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 WorksheetsHier den Haupttitel eintragen 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 - TY - GEN A1 - Raharinirina, N. Alexia A1 - Weber, Marcus A1 - Birk, Ralph A1 - Fackeldey, Konstantin A1 - Klasse, Sarah M. A1 - Richter, Tonio Sebastian T1 - Different Tools and Results for Correspondence Analysis N2 - This is a list of codes generated from ancient egyptian texts. The codes are used for a correspondence analysis (CA). Codes and CA software are available from the linked webpage. Y1 - 2021 U6 - https://doi.org/10.12752/8257 N1 - A detailed description of the software can be found in the code repository at https://github.com/AlexiaNomena/Correspondence_Analysis_User_Friendly (repository version of CA software might include updates). ER - TY - JOUR A1 - Nitzke, Isabel A1 - Fackeldey, Konstantin A1 - Vrabec, Jadran T1 - Long range corrections for inhomogeneous fluids containing a droplet or a bubble JF - Molecular Simulation N2 - Long range corrections for molecular simulations of inhomogeneous fluids with a spherical interface are presented. Correction terms for potential energy, force and virial are derived for the monatomic Lennard–Jones fluid. The method is generalised to the Mie potential and arbitrary molecular structures, employing a numerically efficient centre of mass cut-off scheme. The results are validated by a series of droplet simulations for one-centre and two-centre Lennard–Jones fluids with different cut-off radii rc. Systems with rc=8σ provide a check of self-consistence. Further, a system containing a bubble is investigated for the one-centre Lennard–Jones fluid. The equilibrium properties are almost completely independent on the cut-off radius. In comparison with vapour–liquid equilibrium data for systems without a curved interface, all properties show the expected behaviour. Simulation data are used to approximate the surface tension, which is in good agreement with the findings for planar interfaces, thus verifying the present corrections. Y1 - 2021 U6 - https://doi.org/https://doi.org/10.1080/08927022.2021.1954639 SP - 1 EP - 14 ER - TY - JOUR A1 - Secker, Christopher A1 - Fackeldey, Konstantin A1 - Weber, Marcus A1 - Ray, Sourav A1 - Gorgulla, Christoph A1 - Schütte, Christof T1 - Novel multi-objective affinity approach allows to identify pH-specific μ-opioid receptor agonists JF - Journal of Cheminformatics N2 - Opioids are essential pharmaceuticals due to their analgesic properties, however, lethal side effects, addiction, and opioid tolerance are extremely challenging. The development of novel molecules targeting the μ-opioid receptor (MOR) in inflamed, but not in healthy tissue, could significantly reduce these unwanted effects. Finding such novel molecules can be achieved by maximizing the binding affinity to the MOR at acidic pH while minimizing it at neutral pH, thus combining two conflicting objectives. Here, this multi-objective optimal affinity approach is presented, together with a virtual drug discovery pipeline for its practical implementation. When applied to finding pH-specific drug candidates, it combines protonation state-dependent structure and ligand preparation with high-throughput virtual screening. We employ this pipeline to characterize a set of MOR agonists identifying a morphine-like opioid derivative with higher predicted binding affinities to the MOR at low pH compared to neutral pH. Our results also confirm existing experimental evidence that NFEPP, a previously described fentanyl derivative with reduced side effects, and recently reported β-fluorofentanyls and -morphines show an increased specificity for the MOR at acidic pH when compared to fentanyl and morphine. We further applied our approach to screen a >50K ligand library identifying novel molecules with pH-specific predicted binding affinities to the MOR. The presented differential docking pipeline can be applied to perform multi-objective affinity optimization to identify safer and more specific drug candidates at large scale. Y1 - 2023 U6 - https://doi.org/10.1186/s13321-023-00746-4 VL - 15 ER - TY - JOUR A1 - Gorgulla, Christoph A1 - Jayaraj, Abhilash A1 - Fackeldey, Konstantin A1 - Arthanari, Haribabu T1 - Emerging frontiers in virtual drug discovery: From quantum mechanical methods to deep learning approaches JF - Current Opinion in Chemical Biology N2 - Virtual screening-based approaches to discover initial hit and lead compounds have the potential to reduce both the cost and time of early drug discovery stages, as well as to find inhibitors for even challenging target sites such as protein–protein interfaces. Here in this review, we provide an overview of the progress that has been made in virtual screening methodology and technology on multiple fronts in recent years. The advent of ultra-large virtual screens, in which hundreds of millions to billions of compounds are screened, has proven to be a powerful approach to discover highly potent hit compounds. However, these developments are just the tip of the iceberg, with new technologies and methods emerging to propel the field forward. Examples include novel machine-learning approaches, which can reduce the computational costs of virtual screening dramatically, while progress in quantum-mechanical approaches can increase the accuracy of predictions of various small molecule properties. Y1 - 2022 U6 - https://doi.org/10.1016/j.cbpa.2022.102156 VL - 69 SP - 102156 EP - 102156-12 ER - TY - JOUR A1 - Sechi, Renata A1 - Fackeldey, Konstantin A1 - Chewle, Surahit A1 - Weber, Marcus T1 - SepFree NMF: A Toolbox for Analyzing the Kinetics of Sequential Spectroscopic Data JF - Algorithms N2 - This work addresses the problem of determining the number of components from sequential spectroscopic data analyzed by non-negative matrix factorization without separability assumption (SepFree NMF). These data are stored in a matrix M of dimension “measured times” versus “measured wavenumbers” and can be decomposed to obtain the spectral fingerprints of the states and their evolution over time. SepFree NMF assumes a memoryless (Markovian) process to underline the dynamics and decomposes M so that M=WH, with W representing the components’ fingerprints and H their kinetics. However, the rank of this decomposition (i.e., the number of physical states in the process) has to be guessed from pre-existing knowledge on the observed process. We propose a measure for determining the number of components with the computation of the minimal memory effect resulting from the decomposition; by quantifying how much the obtained factorization is deviating from the Markovian property, we are able to score factorizations of a different number of components. In this way, we estimate the number of different entities which contribute to the observed system, and we can extract kinetic information without knowing the characteristic spectra of the single components. This manuscript provides the mathematical background as well as an analysis of computer generated and experimental sequentially measured Raman spectra. Y1 - 2022 U6 - https://doi.org/10.3390/a15090297 VL - 15 IS - 9 SP - 297 ER - TY - JOUR A1 - Ray, Sourav A1 - Fackeldey, Konstantin A1 - Stein, Christoph A1 - Weber, Marcus T1 - Coarse Grained MD Simulations of Opioid interactions with the µ-opioid receptor and the surrounding lipid membrane JF - Biophysica N2 - In our previous studies, a new opioid (NFEPP) was developed to only selectively bind to the 𝜇-opoid receptor (MOR) in inflamed tissue and thus avoid the severe side effects of fentanyl. We know that NFEPP has a reduced binding affinity to MOR in healthy tissue. Inspired by the modelling and simulations performed by Sutcliffe et al., we present our own results of coarse-grained molecular dynamics simulations of fentanyl and NFEPP with regards to their interaction with the 𝜇-opioid receptor embedded within the lipid cell membrane. For technical reasons, we have slightly modified Sutcliffe’s parametrisation of opioids. The pH-dependent opioid simulations are of interest because while fentanyl is protonated at the physiological pH, NFEPP is deprotonated due to its lower pKa value than that of fentanyl. Here, we analyse for the first time whether pH changes have an effect on the dynamical behaviour of NFEPP when it is inside the cell membrane. Besides these changes, our analysis shows a possible alternative interaction of NFEPP at pH 7.4 outside the binding region of the MOR. The interaction potential of NFEPP with MOR is also depicted by analysing the provided statistical molecular dynamics simulations with the aid of an eigenvector analysis of a transition rate matrix. In our modelling, we see differences in the XY-diffusion profiles of NFEPP compared with fentanyl in the cell membrane. Y1 - 2023 U6 - https://doi.org/10.3390/biophysica3020017 VL - 3 IS - 2 SP - 263 EP - 275 ER - TY - JOUR A1 - Raharinirina, N. Alexia A1 - Fackeldey, Konstantin A1 - Weber, Marcus T1 - Qualitative Euclidean embedding of Disjoint Sets of Points N2 - We consider two disjoint sets of points with a distance metric, or a proximity function, associated with each set. If each set can be separately embedded into separate Euclidean spaces, then we provide sufficient conditions for the two sets to be jointly embedded in one Euclidean space. In this joint Euclidean embedding, the distances between the points are generated by a specific relation-preserving function. Consequently, the mutual distances between two points of the same set are specific qualitative transformations of their mutual distances in their original space; the pairwise distances between the points of different sets can be constructed from an arbitrary proximity function (might require scaling). Y1 - 2022 UR - https://arxiv.org/abs/2212.00058 ER - 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 -