The Condemnation of Hate and the Violence of the Status Quo - Althoff, Sebastian (Cultural Politics)

A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects - Stinner, Christian; Winkler, Michael (Journal of Evolution Equations)
Abstract The quasilinear Keller–Segel system $$\begin{aligned} \left\{ \begin{array}{l} u_t=\nabla \cdot (D(u)\nabla u) - \nabla \cdot (S(u)\nabla v), \\ v_t=\Delta v-v+u, \end{array}\right. \end{aligned}$$ u t = ∇ · ( D ( u ) ∇ u ) - ∇ · ( S ( u ) ∇ v ) , v t = Δ v - v + u , endowed with homogeneous Neumann boundary conditions is considered in a bounded domain $$\Omega \subset {\mathbb {R}}^n$$ Ω ⊂ R n , $$n \ge 3$$ n ≥ 3 , with smooth boundary for sufficiently regular functions D and S satisfying $$D>0$$ D > 0 on $$[0,\infty )$$ [ 0 , ∞ ) , $$S>0$$ S > 0 on $$(0,\infty )$$ ( 0 , ∞ ) and $$S(0)=0$$ S ( 0 ) = 0 . On the one hand, it is shown that if $$\frac{S}{D}$$ S D satisfies the subcritical growth condition $$\begin{aligned} \frac{S(s)}{D(s)} \le C s^\alpha \qquad \text{ for } \text{ all } s\ge 1 \qquad \text{ with } \text{ some } \alpha < \frac{2}{n} \end{aligned}$$ S ( s ) D ( s ) ≤ C s α for all s ≥ 1 with some α < 2 n and $$C>0$$ C > 0 , then for any sufficiently regular initial data there exists a global weak energy solution such that $${ \mathrm{{ess}}} \sup _{t>0} \Vert u(t) \Vert _{L^p(\Omega )}<\infty $$ ess sup t > 0 ‖ u ( t ) ‖ L p ( Ω ) < ∞ for some $$p > \frac{2n}{n+2}$$ p > 2 n n + 2 . On the other hand, if $$\frac{S}{D}$$ S D satisfies the supercritical growth condition $$\begin{aligned} \frac{S(s)}{D(s)} \ge c s^\alpha \qquad \text{ for } \text{ all } s\ge 1 \qquad \text{ with } \text{ some } \alpha > \frac{2}{n} \end{aligned}$$ S ( s ) D ( s ) ≥ c s α for all s ≥ 1 with some α > 2 n and $$c>0$$ c > 0 , then the nonexistence of a global weak energy solution having the boundedness property stated above is shown for some initial data in the radial setting. This establishes some criticality of the value $$\alpha = \frac{2}{n}$$ α = 2 n for $$n \ge 3$$ n ≥ 3 , without any additional assumption on the behavior of D ( s ) as $$s \rightarrow \infty $$ s → ∞ , in particular without requiring any algebraic lower bound for D . When applied to the Keller–Segel system with volume-filling effect for probability distribution functions of the type $$Q(s) = \exp (-s^\beta )$$ Q ( s ) = exp ( - s β ) , $$s \ge 0$$ s ≥ 0 , for global solvability the exponent $$\beta = \frac{n-2}{n}$$ β = n - 2 n is seen to be critical.
Keywords: Mathematics (miscellaneous)

An interpolation inequality involving $L\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system - Wang, Yulan; Winkler, Michael (Journal of the London Mathematical Society)
Abstract In a smoothly bounded two‐dimensional domain and for a given nondecreasing positive unbounded , for each and the inequality is shown to hold for any positive fulfilling This is thereafter applied to nonglobal solutions of the Keller–Segel system coupled to the incompressible Navier–Stokes equations through transport and buoyancy, and it is seen that in any such blow‐up event the corresponding population density cannot remain uniformly integrable over near its explosion time.
Keywords: General Mathematics

Preschoolers' Interactions with Social Robots: Investigating the Potential for Eliciting Metatalk and Critical Technological Thinking - Tolksdorf, Nils Frederik; Wildt, Eugenia; Rohlfing, Katharina (Companion of the 2024 ACM/IEEE International Conference on Human-Robot Interaction)

Do Country Risk Factors Attenuate the Effect of Tax Loss Incentives on Corporate Risk-Taking? - Osswald, Benjamin; Sureth-Sloane, Caren
This study investigates whether country risk factors, including political and fiscal budget risk, attenuate the effectiveness of tax policy tools that aim to encourage corporate risk-taking. Exploiting a cross-country panel, we predict and find that the effectiveness of loss offset rules and tax rate changes is fully attenuated for firms located in high-risk countries. We document the attenuating effect of country risk is more pronounced in high-tax countries or when countries increase their corporate tax rate. Additional tests around the U.S. federal budget crises from 2011 to 2013 indicate that temporarily heightened fiscal budget risk attenuates the effectiveness of loss offset rules even in countries with low political risk. We identify conditions (low political and low fiscal budget risk) under which targeted tax policy tools effectively stimulate risk-taking. This suggests that ensuring taxpayers receive tax refunds is important in times of economic crises with budgetary or political challenges.

Optimizing Communication for Latency Sensitive HPC Applications on up to 48 FPGAs Using ACCL - Meyer, Marius; Kenter, Tobias; Petrica, Lucian; O'Brien, Kenneth; Blott, Michaela; Plessl, Christian (arXiv:2403.18374)
Most FPGA boards in the HPC domain are well-suited for parallel scaling because of the direct integration of versatile and high-throughput network ports. However, the utilization of their network capabilities is often challenging and error-prone because the whole network stack and communication patterns have to be implemented and managed on the FPGAs. Also, this approach conceptually involves a trade-off between the performance potential of improved communication and the impact of resource consumption for communication infrastructure, since the utilized resources on the FPGAs could otherwise be used for computations. In this work, we investigate this trade-off, firstly, by using synthetic benchmarks to evaluate the different configuration options of the communication framework ACCL and their impact on communication latency and throughput. Finally, we use our findings to implement a shallow water simulation whose scalability heavily depends on low-latency communication. With a suitable configuration of ACCL, good scaling behavior can be shown to all 48 FPGAs installed in the system. Overall, the results show that the availability of inter-FPGA communication frameworks as well as the configurability of framework and network stack are crucial to achieve the best application performance with low latency communication.

On the Potential of Multi-objective Automated Algorithm Configuration on Multi-modal Multi-objective Optimisation Problems - Preuß, Oliver Ludger; Rook, Jeroen; Trautmann, Heike (Applications of Evolutionary Computation)

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.

Measuring collective efficacy for inclusion in a global context - Sharma , Umesh; Loreman , Tim; May , Fiona; Romano , Alessandra; Lozano , Caroline Sahli; Avramidis , Elias; Woodcock , Stuart; Subban , Pearl; Kullmann, Harry (European Journal of Special Needs Education)

Governing autonomies. Imagining responsible AI in the European armament project “Future Combat Air System” - Hälterlein, Jens (The Reality of Autonomous Weapon Systems)

The Stellarium Gornergrat: Astrophysics with your own Data - Gschwind, Stéphane; Hohmann, Sascha; Müller, Andreas; Nordine, Jeffrey; Riesen, Timm-Emanuel (Journal of Physics: Conference Series)
Abstract Remote-controlled telescopes in education provide the opportunity to obtain high quality astronomy images for a broad variety of users. The Stellarium Gornergrat is such a telescope. In addition to pure observation, it offers a user-friendly interface and teaching modules so that astronomical and astrophysical projects can be integrated into everyday school life without any special prior knowledge and without requiring a lot of time. This contribution presents the Stellarium project and a provides an overview of several teaching activities.
Keywords: Computer Science Applications; History; Education

Derivation of Miller's rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator - Meyer, Maximilian Tim; Schindlmayr, Arno (Journal of Physics B: Atomic, Molecular and Optical Physics)
Miller's rule is an empirical relation between the nonlinear and linear optical coefficients that applies to a large class of materials but has only been rigorously derived for the classical Lorentz model with a weak anharmonic perturbation. In this work, we extend the proof and present a detailed derivation of Miller's rule for an equivalent quantum-mechanical anharmonic oscillator. For this purpose, the classical concept of velocity-dependent damping inherent to the Lorentz model is replaced by an adiabatic switch-on of the external electric field, which allows a unified treatment of the classical and quantum-mechanical systems using identical potentials and fields. Although the dynamics of the resulting charge oscillations, and hence the induced polarizations, deviate due to the finite zero-point motion in the quantum-mechanical framework, we find that Miller's rule is nevertheless identical in both cases up to terms of first order in the anharmonicity. With a view to practical applications, especially in the context of ab initio calculations for the optical response where adiabatically switched-on fields are widely assumed, we demonstrate that a correct treatment of finite broadening parameters is essential to avoid spurious errors that may falsely suggest a violation of Miller's rule, and we illustrate this point by means of a numerical example.

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.

BQP, meet NP: Search-to-decision reductions and approximate counting - Gharibian, Sevag; Kamminga, Jonas (Proceedings of 51st EATCS International Colloquium on Automata, Languages and Programming (ICALP))
What is the power of polynomial-time quantum computation with access to an NP oracle? In this work, we focus on two fundamental tasks from the study of Boolean satisfiability (SAT) problems: search-to-decision reductions, and approximate counting. We first show that, in strong contrast to the classical setting where a poly-time Turing machine requires $Θ(n)$ queries to an NP oracle to compute a witness to a given SAT formula, quantumly $Θ(\log n)$ queries suffice. We then show this is tight in the black-box model - any quantum algorithm with "NP-like" query access to a formula requires $Ω(\log n)$ queries to extract a solution with constant probability. Moving to approximate counting of SAT solutions, by exploiting a quantum link between search-to-decision reductions and approximate counting, we show that existing classical approximate counting algorithms are likely optimal. First, we give a lower bound in the "NP-like" black-box query setting: Approximate counting requires $Ω(\log n)$ queries, even on a quantum computer. We then give a "white-box" lower bound (i.e. where the input formula is not hidden in the oracle) - if there exists a randomized poly-time classical or quantum algorithm for approximate counting making $o(log n)$ NP queries, then $\text{BPP}^{\text{NP}[o(n)]}$ contains a $\text{P}^{\text{NP}}$-complete problem if the algorithm is classical and $\text{FBQP}^{\text{NP}[o(n)]}$ contains an $\text{FP}^{\text{NP}}$-complete problem if the algorithm is quantum.

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)

An Integrated Fuzzy Analytic Network Process and Fuzzy Regression Method for Bitcoin Price Prediction - Amiri, Arman; Tavana, Madjid; Arman, Hosein (Internet of Things)
Keywords: Management of Technology and Innovation; Artificial Intelligence; Computer Science Applications; Hardware and Architecture; Engineering (miscellaneous); Information Systems; Computer Science (miscellaneous); Software

Data-driven simulation-based decision support system for resource allocation in industry 4.0 and smart manufacturing - Mahmoodi, Ehsan; Fathi, Masood; Tavana, Madjid; Ghobakhloo, Morteza; Ng, Amos H.C. (Journal of Manufacturing Systems)
Keywords: Industrial and Manufacturing Engineering; Hardware and Architecture; Software; Control and Systems Engineering

A systematic review of the soft computing methods shaping the future of the metaverse - Tavana, Madjid; Sorooshian, Shahryar (Applied Soft Computing)
Keywords: Software