We present a numerical method for computing the logarithmic capacity of compact subsets of $\mathbb{C}$, which are bounded by Jordan curves and have finitely connected complement. The subsets may have several components and need not have any special symmetry. The method relies on the conformal map onto lemniscatic domains and, computationally, on the solution of a boundary integral equation with the Neumann kernel. Our numerical examples indicate that the method is fast and accurate. We apply it to give an estimate of the logarithmic capacity of the Cantor middle third set and generalizations of it.

We evaluate methods for causal representation learning (CRL) on a simple, real-world system where these methods are expected to work. The system consists of a controlled optical experiment specifically built for this purpose, which satisfies the core assumptions of CRL and where the underlying causal factors (the inputs to the experiment) are known, providing a ground truth. We select methods representative of different approaches to CRL and find that they all fail to recover the underlying causal factors. To understand the failure modes of the evaluated algorithms, we perform an ablation on the data by substituting the real data-generating process with a simpler synthetic equivalent. The results reveal a reproducibility problem, as most methods already fail on this synthetic ablation despite its simple data-generating process. Additionally, we observe that common assumptions on the mixing function are crucial for the performance of some of the methods but do not hold in the real data. Our efforts highlight the contrast between the theoretical promise of the state of the art and the challenges in its application. We hope the benchmark serves as a simple, real-world sanity check to further develop and validate methodology, bridging the gap towards CRL methods that work in practice. We make all code and datasets publicly available at github.com/simonbing/CRLSanityCheck

The development of continual learning (CL) methods, which aim to learn new tasks in a sequential manner from the training data acquired continuously, has gained great attention in remote sensing (RS). The existing CL methods in RS, while learning new tasks, enhance robustness towards catastrophic forgetting. This is achieved by using a large number of labeled training samples, which is costly and not always feasible to gather in RS. To address this problem, we propose a novel continual self-supervised learning method in the context of masked autoencoders (denoted as CoSMAE). The proposed CoSMAE consists of two components: i) data mixup; and ii) model mixup knowledge distillation. Data mixup is associated with retaining information on previous data distributions by interpolating images from the current task with those from the previous tasks. Model mixup knowledge distillation is associated with distilling knowledge from past models and the current model simultaneously by interpolating their model weights to form a teacher for the knowledge distillation. The two components complement each other to regularize the MAE at the data and model levels to facilitate better generalization across tasks and reduce the risk of catastrophic forgetting. Experimental results show that CoSMAE achieves significant improvements of up to 4.94% over state-of-the-art CL methods applied to MAE. Our code is publicly available at: this https URL.

With the rapid growth of hyperspectral data archives in remote sensing (RS), the need for efficient storage has become essential, driving significant attention toward learning-based hyperspectral image (HSI) compression. However, a comprehensive investigation of the individual and joint effects of spectral and spatial compression on learning-based HSI compression has not been thoroughly examined yet. Conducting such an analysis is crucial for understanding how the exploitation of spectral, spatial, and joint spatio-spectral redundancies affects HSI compression. To address this issue, we propose Adjustable Spatio-Spectral Hyperspectral Image Compression Network (HyCASS), a learning-based model designed for adjustable HSI compression in both spectral and spatial dimensions. HyCASS consists of six main modules: 1) spectral encoder module; 2) spatial encoder module; 3) compression ratio (CR) adapter encoder module; 4) CR adapter decoder module; 5) spatial decoder module; and 6) spectral decoder module. The modules employ convolutional layers and transformer blocks to capture both short-range and long-range redundancies. Experimental results on three HSI benchmark datasets demonstrate the effectiveness of our proposed adjustable model compared to existing learning-based compression models, surpassing the state of the art by up to 2.36 dB in terms of PSNR. Based on our results, we establish a guideline for effectively balancing spectral and spatial compression across different CRs, taking into account the spatial resolution of the HSIs. Our code and pre-trained model weights are publicly available at this https URL .

Barnette's Conjecture claims that all cubic, 3-connected, planar, bipartite graphs are Hamiltonian. We give a translation of this conjecture into the matching-theoretic setting. This allows us to relax the requirement of planarity to give the equivalent conjecture that all cubic, 3-connected, Pfaffian, bipartite graphs are Hamiltonian. A graph, other than the path of length three, is a brace if it is bipartite and any two disjoint edges are part of a perfect matching. Our perspective allows us to observe that Barnette's Conjecture can be reduced to cubic, planar braces. We show a similar reduction to braces for cubic, 3-connected, bipartite graphs regarding four stronger versions of Hamiltonicity. Note that in these cases we do not need planarity. As a practical application of these results, we provide some supplements to a generation procedure for cubic, 3-connected, planar, bipartite graphs discovered by Holton et al. [Hamiltonian Cycles in Cubic 3-Connected Bipartite Planar Graphs, JCTB, 1985]. These allow us to check whether a graph we generated is a brace.

Trajectory prediction is an essential task for successful human robot interaction, such as in autonomous driving. In this work, we address the problem of predicting future pedestrian trajectories in a first person view setting with a moving camera. To that end, we propose a novel action-based contrastive learning loss, that utilizes pedestrian action information to improve the learned trajectory embeddings. The fundamental idea behind this new loss is that trajectories of pedestrians performing the same action should be closer to each other in the feature space than the trajectories of pedestrians with significantly different actions. In other words, we argue that behavioral information about pedestrian action influences their future trajectory. Furthermore, we introduce a novel sampling strategy for trajectories that is able to effectively increase negative and positive contrastive samples. Additional synthetic trajectory samples are generated using a trained Conditional Variational Autoencoder (CVAE), which is at the core of several models developed for trajectory prediction. Results show that our proposed contrastive framework employs contextual information about pedestrian behavior, i.e. action, effectively, and it learns a better trajectory representation. Thus, integrating the proposed contrastive framework within a trajectory prediction model improves its results and outperforms state-of-the-art methods on three trajectory prediction benchmarks [31, 32, 26].

We demonstrate that a three dimensional time-periodically driven (Floquet) lattice can exhibit chiral hinge states and describe their interplay with Weyl physics. A peculiar type of the hinge states are enforced by the repeated boundary reflections with lateral Goos-Hänchen like shifts occurring at the second-order boundaries of our system. Such chiral hinge modes coexist in a wide range of parameters regimes with Fermi arc surface states connecting a pair of Weyl points in a two-band model. We find numerically that these modes still preserve their locality along the hinge and their chiral nature in the presence of local defects and other parameter changes. We trace the robustness of such chiral hinge modes to special band structure unique in a Floquet system allowing all the eigenstates to be localized in quasi-one-dimensional regions parallel to each other when open hinge boundaries are introduced. The implementation of a model featuring both the second-order Floquet skin effect and the Weyl physics is straightforward with ultracold atoms in optical superlattices.

High-dimensional partial differential equations (PDEs) are ubiquitous in economics, science and engineering. However, their numerical treatment poses formidable challenges since traditional grid-based methods tend to be frustrated by the curse of dimensionality. In this paper, we argue that tensor trains provide an appealing approximation framework for parabolic PDEs: the combination of reformulations in terms of backward stochastic differential equations and regression-type methods in the tensor format holds the promise of leveraging latent low-rank structures enabling both compression and efficient computation. Following this paradigm, we develop novel iterative schemes, involving either explicit and fast or implicit and accurate updates. We demonstrate in a number of examples that our methods achieve a favorable trade-off between accuracy and computational efficiency in comparison with state-of-the-art neural network based approaches.

We present a dataset with models of 14 articulated objects commonly found in human environments and with RGB-D video sequences and wrenches recorded of human interactions with them. The 358 interaction sequences total 67 minutes of human manipulation under varying experimental conditions (type of interaction, lighting, perspective, and background). Each interaction with an object is annotated with the ground truth poses of its rigid parts and the kinematic state obtained by a motion capture system. For a subset of 78 sequences (25 minutes), we also measured the interaction wrenches. The object models contain textured three-dimensional triangle meshes of each link and their motion constraints. We provide Python scripts to download and visualize the data. The data is available at this https URL and hosted at this https URL

Quantum computing holds immense potential, yet its practical success depends on multiple factors, including advances in quantum circuit design. In this paper, we introduce a generative approach based on denoising diffusion models (DMs) to synthesize parameterized quantum circuits (PQCs). Extending the recent diffusion model pipeline of Fürrutter et al. [1], our model effectively conditions the synthesis process, enabling the simultaneous generation of circuit architectures and their continuous gate parameters. We demonstrate our approach in synthesizing PQCs optimized for generating high-fidelity Greenberger-Horne-Zeilinger (GHZ) states and achieving high accuracy in quantum machine learning (QML) classification tasks. Our results indicate a strong generalization across varying gate sets and scaling qubit counts, highlighting the versatility and computational efficiency of diffusion-based methods. This work illustrates the potential of generative models as a powerful tool for accelerating and optimizing the design of PQCs, supporting the development of more practical and scalable quantum applications.

Interactive simulation toolkits come in handy when teaching macroeconomic models by facilitating an easy understanding of underlying economic concepts and offering an intuitive approach to the models' comparative statics. Based on the example of the IS-LM model, this paper demonstrates innovative browser-based features well-suited for the shift in education to online platforms accelerated by COVID-19. The free and open-source code can be found alongside the standalone HTML files for the AD-AS and the Solow growth model at this https URL.

We present a quantum extension of a version of Sanov's theorem focussing on a hypothesis testing aspect of the theorem: There exists a sequence of typical subspaces for a given set $\Psi$ of stationary quantum product states asymptotically separating them from another fixed stationary product state. Analogously to the classical case, the exponential separating rate is equal to the infimum of the quantum relative entropy with respect to the quantum reference state over the set $\Psi$. However, while in the classical case the separating subsets can be chosen universal, in the sense that they depend only on the chosen set of i.i.d. processes, in the quantum case the choice of the separating subspaces depends additionally on the reference state.

The apparent invariance of the strong nuclear force under combined charge conjugation and parity (CP) remains an open question in modern physics. Precision experiments with heavy atoms and molecules can provide stringent constraints on CP violation via searches for effects due to permanent electric dipole moments and other CP-odd properties in leptons, hadrons, and nuclei. Radioactive molecules have been proposed as highly sensitive probes for such searches, but experiments with most such molecules have so far been beyond technical reach. Here we report the first production and spectroscopic study of a gas-phase actinium molecule, $^{227}$AcF. We observe the predicted strongest electronic transition from the ground state, which is necessary for efficient readout in searches of symmetry-violating interactions. Furthermore, we perform electronic- and nuclear-structure calculations for $^{227}$AcF to determine its sensitivity to various CP-violating parameters, and find that a realistic, near-term experiment with a precision of 1 mHz would improve current constraints on the CP-violating parameter hyperspace by three orders of magnitude. Our results thus highlight the potential of $^{227}$AcF for exceptionally sensitive searches of CP violation.

The Gromov--Wasserstein (GW) distance and its fused extension (FGW) are powerful tools for comparing heterogeneous data. Their computation is, however, challenging since both distances are based on non-convex, quadratic optimal transport (OT) problems. Leveraging 1D OT, a sliced version of GW has been proposed to lower the computational burden. Unfortunately, this sliced version is restricted to Euclidean geometry and loses invariance to isometries, strongly limiting its application in practice. To overcome these issues, we propose a novel slicing technique for GW as well as for FGW that is based on an appropriate lower bound, hierarchical OT, and suitable quadrature rules for the underlying 1D OT problems. Our novel sliced FGW significantly reduces the numerical effort while remaining invariant to isometric transformations and allowing the comparison of arbitrary geometries. We show that our new distance actually defines a pseudo-metric for structured spaces that bounds FGW from below and study its interpolation properties between sliced Wasserstein and GW. Since we avoid the underlying quadratic program, our sliced distance is numerically more robust and reliable than the original GW and FGW distance; especially in the context of shape retrieval and graph isomorphism testing.

Lyapunov functions play a vital role in the context of control theory for nonlinear dynamical systems. Besides its classical use for stability analysis, Lyapunov functions also arise in iterative schemes for computing optimal feedback laws such as the well-known policy iteration. In this manuscript, the focus is on the Lyapunov function of a nonlinear autonomous finite-dimensional dynamical system which will be rewritten as an infinite-dimensional linear system using the Koopman or composition operator. Since this infinite-dimensional system has the structure of a weak-* continuous semigroup, in a specially weighted $\mathrm{L}^p$-space one can establish a connection between the solution of an operator Lyapunov equation and the desired Lyapunov function. It will be shown that the solution to this operator equation attains a rapid eigenvalue decay which justifies finite rank approximations with numerical methods. The potential benefit for numerical computations will be demonstrated with two short examples.

We present high-quality reference data for two fundamentally important groups of molecular properties related to a compound's utility as a lithium battery electrolyte. The first one is energy changes associated with charge excitations of molecules, namely ionization potential and electron affinity. They were estimated for 7000 randomly chosen molecules with up to 9 non-hydrogen atoms C, N, O, and F (QM9 dataset) using DH-HF, DF-HF-CABS, PNO-LMP2-F12, and PNO-LCCSD(T)-F12 methods as implemented in Molpro software with aug-cc-pVTZ basis set; additionally, we provide the corresponding atomization energies at these levels of theory, as well as CPU time and disk space used during the calculations. The second one is solvation energies for 39 different solvents, which we estimate for 18361 molecules connected to battery design (Electrolyte Genome Project dataset), 309463 randomly chosen molecules with up to 17 non-hydrogen atoms C, N, O, S, and halogens (GDB17 dataset), as well as 88418 amons of ZINC database of commercially available compounds and 37772 amons of GDB17. For these calculations we used the COnductor-like Screening MOdel for Real Solvents (COSMO-RS) method; we additionally provide estimates of gas-phase atomization energies, as well as information about conformers considered during the COSMO-RS calculations, namely coordinates, energies, and dipole moments.

Fluid antenna (FA) technology has emerged as a promising approach in wireless communications due to its capability of providing increased degrees of freedom (DoFs) and exceptional design flexibility. This paper addresses the challenge of direction-of-arrival (DOA) estimation for aligned received signals (ARS) and non-aligned received signals (NARS) by designing two specialized uniform FA structures under time-constrained mobility. For ARS scenarios, we propose a fully movable antenna configuration that maximizes the virtual array aperture, whereas for NARS scenarios, we design a structure incorporating a fixed reference antenna to reliably extract phase information from the signal covariance. To overcome the limitations of large virtual arrays and limited sample data inherent in time-varying channels (TVC), we introduce two novel DOA estimation methods: TMRLS-MUSIC for ARS, combining Toeplitz matrix reconstruction (TMR) with linear shrinkage (LS) estimation, and TMR-MUSIC for NARS, utilizing sub-covariance matrices to construct virtual array responses. Both methods employ Nystrom approximation to significantly reduce computational complexity while maintaining estimation accuracy. Theoretical analyses and extensive simulation results demonstrate that the proposed methods achieve underdetermined DOA estimation using minimal FA elements, outperform conventional methods in estimation accuracy, and substantially reduce computational complexity.

Climate models are essential to understand and project climate change, yet long-standing biases and uncertainties in their projections remain. This is largely associated with the representation of subgrid-scale processes, particularly clouds and convection. Deep learning can learn these subgrid-scale processes from computationally expensive storm-resolving models while retaining many features at a fraction of computational cost. Yet, climate simulations with embedded neural network parameterizations are still challenging and highly depend on the deep learning solution. This is likely associated with spurious non-physical correlations learned by the neural networks due to the complexity of the physical dynamical system. Here, we show that the combination of causality with deep learning helps removing spurious correlations and optimizing the neural network algorithm. To resolve this, we apply a causal discovery method to unveil causal drivers in the set of input predictors of atmospheric subgrid-scale processes of a superparameterized climate model in which deep convection is explicitly resolved. The resulting causally-informed neural networks are coupled to the climate model, hence, replacing the superparameterization and radiation scheme. We show that the climate simulations with causally-informed neural network parameterizations retain many convection-related properties and accurately generate the climate of the original high-resolution climate model, while retaining similar generalization capabilities to unseen climates compared to the non-causal approach. The combination of causal discovery and deep learning is a new and promising approach that leads to stable and more trustworthy climate simulations and paves the way towards more physically-based causal deep learning approaches also in other scientific disciplines.