[{"language":[{"iso":"eng"}],"title":"Design of Hierarchical Excitable Networks","year":"2026","author":[{"id":"97359","first_name":"Sören","last_name":"von der Gracht","orcid":"0000-0002-8054-2058","full_name":"von der Gracht, Sören"},{"first_name":"Alexander","last_name":"Lohse","full_name":"Lohse, Alexander"}],"date_updated":"2026-03-09T08:26:49Z","file":[{"creator":"svdg","date_created":"2026-03-09T08:26:04Z","file_name":"design-of-hierarchical-excitable-networks.pdf","file_size":5179491,"access_level":"closed","relation":"main_file","date_updated":"2026-03-09T08:26:04Z","file_id":"64866","content_type":"application/pdf","success":1}],"date_created":"2026-03-09T08:22:58Z","type":"preprint","department":[{"_id":"101"},{"_id":"841"}],"publication":"arXiv:2603.06157","related_material":{"link":[{"relation":"research_paper","url":"https://s-vdg.github.io/publication/design-of-hierarchical-excitable-networks/design-of-hierarchical-excitable-networks.pdf"}]},"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"}],"_id":"64865","user_id":"97359","ddc":["510"],"status":"public","has_accepted_license":"1","external_id":{"arxiv":["2603.06157"]},"file_date_updated":"2026-03-09T08:26:04Z","citation":{"chicago":"Gracht, Sören von der, and Alexander Lohse. “Design of Hierarchical Excitable Networks.” <i>ArXiv:2603.06157</i>, 2026.","short":"S. von der Gracht, A. Lohse, ArXiv:2603.06157 (2026).","apa":"von der Gracht, S., &#38; Lohse, A. (2026). Design of Hierarchical Excitable Networks. In <i>arXiv:2603.06157</i>.","ieee":"S. von der Gracht and A. Lohse, “Design of Hierarchical Excitable Networks,” <i>arXiv:2603.06157</i>. 2026.","ama":"von der Gracht S, Lohse A. Design of Hierarchical Excitable Networks. <i>arXiv:260306157</i>. Published online 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."}},{"abstract":[{"lang":"eng","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."}],"publication":"Multibody System Dynamics","citation":{"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>.","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>","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>","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>.","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>.","short":"M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R.T. Sato Martín de Almagro, Multibody System Dynamics (2026)."},"type":"journal_article","department":[{"_id":"636"}],"date_created":"2026-01-12T11:33:54Z","date_updated":"2026-01-12T11:35:27Z","publication_status":"published","year":"2026","title":"On the variational discretisation of optimal control problems for unconstrained Lagrangian dynamics","status":"public","publication_identifier":{"issn":["1384-5640","1573-272X"]},"author":[{"last_name":"Konopik","first_name":"Michael","full_name":"Konopik, Michael"},{"last_name":"Leyendecker","first_name":"Sigrid","full_name":"Leyendecker, Sigrid"},{"first_name":"Sofya","last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya","id":"87909"},{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina","id":"16494"},{"full_name":"Sato Martín de Almagro, Rodrigo T.","first_name":"Rodrigo T.","last_name":"Sato Martín de Almagro"}],"doi":"10.1007/s11044-025-10138-1","user_id":"87909","language":[{"iso":"eng"}],"_id":"63557","publisher":"Springer Science and Business Media LLC"},{"file":[{"relation":"main_file","date_updated":"2026-03-16T08:40:04Z","file_name":"homogeneous-coupled-cell-systems-with-high-dimensional-internal-dynamics.pdf","access_level":"closed","file_size":1951746,"file_id":"64980","content_type":"application/pdf","success":1,"creator":"svdg","date_created":"2026-03-16T08:40:04Z"}],"date_created":"2026-03-16T08:39:07Z","type":"journal_article","keyword":["Coupled cell systems","Network dynamics","Dimension reduction","Bifurcation theory","Symmetry","Monoid representation theory"],"department":[{"_id":"101"},{"_id":"841"}],"publication":"Chaos, Solitons & Fractals","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."}],"article_number":"118196","language":[{"iso":"eng"}],"doi":"10.1016/j.chaos.2026.118196","title":"Homogeneous coupled cell systems with high-dimensional internal dynamics","year":"2026","author":[{"id":"97359","last_name":"von der Gracht","orcid":"0000-0002-8054-2058","first_name":"Sören","full_name":"von der Gracht, Sören"},{"full_name":"Nijholt, Eddie","first_name":"Eddie","last_name":"Nijholt"},{"last_name":"Rink","first_name":"Bob","full_name":"Rink, Bob"}],"publication_identifier":{"issn":["0960-0779"]},"publication_status":"published","date_updated":"2026-03-16T08:42:56Z","article_type":"original","intvolume":"       208","external_id":{"arxiv":["2510.06740"]},"file_date_updated":"2026-03-16T08:40:04Z","citation":{"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} }","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>","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>.","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>.","short":"S. von der Gracht, E. Nijholt, B. Rink, Chaos, Solitons &#38; Fractals 208 (2026).","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>"},"publisher":"Elsevier BV","_id":"64979","user_id":"97359","ddc":["510"],"volume":208,"status":"public","has_accepted_license":"1"},{"doi":"10.1016/j.ffa.2026.102828","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S1071579726000390","open_access":"1"}],"article_number":"102828","language":[{"iso":"eng"}],"date_updated":"2026-05-06T15:08:06Z","intvolume":"       114","article_type":"original","year":"2026","title":"The Intersection Distribution: New Results and Perspectives","author":[{"full_name":"Klawuhn, Lukas-André Dominik","orcid":"0009-0009-7736-4885","last_name":"Klawuhn","first_name":"Lukas-André Dominik","id":"91965"},{"full_name":"Huczynska, Sophie","first_name":"Sophie","last_name":"Huczynska"},{"full_name":"Paterson, Maura","last_name":"Paterson","first_name":"Maura"}],"type":"journal_article","department":[{"_id":"100"}],"date_created":"2025-10-08T14:52:20Z","abstract":[{"text":"Intersection distribution and non-hitting index are concepts introduced recently by Li and Pott as a new way to view the behaviour of a collection of finite field polynomials. With both an algebraic interpretation via the intersection of a polynomial with a set of lines, and a geometric interpretation via a (q+1)-set possessing an internal nucleus, the concepts have proved their usefulness as a new way to view various long-standing problems, and have applications in areas such as Kakeya sets. In this paper, by exploiting connections with diverse areas including the theory of algebraic curves, cyclotomy and the enumeration of irreducible polynomials, we establish new results and resolve various Open Problems of Li and Pott. We prove geometric results which shed new light on the relationship between intersection distribution and projective equivalence of polynomials, and algebraic results which describe and characterise the degree of Sf - the index of the largest non-zero entry in the intersection distribution of f. We provide new insights into the non-hitting spectrum, and show the limitations of the non-hitting index as a tool for characterisation. Finally, the benefits provided by the connections to other areas are evidenced in two short new proofs of the cubic case. ","lang":"eng"}],"publication":"Finite Fields and Their Applications","user_id":"91965","volume":114,"_id":"61759","publisher":"Elsevier","status":"public","oa":"1","citation":{"short":"L.-A.D. Klawuhn, S. Huczynska, M. Paterson, Finite Fields and Their Applications 114 (2026).","chicago":"Klawuhn, Lukas-André Dominik, Sophie Huczynska, and Maura Paterson. “The Intersection Distribution: New Results and Perspectives.” <i>Finite Fields and Their Applications</i> 114 (2026). <a href=\"https://doi.org/10.1016/j.ffa.2026.102828\">https://doi.org/10.1016/j.ffa.2026.102828</a>.","ieee":"L.-A. D. Klawuhn, S. Huczynska, and M. Paterson, “The Intersection Distribution: New Results and Perspectives,” <i>Finite Fields and Their Applications</i>, vol. 114, Art. no. 102828, 2026, doi: <a href=\"https://doi.org/10.1016/j.ffa.2026.102828\">10.1016/j.ffa.2026.102828</a>.","apa":"Klawuhn, L.-A. D., Huczynska, S., &#38; Paterson, M. (2026). The Intersection Distribution: New Results and Perspectives. <i>Finite Fields and Their Applications</i>, <i>114</i>, Article 102828. <a href=\"https://doi.org/10.1016/j.ffa.2026.102828\">https://doi.org/10.1016/j.ffa.2026.102828</a>","bibtex":"@article{Klawuhn_Huczynska_Paterson_2026, title={The Intersection Distribution: New Results and Perspectives}, volume={114}, DOI={<a href=\"https://doi.org/10.1016/j.ffa.2026.102828\">10.1016/j.ffa.2026.102828</a>}, number={102828}, journal={Finite Fields and Their Applications}, publisher={Elsevier}, author={Klawuhn, Lukas-André Dominik and Huczynska, Sophie and Paterson, Maura}, year={2026} }","ama":"Klawuhn L-AD, Huczynska S, Paterson M. The Intersection Distribution: New Results and Perspectives. <i>Finite Fields and Their Applications</i>. 2026;114. doi:<a href=\"https://doi.org/10.1016/j.ffa.2026.102828\">10.1016/j.ffa.2026.102828</a>","mla":"Klawuhn, Lukas-André Dominik, et al. “The Intersection Distribution: New Results and Perspectives.” <i>Finite Fields and Their Applications</i>, vol. 114, 102828, Elsevier, 2026, doi:<a href=\"https://doi.org/10.1016/j.ffa.2026.102828\">10.1016/j.ffa.2026.102828</a>."}},{"date_updated":"2026-06-26T06:09:29Z","year":"2026","title":"Error estimates for $A$-stable backward difference full discretizations of Willmore flow of closed surfaces","status":"public","author":[{"last_name":"Bullerjahn","orcid":"https://orcid.org/0009-0003-8460-1574","first_name":"Nils","full_name":"Bullerjahn, Nils","id":"103797"},{"orcid":"0000-0001-9872-3474","first_name":"Balázs","last_name":"Kovács","full_name":"Kovács, Balázs","id":"100441"}],"user_id":"103797","doi":"10.48550/arXiv.2606.25934","_id":"66057","language":[{"iso":"eng"}],"publication":"ArXiv","citation":{"apa":"Bullerjahn, N., &#38; Kovács, B. (2026). Error estimates for $A$-stable backward difference full discretizations of Willmore flow of closed surfaces. <i>ArXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2606.25934\">https://doi.org/10.48550/arXiv.2606.25934</a>","ieee":"N. Bullerjahn and B. Kovács, “Error estimates for $A$-stable backward difference full discretizations of Willmore flow of closed surfaces,” <i>ArXiv</i>, 2026, doi: <a href=\"https://doi.org/10.48550/arXiv.2606.25934\">10.48550/arXiv.2606.25934</a>.","short":"N. Bullerjahn, B. Kovács, ArXiv (2026).","chicago":"Bullerjahn, Nils, and Balázs Kovács. “Error Estimates for $A$-Stable Backward Difference Full Discretizations of Willmore Flow of Closed Surfaces.” <i>ArXiv</i>, 2026. <a href=\"https://doi.org/10.48550/arXiv.2606.25934\">https://doi.org/10.48550/arXiv.2606.25934</a>.","mla":"Bullerjahn, Nils, and Balázs Kovács. “Error Estimates for $A$-Stable Backward Difference Full Discretizations of Willmore Flow of Closed Surfaces.” <i>ArXiv</i>, 2026, doi:<a href=\"https://doi.org/10.48550/arXiv.2606.25934\">10.48550/arXiv.2606.25934</a>.","ama":"Bullerjahn N, Kovács B. Error estimates for $A$-stable backward difference full discretizations of Willmore flow of closed surfaces. <i>ArXiv</i>. Published online 2026. doi:<a href=\"https://doi.org/10.48550/arXiv.2606.25934\">10.48550/arXiv.2606.25934</a>","bibtex":"@article{Bullerjahn_Kovács_2026, title={Error estimates for $A$-stable backward difference full discretizations of Willmore flow of closed surfaces}, DOI={<a href=\"https://doi.org/10.48550/arXiv.2606.25934\">10.48550/arXiv.2606.25934</a>}, journal={ArXiv}, author={Bullerjahn, Nils and Kovács, Balázs}, year={2026} }"},"type":"journal_article","department":[{"_id":"841"}],"date_created":"2026-06-26T06:03:08Z"},{"author":[{"last_name":"Klawuhn","first_name":"Lukas-André Dominik","orcid":"0009-0009-7736-4885","full_name":"Klawuhn, Lukas-André Dominik","id":"91965"},{"full_name":"Bamberg, John","last_name":"Bamberg","first_name":"John"}],"title":"On the association scheme of perfect matchings and their designs","year":"2026","intvolume":"         9","date_updated":"2026-07-10T12:26:11Z","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://alco.centre-mersenne.org/articles/10.5802/alco.490/"}],"doi":"10.5802/alco.490","publication":"Algebraic Combinatorics","issue":"3","abstract":[{"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 $S_{2n}$.","lang":"eng"}],"date_created":"2025-07-02T07:37:23Z","department":[{"_id":"100"}],"type":"journal_article","status":"public","_id":"60491","page":"789-809","volume":9,"user_id":"91965","citation":{"mla":"Klawuhn, Lukas-André Dominik, and John Bamberg. “On the Association Scheme of Perfect Matchings and Their Designs.” <i>Algebraic Combinatorics</i>, vol. 9, no. 3, 2026, pp. 789–809, doi:<a href=\"https://doi.org/10.5802/alco.490\">10.5802/alco.490</a>.","bibtex":"@article{Klawuhn_Bamberg_2026, title={On the association scheme of perfect matchings and their designs}, volume={9}, DOI={<a href=\"https://doi.org/10.5802/alco.490\">10.5802/alco.490</a>}, number={3}, journal={Algebraic Combinatorics}, author={Klawuhn, Lukas-André Dominik and Bamberg, John}, year={2026}, pages={789–809} }","ama":"Klawuhn L-AD, Bamberg J. On the association scheme of perfect matchings and their designs. <i>Algebraic Combinatorics</i>. 2026;9(3):789-809. doi:<a href=\"https://doi.org/10.5802/alco.490\">10.5802/alco.490</a>","ieee":"L.-A. D. Klawuhn and J. Bamberg, “On the association scheme of perfect matchings and their designs,” <i>Algebraic Combinatorics</i>, vol. 9, no. 3, pp. 789–809, 2026, doi: <a href=\"https://doi.org/10.5802/alco.490\">10.5802/alco.490</a>.","apa":"Klawuhn, L.-A. D., &#38; Bamberg, J. (2026). On the association scheme of perfect matchings and their designs. <i>Algebraic Combinatorics</i>, <i>9</i>(3), 789–809. <a href=\"https://doi.org/10.5802/alco.490\">https://doi.org/10.5802/alco.490</a>","chicago":"Klawuhn, Lukas-André Dominik, and John Bamberg. “On the Association Scheme of Perfect Matchings and Their Designs.” <i>Algebraic Combinatorics</i> 9, no. 3 (2026): 789–809. <a href=\"https://doi.org/10.5802/alco.490\">https://doi.org/10.5802/alco.490</a>.","short":"L.-A.D. Klawuhn, J. Bamberg, Algebraic Combinatorics 9 (2026) 789–809."},"oa":"1"},{"department":[{"_id":"100"}],"type":"preprint","date_created":"2026-08-17T10:29:36Z","external_id":{"arxiv":["2608.14437"]},"abstract":[{"lang":"eng","text":"We generalize intersection numbers for combinatorial designs to designs in finite meet-semilattices satisfying suitable regularity conditions. While designs in regular semilattices go back to Delsarte, our regularity assumptions are weaker than his and need not give rise to an association scheme. In this framework, we extend Mendelsohn's equations, prove a generalized Singleton bound with Steiner systems as equality cases, and determine the block intersection distribution at any block of a Steiner system. In particular, this distribution is independent of the chosen block.\r\n  Specializing to several classical semilattice families, our results recover a number of well-known distributions in coding and design theory. In the Hamming and the $q$-Hamming (or bilinear forms) schemes, they give the local distance distributions of MDS and MRD codes, respectively. In the Johnson and $q$-Johnson (or Graßmann) schemes, they reproduce the block intersection distribution of classical and $q$-analog Steiner systems, equivalently the distance distribution of diameter-perfect constant-weight codes and diameter-perfect constant-dimension subspace codes. For the $q$-Johnson schemes, to the best of our knowledge, this result is new. As a further illustration, we apply our theory to designs of perfect matchings.\r\n  Our approach provides a unified treatment of these cases in the strongest form known in the literature, determining the distribution relative to each individual block or codeword, without averaging and without linearity or additivity assumptions. Moreover, it identifies the natural double-counting objects underlying these distributions, leading to formulas in the regularity parameters of the semilattice and avoiding the more cumbersome expressions that arise in eigenvalue-based approaches via the ambient association scheme."}],"citation":{"ama":"Kiermaier M, Klawuhn L-AD. Intersection numbers for designs in regular semilattices. Published online 2026.","bibtex":"@article{Kiermaier_Klawuhn_2026, title={Intersection numbers for designs in regular semilattices}, author={Kiermaier, Michael and Klawuhn, Lukas-André Dominik}, year={2026} }","mla":"Kiermaier, Michael, and Lukas-André Dominik Klawuhn. <i>Intersection Numbers for Designs in Regular Semilattices</i>. 2026.","chicago":"Kiermaier, Michael, and Lukas-André Dominik Klawuhn. “Intersection Numbers for Designs in Regular Semilattices,” 2026.","short":"M. Kiermaier, L.-A.D. Klawuhn, (2026).","apa":"Kiermaier, M., &#38; Klawuhn, L.-A. D. (2026). <i>Intersection numbers for designs in regular semilattices</i>.","ieee":"M. Kiermaier and L.-A. D. Klawuhn, “Intersection numbers for designs in regular semilattices.” 2026."},"user_id":"91965","language":[{"iso":"eng"}],"_id":"66731","date_updated":"2026-08-17T10:31:03Z","author":[{"first_name":"Michael","last_name":"Kiermaier","full_name":"Kiermaier, Michael"},{"full_name":"Klawuhn, Lukas-André Dominik","last_name":"Klawuhn","first_name":"Lukas-André Dominik","orcid":"0009-0009-7736-4885","id":"91965"}],"title":"Intersection numbers for designs in regular semilattices","year":"2026","status":"public"},{"date_created":"2025-05-05T09:23:38Z","department":[{"_id":"636"}],"type":"journal_article","citation":{"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>","short":"K. Flaßkamp, S. Maslovskaya, S. Ober-Blöbaum, B.E. Wembe Moafo, Mathematics of Control, Signals, and Systems (2025).","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>.","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} }","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>.","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>","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>."},"publication":"Mathematics of Control, Signals, and Systems","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>"}],"publisher":"Springer Science and Business Media LLC","_id":"59792","language":[{"iso":"eng"}],"doi":"10.1007/s00498-025-00408-w","user_id":"87909","publication_identifier":{"issn":["0932-4194","1435-568X"]},"author":[{"full_name":"Flaßkamp, Kathrin","last_name":"Flaßkamp","first_name":"Kathrin"},{"id":"87909","full_name":"Maslovskaya, Sofya","first_name":"Sofya","last_name":"Maslovskaya"},{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina","id":"16494"},{"last_name":"Wembe Moafo","first_name":"Boris Edgar","full_name":"Wembe Moafo, Boris Edgar","id":"95394"}],"status":"public","title":"Trim turnpikes for optimal control problems with symmetries","year":"2025","date_updated":"2025-05-05T09:24:09Z","publication_status":"published"},{"department":[{"_id":"542"}],"type":"journal_article","date_created":"2025-05-06T07:38:49Z","abstract":[{"lang":"eng","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."}],"publication":"Discrete Applied Mathematics","doi":"10.1016/j.dam.2025.04.049","language":[{"iso":"eng"}],"intvolume":"       373","publication_status":"published","date_updated":"2025-05-06T07:39:58Z","publication_identifier":{"issn":["0166-218X"]},"author":[{"full_name":"Jin, Ligang","last_name":"Jin","first_name":"Ligang"},{"full_name":"Steffen, Eckhard","last_name":"Steffen","first_name":"Eckhard","orcid":"0000-0002-9808-7401","id":"15548"}],"year":"2025","title":"Information dissemination and confusion in signed networks","citation":{"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>.","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>","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>.","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>.","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} }","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>"},"volume":373,"user_id":"15540","_id":"59806","publisher":"Elsevier BV","page":"99-106","status":"public"},{"status":"public","user_id":"32655","_id":"60048","publisher":"Springer Nature Switzerland","project":[{"name":"Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme","_id":"106","grant_number":"453112019"}],"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>.","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>","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} }","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>","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.","short":"R. Gerlach, S. von der Gracht, M. Dellnitz, in: Lecture Notes in Computer Science, Springer Nature Switzerland, Cham, 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>."},"oa":"1","external_id":{"arxiv":["2503.07576"]},"place":"Cham","publication_status":"published","date_updated":"2025-05-27T08:22:42Z","title":"On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies","year":"2025","author":[{"id":"32655","full_name":"Gerlach, Raphael","first_name":"Raphael","orcid":"0009-0002-4750-2051","last_name":"Gerlach"},{"full_name":"von der Gracht, Sören","orcid":"0000-0002-8054-2058","first_name":"Sören","last_name":"von der Gracht","id":"97359"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"}],"publication_identifier":{"issn":["0302-9743","1611-3349"],"isbn":["9783031917356","9783031917363"]},"doi":"10.1007/978-3-031-91736-3_19","main_file_link":[{"url":" ArXiv:2503.07576","open_access":"1"}],"language":[{"iso":"eng"}],"publication":"Lecture Notes in Computer Science","type":"book_chapter","department":[{"_id":"101"}],"date_created":"2025-05-27T08:17:03Z"},{"status":"public","title":"Error estimates for full discretization of Cahn--Hilliard equation with dynamic boundary conditions","year":"2025","author":[{"full_name":"Bullerjahn, Nils","first_name":"Nils","last_name":"Bullerjahn","orcid":"https://orcid.org/0009-0003-8460-1574","id":"103797"},{"full_name":"Kovács, Balázs","last_name":"Kovács","first_name":"Balázs","orcid":"0000-0001-9872-3474","id":"100441"}],"publication_status":"accepted","date_updated":"2026-02-18T14:46:18Z","article_type":"original","language":[{"iso":"eng"}],"_id":"55459","user_id":"100441","doi":"10.1093/imanum/draf009","publication":"IMA Journal of Numerical Analysis","citation":{"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>","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} }","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>.","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>.","short":"N. Bullerjahn, B. Kovács, IMA Journal of Numerical Analysis (n.d.).","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>","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>."},"date_created":"2024-07-31T09:03:45Z","type":"journal_article","department":[{"_id":"841"}]},{"issue":"5","publication":"IMA Journal of Numerical Analysis","citation":{"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>.","short":"D. Edelmann, B. Kovács, C. Lubich, IMA Journal of Numerical Analysis 45 (2025) 2581--2627.","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>","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>","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} }","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>."},"type":"journal_article","department":[{"_id":"841"}],"date_created":"2024-04-03T09:11:36Z","date_updated":"2026-02-18T14:44:54Z","intvolume":"        45","status":"public","year":"2025","title":"Numerical analysis of an evolving bulk--surface model of tumour growth","author":[{"last_name":"Edelmann","first_name":"Dominik","full_name":"Edelmann, Dominik"},{"full_name":"Kovács, Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474","first_name":"Balázs","id":"100441"},{"full_name":"Lubich, Christian","first_name":"Christian","last_name":"Lubich"}],"user_id":"100441","doi":"10.1093/imanum/drae077","volume":45,"page":"2581--2627","language":[{"iso":"eng"}],"_id":"53141"},{"title":"Maximal regularity of evolving FEMs for parabolic equations on an  evolving surface","year":"2025","status":"public","author":[{"first_name":"Genming","last_name":"Bai","full_name":"Bai, Genming"},{"id":"100441","full_name":"Kovács, Balázs","first_name":"Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474"},{"last_name":"Li","first_name":"Buyang","full_name":"Li, Buyang"}],"date_updated":"2026-02-18T14:47:34Z","_id":"55781","language":[{"iso":"eng"}],"doi":"10.1093/imanum/draf082.","user_id":"100441","publication":"IMA Journal of Numerical Analysis","citation":{"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>","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>","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>","short":"G. Bai, B. Kovács, B. Li, IMA Journal of Numerical Analysis (2025).","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>","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>"},"abstract":[{"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","lang":"eng"}],"external_id":{"arxiv":["2408.14096"]},"date_created":"2024-08-27T07:37:39Z","type":"journal_article","department":[{"_id":"841"}]},{"intvolume":"        93","publication_status":"published","date_updated":"2026-02-25T13:51:50Z","author":[{"last_name":"Weiß","first_name":"Charlene","full_name":"Weiß, Charlene","id":"70420"}],"status":"public","title":"Nontrivial $t$-designs in polar spaces exist for all $t$","year":"2025","volume":93,"user_id":"70420","doi":"10.1007/s10623-024-01471-1","_id":"50299","language":[{"iso":"eng"}],"page":"971 - 981","abstract":[{"lang":"eng","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."}],"citation":{"short":"C. Weiß, Des. Codes Cryptogr. 93 (2025) 971–981.","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>.","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>","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>.","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>","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} }","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>."},"publication":"Des. Codes Cryptogr.","department":[{"_id":"100"}],"type":"journal_article","date_created":"2024-01-08T14:39:54Z"},{"_id":"59794","language":[{"iso":"eng"}],"user_id":"85279","ddc":["510"],"title":"Adaptive higher order reversible integrators for memory efficient deep learning","status":"public","year":"2025","author":[{"id":"87909","full_name":"Maslovskaya, Sofya","first_name":"Sofya","last_name":"Maslovskaya"},{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494"},{"id":"85279","first_name":"Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","full_name":"Offen, Christian"},{"full_name":"Singh, Pranav","last_name":"Singh","first_name":"Pranav"},{"last_name":"Wembe Moafo","first_name":"Boris Edgar","full_name":"Wembe Moafo, Boris Edgar","id":"95394"}],"date_updated":"2025-09-30T15:16:09Z","has_accepted_license":"1","file":[{"file_name":"2410.09537v2.pdf","access_level":"closed","file_size":1830758,"relation":"main_file","date_updated":"2025-05-05T09:28:02Z","file_id":"59795","success":1,"content_type":"application/pdf","creator":"sofyam","date_created":"2025-05-05T09:28:02Z"}],"external_id":{"arxiv":["2410.09537"]},"date_created":"2025-05-05T09:25:28Z","type":"preprint","department":[{"_id":"636"}],"file_date_updated":"2025-05-05T09:28:02Z","citation":{"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.","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>.","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.","short":"S. Maslovskaya, S. Ober-Blöbaum, C. Offen, P. Singh, B.E. Wembe Moafo, (2025).","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} }","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."},"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."}]},{"date_updated":"2025-10-16T11:56:36Z","title":"Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization","year":"2025","author":[{"last_name":"Bot","first_name":"Radu Ioan","full_name":"Bot, Radu Ioan"},{"full_name":"Sonntag, Konstantin","orcid":"https://orcid.org/0000-0003-3384-3496","last_name":"Sonntag","first_name":"Konstantin","id":"56399"}],"main_file_link":[{"url":"https://arxiv.org/pdf/2411.18422"}],"language":[{"iso":"eng"}],"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."}],"publication":"Journal of Mathematical Analysis and Applications","keyword":["Pareto optimization","Lyapunov analysis","gradient-like dynamical systems","inertial dynamics","asymptotic vanishing damping","Tikhonov regularization","strong convergence"],"type":"journal_article","department":[{"_id":"101"},{"_id":"530"},{"_id":"655"}],"file":[{"date_created":"2024-11-28T08:58:00Z","creator":"sonntagk","file_id":"57473","content_type":"application/pdf","file_name":"Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization.pdf","file_size":4291134,"access_level":"open_access","relation":"main_file","date_updated":"2024-11-28T08:58:00Z"}],"date_created":"2024-11-28T08:58:17Z","has_accepted_license":"1","status":"public","user_id":"56399","ddc":["510"],"_id":"57472","file_date_updated":"2024-11-28T08:58:00Z","citation":{"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} }","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.","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.","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.","short":"R.I. Bot, K. Sonntag, Journal of Mathematical Analysis and Applications (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>."},"oa":"1","external_id":{"arxiv":["2411.18422"]}},{"supervisor":[{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"},{"id":"16494","first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"}],"citation":{"mla":"Sonntag, Konstantin. <i>First-Order Methods and Gradient Dynamical Systems for Multiobjective Optimization</i>. Paderborn University, 2025, doi:<a href=\"https://doi.org/10.17619/UNIPB/1-2457\">10.17619/UNIPB/1-2457</a>.","bibtex":"@book{Sonntag_2025, title={First-order methods and gradient dynamical systems for multiobjective optimization}, DOI={<a href=\"https://doi.org/10.17619/UNIPB/1-2457\">10.17619/UNIPB/1-2457</a>}, publisher={Paderborn University}, author={Sonntag, Konstantin}, year={2025} }","ama":"Sonntag K. <i>First-Order Methods and Gradient Dynamical Systems for Multiobjective Optimization</i>. Paderborn University; 2025. doi:<a href=\"https://doi.org/10.17619/UNIPB/1-2457\">10.17619/UNIPB/1-2457</a>","ieee":"K. Sonntag, <i>First-order methods and gradient dynamical systems for multiobjective optimization</i>. Paderborn University, 2025.","apa":"Sonntag, K. (2025). <i>First-order methods and gradient dynamical systems for multiobjective optimization</i>. Paderborn University. <a href=\"https://doi.org/10.17619/UNIPB/1-2457\">https://doi.org/10.17619/UNIPB/1-2457</a>","chicago":"Sonntag, Konstantin. <i>First-Order Methods and Gradient Dynamical Systems for Multiobjective Optimization</i>. Paderborn University, 2025. <a href=\"https://doi.org/10.17619/UNIPB/1-2457\">https://doi.org/10.17619/UNIPB/1-2457</a>.","short":"K. Sonntag, First-Order Methods and Gradient Dynamical Systems for Multiobjective Optimization, Paderborn University, 2025."},"oa":"1","status":"public","has_accepted_license":"1","_id":"62750","publisher":"Paderborn University","ddc":["510"],"user_id":"56399","abstract":[{"text":"Diese Dissertation enthält Beiträge zum Bereich der Mehrzieloptimierung mit einem Fokus auf unbeschränkten Problemen, die auf einem allgemeinen Hilbertraum definiert sind. Für Mehrzieloptimierungsprobleme mit lokal Lipschitz-stetigen Zielfunktionen definieren wir ein multikriterielles Subdifferential, das wir erstmals im Kontext allgemeiner Hilberträume analysieren. Aufbauend auf diesen theoretischen Untersuchungen präsentieren wir ein Abstiegsverfahren, bei welchem in jeder Iteration eine Abstiegsrichtung mittels einer numerischen Approximation des multikriteriellen Subdifferentials bestimmt wird. Im Kontext konvexer, stetig differenzierbarer Zielfunktionen mit Lipschitz-stetigen Gradienten, führen wir eine Familie von dynamischen Gradientensystemen mit Trägheitsterm ein, die bekannte kontinuierliche Systeme aus der skalaren Optimierung verallgemeinern. Wir stellen drei neue Systeme vor: eines mit konstanter Dämpfung, eines mit asymptotisch abnehmender Dämpfung und eines, das zusätzlich eine zeitabhängige Tikhonov-Regularisierung beinhaltet. Aufbauend auf den Untersuchungen der neuen dynamischen Gradientensysteme, entwickeln wir ein beschleunigtes Gradientenverfahren zur Mehrzieloptimierung, das auf einer Diskretisierung des multikriteriellen Gradientensystems mit asymptotisch abnehmender Dämpfung beruht. Das hergeleitete Verfahren bewahrt die günstigen Konvergenzeigenschaften des kontinuierlichen Systems und erreicht eine schnellere Konvergenz als klassische Verfahren.","lang":"eng"},{"lang":"eng","text":"This dissertation contributes to the field of multiobjective optimization, with a focus on unconstrained problems formulated in a general Hilbert space. For multiobjective optimization problems with locally Lipschitz continuous objective functions, we define a multiobjective subdifferential, which we analyze for the first time in the context of general Hilbert spaces. Building on these theoretical investigations, we present a descent method in which, at each iteration, a descent direction is determined via a numerical approximation of the multiobjective subdifferential. In the setting of convex, continuously differentiable objective functions with Lipschitz continuous gradients, we introduce a family of inertial gradient dynamical systems that generalize well-known continuous-time systems from scalar optimization. We present three novel systems: one with constant damping, one with asymptotic vanishing damping, and one combining vanishing damping with time-dependent Tikhonov regularization. Building on the investigation of the novel gradient dynamical systems, we develop an accelerated gradient method for multiobjective optimization via discretization of the multiobjective gradient system with asymptotic vanishing damping. The proposed method retains the favorable convergence properties of the continuous system while achieving faster convergence than standard approaches, such as classical methods."}],"date_created":"2025-12-03T06:55:01Z","department":[{"_id":"101"},{"_id":"530"}],"type":"dissertation","author":[{"orcid":"https://orcid.org/0000-0003-3384-3496","last_name":"Sonntag","first_name":"Konstantin","full_name":"Sonntag, Konstantin","id":"56399"}],"year":"2025","title":"First-order methods and gradient dynamical systems for multiobjective optimization","date_updated":"2025-12-03T07:04:36Z","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://digital.ub.uni-paderborn.de/hs/download/pdf/8141881","open_access":"1"}],"doi":"10.17619/UNIPB/1-2457"},{"citation":{"ieee":"D. A. Kopylov <i>et al.</i>, “Multiphoton, multimode state classification for nonlinear optical circuits,” <i>Physical Review Research</i>, vol. 7, no. 3, Art. no. 033062, 2025, doi: <a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>.","apa":"Kopylov, D. A., Offen, C., Ares, L., Wembe Moafo, B. E., Ober-Blöbaum, S., Meier, T., Sharapova, P. R., &#38; Sperling, J. (2025). Multiphoton, multimode state classification for nonlinear optical circuits. <i>Physical Review Research</i>, <i>7</i>(3), Article 033062. <a href=\"https://doi.org/10.1103/sv6z-v1gk\">https://doi.org/10.1103/sv6z-v1gk</a>","short":"D.A. Kopylov, C. Offen, L. Ares, B.E. Wembe Moafo, S. Ober-Blöbaum, T. Meier, P.R. Sharapova, J. Sperling, Physical Review Research 7 (2025).","chicago":"Kopylov, Denis A., Christian Offen, Laura Ares, Boris Edgar Wembe Moafo, Sina Ober-Blöbaum, Torsten Meier, Polina R. Sharapova, and Jan Sperling. “Multiphoton, Multimode State Classification for Nonlinear Optical Circuits.” <i>Physical Review Research</i> 7, no. 3 (2025). <a href=\"https://doi.org/10.1103/sv6z-v1gk\">https://doi.org/10.1103/sv6z-v1gk</a>.","mla":"Kopylov, Denis A., et al. “Multiphoton, Multimode State Classification for Nonlinear Optical Circuits.” <i>Physical Review Research</i>, vol. 7, no. 3, 033062, American Physical Society (APS), 2025, doi:<a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>.","bibtex":"@article{Kopylov_Offen_Ares_Wembe Moafo_Ober-Blöbaum_Meier_Sharapova_Sperling_2025, title={Multiphoton, multimode state classification for nonlinear optical circuits}, volume={7}, DOI={<a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>}, number={3033062}, journal={Physical Review Research}, publisher={American Physical Society (APS)}, author={Kopylov, Denis A. and Offen, Christian and Ares, Laura and Wembe Moafo, Boris Edgar and Ober-Blöbaum, Sina and Meier, Torsten and Sharapova, Polina R. and Sperling, Jan}, year={2025} }","ama":"Kopylov DA, Offen C, Ares L, et al. Multiphoton, multimode state classification for nonlinear optical circuits. <i>Physical Review Research</i>. 2025;7(3). doi:<a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>"},"project":[{"name":"TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten zu funktionellen Strukturen","_id":"53"},{"_id":"56","name":"TRR 142 - Project Area C"},{"_id":"174","name":"TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen Systemen: Eine theoretische Analyse"},{"name":"PhoQC: Photonisches Quantencomputing","_id":"266"}],"status":"public","publisher":"American Physical Society (APS)","_id":"62980","user_id":"16199","volume":7,"publication":"Physical Review Research","issue":"3","abstract":[{"text":"<jats:p>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 is 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.</jats:p>","lang":"eng"}],"date_created":"2025-12-09T09:08:39Z","type":"journal_article","department":[{"_id":"15"},{"_id":"569"},{"_id":"170"},{"_id":"293"},{"_id":"706"},{"_id":"636"},{"_id":"35"},{"_id":"230"},{"_id":"429"},{"_id":"623"}],"title":"Multiphoton, multimode state classification for nonlinear optical circuits","year":"2025","author":[{"full_name":"Kopylov, Denis A.","first_name":"Denis A.","last_name":"Kopylov"},{"id":"85279","orcid":"0000-0002-5940-8057","last_name":"Offen","first_name":"Christian","full_name":"Offen, Christian"},{"full_name":"Ares, Laura","last_name":"Ares","first_name":"Laura"},{"id":"95394","last_name":"Wembe Moafo","first_name":"Boris Edgar","full_name":"Wembe Moafo, Boris Edgar"},{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina","id":"16494"},{"full_name":"Meier, Torsten","orcid":"0000-0001-8864-2072","first_name":"Torsten","last_name":"Meier","id":"344"},{"id":"60286","full_name":"Sharapova, Polina R.","last_name":"Sharapova","first_name":"Polina R."},{"orcid":"0000-0002-5844-3205","first_name":"Jan","last_name":"Sperling","full_name":"Sperling, Jan","id":"75127"}],"publication_identifier":{"issn":["2643-1564"]},"date_updated":"2025-12-09T09:10:01Z","publication_status":"published","intvolume":"         7","article_number":"033062","language":[{"iso":"eng"}],"doi":"10.1103/sv6z-v1gk"},{"status":"public","year":"2025","title":"Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor","author":[{"full_name":"Kidner, Arnott Jeffery Joel","last_name":"Kidner","first_name":"Arnott Jeffery Joel","id":"111755"},{"last_name":"Steffen","first_name":"Eckhard","orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard","id":"15548"},{"last_name":"Yu","first_name":"Weiqiang","full_name":"Yu, Weiqiang","id":"117508"}],"date_updated":"2025-12-18T13:17:18Z","_id":"63187","language":[{"iso":"eng"}],"user_id":"15540","publication":"arXiv:2512.14285","citation":{"ieee":"A. J. J. Kidner, E. Steffen, and W. Yu, “Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor,” <i>arXiv:2512.14285</i>. 2025.","apa":"Kidner, A. J. J., Steffen, E., &#38; Yu, W. (2025). Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor. In <i>arXiv:2512.14285</i>.","short":"A.J.J. Kidner, E. Steffen, W. Yu, ArXiv:2512.14285 (2025).","chicago":"Kidner, Arnott Jeffery Joel, Eckhard Steffen, and Weiqiang Yu. “Edge-Coloring 4- and 5-Regular Projective Planar Graphs with No Petersen-Minor.” <i>ArXiv:2512.14285</i>, 2025.","mla":"Kidner, Arnott Jeffery Joel, et al. “Edge-Coloring 4- and 5-Regular Projective Planar Graphs with No Petersen-Minor.” <i>ArXiv:2512.14285</i>, 2025.","bibtex":"@article{Kidner_Steffen_Yu_2025, title={Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor}, journal={arXiv:2512.14285}, author={Kidner, Arnott Jeffery Joel and Steffen, Eckhard and Yu, Weiqiang}, year={2025} }","ama":"Kidner AJJ, Steffen E, Yu W. Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor. <i>arXiv:251214285</i>. Published online 2025."},"external_id":{"arxiv":["2512.14285"]},"date_created":"2025-12-17T14:40:23Z","type":"preprint","department":[{"_id":"542"}]},{"date_updated":"2025-12-19T11:23:41Z","author":[{"full_name":"Devillers, Alice","last_name":"Devillers","first_name":"Alice"},{"full_name":"Giudici, Michael","last_name":"Giudici","first_name":"Michael"},{"full_name":"Hawtin, Daniel R.","first_name":"Daniel R.","last_name":"Hawtin"},{"id":"91965","orcid":"0009-0009-7736-4885","first_name":"Lukas-André Dominik","last_name":"Klawuhn","full_name":"Klawuhn, Lukas-André Dominik"},{"first_name":"Luke","last_name":"Morgan","full_name":"Morgan, Luke"}],"title":"Linear dimension of group actions","year":"2025","status":"public","user_id":"91965","language":[{"iso":"eng"}],"_id":"63384","abstract":[{"text":"Two fundamental ways to represent a group are as permutations and as matrices. In this paper, we study linear representations of groups that intertwine with a permutation representation. Recently, D'Alconzo and Di Scala investigated how small the matrices in such a linear representation can be. The minimal dimension of such a representation is the \\emph{linear dimension of the group action} and this has applications in cryptography and cryptosystems.\r\n\r\nWe develop the idea of linear dimension from an algebraic point of view by using the theory of permutation modules. We give structural results about representations of minimal dimension and investigate the implications of faithfulness, transitivity and primitivity on the linear dimension. Furthermore, we compute the linear dimension of several classes of finite primitive permutation groups. We also study wreath products, allowing us to determine the linear dimension of imprimitive group actions. Finally, we give the linear dimension of almost simple finite $2$-transitive groups, some of which may be used for further applications in cryptography. Our results also open up many new questions about linear representations of group actions.","lang":"eng"}],"citation":{"short":"A. Devillers, M. Giudici, D.R. Hawtin, L.-A.D. Klawuhn, L. Morgan, (2025).","chicago":"Devillers, Alice, Michael Giudici, Daniel R. Hawtin, Lukas-André Dominik Klawuhn, and Luke Morgan. “Linear Dimension of Group Actions,” 2025.","apa":"Devillers, A., Giudici, M., Hawtin, D. R., Klawuhn, L.-A. D., &#38; Morgan, L. (2025). <i>Linear dimension of group actions</i>.","ieee":"A. Devillers, M. Giudici, D. R. Hawtin, L.-A. D. Klawuhn, and L. Morgan, “Linear dimension of group actions.” 2025.","ama":"Devillers A, Giudici M, Hawtin DR, Klawuhn L-AD, Morgan L. Linear dimension of group actions. Published online 2025.","bibtex":"@article{Devillers_Giudici_Hawtin_Klawuhn_Morgan_2025, title={Linear dimension of group actions}, author={Devillers, Alice and Giudici, Michael and Hawtin, Daniel R. and Klawuhn, Lukas-André Dominik and Morgan, Luke}, year={2025} }","mla":"Devillers, Alice, et al. <i>Linear Dimension of Group Actions</i>. 2025."},"department":[{"_id":"100"}],"type":"preprint","date_created":"2025-12-19T11:20:46Z","external_id":{"arxiv":["2512.16079"]}}]