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For manifolds equipped with group actions, we have the following natural question: To what extent does the equivariant cohomology determine the equivariant diffeotype? We resolve this question for Hamiltonian circle actions on compact, connected symplectic four-manifolds. They are equivariantly diffeomorphic if and only if their equivariant cohomology rings are isomorphic as algebras over the equivariant cohomology of a point. In fact, we prove a stronger claim: each isomorphism between their equivariant cohomology rings is induced by an equivariant diffeomorphism., Comment: 23 pages, 6 figures

The interaction between light and matter can be enhanced by spatially concentrating the light field to boost the photon energy density and increasing the photon dwell time to prolong energy transfer between light and matter. Traditionally, strong spatial light localization has been achieved using plasmonics, which, despite its effectiveness, entails ohmic losses. Recent advances in nanostructured dielectrics offer an avenue for achieving strong light confinement without metallic losses. However, previous studies primarily focused on minimizing the optical mode volume without adequately addressing light-matter interactions. Here, we develop a nanolaser that simultaneously localizes the electromagnetic field and excited carriers within the same region of a dielectric nanobridge. This extreme dielectric confinement of both light and matter achieves a mode volume below the diffraction limit and a subwavelength carrier volume without the introduction of lateral quantum confinement, enabling continuous-wave lasing at room-temperature. Moreover, we observe a strong correlation between the mode field and carrier distribution, and unexpectedly, the enhanced mode field localization automatically leads to more pronounced carrier localization, promoting self-alignment of light and matter, which significantly reduces the laser threshold. We quantify the intensified light-matter interaction with a newly proposed interaction volume, which generalizes the concept of mode volume to a broad class of active media. Our work lays the ground for developing ultra-efficient optoelectronic devices by greatly enhancing light-matter interactions through advanced material nanostructuring.

Economic historians have long studied market integration and contagion dynamics during periods of warfare and global stress, but there is a lack of model-based evidence on these phenomena. This paper uses an econometric contagion model, the Diebold-Yilmaz framework, to examine the dynamics of economic shocks across European markets in the early modern period. Our findings suggest that key periods of violent conflicts significantly increased food price spillover across cities, causing widespread disruptions across Europe. We also demonstrate the ability of this framework to capture relevant historical dynamics between the main trade centers of the period., Comment: 20 pages

The main result of this paper is that there is sometimes a triangulated equivalence between $D_Q( A )$, the $Q$-shaped derived category of an algebra $A$, and $D( B )$, the classic derived category of a different algebra $B$. By construction, $D_Q( A )$ consists of $Q$-shaped diagrams of $A$-modules for a suitable small category $Q$. Our result concerns the case where $Q$ consists of shifts of indecomposable projective modules over a self-injective $\mathbb{Z}$-graded algebra $\Lambda$. A notable special case is the result by Iyama, Kato, and Miyachi that $D_N( A )$, the $N$-derived category of $A$, is triangulated equivalent to $D( T_{ N-1 }A )$, the classic derived category of $T_{ N-1 }( A )$, which denotes upper diagonal $( N-1 ) \times ( N-1 )$-matrices over $A$. Several other special cases will also be discussed., Comment: 10 pages

The language technology moonshot moment of Generative, Large Language Models (GLLMs) was not limited to English: These models brought a surge of technological applications, investments and hype to low-resource languages as well. However, the capabilities of these models in languages such as Danish were until recently difficult to verify beyond qualitative demonstrations due to a lack of applicable evaluation corpora. We present a GLLM benchmark to evaluate Danoliteracy, a measure of Danish language and cultural competency, across eight diverse scenarios such Danish citizenship tests and abstractive social media question answering. This limited-size benchmark is found to produce a robust ranking that correlates to human feedback at $\rho \sim 0.8$ with GPT-4 and Claude Opus models achieving the highest rankings. Analyzing these model results across scenarios, we find one strong underlying factor explaining $95\%$ of scenario performance variance for GLLMs in Danish, suggesting a $g$ factor of model consistency in language adaption., Comment: 16 pages, 13 figures, submitted to: NoDaLiDa/Baltic-HLT 2025

Multimodal systems have great potential to assist humans in procedural activities, where people follow instructions to achieve their goals. Despite diverse application scenarios, systems are typically evaluated on traditional classification tasks, e.g., action recognition or temporal action segmentation. In this paper, we present a novel evaluation dataset, ProMQA, to measure system advancements in application-oriented scenarios. ProMQA consists of 401 multimodal procedural QA pairs on user recording of procedural activities coupled with their corresponding instruction. For QA annotation, we take a cost-effective human-LLM collaborative approach, where the existing annotation is augmented with LLM-generated QA pairs that are later verified by humans. We then provide the benchmark results to set the baseline performance on ProMQA. Our experiment reveals a significant gap between human performance and that of current systems, including competitive proprietary multimodal models. We hope our dataset sheds light on new aspects of models' multimodal understanding capabilities., Comment: 18 pages, 11 figures

This paper studies a non-commutative generalisation of Coxeter friezes due to Berenstein and Retakh. It generalises several earlier results to this situation: A formula for frieze determinants, a $T$-path formula expressing the Laurent phenomenon, and results on gluing friezes together. One of our tools is a non-commutative version of the weak friezes introduced by Canakci and Jorgensen., Comment: Updated references. 26 pages and 16 figures

This work presents a novel means for understanding learning dynamics and scaling relations in neural networks. We show that certain measures on the spectrum of the empirical neural tangent kernel, specifically entropy and trace, yield insight into the representations learned by a neural network and how these can be improved through architecture scaling. These results are demonstrated first on test cases before being shown on more complex networks, including transformers, auto-encoders, graph neural networks, and reinforcement learning studies. In testing on a wide range of architectures, we highlight the universal nature of training dynamics and further discuss how it can be used to understand the mechanisms behind learning in neural networks. We identify two such dominant mechanisms present throughout machine learning training. The first, information compression, is seen through a reduction in the entropy of the NTK spectrum during training, and occurs predominantly in small neural networks. The second, coined structure formation, is seen through an increasing entropy and thus, the creation of structure in the neural network representations beyond the prior established by the network at initialization. Due to the ubiquity of the latter in deep neural network architectures and its flexibility in the creation of feature-rich representations, we argue that this form of evolution of the network's entropy be considered the onset of a deep learning regime., Comment: 11 pages, 3 figures

A novel balanced air-biased coherent detection scheme for capturing ultrabroadband terahertz (THz) waveforms is implemented. The balanced detection scheme allows for coherent detection at the full repetition rate of the laser system without requiring bias modulation, signal generators, or lock-in amplifiers while doubling the dynamic range and quadrupling the signal-to-noise ratio compared to conventional air-biased coherent detection. These advantages are achieved by rotating the bias electrodes by 90{\deg} relative to the conventional scheme. With a 1 kHz driving laser, the scheme enables sub-second, high-fidelity waveform acquisition with a continuously moving delay stage, demonstrated by collecting 200 waveforms in 100 s. The balanced detection scheme paves the way for much faster and higher quality 2D ultrabroadband terahertz spectroscopy., Comment: 4 pages, 4 figures

The Mittelman-di Cicco-Walker (MDW) H$\alpha$ Sky Survey is an autonomously-operated and ongoing all-sky imaging survey in the narrowband H$\alpha$ wavelength. The survey was founded by amateur astronomers, and is presented here in its first stage of refinement for rigorous scientific use. Each field is exposed through an H$\alpha$ filter with a 3nm bandwidth for a total of four hours, with a pixel scale of 3.2 arcsec. Here, we introduce the first Data Release of the MDW H$\alpha$ Survey (Data Release 0, or DR0), spanning 238 fields in the region of Orion (~3100 deg$^2$). DR0 includes: calibrated mean fields, star-removed mean fields, a point source catalog matched to Data Release 1 of the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS1) and the INT Galactic Plane Survey (IGAPS), and mosaics.

We study the influence of airborne CO2 on the charge state of carboxylate stabilized polymer latex particles suspended in aqueous electrolytes. We combine conductometric experiments interpreted in terms of Hessinger's conductivity model with Poisson-Boltzmann cell (PBC) model calculations with charge regulation boundary conditions. Without CO2, a minority of the weakly acidic surface groups are dissociated and only a fraction of the total number of counter-ions actually contribute to conductivity. The remaining counter-ions exchange freely with added other ions like Na+, K+ or Cs+. From the PBC-calculations we infer a corresponding pKa of 4.26 as well as a renormalized charge in reasonably good agreement with the number of freely mobile counter-ions. Equilibration of salt- and CO2-free suspensions against ambient air leads to a drastic de-charging, which exceeds by far the expected effects of to dissolved CO2 and its dissociation products. Further, no counter-ion-exchange is observed. To reproduce the experimental findings, we have to assume an effective pKa of 6.48. This direct influence of CO2 on the state of surface group dissociation explains our recent finding of a CO2-induced decrease of the {\zeta}-potential and supports the suggestion of an additional charge regulation caused by molecular CO2. Given the importance of charged surfaces in contact with aqueous electrolytes, we anticipate that our observations bear substantial theoretical challenges and important implications for applications ranging from desalination to bio-membranes., Comment: Submitted to Soft Matter, regular article, 22 pages, 6 figures, 65 references, supplementary material of 8 pages with 7 figures

Protein characterization using nanopore-based devices promises to be a breakthrough method in basic research, diagnostics, and analytics. Current research includes the use of machine learning to achieve this task. In this work, a comprehensive statistical analysis of nanopore current signals is performed and demonstrated to be sufficient for classifying up to 42 peptides with over 70 % accuracy. Two sets of features, the statistical moments and the catch22 set, are compared both in their representations and after training small classifier neural networks. We demonstrate that complex features of the events, captured in both the catch22 set and the central moments, are key in classifying peptides with otherwise similar mean currents. These results highlight the efficacy of purely statistical analysis of nanopore data and suggest a path forward for more sophisticated classification techniques.

In this work, we investigate the shape evolution of rotated, embedded, initially cylindrical grains (with [001] cylinder axis) in Ni under an applied synthetic driving force via molecular dynamics simulations and a continuum, disconnection-based grain boundary migration model. For some initial misorientations, the expanding grains form well-defined, faceted shapes, while for others the shapes remain cylindrical. The embedded grains tend to rotate during grain boundary migration, with the direction of rotation dependent on initial misorientation and direction of growth (expand/shrink). The kinetic shapes, which are bounded by low mobility grain boundary planes, differ from equilibrium shapes (bounded by low energy grain boundaries). The multi-mode disconnection model-based predictions are consistent with the molecular dynamics results for faceting tendency, kinetic grain shape, and grain rotation as a function of misorientation and whether the grains are expanding or contracting. This demonstrates that grain boundary migration and associated grain rotation are mediated by disconnection flow along grain boundaries., Comment: 40 pages, 18 figures

These lecture notes in geometric mechanics are meant to convey insight through clear definitions and workable examples. The lecture format adopted here is intended to convey the immediacy of the taught course and to be useful as a basis for other courses. The lecture notes comprise: AP = Applications of Pure maths, e.g., Noether's theorem: Lie group symmetry of Hamilton's variational principle implies conservation laws for its equations of motion.\smallskip PA = Purifications of Applied maths, e.g., Euler fluid dynamics describes geodesic flow on the manifold of smooth invertible maps acting on the domain of flow. \smallskip Both AP and PA appear here, though the difference is not mentioned. It is left to the reader to decide whether it was AP or PA in each of the lectures containing well over sixty solved exercises. An aspect of modern applications emphasised here is the use of the composition of evolutionary maps for multi-physics, multi-timescale interactions including waves interacting with flows in the Euler--Poincar\'e framework in geophysical fluid dynamics (GFD) for ocean and atmosphere dynamics, and in magnetohydrodynamics (MHD) for applications in plasma physics such as magnetic confinement fusion (MFC) and astrophysical processes such as Alfv\'en waves and gravity waves propagating on the Solar tachocline. The topics covered in each lecture can also be gleaned from its table of contents listed at the onset of each lecture., Comment: Textbook in the form of 31 consecutive lectures. arXiv admin note: substantial text overlap with arXiv:0708.1585

This paper investigates the effects of stochastic variations in bathymetry on the solutions of the thermal quasigeostrophic (TQG) equations. These stochastic perturbations generate a variety of different types of ensemble spread in the solution behaviour whilst also preserving the deterministic Lie Poisson structure and Casimir conservation laws. We numerically compare the solution sensitivity, to another type of structure-preserving stochastic perturbation where instead of bathymetry, the velocity is stochastically perturbed.

Superconductivity and magnetism are antagonistic quantum matter, while their intertwining has long been considered in frustrated-lattice systems1-3. In this work, we utilize scanning tunneling microscopy and muon spin resonance to discover time-reversal symmetry-breaking superconductivity in kagome metal Cs(V,Ta)3Sb5, where the Cooper pairing exhibits magnetism and is modulated by it. In the magnetic channel, we observe spontaneous internal magnetism in a full-gap superconducting state. Under perturbations of inverse magnetic fields, we detect a time-reversal asymmetrical interference of Bogoliubov quasi-particles at a circular vector. At this vector, the pairing gap spontaneously modulates, which is distinct from pair density waves occurring at a point vector and consistent with the theoretical proposal of unusual interference effect under time-reversal symmetry-breaking. The correlation between internal magnetism, Bogoliubov quasi-particles, and pairing modulation provides a chain of experimental clues for time-reversal symmetry-breaking kagome superconductivity., Comment: To appear in Nature Materials (2024)

Graph-based holistic scene representations facilitate surgical workflow understanding and have recently demonstrated significant success. However, this task is often hindered by the limited availability of densely annotated surgical scene data. In this work, we introduce an end-to-end framework for the generation and optimization of surgical scene graphs on a downstream task. Our approach leverages the flexibility of graph-based spectral clustering and the generalization capability of foundation models to generate unsupervised scene graphs with learnable properties. We reinforce the initial spatial graph with sparse temporal connections using local matches between consecutive frames to predict temporally consistent clusters across a temporal neighborhood. By jointly optimizing the spatiotemporal relations and node features of the dynamic scene graph with the downstream task of phase segmentation, we address the costly and annotation-burdensome task of semantic scene comprehension and scene graph generation in surgical videos using only weak surgical phase labels. Further, by incorporating effective intermediate scene representation disentanglement steps within the pipeline, our solution outperforms the SOTA on the CATARACTS dataset by 8% accuracy and 10% F1 score in surgical workflow recognition, Comment: 9 pages, 3 figures, 3 tables, MICCAI GRAIL Workshop paper

Absorption of elastic waves in complex media is commonly found to increase linearly with frequency, for both longitudinal and shear waves. This ubiquitous property is observed in media such as rocks, unconsolidated sediments, and human tissue. Absorption is due to relaxation processes at the level of atomic scales and up to the sub-micron scale of biological materials. The effect of these processes is usually expressed as an integral over relaxation frequencies or relaxation times. Here we argue that these processes are thermally activated. Unusual for ultrasonics and seismics, we can therefore transform the expression for absorption from the frequency or time domains to an integral over an activation energy landscape weighted by an energy distribution. The universal power-law property surprisingly corresponds to a flat activation energy landscape. This is the solution which maximizes entropy or randomness. Therefore the linearly increasing absorption corresponds to the energy landscape with the fewest possible constraints., Comment: 9 pages, 4 figures

This paper treats nonlinear wave current interactions in their simplest form, as an overtaking collision. In one spatial dimension, the paper investigates the collision interaction formulated as an initial value problem of a Burgers bore overtaking solutions of two types of nonlinear wave equations, Korteweg de Vries (KdV) and nonlinear Schrodinger (NLS). The bore wave state arising after the overtaking Burgers-KdV collision in numerical simulations is found to depend qualitatively on the balance between nonlinearity and dispersion in the KdV equation. The Burgers-KdV system is also made stochastic by following the stochastic advection by Lie transport approach (SALT)., Comment: 16 pages, 4 figures, 1st version

Cosmological emulators of observables such as the Cosmic Microwave Background (CMB) spectra and matter power spectra commonly use training data sampled from a Latin hypercube. This method often incurs high computational costs by covering less relevant parts of the parameter space, especially in high dimensions where only a small fraction of the parameter space yields a significant likelihood. In this paper, we introduce hypersphere sampling, which instead concentrates sample points in regions with higher likelihoods, significantly enhancing the efficiency and accuracy of emulators. A novel algorithm for sampling within a high-dimensional hyperellipsoid aligned with axes of correlation in the cosmological parameters is presented. This method focuses the distribution of training data points on areas of the parameter space that are most relevant to the models being tested, thereby avoiding the computational redundancies common in Latin hypercube approaches. Comparative analysis using the \textsc{connect} emulation tool demonstrates that hypersphere sampling can achieve similar or improved emulation precision with more than an order of magnitude fewer data points and thus less computational effort than traditional methods. This was tested for both the $\Lambda$CDM model and a 5-parameter extension including Early Dark Energy, massive neutrinos, and additional ultra-relativistic degrees of freedom. Our results suggest that hypersphere sampling holds potential as a more efficient approach for cosmological emulation, particularly suitable for complex, high-dimensional models., Comment: 22 pages, 10 figures