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The growing deployment of low-cost, distributed sensor networks in environmental and biomedical domains has enabled continuous, large-scale health monitoring. However, these systems often face challenges related to degraded data quality caused by sensor drift, noise, and insufficient calibration -- factors that limit their reliability in real-world applications. Traditional machine learning methods for sensor fusion and calibration rely on extensive feature engineering and struggle to capture spatial-temporal dependencies or adapt to distribution shifts across varying deployment conditions. To address these challenges, we propose a novel unsupervised domain adaptation (UDA) method tailored for regression tasks. Our proposed method integrates effectively with Spatial-Temporal Graph Neural Networks and leverages the alignment of perturbed inverse Gram matrices between source and target domains, drawing inspiration from Tikhonov regularization. This approach enables scalable and efficient domain adaptation without requiring labeled data in the target domain. We validate our novel method on real-world datasets from two distinct applications: air quality monitoring and EEG signal reconstruction. Our method achieves state-of-the-art performance which paves the way for more robust and transferable sensor fusion models in both environmental and physiological contexts. Our code is available at https://github.com/EPFL-IMOS/TikUDA.

We introduce a network of coupled oscillators that can learn to solve a classification task from a set of examples -- performing both training and inference through the nonlinear evolution of the system. We accomplish this by combining three key elements to achieve learning: A long-term memory that stores learned responses, analogous to the synapses in biological brains; a short-term memory that stores the neural activations, similar to the firing patterns of neurons; and an evolution law that updates the synapses in response to novel examples, inspired by synaptic plasticity. Achieving all three elements in wave-based information processors such as metamaterials is a significant challenge. Here, we solve it by leveraging the material multistability to implement long-term memory, and harnessing symmetries and thermal noise to realize the learning rule. Our analysis reveals that the learning mechanism, although inspired by synaptic plasticity, also shares parallelisms with bacterial evolution strategies, where mutation rates increase in the presence of noxious stimuli.

In cavity quantum electrodynamics (cQED) and particularly superradiance, emitters are typically assumed to be independent, interacting only through light shared via a common mode. While such photon-mediated interactions lead to a rich spectrum of collective optical effects, direct dipole-dipole interactions within the emitter ensemble are generally viewed as a source of decoherence. Here, we uncover a new role for direct spin-spin interactions as a drive for the superradiant dynamics of a hybrid system of nitrogen-vacancy center spins in diamond coupled to a superconducting microwave cavity. After an initial fast superradiant burst, we observe an unexpected train of subsequent emission pulses followed by quasi-continuous masing for up to one millisecond. We show that this surprising behavior arises from spectral hole refilling, where spin inversion is redistributed into the superradiant window of spins resonant with the cavity. We report measurements that clearly exclude other cQED-related effects, and performed microscopic simulations of up to one million spins, which demonstrate that the observed self-induced masing is indeed driven by dipole-dipole interactions between the spins. These findings open new pathways for exploring complex spin-spin interactions in dense disordered systems and offer possibilities for ultra-narrow linewidth solid-state superradiant masers powered purely by microwave-driven spin control.

In 1995, Kollár conjectured that a smooth complex projective $n$-fold $X$ with generically large fundamental group has Euler characteristic $χ(X, K_X)\geq 0$. In this paper, we prove the conjecture assuming $X$ has linear fundamental group, i.e., there exists a representation $π_1(X)\to {\rm GL}_N(\mathbb{C})$ with finite kernel. We deduce the conjecture by proving a stronger $L^2$ vanishing theorem: for the universal cover $\widetilde{X}$ of such $X$, its $L^2$-Dolbeault cohomology $H_{(2)}^{n,q}(\widetilde{X})=0$ for $q\neq 0$. The main ingredients of the proof are techniques from the linear Shafarevich conjecture along with some analytic methods.

Off-road environments remain significant challenges for autonomous ground vehicles, due to the lack of structured roads and the presence of complex obstacles, such as uneven terrain, vegetation, and occlusions. Traditional perception algorithms, primarily designed for structured environments, often fail in unstructured scenarios. In this paper, traversable area recognition is achieved through semantic scene completion. A novel multimodal method, 3DTTNet, is proposed to generate dense traversable terrain estimations by integrating LiDAR point clouds with monocular images from a forward-facing perspective. By integrating multimodal data, environmental feature extraction is strengthened, which is crucial for accurate terrain modeling in complex terrains. Furthermore, RELLIS-OCC, a dataset with 3D traversable annotations, is introduced, incorporating geometric features such as step height, slope, and unevenness. Through a comprehensive analysis of vehicle obsta cle-crossing conditions and the incorporation of vehicle body structure constraints, four traversability cost labels are generated: lethal, medium-cost, low-cost, and free. Experimental results demonstrate that 3DTTNet outperforms the comparison approaches in 3D traversable area recognition, particularly in off-road environments with irregular geometries and partial occlusions. Specifically, 3DTTNet achieves a 42\% improvement in scene completion IoU compared to other models. The proposed framework is scalable and adaptable to various vehicle platforms, allowing for adjustments to occupancy grid parameters and the integration of advanced dynamic models for traversability cost estimation.