@article{51208, abstract = {{AbstractApproximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute new subgradients that improve a given approximation in case a direction with insufficient descent was computed. Combined with a recently proposed deterministic gradient sampling approach, this yields a deterministic and provably convergent way to approximate subdifferentials for computing descent directions.}}, author = {{Gebken, Bennet}}, issn = {{0926-6003}}, journal = {{Computational Optimization and Applications}}, keywords = {{Applied Mathematics, Computational Mathematics, Control and Optimization}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{A note on the convergence of deterministic gradient sampling in nonsmooth optimization}}}, doi = {{10.1007/s10589-024-00552-0}}, year = {{2024}}, } @article{52218, author = {{Lenz, Peter and Mahnken, Rolf}}, issn = {{0020-7683}}, journal = {{International Journal of Solids and Structures}}, keywords = {{Applied Mathematics, Mechanical Engineering, Mechanics of Materials, Condensed Matter Physics, General Materials Science, Modeling and Simulation}}, publisher = {{Elsevier BV}}, title = {{{Multiscale simulation of polymer curing of composites combined mean-field homogenisation methods at large strains}}}, doi = {{10.1016/j.ijsolstr.2023.112642}}, volume = {{290}}, year = {{2024}}, } @article{52233, abstract = {{ELDIRK methods are defined to have an Explicit Last stage in the general Butcher array of Diagonal Implicit Runge-Kutta methods, with the consequence, that no additional system of equations must be solved, compared to the embedded RK method. Two general formulations for second- and third-order ELDIRK methods have been obtained recently in Mahnken [21] with specific schemes, e.g. for the embedded implicit Euler method, the embedded trapezoidal-rule and the embedded Ellsiepen method. In the first part of this paper, we investigate some general stability characteristics of ELDIRK methods, and it will be shown that the above specific RK schemes are not A-stable. Therefore, in the second part, the above-mentioned general formulations are used for further stability investigations, with the aim to construct new second- and third-order ELDIRK methods which simultaneously are A-stable. Two numerical examples are concerned with the curing for a thermosetting material and phase-field RVE modeling for crystallinity and orientation. The numerical results confirm the theoretical results on convergence order and stability.}}, author = {{Mahnken, Rolf and Westermann, Hendrik}}, issn = {{0178-7675}}, journal = {{Computational Mechanics}}, keywords = {{Applied Mathematics, Computational Mathematics, Computational Theory and Mathematics, Mechanical Engineering, Ocean Engineering, Computational Mechanics}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Construction of A-stable explicit last-stage diagonal implicit Runge–Kutta (ELDIRK) methods}}}, doi = {{10.1007/s00466-024-02442-y}}, year = {{2024}}, } @article{52726, abstract = {{Heteroclinic structures organize global features of dynamical systems. We analyse whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more units. We find that while commonly analysed model equations such as network dynamics on undirected hypergraphs may be useful to describe local dynamics such as cluster synchronization, they give rise to obstructions that allow to design of heteroclinic structures in phase space. By contrast, directed hypergraphs break the homogeneity and lead to vector fields that support heteroclinic structures.}}, author = {{Bick, Christian and von der Gracht, Sören}}, issn = {{2051-1329}}, journal = {{Journal of Complex Networks}}, keywords = {{Applied Mathematics, Computational Mathematics, Control and Optimization, Management Science and Operations Research, Computer Networks and Communications}}, number = {{2}}, publisher = {{Oxford University Press (OUP)}}, title = {{{Heteroclinic dynamics in network dynamical systems with higher-order interactions}}}, doi = {{10.1093/comnet/cnae009}}, volume = {{12}}, year = {{2024}}, } @article{53300, author = {{Brennecken, Dominik}}, issn = {{0022-247X}}, journal = {{Journal of Mathematical Analysis and Applications}}, keywords = {{Applied Mathematics, Analysis}}, number = {{2}}, publisher = {{Elsevier BV}}, title = {{{Hankel transform, K-Bessel functions and zeta distributions in the Dunkl setting}}}, doi = {{10.1016/j.jmaa.2024.128125}}, volume = {{535}}, year = {{2024}}, } @article{52089, abstract = {{AbstractImage restoration via alternating direction method of multipliers (ADMM) has gained large interest within the last decade. Solving standard problems of Gaussian and Poisson noise, the set of “Total Variation” (TV)-based regularizers proved to be efficient and versatile. In the last few years, the “Total Generalized Variation” (TGV) approach combined TV regularizers of different orders adaptively to better suit local regions in the image. This improved the technique significantly. The approach solved the staircase problem inherent of the first-order TV while keeping the beneficial edge preservation. The iterative minimization for the augmented Lagrangian of TGV problems requires four important parameters: two penalty parameters $${\rho }$$ ρ and $${\eta }$$ η and two regularization parameters $${\lambda _{0}}$$ λ 0 and $${\lambda _{1}}$$ λ 1 . The choice of penalty parameters decides on the convergence speed, and the regularization parameters decide on the impact of the respective regularizer and are determined by the noise level in the image. For scientific applications of such algorithms, an automated and thus objective method to determine these parameters is essential to receive unbiased results independent of the user. Obviously, both sets of parameters are to be well chosen to achieve optimal results, too. In this paper, a method is proposed to adaptively choose optimal $${\rho }$$ ρ and $${\eta }$$ η values for the iteration to converge faster, based on the primal and dual residuals arising from the optimality conditions of the augmented Lagrangian. Further, we show how to choose $${\lambda _{0}}$$ λ 0 and $${\lambda _{1}}$$ λ 1 based on the inherent noise in the image.}}, author = {{Zietlow, Christian and Lindner, Jörg K. N.}}, issn = {{1017-1398}}, journal = {{Numerical Algorithms}}, keywords = {{Applied Mathematics}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{ADMM-TGV image restoration for scientific applications with unbiased parameter choice}}}, doi = {{10.1007/s11075-024-01759-2}}, year = {{2024}}, } @article{49326, abstract = {{Many networked systems are governed by non-pairwise interactions between nodes. The resulting higher-order interaction structure can then be encoded by means of a hypernetwork. In this paper we consider dynamical systems on hypernetworks by defining a class of admissible maps for every such hypernetwork. We explain how to classify robust cluster synchronization patterns on hypernetworks by finding balanced partitions, and we generalize the concept of a graph fibration to the hypernetwork context. We also show that robust synchronization patterns are only fully determined by polynomial admissible maps of high order. This means that, unlike in dyadic networks, cluster synchronization on hypernetworks is a higher-order, i.e., nonlinear, effect. We give a formula, in terms of the order of the hypernetwork, for the degree of the polynomial admissible maps that determine robust synchronization patterns. We also demonstrate that this degree is optimal by investigating a class of examples. We conclude by demonstrating how this effect may cause remarkable synchrony breaking bifurcations that occur at high polynomial degree.}}, author = {{von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}}, issn = {{0036-1399}}, journal = {{SIAM Journal on Applied Mathematics}}, keywords = {{Applied Mathematics}}, number = {{6}}, pages = {{2329--2353}}, publisher = {{Society for Industrial & Applied Mathematics (SIAM)}}, title = {{{Hypernetworks: Cluster Synchronization Is a Higher-Order Effect}}}, doi = {{10.1137/23m1561075}}, volume = {{83}}, year = {{2023}}, } @article{50458, abstract = {{AbstractConsider a set of jobs connected to a directed acyclic task graph with a fixed source and sink. The edges of this graph model precedence constraints and the jobs have to be scheduled with respect to those. We introduce the server cloud scheduling problem, in which the jobs have to be processed either on a single local machine or on one of infinitely many cloud machines. For each job, processing times both on the server and in the cloud are given. Furthermore, for each edge in the task graph, a communication delay is included in the input and has to be taken into account if one of the two jobs is scheduled on the server and the other in the cloud. The server processes jobs sequentially, whereas the cloud can serve as many as needed in parallel, but induces costs. We consider both makespan and cost minimization. The main results are an FPTAS for the makespan objective for graphs with a constant source and sink dividing cut and strong hardness for the case with unit processing times and delays.}}, author = {{Maack, Marten and Meyer auf der Heide, Friedhelm and Pukrop, Simon}}, issn = {{0178-4617}}, journal = {{Algorithmica}}, keywords = {{Applied Mathematics, Computer Science Applications, General Computer Science}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Server Cloud Scheduling}}}, doi = {{10.1007/s00453-023-01189-x}}, year = {{2023}}, } @article{51351, author = {{Steffen, Eckhard and Wolf, Isaak Hieronymus}}, issn = {{0166-218X}}, journal = {{Discrete Applied Mathematics}}, keywords = {{Applied Mathematics, Discrete Mathematics and Combinatorics}}, pages = {{185--189}}, publisher = {{Elsevier BV}}, title = {{{Bounds for the chromatic index of signed multigraphs}}}, doi = {{10.1016/j.dam.2023.05.008}}, volume = {{337}}, year = {{2023}}, } @article{52806, author = {{Gilbert, H. and Schürmann, M. and Liebendörfer, M. and Lawson, D. and Hodds, M.}}, issn = {{0020-739X}}, journal = {{International Journal of Mathematical Education in Science and Technology}}, keywords = {{Applied Mathematics, Education, Mathematics (miscellaneous)}}, pages = {{1--26}}, publisher = {{Informa UK Limited}}, title = {{{Post-pandemic online mathematics and statistics support: Practitioners’ opinions in Germany and Great Britain & Ireland}}}, doi = {{10.1080/0020739x.2023.2184282}}, year = {{2023}}, } @article{45971, abstract = {{Abstract An error estimate for a canonical discretization of the harmonic map heat flow into spheres is derived. The numerical scheme uses standard finite elements with a nodal treatment of linearized unit-length constraints. The analysis is based on elementary approximation results and only uses the discrete weak formulation.}}, author = {{Bartels, Sören and Kovács, Balázs and Wang, Zhangxian}}, issn = {{0272-4979}}, journal = {{IMA Journal of Numerical Analysis}}, keywords = {{Applied Mathematics, Computational Mathematics, General Mathematics}}, publisher = {{Oxford University Press (OUP)}}, title = {{{Error analysis for the numerical approximation of the harmonic map heat flow with nodal constraints}}}, doi = {{10.1093/imanum/drad037}}, year = {{2023}}, } @article{53262, author = {{Santamaria, Ignacio and Soleymani, Mohammad and Jorswieck, Eduard and Gutiérrez, Jesús}}, issn = {{1070-9908}}, journal = {{IEEE Signal Processing Letters}}, keywords = {{Applied Mathematics, Electrical and Electronic Engineering, Signal Processing}}, pages = {{923--926}}, publisher = {{Institute of Electrical and Electronics Engineers (IEEE)}}, title = {{{SNR Maximization in Beyond Diagonal RIS-Assisted Single and Multiple Antenna Links}}}, doi = {{10.1109/lsp.2023.3296902}}, volume = {{30}}, year = {{2023}}, } @article{53261, author = {{Soleymani, Mohammad and Santamaria, Ignacio and Jorswieck, Eduard and Clerckx, Bruno}}, issn = {{1536-1276}}, journal = {{IEEE Transactions on Wireless Communications}}, keywords = {{Applied Mathematics, Electrical and Electronic Engineering, Computer Science Applications}}, pages = {{1--1}}, publisher = {{Institute of Electrical and Electronics Engineers (IEEE)}}, title = {{{Optimization of Rate-Splitting Multiple Access in Beyond Diagonal RIS-assisted URLLC Systems}}}, doi = {{10.1109/twc.2023.3324190}}, year = {{2023}}, } @article{53317, author = {{Tao, Youshan and Winkler, Michael}}, issn = {{2163-2480}}, journal = {{Evolution Equations and Control Theory}}, keywords = {{Applied Mathematics, Control and Optimization, Modeling and Simulation}}, number = {{6}}, pages = {{1676--1687}}, publisher = {{American Institute of Mathematical Sciences (AIMS)}}, title = {{{Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities}}}, doi = {{10.3934/eect.2023031}}, volume = {{12}}, year = {{2023}}, } @article{53320, author = {{Winkler, Michael}}, issn = {{0294-1449}}, journal = {{Annales de l'Institut Henri Poincaré C, Analyse non linéaire}}, keywords = {{Mathematical Physics, Analysis, Applied Mathematics}}, publisher = {{European Mathematical Society - EMS - Publishing House GmbH}}, title = {{{A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion}}}, doi = {{10.4171/aihpc/73}}, year = {{2023}}, } @article{53318, author = {{Li, Genglin and Winkler, Michael}}, issn = {{0003-6811}}, journal = {{Applicable Analysis}}, keywords = {{Applied Mathematics, Analysis}}, number = {{1}}, pages = {{45--64}}, publisher = {{Informa UK Limited}}, title = {{{Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities}}}, doi = {{10.1080/00036811.2023.2173183}}, volume = {{103}}, year = {{2023}}, } @article{53328, abstract = {{ As a simplified version of a three-component taxis cascade model accounting for different migration strategies of two population groups in search of food, a two-component nonlocal nutrient taxis system is considered in a two-dimensional bounded convex domain with smooth boundary. For any given conveniently regular and biologically meaningful initial data, smallness conditions on the prescribed resource growth and on the initial nutrient signal concentration are identified which ensure the global existence of a global classical solution to the corresponding no-flux initial-boundary value problem. Moreover, under additional assumptions on the food production source these solutions are shown to be bounded, and to stabilize toward semi-trivial equilibria in the large time limit, respectively. }}, author = {{Tao, Youshan and Winkler, Michael}}, issn = {{0218-2025}}, journal = {{Mathematical Models and Methods in Applied Sciences}}, keywords = {{Applied Mathematics, Modeling and Simulation}}, number = {{01}}, pages = {{103--138}}, publisher = {{World Scientific Pub Co Pte Ltd}}, title = {{{Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers}}}, doi = {{10.1142/s0218202523500045}}, volume = {{33}}, year = {{2023}}, } @article{53324, author = {{Ahn, Jaewook and Winkler, Michael}}, issn = {{0944-2669}}, journal = {{Calculus of Variations and Partial Differential Equations}}, keywords = {{Applied Mathematics, Analysis}}, number = {{6}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system}}}, doi = {{10.1007/s00526-023-02523-5}}, volume = {{62}}, year = {{2023}}, } @article{53329, author = {{Tao, Youshan and Winkler, Michael}}, issn = {{1468-1218}}, journal = {{Nonlinear Analysis: Real World Applications}}, keywords = {{Applied Mathematics, Computational Mathematics, General Economics, Econometrics and Finance, General Engineering, General Medicine, Analysis}}, publisher = {{Elsevier BV}}, title = {{{Analysis of a chemotaxis-SIS epidemic model with unbounded infection force}}}, doi = {{10.1016/j.nonrwa.2022.103820}}, volume = {{71}}, year = {{2023}}, } @article{53326, author = {{Li, Genglin and Winkler, Michael}}, issn = {{1539-6746}}, journal = {{Communications in Mathematical Sciences}}, keywords = {{Applied Mathematics, General Mathematics}}, number = {{2}}, pages = {{299--322}}, publisher = {{International Press of Boston}}, title = {{{Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities}}}, doi = {{10.4310/cms.2023.v21.n2.a1}}, volume = {{21}}, year = {{2023}}, }