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Spot spraying represents an efficient and sustainable method for reducing the amount of pesticides, particularly herbicides, used in agricultural fields. To achieve this, it is of utmost importance to reliably differentiate between crops and weeds, and even between individual weed species in situ and under real-time conditions. To assess suitability for real-time application, different object detection models that are currently state-of-the-art are compared. All available models of YOLOv8, YOLOv9, YOLOv10, and RT-DETR are trained and evaluated with images from a real field situation. The images are separated into two distinct datasets: In the initial data set, each species of plants is trained individually; in the subsequent dataset, a distinction is made between monocotyledonous weeds, dicotyledonous weeds, and three chosen crops. The results demonstrate that while all models perform equally well in the metrics evaluated, the YOLOv9 models, particularly the YOLOv9s and YOLOv9e, stand out in terms of their strong recall scores (66.58 % and 72.36 %), as well as mAP50 (73.52 % and 79.86 %), and mAP50-95 (43.82 % and 47.00 %) in dataset 2. However, the RT-DETR models, especially RT-DETR-l, excel in precision with reaching 82.44 \% on dataset 1 and 81.46 % in dataset 2, making them particularly suitable for scenarios where minimizing false positives is critical. In particular, the smallest variants of the YOLO models (YOLOv8n, YOLOv9t, and YOLOv10n) achieve substantially faster inference times down to 7.58 ms for dataset 2 on the NVIDIA GeForce RTX 4090 GPU for analyzing one frame, while maintaining competitive accuracy, highlighting their potential for deployment in resource-constrained embedded computing devices as typically used in productive setups.

Physical reservoir computing (RC) is a beyond von-Neumann computing paradigm that harnesses the dynamical properties of a complex physical system (reservoir) to process information efficiently in tasks such as pattern recognition. This hardware-centered approach drastically reduces training efforts and holds potential for significantly reduced energy consumption operation. Magnetic skyrmions, topological, particle-like spin textures, are considered highly promising candidates for reservoir computing systems due to their non-linear interactions and established mechanisms for low power manipulation combined with thermally excited dynamics. So far spin-based reservoir computing has been used for static detection or has been based on intrinsic magnetization dynamics timescales, that require cumbersome rescaling of typically slower real-world data. Here we harness the power of time-multiplexed skyrmion RC by adjusting the intrinsic timescales of the reservoir to the timescales of real-world temporal patterns: we recognize hand gestures recorded with range-doppler radar on a millisecond timescale and feed the data as a time-dependent voltage excitation directly into our device. We observe the temporal evolution of the skyrmion trajectory using read-out at just one position of the reservoir, which allows for scaling onto the nanometer scale. We find that our hardware solution exhibits competitive performance compared with a state-of-the-art energy-intensive software-based neural network. The key advantage of our hardware approach lies in its capacity to seamlessly integrate data from sensors without the need for temporal conversion, thanks to the time-dependent input and tunable intrinsic timescales of the skyrmion dynamics in the reservoir. This feature enables real-time feeding of the reservoir, opening a multitude of applications.

This paper reviews the new highly interdisciplinary research field studying the behavior of condensed matter systems exposed to radiation. The paper highlights several relevant examples of recent advances in the field and provides a roadmap for the development of the field in the next decade. Condensed matter systems exposed to radiation may have very different natures, being inorganic, organic or biological, finite or infinite, be composed of many different molecular species or materials, existing in different phases (solid, liquid, gaseous or plasma) and operating under different thermodynamic conditions. The essential and novel element of this research is that, despite the vast diversity of such systems, many of the key phenomena related to the behavior of irradiated systems (such as radiation-induced damage, mechanisms of damage repair and control, radiation protection, etc.) are very similar and can be understood based on the same fundamental theoretical principles and computational approaches. One of the essential features of the aforementioned phenomena concerns their multiscale nature as the manifestation of the radiation-induced effects occurring at different spatial and temporal scales ranging from the atomic to the macroscopic. The multiscale nature of the effects and similarity of their manifestation in systems of different origins necessarily brings together different disciplines, such as physics, chemistry, biology, materials and nano-science, and biomedical research, demonstrating numerous interlinks and commonalities between them. This research field is highly relevant to many novel and emerging technologies and medical applications., Comment: Roadmap paper; 376 pages, 32 figures. Submitted to Chemical Reviews

We study the asymptotic eigenvalue distribution of the Slepian spatiospectral concentration problem within subdomains of the $d$-dimensional unit ball $\mathbb{B}^d$. The clustering of the eigenvalues near zero and one is a well-known phenomenon. Here, we provide an analytical investigation of this phenomenon for two different notions of bandlimit: (a) multivariate polynomials, with the maximal polynomial degree determining the bandlimit, (b) basis functions that separate into radial and spherical contributions (expressed in terms of Jacobi polynomials and spherical harmonics, respectively), with separate maximal degrees for the radial and spherical contributions determining the bandlimit. In particular, we investigate the number of relevant non-zero eigenvalues (the so-called Shannon number) and obtain distinct asymptotic results for both notions of bandlimit, characterized by Jacobi weights $W_0$ and a modification $\widetilde{W_0}$, respectively. The analytic results are illustrated by numerical examples on the 3-d ball.

Subspaces obtained by the orthogonal projection of locally supported square-integrable vector fields onto the Hardy spaces $H_+(\mathbb{S})$ and $H_-(\mathbb{S})$, respectively, play a role in various inverse potential field problems since they characterize the uniquely recoverable components of the underlying sources. Here, we consider approximation in these subspaces by a particular set of spherical basis functions. Error bounds are provided along with further considerations on norm-minimizing vector fields that satisfy the underlying localization constraint. The new aspect here is that the used spherical basis functions are themselves members of the subspaces under consideration.

Given a function in the Hardy space of inner harmonic gradients on the sphere, H+(S), we consider the problem of finding a corresponding function in the Hardy space of outer harmonic gradients on the sphere, H-(S), such that the sum of both functions differs from a locally supported vector field only by a tangential divergence-free contribution. We characterize the subspace of H+(S) that allows such a continuation and show that it is dense but not closed within H+(S). Furthermore, we derive the linear mapping that maps a vector field from this subspace of H+(S) to the corresponding unique vector field in H-(S). The explicit construction uses layer potentials but involves unbounded operators. We indicate some bounded extremal problems supporting a possible numerical evaluation of this mapping between the Hardy components. The original motivation to study this problem comes from an inverse magnetization problem with localization constraints.

Inverse problems arising in (geo)magnetism are typically ill-posed, in particular {they exhibit non-uniqueness}. Nevertheless, there exist nontrivial model spaces on which the problem is uniquely solvable. Our goal is here to describe such spaces that accommodate constraints suited for applications. In this paper we treat the inverse magnetization problem on a Lipschitz domain with fairly general topology. We characterize the subspace of $L^{2}$-vector fields that causes non-uniqueness, and identify a subspace of harmonic gradients on which the inversion becomes unique. This classification has consequences for applications and we present some of them in the context of geo-sciences. In the second part of the paper, we discuss the space of piecewise constant vector fields. This vector space is too large to make the inversion unique. But as we show, it contains a dense subspace in $L^2$ on which the problem becomes uniquely solvable, i.e., magnetizations from this subspace are uniquely determined by their magnetic potential.

For $\partial \Omega$ the boundary of a bounded and connected strongly Lipschitz domain in $\mathbb{R}^{d}$ with $d\geq3$, we prove that any field $f\in L^{2} (\partial \Omega ; \mathbb{R}^{d})$ decomposes, in an unique way, as the sum of three silent vector fields---fields whose magnetic potential vanishes in one or both components of $\mathbb{R}^d\setminus\partial \Omega$. Moreover, this decomposition is orthogonal if and only if $\partial \Omega$ is a sphere. We also show that any $f$ in $L^{2} (\partial \Omega ; \mathbb{R}^{d})$ is uniquely the sum of two silent fields and a Hardy function, in which case the sum is orthogonal regardless of $\partial \Omega$; we express the corresponding orthogonal projections in terms of layer potentials. When $\partial \Omega$ is a sphere, both decompositions coincide and match what has been called the Hardy-Hodge decomposition in the literature.

In Geomagnetism it is of interest to separate the Earth's core magnetic field from the crustal magnetic field. However, measurements by satellites can only sense the sum of the two contributions. In practice, the measured magnetic field is expanded in spherical harmonics and separation into crust and core contribution is achieved empirically, by a sharp cutoff in the spectral domain. In this paper, we derive a mathematical setup in which the two contributions are modeled by harmonic potentials $\Phi_0$ and $\Phi_1$ generated on two different spheres $\mathbb{S}_{R_0}$ (crust) and $\mathbb{S}_{R_1}$ (core) with radii $R_1R_0$, we show that it becomes possible if the magnetization $\mathbf{m}$ generating $\Phi_0$ is localized in a strict subregion of $\mathbb{S}_{R_0}$. Beyond unique recoverability, we show in this case how to numerically reconstruct characteristic features of $\Phi_0$ (e.g., spherical harmonic Fourier coefficients). An alternative way of phrasing the results is that knowledge of $\mathbf{m}$ on a nonempty open subset of $\mathbb{S}_{R_0}$ allows one to perform separation.

Reconstructing magnetizations from measurements of the generated magnetic potential is generally non-unique. The non-uniqueness still remains if one restricts the magnetization to those induced by an ambient magnetic dipole field (i.e., the magnetization is described by a scalar susceptibility and the dipole direction). Here, we investigate the situation under the additional constraint that the susceptibility is either spatially localized in a subregion of the sphere or that it is band-limited. If the dipole direction is known, then the susceptibility is uniquely determined under the spatial localization constraint while it is only determined up to a constant under the the assumption of band-limitedness. If the dipole direction is not known, uniqueness is lost again. However, we show that all dipole directions that could possibly generate the measured magnetic potential need to be zeros of a certain polynomial which can be computed from the given potential. We provide examples of non-uniqueness of the dipole direction and examples on how to find admissible candidates for the dipole direction under the spatial localization constraint.

This paper provides an overview on tools from potential theory on the sphere and some applications in geoscience.

Recovering spherical magnetizations $m$ from magnetic field data in the exterior is a highly non-unique problem. A spherical Hardy-Hodge decomposition supplies information on what contributions of the magnetization $m$ are recoverable but it does not supply geophysically suitable constraints on $m$ that would guarantee uniqueness for the entire magnetization. In this paper, we focus on the case of induced spherical magnetizations and show that uniqueness is guaranteed if one assumes that the magnetization is compactly supported on the sphere. The results are based on ideas presented in Baratchart et al. (2013) for the planar setting., Comment: Minor correction in proof of Theorem 3.2

In many geoscientific applications, multiple noisy observations of different origin need to be combined to improve the reconstruction of a common underlying quantity. This naturally leads to multi-parameter models for which adequate strategies are required to choose a set of 'good' parameters. In this study, we present a fairly general method for choosing such a set of parameters, provided that discrete direct, but maybe noisy, measurements of the underlying quantity are included in the observation data, and the inner product of the reconstruction space can be accurately estimated by the inner product of the discretization space. Then the proposed parameter choice method gives an accuracy that only by an absolute constant multiplier differs from the noise level and the accuracy of the best approximant in the reconstruction and in the discretization spaces.

We provide a space domain oriented separation of magnetic fields into parts generated by sources in the exterior and sources in the interior of a given sphere. The separation itself is well-known in geomagnetic modeling, usually in terms of a spherical harmonic analysis or a wavelet analysis that is spherical harmonic based. In contrast to these frequency oriented methods, we use a more spatially oriented approach in this paper. We derive integral representations with explicitly known convolution kernels. Regularizing these singular kernels allows a multiscale representation of the internal and external contributions to the magnetic field with locally supported wavelets. This representation is applied to a set of CHAMP data for crustal field modeling.