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Approaches based on Koopman operators have shown great promise in forecasting time series data generated by complex nonlinear dynamical systems (NLDS). Although such approaches are able to capture the latent state representation of a NLDS, they still face difficulty in long term forecasting when applied to real world data. Specifically many real-world NLDS exhibit time-varying behavior, leading to nonstationarity that is hard to capture with such models. Furthermore they lack a systematic data-driven approach to perform data assimilation, that is, exploiting noisy measurements on the fly in the forecasting task. To alleviate the above issues, we propose a Koopman operator-based approach (named KODA - Koopman Operator with Data Assimilation) that integrates forecasting and data assimilation in NLDS. In particular we use a Fourier domain filter to disentangle the data into a physical component whose dynamics can be accurately represented by a Koopman operator, and residual dynamics that represents the local or time varying behavior that are captured by a flexible and learnable recursive model. We carefully design an architecture and training criterion that ensures this decomposition lead to stable and long-term forecasts. Moreover, we introduce a course correction strategy to perform data assimilation with new measurements at inference time. The proposed approach is completely data-driven and can be learned end-to-end. Through extensive experimental comparisons we show that KODA outperforms existing state of the art methods on multiple time series benchmarks such as electricity, temperature, weather, lorenz 63 and duffing oscillator demonstrating its superior performance and efficacy along the three tasks a) forecasting, b) data assimilation and c) state prediction.

Hyperspectral image (HI) analysis approaches have recently become increasingly complex and sophisticated. Recently, the combination of spectral-spatial information and superpixel techniques have addressed some hyperspectral data issues, such as the higher spatial variability of spectral signatures and dimensionality of the data. However, most existing superpixel approaches do not account for specific HI characteristics resulting from its high spectral dimension. In this work, we propose a multiscale superpixel method that is computationally efficient for processing hyperspectral data. The Simple Linear Iterative Clustering (SLIC) oversegmentation algorithm, on which the technique is based, has been extended hierarchically. Using a novel robust homogeneity testing, the proposed hierarchical approach leads to superpixels of variable sizes but with higher spectral homogeneity when compared to the classical SLIC segmentation. For validation, the proposed homogeneity-based hierarchical method was applied as a preprocessing step in the spectral unmixing and classification tasks carried out using, respectively, the Multiscale sparse Unmixing Algorithm (MUA) and the CNN-Enhanced Graph Convolutional Network (CEGCN) methods. Simulation results with both synthetic and real data show that the technique is competitive with state-of-the-art solutions.

Qubits that can be efficiently controlled are essential for the development of scalable quantum hardware. While resonant control is used to execute high-fidelity quantum gates, the scalability is challenged by the integration of high-frequency oscillating signals, qubit crosstalk and heating. Here, we show that by engineering the hopping of spins between quantum dots with site-dependent spin quantization axis, quantum control can be established with discrete signals. We demonstrate hopping-based quantum logic and obtain single-qubit gate fidelities of 99.97\%, coherent shuttling fidelities of 99.992\% per hop, and a two-qubit gate fidelity of 99.3\%, corresponding to error rates that have been predicted to allow for quantum error correction. We also show that hopping spins constitute a tuning method by statistically mapping the coherence of a 10-quantum dot system. Our results show that dense quantum dot arrays with sparse occupation could be developed for efficient and high-connectivity qubit registers., Comment: main text with 18 pages and 3 figures, supplementary materials with 64 pages and 26 figures, in a single file

Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based solutions face important challenges when dealing with spatio-temporal PDEs over long time scales. Specifically, the current theory of NOs does not present a systematic framework to perform data assimilation and efficiently correct the evolution of PDE solutions over time based on sparsely sampled noisy measurements. In this paper, we propose a learning-based state-space approach to compute the solution operators to infinite-dimensional semilinear PDEs. Exploiting the structure of semilinear PDEs and the theory of nonlinear observers in function spaces, we develop a flexible recursive method that allows for both prediction and data assimilation by combining prediction and correction operations. The proposed framework is capable of producing fast and accurate predictions over long time horizons, dealing with irregularly sampled noisy measurements to correct the solution, and benefits from the decoupling between the spatial and temporal dynamics of this class of PDEs. We show through experiments on the Kuramoto-Sivashinsky, Navier-Stokes and Korteweg-de Vries equations that the proposed model is robust to noise and can leverage arbitrary amounts of measurements to correct its prediction over a long time horizon with little computational overhead., Comment: ICLR 2024

In hyperspectral sparse unmixing, a successful approach employs spectral bundles to address the variability of the endmembers in the spatial domain. However, the regularization penalties usually employed aggregate substantial computational complexity, and the solutions are very noise-sensitive. We generalize a multiscale spatial regularization approach to solve the unmixing problem by incorporating group sparsity-inducing mixed norms. Then, we propose a noise-robust method that can take advantage of the bundle structure to deal with endmember variability while ensuring inter- and intra-class sparsity in abundance estimation with reasonable computational cost. We also present a general heuristic to select the \emph{most representative} abundance estimation over multiple runs of the unmixing process, yielding a solution that is robust and highly reproducible. Experiments illustrate the robustness and consistency of the results when compared to related methods.

Although considerable effort has been dedicated to improving the solution to the hyperspectral unmixing problem, non-idealities such as complex radiation scattering and endmember variability negatively impact the performance of most existing algorithms and can be very challenging to address. Recently, deep learning-based frameworks have been explored for hyperspectral umixing due to their flexibility and powerful representation capabilities. However, such techniques either do not address the non-idealities of the unmixing problem, or rely on black-box models which are not interpretable. In this paper, we propose a new interpretable deep learning method for hyperspectral unmixing that accounts for nonlinearity and endmember variability. The proposed method leverages a probabilistic variational deep-learning framework, where disentanglement learning is employed to properly separate the abundances and endmembers. The model is learned end-to-end using stochastic backpropagation, and trained using a self-supervised strategy which leverages benefits from semi-supervised learning techniques. Furthermore, the model is carefully designed to provide a high degree of interpretability. This includes modeling the abundances as a Dirichlet distribution, the endmembers using low-dimensional deep latent variable representations, and using two-stream neural networks composed of additive piecewise-linear/nonlinear components. Experimental results on synthetic and real datasets illustrate the performance of the proposed method compared to state-of-the-art algorithms.

Electrically-driven spin resonance is a powerful technique for controlling semiconductor spin qubits. However, it faces challenges in qubit addressability and off-resonance driving in larger systems. We demonstrate coherent bichromatic Rabi control of quantum dot hole spin qubits, offering a spatially-selective approach for large qubit arrays. By applying simultaneous microwave bursts to different gate electrodes, we observe multichromatic resonance lines and resonance anticrossings that are caused by the ac Stark shift. Our theoretical framework aligns with experimental data, highlighting interdot motion as the dominant mechanism for bichromatic driving., Comment: 5 pages, 4 figures

Semiconductor spin qubits have gained increasing attention as a possible platform to host a fault-tolerant quantum computer. First demonstrations of spin qubit arrays have been shown in a wide variety of semiconductor materials. The highest performance for spin qubit logic has been realized in silicon, but scaling silicon quantum dot arrays in two dimensions has proven to be challenging. By taking advantage of high-quality heterostructures and carefully designed gate patterns, we are able to form a tunnel coupled 2 $\times$ 2 quantum dot array in a $^{28}$Si/SiGe heterostructure. We are able to load a single electron in all four quantum dots, thus reaching the (1,1,1,1) charge state. Furthermore we characterise and control the tunnel coupling between all pairs of dots by measuring polarisation lines over a wide range of barrier gate voltages. Tunnel couplings can be tuned from about $30~\rm \mu eV$ up to approximately $400~\rm \mu eV$. These experiments provide a first step toward the operation of spin qubits in $^{28}$Si/SiGe quantum dots in two dimensions., Comment: 8 pages, 6 figures

Multitemporal hyperspectral unmixing (MTHU) is a fundamental tool in the analysis of hyperspectral image sequences. It reveals the dynamical evolution of the materials (endmembers) and of their proportions (abundances) in a given scene. However, adequately accounting for the spatial and temporal variability of the endmembers in MTHU is challenging, and has not been fully addressed so far in unsupervised frameworks. In this work, we propose an unsupervised MTHU algorithm based on variational recurrent neural networks. First, a stochastic model is proposed to represent both the dynamical evolution of the endmembers and their abundances, as well as the mixing process. Moreover, a new model based on a low-dimensional parametrization is used to represent spatial and temporal endmember variability, significantly reducing the amount of variables to be estimated. We propose to formulate MTHU as a Bayesian inference problem. However, the solution to this problem does not have an analytical solution due to the nonlinearity and non-Gaussianity of the model. Thus, we propose a solution based on deep variational inference, in which the posterior distribution of the estimated abundances and endmembers is represented by using a combination of recurrent neural networks and a physically motivated model. The parameters of the model are learned using stochastic backpropagation. Experimental results show that the proposed method outperforms state of the art MTHU algorithms.

Real-time satellite imaging has a central role in monitoring, detecting and estimating the intensity of key natural phenomena such as floods, earthquakes, etc. One important constraint of satellite imaging is the trade-off between spatial/spectral resolution and their revisiting time, a consequence of design and physical constraints imposed by satellite orbit among other technical limitations. In this paper, we focus on fusing multi-temporal, multi-spectral images where data acquired from different instruments with different spatial resolutions is used. We leverage the spatial relationship between images at multiple modalities to generate high-resolution image sequences at higher revisiting rates. To achieve this goal, we formulate the fusion method as a recursive state estimation problem and study its performance in filtering and smoothing contexts. Furthermore, a calibration strategy is proposed to estimate the time-varying temporal dynamics of the image sequence using only a small amount of historical image data. Differently from the training process in traditional machine learning algorithms, which usually require large datasets and computation times, the parameters of the temporal dynamical model are calibrated based on an analytical expression that uses only two of the images in the historical dataset. A distributed version of the Bayesian filtering and smoothing strategies is also proposed to reduce its computational complexity. To evaluate the proposed methodology we consider a water mapping task where real data acquired by the Landsat and MODIS instruments are fused generating high spatial-temporal resolution image estimates. Our experiments show that the proposed methodology outperforms the competing methods in both estimation accuracy and water mapping tasks., Comment: arXiv admin note: substantial text overlap with arXiv:2204.12566

Despite the extensive body of literature focused on remote sensing applications for land cover mapping and the availability of high-resolution satellite imagery, methods for continuously updating classification maps in real-time remain limited, especially when training data is scarce. This paper introduces the Recursive Bayesian Classifier (RBC), which converts any instantaneous classifier into a robust online method through a probabilistic framework that is resilient to non-informative image variations. Three experiments are conducted using Sentinel-2 data: water mapping of the Oroville Dam in California and the Charles River basin in Massachusetts, and deforestation detection in the Amazon. RBC is applied to a Gaussian Mixture Model (GMM), Logistic Regression (LR), and our proposed Spectral Index Classifier (SIC). Results show that RBC significantly enhances classifier robustness in multitemporal settings under challenging conditions, such as cloud cover and cyanobacterial blooms. Specifically, balanced classification accuracy improves by up to 26.95% for SIC, 12.4% for GMM, and 13.81% for LR in water mapping, and by 15.25%, 14.17%, and 14.7% in deforestation detection. Moreover, without additional training data, RBC improves the performance of the state-of-the-art DeepWaterMap and WatNet algorithms by up to 9.62% and 11.03%. These benefits are provided by RBC while requiring minimal supervision and maintaining a low computational cost that remains constant for each time step regardless of the time-series length., Comment: Without supplemental results: 31 pages, 16 figures, 5 tables. With supplemental results: 35 pages, 20 figures, 5 tables

Discovering components that are shared in multiple datasets, next to dataset-specific features, has great potential for studying the relationships between different subjects or tasks in functional Magnetic Resonance Imaging (fMRI) data. Coupled matrix and tensor factorization approaches have been useful for flexible data fusion, or decomposition to extract features that can be used in multiple ways. However, existing methods do not directly recover shared and dataset-specific components, which requires post-processing steps involving additional hyperparameter selection. In this paper, we propose a tensor-based framework for multi-task fMRI data fusion, using a partially constrained canonical polyadic (CP) decomposition model. Differently from previous approaches, the proposed method directly recovers shared and dataset-specific components, leading to results that are directly interpretable. A strategy to select a highly reproducible solution to the decomposition is also proposed. We evaluate the proposed methodology on real fMRI data of three tasks, and show that the proposed method finds meaningful components that clearly identify group differences between patients with schizophrenia and healthy controls.

Highly uniform quantum systems are essential for the practical implementation of scalable quantum processors. While quantum dot spin qubits based on semiconductor technology are a promising platform for large-scale quantum computing, their small size makes them particularly sensitive to their local environment. Here, we present a method to electrically obtain a high degree of uniformity in the intrinsic potential landscape using hysteretic shifts of the gate voltage characteristics. We demonstrate the tuning of pinch-off voltages in quantum dot devices over hundreds of millivolts that then remain stable at least for hours. Applying our method, we homogenize the pinch-off voltages of the plunger gates in a linear array for four quantum dots reducing the spread in pinch-off voltage by one order of magnitude. This work provides a new tool for the tuning of quantum dot devices and offers new perspectives for the implementation of scalable spin qubit arrays.

Semiconducting nanowire Josephson junctions represent an attractive platform to investigate the anomalous Josephson effect and detect topological superconductivity by studying Josephson supercurrent. However, an external magnetic field generally suppresses the supercurrent through hybrid nanowire junctions and significantly limits the field range in which the supercurrent phenomena can be studied. In this work, we investigate the impact of the length of InSb-Al nanowire Josephson junctions on the supercurrent resilience against magnetic fields. We find that the critical parallel field of the supercurrent can be considerably enhanced by reducing the junction length. Particularly, in 30 nm-long junctions supercurrent can persist up to 1.3 T parallel field - approaching the critical field of the superconducting film. Furthermore, we embed such short junctions into a superconducting loop and obtain the supercurrent interference at a parallel field of 1 T. Our findings are highly relevant for multiple experiments on hybrid nanowires requiring a magnetic field-resilient supercurrent., Comment: 17 pages, 5 figures in main text. 22 pages, 10 figures in supporting information

The efficient control of a large number of qubits is one of most challenging aspects for practical quantum computing. Current approaches in solid-state quantum technology are based on brute-force methods, where each and every qubit requires at least one unique control line, an approach that will become unsustainable when scaling to the required millions of qubits. Here, inspired by random access architectures in classical electronics, we introduce the shared control of semiconductor quantum dots to efficiently operate a two-dimensional crossbar array in planar germanium. We tune the entire array, comprising 16 quantum dots, to the few-hole regime and, to isolate an unpaired spin per dot, we confine an odd number of holes in each site. Moving forward, we establish a method for the selective control of the quantum dots interdot coupling and achieve a tunnel coupling tunability over more than 10 GHz. The operation of a quantum electronic device with fewer control terminals than tunable experimental parameters represents a compelling step forward in the construction of scalable quantum technology., Comment: 33 pages including supplementary information

Hyperspectral and multispectral image fusion allows us to overcome the hardware limitations of hyperspectral imaging systems inherent to their lower spatial resolution. Nevertheless, existing algorithms usually fail to consider realistic image acquisition conditions. This paper presents a general imaging model that considers inter-image variability of data from heterogeneous sources and flexible image priors. The fusion problem is stated as an optimization problem in the maximum a posteriori framework. We introduce an original image fusion method that, on the one hand, solves the optimization problem accounting for inter-image variability with an iteratively reweighted scheme and, on the other hand, that leverages light-weight CNN-based networks to learn realistic image priors from data. In addition, we propose a zero-shot strategy to directly learn the image-specific prior of the latent images in an unsupervised manner. The performance of the algorithm is illustrated with real data subject to inter-image variability., Comment: IEEE Trans. Geosci. Remote sens., to be published. Manuscript submitted August 23, 2022; revised Dec. 15, 2022, and Mar. 13, 2023; and accepted Apr. 07, 2023

The co-integration of spin, superconducting, and topological systems is emerging as an exciting pathway for scalable and high-fidelity quantum information technology. High-mobility planar germanium is a front-runner semiconductor for building quantum processors with spin-qubits, but progress with hybrid superconductor-semiconductor devices is hindered because obtaining a superconducting gap free of subgap states (hard gap) has proven difficult. Here we solve this challenge by developing a low-disorder, oxide-free interface between high-mobility planar germanium and a germanosilicide parent superconductor. This superconducting contact is formed by the thermally-activated solid phase reaction between a metal (Pt) and the semiconductor heterostructure (Ge/SiGe). Electrical characterization reveals near-unity transparency in Josephson junctions and, importantly, a hard induced superconducting gap in quantum point contacts. Furthermore, we demonstrate phase control of a Josephson junction and study transport in a gated two-dimensional superconductor-semiconductor array towards scalable architectures. These results expand the quantum technology toolbox in germanium and provide new avenues for exploring monolithic superconductor-semiconductor quantum circuits towards scalable quantum information processing.

Satellite imaging has a central role in monitoring, detecting and estimating the intensity of key natural phenomena. One important feature of satellite images is the trade-off between spatial/spectral resolution and their revisiting time, a consequence of design and physical constraints imposed by satellite orbit among other technical limitations. In this paper, we focus on fusing multi-temporal, multi-spectral images where data acquired from different instruments with different spatial resolutions is used. We leverage the spatial relationship between images at multiple modalities to generate high-resolution image sequences at higher revisiting rates. To achieve this goal, we formulate the fusion method as a recursive state estimation problem and study its performance in filtering and smoothing contexts. The proposed strategy clearly outperforms competing methodologies, which is shown in the paper for real data acquired by the Landsat and MODIS instruments., Comment: Published in IEEE AeroConf 2022

We systematically study three-terminal InSb-Al nanowire devices by using radio-frequency reflectometry. Tunneling spectroscopy measurements on both ends of the hybrid nanowires are performed while systematically varying the chemical potential, magnetic field and junction transparencies. Identifying the lowest-energy state allows for the construction of lowest- and zero-energy state diagrams, which show how the states evolve as a function of the aforementioned parameters. Importantly, comparing the diagrams taken for each end of the hybrids enables the identification of states which do not coexist simultaneously, ruling out a significant amount of the parameter space as candidates for a topological phase. Furthermore, altering junction transparencies filters out zero-energy states sensitive to a local gate potential. Such a measurement strategy significantly reduces the time necessary to identify a potential topological phase and minimizes the risk of falsely recognizing trivial bound states as Majorana zero modes., Comment: Main text: 12 pages, 9 figures. SupplementaryMaterials: 12 pages, 14 figures

In superconducting quantum circuits, aluminum is one of the most widely used materials. It is currently also the superconductor of choice for the development of topological qubits. In this application, however, aluminum-based devices suffer from poor magnetic field compatibility. In this article, we resolve this limitation by showing that adatoms of heavy elements (e.g. platinum) increase the critical field of thin aluminum films by more than a factor of two. Using tunnel junctions, we show that the increased field resilience originates from spin-orbit scattering introduced by Pt. We exploit this property in the context of the superconducting proximity effect in semiconductor-superconductor hybrids, where we show that InSb nanowires strongly coupled to Al/Pt films can maintain superconductivity up to 7T. The two-electron charging effect, a fundamental requirement for topological quantum computation, is shown to be robust against the presence of heavy adatoms. Additionally, we use non-local spectroscopy in a three-terminal geometry to probe the bulk of hybrid devices, showing that it remains free of sub-gap states. Finally, we demonstrate that semiconductor states which are proximitized by Al/Pt films maintain their ability to Zeeman-split in an applied magnetic field. Combined with the chemical stability and well-known fabrication routes of aluminum, Al/Pt emerges as the natural successor to Al-based systems and is a compelling alternative to other superconductors, whenever high-field resilience is required.

In many areas such as computational biology, finance or social sciences, knowledge of an underlying graph explaining the interactions between agents is of paramount importance but still challenging. Considering that these interactions may be based on nonlinear relationships adds further complexity to the topology inference problem. Among the latest methods that respond to this need is a topology inference one proposed by the authors, which estimates a possibly directed adjacency matrix in an online manner. Contrasting with previous approaches based on linear models, the considered model is able to explain nonlinear interactions between the agents in a network. The novelty in the considered method is the use of a derivative-reproducing property to enforce network sparsity, while reproducing kernels are used to model the nonlinear interactions. The aim of this paper is to present a thorough convergence analysis of this method. The analysis is proven to be sane both in the mean and mean square sense. In addition, stability conditions are devised to ensure the convergence of the analyzed method., Comment: 24 pages, 11 of which of which are supplementary material; 4 figures

This work presents a method for designing the weighting parameter required by Wiener-based binaural noise reduction methods. This parameter establishes the desired tradeoff between noise reduction and binaural cue preservation in hearing aid applications. The proposed strategy was specially derived for the preservation of interaural level difference, interaural time difference and interaural coherence binaural cues. It is defined as a function of the average input noise power at the microphones, providing robustness against the influence of joint changes in noise and speech power (Lombard effect), as well as to signal to noise ratio (SNR) variations. A theoretical framework, based on the mathematical definition of the homogeneity degree, is presented and applied to a generic augmented Wiener-based cost function. The theoretical insights obtained are supported bycomputational simulations and psychoacoustic experiments using the multichannel Wiener filter with interaural transfer function preservation technique (MWF-ITF), as a case study. Statistical analysis indicates that the proposed dynamic structure for the weighting parameter and the design method of its fixed part provide significant robustness against changes in the original binaural cues of both speech and residual noise, at the cost of a small decrease in the noise reduction performance, as compared to the use of a purely fixed weighting parameter.

Autoencoder (AEC) networks have recently emerged as a promising approach to perform unsupervised hyperspectral unmixing (HU) by associating the latent representations with the abundances, the decoder with the mixing model and the encoder with its inverse. AECs are especially appealing for nonlinear HU since they lead to unsupervised and model-free algorithms. However, existing approaches fail to explore the fact that the encoder should invert the mixing process, which might reduce their robustness. In this paper, we propose a model-based AEC for nonlinear HU by considering the mixing model a nonlinear fluctuation over a linear mixture. Differently from previous works, we show that this restriction naturally imposes a particular structure to both the encoder and to the decoder networks. This introduces prior information in the AEC without reducing the flexibility of the mixing model. Simulations with synthetic and real data indicate that the proposed strategy improves nonlinear HU.

Multitemporal spectral unmixing (SU) is a powerful tool to process hyperspectral image (HI) sequences due to its ability to reveal the evolution of materials over time and space in a scene. However, significant spectral variability is often observed between collection of images due to variations in acquisition or seasonal conditions. This characteristic has to be considered in the design of SU algorithms. Because of its good performance, the multiple endmember spectral mixture analysis algorithm (MESMA) has been recently used to perform SU in multitemporal scenarios arising in several practical applications. However, MESMA does not consider the relationship between the different HIs, and its computational complexity is extremely high for large spectral libraries. In this work, we propose an efficient multitemporal SU method that exploits the high temporal correlation between the abundances to provide more accurate results at a lower computational complexity. We propose to solve the complex general multitemporal SU problem by separately addressing the endmember selection and the abundance estimation problems. This leads to a simpler solution without sacrificing the accuracy of the results. We also propose a strategy to detect and address abrupt abundance variations in time. Theoretical results demonstrate how the proposed method compares to MESMA in terms of quality, and how effective it is in detecting abundance changes. This analysis provides valuable insight into the conditions under which the algorithm succeeds. Simulation results show that the proposed method achieves state-of-the-art performance at a smaller computational cost.

Several approaches have been proposed to solve the spectral unmixing problem in hyperspectral image analysis. Among them the use of sparse regression techniques aims to characterize the abundances in pixels based on a large library of spectral signatures known a priori. Recently, the integration of image spatial-contextual information significantly enhanced the performance of sparse unmixing. In this work, we propose a computationally efficient multiscale representation method for hyperspectral data adapted to the unmixing problem. The proposed method is based on a hierarchical extension of the SLIC oversegmentation algorithm constructed using a robust homogeneity testing. The image is subdivided into a set of spectrally homogeneous regions formed by pixels with similar characteristics (superpixels). This representation is then used to provide prior spatial regularity information for the abundances of materials present in the scene, improving the conditioning of the unmixing problem. Simulation results illustrate that the method is capable of estimating abundances with high quality and low computational cost, especially in noisy scenarios.