pyfds 0.3.1 - modular field simulation tool - Claes, Leander; Webersen, Manuel

Locally homogeneous Axiom A flows I: projective Anosov subgroups and exponential mixing - Delarue, Benjamin; Monclair, Daniel; Sanders, Andrew (arXiv:2403.14257)
By constructing a non-empty domain of discontinuity in a suitable homogeneous space, we prove that every torsion-free projective Anosov subgroup is the monodromy group of a locally homogeneous contact Axiom A dynamical system with a unique basic hyperbolic set on which the flow is conjugate to the refraction flow of Sambarino. Under the assumption of irreducibility, we utilize the work of Stoyanov to establish spectral estimates for the associated complex Ruelle transfer operators, and by way of corollary: exponential mixing, exponentially decaying error term in the prime orbit theorem, and a spectral gap for the Ruelle zeta function. With no irreducibility assumption, results of Dyatlov-Guillarmou imply the global meromorphic continuation of zeta functions with smooth weights, as well as the existence of a discrete spectrum of Ruelle-Pollicott resonances and (co)-resonant states. We apply our results to space-like geodesic flows for the convex cocompact pseudo-Riemannian manifolds of Danciger-Gu\'eritaud-Kassel, and the Benoist-Hilbert geodesic flow for strictly convex real projective manifolds.

Quantum resonances and scattering poles of classical rank one locally symmetric spaces - Delarue, Benjamin; Hilgert, Joachim (arXiv:2403.14426)
For negatively curved symmetric spaces it is known that the poles of the scattering matrices defined via the standard intertwining operators for the spherical principal representations of the isometry group are either given as poles of the intertwining operators or as quantum resonances, i.e. poles of the meromorphically continued resolvents of the Laplace-Beltrami operator. We extend this result to classical locally symmetric spaces of negative curvature with convex-cocompact fundamental group using results of Bunke and Olbrich. The method of proof forces us to exclude the spectral parameters corresponding to singular Poisson transforms.

Error bounds for kernel-based approximations of the Koopman operator - Philipp, Friedrich; Schaller, Manuel; Worthmann, Karl; Peitz, Sebastian; Nüske, Feliks (Applied and Computational Harmonic Analysis)
We consider the data-driven approximation of the Koopman operator for stochastic differential equations on reproducing kernel Hilbert spaces (RKHS). Our focus is on the estimation error if the data are collected from long-term ergodic simulations. We derive both an exact expression for the variance of the kernel cross-covariance operator, measured in the Hilbert-Schmidt norm, and probabilistic bounds for the finite-data estimation error. Moreover, we derive a bound on the prediction error of observables in the RKHS using a finite Mercer series expansion. Further, assuming Koopman-invariance of the RKHS, we provide bounds on the full approximation error. Numerical experiments using the Ornstein-Uhlenbeck process illustrate our results.

Characterizing Microheterogeneity in Liquid Mixtures via Local Density Fluctuations - Lass, Michael; Kenter, Tobias; Plessl, Christian; Brehm, Martin (Entropy)
We present a novel approach to characterize and quantify microheterogeneity and microphase separation in computer simulations of complex liquid mixtures. Our post-processing method is based on local density fluctuations of the different constituents in sampling spheres of varying size. It can be easily applied to both molecular dynamics (MD) and Monte Carlo (MC) simulations, including periodic boundary conditions. Multidimensional correlation of the density distributions yields a clear picture of the domain formation due to the subtle balance of different interactions. We apply our approach to the example of force field molecular dynamics simulations of imidazolium-based ionic liquids with different side chain lengths at different temperatures, namely 1-ethyl-3-methylimidazolium chloride, 1-hexyl-3-methylimidazolium chloride, and 1-decyl-3-methylimidazolium chloride, which are known to form distinct liquid domains. We put the results into the context of existing microheterogeneity analyses and demonstrate the advantages and sensitivity of our novel method. Furthermore, we show how to estimate the configuration entropy from our analysis, and we investigate voids in the system. The analysis has been implemented into our program package TRAVIS and is thus available as free software.

Optimisation and Evaluation of Breadth First Search with oneAPI/SYCL on Intel FPGAs: from Describing Algorithms to Describing Architectures - Olgu, Kaan; Kenter, Tobias; Nunez-Yanez, Jose; Mcintosh-Smith, Simon (Proceedings of the 12th International Workshop on OpenCL and SYCL)

IPA: Inference Pipeline Adaptation to Achieve High Accuracy and Cost-Efficiency - Ghafouri, Saeid; Razavi, Kamran; Salmani, Mehran; Sanaee, Alireza; Lorido Botran, Tania; Wang, Lin; Doyle, Joseph; Jamshidi, Pooyan (Journal of Systems Research (JSys))

Numerical surgery for mean curvature flow of surfaces - Kovács, Balázs (SIAM Journal on Scientific Computing)

Hankel transform, K-Bessel functions and zeta distributions in the Dunkl setting - Brennecken, Dominik (Journal of Mathematical Analysis and Applications)
Keywords: Applied Mathematics; Analysis

Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces - Papageorgiou, Efthymia (Journal of Evolution Equations)
Abstract This work deals with the extension problem for the fractional Laplacian on Riemannian symmetric spaces G / K of noncompact type and of general rank, which gives rise to a family of convolution operators, including the Poisson operator. More precisely, motivated by Euclidean results for the Poisson semigroup, we study the long-time asymptotic behavior of solutions to the extension problem for $$L^1$$ L 1 initial data. In the case of the Laplace–Beltrami operator, we show that if the initial data are bi- K -invariant, then the solution to the extension problem behaves asymptotically as the mass times the fundamental solution, but this convergence may break down in the non-bi- K -invariant case. In the second part, we investigate the long-time asymptotic behavior of the extension problem associated with the so-called distinguished Laplacian on G / K . In this case, we observe phenomena which are similar to the Euclidean setting for the Poisson semigroup, such as $$L^1$$ L 1 asymptotic convergence without the assumption of bi- K -invariance.
Keywords: Mathematics (miscellaneous)

Research on curriculum resources in mathematics education: a survey of the field - Rezat, Sebastian (ZDM – Mathematics Education)

Digitalisierung als Chance für alle Prinzipien guten Unterrichts - Barzel, Bärbel; Greefrath, Gilbert; Nagel, Mareike; Hoffmann, Max (mathematik lehren)
athematische Kompetenzen digital zu fördern und digitale Kompetenzen mathematisch zu fördern – dies ist eine Forderung der neuen Bildungsstandards mit Blick auf eine Bildung in der digitalen Welt. Gerade das Potenzial digitaler Medien für das fachliche Lernen wurde in vielen Studien bestätigt. Eine sinnvoll gestaltete Einbettung digitaler Medien bietet die Chance, allen fünf Prinzipien eines guten Unterrichts gerecht zu werden: Verstehensorientierung, Durchgängigkeit, kognitive Aktivierung, Lernendenorientierung & Adaptivität und Kommunikationsförderung. Die flächendeckende Nutzung digitaler Medien etabliert sich bislang nur zögerlich. Aber wie können wir Lehrkräfte stärken, digitale Medien sinnvoll einzusetzen? Wir möchten hier die Bandbreite der Möglichkeiten an Beispielen verdeutlichen, ihren Einsatz motivieren und Wege für einen guten Unterricht aufzeigen.

31 Sprachbildung im berufsbezogenen Mathematikunterricht. - Prediger, Susanne; Wessel, Lena (Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis)

Implementation of Different Communication Structures for a Rocket Chip Based RISC-V Grid of Processing Cells - Luchterhandt, Lars; Nellius, Tom; Beck, Robert; Dömer, Rainer; Kneuper, Pascal; Müller, Wolfgang; Sadiye, Babak (MBMV 2024 - 27. Workshop Methoden und Beschreibungssprachen zur Modellierung und Verifikation von Schaltungen und Systemen“)
RISC-V has received worldwide acceptance in the industry and by the academic community. As of today, multiple RISC-V applications and variants are under investigation for embedded IoT systems, from resource-limited single-core processors up to multi-core systems for High-Performance Computing (HPC). Recently, the Grid of Processing Cells (GPC) platform has been proposed as a scalable parallel grid-oriented network of processor cores with local memories. This paper describes a prototype design of the GPC platform for hardware implementation at Register-Transfer Level (RTL) based on modified RISC-V Rocket processors with scratchpad memories. It introduces a scalable Chisel-based implementation of the modified Rocket cores with RTL generation and a functional test using Verilator simulation. This work also includes the adaptation of the Chipyard software toolchain to extend the compiler to multi-core grids with different local address spaces.

A Scalable RISC-V Hardware Platform for Intelligent Sensor Processing - Palomero Bernardo, Paul; Schmid, Patrick; Bringmann, Oliver; Iftekhar, Mohammed; Sadiye, Babak; Müller, Wolfgang; Koch, Andreas; Jentsch, Eyck; Sauer, Axel; Feldner, Ingo; Ecker, Wolfgang (DATE 24 - Design Automation and Test in Europe)

Empowering Students for the Data-Driven World: A Qualitative Study of the Relevance of Learning about Data-Driven Technologies - Höper, Lukas; Schulte, Carsten (Informatics in Education)
In K-12 computing education, there is a need to identify and teach concepts that are relevant to understanding machine learning technologies. Studies of teaching approaches often evaluate whether students have learned the concepts. However, scant research has examined whether such concepts support understanding digital artefacts from everyday life and developing agency in a digital world. This paper presents a qualitative study that explores students’ perspectives on the relevance of learning concepts of data-driven technologies for navigating the digital world. The underlying approach of the study is data awareness, which aims to support students in understanding and reflecting on such technologies to develop agency in a data-driven world. This approach teaches students an explanatory model encompassing several concepts of the role of data in data-driven technologies. We developed an intervention and conducted retrospective interviews with students. Findings from the analysis of the interviews indicate that students can analyse and understand data-driven technologies from their everyday lives according to the central role of data. In addition, students’ answers revealed four areas of how learning about data-driven technologies becomes relevant to them. The paper concludes with a preliminary model suggesting how computing education can make concepts of data-driven technologies meaningful for students to understand and navigate the digital world.
Keywords: Computer Science Applications; Communication; Education; General Engineering

Geodesic Interpolation of Frame-Wise Speaker Embeddings for the Diarization of Meeting Scenarios - Cord-Landwehr, Tobias; Boeddeker, Christoph; Zorilă, Cătălin; Doddipatla, Rama; Haeb-Umbach, Reinhold (ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP))

Noctua 2 Supercomputer - Bauer, Carsten; Kenter, Tobias; Lass, Michael; Mazur, Lukas; Meyer, Marius; Nitsche, Holger; Riebler, Heinrich; Schade, Robert; Schwarz, Michael; Winnwa, Nils; Wiens, Alex; Wu, Xin; et al. (Journal of large-scale research facilities)
Noctua 2 is a supercomputer operated at the Paderborn Center for Parallel Computing (PC2) at Paderborn University in Germany. Noctua 2 was inaugurated in 2022 and is an Atos BullSequana XH2000 system. It consists mainly of three node types: 1) CPU Compute nodes with AMD EPYC processors in different main memory configurations, 2) GPU nodes with NVIDIA A100 GPUs, and 3) FPGA nodes with Xilinx Alveo U280 and Intel Stratix 10 FPGA cards. While CPUs and GPUs are known off-the-shelf components in HPC systems, the operation of a large number of FPGA cards from different vendors and a dedicated FPGA-to-FPGA network are unique characteristics of Noctua 2. This paper describes in detail the overall setup of Noctua 2 and gives insights into the operation of the cluster from a hardware, software and facility perspective.
Keywords: Noctua 2; Supercomputer; FPGA; PC2; Paderborn Center for Parallel Computing

Visual Tracking Nonlinear Model Predictive Control Method for Autonomous Wind Turbine Inspection - Amer, Abdelhakim; Mehndiratta, Mohit; le Fevre Sejersen, Jonas; Pham, Huy Xuan; Kayacan, Erdal (2023 21st International Conference on Advanced Robotics (ICAR))

Analysis and Simulation of a Photonic Multiband FMCW Radar Sensor System using Nyquist Pulses - Kruse, Stephan; Schwabe, Tobias; Kneuper, Pascal; Kurz, Heiko G.; Meinecke, March-Michael; Scheytt, Christoph (German Microwave Conference (GeMiC))