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We consider a microscopic model of $N$ magnetic nanoparticles in a Stokes flow. We assume that the temperature is above the critical N\'eel temperature such that the particles' magnetizations undergo random flip with rate $1/\varepsilon$. The microscopic system is the modeled through a piecewise deterministic Markov jump process. We show that for large $N$, small particle volume fraction and small $\varepsilon$, the system can be effectively described by a multiscale model.

Excitons in Transition Metal Dichalcogenides (TMDs) acquire a spin-like quantum number, a pseudospin, originating from the crystal's discrete rotational symmetry. Here, we break this symmetry using a tunable uniaxial strain, effectively generating a pseudomagnetic field exceeding 40 Tesla. Under this large field, we demonstrate pseudospin analogs of spintronic phenomena such as the Zeeman effect and Larmor precession. Moreover, we determine previously inaccessible fundamental properties of TMDs, including the strength of the depolarizing field responsible for the loss of exciton coherence. Finally, we uncover the bosonic -- as opposed to fermionic -- nature of many-body excitonic species using the pseudomagnetic equivalent of the $g$-factor spectroscopy. Our work is the first step toward establishing this spectroscopy as a universal method for probing correlated many-body states and realizing pseudospin analogs of spintronic devices.

We prove logarithmic growth bounds on Sobolev norms of the focusing mass-critical NLS and gKdV equations on the torus, which hold almost surely under the focusing Gibbs measure with optimal mass threshold constructed by Oh, Sosoe, and Tolomeo. More precisely, we will establish almost sure growth bounds for solutions $u(t)$ of the equations of the form \[ \sup_{t \in [-T,T]} \lVert u(t) \rVert_{H^s(\mathbb{T})} \lesssim_{s, u_0} \log(2+T)\] with initial data $u_0 \in H^s(\mathbb{T})$ for $s< \frac{1}{2}$. The proof uses a generalisation of Bourgain's invariant measure argument for measures in a suitable Orlicz space., Comment: 15 pages

We give a status report on new developments within the Whizard event generator. Important new features comprise NLO electroweak automation (incl. extension to BSM processes like SMEFT), loop-induced processes and new developments in the UFO interface. We highlight work in progress and further plans, such as the implementation of electroweak PDFs, photon radiation, the exclusive top threshold and features for exotic new physics searches., Comment: Presented at the International Workshop on Future Linear Colliders (LCWS 2024), 8-11 July 2024, contribution accepted by EPJ Web of Conferences

The oblique collisions and dynamical interference patterns of two-dimensional dispersive shock waves are studied numerically and analytically via the temporal dynamics induced by wedge-shaped initial conditions for the Kadomtsev-Petviashvili II equation. Various asymptotic wave patterns are identified, classified and characterized in terms of the incidence angle and the amplitude of the initial step, which can give rise to either subcritical or supercritical configurations, including the generalization to dispersive shock waves of the Mach reflection and expansion of viscous shocks and line solitons. An eightfold amplification of the amplitude of an obliquely incident flow upon a wall at the critical angle is demonstrated., Comment: 10 pages, 11 figures

We develop a method for the transfer of perfect strategies between various classes of two-player, one round cooperative non-local games with quantum inputs and outputs using the simulation paradigm in quantum information theory. We show that such a transfer is possible when canonically associated operator spaces for each game are quantum homomorphic or isomorphic, as defined in the joint work of H. and Todorov (2024). We examine a new class of QNS correlations, needed for the transfer of strategies between games, and characterize them in terms of states on tensor products of canonical operator systems. We define jointly tracial correlations and show they correspond to traces acting on tensor products of canonical ${\rm C}^{*}$-algebras associated with individual game parties. We then make an inquiry into the initial application of such results to the study of concurrent quantum games., Comment: Comments welcome!

Starting from microscopic $N$ particle systems, we study the derivation of Doi type models for suspensions of non-spherical particles in Stokes flows. While Doi models accurately describe the effective evolution of the spatial particle density to the first order in the particle volume fraction, this accuracy fails regarding the evolution of the particle orientations. We rigorously attribute this failure to the singular interaction of the particles via a $-3$-homogeneous kernel. In the situation that the particles are initially distributed according to a stationary ergodic point process, we identify the limit of this singular interaction term. It consists of two parts. The first corresponds to a classical term in Doi type models. The second new term depends on the (microscopic) $2$-point correlation of the point process. By including this term, we provide a modification of the Doi model that is accurate to first order in the particle volume fraction.

Being able to recognise defects in industrial objects is a key element of quality assurance in production lines. Our research focuses on visual anomaly detection in RGB images. Although Convolutional Neural Networks (CNNs) achieve high accuracies in this task, end users in industrial environments receive the model's decisions without additional explanations. Therefore, it is of interest to enrich the model's outputs with further explanations to increase confidence in the model and speed up anomaly detection. In our work, we focus on (1) CNN-based classification models and (2) the further development of a model-agnostic explanation algorithm for black-box classifiers. Additionally, (3) we demonstrate how we can establish an interactive interface that allows users to further correct the model's output. We present our NearCAIPI Interaction Framework, which improves AI through user interaction, and show how this approach increases the system's trustworthiness. We also illustrate how NearCAIPI can integrate human feedback into an interactive process chain.

We consider a mean-field optimal control problem with general dynamics including common noise and jumps and show that its minimizers are Nash equilibria of an associated mean-field game of controls. These types of games are necessarily potential, and the Nash equilibria obtained as the minimizers of the control problems are naturally related to the McKean-Vlasov equations of Langevin type. We provide several examples to motivate the general theory including the Cucker-Smale Flocking and Kuramoto mean-field games. The invariance property of the value function of these control problems, utilized in our proof, is also proved.

The turbulent ionosphere causes phase shifts to incoming radio waves on a broad range of temporal and spatial scales. When an interferometer is not sufficiently calibrated for the direction-dependent ionospheric effects, the time-varying phase shifts can cause the signal to decorrelate. The ionosphere's influence over various spatiotemporal scales introduces a baseline-dependent effect on the interferometric array. We study the impact of baseline-dependent decorrelation on high-redshift observations with the Low Frequency Array (LOFAR). Datasets with a range of ionospheric corruptions are simulated using a thin-screen ionosphere model, and calibrated using the state-of-the-art LOFAR Epoch of Reionisation pipeline. For the first time ever, we show the ionospheric impact on various stages of the calibration process including an analysis of the transfer of gain errors from longer to shorter baselines using realistic end-to-end simulations. We find that direction-dependent calibration for source subtraction leaves excess power of up to two orders of magnitude above the thermal noise at the largest spectral scales in the cylindrically averaged auto-power spectrum under normal ionospheric conditions. However, we demonstrate that this excess power can be removed through Gaussian process regression, leaving no excess power above the ten per cent level for a $5~$km diffractive scale. We conclude that ionospheric errors, in the absence of interactions with other aggravating effects, do not constitute a dominant component in the excess power observed in LOFAR Epoch of Reionisation observations of the North Celestial Pole. Future work should therefore focus on less spectrally smooth effects, such as beam modelling errors., Comment: 22 pages, 20 figures. Accepted for publication in Monthly Notices of the Royal Astronomical Society (MNRAS)

Current radio interferometers output multi-petabyte-scale volumes of data per year making the storage, transfer, and processing of this data a sizeable challenge. This challenge is expected to grow with the next-generation telescopes such as the Square Kilometre Array. Lossy compression of interferometric data post-correlation can abate this challenge. However, since high-redshift 21-cm studies impose strict precision requirements, the impact of such lossy data compression on the 21-cm signal power spectrum statistic should be understood. We apply Dysco visibility compression, a technique to normalize and quantize specifically designed for radio interferometric data. We establish the level of the compression noise in the power spectrum in comparison to the thermal noise as well as its coherency behavior. Finally, for optimal compression results, we compare the compression noise obtained from different compression settings to a nominal 21-cm signal power. From a single night of observation, we find that the noise introduced due to the compression is more than five orders of magnitude lower than the thermal noise level in the power spectrum. The noise does not affect calibration. The compression noise shows no correlation with the sky signal and has no measurable coherent component. The level of compression error in the power spectrum ultimately depends on the compression settings. Dysco visibility compression is found to be of insignificant concern for 21-cm power spectrum studies. Hence, data volumes can be safely reduced by factors of $\sim 4$ and with insignificant bias to the final power spectrum. Data from SKA-low will likely be compressible by the same factor as LOFAR, owing to the similarities of the two instruments. The same technique can be used to compress data from other telescopes, but a small adjustment of the compression parameters might be required., Comment: 12 pages, 9 figures, and 3 tables; submitted to Astronomy and Astrophysics (A&A)

One of the main obstacles preventing the detection of the redshifted 21-cm signal from neutral hydrogen in the early Universe is the astrophysical foreground emission, which is several orders of magnitude brighter than the signal. The foregrounds, due to their smooth spectra, are expected to predominantly occupy a region in the cylindrical power spectrum known as the foreground wedge. However, the conventional equations describing the extent of the foreground wedge are derived under a flat-sky approximation. This assumption breaks down for tracking wide-field instruments, thus rendering these equations inapplicable in these situations. In this paper, we derive equations for the full sky foreground wedge and show that the foregrounds can potentially extend far beyond what the conventional equations suggest. We also derive the equations that describe a specific bright source in the cylindrical power spectrum space. The validity of both sets of equations is tested against numerical simulations. Many current and upcoming interferometers (e.g., LOFAR, NenuFAR, MWA, SKA) are wide-field phase-tracking instruments. These equations give us new insights into the nature of foreground contamination in the cylindrical power spectra estimated using wide-field instruments. Additionally, they allow us to accurately associate features in the power spectrum to foregrounds or instrumental effects. The equations are also important for correctly selecting the "EoR window" for foreground avoidance analyses, and for planning 21-cm observations. In future analyses, it is recommended to use these updated horizon lines to indicate the foreground wedge in the cylindrical power spectrum accurately. The new equations for generating the updated wedge lines are made available in a Python library, pslines., Comment: 20 pages, 13 figures, and 2 tables; accepted for publication in Astronomy and Astrophysics (A&A)

Distributed systems can be found in various applications, e.g., in robotics or autonomous driving, to achieve higher flexibility and robustness. Thereby, data flow centric applications such as Deep Neural Network (DNN) inference benefit from partitioning the workload over multiple compute nodes in terms of performance and energy-efficiency. However, mapping large models on distributed embedded systems is a complex task, due to low latency and high throughput requirements combined with strict energy and memory constraints. In this paper, we present a novel approach for hardware-aware layer scheduling of DNN inference in distributed embedded systems. Therefore, our proposed framework uses a graph-based algorithm to automatically find beneficial partitioning points in a given DNN. Each of these is evaluated based on several essential system metrics such as accuracy and memory utilization, while considering the respective system constraints. We demonstrate our approach in terms of the impact of inference partitioning on various performance metrics of six different DNNs. As an example, we can achieve a 47.5 % throughput increase for EfficientNet-B0 inference partitioned onto two platforms while observing high energy-efficiency.

We calculate the influence of diffusive and ballistic transport on ultrafast magnetization in thick metallic films. When only diffusive transport is present, gradients of magnetization in the material remain up to picosecond timescales. In contrast, in the extreme superdiffusive limit where ballistic transport dominates, the magnetization changes homogeneously in space. We calculate the measurable magneto-optical responses for a $\SI{40}{\nano\meter}$ Nickel film. Although the resulting Kerr rotation dynamics are found to be very similar in the two limits of transport, our simulations reveal a clear signature of magnetization gradients in the Kerr ellipticity dynamics, namely a strong probe-angle dependence for the case when diffusive transport allows gradients to persist. We then perform probe-angle dependent complex magneto-optical Kerr effect (CMOKE) measurements on an excited \SI{40}{\nano\meter} Nickel film. The angle dependence of the measured Kerr signals closely matches the simulated response with diffusive transport. Therefore we conclude that the influence of ballistic transport on ultrafast magnetization dynamics in such films is negligible.

The Riemann problem for the discrete conservation law $2 \dot{u}_n + u^2_{n+1} - u^2_{n-1} = 0$ is classified using Whitham modulation theory, a quasi-continuum approximation, and numerical simulations. A surprisingly elaborate set of solutions to this simple discrete regularization of the inviscid Burgers' equation is obtained. In addition to discrete analogues of well-known dispersive hydrodynamic solutions -- rarefaction waves (RWs) and dispersive shock waves (DSWs) -- additional unsteady solution families and finite time blow-up are observed. Two solution types exhibit no known conservative continuum correlates: (i) a counterpropagating DSW and RW solution separated by a symmetric, stationary shock and (ii) an unsteady shock emitting two counter-propagating periodic wavetrains with the same frequency connected to a partial DSW or a RW. Another class of solutions called traveling DSWs, (iii), consists of a partial DSW connected to a traveling wave comprised of a periodic wavetrain with a rapid transition to a constant. Portions of solutions (ii) and (iii) are interpreted as shock solutions of the Whitham modulation equations., Comment: 34 pages, 24 figures

We consider the solutions $\rho_\varepsilon, \mathbf{u}_\varepsilon$ to the compressible Navier-Stokes equations (NSE) in a domain periodically perforated by holes of diameter $\varepsilon>0$. We focus on the case where the diameter of the holes is of the same order as the distance between neighboring holes. This is the same setting investigated in the paper by Masmoudi [\url{http://www.numdam.org/article/COCV_2002__8__885_0.pdf}], where convergence $\rho_\varepsilon, \mathbf{u}_\varepsilon$ of the system to the porous medium equation has been shown. We prove a quantitative version of this convergence result provided that the solution of the limiting system is sufficiently regular. The proof builds on the relative energy inequality satisfied by the compressible NSE.

In this perspective, we discuss thermal imbalance and the associated electron-mediated thermal transport in quantum electronic devices at very low temperatures. We first present the theoretical approaches describing heat transport in nanoscale conductors at low temperatures, in which quantum confinement and interactions play an important role. We then discuss the experimental techniques for generating and measuring heat currents and temperature gradients on the nanoscale. Eventually we review the most important quantum effects on heat transport, and discuss implications for quantum technologies and future directions in the field., Comment: To appear in Appl. Phys. Lett. as a Perspective

We study a natural application of contract design in the context of sequential exploration problems. In our principal-agent setting, a search task is delegated to an agent. The agent performs a sequential exploration of $n$ boxes, suffers the exploration cost for each inspected box, and selects the content (called the prize) of one inspected box as outcome. Agent and principal obtain an individual value based on the selected prize. To influence the search, the principal a-priori designs a contract with a non-negative payment to the agent for each potential prize. The goal of the principal is to maximize her expected reward, i.e., value minus payment. Interestingly, this natural contract scenario shares close relations with the Pandora's Box problem. We show how to compute optimal contracts for the principal in several scenarios. A popular and important subclass is that of linear contracts, and we show how to compute optimal linear contracts in polynomial time. For general contracts, we obtain optimal contracts under the standard assumption that the agent suffers cost but obtains value only from the transfers by the principal. More generally, for general contracts with non-zero agent values for outcomes we show how to compute an optimal contract in two cases: (1) when each box has only one prize with non-zero value for principal and agent, (2) for i.i.d. boxes with a single prize with positive value for the principal., Comment: Accepted to STACS 2025

The recent banking crisis has again emphasized the importance of understanding and mitigating systemic risk in financial networks. In this paper, we study a market-driven approach to rescue a bank in distress based on the idea of claims trading, a notion defined in Chapter 11 of the U.S. Bankruptcy Code. We formalize the idea in the context of financial networks by Eisenberg and Noe. For two given banks v and w, we consider the operation that w takes over some claims of v and in return gives liquidity to v to ultimately rescue v. We study the structural properties and computational complexity of decision and optimization problems for several variants of claims trading. When trading incoming edges of v, we show that there is no trade in which both banks v and w strictly improve their assets. We therefore consider creditor-positive trades, in which v profits strictly and w remains indifferent. For a given set C of incoming edges of v, we provide an efficient algorithm to compute payments by w that result in maximal assets of v. When the set C must also be chosen, the problem becomes weakly NP-hard. Our main result here is a bicriteria FPTAS to compute an approximate trade. The approximate trade results in nearly the optimal amount of assets of v in any exact trade. Our results extend to the case in which banks use general monotone payment functions and the emerging clearing state can be computed efficiently. In contrast, for trading outgoing edges of v, the goal is to maximize the increase in assets for the creditors of v. Notably, for these results the characteristics of the payment functions of the banks are essential. For payments ranking creditors one by one, we show NP-hardness of approximation within a factor polynomial in the network size, when the set of claims C is part of the input or not. Instead, for proportional payments, our results indicate more favorable conditions.

We propose a new mean-field game model with two states to study synchronization phenomena, and we provide a comprehensive characterization of stationary and dynamic equilibria along with their stability properties. The game undergoes a phase transition with increasing interaction strength. In the subcritical regime, the uniform distribution, representing incoherence, is the unique and stable stationary equilibrium. Above the critical interaction threshold, the uniform equilibrium becomes unstable and there is a multiplicity of stationary equilibria that are self-organizing. Under a discounted cost, dynamic equilibria spiral around the uniform distribution before converging to the self-organizing equilibria. With an ergodic cost, however, unexpected periodic equilibria around the uniform distribution emerge., Comment: 16 pages, 8 figures

Generative AI applications present unique design challenges. As generative AI technologies are increasingly being incorporated into mainstream applications, there is an urgent need for guidance on how to design user experiences that foster effective and safe use. We present six principles for the design of generative AI applications that address unique characteristics of generative AI UX and offer new interpretations and extensions of known issues in the design of AI applications. Each principle is coupled with a set of design strategies for implementing that principle via UX capabilities or through the design process. The principles and strategies were developed through an iterative process involving literature review, feedback from design practitioners, validation against real-world generative AI applications, and incorporation into the design process of two generative AI applications. We anticipate the principles to usefully inform the design of generative AI applications by driving actionable design recommendations., Comment: 34 pages, 4 figures. To be published in CHI 2024

Momentum-indirect excitons composed of electrons and holes in different valleys define optoelectronic properties of many semiconductors, but are challenging to detect due to their weak coupling to light. The identification of an excitons' valley character is further limited by complexities associated with momentum-selective probes. Here, we study the photoluminescence of indirect excitons in controllably strained prototypical 2D semiconductors (WSe$_2$, WS$_2$) at cryogenic temperatures. We find that these excitons i) exhibit valley-specific energy shifts, enabling their valley fingerprinting, and ii) hybridize with bright excitons, becoming directly accessible to optical spectroscopy methods. This approach allows us to identify multiple previously inaccessible excitons with wavefunctions residing in K, $\Gamma$, or Q valleys in the momentum space as well as various types of defect-related excitons. Overall, our approach is well-suited to unravel and tune intervalley excitons in various semiconductors., Comment: 9 pages, 4 figures, 1 table

Strong light fields have created spectacular opportunities to tailor novel functionalities of solids. Floquet-Bloch states can form under periodic driving of electrons and enable exotic quantum phases. On subcycle time scales, lightwaves can simultaneously drive intraband currents and interband transitions, which enable high-harmonic generation (HHG) and pave the way towards ultrafast electronics. Yet, the interplay of intra- and interband excitations as well as their relation with Floquet physics have been key open questions as dynamical aspects of Floquet states have remained elusive. Here we provide this pivotal link by pioneering the ultrafast buildup of Floquet-Bloch bands with time- and angle-resolved photoemission spectroscopy. We drive surface states on a topological insulator with mid-infrared fields - strong enough for HHG - and directly monitor the transient band structure with subcycle time resolution. Starting with strong intraband currents, we observe how Floquet sidebands emerge within a single optical cycle; intraband acceleration simultaneously proceeds in multiple sidebands until high-energy electrons scatter into bulk states and dissipation destroys the Floquet bands. Quantum nonequilibrium calculations explain the simultaneous occurrence of Floquet states with intra- and interband dynamics. Our joint experiment-theory study opens up a direct time-domain view of Floquet physics and explores the fundamental frontiers of ultrafast band-structure engineering., Comment: 45 pages, 4 figures, 10 extended data figures

Time-resolved photoemission orbital tomography (tr-POT) offers unique possibilities for tracing molecular electron dynamics. The recorded pump-induced changes of the angle-resolved photoemission intensities allow to characterize unoccupied molecular states in momentum space and to deduce the incoherent temporal evolution of their population. Here, we show for the example of CuPc/Cu(001)-2O that the method also gives access to the coherent regime and that different excitation pathways can be disentangled by a careful analysis of the time-dependent change of the photoemission momentum pattern. In particular, we demonstrate by varying photon energy and polarization of the pump light, how the incoherent temporal evolution of the LUMO distribution can be distinguished from coherent contributions of the projected HOMO. Moreover, we report the selective excitation of molecules with a specific orientation at normal incidence by aligning the electric field of the pump light along the molecular axis.

We introduce quantum homomorphisms between quantum hypergraphs through the existence of perfect strategies for quantum non-local games, canonically associated with the quantum hypergraphs. We show that the relation of homomorphism of a given type satisfies natural analogues of the properties of a pre-order. We show that quantum hypergraph homomorphisms of local type are closely related, and in some cases identical, to the TRO equivalence of finite dimensionally acting operator spaces, canonically associated with the hypergraphs.

The redshifted 21 cm signal from neutral hydrogen is a direct probe of the physics of the early universe and has been an important science driver of many present and upcoming radio interferometers. In this study we use a single night of observations with the New Extension in Nan\c{c}ay Upgrading LOFAR (NenuFAR) to place upper limits on the 21 cm power spectrum from cosmic dawn at a redshift of $z$ = 20.3. NenuFAR is a new low-frequency radio interferometer, operating in the 10-85 MHz frequency range, currently under construction at the Nan\c{c}ay Radio Observatory in France. It is a phased array instrument with a very dense uv coverage at short baselines, making it one of the most sensitive instruments for 21 cm cosmology analyses at these frequencies. Our analysis adopts the foreground subtraction approach, in which sky sources are modeled and subtracted through calibration and residual foregrounds are subsequently removed using Gaussian process regression. The final power spectra are constructed from the gridded residual data cubes in the uv plane. Signal injection tests are performed at each step of the analysis pipeline, the relevant pipeline settings are optimized to ensure minimal signal loss, and any signal suppression is accounted for through a bias correction on our final upper limits. We obtain a best 2$\sigma$ upper limit of $2.4\times 10^7$ $\text{mK}^{2}$ at $z$ = 20.3 and $k$ = 0.041 $h\,\text{cMpc}^{-1}$. We see a strong excess power in the data, making our upper limits two orders of magnitude higher than the thermal noise limit. We investigate the origin and nature of this excess power and discuss further improvements to the analysis pipeline that can potentially mitigate it and consequently allow us to reach thermal noise sensitivity when multiple nights of observations are processed in the future., Comment: 27 pages, 21 figures, and 6 tables; accepted for publication in Astronomy and Astrophysics (A&A); language edits implemented; typos corrected

One of the most promising developments in computer vision in recent years is the use of generative neural networks for functionality condition-based 3D design reconstruction and generation. Here, neural networks learn dependencies between functionalities and a geometry in a very effective way. For a neural network the functionalities are translated in conditions to a certain geometry. But the more conditions the design generation needs to reflect, the more difficult it is to learn clear dependencies. This leads to a multi criteria design problem due various conditions, which are not considered in the neural network structure so far. In this paper, we address this multi-criteria challenge for a 3D design use case related to an unmanned aerial vehicle (UAV) motor mount. We generate 10,000 abstract 3D designs and subject them all to simulations for three physical disciplines: mechanics, thermodynamics, and aerodynamics. Then, we train a Conditional Variational Autoencoder (CVAE) using the geometry and corresponding multicriteria functional constraints as input. We use our trained CVAE as well as the Marching cubes algorithm to generate meshes for simulation based evaluation. The results are then evaluated with the generated UAV designs. Subsequently, we demonstrate the ability to generate optimized designs under self-defined functionality conditions using the trained neural network.

Measurement of the redshifted 21-cm signal of neutral hydrogen from the Cosmic Dawn (CD) and Epoch of Reionisation (EoR) promises to unveil a wealth of information about the astrophysical processes during the first billion years of evolution of the universe. The AARTFAAC Cosmic Explorer (ACE) utilises the AARTFAAC wide-field imager of LOFAR to measure the power spectrum of the intensity fluctuations of the redshifted 21-cm signal from the CD at z~18. The RFI from various sources contaminates the observed data and it is crucial to exclude the RFI-affected data in the analysis for reliable detection. In this work, we investigate the impact of non-ground-based transient RFI using cross-power spectra and cross-coherence metrics to assess the correlation of RFI over time and investigate the level of impact of transient RFI on the ACE 21-cm power spectrum estimation. We detected moving sky-based transient RFI sources that cross the field of view within a few minutes and appear to be mainly from aeroplane communication beacons at the location of the LOFAR core in the 72-75 MHz band, by inspecting filtered images. This transient RFI is mostly uncorrelated over time and is only expected to dominate over the thermal noise for an extremely deep integration time of 3000 hours or more with a hypothetical instrument that is sky temperature dominated at 75 MHz. We find no visible correlation over different k-modes in Fourier space in the presence of noise for realistic thermal noise scenarios. We conclude that the sky-based transient RFI from aeroplanes, satellites and meteorites at present does not pose a significant concern for the ACE analyses at the current level of sensitivity and after integrating over the available 500 hours of observed data. However, it is crucial to mitigate or filter such transient RFI for more sensitive experiments aiming for significantly deeper integration., Comment: 13 pages, 9 figures, and 3 tables; accepted for publication in Astronomy and Astrophysics (A&A)

We consider the sedimentation of $N$ spherical particles with identical radii $R$ in a Stokes flow in $\mathbb R^3$. The particles satisfy a no-slip boundary condition and are subject to constant gravity. The dynamics of the particles is modeled by Newton's law but with very small particle inertia as $N$ tends to infinity and $R$ to $0$. In a mean-field scaling we show that the evolution of the $N$-particle system is well approximated by the Vlasov-Stokes equation. In contrast to the transport-Stokes equation considered in the first part of this series, \cite{HoferSchubert23}, the Vlasov-Stokes equation takes into account the (small) inertia. Therefore we obtain improved error estimates. We also improve previous results on the Cauchy problem for the Vlasov-Stokes equation and on its convergence to the transport-Stokes equation in the limit of vanishing inertia. The proofs are based on relative energy estimates. In particular, we show new stability estimates for the Vlasov-Stokes equation in the $2$-Wasserstein distance. By combining a Lagrangian approach with a study of the energy dissipation, we obtain uniform stability estimates for arbitrary small particle inertia. We show that a corresponding stability estimate continues to hold for the empirical particle density which formally solves the Vlasov-Stokes equation up to an error. To this end we exploit certain uniform control on the particle configuration thanks to results in the first part \cite{HoferSchubert23}., Comment: All comments welcome

Decentralized autonomous organizations (DAOs) are a new, rapidly-growing class of organizations governed by smart contracts. Here we describe how researchers can contribute to the emerging science of DAOs and other digitally-constituted organizations. From granular privacy primitives to mechanism designs to model laws, we identify high-impact problems in the DAO ecosystem where existing gaps might be tackled through a new data set or by applying tools and ideas from existing research fields such as political science, computer science, economics, law, and organizational science. Our recommendations encompass exciting research questions as well as promising business opportunities. We call on the wider research community to join the global effort to invent the next generation of organizations., Comment: includes major coordination problems

We study the multiscale viscoelastic Doi model for suspensions of Brownian rigid rod-like particles, as well as its generalization by Saintillan and Shelley for self-propelled particles. We consider the regime of a small Weissenberg number, which corresponds to a fast rotational diffusion compared to the fluid velocity gradient, and we analyze the resulting hydrodynamic approximation. More precisely, we show the asymptotic validity of macroscopic nonlinear viscoelastic models, in form of so-called ordered fluid models, as an expansion in the Weissenberg number. The result holds for zero Reynolds number in 3D and for arbitrary Reynolds number in 2D. Along the way, we establish several new well-posedness and regularity results for nonlinear fluid models, which may be of independent interest., Comment: 64 pages

We study a novel approach to information design in the standard traffic model of network congestion games. It captures the natural condition that the demand is unknown to the users of the network. A principal (e.g., a mobility service) commits to a signaling strategy, observes the realized demand and sends a (public) signal to agents (i.e., users of the network). Based on the induced belief about the demand, the users then form an equilibrium. We consider the algorithmic goal of the principal: Compute a signaling scheme that minimizes the expected total cost of the induced equilibrium. We concentrate on single-commodity networks and affine cost functions, for which we obtain the following results. First, we devise a fully polynomial-time approximation scheme (FPTAS) for the case that the demand can only take two values. It relies on several structural properties of the cost of the induced equilibrium as a function of the updated belief about the distribution of demands. We show that this function is piecewise linear for any number of demands, and monotonic for two demands. Second, we give a complete characterization of the graph structures for which it is optimal to fully reveal the information about the realized demand. This signaling scheme turns out to be optimal for all cost functions and probability distributions over demands if and only if the graph is series-parallel. Third, we propose an algorithm that computes the optimal signaling scheme for any number of demands whose time complexity is polynomial in the number of supports that occur in a Wardrop equilibrium for some demand. Finally, we conduct a computational study that tests this algorithm on real-world instances., Comment: arXiv admin note: text overlap with arXiv:2205.09823

The generalized nonlinear Schr\"odinger equation with full dispersion (FDNLS) is considered in the semiclassical regime. The Whitham modulation equations are obtained for the FDNLS equation with general linear dispersion and a generalized, local nonlinearity. Assuming the existence of a four-parameter family of two-phase solutions, a multiple-scales approach yields a system of four independent, first order, quasi-linear conservation laws of hydrodynamic type that correspond to the slow evolution of the two wavenumbers, mass, and momentum of modulated periodic traveling waves. The modulation equations are further analyzed in the dispersionless and weakly nonlinear regimes. The ill-posedness of the dispersionless equations corresponds to the classical criterion for modulational instability (MI). For modulations of linear waves, ill-posedness coincides with the generalized MI criterion, recently identified by Amiranashvili and Tobisch (New J. Phys. 21 (2019)). A new instability index is identified by the transition from real to complex characteristics for the weakly nonlinear modulation equations. This instability is associated with long-wavelength modulations of nonlinear two-phase wavetrains and can exist even when the corresponding one-phase wavetrain is stable according to the generalized MI criterion. Another interpretation is that, while infinitesimal perturbations of a periodic wave may not grow, small but finite amplitude perturbations may grow, hence this index identifies a nonlinear instability mechanism for one-phase waves. Classifications of instability indices for multiple FDNLS equations with higher order dispersion, including applications to finite depth water waves and the discrete NLS equation are presented and compared with direct numerical simulations., Comment: 26 pages, 7 figures

The existence and properties of envelope solitary waves on a periodic, traveling wave background, called traveling breathers, are investigated numerically in representative nonlocal dispersive media. Using a fixed point computational scheme, a space-time boundary value problem for bright traveling breather solutions is solved for the weakly nonlinear Benjamin-Bona-Mahony equation, a nonlocal, regularized shallow water wave model, and the strongly nonlinear conduit equation, a nonlocal model of viscous core-annular flows. Curves of unit-mean traveling breather solutions within a three-dimensional parameter space are obtained. Resonance due to nonconvex, rational linear dispersion leads to a nonzero oscillatory background upon which traveling breathers propagate. These solutions exhibit a topological phase jump, so act as defects within the periodic background. For small amplitudes, traveling breathers are well-approximated by bright soliton solutions of the nonlinear Schr\"odinger equation with a negligibly small periodic background. These solutions are numerically continued into the large amplitude regime as elevation defects on cnoidal or cnoidal-like periodic traveling wave backgrounds. This study of bright traveling breathers provides insight into systems with nonconvex, nonlocal dispersion that occur in a variety of media such as internal oceanic waves subject to rotation and short, intense optical pulses., Comment: 12 pages, 12 figures

We report the detection of 21 cm emission at an average redshift $\bar{z} = 2.3$ in the cross-correlation of data from the Canadian Hydrogen Intensity Mapping Experiment (CHIME) with measurements of the Lyman-$\alpha$ forest from eBOSS. Data collected by CHIME over 88 days in the $400-500$~MHz frequency band ($1.8 < z < 2.5$) are formed into maps of the sky and high-pass delay filtered to suppress the foreground power, corresponding to removing cosmological scales with $k_\parallel \lesssim 0.13\ \text{Mpc}^{-1}$ at the average redshift. Line-of-sight spectra to the eBOSS background quasar locations are extracted from the CHIME maps and combined with the Lyman-$\alpha$ forest flux transmission spectra to estimate the 21 cm-Lyman-$\alpha$ cross-correlation function. Fitting a simulation-derived template function to this measurement results in a $9\sigma$ detection significance. The coherent accumulation of the signal through cross-correlation is sufficient to enable a detection despite excess variance from foreground residuals $\sim6-10$ times brighter than the expected thermal noise level in the correlation function. These results are the highest-redshift measurement of \tcm emission to date, and set the stage for future 21 cm intensity mapping analyses at $z>1.8$.

The large time $t$ asymptotics for scalar, constant coefficient,linear, third order, dispersive equations are obtained for asymptotically time-periodic Dirichlet boundary data and zero initial data on the half-line modeling a wavemaker acting upon an initially quiescent medium. The asymptotic Dirichlet-to-Neumann (D-N) map is constructed by expanding upon the recently developed $Q$-equation method. The D-N map is proven to be unique if and only if the radiation condition that selects the unique wavenumber branch of the dispersion relation for a sinusoidal, time-dependent boundary condition holds: (i) for frequencies in a finite interval, the wavenumber is real and corresponds to positive group velocity, (ii) for frequencies outside the interval, the wavenumber is complex with positive imaginary part. For fixed spatial location $x$, the corresponding asymptotic solution is (i) a traveling wave or (ii) a spatially decaying, time-periodic wave. Uniform-in-$x$ asymptotic solutions for the physical cases of the linearized Korteweg-de Vries and Benjamin-Bona-Mahony (BBM) equations are obtained via integral asymptotics. The linearized BBM asymptotics are found to quantitatively agree with viscous core-annular fluid experiments.

We consider a finite number of $N$ statistically equal agents, each moving on a finite set of states according to a continuous-time Markov Decision Process (MDP). Transition intensities of the agents and generated rewards depend not only on the state and action of the agent itself, but also on the states of the other agents as well as the chosen action. Interactions like this are typical for a wide range of models in e.g. biology, epidemics, finance, social science and queueing systems among others. The aim is to maximize the expected discounted reward of the system, i.e. the agents have to cooperate as a team. Computationally this is a difficult task when $N$ is large. Thus, we consider the limit for $N\to\infty.$ In contrast to other papers we treat this problem from an MDP perspective. This has the advantage that we need less regularity assumptions in order to construct asymptotically optimal strategies than using viscosity solutions of HJB equations. The convergence rate is $1/\sqrt{N}$. We show how to apply our results using two examples: a machine replacement problem and a problem from epidemics. We also show that optimal feedback policies from the limiting problem are not necessarily asymptotically optimal.

We study threshold testing, an elementary probing model with the goal to choose a large value out of $n$ i.i.d. random variables. An algorithm can test each variable $X_i$ once for some threshold $t_i$, and the test returns binary feedback whether $X_i \ge t_i$ or not. Thresholds can be chosen adaptively or non-adaptively by the algorithm. Given the results for the tests of each variable, we then select the variable with highest conditional expectation. We compare the expected value obtained by the testing algorithm with expected maximum of the variables. Threshold testing is a semi-online variant of the gambler's problem and prophet inequalities. Indeed, the optimal performance of non-adaptive algorithms for threshold testing is governed by the standard i.i.d. prophet inequality of approximately $0.745+o(1)$ as $n \to \infty$. We show how adaptive algorithms can significantly improve upon this ratio. Our adaptive testing strategy guarantees a competitive ratio of at least $0.869-o(1)$. Moreover, we show that there are distributions that admit only a constant ratio $c < 1$, even when $n \to \infty$. Finally, when each box can be tested multiple times (with $n$ tests in total), we design an algorithm that achieves a ratio of $1-o(1)$.

In 1991 H\'ebrard introduced a factorization of words that turned out to be a powerful tool for the investigation of a word's scattered factors (also known as (scattered) subwords or subsequences). Based on this, first Karandikar and Schnoebelen introduced the notion of $k$-richness and later on Barker et al. the notion of $k$-universality. In 2022 Fleischmann et al. presented a generalization of the arch factorization by intersecting the arch factorization of a word and its reverse. While the authors merely used this factorization for the investigation of shortest absent scattered factors, in this work we investigate this new $\alpha$-$\beta$-factorization as such. We characterize the famous Simon congruence of $k$-universal words in terms of $1$-universal words. Moreover, we apply these results to binary words. In this special case, we obtain a full characterization of the classes and calculate the index of the congruence. Lastly, we start investigating the ternary case, present a full list of possibilities for $\alpha\beta\alpha$-factors, and characterize their congruence.