eng"}],"_id":"53437","user_id":"49153","status":"public","type":"conference","publication":"11th IEEE International Conference on Computing, Networking and Communications (ICNC 2024)"},{"quality_controlled":"1","issue":"1","year":"2024","publisher":"IOP Publishing","date_created":"2024-04-11T12:37:49Z","title":"The Stellarium Gornergrat: Astrophysics with your own Data","publication":"Journal of Physics: Conference Series","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>Remote-controlled telescopes in education provide the opportunity to obtain high quality astronomy images for a broad variety of users. The Stellarium Gornergrat is such a telescope. In addition to pure observation, it offers a user-friendly interface and teaching modules so that astronomical and astrophysical projects can be integrated into everyday school life without any special prior knowledge and without requiring a lot of time. This contribution presents the Stellarium project and a provides an overview of several teaching activities.</jats:p>"}],"keyword":["Computer Science Applications","History","Education"],"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["1742-6588","1742-6596"]},"citation":{"ama":"Gschwind S, Hohmann S, Müller A, Nordine J, Riesen T-E. 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Riesen, “The Stellarium Gornergrat: Astrophysics with your own Data,” <i>Journal of Physics: Conference Series</i>, vol. 2727, no. 1, Art. no. 012011, 2024, doi: <a href=\"https://doi.org/10.1088/1742-6596/2727/1/012011\">10.1088/1742-6596/2727/1/012011</a>.","mla":"Gschwind, Stéphane, et al. “The Stellarium Gornergrat: Astrophysics with Your Own Data.” <i>Journal of Physics: Conference Series</i>, vol. 2727, no. 1, 012011, IOP Publishing, 2024, doi:<a href=\"https://doi.org/10.1088/1742-6596/2727/1/012011\">10.1088/1742-6596/2727/1/012011</a>.","bibtex":"@article{Gschwind_Hohmann_Müller_Nordine_Riesen_2024, title={The Stellarium Gornergrat: Astrophysics with your own Data}, volume={2727}, DOI={<a href=\"https://doi.org/10.1088/1742-6596/2727/1/012011\">10.1088/1742-6596/2727/1/012011</a>}, number={1012011}, journal={Journal of Physics: Conference Series}, publisher={IOP Publishing}, author={Gschwind, Stéphane and Hohmann, Sascha and Müller, Andreas and Nordine, Jeffrey and Riesen, Timm-Emanuel}, year={2024} }","short":"S. Gschwind, S. Hohmann, A. Müller, J. Nordine, T.-E. Riesen, Journal of Physics: Conference Series 2727 (2024).","apa":"Gschwind, S., Hohmann, S., Müller, A., Nordine, J., &#38; Riesen, T.-E. (2024). The Stellarium Gornergrat: Astrophysics with your own Data. <i>Journal of Physics: Conference Series</i>, <i>2727</i>(1), Article 012011. <a href=\"https://doi.org/10.1088/1742-6596/2727/1/012011\">https://doi.org/10.1088/1742-6596/2727/1/012011</a>"},"intvolume":"      2727","date_updated":"2024-04-12T11:34:19Z","oa":"1","author":[{"first_name":"Stéphane","last_name":"Gschwind","full_name":"Gschwind, Stéphane"},{"first_name":"Sascha","id":"94328","full_name":"Hohmann, Sascha","last_name":"Hohmann","orcid":"0000-0001-6145-3466"},{"first_name":"Andreas","last_name":"Müller","full_name":"Müller, Andreas"},{"first_name":"Jeffrey","last_name":"Nordine","full_name":"Nordine, Jeffrey"},{"first_name":"Timm-Emanuel","full_name":"Riesen, Timm-Emanuel","last_name":"Riesen"}],"volume":2727,"main_file_link":[{"open_access":"1","url":"https://iopscience.iop.org/article/10.1088/1742-6596/2727/1/012011/pdf"}],"conference":{"name":"3rd World Conference on Physics Education","start_date":"2021-12-13","end_date":"2021-12-16","location":"Hanoi"},"doi":"10.1088/1742-6596/2727/1/012011","type":"journal_article","status":"public","_id":"53417","user_id":"94328","article_number":"012011"},{"language":[{"iso":"ger"}],"user_id":"105","series_title":"Paderborner Gastdozentur für Schriftstellerinnen und Schriftsteller","department":[{"_id":"465"},{"_id":"5"}],"_id":"53473","status":"public","editor":[{"first_name":"Stefan","full_name":"Elit, Stefan","last_name":"Elit"},{"first_name":"Norbert Otto","full_name":"Eke, Norbert Otto","last_name":"Eke"}],"type":"book_chapter","publication":"‚Topographisches‘ Schreiben: Lea Streisand, Paderborn, Wintersemester 2022/2023","title":"‚Schelmische‘ Post-DDR-Romane: Ingo Schulzes „Peter Holtz“ und Lea Streisands „Hufeland, Ecke Bötzow“","author":[{"first_name":"Stefan","id":"105","full_name":"Elit, Stefan","last_name":"Elit","orcid":"0000-0002-4719-1073"}],"date_created":"2024-04-12T16:05:19Z","volume":"41.","date_updated":"2024-04-12T16:06:59Z","publisher":"Aisthesis","citation":{"ama":"Elit S. ‚Schelmische‘ Post-DDR-Romane: Ingo Schulzes „Peter Holtz“ und Lea Streisands „Hufeland, Ecke Bötzow“. In: Elit S, Eke NO, eds. <i>‚Topographisches‘ Schreiben: Lea Streisand, Paderborn, Wintersemester 2022/2023</i>. Vol 41. Paderborner Gastdozentur für Schriftstellerinnen und Schriftsteller. Aisthesis; 2024:137-154.","chicago":"Elit, Stefan. “‚Schelmische‘ Post-DDR-Romane: Ingo Schulzes „Peter Holtz“ und Lea Streisands „Hufeland, Ecke Bötzow“.” In <i>‚Topographisches‘ Schreiben: Lea Streisand, Paderborn, Wintersemester 2022/2023</i>, edited by Stefan Elit and Norbert Otto Eke, 41.:137–54. Paderborner Gastdozentur für Schriftstellerinnen und Schriftsteller. Bielefeld: Aisthesis, 2024.","ieee":"S. Elit, “‚Schelmische‘ Post-DDR-Romane: Ingo Schulzes „Peter Holtz“ und Lea Streisands „Hufeland, Ecke Bötzow“,” in <i>‚Topographisches‘ Schreiben: Lea Streisand, Paderborn, Wintersemester 2022/2023</i>, vol. 41., S. Elit and N. O. Eke, Eds. Bielefeld: Aisthesis, 2024, pp. 137–154.","bibtex":"@inbook{Elit_2024, place={Bielefeld}, series={Paderborner Gastdozentur für Schriftstellerinnen und Schriftsteller}, title={‚Schelmische‘ Post-DDR-Romane: Ingo Schulzes „Peter Holtz“ und Lea Streisands „Hufeland, Ecke Bötzow“}, volume={41.}, booktitle={‚Topographisches‘ Schreiben: Lea Streisand, Paderborn, Wintersemester 2022/2023}, publisher={Aisthesis}, author={Elit, Stefan}, editor={Elit, Stefan and Eke, Norbert Otto}, year={2024}, pages={137–154}, collection={Paderborner Gastdozentur für Schriftstellerinnen und Schriftsteller} }","mla":"Elit, Stefan. “‚Schelmische‘ Post-DDR-Romane: Ingo Schulzes „Peter Holtz“ und Lea Streisands „Hufeland, Ecke Bötzow“.” <i>‚Topographisches‘ Schreiben: Lea Streisand, Paderborn, Wintersemester 2022/2023</i>, edited by Stefan Elit and Norbert Otto Eke, vol. 41., Aisthesis, 2024, pp. 137–54.","short":"S. Elit, in: S. Elit, N.O. Eke (Eds.), ‚Topographisches‘ Schreiben: Lea Streisand, Paderborn, Wintersemester 2022/2023, Aisthesis, Bielefeld, 2024, pp. 137–154.","apa":"Elit, S. (2024). ‚Schelmische‘ Post-DDR-Romane: Ingo Schulzes „Peter Holtz“ und Lea Streisands „Hufeland, Ecke Bötzow“. In S. Elit &#38; N. O. Eke (Eds.), <i>‚Topographisches‘ Schreiben: Lea Streisand, Paderborn, Wintersemester 2022/2023: Vol. 41.</i> (pp. 137–154). Aisthesis."},"page":"137-154","year":"2024","place":"Bielefeld","publication_status":"published","publication_identifier":{"isbn":["978-3-8498-1957-6"],"eisbn":["978-3-8498-1958-3"]}},{"file_date_updated":"2024-04-04T09:24:22Z","isi":"1","article_number":"095001","article_type":"original","department":[{"_id":"296"},{"_id":"230"},{"_id":"15"},{"_id":"170"},{"_id":"35"}],"user_id":"458","_id":"52723","status":"public","type":"journal_article","doi":"10.1088/1361-6455/ad369c","volume":57,"author":[{"full_name":"Meyer, Maximilian Tim","id":"77895","orcid":"0009-0003-4899-0920","last_name":"Meyer","first_name":"Maximilian Tim"},{"full_name":"Schindlmayr, Arno","id":"458","orcid":"0000-0002-4855-071X","last_name":"Schindlmayr","first_name":"Arno"}],"oa":"1","date_updated":"2024-04-13T11:20:56Z","intvolume":"        57","citation":{"apa":"Meyer, M. T., &#38; Schindlmayr, A. (2024). Derivation of Miller’s rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator. <i>Journal of Physics B: Atomic, Molecular and Optical Physics</i>, <i>57</i>(9), Article 095001. <a href=\"https://doi.org/10.1088/1361-6455/ad369c\">https://doi.org/10.1088/1361-6455/ad369c</a>","mla":"Meyer, Maximilian Tim, and Arno Schindlmayr. “Derivation of Miller’s Rule for the Nonlinear Optical Susceptibility of a Quantum Anharmonic Oscillator.” <i>Journal of Physics B: Atomic, Molecular and Optical Physics</i>, vol. 57, no. 9, 095001, IOP Publishing, 2024, doi:<a href=\"https://doi.org/10.1088/1361-6455/ad369c\">10.1088/1361-6455/ad369c</a>.","short":"M.T. Meyer, A. Schindlmayr, Journal of Physics B: Atomic, Molecular and Optical Physics 57 (2024).","bibtex":"@article{Meyer_Schindlmayr_2024, title={Derivation of Miller’s rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator}, volume={57}, DOI={<a href=\"https://doi.org/10.1088/1361-6455/ad369c\">10.1088/1361-6455/ad369c</a>}, number={9095001}, journal={Journal of Physics B: Atomic, Molecular and Optical Physics}, publisher={IOP Publishing}, author={Meyer, Maximilian Tim and Schindlmayr, Arno}, year={2024} }","chicago":"Meyer, Maximilian Tim, and Arno Schindlmayr. “Derivation of Miller’s Rule for the Nonlinear Optical Susceptibility of a Quantum Anharmonic Oscillator.” <i>Journal of Physics B: Atomic, Molecular and Optical Physics</i> 57, no. 9 (2024). <a href=\"https://doi.org/10.1088/1361-6455/ad369c\">https://doi.org/10.1088/1361-6455/ad369c</a>.","ieee":"M. T. Meyer and A. Schindlmayr, “Derivation of Miller’s rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator,” <i>Journal of Physics B: Atomic, Molecular and Optical Physics</i>, vol. 57, no. 9, Art. no. 095001, 2024, doi: <a href=\"https://doi.org/10.1088/1361-6455/ad369c\">10.1088/1361-6455/ad369c</a>.","ama":"Meyer MT, Schindlmayr A. Derivation of Miller’s rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator. <i>Journal of Physics B: Atomic, Molecular and Optical Physics</i>. 2024;57(9). doi:<a href=\"https://doi.org/10.1088/1361-6455/ad369c\">10.1088/1361-6455/ad369c</a>"},"has_accepted_license":"1","publication_identifier":{"eissn":["1361-6455"],"issn":["0953-4075"]},"publication_status":"published","language":[{"iso":"eng"}],"ddc":["530"],"external_id":{"isi":["001196678300001"]},"file":[{"date_created":"2024-04-04T09:24:22Z","creator":"schindlm","date_updated":"2024-04-04T09:24:22Z","access_level":"open_access","file_name":"Meyer_2024_J._Phys._B _At._Mol._Opt._Phys._57_095001.pdf","file_id":"53204","file_size":358155,"description":"Creative Commons Attribution 4.0 International Public License (CC BY 4.0)","title":"Derivation of Miller's rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator","content_type":"application/pdf","relation":"main_file"}],"abstract":[{"lang":"eng","text":"Miller's rule is an empirical relation between the nonlinear and linear optical coefficients that applies to a large class of materials but has only been rigorously derived for the classical Lorentz model with a weak anharmonic perturbation. In this work, we extend the proof and present a detailed derivation of Miller's rule for an equivalent quantum-mechanical anharmonic oscillator. For this purpose, the classical concept of velocity-dependent damping inherent to the Lorentz model is replaced by an adiabatic switch-on of the external electric field, which allows a unified treatment of the classical and quantum-mechanical systems using identical potentials and fields. Although the dynamics of the resulting charge oscillations, and hence the induced polarizations, deviate due to the finite zero-point motion in the quantum-mechanical framework, we find that Miller's rule is nevertheless identical in both cases up to terms of first order in the anharmonicity. With a view to practical applications, especially in the context of ab initio calculations for the optical response where adiabatically switched-on fields are widely assumed, we demonstrate that a correct treatment of finite broadening parameters is essential to avoid spurious errors that may falsely suggest a violation of Miller's rule, and we illustrate this point by means of a numerical example."}],"publication":"Journal of Physics B: Atomic, Molecular and Optical Physics","title":"Derivation of Miller's rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator","date_created":"2024-03-22T08:44:39Z","publisher":"IOP Publishing","year":"2024","issue":"9","quality_controlled":"1"},{"language":[{"iso":"eng"}],"article_number":"322","user_id":"24135","department":[{"_id":"27"},{"_id":"518"},{"_id":"803"}],"project":[{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"_id":"53474","status":"public","abstract":[{"lang":"eng","text":"We present a novel approach to characterize and quantify microheterogeneity and microphase separation in computer simulations of complex liquid mixtures. Our post-processing method is based on local density fluctuations of the different constituents in sampling spheres of varying size. It can be easily applied to both molecular dynamics (MD) and Monte Carlo (MC) simulations, including periodic boundary conditions. Multidimensional correlation of the density distributions yields a clear picture of the domain formation due to the subtle balance of different interactions. We apply our approach to the example of force field molecular dynamics simulations of imidazolium-based ionic liquids with different side chain lengths at different temperatures, namely 1-ethyl-3-methylimidazolium chloride, 1-hexyl-3-methylimidazolium chloride, and 1-decyl-3-methylimidazolium chloride, which are known to form distinct liquid domains. We put the results into the context of existing microheterogeneity analyses and demonstrate the advantages and sensitivity of our novel method. Furthermore, we show how to estimate the configuration entropy from our analysis, and we investigate voids in the system. The analysis has been implemented into our program package TRAVIS and is thus available as free software."}],"type":"journal_article","publication":"Entropy","doi":"10.3390/e26040322","title":"Characterizing Microheterogeneity in Liquid Mixtures via Local Density Fluctuations","date_created":"2024-04-12T18:31:39Z","author":[{"first_name":"Michael","id":"24135","full_name":"Lass, Michael","orcid":"0000-0002-5708-7632","last_name":"Lass"},{"last_name":"Kenter","full_name":"Kenter, Tobias","id":"3145","first_name":"Tobias"},{"first_name":"Christian","orcid":"0000-0001-5728-9982","last_name":"Plessl","full_name":"Plessl, Christian","id":"16153"},{"full_name":"Brehm, Martin","id":"100167","last_name":"Brehm","first_name":"Martin"}],"volume":26,"publisher":"MDPI AG","date_updated":"2024-04-12T18:34:32Z","citation":{"chicago":"Lass, Michael, Tobias Kenter, Christian Plessl, and Martin Brehm. “Characterizing Microheterogeneity in Liquid Mixtures via Local Density Fluctuations.” <i>Entropy</i> 26, no. 4 (2024). <a href=\"https://doi.org/10.3390/e26040322\">https://doi.org/10.3390/e26040322</a>.","ieee":"M. Lass, T. Kenter, C. Plessl, and M. Brehm, “Characterizing Microheterogeneity in Liquid Mixtures via Local Density Fluctuations,” <i>Entropy</i>, vol. 26, no. 4, Art. no. 322, 2024, doi: <a href=\"https://doi.org/10.3390/e26040322\">10.3390/e26040322</a>.","ama":"Lass M, Kenter T, Plessl C, Brehm M. Characterizing Microheterogeneity in Liquid Mixtures via Local Density Fluctuations. <i>Entropy</i>. 2024;26(4). doi:<a href=\"https://doi.org/10.3390/e26040322\">10.3390/e26040322</a>","short":"M. Lass, T. Kenter, C. Plessl, M. Brehm, Entropy 26 (2024).","mla":"Lass, Michael, et al. “Characterizing Microheterogeneity in Liquid Mixtures via Local Density Fluctuations.” <i>Entropy</i>, vol. 26, no. 4, 322, MDPI AG, 2024, doi:<a href=\"https://doi.org/10.3390/e26040322\">10.3390/e26040322</a>.","bibtex":"@article{Lass_Kenter_Plessl_Brehm_2024, title={Characterizing Microheterogeneity in Liquid Mixtures via Local Density Fluctuations}, volume={26}, DOI={<a href=\"https://doi.org/10.3390/e26040322\">10.3390/e26040322</a>}, number={4322}, journal={Entropy}, publisher={MDPI AG}, author={Lass, Michael and Kenter, Tobias and Plessl, Christian and Brehm, Martin}, year={2024} }","apa":"Lass, M., Kenter, T., Plessl, C., &#38; Brehm, M. (2024). Characterizing Microheterogeneity in Liquid Mixtures via Local Density Fluctuations. <i>Entropy</i>, <i>26</i>(4), Article 322. <a href=\"https://doi.org/10.3390/e26040322\">https://doi.org/10.3390/e26040322</a>"},"intvolume":"        26","year":"2024","issue":"4","publication_status":"published","publication_identifier":{"issn":["1099-4300"]}},{"editor":[{"first_name":"Norbert","last_name":"Eke","id":"104","full_name":"Eke, Norbert"},{"first_name":"Stefan","id":"105","full_name":"Elit, Stefan","last_name":"Elit","orcid":"0000-0002-4719-1073"}],"status":"public","type":"book_editor","language":[{"iso":"ger"}],"_id":"53472","department":[{"_id":"465"},{"_id":"5"}],"user_id":"105","series_title":"Paderborner Gastdozentur für Schriftstellerinnen und Schriftsteller","year":"2024","place":"Bielefeld","page":"178","citation":{"ama":"Eke N, Elit S, eds. <i>’Topographisches‘ Schreiben: Lea Streisand. Paderborn Wintersemester 2022/23</i>. Vol 41. Aisthesis; 2024.","chicago":"Eke, Norbert, and Stefan Elit, eds. <i>’Topographisches‘ Schreiben: Lea Streisand. Paderborn Wintersemester 2022/23</i>. Vol. 41. Paderborner Gastdozentur für Schriftstellerinnen und Schriftsteller. Bielefeld: Aisthesis, 2024.","ieee":"N. Eke and S. Elit, Eds., <i>’Topographisches‘ Schreiben: Lea Streisand. Paderborn Wintersemester 2022/23</i>, vol. 41. Bielefeld: Aisthesis, 2024.","mla":"Eke, Norbert, and Stefan Elit, editors. <i>’Topographisches‘ Schreiben: Lea Streisand. Paderborn Wintersemester 2022/23</i>. Aisthesis, 2024.","bibtex":"@book{Eke_Elit_2024, place={Bielefeld}, series={Paderborner Gastdozentur für Schriftstellerinnen und Schriftsteller}, title={’Topographisches‘ Schreiben: Lea Streisand. Paderborn Wintersemester 2022/23}, volume={41.}, publisher={Aisthesis}, year={2024}, collection={Paderborner Gastdozentur für Schriftstellerinnen und Schriftsteller} }","short":"N. Eke, S. Elit, eds., ’Topographisches‘ Schreiben: Lea Streisand. Paderborn Wintersemester 2022/23, Aisthesis, Bielefeld, 2024.","apa":"Eke, N., &#38; Elit, S. (Eds.). (2024). <i>’Topographisches‘ Schreiben: Lea Streisand. Paderborn Wintersemester 2022/23: Vol. 41.</i> Aisthesis."},"publication_identifier":{"isbn":["978-3-8498-1957-6"],"eisbn":["978-3-8498-1958-3"]},"publication_status":"published","title":"'Topographisches‘ Schreiben: Lea Streisand. Paderborn Wintersemester 2022/23","publisher":"Aisthesis","date_updated":"2024-04-12T16:19:16Z","volume":"41.","date_created":"2024-04-12T15:56:15Z"},{"publication_identifier":{"isbn":["978-3-8498-1957-6"]},"publication_status":"published","page":"7-10 (mit Stefan Elit)","citation":{"ieee":"N. Eke, “‚Topographisches‘ Schreiben. Lea Streisand, Paderborn Wintersemester 2022/23: Die 41. Gastdozentur für Schriftstellerinnen und Schriftsteller. Zur Einführung.,” in <i>‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23</i>, N. O. Eke and E. Stefan, Eds. Bielefeld: Aisthesis, 2024, pp. 7-10 (mit Stefan Elit).","chicago":"Eke, Norbert. “‚Topographisches‘ Schreiben. Lea Streisand, Paderborn Wintersemester 2022/23: Die 41. Gastdozentur für Schriftstellerinnen und Schriftsteller. Zur Einführung.” In <i>‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23</i>, edited by Norbert Otto Eke and Elit Stefan, 7-10 (mit Stefan Elit). Bielefeld: Aisthesis, 2024.","ama":"Eke N. ‚Topographisches‘ Schreiben. Lea Streisand, Paderborn Wintersemester 2022/23: Die 41. Gastdozentur für Schriftstellerinnen und Schriftsteller. Zur Einführung. In: Eke NO, Stefan E, eds. <i>‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23</i>. Aisthesis; 2024:7-10 (mit Stefan Elit).","apa":"Eke, N. (2024). ‚Topographisches‘ Schreiben. Lea Streisand, Paderborn Wintersemester 2022/23: Die 41. Gastdozentur für Schriftstellerinnen und Schriftsteller. Zur Einführung. In N. O. Eke &#38; E. Stefan (Eds.), <i>‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23</i> (pp. 7-10 (mit Stefan Elit)). Aisthesis.","short":"N. Eke, in: N.O. Eke, E. Stefan (Eds.), ‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23, Aisthesis, Bielefeld, 2024, pp. 7-10 (mit Stefan Elit).","bibtex":"@inbook{Eke_2024, place={Bielefeld}, title={‚Topographisches‘ Schreiben. Lea Streisand, Paderborn Wintersemester 2022/23: Die 41. Gastdozentur für Schriftstellerinnen und Schriftsteller. Zur Einführung.}, booktitle={‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23}, publisher={Aisthesis}, author={Eke, Norbert}, editor={Eke, Norbert Otto and Stefan, Elit}, year={2024}, pages={7-10 (mit Stefan Elit)} }","mla":"Eke, Norbert. “‚Topographisches‘ Schreiben. Lea Streisand, Paderborn Wintersemester 2022/23: Die 41. Gastdozentur für Schriftstellerinnen und Schriftsteller. Zur Einführung.” <i>‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23</i>, edited by Norbert Otto Eke and Elit Stefan, Aisthesis, 2024, pp. 7-10 (mit Stefan Elit)."},"year":"2024","place":"Bielefeld","author":[{"full_name":"Eke, Norbert","id":"104","last_name":"Eke","first_name":"Norbert"}],"date_created":"2024-04-10T10:03:47Z","publisher":"Aisthesis","date_updated":"2024-04-15T05:49:13Z","title":"‚Topographisches‘ Schreiben. Lea Streisand, Paderborn Wintersemester 2022/23: Die 41. Gastdozentur für Schriftstellerinnen und Schriftsteller. Zur Einführung.","publication":"‚Topographisches‘ Schreiben: Lea Streisand – Paderborn Wintersemester 2022/23","type":"book_chapter","status":"public","editor":[{"full_name":"Eke, Norbert Otto","last_name":"Eke","first_name":"Norbert Otto"},{"first_name":"Elit","full_name":"Stefan, Elit","last_name":"Stefan"}],"user_id":"104","_id":"53396","language":[{"iso":"ger"}]}]
