Isothermic nets with spherical parameter lines from discrete holomorphic maps 2024 March 2403.13476 preprint Tim Hoffmann Gudrun Szewieczek Constant mean curvature surfaces from ring patterns: Geometry from combinatorics 2024 2410.08915 arXiv math.DG 10.48550/arXiv.2410.08915 preprint Alexander I. Bobenko Tim Hoffmann Nina Smeenk Discrete Lorentz surfaces and s-embeddings II: maximal surfaces 2024 arXiv math.DG 10.48550/arXiv.2411.19055 preprint Niklas Christoph Affolter Felix Dellinger Christian Müller Denis Polly Nina Smeenk In 1883, Darboux gave a local classification of isothermic surfaces with one family of planar curvature lines using complex analytic methods. His choice of real reduction cannot contain tori. We classify isothermic tori with one family of planar curvature lines. They are found in the second real reduction of Darboux's description. We give explicit theta function formulas for the family of plane curves. These curves are particular area constrained hyperbolic elastica. With a Euclidean gauge, the Euler--Lagrange equation is lower order than expected. In our companion paper (arXiv:2110.06335) we use such isothermic tori to construct the first examples of compact Bonnet pairs: two isometric tori related by a mean curvature preserving isometry. They are also the first pair of isometric compact immersions that are analytic. Additionally, we study the finite dimensional moduli space characterizing when the second family of curvature lines is spherical. Isothermic tori with planar and spherical curvature lines are natural generalizations of Wente constant mean curvature tori, discovered in 1986. Wente tori are recovered in a limit case of our formulas. 2312.14956 Isothermic tori with one family of planar curvature lines and area constrained hyperbolic elastica 2024 preprint Alexander I. Bobenko Tim Hoffmann Andrew O. Sageman-Furnas Rate and bifurcation induced transitions in asymptotically slow-fast systems 2024 January 2401.08482 preprint S. Jelbart Skew parallelogram nets and universal factorization 2024 January 2401.08467 preprint Tim Hoffmann Andrew O. Sageman-Furnas Jannik Steinmeier The geometry of discrete asymptotic-geodesic 4-webs in isotropic 3-space Monatsh. Math. Monatshefte f\"{u}r Mathematik 203 2024 1 223--246 10.1007/s00605-023-01916-0 Christian M\"{u}ller Helmut Pottmann The geometry of discrete asymptotic-geodesic 4-webs in isotropic 3-space Monatsh. Math. Monatshefte f\"{u}r Mathematik 203 2024 1 223--246 10.1007/s00605-023-01916-0 Christian M\"{u}ller Helmut Pottmann Understanding broad-spike oscillations in a model of intracellular calcium dynamics 2024 January 2401.16839 preprint B. Rahmani S. Jelbart V. Kirk J. Sneyd Circular Nets with Spherical Parameter Lines and Terminating Laplace Sequences 2023 December 2312.04341 preprint Alexander I. Bobenko Alexander Y. Fairley Force-Free Fields are Conformally Geodesic 2023 December 2312.05252 preprint Albert Chern Oliver Gross Möbius invariant Y-systems (cluster structures) for Miquel dynamics 2023 December preprint 2312.07367 Niklas C Affolter Decorated discrete conformal equivalence in non-Euclidean geometries 2023 October preprint 2310.17529 Alexander I. Bobenko Carl O. R. Lutz Discrete Isothermic Nets Based on Checkerboard Patterns 2023 September Discrete & Computational Geometry https://link.springer.com/article/10.1007/s00454-023-00558-1 Felix Dellinger Extending discrete geometric singular perturbation theory to non-hyperbolic points 2023 August preprint 2308.06141 S. Jelbart C. Kuehn Neural Poisson Surface Reconstruction: Resolution-Agnostic Shape Reconstruction from Point Clouds 2023 August arXiv:2308.01766 preprint Hector Andrade-Loarca Julius Hege Daniel Cremers Gitta Kutyniok Plasma Knots Physics Letters A 2023 August https://www.sciencedirect.com/science/article/abs/pii/S0375960123003663 Oliver Gross Ulrich Pinkall Peter Schröder Motion from Shape Change ACM Transactions on Graphics 2023 July https://olligross.github.io/projects/MotionFromShapeChange/MotionFromShapeChange_project.html 10.1145/3592417 Oliver Gross Yousuf Soliman Marcel Padilla Felix Knöppel Ulrich Pinkall Peter Schröder Discrete orthogonal structures 2023 June Computers & Graphics https://www.sciencedirect.com/science/article/abs/pii/S0097849323000791?via%3Dihub Felix Dellinger Xinye Li Hui Wang Integral preserving discretization of 2D Toda lattices Journal of Physics A: Mathematical and Theoretical 2023 June 2306.01632 Sergey V. Smirnov Decorated discrete conformal maps and convex polyhedral cusps 2023 May preprint 2305.10988 Alexander I. Bobenko Carl O. R. Lutz Canonical tessellations of decorated hyperbolic surfaces Geom Dedicata 2023 April 217 14 1-37 10.1007/s10711-022-00746-y 2206.13461 Carl O. R. Lutz Energy Scaling Laws for Microstructures: From Helimagnets to Martensites 2023 April cvgmt preprint Janusz Ginster Barbara Zwicknagl Discrete Yamabe Problem for Polyhedral Surfaces Discrete \& Computational Geometry 2023 March 10.1007/s00454-023-00484-2 2103.15693 Hana Dal Poz Kouřimská A Formal Geometric Blow-up Method for Pattern Forming Systems 2023 February preprint 2302.06343 Samuel Jelbart Christian Kuehn Deployable strip structures ACM Trans. Graph. 2023 103 1-16 D. Liu D. Pellis Y.-C. Chiang F. Rist J. Wallner H. Pottmann Meshes with Spherical Faces ACM Trans. Graphics 42 6 177 19 2023 Proc. SIGGRAPH Asia 10.1145/3618345 Martin Kilian Antonio S Ramos Cisneros Helmut Pottmann Christian M{\"u}ller Handbook of Mathematical Science Communication My Experience of Producing Mathematical Films World Scientific Singapore 231-246 2023 January https://doi.org/10.1142/9789811253072_0013 Ekaterina Eremenko Anna Maria Hartkopf Erin Henning Neural Implicit Representations for Physical Parameter Inference From a Single Video Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision 2023 2093-2103 2204.14030 Florian Hofherr Lukas Koestler Florian Bernard Daniel Cremers We introduce orthogonal ring patterns consisting of pairs of concentric circles generalizing circle patterns. We show that orthogonal ring patterns are governed by the same equation as circle patterns. For every ring pattern there exists a one parameter family of patterns that interpolates between a circle pattern and its dual. We construct ring patterns analogues of the Doyle spiral, Erf and $$z^\alpha $$functions. We also derive a variational principle and compute ring patterns based on Dirichlet and Neumann boundary conditions. arXiv 2021-11-12 16:04:29 +0100 2024-03-20 15:01:59 +0100 1911.07095 Geometriae Dedicata 11 Orthogonal ring patterns in the plane 218 2023 10.1007/s10711-023-00859-y Alexander I. Bobenko Tim Hoffmann Thilo R{\"o}rig PL Morse theory in low dimensions Advances in Geometry 2023 January http://page.mi.fu-berlin.de/rote/Papers/pdf/PL+Morse+theory+in+low+dimensions.pdf Romain Grunert Wolfgang Kühnel Günter Rote Pl Morse theory in low dimensions. Advances in Geometry 23 1 135-150 2023 January 1912.05054 http://doi.org/10.1515/advgeom-2022-0027 Romain Grunert Wolfgang Kühnel Günter Rote Smooth and discrete cone-nets Results Math. Results in Mathematics 78 2023 3 Paper No. 110, 40 10.1007/s00025-023-01884-9 Martin Kilian Christian M\"{u}ller Jonas Tervooren Energy Scaling Law for a Singularly Perturbed Four-Gradient Problem in Helimagnetism Journal of Nonlinear Science 2022 December 10.1007/s00332-022-09847-0 Janusz Ginster Barbara Zwicknagl Über die Wissenschaft der Wissenschaftskommunikation in Mathematik Mitteilungen der Deutschen Mathematiker-Vereinigung 30 4 2022 December 261-265 https://doi.org/10.1515/dmvm-2022-0084 Anna Maria Hartkopf Erin Henning Geometric blow-up for folded limit cycle manifolds in three time-scale systems 2022 August Nonlinear Science 2208.01361 Samuel Jelbart Sara-Viola Kuntz Christian Kuehn Filament based plasma ACM Transactions on Graphics 2022 July 10.1145/3528223.3530102 Marcel Padilla Oliver Gross Felix Knöppel Ulrich Pinkall Peter Schröder Geometric blow-up of a dynamic Turing instability in the Swift-Hohenberg equation 2022 July preprint 2207.03967 Felix Hummel Samuel Jelbart Christian Kuehn The Schwarzian octahedron recurrence (dSKP equation) I: explicit solutions 2022 July Combinatoral Theory 2208.00239 https://escholarship.org/uc/item/2jq67049 Niklas Christoph Affolter Béatrice de Tilière Paul Melotti The Schwarzian octahedron recurrence (dSKP equation) II: geometric systems 2022 July 2208.00244 preprint Niklas Christoph Affolter Béatrice de Tilière Paul Melotti On Discrete Conjugate Semi-Geodesic Nets International Mathematics Research Notices 2022 June 10.1093/imrn/rnaa394 Tim Hoffmann Wolfgang K Schief Jannik Steinmeier Half-Inverse Gradients for Physical Deep Learning International Conference on Learning Representations 2022 March https://arxiv.org/abs/2203.10131 Patrick Schnell Philipp Holl Nils Thuerey Deep microlocal reconstruction for limited-angle tomography Applied and Computational Harmonic Analysis 2022 January https://www.sciencedirect.com/science/article/pii/S1063520321001081 Héctor Andrade-Loarca Gitta Kutyniok Ozan Öktem Philipp Petersen We introduce an algorithm to remesh triangle meshes representing developable surfaces to planar quad dominant meshes. The output of our algorithm consists of planar quadrilateral (PQ) strips that are aligned to principal curvature directions and closely approximate the curved parts of the input developable, and planar polygons representing the flat parts of the input that connect the PQ strips. Developable PQ-strip meshes are useful in many areas of shape modeling, thanks to the simplicity of fabrication from flat sheet material. Unfortunately, they are difficult to model due to their restrictive combinatorics. Other representations of developable surfaces, such as arbitrary triangle or quad meshes, are more suitable for interactive freeform modeling but generally have non-planar faces or are not aligned to principal curvatures. Our method leverages the modeling flexibility of non-ruling-based representations of developable surfaces while still obtaining developable, curvature-aligned PQ-strip meshes. Our algorithm optimizes for a scalar function on the input mesh, such that its isolines are extrinsically straight and align well to the locally estimated ruling directions. The condition that guarantees straight isolines is non-linear of high order and numerically difficult to enforce in a straightforward manner. We devise an alternating optimization method that makes our problem tractable and practical to compute. Our method works automatically on any developable input, including multiple patches and curved folds, without explicit domain decomposition. We demonstrate the effectiveness of our approach on a variety of developable surfaces and show how our remeshing can be used alongside handle-based interactive freeform modeling of developable shapes. arXiv 2021-07-16 13:35:29 +0200 2024-03-20 15:07:08 +0100 2103.00239 ACM Transactions on Graphics (TOG) 3 29:1--18 cs.GR Dev2PQ: Planar Quadrilateral Strip Remeshing of Developable Surfaces 41 2022 10.1145/3510002 Floor Verhoeven Amir Vaxman Tim Hoffmann Olga Sorkine-Hornung The contribution of this paper is twofold. First, we generalize the definition of discrete isothermic surfaces. Compared with the previous ones, it covers more discrete surfaces, e.g., the associated families of discrete isothermic minimal and non-zero constant mean curvature (CMC in short) surfaces, whose counterpart in smooth case are isothermic surfaces. Second, we show that the discrete isothermic CMC surfaces can be obtained by the discrete holomorphic data (a solution of the additive rational Toda system) via the discrete generalized Weierstrass type representation. arXiv 2021-07-16 13:36:46 +0200 2024-03-20 15:10:03 +0100 2003.07286 Geometriae Dedicata 71 math.DG Discrete Constant Mean Curvature Surfaces on General Graphs 216 2022 10.1007/s10711-022-00733-3 Tim Hoffmann Shimpei Kobayashi Zi Ye Discrete Geometric Singular Perturbation Theory Discrete and Continuous Dynamical Systems 2022 January 2201.06996 Samuel Jelbart Christian Kuehn Equilibrium stressability of multidimensional frameworks Eur. J. Math. European Journal of Mathematics 8 2022 1 33--61 10.1007/s40879-021-00523-3 Oleg Karpenkov Christian M\"{u}ller Gaiane Panina Brigitte Servatius Herman Servatius Dirk Siersma Asymptotic Self-Similarity of Minimizers and Local Bounds in a Model of Shape-Memory Alloys Journal of Elasticity 2021 December 10.1007/s10659-021-09862-4 Sergio Conti Johannes Diermeier Melanie Koser Barbara Zwicknagl Compact Bonnet Pairs: isometric tori with the same curvatures 2021 October 2110.06335 preprint Alexander I. Bobenko Tim Hoffmann Andrew O. Sageman-Furnas Process-oriented geometric singular perturbation theory and calcium dynamics SIAM Journal on Applied Dynamical Systems 2021 September 2104.07304 Samuel Jelbart Nathan Pages Vivien Kirk James Sneyd Martin Wechselberger Cross-ratio dynamics and the dimer cluster integrable system 2021 August 2108.12692 preprint Niklas Affolter Terrence George Sanjay Ramassamy Discrete Conformal Equivalence of Polyhedral Surfaces ACM Trans. Graph. 40 4 103:1-103:20 August 2021 ACM New York, NY, USA 10.1145/3450626.3459763 Mark Gillespie Boris Springborn Keenan Crane Investigations of structures in the parameter space of three-dimensional Turing-like patterns 2021 July HAL https://hal.science/hal-03270664/file/AUTOMATA2021-exploratory15.pdf Martin Skrodzki Ulrich Reitebuch Eric Zimmermann A discrete version of Liouville's theorem on conformal maps Geom Dedicata 2021 April 214 389-398 10.1007/s10711-021-00621-2 1911.00966 Ulrich Pinkall Boris Springborn Data-driven entropic spatially inhomogeneous evolutionary games 2021 March preprint 2103.05429 Mauro Bonafini Massimo Fornasier Bernhard Schmitzer Singularly perturbed boundary-equilibrium bifurcations Nonlinearity 2021 March 2103.09613 Samuel Jelbart Kristian Uldall Kristiansen Martin Wechselberger "A Large-Scale Evaluation Of Shape-Aware Neighborhood Weights And Neighborhood Sizes" "Computer-Aided Design" 141 103107 2021 10.1016/j.cad.2021.103107 "Martin Skrodzki Eric Zimmermann" "Surface Denoising Based on Normal Filtering in a Robust Statistics Framework" "Proceedings of the Forum "Math-for-Industry" 2018" 35 103–132 2021 10.1007/978-981-16-5576-0_6 Springer Singapore Sunil Kumar Yadav Martin Skrodzki Eric Zimmermann Konrad Polthier A dimension-reduction model for brittle fractures on thin shells with mesh adaptivity Mathematical Models and Methods in Applied Sciences 31 01 37--81 2021 10.1142/S0218202521500020 2004.08871 Stefano Almi Sandro Belz Stefano Micheletti Simona Perotto Discrete curvature and torsion from cross-ratios Ann. Mat. Pura Appl. (4) Annali di Matematica Pura ed Applicata. Series IV 200 2021 5 1935--1960 10.1007/s10231-021-01065-x Christian M\"{u}ller Amir Vaxman Geometric criteria for realizability of tensegrities in higher dimensions SIAM J. Discrete Math. SIAM Journal on Discrete Mathematics 35 2021 2 637--660 10.1137/19M1281903 Oleg Karpenkov Christian Mueller Nets of lines with the combinatorics of the square grid and with touching inscribed conics Discrete and Comp. Geometry 2021 10.1007/s00454-021-00277-5 1911.08477 Alexander I. Bobenko Alexander Y. Fairley This paper introduces a generative model for 3D surfaces based on a representation of shapes with mean curvature and metric, which are invariant under rigid transformation. Hence, compared with existing 3D machine learning frameworks, our model substantially reduces the influence of translation and rotation. In addition, the local structure of shapes will be more precisely captured, since the curvature is explicitly encoded in our model. Specifically, every surface is first conformally mapped to a canonical domain, such as a unit disk or a unit sphere. Then, it is represented by two functions: the mean curvature half-density and the vertex density, over this canonical domain. Assuming that input shapes follow a certain distribution in a latent space, we use the variational autoencoder to learn the latent space representation. After the learning, we can generate variations of shapes by randomly sampling the distribution in the latent space. Surfaces with triangular meshes can be reconstructed from the generated data by applying isotropic remeshing and spin transformation, which is given by Dirac equation. We demonstrate the effectiveness of our model on datasets of man-made and biological shapes and compare the results with other methods. 10.1111/cgf.14094 Computer Graphics Forum October A Curvature and Density-based Generative Representation of Shapes 40 2020 https://doi.org/10.1111/cgf.14094 Z. Ye Nobuyuki Umetani Takeo Igarashi T. Hoffmann On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs 2020 August Discrete and Computational Geometry 10.1007/s00454-020-00240-w 1908.00856 Arseniy V. Akopyan Alexander I. Bobenko Wolfgang K. Schief Jan Techter Variational shape approximation of point set surfaces Computer Aided Geometric Design 2020 June 10.1016/j.cagd.2020.101875 2005.01003 Martin Skrodzki Eric Zimmermann Konrad Polthier Adopt a polyhedron 2020 April Chalkdust https://chalkdustmagazine.com/features/adopt-a-polyhedron/ Mara Kortenkamp Erin Henning Anna Maria Hartkopf The Ribaucour families of discrete R-congruences 2020 April preprint 2004.04447 Thilo Rörig Gudrun Szewieczek In differential geometry of surfaces the Dirac operator appears intrinsically as a tool to address the immersion problem as well as in an extrinsic flavour (that comes with spin transformations to comformally transfrom immersions) and the two are naturally related. In this paper we consider a corresponding pair of discrete Dirac operators, the latter on discrete surfaces with polygonal faces and normals defined on each face, and show that many key properties of the smooth theory are preserved. In particular, the corresponding spin transformations, conformal invariants for them, and the relation between this operator and its intrinsic counterpart are discussed. 2018-03-03 16:01:07 +0000 2021-11-15 15:53:09 +0100 https://arxiv.org/abs/1802.06278 J. Exp. Math. A discrete extrinsic and intrinsic {Dirac} operator 2018 2020 1802.06278 10.1080/10586458.2020.1727798 Tim Hoffmann Zi Ye A Mathematical Musical: “Dimensionen in Neukölln” 459--462 Proceedings of Bridges 2020: Mathematics, Art, Music, Architecture, Education, Culture 2020 978-1-938664-36-6 1099-6702 Tessellations Publishing Phoenix, Arizona http://archive.bridgesmathart.org/2020/bridges2020-459.html René M. Broeders Anna M. Hartkopf Carolyn Yackel Robert Bosch Eve Torrence Kristóf Fenyvesi Architectural freeform surfaces designed for cost-effective paneling mold re-use 2020 Advances in Architectural Geometry preprint https://www.geometrie.tuwien.ac.at/geom/ig/publications/aagweingarten/aagweingarten.pdf Davide Pellis Martin Kilian Hui Wang Caigui Jiang Christian M{\"u}ller Helmut Pottmann Extended and symmetric loss of stability for canards in planar fast-slow maps 2020 January preprint 1912.10286 M. Engel H. Jardon-Kojakhmetov 10.1515/dmvm-2020-0050 Mathematik als Sport. Ein Gespräch mit Lisa Sauermann Mitteilungen der Deutschen Mathematiker-Vereinigung 3 28 2020 162--170 Günter M. Ziegler Predicting sparse circle maps from their dynamics 2020 January 1911.06312 preprint F. Krahmer C. Kuehn N. Sissouno Principal Symmetric Meshes ACM Trans. Graphics 39 4 Article 127 17 2020 Proc. SIGGRAPH 10.1145/3386569.3392446 Davide Pellis Hui Wang Florian Rist Martin Kilian Helmut Pottmann Christian M{\"u}ller Confocal conics and 4-webs of maximal rank 2019 December 1912.01817 preprint Sergey I. Agafonov A random dynamical systems perspective on isochronicity for stochastic oscillations 2019 November 1911.08993 preprint M. Engel C. Kuehn Curve-pleated Structures ACM Trans. Graph. November 2019 38 6 November 2019 0730-0301 169:1--169:13 169 13 10.1145/3355089.3356540 3356540 ACM New York, NY, USA computational fabrication, computational origami, conical mesh, curved crease, developable surface, discrete differential geometry, pleated surface, pseudo-geodesic 608 https://www.discretization.de/publications/file/608 Caigui Jiang Klara Mundilova Florian Rist Johannes Wallner Helmut Pottmann Discrete Geodesic Parallel Coordinates ACM Trans. Graph. November 2019 38 6 November 2019 0730-0301 173:1--173:13 173 13 10.1145/3355089.3356541 3356541 ACM New York, NY, USA architectural geometry, computational fabrication, discrete differential geometry, geodesic, geodesic parallel coordinates, geodesic strip, isometry, paneling 607 https://www.discretization.de/publications/file/607 Hui Wang Davide Pellis Florian Rist Helmut Pottmann Christian Müller One-Bit Sigma-Delta modulation on the circle 2019 November preprint 587 https://www.discretization.de/publications/file/587 Olga Graf Felix Krahmer Sara Krause-Solberg Preprint 1910.05241 Combinatorial inscribability obstructions for higher-dimensional polytopes 2019 October Joseph Doolittle Jean-Philippe Labbé Carsten Lange Rainer Sinn Jonathan Speer Günter M. Ziegler Developments towards Mathematical Citizen Science 10.17605/OSF.IO/WBS8Y OSF 2019 September Forum Citizen Science 2019 53--58 Anna M Hartkopf Ideal Hyperbolic Polyhedra and Discrete Uniformization Discrete Comput. Geom. 2019 September 05 1432-0444 10.1007/s00454-019-00132-8 1707.06848 Boris Springborn Maximal fluctuations on periodic lattices: an approach via quantitative Wulff inequalities Commun. Math. Phys. 2019 September preprint http://cvgmt.sns.it/paper/4195/ M. Cicalese G.P. Leonardi One-Bit Unlimited Sampling Proc. IEEE Intl. Conf. Acoustics Speach Signal Proc. (ICASSP 2019) 10.1109/ICASSP.2019.8683266 2019 September 442 https://www.discretization.de/publications/file/442 Olga Graf Ayush Bhandari Felix Krahmer Robust One-bit Compressed Sensing With Manifold Data Proc. Intl. Conf. on Sampling Theory and Applications (SampTA '19) https://sampta2019.sciencesconf.org/267528/document 2019 September M. Iwen S. Dirksen J. Maly S. Krause-Solberg Discretized fast-slow systems near pitchfork singularities Journal of Difference Equations and Applications, Vol. 25, No. 7, pp. 1024-1051 2019 August 10.1080/10236198.2019.1647185 L. Arcidiacono M. Engel C. Kuehn From the N-clock model to the XY model: emergence of concentration effects in the variational analysis 2019 August preprint http://cvgmt.sns.it/paper/4432/ G. Orlando M. Cicalese M. Ruf Holes and dependences in an ordered complex Computer Aided Geometric Design 2019 Elsevier August http://pub.ist.ac.at/~edels/Papers/2018-J-06-HolesDependences.pdf Herbert Edelsbrunner Katharina Ölsböck Ripser: efficient computation of Vietoris-Rips persistence barcodes 2019 August 1908.02518 preprint Ulrich Bauer Vector-relation configurations and plabic graphs 2019 August Selecta Mathematica 1908.06959 https://link.springer.com/article/10.1007/s00029-023-00898-z Niklas Affolter Max Glick Pavlo Pylyavskyy Sanjay Ramassamy Discrete-to-continuum limits of multi-body systems with bulk and surface long-range interactions 2019 July preprint http://cvgmt.sns.it/paper/4406/ A. Bach M. Cicalese A. Braides Discretized fast-slow systems with canard points in two dimensions 2019 July 1907.06574 preprint M. Engel C. Kuehn M. Petrera Y. Suris Minimal n-Noids in hyperbolic and anti-de Sitter 3-space Proceedings A of Royal Society 1902.07992 2019 July 10.1098/rspa.2019.0173 Alexander I Bobenko Sebastian Heller Nicholas Schmitt On Bubble Rings and Ink Chandeliers ACM Trans. Graph. 38, 4, Article 129 2019 July 10.1145/3306346.3322962 Marcel Padilla Albert Chern Felix Knöppel Ulrich Pinkall Peter Schröder Approximation properties of hybrid shearlet-wavelet frames for Sobolev spaces 1712.01047 Advances in Computational Mathematics 2019 June 45 3 1581--1606 1572-9044 10.1007/s10444-019-09679-9 Philipp Petersen Mones Raslan 10.1088/1361-6420/ab10ca 2019 June {IOP} Publishing 35 6 064002 Learning The Invisible: A Hybrid Deep Learning-Shearlet Framework for Limited Angle Computed Tomography Inverse Problems The high complexity of various inverse problems poses a significant challenge to model-based reconstruction schemes, which in such situations often reach their limits. At the same time, we witness an exceptional success of data-based methodologies such as deep learning. However, in the context of inverse problems, deep neural networks mostly act as black box routines, used for instance for a somewhat unspecified removal of artifacts in classical image reconstructions. In this paper, we will focus on the severely ill-posed inverse problem of limited angle computed tomography, in which entire boundary sections are not captured in the measurements. We will develop a hybrid reconstruction framework that fuses model-based sparse regularization with data-driven deep learning. Our method is reliable in the sense that we only learn the part that can provably not be handled by model-based methods, while applying the theoretically controllable sparse regularization technique to the remaining parts. Such a decomposition into visible and invisible segments is achieved by means of the shearlet transform that allows to resolve wavefront sets in the phase space. Furthermore, this split enables us to assign the clear task of inferring unknown shearlet coefficients to the neural network and thereby offering an interpretation of its performance in the context of limited angle computed tomography. Our numerical experiments show that our algorithm significantly surpasses both pure model- and more data-based reconstruction methods. 1811.04602 Tatiana A. Bubba Gitta Kutyniok Matti Lassas Maximilian März Wojciech Samek Samuli Siltanen Vignesh Srinivasan A BDF2-approach for the non-linear Fokker-Planck equation Discrete Contin. Dyn. Syst. Discrete and Continuous Dynamical Systems. Series A 39 5 2893--2913 1078-0947 2019 May 10.3934/dcds.2019120 1801.09603 Simon Plazotta Conditioned Lyapunov exponents for random dynamical systems Transactions of the American Mathematical Society 372(9), 2019 2019 May 10.1090/tran/7803 M. Engel J.S.W. Lamb M. Rasmussen Discretized fast-slow systems near transcritical singularities Nonlinearity, Vol. 32, No. 7, 2365-2391 2019 May 10.1088/1361-6544/ab15c1 M. Engel C. Kuehn Multi-Nets. Classification of discrete and smooth surfaces with characteristic properties on arbitrary parameter rectangles Discrete Comput. Geom. Discrete {\&} Computational Geometry 2019 May 1432-0444 10.1007/s00454-019-00101-1 1802.05063 Alexander I Bobenko Helmut Pottmann Thilo Rörig Checkerboard incircular nets: Laguerre geometry and parametrisation Geometriae Dedicata 2019 April 10 We present a procedure which allows one to integrate explicitly the class of checkerboard IC-nets which has recently been introduced as a generalisation of incircular (IC) nets. The latter class of privileged congruences of lines in the plane is known to admit a great variety of geometric properties which are also present in the case of checkerboard IC-nets. The parametrisation obtained in this manner is reminiscent of that associated with elliptic billiards. Connections with discrete confocal coordinate systems and the fundamental QRT maps of integrable systems theory are made. The formalism developed in this paper is based on the existence of underlying pencils of conics and quadrics which is exploited in a Laguerre geometric setting. 1572-9168 10.1007/s10711-019-00449-x 1808.07254 Alexander I. Bobenko Wolfgang K. Schief Jan Techter Cotorsion torsion triples and the representation theory of filtered hierarchical clustering 2019 April preprint 1904.07322 Ulrich Bauer Magnus B. Botnan Steffen Oppermann Johan Steen On fast-slow consensus networks with a dynamic weight 1904.02690 1--48 2019 April preprint Hildeberto Jardón-Kojakhmetov Christian Kuehn A Reflectionless Discrete Perfectly Matched Layer 2019 With minor revision accepted by Journal of Computational Physics. March 1804.01390v2 Albert Chern Convex Equipartitions of Colored Point Sets Discrete & Computational Geometry 2019 March 01 61 2 355--363 We show that any d-colored set of points in general position in {\$}{\$}{\{}{\backslash}mathbb {\{}R{\}}{\}}^d{\$}{\$}Rdcan be partitioned into n subsets with disjoint convex hulls such that the set of points and all color classes are partitioned as evenly as possible. This extends results by Holmsen, Kyn{\v{c}}l {\&} Valculescu (Comput Geom 65:35--42, 2017) and establishes a special case of their general conjecture. Our proof utilizes a result obtained independently by Sober{\'o}n and by Karasev in 2010, on simultaneous equipartitions of d continuous measures in {\$}{\$}{\{}{\backslash}mathbb {\{}R{\}}{\}}^d{\$}{\$}Rdby n convex regions. This gives a convex partition of {\$}{\$}{\{}{\backslash}mathbb {\{}R{\}}{\}}^d{\$}{\$}Rdwith the desired properties, except that points may lie on the boundaries of the regions. In order to resolve the ambiguous assignment of these points, we set up a network flow problem. The equipartition of the continuous measures gives a fractional flow. The existence of an integer flow then yields the desired partition of the point set. 1432-0444 10.1007/s00454-017-9959-7 Pavle V. M. Blagojević Günter Rote Johanna K. Steinmeyer Günter M. Ziegler Modified equations for variational integrators applied to Lagrangians linear in velocities J. Geom. Mech. 2019 11 1 1--22 10.3934/jgm.2019001 1709.09567 March Mats Vermeeren Continuum limits of pluri-Lagrangian systems J. Integrable Syst. 2019 February 4 1 1--34 10.1093/integr/xyy020 1706.06830 Mats Vermeeren Duck traps: two-dimensional critical manifolds in planar systems Dynamical Systems: An International Journal, Vol. 34, No. 4, pp. 584-612, 2019 February 10.1080/14689367.2019.1575337 C. Kuehn C. Münch Random finite-difference discretizations of the Ambrosio-Tortorelli functional with optimal mesh size 2019 February preprint 1902.08437 A. Bach M. Cicalese M. Ruf Tverberg-Type Theorems for Matroids: A Counterexample and a Proof Combinatorica 2019 February 11 1439-6912 10.1007/s00493-018-3846-6 Pavle V. M. Blagojević Albert Haase Günter M. Ziegler A convergent Lagrangian discretization for $p$-Laplace and flux-limited diffusion equations preprint 1906.01321 2019 Oliver Junge Benjamin Söllner A leap forward: a user study on gestural geometry exploration Journal of Mathematics and the Arts 13 4 369-382 2019 Taylor & Francis 10.1080/17513472.2019.1667209 Martin Skrodzki Ulrike Bath Kevin Guo Konrad Polthier A Markov jump process modelling animal group size statistics Communications in Mathematical Sciences 2019 January P. Degond M.Engel J.Liu R. Pego A survey on the blow-up method for fast-slow systems 1901.01402 1--41 2019 Preprint H. Jardon-Kojakhmetov C. 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Blagojević Aleksandra S. Dimitrijević Blagojević Günter M. Ziegler A construction of commuting systems of integrable symplectic birational maps Preprint 2016 1607.07085 Matteo Petrera Yuri B Suris A construction of commuting systems of integrable symplectic birational maps. Lie-Poisson case Preprint 2016 1612.04349 Matteo Petrera Yuri B Suris A note on the expansion of the smallest eigenvalue distribution of the LUE at the hard edge The Annals of Applied Probability 26 3 1942--1946 2016 Institute of Mathematical Statistics 10.1214/15-AAP1121 1504.00235 Folkmar Bornemann Israel J. Math. A universality theorem for projectively unique polytopes and a conjecture of Shephard 2016 1301.2960 211 239-255 Karim Adiprasito Arnau Padrol Advances in Discrete Differential Geometry Preprint at arxiv Springer A variational principle for cyclic polygons with prescribed edge lengths 2016 1506.08069 H. Kourimska L. Skuppin B. Springborn A. I. 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Bobenko Advances in Discrete Differential Geometry Springer Discrete conformal maps: Boundary value problems, circle domains, Fuchsian and Schottky uniformization 2016 Preprint 194 https://www.discretization.de/publications/file/194 A. I. Bobenko S. Sechelmann B. Springborn A. I. Bobenko 2016 978-4-431-55341-0 Applications + Practical Conceptualization + Mathematics = fruitful Innovation 11 Mathematics for Industry 10.1007/978-4-431-55342-7_22 Discrete Geometry for Reliable Surface Quad-Remeshing Springer Japan Geometry processing; Simplicial surfaces; Surface parametrization; Branched covering; QuadCover algorithm; Hodge decomposition; Minimal surfaces 261--275 English Robert S. Anderssen Philip Broadbridge Yasuhide Fukumoto Kenji Kajiwara Tsuyoshi Takagi Evgeny Verbitskiy Masato Wakayama Konrad Polthier Faniry Razafindrazaka Geometry and freeform architecture 2016 Mathematics and Society EMS 978-3-03719-164-4 10.4171/164 131-151 Helmut Pottmann Johannes Wallner Wolfgang K{\"o}nig Advances in Discrete Differential Geometry Springer Holomorphic Vector Fields and Quadratic Differentials on Planar Triangular Meshes 2016 1506.08099 W. Y. Lam U. Pinkall A. I. Bobenko Hyperplane mass partitions via relative equivariant obstruction theory Documenta Mathematica 21 735--771 2016 1509.02959 http://emis.ams.org/journals/DMJDMV/vol-21/20.pdf Pavle V. M. Blagojević Florian Frick Albert Haase Günter M. Ziegler Low volume-fraction microstructures in martensites and crystal plasticity Math. Models Methods Appl. Sci. 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Bobenko Relative Stanley-Reisner theory and Upper Bound Theorems for Minkowski sums Publ. Math. Inst. Hautes Études Sci. 2016 124 99–163 1405.7368 10.1007/s10240-016-0083-7 Karim Adiprasito Raman Sanyal Rigid multiview varieties International Journal of Algebra and Computation 26 04 775--788 2016 World Scientific 10.1142/S021819671650034X 1509.03257 Michael Joswig Joe Kileel Bernd Sturmfels André Wagner Advances in Discrete Differential Geometry Springer S-conical cmc surfaces. Towards a unified theory of discrete surfaces with constant mean curvature 2016 10.1007/978-3-662-50447-5_9 198 https://www.discretization.de/publications/file/198 A. I. Bobenko T. Hoffmann A. I. Bobenko Singular values and evenness symmetry in random matrix theory Forum Mathematicum 28 5 873--891 2016 10.1515/forum-2015-0055 1503.07383 Folkmar Bornemann Peter J Forrester Six topics on inscribable polytopes Advances in Discrete Differential Geometry 407--419 2016 Springer 1511.03458 10.1007/978-3-662-50447-5_13 Arnau Padrol Günter M Ziegler Tverberg’s theorem at 50: extensions and counterexamples Notices of the AMS 63 7 732--739 2016 10.1090/noti1415 Imre Bárány Pavle V. M. Blagojević Günter M. Ziegler Two-dimensional variational systems on the root lattice $Q(A_N)$ 2016 1601.05296 preprint R. Boll Vertex normals and face curvatures of triangle meshes http://www.geometrie.tugraz.at/wallner/3curv.pdf Advances in Discrete Differential Geometry Springer 2016 20 pp., accepted Xian Sun Caigui Jiang Johannes Wallner Helmut Pottmann A. I. Bobenko Weighted digraphs and tropical cones Linear Algebra and its Applications 501 304--343 2016 Elsevier 10.1016/j.laa.2016.02.027 1503.04707 Michael Joswig Georg Loho Whitney numbers of arrangements via measure concentration of intrinsic volumes Preprint 2016 1606.09412 Karim Adiprasito Raman Sanyal „Was ist Mathematik" lernen und lehren Mathematische Semesterberichte 63 1 155--169 2016 Springer 10.1007/s00591-016-0167-y Andreas Loos Günter M Ziegler New Journal of Physics 11 113027 Optimal control of Bose-Einstein condensates in three dimensions http://stacks.iop.org/1367-2630/17/i=11/a=113027 17 2015 November J-F Mennemann D Matthes R-M Weishäupl T Langen Generation of real algebraic loci via complex detours preprint 2015 October 1510.05464 Stefan Kranich 13644801 http://dx.doi.org/10.1016/j.comgeo.2014.08.010 10.1016/j.comgeo.2014.08.010 09257721 Computational Geometry September 8 606--621 2015-06-12 23:10:34 2 Homological reconstruction and simplification in $\mathbb R^3$ 48 2015 Dominique Attali Ulrich Bauer Olivier Devillers Marc Glisse André Lieutier Hyperplane mass partitions via relative Equivariant Obstruction Theory 2015 September preprint 1509.02959 Pavle V. M. Blagojevic Florian Frick Albert Haase Günter M. Ziegler MDS Preprint 2015 August Realizability and inscribability for some simplicial spheres and matroid polytopes 1508.02531 Moritz Firsching Preprint 2015 August Scribability Problems for Polytopes 1508.03537 Hao Chen Arnau Padrol Shearlet approximation of functions with discontinuous derivatives preprint August 1508.00409 2015 Philipp Petersen GPU-based visualization of domain-coloured algebraic Riemann surfaces 1507.04571 preprint 2015 July Stefan Kranich Stripe patterns on surfaces ACM Trans. Graph., 34(4):39:1--39:11 2015 July F. Knöppel K. Crane U. Pinkall P. Schröder The Singular Values of the GOE Random Matrices: Theory Appl. 04, 1550009 (2015) (32 pages) 2015 June 10.1142/S2010326315500094 1502.05946 Folkmar Bornemann Michael La Croix An epsilon-delta bound for plane algebraic curves and its use for certified homotopy continuation of systems of plane algebraic curves 1505.03432 preprint 2015 May Stefan Kranich Combinatorica accepted, preprint at arxiv The universality theorem for neighborly polytopes 2015 February 1402.7207 Karim Adiprasito Arnau Padrol A convergent Lagrangian discretization for a nonlinear fourth order equation Found. Comput. Math. 2015 online first 1410.1728 Daniel Matthes Horst Osberger A dynamical solution to the Basel problem preprint 2015 1506.05288 M. Vermeeren 2015 1615-3375 Foundations of Computational Mathematics 10.1007/s10208-015-9271-y A Laplace Operator on Semi-Discrete Surfaces Springer US Laplace operator; Semi-discrete surfaces; Quadrilateral meshes; Consistency; Primary 53B20; Secondary 53A05; 41A25 1-36 English Wolfgang Carl A new phase space density for quantum expectations 2015 1506.08880 24pp J. Keller C. Lasser T. Ohsawa 2015 1017-1398 Numerical Algorithms 68 1 10.1007/s11075-014-9895-z An improved Talbot method for numerical Laplace transform inversion Springer US Inverse Laplace transform; Talbot’s method; Trapezoidal rule; Midpoint rule; 65R10; 65Z05 167-183 English 1304.2505 Benedict Dingfelder J.A.C. Weideman An invariant class of Hermite type multivariate polynomials for the Wigner transform 1505.06192 2015 22pp H. Dietert J. Keller S. Troppmann Anisotropic multiscale systems on bounded domains preprint 2015 1510.04538 P. Grohs G. Kutyniok J. Ma P. Petersen Advances in Mathematics accepted Approximation and convergence of the intrinsic volume 2015 http://pub.ist.ac.at/~edels/Papers/2014-J-06-FirstIntVolume.pdf Herbert Edelsbrunner Florian Pausinger Architectural Geometry Computers and Graphics 2015 47 145-164 http://www.geometrie.tugraz.at/wallner/survey.pdf 10.1016/j.cag.2014.11.002 Helmut Pottmann Michael Eigensatz Amir Vaxman Johannes Wallner Cayley-Bacharach Formulas The American Mathematical Monthly, 122(9):845--854 2015 The Cayley-Bacharach Theorem states that all cubic curves through eight given points in the plane also pass through a unique ninth point. We write that point as an explicit rational function in the other eight. 1405.6438 Jürgen Richter-Gebert Qingchun Ren Bernd Sturmfels Classification of edges using compactly supported shearlets Applied and Computational Harmonic Analysis 2015 10.1016/j.acha.2015.08.006 1411.5657 Gitta Kutyniok Philipp Petersen Close-to-conformal deformations of volumes ACM Transactions on Graphics 34 4 56 2015 ACM A. Chern U. Pinkall P. Schröder Combinatorial positivity of translation-invariant valuations and a discrete Hadwiger theorem 2015 J. Eur. Math. Soc. (JEMS) accepted for publication, preprint on arxiv 1505.07440 Katharina Jochemko Raman Sanyal Conformal mesh deformations with Möbius transformations ACM Trans. Graphics 34 4 $\#$ 55, 1--11 2015 Proc. SIGGRAPH Amir Vaxman Christian Müller Ofir Weber Conformal mesh deformations with Möbius transformations ACM Transactions on Graphics (TOG) 34 4 55 2015 ACM http://www.geometrie.tuwien.ac.at/geom/ig/publications/2015/conformal2015/conformal2015.pdf Amir Vaxman Christian Müller Ofir Weber Convergence of a Fully Discrete Variational Scheme for a Thin Film Equation Radon Series on Computational and Applied Mathematics 2015 1509.01513 accepted Horst Osberger Daniel Matthes Dirac Structures in Vakonomic Mechanics J. Geom. Phys. accepted 2015 1405.5394 Fernando Jiménez Hiroaki Yoshimura Discrete conformal maps and ideal hyperbolic polyhedra Geom. Topol. 2015 19 4 2155-2215 10.2140/gt.2015.19.2155 1005.2698 A. I. Bobenko U. Pinkall B. Springborn Discrete line complexes and integrable evolution of minors Proc. Royal Soc. A 2015 471 2175 23 pp. 10.1098/rspa.2014.0819 1410.5794 A. I. Bobenko W. Schief Discrete pluriharmonic functions as solutions of linear pluri-Lagrangian systems Commun. Math. Phys. 2015 336 1 199--215 1403.2876 A. I. Bobenko Yu. B. Suris Discrete uniformization of finite branched covers over the Riemann sphere via hyper-ideal circle patterns 2015 preprint 1510.04053 A. I. Bobenko N. Dimitrov S. Sechelmann Domain formation in magnetic polymer composites: an approach via stochastic homogenization Archive for Rational Mechanics and Analysis 218 2 945--984 10.1007/s00205-015-0873-y 2015 Springer Roberto Alicandro Marco Cicalese Matthias Ruf Dyck path triangulations and extendability Journal of Combinatorial Theory, Series A 2015 131 0 187-208 1402.5111 http://www.sciencedirect.com/science/article/pii/S009731651400140X Cesar Ceballos Arnau Padrol Camilo Sarmiento Experimental Math. 2015 1408.0688 10.1080/10586458.2015.1015084 Enumeration of neighborly polytopes and oriented matroids 24 489-505 Hiroyuki Miyata Arnau Padrol Exponential Convergence to Equilibrium in a Coupled Gradient Flow System Modelling Chemotaxis Analysis & PDE 8 2 425-466 1310.3977 2015 Jonathan Zinsl Daniel Matthes Frustrated ferromagnetic spin chains: a variational approach to chirality transitions Journal of Nonlinear Science, 25(291-313) 2015 M. Cicalese F. Solombrino Hamilton-Dirac systems for charged particles in gauge fields J. Geom. Phys., 94:35-49 2015 1410.3249 F. Jiménez 10.1007/s00025-015-0453-3 1422-6383 Results in Mathematics 52C26; 52A55; 57M50; 52C25; Hyper-ideal circle pattern; cell complex; hyper-ideal tetrahedron; hyperbolic volume; variational principle English 1-45 Springer Basel Hyper-ideal Circle Patterns with Cone Singularities 2015 1406.6741 N. Dimitrov 10.1098/rspa.2015.0254 Ideal geometry of periodic entanglements 471 2181 2015 P. R. Soc. A 2015.0254 Myfanwy E. Evans Vanessa Robins Stephen Hyde 13591814 http://jocg.org/index.php/jocg/article/view/205 Journal of Computational Geometry 2 162--191 2015-04-25 20:42:42 2 Induced matchings and the algebraic stability of persistence barcodes http://jocg.org/index.php/jocg/article/view/205 6 2015 Ulrich Bauer Michael Lesnick Interactive design of developable surfaces ACM Trans. Graphics accepted 2015 http://www.geometrie.tugraz.at/wallner/abw.pdf Chengcheng Tang Pengbo Bo Johannes Wallner Helmut Pottmann Isothermic Triangulated Surfaces 2015 January 1501.02587 preprint Wai Yeung Lam Ulrich Pinkall 10.1016/j.jmaa.2015.03.001 Journal of Mathematical Analysis and Applications 238-257 Linear independence of compactly supported separable shearlet systems 428 2015 1404.1690 Jackie Ma Philipp Petersen Long-Time Behaviour of a Fully Discrete Lagrangian Scheme for a Family of Fourth Order Submitted 1501.04800 2015 Horst Osberger Many projectively unique polytopes Inventiones math. 2015 199 581-652 1212.5812 10.1007/s00222-014-0519-y Günter M. Ziegler Karim Adiprasito Minima of invariant functions: The inverse problem Acta Applicandae Mathematicae, 137(1):233-252 10.1007/s10440-014-9997-6 accepted for publication by Acta Applicandae Mathematicae 2015 Jürgen Scheurle Sebastian Walcher Moduli of tropical plane curves Research in the Mathematical Sciences 2 1 4 2015 Springer 10.1186/s40687-014-0018-1 Sarah Brodsky Michael Joswig Ralph Morrison Bernd Sturmfels Multiscale geometry of the Olsen model and non-classical relaxation oscillations J. Nonlinear Sci. 25 3 583--629 2015 10.1007/s00332-015-9235-z C. Kuehn P. Szmolyan New developments on the Geometric Nonholonomic Integrator Nonlinearity, 28:871-900 2015 1312.1587 Sebastián Ferraro Fernando Jiménez David Martín de Diego Non-Hermitian propagation of Hagedorn wavepackets 1507.02858 2015 33pp C. Lasser R. Schubert S. Troppmann On integrability of discrete variational systems: Octahedron relations Internat. Math. Res. Notes 2015 2015 rnv140, 24 pp. 1406.0741 R. Boll M. Petrera Yu. B. Suris On the discretization of nonholonomic dynamics in $\mathbb{R}^n$ J. Geom. Mechanics, 7(1):43-80 2015 1407.2116 Fernando Jimenez Juergen Scheurle On the discretization of the Euler-Poincaré-Suslov equations in $SO(3)$ preprint 1506.01289 2015 F. Jiménez J. Scheurle Perfect Matching Quad Layouts for Manifold Meshes Computer Graphics Forum (proceedings of EUROGRAPHICS Symposium on Geometry Processing) 34 5 2015 http://www.mi.fu-berlin.de/en/math/groups/ag-geom/publications/db/2015_RRP_PerfectMatchingQuadLayoutsForManifoldMeshes_New.pdf Faniry H. Razafindrazaka Ulrich Reitebuch Konrad Polthier Polyhedral Patterns ACM Trans. Graphics Proc. SIGGRAPH Asia 2015 34 Caigui Jiang Chengcheng Tang Amir Vaxman Peter Wonka Helmut Pottmann Realization of Regular Maps Large Genus 239--252 Topological and Statistical Methods for Complex Data 2015 978-3-662-44900-4 10.1007/978-3-662-44900-4_14 Springer Berlin Heidelberg http://page.mi.fu-berlin.de/faniry/files/faniryTSCD2015.pdf Faniry Razafindrazaka Konrad Polthier Valerio Pascucci Janine Bennet Fabien Vivodtzev Preprint S-conical minimal surfaces. Towards a unified theory of discrete minimal surfaces. 2015 199 https://www.discretization.de/publications/file/199 A. I. Bobenko T. Hoffmann B. König S. Sechelmann Semi-Discrete Constant Mean Curvature Surfaces Math. Z. 2015 459-478 279 10.1007/s00209-014-1377-4 http://www.geometrie.tuwien.ac.at/cmueller/sdcmc.pdf Christian Müller Semi-discrete constant mean curvature surfaces Mathematische Zeitschrift 279 1-2 459--478 2015 Springer 10.1007/s00209-014-1377-4 http://www.geometrie.tuwien.ac.at/geom/ig/publications/2015/sdcmc2015/sdcmc.pdf Christian Müller Smoothing discrete Morse theory 2015 Annali Sc. Norm. Sup. Cl. Sci. accepted, preprint at arxiv 1212.0885 B. Benedetti Subdivisions, shellability, and collapsibility of products 2015 accepted, preprint at arxiv Combinatorica 1202.6606 K. Adiprasito B. Benedetti 1409.2667 Duke Math.~J. accepted The asymptotic behaviour of the discrete holomorphic map $Z^a$ via the Riemann-Hilbert method 2015 A. I. Bobenko A. Its European Journal of Combinatorics (special issue in honour of Michel Las Vergnas) 159–179 50 2015 1209.5712 The degree of point configurations: Ehrhart theory, Tverberg points and almost neighborly polytopes Benjamin Nill Arnau Padrol Tight complexes in $3$-space admit perfect discrete Morse functions Eur. J. Comb. 2015 45 71--84 1202.3390 K. Adiprasito B. Benedetti Touch und Tablet: Stationen einer Designstudie Heintz, G., Pinkernell, G., Schacht, F. (Hrsg.): Digitale Werkzeuge für den Mathematikunterricht. Festschrift für Hans-Jürgen Elschenbroich 2015 http://science-to-touch.com/articles Jürgen Richter-Gebert Transport Distances and Geodesic Convexity for Systems of Degenerate Diffusion Equations Calculus of Variations and Partial Differential Equations 1409.6520 2015 accepted Jonathan Zinsl Daniel Matthes Tropicalizing the simplex algorithm SIAM Journal on Discrete Mathematics 29 2 751--795 2015 SIAM 10.1137/130936464 1308.0454 Xavier Allamigeon Pascal Benchimol Stéphane Gaubert Michael Joswig Twisted x-rays: incoming waveforms yielding discrete diffraction patterns for helical structures 1506.04240 2015 G. Friesecke R. D. James D. Jüstel Discrete Comput. Geom. 412-431 Universality theorems for inscribed polytopes and Delaunay triangulations 54 2015 1406.7831 Karim Adiprasito Arnau Padrol Louis Theran Variational symmetries and pluri-Lagrangian systems Dynamical Systems, Number Theory and Applications: A Festschrift in Honor of Professor Armin Leutbecher's 80th Birthday World Scientific Singapore 2015 1307.2639 Yu. B. Suris Th. Hagen F. Rupp J. Scheurle Discrete Riemann surfaces: linear discretization and its convergence J. reine und angew. Math. 2014 October 10.1515/crelle-2014-0065 1210.0561 Alexander Bobenko Mikhail Skopenkov Surface panelization using periodic conformal maps Advances in Architectural Geometry 2014 2014 September Springer Best Paper Award Thilo Rörig Stefan Sechelmann Agata Kycia Moritz Fleischmann Philippe Block Jan Knippers Niloy Mitra Wenping Wang Quasi-classical description of molecular dynamics based on Egorov's theorem The Journal of Chemical Physics 2014 August 141 5 054104 10.1063/1.4891517 1405.7355 Johannes Keller Caroline Lasser $\alpha$-Molecules preprint 2014 July 1407.4424 Philipp Grohs Sandra Keiper Gitta Kutyniok Martin Schäfer A methodology for obtaining asymptotic estimates for the exponentially small splitting of separatrices to whiskered tori with quadratic frequencies 2014 July 1407.6524 To appear in Research Perspectives CRM Barcelona A. Delshams M. Gonchenko P. Gutiérrez Kinematics of Expansive Planar Periodic Mechanisms Advances in Robot Kinematics (ARK'14) 2014 July preprint 53 https://www.discretization.de/publications/file/53 Ciprian S. Borcea Ileana Streinu On dynamics and bifurcations of area-preserving maps with homoclinic tangencies 2014 July Submitted to Nonlinearity 1407.5473 A. Delshams M. Gonchenko S. Gonchenko Regularization and Numerical Solution of the Inverse Scattering Problem using Shearlet Frames 2014 July 1407.7349 preprint Gitta Kutyniok Volker Mehrmann Philipp Petersen Smoke Rings from Smoke ACM Trans. Graph. July 2014 33 4 July 2014 0730-0301 140:1--140:8 140 8 10.1145/2601097.2601171 2601171 ACM New York, NY, USA DEC, Schrödinger operator, fluid simulation, hairpin removal, hybrid methods, vortex filaments, vortex reconnection http://page.math.tu-berlin.de/~pinkall/smoke-rings-from-smoke.pdf Steffen Weißmann Ulrich Pinkall Peter Schröder Landau–Zener type surface hopping algorithms The Journal of Chemical Physics 2014 June 140 22 224108 - 10.1063/1.4882073 1403.4859 Andrey K. Belyaev Caroline Lasser Giulio Trigila Liftings and stresses for planar periodic frameworks in Proc. 30th Symposium on Computational Geometry (SoCG'14) 2014 June preprint 54 https://www.discretization.de/publications/file/54 Ciprian S. Borcea Ileana Streinu 2014 May 1069-5869 Journal of Fourier Analysis and Applications 20 4 10.1007/s00041-014-9330-9 Hagedorn Wavepackets in Time-Frequency and Phase Space Springer US Hermite functions; Hagedorn wavepackets; Wigner transform; FBI transform; Husismi transform; Ladder operators; 42C05; 42A38; 65R10 679-714 English 1303.5192 Caroline Lasser Stephanie Troppmann 10.1088/0951-7715/27/6/1351 https://doi.org/10.1088%2F0951-7715%2F27%2F6%2F1351 2014 may {IOP} Publishing 27 6 1351-1366 Normal hyperbolicity and unbounded critical manifolds Nonlinearity This work is motivated by mathematical questions arising in differential equation models for autocatalytic reactions. We extend the local theory of singularities in fast–slow polynomial vector fields to classes of unbounded manifolds which lose normal hyperbolicity due to an alignment of the tangent and normal bundles. A projective transformation is used to localize the unbounded problem. Then the blow-up method is employed to characterize the loss of normal hyperbolicity for the transformed slow manifolds. Our analysis yields a rigorous scaling law for all unbounded manifolds which exhibit a power-law decay for the alignment with a fast subsystem domain. Furthermore, the proof also provides a technical extension of the blow-up method itself by augmenting the analysis with an optimality criterion for the blow-up exponents. Christian Kuehn April Preprint 2014 1404.2443 Polygons as slices of higher-dimensional polytopes Arnau Padrol Julian Pfeifle Differential-Based Geometry and Texture Editing with Brushes J. Math. Imaging Vis. February 2014 48 2 February 2014 0924-9907 359--368 10 10.1007/s10851-013-0443-6 2582777 Kluwer Academic Publishers Norwell, MA, USA Deformation, Geometry brush, Interactive modeling, Texture editing Niklas Krauth Matthias Nieser Konrad Polthier 2014 February 0046-5755 Geometriae Dedicata 168 1 10.1007/s10711-013-9830-9 Discretization of asymptotic line parametrizations using hyperboloid surface patches Springer Netherlands Discrete differential geometry; Discrete asymptotic line parametrization; A-nets; Hyperboloids; Projective geometry; Plücker line geometry; 51M30; 53A05; 65D17 265-289 English 1112.3508 Emanuel Huhnen-Venedey Thilo Rörig 2014 February 0040-5779 Theoretical and Mathematical Physics 178 2 10.1007/s11232-014-0135-4 Landau-Lifshitz equation, uniaxial anisotropy case: Theory of exact solutions Pleiades Publishing multisoliton solution; ferromagnetism; finite-gap integration; theta function 143-193 English R.F. Bikbaev A.I. Bobenko A.R. Its What is integrability of discrete variational systems? 470 2162 2014 February 10.1098/rspa.2013.0550 We propose a notion of a pluri-Lagrangian problem, which should be understood as an analogue of multi-dimensional consistency for variational systems. This is a development along the line of research of discrete integrable Lagrangian systems initiated in 2009 by Lobb and Nijhoff, however, having its more remote roots in the theory of pluriharmonic functions, in the Z-invariant models of statistical mechanics and their quasiclassical limit, as well as in the theory of variational symmetries going back to Noether. A d-dimensional pluri-Lagrangian problem can be described as follows: given a d-form on an m-dimensional space (called multi-time, m>d), whose coefficients depend on a sought-after function x of m independent variables (called field), find those fields x which deliver critical points to the action functionals for any d-dimensional manifold Σ in the multi-time. We derive the main building blocks of the multi-time Euler–Lagrange equations for a discrete pluri-Lagrangian problem with d=2, the so-called corner equations, and discuss the notion of consistency of the system of corner equations. We analyse the system of corner equations for a special class of three-point two-forms, corresponding to integrable quad-equations of the ABS list. This allows us to close a conceptual gap of the work by Lobb and Nijhoff by showing that the corresponding two-forms are closed not only on solutions of (non-variational) quad-equations, but also on general solutions of the corresponding corner equations. We also find an example of a pluri-Lagrangian system not coming from a multi-dimensionally consistent system of quad-equations. http://rspa.royalsocietypublishing.org/content/470/2162/20130550.abstract Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 1307.0523 Raphael Boll Matteo Petrera Yuri B. Suris Affine arc length polylines and curvature continuous uniform B-splines Computer-Aided Geom. Design 31 2014 http://www.geometrie.tuwien.ac.at/geom/fg4/sn/2014/affarclen/affine-arc-length-2014-kaeferboeck.pdf Florian Käferböck Asymptotic Behavior of Gradient Flows Driven by Nonlocal Power Repulsion and Attraction Potentials in One Dimension accepted at SIAM-MA 2014 January 1401.2338 Marco Di Francesco Massimo Fornasier Jan-Christian Hütter Daniel Matthes 10.1007/s00365-013-9199-x Constructive Approximation. An International Journal for Approximations and Expansions 0176-4276 Constr. Approx. Nader El-Khatib 1 151--171 Automatic deformation of Riemann-Hilbert problems with applications to the Painlevé II transcendents 39 2014 G. Wechslberger F. Bornemann Cell packing structures Computer-Aided Design 2014 http://www.geometrie.tuwien.ac.at/geom/fg4/sn/2014/cps/cps.pdf 10.1016/j.cad.2014.02.009 to appear. Special issue on Material Ecology Helmut Pottmann Caigui Jiang Mathias Höbinger Jun Wang Philippe Bompas Johannes Wallner Complex Polynomial Mandalas and their Symmetries 433--436 Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture 2014 978-1-938664-11-3 1099-6702 Tessellations Publishing Phoenix, Arizona http://archive.bridgesmathart.org/2014/bridges2014-433.html Zoi Tokoutsi Konstantin Poelke Konrad Polthier George Hart Gary Greenfield Reza Sarhangi Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio Regul. Chaotic Dyn. Regular and Chaotic Dynamics. International Scientific Journal 19 2014 6 663--680 1560-3547 37J40 (70H08) 3284607 Gabriella Pinzari 10.1134/S1560354714060057 1409.4944 Amadeu Delshams Marina Gonchenko Pere Gutiérrez Convergence of a Variational Lagrangian Scheme for a Nonlinear Drift Diffusion Equation ESAIM: Mathematical Modelling and Numerical Analysis 48 03 697-726 2014 1301.0747 Cambridge Univ Press Daniel Matthes Horst Osberger Corrections to Wigner type phase space methods Nonlinearity 27 12 2951-2974 http://stacks.iop.org/0951-7715/27/i=12/a=2951 10.1088/0951-7715/27/12/2951 1403.2839 2014 Over decades, the time evolution of Wigner functions along classical Hamiltonian flows has been used for approximating key signatures of molecular quantum systems. Such approximations are for example the Wigner phase space method, the linearized semiclassical initial value representation, or the statistical quasiclassical method. The mathematical backbone of these approximations is Egorov's theorem. In this paper, we reformulate the well-known second order correction to Egorov's theorem as a system of ordinary differential equations and derive an algorithm with improved asymptotic accuracy for the computation of expectation values. For models with easily evaluated higher order derivatives of the classical Hamiltonian, the new algorithm's corrections are computationally less expensive than the leading order Wigner method. Numerical test calculations for a two-dimensional torsional system confirm the theoretical accuracy and efficiency of the new method. Wolfgang Gaim Caroline Lasser Delaunay triangulations with disconnected realization spaces 30th Annual Symposium on Computational Geometry, SOCG'14, Kyoto, Japan, June 08 - 11, 2014 2014 163 - 170 ACM 10.1145/2582112.2582119 978-1-4503-2594-3 Arnau Padrol Louis Theran Siu-Wing Cheng Olivier Devillers 10.1007/s00454-014-9622-5 0179-5376 Discrete and Computational Geometry Königs dual; Christoffel transformation; Discrete conjugate net; Space form; Constant mean curvature; Mixed area; 53A10; 53C42; 53A15; 53A30; 37K25; 37K35 English 4 612-629 Springer US Discrete constant mean curvature nets in space forms: Steiner's formula and Christoffel duality 52 2014 1409.2001 Alexander I. Bobenko Udo Hertrich-Jeromin Inna Lukyanenko Dualizable Shearlet Frames and Sparse Approximation preprint 2014 130 https://www.discretization.de/publications/file/130 Gitta Kutyniok Wang-Q Lim Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tori with quadratic and cubic frequencies Electron. Res. Announc. Math. Sci. Electronic Research Announcements in Mathematical Sciences 21 2014 41--61 1935-9179 37J40 (34C45 70H08) 3260128 Igor O. Parasyuk 10.3934/era.2014.21.41 1306.0728 Amadeu Delshams Marina Gonchenko Pere Gutiérrez Exponentially Small Lower Bounds for the Splitting of Separatrices to Whiskered Tori with Frequencies of Constant Type International Journal of Bifurcation and Chaos 24 08 1440011 2014 10.1142/S0218127414400112 1402.1654 Amadeu Delshams Marina Gonchenko Pere Gutiérrez Extremal examples of collapsible complexes and random discrete Morse theory 2014 preprint 1404.4239 K. Adiprasito B. Benedetti F. H. Lutz Foldable triangulations of lattice polygons Amer. Math. Monthly 121 8 2014 706-710 10.4169/amermathmont.121.08.706 1207.6865 Michael Joswig Günter M. Ziegler Form-finding with Polyhedral Meshes Made Simple ACM Trans. Graphics 2014 33 4 $\#$70,1-9 Proc. SIGGRAPH http://www.geometrie.tugraz.at/wallner/formfinding2.pdf 10.1145/2601097.2601213 Chengcheng Tang Xiang Sun Alexandra Gomes Johannes Wallner Helmut Pottmann Freeform Honeycomb Structures Comput. Graph. Forum 33 5 2014 185-194 Proc. Symposium Geometry Processing http:/www.geometrie.tugraz.at/wallner/hexstructure.pdf 10.1111/cgf.12444 Caigui Jiang Jun Wang Johannes Wallner Helmut Pottmann European Conference on Computer Vision (ECCV) 14 32--46 Generalized Connectivity Constraints for Spatio-temporal {3D} Reconstruction 10.1007/978-3-319-10593-2_3 2014 M. R. Oswald J. Stühmer D. Cremers Geodesically Convex Energies and Confinement of Solutions for a Multi-Component System of Nonlocal Interaction Equations Submitted 1412.3266 2014 Jonathan Zinsl Interactive modeling of architectural freeform structures - combining geometry with fabrication and statics Advances in Architectural Geometry 2014 Springer http://www.geometrie.tuwien.ac.at/geom/fg4/sn/2014/interactive/interactive.pdf Caigui Jiang Chengcheng Tang Marko Tomičić Johannes Wallner Helmut Pottmann P. Block J. Knippers W. Wang Many neighborly inscribed polytopes and Delaunay triangulations 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) DMTCS Proceedings 2014 161-168 http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/view/dmAT0115 Bernd Gonska Arnau Padrol Metastability and dynamics of discrete topological singularities in two dimensions: a Gamma-convergence approach Archive for Rational Mechanics and Analysis, 214(1):269--330 2014 A. Garroni R. Alicandro L. De Luca M. Ponsiglione Microstructures in low-hysteresis shape memory alloys: scaling regimes and optimal needle shapes Arch. Ration. Mech. Anal. Archive for Rational Mechanics and Analysis 213 2014 2 355-421 0003-9527 10.1007/s00205-014-0736-y Barbara Zwicknagl On bifurcations of area-preserving and nonorientable maps with quadratic homoclinic tangencies Regul. Chaotic Dyn. Regular and Chaotic Dynamics. International Scientific Journal 19 2014 6 702--717 1560-3547 37C05 (37C29 37E30 37G25) 3284610 M. L. Blank 10.1134/S1560354714060082 1410.5704 Amadeu Delshams Marina Gonchenko Sergey V. Gonchenko On Discrete Constant Mean Curvature Surfaces Discrete Comput. Geom. 51 2014 3 516--538 10.1007/s00454-014-9577-6 http://www.geometrie.tuwien.ac.at/cmueller/cmc.pdf Christian Müller On offsets and curvatures for discrete and semidiscrete surfaces 2014 Beitr. Algebra Geom. 55 207-228 http://www.geometrie.tugraz.at/wallner/sdcurv.pdf 10.1007/s13366-013-0146-6 MR3167790 Oleg Karpenkov Johannes Wallner On Weingarten Transformations of Hyperbolic Nets 2014 10.1093/imrn/rnt354 Weingarten transformations of smooth surfaces, which, by definition, preserve asymptotic lines have been studied extensively in classical differential geometry, and they also play an important role in connection with the modern geometric theory of integrable systems. Their natural discrete analogs have been investigated in great detail in the area of (integrable) discrete differential geometry and can be traced back at least to the early 1950s. Here, we propose a canonical analog of (discrete) Weingarten transformations for hyperbolic nets, that is, C1-surfaces which constitute hybrids of smooth and discrete surfaces “parameterized” in terms of asymptotic coordinates. We prove the existence of Weingarten pairs and analyze their geometric and algebraic properties. http://imrn.oxfordjournals.org/content/early/2014/01/24/imrn.rnt354.abstract International Mathematics Research Notices 1305.4783 Emanuel Huhnen-Venedey Wolfgang K. Schief Parabolic molecules Found. Comput. Math. Foundations of Computational Mathematics. The Journal of the Society for the Foundations of Computational Mathematics 14 2014 2 299--337 1615-3375 42C15 3179586 10.1007/s10208-013-9170-z Philipp Grohs Gitta Kutyniok Random discrete Morse theory and a new library of triangulations Experimental Mathematics 2014 23 1 66-94 1303.6422 B. Benedetti F. H. Lutz Regular Surfaces and Regular Maps 225--234 Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture 2014 978-1-938664-11-3 1099-6702 Tessellations Publishing Phoenix, Arizona http://archive.bridgesmathart.org/2014/bridges2014-225.html Faniry Razafindrazaka Konrad Polthier George Hart Gary Greenfield Reza Sarhangi Ropelength Criticality Geom. Topol. 18 1973--2043 2014 1102.3234 Jason Cantarella Joseph H. G. Fu Robert B. Kusner John M. Sullivan Shaping the skin: the interplay of mesoscale geometry and corneocyte swelling http://link.aps.org/doi/10.1103/PhysRevLett.112.038102 3 112 2014 Phys. Rev. Lett. Physical Review Letters 038102:1--5 Myfanwy E. Evans Roland Roth ShearLab 3D: Faithful Digital Shearlet Transforms based on Compactly Supported Shearlets Preprint 2014 January 1402.5670 49 https://www.discretization.de/publications/file/49 Gitta Kutyniok Wang-Q Lim Rafael Reisenhofer Sigma-Delta quantization of sub-Gaussian frame expansions and its application to compressed sensing Inform. Inference 2014 1 40-58 3 f.krahmer 2013.04.23 http://num.math.uni-goettingen.de/~f.krahmer/KSY13 F. Krahmer R. Saab Ö. Yilmaz Smoke rings from smoke ACM Transactions on Graphics, 33 2014 S. Weissmann U. Pinkall P. Schröder Smooth surfaces from rational bilinear patches Comput. Aided Geom. Design Computer Aided Geometric Design 31 2014 1 1--12 http://www.geometrie.tuwien.ac.at/geom/fg4/sn/2014/hypnets/hypnets.pdf 10.1016/j.cagd.2013.11.001 Ling Shi Jun Wang Helmut Pottmann Suprema of Chaos Processes and the Restricted Isometry Property Comm. Pure Appl. Math. 2014 11 1877-1904 67 f.krahmer 2012.07.01 http://num.math.uni-goettingen.de/~f.krahmer/KMR12.pdf F. Krahmer S. Mendelson H. Rauhut Teaching and Learning "What is Mathematics" Proc. International Congress of Mathematicians, Seoul 2014 IV 1201-1215 2014 Kyung Moon Books Seoul, Korea 68 https://www.discretization.de/publications/file/68 Günter M. Ziegler Andreas Loos New York, NY, USA Proceedings of the Thirtieth Annual Symposium on Computational Geometry 13606519 http://portal.acm.org/citation.cfm?id=2582112.2582167 http://dx.doi.org/10.1145/2582112.2582167 10.1145/2582112.2582167 978-1-4503-2594-3 Kyoto, Japan 2015-05-08 13:26:57 2 ACM SOCG'14 The Morse Theory of Cech and Delaunay Filtrations 2014 Ulrich Bauer Herbert Edelsbrunner Foundations of Computational Mathematics 13478981 http://dx.doi.org/10.1007/s10208-014-9223-y http://link.springer.com/article/10.1007/s10208-014-9223-y 10.1007/s10208-014-9223-y computational-topology 1--32 2015-01-09 16:31:53 2 Springer US The Persistent Homology of a Self-Map 2014 Herbert Edelsbrunner Grzegorz Jablonski Marian Mrozek Tight and non-tight topological Tverberg type theorems Oberwolfach Reports 2014 11 3 2284-2287 67 https://www.discretization.de/publications/file/67 Pavle V. M. Blagojevic Florian Frick Benjamin Matschke Günter M. Ziegler Tverberg plus constraints Bulletin of the London Mathematical Society Extended Abstract: Oberwolfach Reports, 11(1):14-16, 2014 2014 46 953-967 1401.0690 10.1112/blms/bdu049 http://blms.oxfordjournals.org/cgi/content/abstract/bdu049?ijkey=s0zAd5sXaMm0aIt Pavle V. M. Blagojevic Florian Frick Günter M. Ziegler Variational Laplacians for semidiscrete surfaces 2014 submitted http://www.geometrie.tugraz.at/carl/gradients.pdf Wolfgang Carl Johannes Wallner Diskretisierung in Geometrie und Dynamik - Elastische Stäbe und Rauchringe Mitteilungen der DMV 21 1 218-224 2013 December http://www.degruyter.com/view/j/dmvm.2013.21.issue-00004/issue-files/dmvm.2013.21.issue-00004.xml A.I. Bobenko B. Springborn Many neighborly polytopes and oriented matroids. Discrete \& Computational Geometry Discrete Comput. 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Lutz Helmut Pottmann Jan Techter PDE Dynamics Mathematical Modeling and Computation 23 Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA 2019 xiii+245 978-1-61197-565-9; 978-1-61197-566-6 https://my.siam.org/Store/Product/viewproduct/?ProductId=30604306 Christian Kuehn A Discrete Hilbert Transform with Circle Packings 978-3-658-20456-3/pbk; 978-3-658-20457-0/ebook xi + 102 2017 BestMasters Series Springer Spektrum, Weisbaden 10.1007/978-3-658-20457-0 Dominic Volland Mathematical Physics III - Integrable Systems of Classical Mechanics. Lecture Notes Logos Verlag Berlin GmbH 2015 978-3-8325-3950-4 http://www.logos-verlag.de/cgi-bin/engbuchmid?isbn=3950&lng=deu&id= Matteo Petrera Multiple time scale dynamics Applied Mathematical Sciences 191 Springer, Cham 2015 xiv+814 978-3-319-12315-8; 978-3-319-12316-5 10.1007/978-3-319-12316-5 Christian Kuehn Mathematical Physics II: Classical Statistical Mechanics. Lecture Notes Logos Verlag Berlin GmbH 2014 978-3-8325-3719-7 http://www.logos-verlag.de/cgi-bin/engbuchmid?isbn=3719&lng=deu&id= Matteo Petrera The Impact of Applications on Mathematics. Proceedings of the Forum of Mathematics for Industry 2013 Springer Japan 2014 978-4-431-54906-2 Agriculture Processing Modelling, Cryptography Research, IMI, Mathematical Modelling, Medical Modelling, MfI, Scientific Computation Masato Wakayama Robert S. Anderssen Jin Cheng Yasuhide Fukumoto Robert McKibbin Konrad Polthier Tsuyoshi Takagi Kim-Chuan (Editors) Toh Masato Wakayama Robert S. Anderssen Jin Cheng Yasuhide Fukumoto Robert McKibbin Konrad Polthier Tsuyoshi Takagi Kim-Chuan Toh ZEIT-Akademie Mathematik Zeitverlag Gerd Bucerius Hamburg 2014 4 DVDs mit Begleitheft (95 Seiten) Günter M. Ziegler Andreas Loos Immagini Della Matematica Springer Italia 2013 978-88-6030-619-7 Georg Glaeser Konrad Polthier Mathematical Physics I: Dynamical Systems and Classical Mechanics. Lecture Notes Logos Verlag Berlin GmbH 2013 978-3-8325-3569-8 http://www.logos-verlag.de/cgi-bin/engbuchmid?isbn=3569&lng=deu&id= Matteo Petrera Polyhedral and algebraic methods in computational geometry Universitext Revised and updated translation of the 2008 German original Springer London 2013 x+250 978-1-4471-4816-6; 978-1-4471-4817-3 51-01 (13P10 52-01 52B55) 2905853 10.1007/978-1-4471-4817-3 Michael Joswig Thorsten Theobald Surprenantes images de mathématiques Belin Janie Molard(Übersetzerin) 2013 978-27-0115-695-8 Georg Glaeser Konrad Polthier Springer The Cinderella.2 Manual: Working with The Interactive Geometry Software 2012 https://www.springer.com/de/book/9783540349242 J. Richter-Gebert U. Kortenkamp Wiskunde in beeld Uitgevrij Veen Magazines BV 2012 Nederlands 978-90-8571-250-3 Georg Glaeser Konrad Polthier Springer Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry 2011 J. Richter-Gebert Bilder der Mathematik Springer Spektrum 2 Nachdruck 2014 2010 978-3-662-43416-1 Georg Glaeser Konrad Polthier Decorated Discrete Conformal Equivalence, Canonical Tessellations, and Polyhedral Realization TU Berlin Doctoral thesis 2024 10.14279/ depositonce-20357 Carl O. R. Lutz Q-Nets and Quadrics TU Berlin Doctoral thesis 2023 September 10.14279/depositonce-18877 Alexander Yves Fairley The solar corona: modeled, discretized, visualized TU Berlin Doctoral thesis 2023 September 10.14279/depositonce-18889 Marcel Padilla Discrete differential geometry and cluster algebras via TCD maps Doctoral thesis TU Berlin 2023 March 10.14279/depositonce-17600 2305.02212 Niklas C. Affolter Discrete confocal quadrics and checkerboard incircular nets TU Berlin 2021 10.1007/978-3-030-81847-0 Jan Techter Polyhedral surfaces of constant curvature and discrete uniformization Doctoral thesis TU Berlin 2020 March 10.14279/depositonce-9883 Hana Kourimská 2020 Mathematical Science Communication 10.17169/refubium-28451 Freie Universität Berlin Anna Maria Hartkopf TU München Discrete spin geometry for surface immersions 2019 Zi Ye A Geometric Construction for the Associated Family of S–Isothermic CMC Surfaces 2018 September http://mediatum.ub.tum.de?id=1368384 TU München Benno König Non-standard Analysis in Projective Geometry 2018 Technische Universität München http://mediatum.ub.tum.de/1444961 Michael Strobel Fundamental Properties of Phirotopes Dissertation 2017 July http://mediatum.ub.tum.de/603815?show_id=1341483 Technische Universität München Katharina Schaar Piecewise linear Morse theory. Freie Universität Berlin 2017 https://refubium.fu-berlin.de/handle/fub188/12531 Romain Grunert f-Vector Spaces of Polytopes, Spheres, and Eulerian Lattices FU Berlin 2016 June vii+132 pages urn:nbn:de:kobv:188-fudissthesis000000103149-2 http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000103149 Philip Brinkmann Variational Methods for Discrete Surface Parameterization. Applications and Implementation Doctoral thesis TU Berlin 2016 June http://dx.doi.org/10.14279/depositonce-5415 Stefan Sechelmann Continuity in Dynamic Geometry: An Algorithmic Approach 2016 April TU München http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:91-diss-20160418-1281075-1-5 Stefan Kranich Optimization Methods in Discrete Geometry FU Berlin 2016 January 85 pages http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000101268 Moritz Firsching Quantum Dynamics on Potential Energy Surfaces-Simpler States and Simpler Dynamics TU München 2015 October 187 https://www.discretization.de/publications/file/187 J. Keller Fully variational Lagrangian discretizations for second and fourth order evolution equations Technische Universität München 2015 September Dissertation https://mediatum.ub.tum.de/1271651 182 https://www.discretization.de/publications/file/182 H. Osberger Automatic Contour Deformation of Riemann-Hilbert Problems TU Munich 2015 July 192 https://www.discretization.de/publications/file/192 G. Wechslberger Complex Line Bundles over Simplicial Complexes TU Berlin 2015 Dissertation 191 https://www.discretization.de/publications/file/191 F. Knöppel Discrete Riemann surfaces and integrable systems 2014 September TU Berlin urn:nbn:de:kobv:83-opus4-56591 http://opus4.kobv.de/opus4-tuberlin/frontdoor/index/index/docId/5659 Alexander I. Bobenko and Dmitry Chelkak Alexander I. Bobenko Felix Günther Cyclidic and hyperbolic nets: A piecewise smooth discretization of orthogonal and asymptotic nets in discrete differential geometry TU Berlin 2014 Alexander I. Bobenko Emanuel Huhnen-Venedey Parameterizations in the Configuration Space and Approximations of Related Surfaces Freie Universität Berlin 2014 http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000096803 Dror Atariah Spinor representation of Bryant surfaces with catenoidal and smooth ends TU Berlin 2014 Alexander I. Bobenko Tatiana Pavljukevich Crystalline Order, Surface Energy Densities and Wulff Shapes: Emergence from Atomistic Models Dissertation Technische Universität München München 2013 http://mediatum.ub.tum.de/node?id=1142127 Gero Friesecke and Georg Dolzmann and Irene Fonseca Gero Friesecke Yuen Au Yeung Convergence of discrete holomorphic integrals on orthodiagonal discrete Riemann surfaces TU Berlin master thesis 2024 June 806 https://www.discretization.de/publications/file/806 Maximilian Pschigode Neighborhood Computation of Point Set Surfaces Freie University Berlin 2014 202 https://www.discretization.de/publications/file/202 Martin Skrodzki Infinitesimal conformal deformations of triangulated surfaces Technische Universität Berlin 2013 190 https://www.discretization.de/publications/file/190 W.Y. Lam A Large-Scale Evaluation Of Shape-Aware Neighborhood Weights And Neighborhood Sizes 2021 December Computer-Aided Design https://ms-math-computer.science/posters/2020_large_scale_evaluation.pdf Martin Skrodzki Eric Zimmermann {Investigations of structures in the parameter space of three-dimensional Turing-like patterns} https://ms-math-computer.science/posters/2020_visually_3D_Turing.pdf {AUTOMATA2021} 2021 July Martin Skrodzki Ulrich Reitebuch Eric Zimmermann Processing of Point Set Surfaces 2019 September FU Berlin https://ms-math-computer.science/posters/2019_icerm.pdf Martin Skrodzki Eric Zimmermann Ulrich Reitebuch Sunil Yadav Konrad Polthier Die Superellipse Mathematikkalender Meyerthole Siems Kohlruss Gesellschaft für aktuarische Beratung 2019 August Günter M. Ziegler Variational Shape Approximation of Point Set Surfaces IGS 2019 International Geometry Summit - Poster Proceedings 54--57 2019 https://drive.google.com/file/d/1eq3LDDOtpFH77fXsv37ugk7ORdf5k3e1/view Martin Skrodzki Eric Zimmermann Konrad Polthier One-bit sigma-delta modulation on a closed loop poster 2018 november 443 https://www.discretization.de/publications/file/443 Felix Krahmer Sara Krause-Solberg Olga Graf Analysis of NVT-based Point Set Denoising in Parameter Space 2018 June Computers & Graphics https://ms-math-computer.science/posters/2018_smi.pdf Eric Zimmermann Sunil Yadav Martin Skrodzki Ulrich Reitebuch Konrad Polthier The Mayer-Vietoris Pyramid Sheaf-theoretically Poster Session: Bridging Statistics and Sheaves at IMA, Minneapolis 2018 May http://bfluhr.com/bucket/poster-ima.pdf Benedikt Fluhr Asymptotical & Combinatorial Results on the Neighborhood Grid Data Structure 2018 March Einstein Workshop Discrete Geometry and Topology https://ms-math-computer.science/posters/2018_einstein_workshop.pdf Martin Skrodzki Ulrich Reitebuch Konrad Polthier Computational and Structural Aspects of Point Set Surfaces 2018 February BMS Days 2018 https://ms-math-computer.science/posters/2018_bms_days.pdf Martin Skrodzki Ulrich Reitebuch Konrad Polthier Computational and Structural Aspects of Point Set Surfaces 2017 July SIAM Conference on Industrial and Applied Geometry https://ms-math-computer.science/posters/2017_siam_2.pdf Martin Skrodzki Ulrich Reitebuch Computational and Structural Aspects of Point Set Surfaces 2017 February BMS Days 2017 https://ms-math-computer.science/posters/2017_bms_days.pdf Martin Skrodzki Planar quad layout on NURBS-surfaces from symmetric conjugate curves Presented at Advances in Architectural Geometry 2014 2014 September 141 https://www.discretization.de/publications/file/141 Christoph Seidel Thilo Rörig Stefan Sechelmann Polytopia 2024 February https://www.polytopia.eu/ Adopt a Polyeder Anna Hartkopf Stefan Auerbach Martin Skrodzki http://www.science-to-touch.com/DGD CindyJS: A growing collection of interactive demonstrations 2015 Ulrich Kortenkamp Stefan Kranich Jürgen Richter-Gebert M. Strobel Martin von Gagern J. Wurster