[{"language":[{"iso":"eng"}],"ddc":["510"],"external_id":{"arxiv":["2603.06157"]},"file":[{"relation":"main_file","success":1,"content_type":"application/pdf","file_id":"64866","access_level":"closed","file_name":"design-of-hierarchical-excitable-networks.pdf","file_size":5179491,"creator":"svdg","date_created":"2026-03-09T08:26:04Z","date_updated":"2026-03-09T08:26:04Z"}],"abstract":[{"text":"We provide a method to systematically construct vector fields for which the dynamics display transitions corresponding to a desired hierarchical connection structure. This structure is given as a finite set of directed graphs $\\mathbf{G}_1,\\dotsc,\\mathbf{G}_N$ (the lower level), together with another digraph $\\mathbfΓ$ on $N$ vertices (the top level). The dynamic realizations of $\\mathbf{G}_1,\\dotsc,\\mathbf{G}_N$ are heteroclinic networks and they can be thought of as individual connection patterns on a given set of states. Edges in $\\mathbfΓ$ correspond to transitions between these different patterns. In our construction, the connections given through $\\mathbfΓ$ are not heteroclinic, but excitable with zero threshold. This describes a dynamical transition between two invariant sets where every $δ$-neighborhood of the first set contains an initial condition with $ω$-limit in the second set. Thus, we prove a theorem that allows the systematic creation of hierarchical networks that are excitable on the top level, and heteroclinic on the lower level. Our results modify and extend the simplex realization method by Ashwin & Postlethwaite.","lang":"eng"}],"publication":"arXiv:2603.06157","title":"Design of Hierarchical Excitable Networks","date_created":"2026-03-09T08:22:58Z","year":"2026","file_date_updated":"2026-03-09T08:26:04Z","department":[{"_id":"101"},{"_id":"841"}],"user_id":"97359","_id":"64865","status":"public","type":"preprint","author":[{"first_name":"Sören","last_name":"von der Gracht","orcid":"0000-0002-8054-2058","id":"97359","full_name":"von der Gracht, Sören"},{"full_name":"Lohse, Alexander","last_name":"Lohse","first_name":"Alexander"}],"date_updated":"2026-03-09T08:26:49Z","citation":{"ama":"von der Gracht S, Lohse A. Design of Hierarchical Excitable Networks. <i>arXiv:260306157</i>. Published online 2026.","chicago":"Gracht, Sören von der, and Alexander Lohse. “Design of Hierarchical Excitable Networks.” <i>ArXiv:2603.06157</i>, 2026.","ieee":"S. von der Gracht and A. Lohse, “Design of Hierarchical Excitable Networks,” <i>arXiv:2603.06157</i>. 2026.","apa":"von der Gracht, S., &#38; Lohse, A. (2026). Design of Hierarchical Excitable Networks. In <i>arXiv:2603.06157</i>.","short":"S. von der Gracht, A. Lohse, ArXiv:2603.06157 (2026).","bibtex":"@article{von der Gracht_Lohse_2026, title={Design of Hierarchical Excitable Networks}, journal={arXiv:2603.06157}, author={von der Gracht, Sören and Lohse, Alexander}, year={2026} }","mla":"von der Gracht, Sören, and Alexander Lohse. “Design of Hierarchical Excitable Networks.” <i>ArXiv:2603.06157</i>, 2026."},"related_material":{"link":[{"url":"https://s-vdg.github.io/publication/design-of-hierarchical-excitable-networks/design-of-hierarchical-excitable-networks.pdf","relation":"research_paper"}]},"has_accepted_license":"1"},{"abstract":[{"text":"We discretise a recently proposed new Lagrangian approach to optimal control problems with dynamics described by force-controlled Euler-Lagrange equations (Konopik et al., in Nonlinearity 38:11, 2025). The resulting discretisations are in the form of discrete Lagrangians. We show that the discrete necessary conditions for optimality obtained provide variational integrators for the continuous problem, akin to Karush-Kuhn-Tucker (KKT) conditions for standard direct approaches. This approach paves the way for the use of variational error analysis to derive the order of convergence of the resulting numerical schemes for both state and costate variables and to apply discrete Noether’s theorem to compute conserved quantities, distinguishing itself from existing geometric approaches. We show for a family of low-order discretisations that the resulting numerical schemes are ‘doubly-symplectic’, meaning they yield forced symplectic integrators for the underlying controlled mechanical system and overall symplectic integrators in the state-adjoint space. Multi-body dynamics examples are solved numerically using the new approach. In addition, the new approach is compared to standard direct approaches in terms of computational performance and error convergence. The results highlight the advantages of the new approach, namely, better performance and convergence behaviour of state and costate variables consistent with variational error analysis and automatic preservation of certain first integrals.","lang":"eng"}],"status":"public","publication":"Multibody System Dynamics","type":"journal_article","language":[{"iso":"eng"}],"_id":"63557","department":[{"_id":"636"}],"user_id":"87909","year":"2026","citation":{"chicago":"Konopik, Michael, Sigrid Leyendecker, Sofya Maslovskaya, Sina Ober-Blöbaum, and Rodrigo T. Sato Martín de Almagro. “On the Variational Discretisation of Optimal Control Problems for Unconstrained Lagrangian Dynamics.” <i>Multibody System Dynamics</i>, 2026. <a href=\"https://doi.org/10.1007/s11044-025-10138-1\">https://doi.org/10.1007/s11044-025-10138-1</a>.","ieee":"M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, and R. T. Sato Martín de Almagro, “On the variational discretisation of optimal control problems for unconstrained Lagrangian dynamics,” <i>Multibody System Dynamics</i>, 2026, doi: <a href=\"https://doi.org/10.1007/s11044-025-10138-1\">10.1007/s11044-025-10138-1</a>.","ama":"Konopik M, Leyendecker S, Maslovskaya S, Ober-Blöbaum S, Sato Martín de Almagro RT. On the variational discretisation of optimal control problems for unconstrained Lagrangian dynamics. <i>Multibody System Dynamics</i>. Published online 2026. doi:<a href=\"https://doi.org/10.1007/s11044-025-10138-1\">10.1007/s11044-025-10138-1</a>","mla":"Konopik, Michael, et al. “On the Variational Discretisation of Optimal Control Problems for Unconstrained Lagrangian Dynamics.” <i>Multibody System Dynamics</i>, Springer Science and Business Media LLC, 2026, doi:<a href=\"https://doi.org/10.1007/s11044-025-10138-1\">10.1007/s11044-025-10138-1</a>.","short":"M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R.T. Sato Martín de Almagro, Multibody System Dynamics (2026).","bibtex":"@article{Konopik_Leyendecker_Maslovskaya_Ober-Blöbaum_Sato Martín de Almagro_2026, title={On the variational discretisation of optimal control problems for unconstrained Lagrangian dynamics}, DOI={<a href=\"https://doi.org/10.1007/s11044-025-10138-1\">10.1007/s11044-025-10138-1</a>}, journal={Multibody System Dynamics}, publisher={Springer Science and Business Media LLC}, author={Konopik, Michael and Leyendecker, Sigrid and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Sato Martín de Almagro, Rodrigo T.}, year={2026} }","apa":"Konopik, M., Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., &#38; Sato Martín de Almagro, R. T. (2026). On the variational discretisation of optimal control problems for unconstrained Lagrangian dynamics. <i>Multibody System Dynamics</i>. <a href=\"https://doi.org/10.1007/s11044-025-10138-1\">https://doi.org/10.1007/s11044-025-10138-1</a>"},"publication_identifier":{"issn":["1384-5640","1573-272X"]},"publication_status":"published","title":"On the variational discretisation of optimal control problems for unconstrained Lagrangian dynamics","doi":"10.1007/s11044-025-10138-1","date_updated":"2026-01-12T11:35:27Z","publisher":"Springer Science and Business Media LLC","date_created":"2026-01-12T11:33:54Z","author":[{"first_name":"Michael","full_name":"Konopik, Michael","last_name":"Konopik"},{"last_name":"Leyendecker","full_name":"Leyendecker, Sigrid","first_name":"Sigrid"},{"first_name":"Sofya","last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya","id":"87909"},{"first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina"},{"first_name":"Rodrigo T.","last_name":"Sato Martín de Almagro","full_name":"Sato Martín de Almagro, Rodrigo T."}]},{"status":"public","type":"journal_article","file_date_updated":"2026-03-16T08:40:04Z","article_type":"original","article_number":"118196","user_id":"97359","department":[{"_id":"101"},{"_id":"841"}],"_id":"64979","citation":{"ama":"von der Gracht S, Nijholt E, Rink B. Homogeneous coupled cell systems with high-dimensional internal dynamics. <i>Chaos, Solitons &#38; Fractals</i>. 2026;208. doi:<a href=\"https://doi.org/10.1016/j.chaos.2026.118196\">10.1016/j.chaos.2026.118196</a>","chicago":"Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Homogeneous Coupled Cell Systems with High-Dimensional Internal Dynamics.” <i>Chaos, Solitons &#38; Fractals</i> 208 (2026). <a href=\"https://doi.org/10.1016/j.chaos.2026.118196\">https://doi.org/10.1016/j.chaos.2026.118196</a>.","ieee":"S. von der Gracht, E. Nijholt, and B. Rink, “Homogeneous coupled cell systems with high-dimensional internal dynamics,” <i>Chaos, Solitons &#38; Fractals</i>, vol. 208, Art. no. 118196, 2026, doi: <a href=\"https://doi.org/10.1016/j.chaos.2026.118196\">10.1016/j.chaos.2026.118196</a>.","apa":"von der Gracht, S., Nijholt, E., &#38; Rink, B. (2026). Homogeneous coupled cell systems with high-dimensional internal dynamics. <i>Chaos, Solitons &#38; Fractals</i>, <i>208</i>, Article 118196. <a href=\"https://doi.org/10.1016/j.chaos.2026.118196\">https://doi.org/10.1016/j.chaos.2026.118196</a>","bibtex":"@article{von der Gracht_Nijholt_Rink_2026, title={Homogeneous coupled cell systems with high-dimensional internal dynamics}, volume={208}, DOI={<a href=\"https://doi.org/10.1016/j.chaos.2026.118196\">10.1016/j.chaos.2026.118196</a>}, number={118196}, journal={Chaos, Solitons &#38; Fractals}, publisher={Elsevier BV}, author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}, year={2026} }","mla":"von der Gracht, Sören, et al. “Homogeneous Coupled Cell Systems with High-Dimensional Internal Dynamics.” <i>Chaos, Solitons &#38; Fractals</i>, vol. 208, 118196, Elsevier BV, 2026, doi:<a href=\"https://doi.org/10.1016/j.chaos.2026.118196\">10.1016/j.chaos.2026.118196</a>.","short":"S. von der Gracht, E. Nijholt, B. Rink, Chaos, Solitons &#38; Fractals 208 (2026)."},"intvolume":"       208","publication_status":"published","publication_identifier":{"issn":["0960-0779"]},"has_accepted_license":"1","doi":"10.1016/j.chaos.2026.118196","author":[{"last_name":"von der Gracht","orcid":"0000-0002-8054-2058","full_name":"von der Gracht, Sören","id":"97359","first_name":"Sören"},{"first_name":"Eddie","last_name":"Nijholt","full_name":"Nijholt, Eddie"},{"full_name":"Rink, Bob","last_name":"Rink","first_name":"Bob"}],"volume":208,"date_updated":"2026-03-16T08:42:56Z","file":[{"file_size":1951746,"access_level":"closed","file_name":"homogeneous-coupled-cell-systems-with-high-dimensional-internal-dynamics.pdf","file_id":"64980","date_updated":"2026-03-16T08:40:04Z","date_created":"2026-03-16T08:40:04Z","creator":"svdg","success":1,"relation":"main_file","content_type":"application/pdf"}],"abstract":[{"lang":"eng","text":"We investigate homogeneous coupled cell systems with high-dimensional internal dynamics. In many studies on network dynamics, the analysis is restricted to networks with one-dimensional internal dynamics. Here, we show how symmetry explains the relation between dynamical behavior of systems with one-dimensional internal dynamics and with higher dimensional internal dynamics, when the underlying network topology is the same. Fundamental networks of homogeneous coupled cell systems (B. Rink, J. Sanders. Coupled Cell Networks and Their Hidden Symmetries. SIAM J. Math. Anal. 46.2 (2014)) can be expressed in terms of monoid representations, which uniquely decompose into indecomposable subrepresentations. In the high-dimensional internal dynamics case, these subrepresentations are isomorphic to multiple copies of those one computes in the one-dimensional internal dynamics case. This has interesting implications for possible center subspaces in bifurcation analysis. We describe the effect on steady state and Hopf bifurcations in l-parameter families of network vector fields. The main results in that regard are that (1) generic one-parameter steady state bifurcations are qualitatively independent of the dimension of the internal dynamics and that, (2) in order to observe all generic l-parameter bifurcations that may occur for internal dynamics of any dimension, the internal dynamics has to be at least l-dimensional for steady state bifurcations and 2l-dimensional for Hopf bifurcations. Furthermore, we illustrate how additional structure in the network can be exploited to obtain even greater understanding of bifurcation scenarios in the high-dimensional case beyond qualitative statements about the collective dynamics. One-parameter steady state bifurcations in feedforward networks exhibit an unusual amplification in the asymptotic growth rates of individual cells, when these are one-dimensional (S. von der Gracht, E. Nijholt, B. Rink. Amplified steady state bifurcations in feedforward networks. Nonlinearity 35.4 (2022)). As another main result, we prove that (3) the same cells exhibit this amplifying effect with the same growth rates when the internal dynamics is high-dimensional."}],"publication":"Chaos, Solitons & Fractals","language":[{"iso":"eng"}],"ddc":["510"],"keyword":["Coupled cell systems","Network dynamics","Dimension reduction","Bifurcation theory","Symmetry","Monoid representation theory"],"external_id":{"arxiv":["2510.06740"]},"year":"2026","title":"Homogeneous coupled cell systems with high-dimensional internal dynamics","date_created":"2026-03-16T08:39:07Z","publisher":"Elsevier BV"},{"date_created":"2025-05-05T09:23:38Z","author":[{"last_name":"Flaßkamp","full_name":"Flaßkamp, Kathrin","first_name":"Kathrin"},{"id":"87909","full_name":"Maslovskaya, Sofya","last_name":"Maslovskaya","first_name":"Sofya"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"full_name":"Wembe Moafo, Boris Edgar","id":"95394","last_name":"Wembe Moafo","first_name":"Boris Edgar"}],"date_updated":"2025-05-05T09:24:09Z","publisher":"Springer Science and Business Media LLC","doi":"10.1007/s00498-025-00408-w","title":"Trim turnpikes for optimal control problems with symmetries","publication_identifier":{"issn":["0932-4194","1435-568X"]},"publication_status":"published","citation":{"mla":"Flaßkamp, Kathrin, et al. “Trim Turnpikes for Optimal Control Problems with Symmetries.” <i>Mathematics of Control, Signals, and Systems</i>, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s00498-025-00408-w\">10.1007/s00498-025-00408-w</a>.","bibtex":"@article{Flaßkamp_Maslovskaya_Ober-Blöbaum_Wembe Moafo_2025, title={Trim turnpikes for optimal control problems with symmetries}, DOI={<a href=\"https://doi.org/10.1007/s00498-025-00408-w\">10.1007/s00498-025-00408-w</a>}, journal={Mathematics of Control, Signals, and Systems}, publisher={Springer Science and Business Media LLC}, author={Flaßkamp, Kathrin and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Wembe Moafo, Boris Edgar}, year={2025} }","short":"K. Flaßkamp, S. Maslovskaya, S. Ober-Blöbaum, B.E. Wembe Moafo, Mathematics of Control, Signals, and Systems (2025).","apa":"Flaßkamp, K., Maslovskaya, S., Ober-Blöbaum, S., &#38; Wembe Moafo, B. E. (2025). Trim turnpikes for optimal control problems with symmetries. <i>Mathematics of Control, Signals, and Systems</i>. <a href=\"https://doi.org/10.1007/s00498-025-00408-w\">https://doi.org/10.1007/s00498-025-00408-w</a>","chicago":"Flaßkamp, Kathrin, Sofya Maslovskaya, Sina Ober-Blöbaum, and Boris Edgar Wembe Moafo. “Trim Turnpikes for Optimal Control Problems with Symmetries.” <i>Mathematics of Control, Signals, and Systems</i>, 2025. <a href=\"https://doi.org/10.1007/s00498-025-00408-w\">https://doi.org/10.1007/s00498-025-00408-w</a>.","ieee":"K. Flaßkamp, S. Maslovskaya, S. Ober-Blöbaum, and B. E. Wembe Moafo, “Trim turnpikes for optimal control problems with symmetries,” <i>Mathematics of Control, Signals, and Systems</i>, 2025, doi: <a href=\"https://doi.org/10.1007/s00498-025-00408-w\">10.1007/s00498-025-00408-w</a>.","ama":"Flaßkamp K, Maslovskaya S, Ober-Blöbaum S, Wembe Moafo BE. Trim turnpikes for optimal control problems with symmetries. <i>Mathematics of Control, Signals, and Systems</i>. Published online 2025. doi:<a href=\"https://doi.org/10.1007/s00498-025-00408-w\">10.1007/s00498-025-00408-w</a>"},"year":"2025","department":[{"_id":"636"}],"user_id":"87909","_id":"59792","language":[{"iso":"eng"}],"publication":"Mathematics of Control, Signals, and Systems","type":"journal_article","status":"public","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n          <jats:p>Motivated by mechanical systems with symmetries, we focus on optimal control problems possessing certain symmetries. Following recent works (Faulwasser in Math Control Signals Syst 34:759–788 2022; Trélat in Math Control Signals Syst 35:685–739 2023), which generalized the classical concept of <jats:italic>static turnpike to manifold turnpike</jats:italic> we extend the <jats:italic>exponential turnpike property</jats:italic> to the <jats:italic>exponential trim turnpike</jats:italic> for control systems with symmetries induced by abelian or non-abelian groups. Our analysis is mainly based on the geometric reduction of control systems with symmetries. More concretely, we first reduce the control system on the quotient space and state the turnpike theorem for the reduced problem. Then we use the group properties to obtain the <jats:italic>trim turnpike theorem</jats:italic> for the full problem. Finally, we illustrate our results on the Kepler problem and the rigid body problem.\r\n</jats:p>"}]},{"abstract":[{"text":"We introduce a model of information dissemination in signed networks. It is a discrete-time process in which uninformed actors incrementally receive information from their informed neighbors or from the outside. Our goal is to minimize the number of confused actors — that is, the number of actors who receive contradictory information. We prove upper bounds for the number of confused actors in signed networks and in equivalence classes of signed networks. In particular, we show that there are signed networks where, for any information placement strategy, almost 60% of the actors are confused. Furthermore, this is also the case when considering the minimum number of confused actors within an equivalence class of signed graphs.","lang":"eng"}],"status":"public","type":"journal_article","publication":"Discrete Applied Mathematics","language":[{"iso":"eng"}],"_id":"59806","user_id":"15540","department":[{"_id":"542"}],"year":"2025","citation":{"ama":"Jin L, Steffen E. Information dissemination and confusion in signed networks. <i>Discrete Applied Mathematics</i>. 2025;373:99-106. doi:<a href=\"https://doi.org/10.1016/j.dam.2025.04.049\">10.1016/j.dam.2025.04.049</a>","chicago":"Jin, Ligang, and Eckhard Steffen. “Information Dissemination and Confusion in Signed Networks.” <i>Discrete Applied Mathematics</i> 373 (2025): 99–106. <a href=\"https://doi.org/10.1016/j.dam.2025.04.049\">https://doi.org/10.1016/j.dam.2025.04.049</a>.","ieee":"L. Jin and E. Steffen, “Information dissemination and confusion in signed networks,” <i>Discrete Applied Mathematics</i>, vol. 373, pp. 99–106, 2025, doi: <a href=\"https://doi.org/10.1016/j.dam.2025.04.049\">10.1016/j.dam.2025.04.049</a>.","bibtex":"@article{Jin_Steffen_2025, title={Information dissemination and confusion in signed networks}, volume={373}, DOI={<a href=\"https://doi.org/10.1016/j.dam.2025.04.049\">10.1016/j.dam.2025.04.049</a>}, journal={Discrete Applied Mathematics}, publisher={Elsevier BV}, author={Jin, Ligang and Steffen, Eckhard}, year={2025}, pages={99–106} }","short":"L. Jin, E. Steffen, Discrete Applied Mathematics 373 (2025) 99–106.","mla":"Jin, Ligang, and Eckhard Steffen. “Information Dissemination and Confusion in Signed Networks.” <i>Discrete Applied Mathematics</i>, vol. 373, Elsevier BV, 2025, pp. 99–106, doi:<a href=\"https://doi.org/10.1016/j.dam.2025.04.049\">10.1016/j.dam.2025.04.049</a>.","apa":"Jin, L., &#38; Steffen, E. (2025). Information dissemination and confusion in signed networks. <i>Discrete Applied Mathematics</i>, <i>373</i>, 99–106. <a href=\"https://doi.org/10.1016/j.dam.2025.04.049\">https://doi.org/10.1016/j.dam.2025.04.049</a>"},"intvolume":"       373","page":"99-106","publication_status":"published","publication_identifier":{"issn":["0166-218X"]},"title":"Information dissemination and confusion in signed networks","doi":"10.1016/j.dam.2025.04.049","date_updated":"2025-05-06T07:39:58Z","publisher":"Elsevier BV","author":[{"first_name":"Ligang","full_name":"Jin, Ligang","last_name":"Jin"},{"first_name":"Eckhard","id":"15548","full_name":"Steffen, Eckhard","last_name":"Steffen","orcid":"0000-0002-9808-7401"}],"date_created":"2025-05-06T07:38:49Z","volume":373},{"main_file_link":[{"url":" ArXiv:2503.07576","open_access":"1"}],"doi":"10.1007/978-3-031-91736-3_19","date_updated":"2025-05-27T08:22:42Z","oa":"1","author":[{"orcid":"0009-0002-4750-2051","last_name":"Gerlach","full_name":"Gerlach, Raphael","id":"32655","first_name":"Raphael"},{"first_name":"Sören","full_name":"von der Gracht, Sören","id":"97359","orcid":"0000-0002-8054-2058","last_name":"von der Gracht"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"}],"place":"Cham","citation":{"mla":"Gerlach, Raphael, et al. “On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies.” <i>Lecture Notes in Computer Science</i>, Springer Nature Switzerland, 2025, doi:<a href=\"https://doi.org/10.1007/978-3-031-91736-3_19\">10.1007/978-3-031-91736-3_19</a>.","bibtex":"@inbook{Gerlach_von der Gracht_Dellnitz_2025, place={Cham}, title={On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies}, DOI={<a href=\"https://doi.org/10.1007/978-3-031-91736-3_19\">10.1007/978-3-031-91736-3_19</a>}, booktitle={Lecture Notes in Computer Science}, publisher={Springer Nature Switzerland}, author={Gerlach, Raphael and von der Gracht, Sören and Dellnitz, Michael}, year={2025} }","short":"R. Gerlach, S. von der Gracht, M. Dellnitz, in: Lecture Notes in Computer Science, Springer Nature Switzerland, Cham, 2025.","apa":"Gerlach, R., von der Gracht, S., &#38; Dellnitz, M. (2025). On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies. In <i>Lecture Notes in Computer Science</i>. Springer Nature Switzerland. <a href=\"https://doi.org/10.1007/978-3-031-91736-3_19\">https://doi.org/10.1007/978-3-031-91736-3_19</a>","ama":"Gerlach R, von der Gracht S, Dellnitz M. On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies. In: <i>Lecture Notes in Computer Science</i>. Springer Nature Switzerland; 2025. doi:<a href=\"https://doi.org/10.1007/978-3-031-91736-3_19\">10.1007/978-3-031-91736-3_19</a>","ieee":"R. Gerlach, S. von der Gracht, and M. Dellnitz, “On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies,” in <i>Lecture Notes in Computer Science</i>, Cham: Springer Nature Switzerland, 2025.","chicago":"Gerlach, Raphael, Sören von der Gracht, and Michael Dellnitz. “On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies.” In <i>Lecture Notes in Computer Science</i>. Cham: Springer Nature Switzerland, 2025. <a href=\"https://doi.org/10.1007/978-3-031-91736-3_19\">https://doi.org/10.1007/978-3-031-91736-3_19</a>."},"publication_status":"published","publication_identifier":{"issn":["0302-9743","1611-3349"],"isbn":["9783031917356","9783031917363"]},"project":[{"grant_number":"453112019","_id":"106","name":"Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme"}],"_id":"60048","user_id":"32655","department":[{"_id":"101"}],"status":"public","type":"book_chapter","title":"On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies","publisher":"Springer Nature Switzerland","date_created":"2025-05-27T08:17:03Z","year":"2025","language":[{"iso":"eng"}],"external_id":{"arxiv":["2503.07576"]},"publication":"Lecture Notes in Computer Science"},{"doi":"10.1093/imanum/draf009","title":"Error estimates for full discretization of Cahn--Hilliard equation with dynamic boundary conditions","date_created":"2024-07-31T09:03:45Z","author":[{"first_name":"Nils","last_name":"Bullerjahn","orcid":"https://orcid.org/0009-0003-8460-1574","id":"103797","full_name":"Bullerjahn, Nils"},{"first_name":"Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474","id":"100441","full_name":"Kovács, Balázs"}],"date_updated":"2026-02-18T14:46:18Z","citation":{"apa":"Bullerjahn, N., &#38; Kovács, B. (n.d.). Error estimates for full discretization of Cahn--Hilliard equation with dynamic boundary conditions. <i>IMA Journal of Numerical Analysis</i>. <a href=\"https://doi.org/10.1093/imanum/draf009\">https://doi.org/10.1093/imanum/draf009</a>","bibtex":"@article{Bullerjahn_Kovács, title={Error estimates for full discretization of Cahn--Hilliard equation with dynamic boundary conditions}, DOI={<a href=\"https://doi.org/10.1093/imanum/draf009\">10.1093/imanum/draf009</a>}, journal={IMA Journal of Numerical Analysis}, author={Bullerjahn, Nils and Kovács, Balázs} }","short":"N. Bullerjahn, B. Kovács, IMA Journal of Numerical Analysis (n.d.).","mla":"Bullerjahn, Nils, and Balázs Kovács. “Error Estimates for Full Discretization of Cahn--Hilliard Equation with Dynamic Boundary Conditions.” <i>IMA Journal of Numerical Analysis</i>, doi:<a href=\"https://doi.org/10.1093/imanum/draf009\">10.1093/imanum/draf009</a>.","ama":"Bullerjahn N, Kovács B. Error estimates for full discretization of Cahn--Hilliard equation with dynamic boundary conditions. <i>IMA Journal of Numerical Analysis</i>. doi:<a href=\"https://doi.org/10.1093/imanum/draf009\">10.1093/imanum/draf009</a>","ieee":"N. Bullerjahn and B. Kovács, “Error estimates for full discretization of Cahn--Hilliard equation with dynamic boundary conditions,” <i>IMA Journal of Numerical Analysis</i>, doi: <a href=\"https://doi.org/10.1093/imanum/draf009\">10.1093/imanum/draf009</a>.","chicago":"Bullerjahn, Nils, and Balázs Kovács. “Error Estimates for Full Discretization of Cahn--Hilliard Equation with Dynamic Boundary Conditions.” <i>IMA Journal of Numerical Analysis</i>, n.d. <a href=\"https://doi.org/10.1093/imanum/draf009\">https://doi.org/10.1093/imanum/draf009</a>."},"year":"2025","publication_status":"accepted","language":[{"iso":"eng"}],"article_type":"original","user_id":"100441","department":[{"_id":"841"}],"_id":"55459","status":"public","type":"journal_article","publication":"IMA Journal of Numerical Analysis"},{"doi":"10.1093/imanum/drae077","title":"Numerical analysis of an evolving bulk--surface model of tumour growth","volume":45,"date_created":"2024-04-03T09:11:36Z","author":[{"full_name":"Edelmann, Dominik","last_name":"Edelmann","first_name":"Dominik"},{"full_name":"Kovács, Balázs","id":"100441","last_name":"Kovács","orcid":"0000-0001-9872-3474","first_name":"Balázs"},{"full_name":"Lubich, Christian","last_name":"Lubich","first_name":"Christian"}],"date_updated":"2026-02-18T14:44:54Z","page":"2581--2627","intvolume":"        45","citation":{"apa":"Edelmann, D., Kovács, B., &#38; Lubich, C. (2025). Numerical analysis of an evolving bulk--surface model of tumour growth. <i>IMA Journal of Numerical Analysis</i>, <i>45</i>(5), 2581--2627. <a href=\"https://doi.org/10.1093/imanum/drae077\">https://doi.org/10.1093/imanum/drae077</a>","mla":"Edelmann, Dominik, et al. “Numerical Analysis of an Evolving Bulk--Surface Model of Tumour Growth.” <i>IMA Journal of Numerical Analysis</i>, vol. 45, no. 5, 2025, pp. 2581--2627, doi:<a href=\"https://doi.org/10.1093/imanum/drae077\">10.1093/imanum/drae077</a>.","bibtex":"@article{Edelmann_Kovács_Lubich_2025, title={Numerical analysis of an evolving bulk--surface model of tumour growth}, volume={45}, DOI={<a href=\"https://doi.org/10.1093/imanum/drae077\">10.1093/imanum/drae077</a>}, number={5}, journal={IMA Journal of Numerical Analysis}, author={Edelmann, Dominik and Kovács, Balázs and Lubich, Christian}, year={2025}, pages={2581--2627} }","short":"D. Edelmann, B. Kovács, C. Lubich, IMA Journal of Numerical Analysis 45 (2025) 2581--2627.","chicago":"Edelmann, Dominik, Balázs Kovács, and Christian Lubich. “Numerical Analysis of an Evolving Bulk--Surface Model of Tumour Growth.” <i>IMA Journal of Numerical Analysis</i> 45, no. 5 (2025): 2581--2627. <a href=\"https://doi.org/10.1093/imanum/drae077\">https://doi.org/10.1093/imanum/drae077</a>.","ieee":"D. Edelmann, B. Kovács, and C. Lubich, “Numerical analysis of an evolving bulk--surface model of tumour growth,” <i>IMA Journal of Numerical Analysis</i>, vol. 45, no. 5, pp. 2581--2627, 2025, doi: <a href=\"https://doi.org/10.1093/imanum/drae077\">10.1093/imanum/drae077</a>.","ama":"Edelmann D, Kovács B, Lubich C. Numerical analysis of an evolving bulk--surface model of tumour growth. <i>IMA Journal of Numerical Analysis</i>. 2025;45(5):2581--2627. doi:<a href=\"https://doi.org/10.1093/imanum/drae077\">10.1093/imanum/drae077</a>"},"year":"2025","issue":"5","language":[{"iso":"eng"}],"department":[{"_id":"841"}],"user_id":"100441","_id":"53141","status":"public","publication":"IMA Journal of Numerical Analysis","type":"journal_article"},{"date_updated":"2026-02-18T14:47:34Z","author":[{"full_name":"Bai, Genming","last_name":"Bai","first_name":"Genming"},{"first_name":"Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474","id":"100441","full_name":"Kovács, Balázs"},{"first_name":"Buyang","last_name":"Li","full_name":"Li, Buyang"}],"date_created":"2024-08-27T07:37:39Z","title":"Maximal regularity of evolving FEMs for parabolic equations on an  evolving surface","doi":"10.1093/imanum/draf082.","year":"2025","citation":{"ieee":"G. Bai, B. Kovács, and B. Li, “Maximal regularity of evolving FEMs for parabolic equations on an  evolving surface,” <i>IMA Journal of Numerical Analysis</i>, 2025, doi: <a href=\"https://doi.org/10.1093/imanum/draf082.\">10.1093/imanum/draf082.</a>","chicago":"Bai, Genming, Balázs Kovács, and Buyang Li. “Maximal Regularity of Evolving FEMs for Parabolic Equations on an  Evolving Surface.” <i>IMA Journal of Numerical Analysis</i>, 2025. <a href=\"https://doi.org/10.1093/imanum/draf082.\">https://doi.org/10.1093/imanum/draf082.</a>","ama":"Bai G, Kovács B, Li B. Maximal regularity of evolving FEMs for parabolic equations on an  evolving surface. <i>IMA Journal of Numerical Analysis</i>. Published online 2025. doi:<a href=\"https://doi.org/10.1093/imanum/draf082.\">10.1093/imanum/draf082.</a>","apa":"Bai, G., Kovács, B., &#38; Li, B. (2025). Maximal regularity of evolving FEMs for parabolic equations on an  evolving surface. <i>IMA Journal of Numerical Analysis</i>. <a href=\"https://doi.org/10.1093/imanum/draf082.\">https://doi.org/10.1093/imanum/draf082.</a>","short":"G. Bai, B. Kovács, B. Li, IMA Journal of Numerical Analysis (2025).","bibtex":"@article{Bai_Kovács_Li_2025, title={Maximal regularity of evolving FEMs for parabolic equations on an  evolving surface}, DOI={<a href=\"https://doi.org/10.1093/imanum/draf082.\">10.1093/imanum/draf082.</a>}, journal={IMA Journal of Numerical Analysis}, author={Bai, Genming and Kovács, Balázs and Li, Buyang}, year={2025} }","mla":"Bai, Genming, et al. “Maximal Regularity of Evolving FEMs for Parabolic Equations on an  Evolving Surface.” <i>IMA Journal of Numerical Analysis</i>, 2025, doi:<a href=\"https://doi.org/10.1093/imanum/draf082.\">10.1093/imanum/draf082.</a>"},"external_id":{"arxiv":["2408.14096"]},"_id":"55781","department":[{"_id":"841"}],"user_id":"100441","language":[{"iso":"eng"}],"publication":"IMA Journal of Numerical Analysis","type":"journal_article","abstract":[{"lang":"eng","text":"In this paper, we prove that spatially semi-discrete evolving finite element\r\nmethod for parabolic equations on a given evolving hypersurface of arbitrary\r\ndimensions preserves the maximal $L^p$-regularity at the discrete level. We\r\nfirst establish the results on a stationary surface and then extend them, via a\r\nperturbation argument, to the case where the underlying surface is evolving\r\nunder a prescribed velocity field. The proof combines techniques in evolving\r\nfinite element method, properties of Green's functions on (discretised) closed\r\nsurfaces, and local energy estimates for finite element methods"}],"status":"public"},{"status":"public","abstract":[{"text":"A finite classical polar space of rank $n$ consists of the totally isotropic\r\nsubspaces of a finite vector space over $\\mathbb{F}_q$ equipped with a\r\nnondegenerate form such that $n$ is the maximal dimension of such a subspace. A\r\n$t$-$(n,k,\\lambda)$ design in a finite classical polar space of rank $n$ is a\r\ncollection $Y$ of totally isotropic $k$-spaces such that each totally isotropic\r\n$t$-space is contained in exactly $\\lambda$ members of $Y$. Nontrivial examples\r\nare currently only known for $t\\leq 2$. We show that $t$-$(n,k,\\lambda)$\r\ndesigns in polar spaces exist for all $t$ and $q$ provided that\r\n$k>\\frac{21}{2}t$ and $n$ is sufficiently large enough. The proof is based on a\r\nprobabilistic method by Kuperberg, Lovett, and Peled, and it is thus\r\nnonconstructive.","lang":"eng"}],"type":"journal_article","publication":"Des. Codes Cryptogr.","language":[{"iso":"eng"}],"user_id":"70420","department":[{"_id":"100"}],"_id":"50299","citation":{"ama":"Weiß C. Nontrivial $t$-designs in polar spaces exist for all $t$. <i>Des Codes Cryptogr</i>. 2025;93:971-981. doi:<a href=\"https://doi.org/10.1007/s10623-024-01471-1\">10.1007/s10623-024-01471-1</a>","chicago":"Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All $t$.” <i>Des. Codes Cryptogr.</i> 93 (2025): 971–81. <a href=\"https://doi.org/10.1007/s10623-024-01471-1\">https://doi.org/10.1007/s10623-024-01471-1</a>.","ieee":"C. Weiß, “Nontrivial $t$-designs in polar spaces exist for all $t$,” <i>Des. Codes Cryptogr.</i>, vol. 93, pp. 971–981, 2025, doi: <a href=\"https://doi.org/10.1007/s10623-024-01471-1\">10.1007/s10623-024-01471-1</a>.","bibtex":"@article{Weiß_2025, title={Nontrivial $t$-designs in polar spaces exist for all $t$}, volume={93}, DOI={<a href=\"https://doi.org/10.1007/s10623-024-01471-1\">10.1007/s10623-024-01471-1</a>}, journal={Des. Codes Cryptogr.}, author={Weiß, Charlene}, year={2025}, pages={971–981} }","short":"C. Weiß, Des. Codes Cryptogr. 93 (2025) 971–981.","mla":"Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All $t$.” <i>Des. Codes Cryptogr.</i>, vol. 93, 2025, pp. 971–81, doi:<a href=\"https://doi.org/10.1007/s10623-024-01471-1\">10.1007/s10623-024-01471-1</a>.","apa":"Weiß, C. (2025). Nontrivial $t$-designs in polar spaces exist for all $t$. <i>Des. Codes Cryptogr.</i>, <i>93</i>, 971–981. <a href=\"https://doi.org/10.1007/s10623-024-01471-1\">https://doi.org/10.1007/s10623-024-01471-1</a>"},"page":"971 - 981","intvolume":"        93","year":"2025","publication_status":"published","doi":"10.1007/s10623-024-01471-1","title":"Nontrivial $t$-designs in polar spaces exist for all $t$","date_created":"2024-01-08T14:39:54Z","author":[{"full_name":"Weiß, Charlene","id":"70420","last_name":"Weiß","first_name":"Charlene"}],"volume":93,"date_updated":"2026-02-25T13:51:50Z"},{"year":"2025","date_created":"2024-10-01T13:29:43Z","publisher":"Schloss Dagstuhl -- Leibniz-Zentrum für Informatik","title":"Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility","publication":"28th International Conference on Principles of Distributed Systems (OPODIS 2024)","abstract":[{"lang":"eng","text":"In the general pattern formation (GPF) problem, a swarm of simple autonomous,\r\ndisoriented robots must form a given pattern. The robots' simplicity imply a\r\nstrong limitation: When the initial configuration is rotationally symmetric,\r\nonly patterns with a similar symmetry can be formed [Yamashita, Suzyuki; TCS\r\n2010]. The only known algorithm to form large patterns with limited visibility\r\nand without memory requires the robots to start in a near-gathering (a swarm of\r\nconstant diameter) [Hahn et al.; SAND 2024]. However, not only do we not know\r\nany near-gathering algorithm guaranteed to preserve symmetry but most natural\r\ngathering strategies trivially increase symmetries [Castenow et al.; OPODIS\r\n2022].\r\n  Thus, we study near-gathering without changing the swarm's rotational\r\nsymmetry for disoriented, oblivious robots with limited visibility (the\r\nOBLOT-model, see [Flocchini et al.; 2019]). We introduce a technique based on\r\nthe theory of dynamical systems to analyze how a given algorithm affects\r\nsymmetry and provide sufficient conditions for symmetry preservation. Until\r\nnow, it was unknown whether the considered OBLOT-model allows for any\r\nnon-trivial algorithm that always preserves symmetry. Our first result shows\r\nthat a variant of Go-to-the-Average always preserves symmetry but may sometimes\r\nlead to multiple, unconnected near-gathering clusters. Our second result is a\r\nsymmetry-preserving near-gathering algorithm that works on swarms with a convex\r\nboundary (the outer boundary of the unit disc graph) and without holes (circles\r\nof diameter 1 inside the boundary without any robots)."}],"external_id":{"arxiv":["2409.19277"]},"language":[{"iso":"eng"}],"keyword":["Swarm Algorithm","Swarm Robots","Distributed Algorithm","Pattern Formation","Limited Visibility","Oblivious"],"publication_status":"published","publication_identifier":{"isbn":["978-3-95977-360-7"],"issn":["1868-8969"]},"citation":{"apa":"Gerlach, R., von der Gracht, S., Hahn, C., Harbig, J., &#38; Kling, P. (2025). Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility. In S. Bonomi, L. Galletta,  Etienne Rivière, &#38;  Valerio Schiavoni (Eds.), <i>28th International Conference on Principles of Distributed Systems (OPODIS 2024)</i> (Vol. 324). Schloss Dagstuhl -- Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2024.13\">https://doi.org/10.4230/LIPIcs.OPODIS.2024.13</a>","short":"R. Gerlach, S. von der Gracht, C. Hahn, J. Harbig, P. Kling, in: S. Bonomi, L. Galletta,  Etienne Rivière,  Valerio Schiavoni (Eds.), 28th International Conference on Principles of Distributed Systems (OPODIS 2024), Schloss Dagstuhl -- Leibniz-Zentrum für Informatik, 2025.","mla":"Gerlach, Raphael, et al. “Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility.” <i>28th International Conference on Principles of Distributed Systems (OPODIS 2024)</i>, edited by Silvia Bonomi et al., vol. 324, Schloss Dagstuhl -- Leibniz-Zentrum für Informatik, 2025, doi:<a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2024.13\">10.4230/LIPIcs.OPODIS.2024.13</a>.","bibtex":"@inproceedings{Gerlach_von der Gracht_Hahn_Harbig_Kling_2025, series={Leibniz International Proceedings in Informatics (LIPIcs)}, title={Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility}, volume={324}, DOI={<a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2024.13\">10.4230/LIPIcs.OPODIS.2024.13</a>}, booktitle={28th International Conference on Principles of Distributed Systems (OPODIS 2024)}, publisher={Schloss Dagstuhl -- Leibniz-Zentrum für Informatik}, author={Gerlach, Raphael and von der Gracht, Sören and Hahn, Christopher and Harbig, Jonas and Kling, Peter}, editor={Bonomi, Silvia and Galletta, Letterio and Rivière,  Etienne and Schiavoni,  Valerio}, year={2025}, collection={Leibniz International Proceedings in Informatics (LIPIcs)} }","ieee":"R. Gerlach, S. von der Gracht, C. Hahn, J. Harbig, and P. Kling, “Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility,” in <i>28th International Conference on Principles of Distributed Systems (OPODIS 2024)</i>, Lucca, Italy, 2025, vol. 324, doi: <a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2024.13\">10.4230/LIPIcs.OPODIS.2024.13</a>.","chicago":"Gerlach, Raphael, Sören von der Gracht, Christopher Hahn, Jonas Harbig, and Peter Kling. “Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility.” In <i>28th International Conference on Principles of Distributed Systems (OPODIS 2024)</i>, edited by Silvia Bonomi, Letterio Galletta,  Etienne Rivière, and  Valerio Schiavoni, Vol. 324. Leibniz International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl -- Leibniz-Zentrum für Informatik, 2025. <a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2024.13\">https://doi.org/10.4230/LIPIcs.OPODIS.2024.13</a>.","ama":"Gerlach R, von der Gracht S, Hahn C, Harbig J, Kling P. Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility. In: Bonomi S, Galletta L, Rivière  Etienne, Schiavoni  Valerio, eds. <i>28th International Conference on Principles of Distributed Systems (OPODIS 2024)</i>. Vol 324. Leibniz International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl -- Leibniz-Zentrum für Informatik; 2025. doi:<a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2024.13\">10.4230/LIPIcs.OPODIS.2024.13</a>"},"intvolume":"       324","author":[{"first_name":"Raphael","id":"32655","full_name":"Gerlach, Raphael","orcid":"0009-0002-4750-2051","last_name":"Gerlach"},{"full_name":"von der Gracht, Sören","id":"97359","last_name":"von der Gracht","orcid":"0000-0002-8054-2058","first_name":"Sören"},{"last_name":"Hahn","full_name":"Hahn, Christopher","first_name":"Christopher"},{"last_name":"Harbig","id":"47213","full_name":"Harbig, Jonas","first_name":"Jonas"},{"last_name":"Kling","full_name":"Kling, Peter","first_name":"Peter"}],"volume":324,"oa":"1","date_updated":"2025-01-09T11:39:19Z","main_file_link":[{"url":"https://arxiv.org/abs/2409.19277","open_access":"1"}],"conference":{"start_date":"2024-12-11","name":"28th International Conference on Principles of Distributed Systems (OPODIS 2024)","location":"Lucca, Italy","end_date":"2024-12-13"},"doi":"10.4230/LIPIcs.OPODIS.2024.13","type":"conference","status":"public","editor":[{"first_name":"Silvia","full_name":"Bonomi, Silvia","last_name":"Bonomi"},{"full_name":"Galletta, Letterio","last_name":"Galletta","first_name":"Letterio"},{"first_name":" Etienne","last_name":"Rivière","full_name":"Rivière,  Etienne"},{"first_name":" Valerio","full_name":"Schiavoni,  Valerio","last_name":"Schiavoni"}],"series_title":"Leibniz International Proceedings in Informatics (LIPIcs)","user_id":"97359","department":[{"_id":"101"}],"project":[{"grant_number":"453112019","name":"Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme","_id":"106"}],"_id":"56298"},{"date_updated":"2025-02-07T08:28:48Z","author":[{"orcid":"https://orcid.org/0009-0003-8460-1574","last_name":"Bullerjahn","id":"103797","full_name":"Bullerjahn, Nils","first_name":"Nils"}],"date_created":"2025-02-07T08:27:10Z","title":"Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions","doi":"10.48550/ARXIV.2502.03847","year":"2025","citation":{"bibtex":"@article{Bullerjahn_2025, title={Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions}, DOI={<a href=\"https://doi.org/10.48550/ARXIV.2502.03847\">10.48550/ARXIV.2502.03847</a>}, journal={arXiv}, author={Bullerjahn, Nils}, year={2025} }","short":"N. Bullerjahn, ArXiv (2025).","mla":"Bullerjahn, Nils. “Error Estimates for Full Discretization by an Almost Mass Conservation Technique for Cahn--Hilliard Systems with Dynamic Boundary Conditions.” <i>ArXiv</i>, 2025, doi:<a href=\"https://doi.org/10.48550/ARXIV.2502.03847\">10.48550/ARXIV.2502.03847</a>.","apa":"Bullerjahn, N. (2025). Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions. <i>ArXiv</i>. <a href=\"https://doi.org/10.48550/ARXIV.2502.03847\">https://doi.org/10.48550/ARXIV.2502.03847</a>","ama":"Bullerjahn N. Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions. <i>arXiv</i>. Published online 2025. doi:<a href=\"https://doi.org/10.48550/ARXIV.2502.03847\">10.48550/ARXIV.2502.03847</a>","ieee":"N. Bullerjahn, “Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions,” <i>arXiv</i>, 2025, doi: <a href=\"https://doi.org/10.48550/ARXIV.2502.03847\">10.48550/ARXIV.2502.03847</a>.","chicago":"Bullerjahn, Nils. “Error Estimates for Full Discretization by an Almost Mass Conservation Technique for Cahn--Hilliard Systems with Dynamic Boundary Conditions.” <i>ArXiv</i>, 2025. <a href=\"https://doi.org/10.48550/ARXIV.2502.03847\">https://doi.org/10.48550/ARXIV.2502.03847</a>."},"_id":"58532","department":[{"_id":"841"}],"user_id":"103797","language":[{"iso":"eng"}],"publication":"arXiv","type":"journal_article","status":"public"},{"title":"Multiphoton, multimode state classification for nonlinear optical circuits ","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2502.05123","open_access":"1"}],"oa":"1","date_updated":"2025-02-10T08:36:12Z","author":[{"full_name":"Kopylov, Denis","id":"98502","last_name":"Kopylov","first_name":"Denis"},{"orcid":"0000-0002-5940-8057","last_name":"Offen","full_name":"Offen, Christian","id":"85279","first_name":"Christian"},{"first_name":"Laura","last_name":"Ares","full_name":"Ares, Laura"},{"id":"95394","full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo","first_name":"Boris Edgar"},{"full_name":"Ober-Blöbaum, Sina","id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina"},{"id":"344","full_name":"Meier, Torsten","last_name":"Meier","orcid":"0000-0001-8864-2072","first_name":"Torsten"},{"last_name":"Sharapova","full_name":"Sharapova, Polina","id":"60286","first_name":"Polina"},{"first_name":"Jan","last_name":"Sperling","orcid":"0000-0002-5844-3205","full_name":"Sperling, Jan","id":"75127"}],"date_created":"2025-02-10T08:26:45Z","year":"2025","citation":{"apa":"Kopylov, D., Offen, C., Ares, L., Wembe Moafo, B. E., Ober-Blöbaum, S., Meier, T., Sharapova, P., &#38; Sperling, J. (n.d.). <i>Multiphoton, multimode state classification for nonlinear optical circuits </i>.","short":"D. Kopylov, C. Offen, L. Ares, B.E. Wembe Moafo, S. Ober-Blöbaum, T. Meier, P. Sharapova, J. Sperling, (n.d.).","mla":"Kopylov, Denis, et al. <i>Multiphoton, Multimode State Classification for Nonlinear Optical Circuits </i>.","bibtex":"@article{Kopylov_Offen_Ares_Wembe Moafo_Ober-Blöbaum_Meier_Sharapova_Sperling, title={Multiphoton, multimode state classification for nonlinear optical circuits }, author={Kopylov, Denis and Offen, Christian and Ares, Laura and Wembe Moafo, Boris Edgar and Ober-Blöbaum, Sina and Meier, Torsten and Sharapova, Polina and Sperling, Jan} }","ama":"Kopylov D, Offen C, Ares L, et al. Multiphoton, multimode state classification for nonlinear optical circuits .","chicago":"Kopylov, Denis, Christian Offen, Laura Ares, Boris Edgar Wembe Moafo, Sina Ober-Blöbaum, Torsten Meier, Polina Sharapova, and Jan Sperling. “Multiphoton, Multimode State Classification for Nonlinear Optical Circuits ,” n.d.","ieee":"D. Kopylov <i>et al.</i>, “Multiphoton, multimode state classification for nonlinear optical circuits .” ."},"publication_status":"submitted","language":[{"iso":"eng"}],"_id":"58544","external_id":{"arxiv":["2502.05123"]},"user_id":"85279","department":[{"_id":"623"},{"_id":"15"},{"_id":"636"}],"abstract":[{"text":"We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials and is invariant under unitary transformations. The classes physically correspond to field excitations in terms of single and multiple photons, each of which being in an arbitrary irreducible superposition of quantized modes. We further show how the transitions between classes are rendered possible by photon addition, photon subtraction, and photon-projection nonlinearities. We explicitly put forward a design for a multilayer interferometer in which the states for different classes can be generated with state-of-the-art experimental techniques. Limitations of the proposed designs are analyzed using the introduced classification, providing a benchmark for the robustness of certain states and classes. ","lang":"eng"}],"status":"public","type":"preprint"},{"year":"2025","date_created":"2025-03-11T08:21:05Z","title":"Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems","publication":"arXiv:2503.07576","abstract":[{"text":"In this article, we investigate symmetry properties of distributed systems of mobile robots. We consider a swarm of n robots in the OBLOT model and analyze their collective Fsync dynamics using of equivariant dynamical systems theory. To this end, we show that the corresponding evolution function commutes with rotational and reflective transformations of R^2. These form a group that is isomorphic to O(2) x S_n, the product group of the orthogonal group and the permutation on n elements. The theory of equivariant dynamical systems is used to deduce a hierarchy along which symmetries of a robot swarm can potentially increase following an arbitrary protocol. By decoupling the Look phase from the Compute and Move phases in the mathematical description of an LCM cycle, this hierarchy can be characterized in terms of automorphisms of connectivity graphs. In particular, we find all possible types of symmetry increase, if the decoupled Compute and Move phase is invertible. Finally, we apply our results to protocols which induce state-dependent linear dynamics, where the reduced system consisting of only the Compute and Move phase is linear.","lang":"eng"}],"file":[{"relation":"main_file","content_type":"application/pdf","file_name":"Analyzing_Symmetries_of_Swarms_of_Mobile_Robots_Using_Equivariant_Dynamical_Systems.pdf","access_level":"open_access","file_id":"58954","file_size":812198,"creator":"svdg","date_created":"2025-03-11T08:27:32Z","date_updated":"2025-03-11T08:27:32Z"}],"external_id":{"arxiv":["2503.07576"]},"ddc":["004"],"keyword":["dynamical systems","coupled systems","distributed computing","robot swarms","autonomous mobile robots","symmetry","equivariant dynamics"],"language":[{"iso":"eng"}],"has_accepted_license":"1","citation":{"ama":"Gerlach R, von der Gracht S. Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems. <i>arXiv:250307576</i>. Published online 2025.","ieee":"R. Gerlach and S. von der Gracht, “Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems,” <i>arXiv:2503.07576</i>. 2025.","chicago":"Gerlach, Raphael, and Sören von der Gracht. “Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems.” <i>ArXiv:2503.07576</i>, 2025.","apa":"Gerlach, R., &#38; von der Gracht, S. (2025). Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems. In <i>arXiv:2503.07576</i>.","bibtex":"@article{Gerlach_von der Gracht_2025, title={Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems}, journal={arXiv:2503.07576}, author={Gerlach, Raphael and von der Gracht, Sören}, year={2025} }","short":"R. Gerlach, S. von der Gracht, ArXiv:2503.07576 (2025).","mla":"Gerlach, Raphael, and Sören von der Gracht. “Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant  Dynamical Systems.” <i>ArXiv:2503.07576</i>, 2025."},"page":"23","date_updated":"2025-03-11T08:53:02Z","oa":"1","author":[{"last_name":"Gerlach","orcid":"0009-0002-4750-2051","id":"32655","full_name":"Gerlach, Raphael","first_name":"Raphael"},{"first_name":"Sören","last_name":"von der Gracht","orcid":"0000-0002-8054-2058","id":"97359","full_name":"von der Gracht, Sören"}],"type":"preprint","status":"public","project":[{"_id":"106","name":"Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme","grant_number":"453112019"}],"_id":"58953","user_id":"97359","department":[{"_id":"101"}],"file_date_updated":"2025-03-11T08:27:32Z"},{"doi":"10.1007/s00493-025-00144-4","volume":45,"author":[{"last_name":"Ma","full_name":"Ma, Yulai","first_name":"Yulai"},{"first_name":"Davide","full_name":"Mattiolo, Davide","last_name":"Mattiolo"},{"first_name":"Eckhard","id":"15548","full_name":"Steffen, Eckhard","last_name":"Steffen","orcid":"0000-0002-9808-7401"},{"full_name":"Wolf, Isaak H.","last_name":"Wolf","first_name":"Isaak H."}],"date_updated":"2025-03-27T09:48:48Z","intvolume":"        45","citation":{"mla":"Ma, Yulai, et al. “Sets of R-Graphs That Color All r-Graphs.” <i>Combinatorica</i>, vol. 45, no. 2, 16, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s00493-025-00144-4\">10.1007/s00493-025-00144-4</a>.","short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, Combinatorica 45 (2025).","bibtex":"@article{Ma_Mattiolo_Steffen_Wolf_2025, title={Sets of r-Graphs that Color All r-Graphs}, volume={45}, DOI={<a href=\"https://doi.org/10.1007/s00493-025-00144-4\">10.1007/s00493-025-00144-4</a>}, number={216}, journal={Combinatorica}, publisher={Springer Science and Business Media LLC}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak H.}, year={2025} }","apa":"Ma, Y., Mattiolo, D., Steffen, E., &#38; Wolf, I. H. (2025). Sets of r-Graphs that Color All r-Graphs. <i>Combinatorica</i>, <i>45</i>(2), Article 16. <a href=\"https://doi.org/10.1007/s00493-025-00144-4\">https://doi.org/10.1007/s00493-025-00144-4</a>","ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Sets of r-Graphs that Color All r-Graphs. <i>Combinatorica</i>. 2025;45(2). doi:<a href=\"https://doi.org/10.1007/s00493-025-00144-4\">10.1007/s00493-025-00144-4</a>","chicago":"Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak H. Wolf. “Sets of R-Graphs That Color All r-Graphs.” <i>Combinatorica</i> 45, no. 2 (2025). <a href=\"https://doi.org/10.1007/s00493-025-00144-4\">https://doi.org/10.1007/s00493-025-00144-4</a>.","ieee":"Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Sets of r-Graphs that Color All r-Graphs,” <i>Combinatorica</i>, vol. 45, no. 2, Art. no. 16, 2025, doi: <a href=\"https://doi.org/10.1007/s00493-025-00144-4\">10.1007/s00493-025-00144-4</a>."},"publication_identifier":{"issn":["0209-9683","1439-6912"]},"publication_status":"published","article_number":"16","department":[{"_id":"542"}],"user_id":"15540","_id":"59169","status":"public","type":"journal_article","title":"Sets of r-Graphs that Color All r-Graphs","date_created":"2025-03-27T09:46:34Z","publisher":"Springer Science and Business Media LLC","year":"2025","issue":"2","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"An r-regular graph is an r-graph, if every odd set of vertices is connected to its complement by at least r edges. Let G and H be r-graphs. An H-coloring of G is a mapping such that each r adjacent edges of G are mapped to r adjacent edges of H. For every , let be an inclusion-wise minimal set of connected r-graphs, such that for every connected r-graph G there is an which colors G. The Petersen Coloring Conjecture states that consists of the Petersen graph P. We show that if true, then this is a very exclusive situation. Our main result is that either or is an infinite set and if , then is an infinite set. In particular, for all , is unique. We first characterize and then prove that if contains more than one element, then it is an infinite set. To obtain our main result we show that contains the smallest r-graphs of class 2 and the smallest poorly matchable r-graphs, and we determine the smallest r-graphs of class 2."}],"publication":"Combinatorica"},{"citation":{"apa":"Offen, C. (2025). Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification. <i>Mathematics of Computation</i>. <a href=\"https://doi.org/10.1090/mcom/4120\">https://doi.org/10.1090/mcom/4120</a>","bibtex":"@article{Offen_2025, title={Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification}, DOI={<a href=\"https://doi.org/10.1090/mcom/4120\">10.1090/mcom/4120</a>}, journal={Mathematics of Computation}, publisher={American Mathematical Society}, author={Offen, Christian}, year={2025} }","mla":"Offen, Christian. “Machine Learning of Continuous and Discrete Variational ODEs with Convergence Guarantee and Uncertainty Quantification.” <i>Mathematics of Computation</i>, American Mathematical Society, 2025, doi:<a href=\"https://doi.org/10.1090/mcom/4120\">10.1090/mcom/4120</a>.","short":"C. Offen, Mathematics of Computation (2025).","chicago":"Offen, Christian. “Machine Learning of Continuous and Discrete Variational ODEs with Convergence Guarantee and Uncertainty Quantification.” <i>Mathematics of Computation</i>, 2025. <a href=\"https://doi.org/10.1090/mcom/4120\">https://doi.org/10.1090/mcom/4120</a>.","ieee":"C. Offen, “Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification,” <i>Mathematics of Computation</i>, 2025, doi: <a href=\"https://doi.org/10.1090/mcom/4120\">10.1090/mcom/4120</a>.","ama":"Offen C. Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification. <i>Mathematics of Computation</i>. Published online 2025. doi:<a href=\"https://doi.org/10.1090/mcom/4120\">10.1090/mcom/4120</a>"},"related_material":{"link":[{"relation":"software","description":"GitHub","url":"https://github.com/Christian-Offen/Lagrangian_GP"}]},"publication_status":"epub_ahead","has_accepted_license":"1","doi":"10.1090/mcom/4120","author":[{"last_name":"Offen","orcid":"0000-0002-5940-8057","full_name":"Offen, Christian","id":"85279","first_name":"Christian"}],"oa":"1","date_updated":"2025-06-29T13:03:55Z","status":"public","type":"journal_article","file_date_updated":"2025-05-02T13:20:31Z","article_type":"original","user_id":"85279","department":[{"_id":"636"}],"project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"_id":"53805","year":"2025","quality_controlled":"1","title":"Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification","date_created":"2024-04-30T16:04:40Z","publisher":"American Mathematical Society","file":[{"relation":"main_file","content_type":"application/pdf","description":"The article introduces a method to learn dynamical systems that\nare governed by Euler–Lagrange equations from data. The method is based on\nGaussian process regression and identifies continuous or discrete Lagrangians\nand is, therefore, structure preserving by design. A rigorous proof of con-\nvergence as the distance between observation data points converges to zero\nand lower bounds for convergence rates are provided. Next to convergence\nguarantees, the method allows for quantification of model uncertainty, which\ncan provide a basis of adaptive sampling techniques. We provide efficient uncertainty quantification of any observable that is linear in the Lagrangian,\nincluding of Hamiltonian functions (energy) and symplectic structures, which\nis of interest in the context of system identification. The article overcomes\nmajor practical and theoretical difficulties related to the ill-posedness of the\nidentification task of (discrete) Lagrangians through a careful design of geometric regularisation strategies and through an exploit of a relation to convex\nminimisation problems in reproducing kernel Hilbert spaces.","file_size":1819189,"title":"Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification ","file_name":"L_Collocation_ODE_mcom-l-template.pdf","file_id":"59759","access_level":"open_access","date_updated":"2025-05-02T13:20:31Z","date_created":"2025-05-02T13:20:31Z","creator":"coffen"}],"abstract":[{"text":"The article introduces a method to learn dynamical systems that are governed by Euler–Lagrange equations from data. The method is based on Gaussian process regression and identifies continuous or discrete Lagrangians and is, therefore, structure preserving by design. A rigorous proof of convergence as the distance between observation data points converges to zero and lower bounds for convergence rates are provided. Next to convergence guarantees, the method allows for quantification of model uncertainty, which can provide a basis of adaptive sampling techniques. We provide efficient uncertainty quantification of any observable that is linear in the Lagrangian, including of Hamiltonian functions (energy) and symplectic structures, which is of interest in the context of system identification. The article overcomes major practical and theoretical difficulties related to the ill-posedness of the identification task of (discrete) Lagrangians through a careful design of geometric regularisation strategies and through an exploit of a relation to convex minimisation problems in reproducing kernel Hilbert spaces.","lang":"eng"}],"publication":"Mathematics of Computation","language":[{"iso":"eng"}],"ddc":["510"],"external_id":{"arxiv":["arXiv:2404.19626"]}},{"type":"preprint","status":"public","abstract":[{"lang":"eng","text":"We investigate generalisations of 1-factorisations and hyperfactorisations of the complete graph $K_{2n}$. We show that they are special subsets of the association scheme obtained from the Gelfand pair $(S_{2n},S_2 \\wr S_n)$. This unifies and extends results by Cameron (1976) and gives rise to new existence and non-existence results. Our methods involve working in the group algebra $\\mathbb{C}[S_{2n}]$ and using the representation theory of $S_{2n}$."}],"user_id":"91965","department":[{"_id":"100"}],"external_id":{"arxiv":["2507.00813"]},"_id":"60491","language":[{"iso":"eng"}],"citation":{"ama":"Klawuhn L-AD, Bamberg J. On the association scheme of perfect matchings and their designs. Published online 2025.","ieee":"L.-A. D. Klawuhn and J. Bamberg, “On the association scheme of perfect matchings and their designs.” 2025.","chicago":"Klawuhn, Lukas-André Dominik, and John Bamberg. “On the Association Scheme of Perfect Matchings and Their Designs,” 2025.","apa":"Klawuhn, L.-A. D., &#38; Bamberg, J. (2025). <i>On the association scheme of perfect matchings and their designs</i>.","short":"L.-A.D. Klawuhn, J. Bamberg, (2025).","bibtex":"@article{Klawuhn_Bamberg_2025, title={On the association scheme of perfect matchings and their designs}, author={Klawuhn, Lukas-André Dominik and Bamberg, John}, year={2025} }","mla":"Klawuhn, Lukas-André Dominik, and John Bamberg. <i>On the Association Scheme of Perfect Matchings and Their Designs</i>. 2025."},"year":"2025","date_created":"2025-07-02T07:37:23Z","author":[{"first_name":"Lukas-André Dominik","id":"91965","full_name":"Klawuhn, Lukas-André Dominik","last_name":"Klawuhn","orcid":"0009-0009-7736-4885"},{"first_name":"John","full_name":"Bamberg, John","last_name":"Bamberg"}],"date_updated":"2025-07-02T07:47:09Z","title":"On the association scheme of perfect matchings and their designs"},{"status":"public","abstract":[{"lang":"eng","text":"We introduce the concept of a k-token signed graph and study some of its combinatorial and algebraic properties. We prove that two switching isomorphic signed graphs have switching isomorphic token graphs. Moreover, we show that the Laplacian spectrum of a balanced signed graph is contained in the Laplacian spectra of its k-token signed graph. Besides, we introduce and study the unbalance level of a signed graph, which is a new parameter that measures how far a signed graph is from being balanced. Moreover, we study the relation between the frustration index and the unbalance level of signed graphs and their token signed graphs."}],"publication":"Journal of Algebraic Combinatorics","type":"journal_article","language":[{"iso":"eng"}],"article_number":"7","department":[{"_id":"542"}],"user_id":"15540","_id":"61042","intvolume":"        62","citation":{"bibtex":"@article{Dalfó_Fiol_Steffen_2025, title={On token signed graphs}, volume={62}, DOI={<a href=\"https://doi.org/10.1007/s10801-025-01416-4\">10.1007/s10801-025-01416-4</a>}, number={17}, journal={Journal of Algebraic Combinatorics}, publisher={Springer Science and Business Media LLC}, author={Dalfó, C. and Fiol, M. A. and Steffen, Eckhard}, year={2025} }","short":"C. Dalfó, M.A. Fiol, E. Steffen, Journal of Algebraic Combinatorics 62 (2025).","mla":"Dalfó, C., et al. “On Token Signed Graphs.” <i>Journal of Algebraic Combinatorics</i>, vol. 62, no. 1, 7, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s10801-025-01416-4\">10.1007/s10801-025-01416-4</a>.","apa":"Dalfó, C., Fiol, M. A., &#38; Steffen, E. (2025). On token signed graphs. <i>Journal of Algebraic Combinatorics</i>, <i>62</i>(1), Article 7. <a href=\"https://doi.org/10.1007/s10801-025-01416-4\">https://doi.org/10.1007/s10801-025-01416-4</a>","ama":"Dalfó C, Fiol MA, Steffen E. On token signed graphs. <i>Journal of Algebraic Combinatorics</i>. 2025;62(1). doi:<a href=\"https://doi.org/10.1007/s10801-025-01416-4\">10.1007/s10801-025-01416-4</a>","ieee":"C. Dalfó, M. A. Fiol, and E. Steffen, “On token signed graphs,” <i>Journal of Algebraic Combinatorics</i>, vol. 62, no. 1, Art. no. 7, 2025, doi: <a href=\"https://doi.org/10.1007/s10801-025-01416-4\">10.1007/s10801-025-01416-4</a>.","chicago":"Dalfó, C., M. A. Fiol, and Eckhard Steffen. “On Token Signed Graphs.” <i>Journal of Algebraic Combinatorics</i> 62, no. 1 (2025). <a href=\"https://doi.org/10.1007/s10801-025-01416-4\">https://doi.org/10.1007/s10801-025-01416-4</a>."},"year":"2025","issue":"1","publication_identifier":{"issn":["0925-9899","1572-9192"]},"publication_status":"published","doi":"10.1007/s10801-025-01416-4","title":"On token signed graphs","volume":62,"date_created":"2025-08-28T07:50:03Z","author":[{"first_name":"C.","full_name":"Dalfó, C.","last_name":"Dalfó"},{"first_name":"M. A.","full_name":"Fiol, M. A.","last_name":"Fiol"},{"full_name":"Steffen, Eckhard","id":"15548","orcid":"0000-0002-9808-7401","last_name":"Steffen","first_name":"Eckhard"}],"date_updated":"2025-08-28T07:57:27Z","publisher":"Springer Science and Business Media LLC"},{"status":"public","file":[{"creator":"sofyam","date_created":"2025-05-05T09:28:02Z","date_updated":"2025-05-05T09:28:02Z","file_id":"59795","file_name":"2410.09537v2.pdf","access_level":"closed","file_size":1830758,"content_type":"application/pdf","relation":"main_file","success":1}],"abstract":[{"lang":"eng","text":"The depth of networks plays a crucial role in the effectiveness of deep learning. However, the memory requirement for backpropagation scales linearly with the number of layers, which leads to memory bottlenecks during training. Moreover, deep networks are often unable to handle time-series data appearing at irregular intervals. These issues can be resolved by considering continuous-depth networks based on the neural ODE framework in combination with reversible integration methods that allow for variable time-steps. Reversibility of the method ensures that the memory requirement for training is independent of network depth, while variable time-steps are required for assimilating time-series data on irregular intervals. However, at present, there are no known higher-order reversible methods with this property. High-order methods are especially important when a high level of accuracy in learning is required or when small time-steps are necessary due to large errors in time integration of neural ODEs, for instance in context of complex dynamical systems such as Kepler systems and molecular dynamics. The requirement of small time-steps when using a low-order method can significantly increase the computational cost of training as well as inference. In this work, we present an approach for constructing high-order reversible methods that allow adaptive time-stepping. Our numerical tests show the advantages in computational speed when applied to the task of learning dynamical systems."}],"type":"preprint","language":[{"iso":"eng"}],"file_date_updated":"2025-05-05T09:28:02Z","ddc":["510"],"department":[{"_id":"636"}],"user_id":"85279","external_id":{"arxiv":["2410.09537"]},"_id":"59794","citation":{"ama":"Maslovskaya S, Ober-Blöbaum S, Offen C, Singh P, Wembe Moafo BE. Adaptive higher order reversible integrators for memory efficient deep learning. Published online 2025.","ieee":"S. Maslovskaya, S. Ober-Blöbaum, C. Offen, P. Singh, and B. E. Wembe Moafo, “Adaptive higher order reversible integrators for memory efficient deep learning.” 2025.","chicago":"Maslovskaya, Sofya, Sina Ober-Blöbaum, Christian Offen, Pranav Singh, and Boris Edgar Wembe Moafo. “Adaptive Higher Order Reversible Integrators for Memory Efficient Deep Learning,” 2025.","apa":"Maslovskaya, S., Ober-Blöbaum, S., Offen, C., Singh, P., &#38; Wembe Moafo, B. E. (2025). <i>Adaptive higher order reversible integrators for memory efficient deep learning</i>.","mla":"Maslovskaya, Sofya, et al. <i>Adaptive Higher Order Reversible Integrators for Memory Efficient Deep Learning</i>. 2025.","bibtex":"@article{Maslovskaya_Ober-Blöbaum_Offen_Singh_Wembe Moafo_2025, title={Adaptive higher order reversible integrators for memory efficient deep learning}, author={Maslovskaya, Sofya and Ober-Blöbaum, Sina and Offen, Christian and Singh, Pranav and Wembe Moafo, Boris Edgar}, year={2025} }","short":"S. Maslovskaya, S. Ober-Blöbaum, C. Offen, P. Singh, B.E. Wembe Moafo, (2025)."},"year":"2025","has_accepted_license":"1","title":"Adaptive higher order reversible integrators for memory efficient deep learning","author":[{"first_name":"Sofya","full_name":"Maslovskaya, Sofya","id":"87909","last_name":"Maslovskaya"},{"first_name":"Sina","id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"},{"first_name":"Christian","id":"85279","full_name":"Offen, Christian","last_name":"Offen","orcid":"0000-0002-5940-8057"},{"last_name":"Singh","full_name":"Singh, Pranav","first_name":"Pranav"},{"first_name":"Boris Edgar","id":"95394","full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo"}],"date_created":"2025-05-05T09:25:28Z","date_updated":"2025-09-30T15:16:09Z"},{"external_id":{"arxiv":["2411.18422"]},"ddc":["510"],"keyword":["Pareto optimization","Lyapunov analysis","gradient-like dynamical systems","inertial dynamics","asymptotic vanishing damping","Tikhonov regularization","strong convergence"],"language":[{"iso":"eng"}],"publication":"Journal of Mathematical Analysis and Applications","abstract":[{"lang":"eng","text":"In this paper we introduce, in a Hilbert space setting, a second order dynamical system with asymptotically vanishing damping and vanishing Tikhonov regularization that approaches a multiobjective optimization problem with convex and differentiable components of the objective function. Trajectory solutions are shown to exist in finite dimensions. We prove fast convergence of the function values, quantified in terms of a merit function. Based on the regime considered, we establish both weak and, in some cases, strong convergence of trajectory solutions toward a weak Pareto optimal solution. To achieve this, we apply Tikhonov regularization individually to each component of the objective function. This work extends results from single objective convex optimization into the multiobjective setting."}],"file":[{"content_type":"application/pdf","relation":"main_file","creator":"sonntagk","date_created":"2024-11-28T08:58:00Z","date_updated":"2024-11-28T08:58:00Z","file_name":"Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization.pdf","file_id":"57473","access_level":"open_access","file_size":4291134}],"date_created":"2024-11-28T08:58:17Z","title":"Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization","year":"2025","_id":"57472","user_id":"56399","department":[{"_id":"101"},{"_id":"530"},{"_id":"655"}],"file_date_updated":"2024-11-28T08:58:00Z","type":"journal_article","status":"public","date_updated":"2025-10-16T11:56:36Z","oa":"1","author":[{"full_name":"Bot, Radu Ioan","last_name":"Bot","first_name":"Radu Ioan"},{"last_name":"Sonntag","orcid":"https://orcid.org/0000-0003-3384-3496","id":"56399","full_name":"Sonntag, Konstantin","first_name":"Konstantin"}],"main_file_link":[{"url":"https://arxiv.org/pdf/2411.18422"}],"has_accepted_license":"1","citation":{"ama":"Bot RI, Sonntag K. Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization. <i>Journal of Mathematical Analysis and Applications</i>. Published online 2025.","chicago":"Bot, Radu Ioan, and Konstantin Sonntag. “Inertial Dynamics with Vanishing Tikhonov Regularization for Multobjective Optimization.” <i>Journal of Mathematical Analysis and Applications</i>, 2025.","ieee":"R. I. Bot and K. Sonntag, “Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization,” <i>Journal of Mathematical Analysis and Applications</i>, 2025.","apa":"Bot, R. I., &#38; Sonntag, K. (2025). Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization. <i>Journal of Mathematical Analysis and Applications</i>.","short":"R.I. Bot, K. Sonntag, Journal of Mathematical Analysis and Applications (2025).","bibtex":"@article{Bot_Sonntag_2025, title={Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization}, journal={Journal of Mathematical Analysis and Applications}, author={Bot, Radu Ioan and Sonntag, Konstantin}, year={2025} }","mla":"Bot, Radu Ioan, and Konstantin Sonntag. “Inertial Dynamics with Vanishing Tikhonov Regularization for Multobjective Optimization.” <i>Journal of Mathematical Analysis and Applications</i>, 2025."}}]