Repository: Freie Universität Berlin, Math Department

Items where Year is 2023

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Number of items: 94.

Article

Alphonse, Amal and Caetano, Diogo and Djurdjevac, Ana and Elliott, Charles M. (2023) Function spaces, time derivatives and compactness for evolving families of Banach spaces with applications to PDEs. Journal of Differential Equations, 353 . pp. 268-338.

Arts, Marloes and Garcia Sattorras, Victor and Huang, Chin-Wei and Zuegner, Daniel and Federici, Marco and Clementi, Cecilia and Noé, Frank and Pinsler, Robert and van den Berg, Rianne (2023) Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics. JCTC - Journal of Chemical Theory and Computation, 19 . pp. 6151-6159.

Bardos, Claude and Boutros, Daniel W. and Titi, Edriss (2023) Hoelder regularity of the pressure for weak solutions of the 3D Euler equations in bounded domains. Preprint . pp. 1-35. (Unpublished)

Bardos, Claude and Liu, Xin and Titi, Edriss (2023) Derivation of a generalized quasi-geostrophic approximation for inviscid ows in a channel domain: The fast waves correction. pp. 1-33. (Unpublished)

Barua, Amlan K. and Chew, Ray and Li, Shuwang and Lowengrub, John and Münch, Andreas and Wagner, Barbara (2023) Sharp-interface problem of the Ohta-Kawasaki model for symmetric diblock copolymers. Journal of Computational Physics, 481 .

Bittracher, Andreas and Mollenhauer, Mattes and Koltai, Péter and Schütte, Ch. (2023) Optimal Reaction Coordinates: Variational Characterization and Sparse Computation. Multiscale Modeling & Simulation, 21 (2). ISSN ISSN (print): 1540-3459 ISSN (online): 1540-3467

Bittracher, Andreas and Mollenhauer, Mattes and Koltai, Péter and Schütte, Christof (2023) Optimal Reaction Coordinates: Variational Characterization and Sparse Computation. Multiscale Modeling & Simulation, 21 (2). pp. 449-488.

Bleich, Amnon and Linnemann, Antje and Benjamin, Jaidi and Bjoern, H. Diem and Conrad, T. O. F. (2023) Enhancing ECG Analysis of Implantable Cardiac Monitor Data: An Efficient Pipeline for Multi-Label Classification. Machine Learning and Knowledge Extraction, 5 (4). ISSN 2504-4990

Blumenthal, Alex and Engel, Maximilian and Neamţu, Alexandra (2023) On the pitchfork bifurcation for the Chafee-Infante equation with additive noise. Probability Theory and Related Fields, 187 . pp. 603-627.

Bogdanow, Boris and Gruska, Iris and Mühlberg, Lars and Protze, Jonas and Hohensee, Svea and Vetter, Barbara and Bosse, Jens B. and Lehmann, Martin and Sadeghi, Mohsen and Wiebusch, Lüder and Liu, Fan (2023) Spatially resolved protein map of intact human cytomegalovirus virions. Nature Microbiology, 8 . pp. 1732-1747.

Borrell, Enric Ribera and Quer, Jannes and Richter, Lorenz and Schütte, Christof (2023) Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics. Preprint to appear in SISC 2024 . (In Press)

Boutros, Daniel W. and Markfelder, Simon and Titi, Edriss (2023) Nonuniqueness of generalised weak solutions to the primitive and Prandtl equations. arXiv . pp. 1-73. (Unpublished)

Bäumer, D. and Hittmeir, S. and Klein, R. (2023) Scaling approaches to quasi-geostrophic theory for moist, precipitating air. J. Atmos. Sci. . pp. 1-18.

Charron, Nicholas E. and Musil, Felix and Guljas, Andrea and Chen, Yaoyi and Bonneau, Klara and Pasos-Trejo, Aldo S. and Venturin, Jacopo and Gusew, Daria and Zaporozhets, Iryna and Krämer, Andreas and Templeton, Clark and Kelkar, Atharva and Durumeric, Alexander E.P. and Olsson, Simon and Pérez, Adrià and Majewski, Maciej and Husic, Brooke E. and Patel, Ankit and Fabritiis, Gianni De and Noé, Frank and Clementi, Cecilia (2023) Navigating protein landscapes with a machine-learned transferable coarse-grained model. Preprint . (Unpublished)

Chemnitz, Dennis and Engel, Maximilian (2023) Positive Lyapunov Exponent in the Hopf Normal Form with Additive Noise. Communications in Mathematical Physics, 402 . pp. 1807-1843.

Chemnitz, Robin and Engel, Maximilian and Koltai, Péter (2023) Continuous-time extensions of discrete-time cocycles. Contemporary Mathematics . (In Press)

Chew, R. and Schlutow, M. and Klein, R. (2023) An unstable mode of the stratified atmosphere under the non-traditional Coriolis acceleration. Journal of Fluid Mechanics, 967 .

Coghi, Michele and Nilssen, Torstein and Nüsken, Nikolas and Reich, Sebastian (2023) Rough McKean–Vlasov dynamics for robust ensemble Kalman filtering. The Annals of Applied Probability, 33 (6b). pp. 5693-5752.

Durumeric, Alexander E.P. and Charron, Nicholas E. and Templeton, Clark and Musil, Félix and Bonneau, Klara and Pasos-Trejo, Aldo S. and Chen, Yaoyi and Kelkar, Atharva and Noé, Frank and Clementi, Cecilia (2023) Machine learned coarse-grained protein force-fields: Are we there yet? Current Opinion in Structural Biology, 79 .

Dyhr, Michael C. A. and Sadeghi, Mohsen and Moynova, Ralista and Knappe, Carolin and Burcu Kepsutlu, Çakmak and Werner, Stephan and Schneider, Gerd and McNally, James and Noé, Frank and Ewers, Helge (2023) 3D surface reconstruction of cellular cryo-soft X-ray microscopy tomograms using semisupervised deep learning. Proceedings of the National Academy of Sciences of the United States of America (PNAS), 120 (24).

Engel, Maximilian and Gottwald, Georg A. (2023) Canards in modified equations for Euler discretizations. Preprint to appear in Contemporary Mathematics . (In Press)

Engel, Maximilian and Olicon-Méndez, Guillermo (2023) Noise-induced instabilities in a stochastic Brusselator. Preprint to appear in Contemporary Mathematics . (In Press)

Engel, Maximilian and Olicón-Mendez, Guillermo (2023) A singular perturbation analysis for the Brusselator. Preprint . (Submitted)

Engel, Maximilian and Piliouras, Georgios (2023) A stochastic variant of replicator dynamics in zero-sum games and its invariant measures. Physica D: Nonlinear Phenomena, 456 .

Ernst, Ariane and Falkenhagen, Undine and Winkelmann, Stefanie (2023) Model reduction for Ca²+ -induced vesicle fusion dynamics. Proceedings in Applied Mathematics and Mechanics, 23 (4).

Ernst, Ariane and Unger, Nathalie and Schütte, Christof and Walter, Alexander M. and Winkelmann, Stefanie (2023) Rate-limiting recovery processes in neurotransmission under sustained stimulation. Mathematical Biosciences, 362 . p. 109023.

Fradon, Myriam and Kern, Julian and Roelly, Sylvie and Zass, Alexander (2023) Diffusion dynamics for an infinite system of two-type spheres and the associated depletion effect. Preprint submitted to Stochastic Processes and their Applications . (Submitted)

Froyland, Gary and Koltai, Péter (2023) Detecting the birth and death of finite-time coherent sets. Communications on Pure and Applied Mathematics, 76 (12). pp. 3642-3684.

Gelß, P. and Issagali, A. and Kornhuber, R. (2023) Fredholm integral equations for function approximation and the training of neural networks. arXiv . (Submitted)

Gelß, P. and Matera, S. and Klein, R. and Schmidt, B. (2023) Quantum Dynamics of Coupled Excitons and Phonons in Chain-Like Systems: Tensor Train Approaches and Higher-Order Propagators. J. Chem. Phys. . (Submitted)

Gertler, Charles G. and O’Gorman, Paul A. and Pfahl, Stephan (2023) Moist available potential energy of the mean state of the atmosphere and the thermodynamic potential for warm conveyor belts and convection. Weather Clim. Dynam., 4 . pp. 361-379.

Giurgiu, Mădălina and Wittstruck, Nadine and Rodriguez-Fos, Elias and Chamorro González, Rocío and Brückner, Lotte and Krienelke-Szymansky, Annabell and Helmsauer, Konstantin and Hartebrodt, Anne and Koche, Richard P. and Haase, Kerstin and Reinert, Knut and Henssen, Anton G. (2023) Decoil: Reconstructing extrachromosomal DNA structural heterogeneity from long-read sequencing data. bioRxiv - The Preprint Server for Biology .

Grosu, C. and Panosetti, C. and Merz, S. and Jakes, P. and Matera, S. and Eichel, R.A. and Granwehr, J. and Scheurer, C. (2023) Revisiting the storage capacity limit of graphite battery anodes: spontaneous lithium overintercalation at ambient pressure. PRX Energy, 2 .

Hanu, Matei and Hesser, Jürgen and Kanschat, Guido and Moviglia, Javier and Schillings, Claudia and Stallkamp, Jan (2023) Ensemble Kalman Inversion for Image Guided Guide Wire Navigation in Vascular Systems. arXiv . (Submitted)

Hanu, Matei and Latz, J. and Schillings, Claudia (2023) Subsampling in ensemble Kalman inversion. Inverse Problems, 39 (9).

Hanu, Matei and Weissmann, Simon (2023) On the ensemble Kalman inversion under inequality constraints. arXiv . (Submitted)

Harikrishnan, A. P. and Ansorge, C. and Klein, R. and Vercauteren, N. (2023) Geometry and organization of coherent structures in stably stratified atmospheric boundary layers. Journal of Fluid Mechanics . (Submitted)

Harikrishnan, A. P. and Rodal, M. and Klein, R. and Margerit, D, and Vercauteren, N. (2023) On the motion of hair-pin filaments in the atmospheric boundary layer. Physics of Fluids, 35 (7).

Hirt, M. and Craig, G.C. and Klein, R. (2023) Scale-interactions between the meso- and synoptic scales and the impact of diabatic heating. QJRMS, 149 (753). pp. 1319-1334.

Hittmeir, S. and Klein, R. and Li, J. and Titi, Edriss (2023) Global well-posedness for the thermodynamically refined passively transported nonlinear moisture dynamics with phase changes. Journal of Nonlinear Science, 33 (65). ISSN Online: 1432-1467 Print: 0938-8974

Huysmans, Lucas and Titi, Edriss (2023) Non-Uniqueness and Inadmissibility of the Vanishing Viscosity Limit of the Passive Scalar Transport Equation. arXiv . (Unpublished)

Jong-Bolm, Daniëlle de and Sadeghi, Mohsen and Bogaciu, Cristian A. and Bao, Guobin and Klaehn, Gabriele and Hoff, Merle and Mittelmeier, Lucas and Basmanav, F. Buket and Noé, Frank and Rizzoli, Silvio O. (2023) Protein nanobarcodes enable single-step multiplexed fluorescence imaging. PLOS BIOLOGY, 21 (12).

Jung, S. and Schwedhelm, J.C. and Schillings, Claudia and Keuper, M. (2023) Happy People--Image Synthesis as Black-Box Optimization Problem in the Discrete Latent Space of Deep Generative Models. arXiv . (Submitted)

Kaatz, L. and Schmalholz, Stefan M. and John, T. (2023) Numerical Simulations Reproduce Field Observations Showing Transient Weakening During Shear Zone Formation by Diffusional Hydrogen Influx and H2O Inflow. Geochemistry, Geophysics, Geosystems, 24 (5).

Kern, Julian (2023) Exponential equivalence for misanthrope processes in contact with weak reservoirs and applications to totally asymmetric exclusion processes. Preprint . (Unpublished)

Kern, Julian (2023) Skorokhod topologies: What they are and why we should care. Mathematische Semesterberichte .

Kern, Julian and Wiederhold, Bastian (2023) A Λ-Fleming-Viot type model with intrinsically varying population size. Electronic Journal of Probability . (Submitted)

Koronaki, D. Eleni and Evangelou, Nikolaos and Martin-Linares, Cristina P. and Titi, Edriss and Kevrekidis, Ioannis G. (2023) Nonlinear dimensionality reduction then and now: AIMs for dissipative PDEs in the ML era. Preprint . (Unpublished)

Krämer, Andreas and Durumeric, Alexander E.P. and Charron, Nicholas E. and Chen, Yaoyi and Clementi, Cecilia and Noé, Frank (2023) Statistically Optimal Force Aggregation for Coarse-Graining Molecular Dynamics. The Journal of Physical Chemistry, 14 . pp. 3970-3979.

Köhler, Jonas and Chen, Yaoyi and Krämer, Andreas and Clementi, Cecilia and Noé, Frank (2023) Flow-Matching: Efficient Coarse-Graining of Molecular Dynamics without Forces. J. Chem. Theory Comput., 19 (3). pp. 942-952.

Lai, King Chun and Matera, S. and Scheurer, C. and Reuter, K. (2023) A fuzzy classification framework to identify equivalent atoms in complex materials and molecules. Journal of Chemical Physics, 159 (2). ISSN 0021-9606

Lelièvre, Tony and Pigeon, Thomas and Stoltz, Gabriel and Zhang, Wei (2023) Analyzing multimodal probability measures with autoencoders. To appear in The Journal of Physical Chemistry B . (In Press)

Li, Z. and Meunier, D. and Mollenhauer, M. and Gretton, A. (2023) Towards Optimal Sobolev Norm Rates for the Vector-Valued Regularized Least-Squares Algorithm. arXiv . (Submitted)

Li, Z. and Meunier, D. and Mollenhauer, Mattes and Gretton, A. (2023) Optimal Rates for Regularized Conditional Mean Embedding Learning. Advances in Neural Information Processing Systems (NeurIPS), 36 . (Submitted)

Liero, Matthias and Mielke, Alexander and Savaré, Giuseppe (2023) Fine properties of geodesics and geodesic lambda-convexity for the Hellinger-Kantorovich distance. Archive for Rational Mechanics and Analysis, 247 (112).

Maity, Priyanka and Bittracher, Andreas and Koltai, Péter and Schumacher, Jörg (2023) Collective variables between large-scale states in turbulent convection. Physical Review Research, 5 (3).

Majewski, Maciej and Pérez, Adrià and Thölke, Philipp and Doerr, Stefan and Charron, Nicholas E. and Giorgino, Toni and Husic, Brooke E. and Clementi, Cecilia and Noé, Frank and De Fabritiis, Gianni (2023) Machine Learning Coarse-Grained Potentials of Protein Thermodynamics. Nature Communications, 14 .

Matera, S. and Dortaj, S. (2023) Efficient global sensitivity analysis of kinetic Monte Carlo simulations using Cramérs–von Mises distance. Journal of Chemical Physics . ISSN Online ISSN 1089-7690 Print ISSN 0021-9606

Mehringer, Svenja and Seiler, Enrico and Droop, Felix and Darvish, Mitra and Rahn, René and Vingron, Martin and Reinert, Knut (2023) Hierarchical Interleaved Bloom Filter: enabling ultrafast, approximate sequence queries. Genome Biology, 24 (131). ISSN 1474-760X

Melnyk, Kateryna and Weimann, K. and Conrad, T. O. F. (2023) Understanding microbiome dynamics via interpretable graph representation learning. Scientific Reports, 13 (2058). ISSN 2045-2322

Mielke, Alexander (2023) Non-equilibrium steady states as saddle points and EDP-convergence for slow-fast gradient systems. Journal of Mathematical Physics, 64 (12).

Mischau, A. (2023) Den Ballast tradierter Zerrbilder in Mathematikschulbüchern endlich abwerfen. Mitteilungen der Deutschen Mathematiker-Vereinigung, 31 (1).

Mohammadi, Somayeh and PourKarimi, Latif and Droop, Felix and De Mecquenem, Ninon and Leser, Ulf and Reinert, Knut (2023) A mathematical programming approach for resource allocation of data analysis workflows on heterogeneous clusters. The Journal of Supercomputing, 79 (17). pp. 19019-19048. ISSN 0920-8542

Mollenhauer, Mattes and Schillings, Claudia (2023) On the concentration of subgaussian vectors and positive quadratic forms in Hilbert spaces. arXiv . (Submitted)

Montefusco, Alberto and Schütte, Christof and Winkelmann, Stefanie (2023) A route to the hydrodynamic limit of a reaction-diffusion master equation using gradient structures. Society for Industrial and Applied Mathematic (siam), 83 (2). pp. 836-861.

Müller, Sebastian and Paltra, Sydney and Rehmann, Jakob and Nagel, Kai and Conrad, T. O. F. (2023) Explicit Modelling of Antibody Levels for Infectious Disease Simulations in the Context of SARS-CoV-2. iScience, 26 (9). ISSN 2589-0042

Nickl, Richard and Titi, Edriss (2023) On posterior consistency of data assimilation with Gaussian process priors: the 2D Navier-Stokes equations. ArXiv . (Unpublished)

Nowatzky, Yannek and Benner, Philipp and Reinert, Knut and Muth, Thilo (2023) Mistle: bringing spectral library predictions to metaproteomics with an efficient search index. Bioinformatics, 39 (6). ISSN 1367-4811

Nüsken, Nikolas and Richter, Lorenz (2023) Interpolating Between BSDEs and PINNs: Deep Learning for Elliptic and Parabolic Boundary Value Problems. Journal of Machine Learning, 2 . pp. 31-64.

Pacey, George and Pfahl, Stephan and Schielicke, Lisa and Wapler, Kathrin (2023) The climatology and nature of warm-season convective cells in cold-frontal environments over Germany. Natural Hazards Earth System Sciences, 23 (12). pp. 3703-3721.

Pan, Chenxu and Rahn, René and Heller, David and Reinert, Knut (2023) Linear: a framework to enable existing software to resolve structural variants in long reads with flexible and efficient alignment-free statistical models. Briefings in Bioinformatics, 24 (2). ISSN 1467-5463; Online ISSN 1477-4054

Piro, Vitor C and Renard, Bernhard Y (2023) Contamination detection and microbiome exploration with GRIMER. GigaScience, 12 . ISSN 2047-217X

Piro, Vitor C. and Reinert, Knut (2023) ganon2: up-to-date and scalable metagenomics analysis. bioRxiv preprint .

Polzin, Robert and Klebanov, Ilja and Nüsken, Nikolas and Koltai, Péter (2023) Nonnegative matrix factorization for coherent set identification by direct low rank maximum likelihood estimation. arXiv . pp. 1-43. (Unpublished)

Reible, Benedikt M. and Hille, Julian F. and Hartmann, Carsten and Delle Site, Luigi (2023) Finite-size effects and thermodynamic accuracy in many-particle systems. Physical Review Research, 5 (2).

Richter, Lorenz and Berner, Julius and Liu, Guang-Horng (2023) Improved sampling via learned diffusions. Preprint . (Unpublished)

Richter, Lorenz and Sallandt, Leon and Nüsken, Nikolas (2023) From continuous-time formulations to discretization schemes: tensor trains and robust regression for BSDEs and parabolic PDEs. Preprint . (Unpublished)

Riedel, J. and Gelß, P. and Klein, R. and Schmidt, B. (2023) WaveTrain: A Python Package for Numerical Quantum Mechanics of Chain-Like Systems Based on Tensor Trains. J. Chem. Phys. (164801), 158 (16). ISSN 0021-9606

Schillings, Claudia and Totzeck, Claudia and Wacker, Philipp (2023) Ensemble-based gradient inference for particle methods in optimization and sampling. SIAM/ASA Journal on Uncertainty Quantification, 11 (3). pp. 757-787.

Schütte, Christof and Klus, Stefan and Hartmann, Carsten (2023) Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning. Acta Numerica, 32 . pp. 517-673.

Straube, Arthur V. and Winkelmann, Stefanie and Höfling, Felix (2023) Accurate reduced models for the pH oscillations in the urea-urease reaction confined to giant lipid vesicles. J. Phys. Chem. B, 127 (13). pp. 2955-2967.

Thies, Arne and Sunkara, Vikram and Ray, Sourav and Wulkow, Hanna and Özgür Celik, M. and Yergöz, Fatih and Schütte, Christof and Stein, Christoph and Weber, Marcus and Winkelmann, Stefanie (2023) Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design. Scientific Reports, 13 (1). p. 607.

Unanue, Alvaro de Diego and Froyland, Gary and Junge, Oliver and Koltai, Péter (2023) A dynamic p-Laplacian. Preprint . (Unpublished)

Wang, Yuwei and Lian, Bin and Zhang, Haohui and Zhong, Yuanke and He, Jie and Wu, Fashuai and Reinert, Knut and Shang, Xuequn and Yang, Hui and Hu, Jialu and Mathelier, Anthony (2023) A multi-view latent variable model reveals cellular heterogeneity in complex tissues for paired multimodal single-cell data. Bioinformatics, 39 (1). ISSN 1367-4803

Weimann, K. and Conrad, T. O. F. (2023) Predicting Coma Recovery After Cardiac Arrest With Residual Neural Networks. Computing in Cardiology (CinC) 2023, 50 .

Yang, Wangfei and Templeton, Clark and Rosenberger, David and Bittracher, Andreas and Nüske, Feliks and Noé, Frank and Clementi, Cecilia (2023) Slicing and Dicing: Optimal Coarse-Grained Representation to Preserve Molecular Kinetics. ACS Cent. Sci., 9 (2). pp. 186-196.

Zafferi, Andrea and Huber, Konstantin and Peschka, Dirk and Vrijmoed, Johannes and John, Timm and Thomas, Marita (2023) A porous-media model for reactive fluid-rock interaction in a dehydrating rock. Preprint . pp. 1-22. (Unpublished)

del Razo, M.J. and Winkelmann, S. and Klein, R. and Höfling, F. (2023) Chemical diffusion master equation: formulations of reaction–diffusion processes on the molecular level. J. Math. Phys., 64 (013304).

von Kleist, M. and Raharinirina, Alexia and Gubela, Nils and Börnigen, Daniela and Smith, Maureen and Oh, Djin-Ye and Budt, Matthias and Mache, Christin and Schillings, Claudia and Fuchs, Stephan and Dürrwald, Ralf and Wolff, Thorsten and Hoelzer, Martin and Sofia, Paraskevopoulou (2023) SARS-CoV-2 Evolution on a Dynamic Immune Landscape. Biological Sciences . (Submitted)

Book Section

Gürtler, S. and Mischau, A. and Lieben, C. and Wiebe, J. and Wolf, S. (2023) Das Decision Theatre Lab: transdisziplinäre Lehr- und Lernformate in der Mathematik. In: Konstantin Kirpijanov, Thorsten Philipp und Thorsten Roelcke (Hrsg.). Transferwissenschaften: , Verlag Peter Lang, S. 221-238. ISBN (Hardcover) ; (DOI - open access). In: Transferwissenschaften: Mode oder Mehrwert? Peter Lang Gmbh, Internationaler Verlag Der Wissenschaften. ISBN 9783631883860

Haase, C. and Mischau, A. and Walter, L. and Weygandt, B. (2023) Mathematik entdecken (Berlin). In: Unterstützungsmaßnahmen in mathematikbezogenen Studiengängen. Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik. Springer Spektrum, Berlin, Heidelberg, pp. 395-425. ISBN Print: 978-3-662-64832-2 Online: 978-3-662-64833-9

Conference or Workshop Item

Matera, S. and Merdon, C. and Runge, D. (2023) Reduced Basis Approach for Convection-Diffusion Equations with Non-linear Boundary Reaction Conditions. In: International Conference on Finite Volumes for Complex Applications, 30 October - 3 November 2023, Strasbourg, France.

Royset, Johannes and Ruthotto, Lars and Schillings, Claudia and Surowiec, Thomas M. (2023) Workshop Report 21w5167 Optimization under Uncertainty: Learning and Decision Making in 2021. In: held virtually hosted by the, Feb 8 - 12, 2023, Banff International Research Station for Mathematical Innovation and Discovery (BIRS).

Schubotz, Moritz and Ferrer, Eloi and Stegmüller, Johannes and Mietchen, Daniel and Teschke, Olaf and Pusch, Larissa and Conrad, T. O. F. (2023) Bravo MaRDI: A Wikibase Knowledge Graph on Mathematics. In: Proceedings of the 4th Wikidata Workshop 2022 co-located with the 22st International Semantic Web Conference (ISWC2023), Athens, Greece, November 2023. (In Press)

This list was generated on Wed Oct 2 12:51:57 2024 CEST.