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We report a theoretical study of multiterminal Josephson junctions under the influence of a magnetic field $B$. We consider a ballistic rectangular two-dimensional metal $N_0$ connected by the edges to the left, right, top and bottom superconductors $S_L$, $S_R$, $S_T$ and $S_B$, respectively. We numerically calculate in the large-gap approximation the critical current $I_c$ versus $B$ between the left and right $S_L$ and $S_R$ for various aspect ratios, with the top and bottom $S_T$ and $S_B$ playing the role of superconducting mirrors. We find the critical current $I_c$ to be enhanced by orders of magnitude, especially at long distance, due to the phase rigidity provided by the mirrors. We obtain superconducting quantum interference device-like magnetic oscillations. With symmetric couplings, the self-consistent superconducting phase variables of the top and bottom mirrors take the values $0$ or $\pi$, as for emerging Ising degrees of freedom. We propose a simple effective Josephson junction circuit model that is compatible with these microscopic numerical calculations. From the $I_c(B)$ patterns we infer where the supercurrent flows in various device geometries. In particular in the elongated geometry, we show that the supercurrent flows between all pairs of contacts, which allows exploring the full phase space of the relevant phase differences., Comment: 15 pages, 6 figures, minor modifications

How areas of land are allocated for different uses, such as forests, urban areas, and agriculture, has a large effect on the terrestrial carbon balance, and therefore climate change. Based on available historical data on land-use changes and a simulation of the associated carbon emissions and removals, a surrogate model can be learned that makes it possible to evaluate the different options available to decision-makers efficiently. An evolutionary search process can then be used to discover effective land-use policies for specific locations. Such a system was built on the Project Resilience platform and evaluated with the Land-Use Harmonization dataset LUH2 and the bookkeeping model BLUE. It generates Pareto fronts that trade off carbon impact and amount of land-use change customized to different locations, thus providing a potentially useful tool for land-use planning.

We analyze the radiative forces between two dielectric nanospheres mediated via the quantum and thermal fluctuations of the electromagnetic field in the presence of an external drive. We generalize the scattering theory description of fluctuation forces to include external quantum fields, allowing them to be in an arbitrary quantum state. The known trapping and optical binding potentials are recovered for an external coherent state. We demonstrate that an external squeezed vacuum state creates similar potentials to a laser, despite its zero average intensity. Moreover, Schr\"odinger cat states of the field can enhance or suppress the optical potential depending on whether they are odd or even. Considering the nanospheres trapped by optical tweezers, we examine the total interparticle potential as a function of various experimentally relevant parameters, such as the field intensity, polarization, and phase of the trapping lasers. We demonstrate that an appropriate set of parameters could produce mutual bound states of the two nanospheres with potential depth as large as $\sim200$ K. Our results are pertinent to ongoing experiments with trapped nanospheres in the macroscopic quantum regime, paving the way for engineering interactions among macroscopic quantum systems.

In-context Learning (ICL) is the ability of Large Language Models (LLMs) to perform new tasks when conditioned on prompts comprising a few task examples. However, ICL performance can be critically sensitive to the choice of examples. To dynamically select the best examples for every test input, we propose Example Gisting, a novel approach for training example encoders through supervised fine-tuning with an attention bottleneck between the inputs and outputs. These gist models form the basis for GistScore, a novel metric for scoring and selecting informative examples. Further, we experiment with two variations: (1) fine-tuning gist models for each dataset and (2) multi-task training a single model on a large collection of datasets. The latter can be used for new tasks out-of-the-box, enabling a training-free ICL pipeline. Evaluations with 21 datasets spanning 9 tasks and 8 diverse LLMs show that our fine-tuned models get state-of-the-art ICL performance with over 20% absolute gain over off-the-shelf retrievers and 5% over the best prior methods. Further, our multi-task model generalizes well to new tasks, datasets, and prompt templates. Selection using this model matches or outperforms prior methods while being three orders of magnitude faster than the strongest training-free baseline.

We present JCMT POL-2 850 um dust polarization observations and Mimir H band stellar polarization observations toward the starless core L1512. We detect the highly-ordered core-scale magnetic field traced by the POL-2 data, of which the field orientation is consistent with the parsec-scale magnetic fields traced by Planck data, suggesting the large-scale fields thread from the low-density region to the dense core region in this cloud. The surrounding magnetic field traced by the Mimir data shows a wider variation in the field orientation, suggesting there could be a transition of magnetic field morphology at the envelope scale. L1512 was suggested to be presumably older than 1.4 Myr in a previous study via time-dependent chemical analysis, hinting that the magnetic field could be strong enough to slow the collapse of L1512. In this study, we use the Davis-Chandrasekhar-Fermi method to derive a plane-of-sky magnetic field strength ($B_{pos}$) of 18$\pm$7 uG and an observed mass-to-flux ratio ($\lambda_{obs}$) of 3.5$\pm$2.4, suggesting that L1512 is magnetically supercritical. However, the absence of significant infall motion and the presence of an oscillating envelope are inconsistent with the magnetically supercritical condition. Using a Virial analysis, we suggest the presence of a hitherto hidden line-of-sight magnetic field strength of ~27 uG with a mass-to-flux ratio ($\lambda_{tot}$) of ~1.6, in which case both magnetic and kinetic pressures are important in supporting the L1512 core. On the other hand, L1512 may have just reached supercriticality and will collapse at any time., Comment: 25 pages, 10 figures, accepted for publication in ApJ

All-solid-state batteries are currently developed at high pace and show a strong potential for market introduction within the next years. Though their performance has improved considerably over the last years, investigation of their sustainability and the development of suitable recycling strategies have received less attention. However, their potential for efficient circular processes must be accessed comprehensively. In this article, we investigate the separation of the solid electrolyte beta-Li3PS4 from different lithium transition metal oxide electrode materials (LiCoO2, LiMn2O4, LiNi0.8Mn0.1Co0.1O2, LiFePO4, LiNi0.85Co0.1Al0.05O2 and Li4Ti5O12) via an approach based on the dissolution and subsequent recrystallization of the thiophosphate using N-methylformamide as solvent. A combination of X-ray diffraction, scanning electron microscopy, energy-dispersive X-ray spectroscopy, inductively coupled plasma-mass spectrometry, iodometric titration and X-ray photoelectron spectroscopy as well as electrochemical impedance spectroscopy and electrochemical characterization was used to characterize the electrolyte and electrode materials before and after separation. We find that the presence of electrode materials in the dissolution process can lead to significant chemical reactions. These interactions can (but most not) lead to strong alteration of the electrochemical characteristics of the individual compounds. Thus, we show that an efficient recovery of materials will likely depend on the precise material combination within an all-solid-state battery.

Controlling single-electron states becomes increasingly important due to the wide-ranging advances in electron quantum optics. Single-electron control enables coherent manipulation of individual electrons and the ability to exploit the wave nature of electrons, which offers various opportunities for quantum information processing, sensing, and metrology. A unique opportunity offering new degrees of freedom for single-electron control is provided when considering non-uniform magnetic fields. Considering the modeling perspective, conventional electron quantum transport theories are commonly based on gauge-dependent electromagnetic potentials. A direct formulation in terms of intuitive electromagnetic fields is thus not possible. In an effort to rectify this, a gauge-invariant formulation of the Wigner equation for general electromagnetic fields has been proposed in [Nedjalkov et al., Phys. Rev. B., 2019, 99, 014423]. However, the complexity of this equation requires to derive a more convenient formulation for linear electromagnetic fields [Nedjalkov et al., Phys. Rev. A., 2022, 106, 052213]. This formulation directly includes the classical formulation of the Lorentz force and higher-order terms depending on the magnetic field gradient, that are negligible for small variations of the magnetic field. In this work, we generalize this equation in order to include a general, non-uniform electric field and a linear, non-uniform magnetic field. The thus obtained formulation has been applied to investigate the capabilities of a linear, non-uniform magnetic field to control single-electron states in terms of trajectory, interference patterns, and dispersion. This has led to explore a new type of transport inside electronic waveguides based on snake trajectories and also to explore the possibility to split wavepackets to realize edge states.

We present experiments in which self-assembled InAs quantum dots are coupled to a thin, suspended-beam GaAs resonator. The quantum dots are driven resonantly and the resonance fluorescence is detected. The narrow quantum-dot linewidths, just a factor of three larger than the transform limit, result in a high sensitivity to the mechanical motion. We show that one quantum dot couples to eight mechanical modes spanning a frequency range from $30$ to $600~\mathrm{MHz}$: one quantum dot provides an extensive characterisation of the mechanical resonator. The coupling spans the unresolved-sideband to the resolved-sideband regimes. Finally, we present the first detection of thermally-driven phonon sidebands (at $4.2~\mathrm{K}$) in the resonance-fluoresence spectrum.

A promising route towards the heralded creation and annihilation of single-phonons is to couple a single-photon emitter to a mechanical resonator. The challenge lies in reaching the resolved-sideband regime with a large coupling rate and a high mechanical quality factor. We achieve all of this by coupling self-assembled InAs quantum dots to a small-mode-volume phononic-crystal resonator with mechanical frequency $\Omega_\mathrm{m}/2\pi = 1.466~\mathrm{GHz}$ and quality factor $Q_\mathrm{m} = 2.1\times10^3$. Thanks to the high coupling rate of $g_\mathrm{ep}/2\pi = 2.9~\mathrm{MHz}$, and by exploiting a matching condition between the effective Rabi and mechanical frequencies, we are able to observe the interaction between the two systems. Our results represent a major step towards quantum control of the mechanical resonator via a single-photon emitter.

Context. Blazar AO 0235+164, located at redshift z = 0.94, has undergone several sharp multi-spectral-range flaring episodes during the last decades. In particular, the episodes peaking in 2008 and 2015, that received extensive multi-wavelength coverage, exhibited interesting behavior. Aims. We study the actual origin of these two observed flares by constraining the properties of the observed photo-polarimetric variability, those of the broad-band spectral energy-distribution and the observed time-evolution behavior of the source as seen by ultra-high resolution total-flux and polarimetric Very-long-baseline interferometry (VLBI) imaging. Methods. The analysis of VLBI images allows us to constrain kinematic and geometrical parameters of the 7 mm jet. We use the Discrete Correlation Function to compute the statistical correlation and the delays between emission at different spectral ranges. Multi-epoch modeling of the spectral energy distributions allows us to propose specific models of emission; in particular for the unusual spectral features observed in this source in the X-ray region of the spectrum during strong multi spectral-range flares. Results. We find that these X-ray spectral features can be explained by an emission component originating in a separate particle distribution than the one responsible for the two standard blazar bumps. This is in agreement with the results of our correlation analysis that do not find a strong correlation between the X-rays and the remaining spectral ranges. We find that both external Compton dominated and synchrotron self-Compton dominated models can explain the observed spectral energy distributions. However, synchrotron self-Compton models are strongly favored by the delays and geometrical parameters inferred from the observations.

Optimizing the energy efficiency of driving processes provides valuable insights into the underlying physics and is of crucial importance for numerous applications, from biological processes to the design of machines and robots. Knowledge of optimal driving protocols is particularly valuable at the microscale, where energy supply is often limited. Here we investigate experimentally and theoretically the paradigmatic optimization problem of moving a potential carrying a load through a fluid, in a finite time and over a given distance, in such a way that the required work is minimal. An important step towards more realistic systems is the consideration of memory effects in the surrounding fluid, which are ubiquitous in real-world applications. Therefore, our experiments were performed in viscous and viscoelastic media, which are typical environments for synthetic and biological processes on the microscale. Despite marked differences between the protocols in both fluids, we find that the optimal control protocol and the corresponding average particle trajectory always obey a time-reversal symmetry. We show that this symmetry, which surprisingly applies here to a class of processes far from thermal equilibrium, holds universally for various systems, including active, granular, and long-range correlated media in their linear regimes. The uncovered symmetry provides a rigorous and versatile criterion for optimal control that greatly facilitates the search for energy-efficient transport strategies in a wide range of systems. Using a machine learning algorithm, we demonstrate that the algorithmic exploitation of time-reversal symmetry can significantly enhance the performance of numerical optimization algorithms., Comment: 16 pages with 10 figures, accepted for publication in PRX

Structured illumination can reject out-of-focus signal from a sample, enabling high-speed and high-contrast imaging over large areas with widefield detection optics. Currently, this optical-sectioning technique is limited by image reconstruction artefacts and the need for sequential imaging of multiple colour channels. We combine multicolour interferometric pattern generation with machine-learning processing, permitting high-contrast, real-time reconstruction of image data. The method is insensitive to background noise and unevenly phase-stepped illumination patterns. We validate the method in silico and demonstrate its application on diverse specimens, ranging from fixed and live biological cells to synthetic biosystems, imaging at up to 37 Hz across a 44 x 44 $\mu m^2$ field of view.

The analysis of configurable systems, i.e., systems those behaviors depend on parameters or support various features, is challenging due to the exponential blowup arising in the number of configuration options. This volume contains the post-proceedings of TiCSA 2023, the first workshop on Trends in Configurable Systems Analysis, where current challenges and solutions in configurable systems analysis were presented and discussed.

We investigate the structural and dynamic properties of active Brownian particles (APs) confined within a soft annulus-shaped channel. Depending on the strength of the confinement and the P\'eclet number, we observe a novel re-entrant behavior that is not present in unconfined systems. Our findings are substantiated by numerical simulations and analytical considerations, revealing that this behavior arises from the strong coupling between the P\'eclet number and the effective confining dimensionality of the APs. Beyond highlighting the important influence of soft boundaries on APs, our research holds significance for future applications of micro-robotic systems.

We present the generation of transient polarization gratings at the nanoscale, achieved using a tailored accelerator configuration of the FERMI free electron laser. We demonstrate the capabilities of such a transient polarization grating by comparing its induced dynamics with the ones triggered by a more conventional intensity grating on a thin film ferrimagnetic alloy. While the signal of the intensity grating is dominated by the thermoelastic response of the system, such a contribution is suppressed in the case of the polarization grating. This exposes helicity-dependent magnetization dynamics that have so-far remained hidden under the large thermally driven response. We anticipate nanoscale transient polarization gratings to become useful for the study of any physical, chemical and biological systems possessing chiral symmetry.

We present the multiwavelength flaring activity of the blazar AO 0235+164 during its recent active period from 2013 to 2019. From a discrete correlation function (DCF) analysis, we find a significant (>95%) correlation between radio and $\gamma$-ray light curves with flares at longer wavelengths following flares at shorter wavelengths. We identify a new jet component in 43 GHz VLBA data that was ejected from the radio core on MJD $57246^{+26}_{-30}$ (2015 August 12), during the peak of the 2015 radio flare. From the analysis of the jet component, we derived a Doppler factor of $\delta_{\rm var}=28.5\pm8.4$, a bulk Lorentz factor of $\Gamma=16.8^{+3.6}_{-3.1}$, and an intrinsic viewing angle of $\theta_{\rm v}=1.42^{+1.07}_{-0.52}\textrm{ degrees}$. Investigation of the quasi-simultaneous radio data revealed a partially absorbed spectrum with the turnover frequency varying in the range of $10-70$ GHz and the peak flux density varying in the range of $0.7-4$ Jy. We find the synchrotron self-absorption magnetic field strength to be $B_{\rm SSA}=15.3^{+12.6}_{-14.0}$ mG at the peak of the 2015 radio flare, which is comparable to the equipartition magnetic field strength of $B_{\rm EQ}=43.6^{+10.6}_{-10.4}$ mG calculated for the same epoch. Additional analysis of the radio emission region in the relativistic jet of AO 0235+164 suggests that it did not significantly deviate from equipartition during its recent flaring activity., Comment: 13 pages, 11 figures, 4 tables; Accepted for publication in MNRAS

The sequence $(\operatorname{Ass}(R/I^n))_{n\in\mathbb{N}}$ of associated primes of powers of a monomial ideal $I$ in a polynomial ring $R$ eventually stabilizes by a known result by Markus Brodmann. L\^e Tu\^an Hoa gives an upper bound for the index where the stabilization occurs. This bound depends on the generators of the ideal and is obtained by separately bounding the powers of $I$ after which said sequence is non-decreasing and non-increasing, respectively. In this paper, we focus on the latter and call the smallest such number the copersistence index. We take up the proof idea of L\^e Tu\^an Hoa, who exploits a certain system of inequalities whose solution sets store information about the associated primes of powers of $I$. However, these proofs are entangled with a specific choice for the system of inequalities. In contrast to that, we present a generic ansatz to obtain an upper bound for the copersistence index that is uncoupled from this choice of the system. We establish properties for a system of inequalities to be eligible for this approach to work. We construct two suitable inequality systems to demonstrate how this ansatz yields upper bounds for the copersistence index and compare them with Hoa's. One of the two systems leads to an improvement of the bound by an exponential factor.

Heterostructures of two-dimensional transition metal dichalcogenides (TMDs) are emerging as a promising platform for investigating exotic correlated states of matter. Here, we propose to engineer Bose-Fermi mixtures in these systems by coupling inter-layer excitons to doped charges in a trilayer structure. Their interactions are determined by the inter-layer trion, whose spin-selective nature allows excitons to mediate an attractive interaction between charge carriers of only one spin species. Remarkably, we find that this causes the system to become unstable to topological p+ip superconductivity at low temperatures. We then demonstrate a general mechanism to develop and control this unconventional state by tuning the trion binding energy using a solid-state Feshbach resonance., Comment: 11 pages, 5 figures. Final version

Feshbach resonances play a vital role in the success of cold atoms investigating strongly-correlated physics. The recent observation of their solid-state analog in the scattering of holes and intralayer excitons in transition metal dichalcogenides [Schwartz et al., Science 374, 336 (2021)] holds compelling promise for bringing fully controllable interactions to the field of semiconductors. Here, we demonstrate how tunneling-induced layer hybridization can lead to the emergence of two distinct classes of Feshbach resonances in atomically thin semiconductors. Based on microscopic scattering theory we show that these two types of Feshbach resonances allow to tune interactions between electrons and both short-lived intralayer, as well as long-lived interlayer excitons. We predict the exciton-electron scattering phase shift from first principles and show that the exciton-electron coupling is fully tunable from strong to vanishing interactions. The tunability of interactions opens the avenue to explore Bose-Fermi mixtures in solid-state systems in regimes that were previously only accessible in cold atom experiments., Comment: 6+3 pages, 4+1 figures

Applying a Weyl-Stratonovich transform to the evolution equation of the Wigner function in an electromagnetic field yields a multidimensional gauge-invariant equation which is numerically very challenging to solve. In this work, we apply simplifying assumptions for linear electromagnetic fields and the evolution of an electron in a plane (two-dimensional transport), which reduces the complexity and enables to gain first experiences with a gauge-invariant Wigner equation. We present an equation analysis and show that a finite difference approach for solving the high-order derivatives allows for reformulation into a Fredholm integral equation. The resolvent expansion of the latter contains consecutive integrals, which is favorable for Monte Carlo solution approaches. To that end, we present two stochastic (Monte Carlo) algorithms that evaluate averages of generic physical quantities or directly the Wigner function. The algorithms give rise to a quantum particle model, which interprets quantum transport in heuristic terms.

Fingerprints have long been recognized as a unique and reliable means of personal identification. Central to the analysis and enhancement of fingerprints is the concept of the fingerprint core. Although the location of the core is used in many applications, to the best of our knowledge, this study is the first to investigate the empirical distribution of the core over a large, combined dataset of rolled, as well as plain fingerprint recordings. We identify and investigate the extent of incomplete rolling during the rolled fingerprint acquisition and investigate the centrality of the core. After correcting for the incomplete rolling, we find that the core deviates from the fingerprint center by 5.7% $\pm$ 5.2% to 7.6% $\pm$ 6.9%, depending on the finger. Additionally, we find that the assumption of normal distribution of the core position of plain fingerprint recordings cannot be rejected, but for rolled ones it can. Therefore, we use a multi-step process to find the distribution of the rolled fingerprint recordings. The process consists of an Anderson-Darling normality test, the Bayesian Information Criterion to reduce the number of possible candidate distributions and finally a Generalized Monte Carlo goodness-of-fit procedure to find the best fitting distribution. We find the non-central Fischer distribution best describes the cores' horizontal positions. Finally, we investigate the correlation between mean core position offset and the NFIQ 2 score and find that the NFIQ 2 prefers rolled fingerprint recordings where the core sits slightly below the fingerprint center.

The extend of tool wear significantly affects blanking processes and has a decisive impact on product quality and productivity. For this reason, numerous scientists have addressed their research to wear monitoring systems in order to identify or even predict critical wear at an early stage. Existing approaches are mainly based on indirect monitoring using time series, which are used to detect critical wear states via thresholds or machine learning models. Nevertheless, differentiation between types of wear phenomena affecting the tool during blanking as well as quantification of worn surfaces is still limited in practice. While time series data provides partial insights into wear occurrence and evolution, direct monitoring techniques utilizing image data offer a more comprehensive perspective and increased robustness when dealing with varying process parameters. However, acquiring and processing this data in real-time is challenging. In particular, high dynamics combined with increasing strokes rates as well as the high dimensionality of image data have so far prevented the development of direct image-based monitoring systems. For this reason, this paper demonstrates how high-resolution images of tools at 600 spm can be captured and subsequently processed using semantic segmentation deep learning algorithms, more precisely Fully Convolutional Networks (FCN). 125,000 images of the tool are taken from successive strokes, and microscope images are captured to investigate the worn surfaces. Based on findings from the microscope images, selected images are labeled pixel by pixel according to their wear condition and used to train a FCN (U-Net).

Continual learning is a desirable feature in many modern machine learning applications, which allows in-field adaptation and updating, ranging from accommodating distribution shift, to fine-tuning, and to learning new tasks. For applications with privacy and low latency requirements, the compute and memory demands imposed by continual learning can be cost-prohibitive for resource-constraint edge platforms. Reducing computational precision through fully quantized training (FQT) simultaneously reduces memory footprint and increases compute efficiency for both training and inference. However, aggressive quantization especially integer FQT typically degrades model accuracy to unacceptable levels. In this paper, we propose a technique that leverages inexpensive Hadamard transforms to enable low-precision training with only integer matrix multiplications. We further determine which tensors need stochastic rounding and propose tiled matrix multiplication to enable low-bit width accumulators. We demonstrate the effectiveness of our technique on several human activity recognition datasets and CIFAR100 in a class incremental learning setting. We achieve less than 0.5% and 3% accuracy degradation while we quantize all matrix multiplications inputs down to 4-bits with 8-bit accumulators.

We show how the relatively initial or relatively terminal fixed points for a well-behaved functor $F$ form a pair of adjoint functors between $F$-coalgebras and $F$-algebras. We use the language of locally presentable categories to find sufficient conditions for existence of this adjunction. We show that relative fixed points may be characterized as (co)equalizers of the free (co)monad on $F$. In particular, when $F$ is a polynomial functor on $\mathsf{Set}$ the relative fixed points are a quotient or subset of the free term algebra or the cofree term coalgebra. We give examples of the relative fixed points for polynomial functors and an example which is the Sierpinski carpet. Lastly, we prove a general preservation result for relative fixed points., Comment: 26 pages

Assigning patients to rooms and nurses to patients are critical tasks within hospitals that directly affect patient and staff satisfaction, quality of care, and hospital efficiency. Both patient-to-room assignments and nurse-to-patient assignments are typically agreed upon at the ward level, and they interact in several ways such as jointly determining the walking distances nurses must cover between different patient rooms. This motivates to consider both problems jointly in an integrated fashion. This paper presents the first optimization models and algorithms for the integrated patient-to-room and nurse-to-patient assignment problem. We provide a mixed integer programming formulation of the integrated problem that considers the typical objectives from the single problems as well as additional objectives that can only be properly evaluated when integrating both problems. Moreover, motivated by the inherent complexity that results from integrating these two NP-hard and already computationally challenging problems, we devise an efficient heuristic for the integrated patient-to-room and nurse-to-patient assignment problem. To evaluate the running time and quality of the solution obtained with the heuristic, we conduct extensive computational experiments on both artificial and real-world instances. The artificial instances are generated by a parameterized instance generator for the integrated problem that is made freely available.

The openness of modern IT systems and their permanent change make it challenging to keep these systems secure. A combination of regression and security testing called security regression testing, which ensures that changes made to a system do not harm its security, are therefore of high significance and the interest in such approaches has steadily increased. In this article we present a systematic classification of available security regression testing approaches based on a solid study of background and related work to sketch which parts of the research area seem to be well understood and evaluated, and which ones require further research. For this purpose we extract approaches relevant to security regression testing from computer science digital libraries based on a rigorous search and selection strategy. Then, we provide a classification of these according to security regression approach criteria: abstraction level, security issue, regression testing techniques, and tool support, as well as evaluation criteria, for instance evaluated system, maturity of the system, and evaluation measures. From the resulting classification we derive observations with regard to the abstraction level, regression testing techniques, tool support as well as evaluation, and finally identify several potential directions of future research.

Estimating high resolution models of the Earth's core magnetic field and its time variation in the polar regions requires that one can adequately account for magnetic signals produced by polar ionospheric currents, which vary on a wide range of time and length scales. Limitations of existing ionospheric field models in the challenging polar regions can adversely affect core field models, which in turn has important implications for studies of the core flow dynamics in those regions. Here we implement a new approach to co-estimate a climatological model of the ionospheric field together with a model of the internal and magnetospheric fields within the CHAOS geomagnetic field modelling framework. The parametrization of the ionospheric field exploits non-orthogonal magnetic coordinates and scales linearly with external driving parameters related to the solar wind and the interplanetary magnetic field. Using this approach we derive a new geomagnetic field model from measurements of the magnetic field collected by low Earth orbit satellites, which in addition to the internal field provides estimates of the typical current system in the polar ionosphere. We find that the time derivative of the estimated internal field is less contaminated by the polar currents, which is mostly visible in the zonal and near-zonal terms at high spherical harmonic degrees. Distinctive patches of strong secular variation at the core-mantle boundary, which have important implications for core dynamics, persist. Relaxing the temporal regularisation reveals annual oscillations, which could indicate remaining ionospheric field or related induced signals in the internal field model. Using principal component analysis we find that the annual oscillations mostly affect the zonal low-degree spherical harmonics of the internal field., Comment: 26 pages, 15 figures, 3 tables

We fully classify automatic sequences $a$ over a finite alphabet $\Omega$ with the property that each word over $\Omega$ appears is $a$ along an arithmetic progression. Using the terminology introduced by Avgustinovich, Fon-Der-Flaass and Frid, these are the automatic sequences with the maximal possible arithmetical subword complexity. More generally, we obtain an asymptotic formula for arithmetical (and even polynomial) subword complexity of a given automatic sequence $a$., Comment: 14 pages, comments welcome

As infrastructure ages, the need for efficient monitoring methods becomes increasingly critical. Bridge Weigh-In-Motion (BWIM) systems are crucial for cost-efficient load and thus residual service life determination of road and railway infrastructure. However, conventional BWIM systems require additional sensors for axle detection, which have to be installed in potentially inaccessible locations or in locations that interfere with bridge operation. This study addresses this challenge by replacing dedicated axle detectors with a novel approach to real-time detection of train axles using sensors arbitrarily placed on bridges. The proposed Virtual Axle Detector with Enhanced Receptive Field (VADER) has been validated on a single-track railway bridge, demonstrating that it achieves to detect 99.9% of axles with a spatial error of 3.69cm using only acceleration measurements. Using raw data as input outperforms the state-of-the-art spectrogram-based method in both speed and memory usage by 99%, making real-time application feasible for the first time. Additionally, we introduce the Maximum Receptive Field (MRF) rule, a novel approach to optimise hyperparameters of Convolutional Neural Networks (CNNs) based on the size of objects, which in this case relates to the fundamental frequency of a bridge. The MRF rule effectively narrows the hyperparameter search space, potentially replacing the need for extensive hyperparameter tuning. Since the MRF rule is theoretically applicable to all unstructured data, it could have implications for a wide range of deep learning problems from earthquake prediction to object recognition.