TY - GEN A1 - Witzig, Jakob A1 - Beckenbach, Isabel A1 - Eifler, Leon A1 - Fackeldey, Konstantin A1 - Gleixner, Ambros A1 - Grever, Andreas A1 - Weber, Marcus T1 - Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes N2 - In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to the time scale of interest, i.e., of the whole process. In this setting, the detection of a global cyclic behavior of the process becomes difficult because transitions between individual states may appear almost reversible on the small time scale of the simulation. We address this difficulty using a mixed-integer programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. For a synthetic genetic regulatory network consisting of a ring-oscillator with three genes, we show that this approach can detect the most productive overall cycle, outperforming classical spectral analysis methods. Our method applies to general non-equilibrium steady state systems such as catalytic reactions, for which the objective value computes the effectiveness of the catalyst. T3 - ZIB-Report - 16-39 KW - Non-reversible Markov Processes KW - NESS KW - Mixed-Integer Programming KW - Markov State Models Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-60353 SN - 1438-0064 ER - TY - JOUR A1 - Witzig, Jakob A1 - Beckenbach, Isabel A1 - Eifler, Leon A1 - Fackeldey, Konstantin A1 - Gleixner, Ambros A1 - Grever, Andreas A1 - Weber, Marcus T1 - Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes JF - Multiscale Modeling and Simulation N2 - In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to the time scale of interest, i.e., of the whole process. In this setting, the detection of a global cyclic behavior of the process becomes difficult because transitions between individual states may appear almost reversible on the small time scale of the simulation. We address this difficulty using a mixed-integer programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. For a synthetic genetic regulatory network consisting of a ring-oscillator with three genes, we show that this approach can detect the most productive overall cycle, outperforming classical spectral analysis methods. Our method applies to general non-equilibrium steady state systems such as catalytic reactions, for which the objective value computes the effectiveness of the catalyst. KW - Markov State Models KW - NESS KW - Non-reversible Markov Processes KW - Mixed-Integer Programming Y1 - 2018 U6 - https://doi.org/10.1137/16M1091162 SN - 1438-0064 VL - 16 IS - 1 SP - 248 EP - 265 ER - TY - JOUR A1 - Gorgulla, Christoph A1 - Garza, Alejandro J. A1 - Kapil, Venkat A1 - Fackeldey, Konstantin T1 - QUASAR: A Flexible QM-MM Method for Biomolecular Systems based on Restraining Spheres JF - Computer Physics Communications N2 - Quantum mechanical models of molecules theoretically offer unprecedented accuracy in predicting values associated with these systems, including the free energy of interaction between two molecules. However, high-accuracy quantum mechanical methods are computationally too expensive to be applied to larger systems, including most biomolecular systems such as proteins. To circumvent this challenge, the hybrid quantum mechanics/molecular mechanics (QM/MM) method was developed, allowing one to treat only the most important part of the system on the quantum mechanical level and the remaining part on the classical level. To date, QM/MM simulations for biomolecular systems have been carried out almost exclusively on the electronic structure level, neglecting nuclear quantum effects (NQEs). Yet NQEs can play a major role in biomolecular systems [1]. Here, we present i-QI, a QM/MM client for the path integral molecular dynamics (PIMD) software i-PI [2, 3, 4]. i-QI allows for carrying out QM/MM simulations simultaneously, allowing for the inclusion of electronic as well as nuclear quantum effects. i-QI implements a new QM/MM scheme based on constraining potentials called QUASAR, which allows handling diffusive systems, such as biomolecules solvated in water solvent. The QUASAR method is suitable in particular when the properties of interest are equilibrium properties, such as the free energy of binding. i-QI is freely available and open source, and we demonstrate it on a test system. KW - QM-MM Methods KW - Path Integral KW - biomolecular systems KW - CADD KW - Free Energy KW - Binding Y1 - 2025 U6 - https://doi.org/10.1016/j.cpc.2025.109949 SN - 0010-4655 VL - 320 ER - TY - JOUR A1 - Gonnermann-Müller, Jana A1 - Haase, Jennifer A1 - Leins, Nicolas A1 - Igel, Moritz A1 - Fackeldey, Konstantin A1 - Pokutta, Sebastian T1 - FACET: Multi-Agent AI Supporting Teachers in Scaling Differentiated Learning for Diverse Students JF - arXiv N2 - Classrooms are becoming increasingly heterogeneous, comprising learners with diverse performance and motivation levels, language proficiencies, and learning differences such as dyslexia and ADHD. While teachers recognize the need for differentiated instruction, growing workloads create substantial barriers, making differentiated instruction an ideal that is often unrealized in practice. Current AI educational tools, which promise differentiated materials, are predominantly student-facing and performance-centric, ignoring other aspects that shape learning outcomes. We introduce FACET, a teacher-facing multi-agent framework designed to address these gaps by supporting differentiation that accounts for motivation, performance, and learning differences. Developed with educational stakeholders from the outset, the framework coordinates four specialized agents, including learner simulation, diagnostic assessment, material generation, and evaluation within a teacher-in-the-loop design. School principals (N = 30) shaped system requirements through participatory workshops, while in-service K-12 teachers (N = 70) evaluated material quality. Mixed-methods evaluation demonstrates strong perceived value for inclusive differentiation. Practitioners emphasized both the urgent need arising from classroom heterogeneity and the importance of maintaining pedagogical autonomy as a prerequisite for adoption. We discuss implications for future school deployment and outline partnerships for longitudinal classroom implementation. Y1 - 2026 U6 - https://doi.org/https://arxiv.org/abs/2601.22788 ER - TY - JOUR A1 - Gonnermann-Müller, Jana A1 - Haase, Jennifer A1 - Fackeldey, Konstantin A1 - Pokutta, Sebastian T1 - FACET: Teacher-Centred LLM-Based Multi-Agent Systems-Towards Personalized Educational Worksheets N2 - The increasing heterogeneity of student populations poses significant challenges for teachers, particularly in mathematics education, where cognitive, motivational, and emotional differences strongly influence learning outcomes. While AI-driven personalization tools have emerged, most remain performance-focused, offering limited support for teachers and neglecting broader pedagogical needs. This paper presents the FACET framework, a teacher-facing, large language model (LLM)-based multi-agent system designed to generate individualized classroom materials that integrate both cognitive and motivational dimensions of learner profiles. The framework comprises three specialized agents: (1) learner agents that simulate diverse profiles incorporating topic proficiency and intrinsic motivation, (2) a teacher agent that adapts instructional content according to didactical principles, and (3) an evaluator agent that provides automated quality assurance. We tested the system using authentic grade 8 mathematics curriculum content and evaluated its feasibility through a) automated agent-based assessment of output quality and b) exploratory feedback from K-12 in-service teachers. Results from ten internal evaluations highlighted high stability and alignment between generated materials and learner profiles, and teacher feedback particularly highlighted structure and suitability of tasks. The findings demonstrate the potential of multi-agent LLM architectures to provide scalable, context-aware personalization in heterogeneous classroom settings, and outline directions for extending the framework to richer learner profiles and real-world classroom trials. Y1 - 2025 ER -