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In 2023, the CO2 growth rate was 3.37 +/- 0.11 ppm at Mauna Loa, 86% above the previous year, and hitting a record high since observations began in 1958, while global fossil fuel CO2 emissions only increased by 0.6 +/- 0.5%. This implies an unprecedented weakening of land and ocean sinks, and raises the question of where and why this reduction happened. Here we show a global net land CO2 sink of 0.44 +/- 0.21 GtC yr-1, the weakest since 2003. We used dynamic global vegetation models, satellites fire emissions, an atmospheric inversion based on OCO-2 measurements, and emulators of ocean biogeochemical and data driven models to deliver a fast-track carbon budget in 2023. Those models ensured consistency with previous carbon budgets. Regional flux anomalies from 2015-2022 are consistent between top-down and bottom-up approaches, with the largest abnormal carbon loss in the Amazon during the drought in the second half of 2023 (0.31 +/- 0.19 GtC yr-1), extreme fire emissions of 0.58 +/- 0.10 GtC yr-1 in Canada and a loss in South-East Asia (0.13 +/- 0.12 GtC yr-1). Since 2015, land CO2 uptake north of 20 degree N declined by half to 1.13 +/- 0.24 GtC yr-1 in 2023. Meanwhile, the tropics recovered from the 2015-16 El Nino carbon loss, gained carbon during the La Nina years (2020-2023), then switched to a carbon loss during the 2023 El Nino (0.56 +/- 0.23 GtC yr-1). The ocean sink was stronger than normal in the equatorial eastern Pacific due to reduced upwelling from La Nina's retreat in early 2023 and the development of El Nino later. Land regions exposed to extreme heat in 2023 contributed a gross carbon loss of 1.73 GtC yr-1, indicating that record warming in 2023 had a strong negative impact on the capacity of terrestrial ecosystems to mitigate climate change.

We are interested in the distribution of Wishart samples after forgetting their scaling factors. We call such a distribution a projective Wishart distribution. We show that projective Wishart distributions have strong links with the affine-invariant geometry of symmetric positive definite matrices in the real case or Hermitian positive definite matrices in the complex case. First, the Fr{\'e}chet mean of a projective Wishart distribution is the covariance parameter, up to a scaling factor, of the corresponding Wishart distribution. Second, in the case of 2 by 2 matrices, the densities have simple expressions in term of the affine-invariant distance.

Electroencephalography (EEG) data is often collected from diverse contexts involving different populations and EEG devices. This variability can induce distribution shifts in the data $X$ and in the biomedical variables of interest $y$, thus limiting the application of supervised machine learning (ML) algorithms. While domain adaptation (DA) methods have been developed to mitigate the impact of these shifts, such methods struggle when distribution shifts occur simultaneously in $X$ and $y$. As state-of-the-art ML models for EEG represent the data by spatial covariance matrices, which lie on the Riemannian manifold of Symmetric Positive Definite (SPD) matrices, it is appealing to study DA techniques operating on the SPD manifold. This paper proposes a novel method termed Geodesic Optimization for Predictive Shift Adaptation (GOPSA) to address test-time multi-source DA for situations in which source domains have distinct $y$ distributions. GOPSA exploits the geodesic structure of the Riemannian manifold to jointly learn a domain-specific re-centering operator representing site-specific intercepts and the regression model. We performed empirical benchmarks on the cross-site generalization of age-prediction models with resting-state EEG data from a large multi-national dataset (HarMNqEEG), which included $14$ recording sites and more than $1500$ human participants. Compared to state-of-the-art methods, our results showed that GOPSA achieved significantly higher performance on three regression metrics ($R^2$, MAE, and Spearman's $\rho$) for several source-target site combinations, highlighting its effectiveness in tackling multi-source DA with predictive shifts in EEG data analysis. Our method has the potential to combine the advantages of mixed-effects modeling with machine learning for biomedical applications of EEG, such as multicenter clinical trials.

We consider a system of binary interacting chains describing the dynamics of a group of $N$ components that, at each time unit, either send some signal to the others or remain silent otherwise. The interactions among the chains are encoded by a directed Erd\"os-R\'enyi random graph with unknown parameter $ p \in (0, 1) .$ Moreover, the system is structured within two populations (excitatory chains versus inhibitory ones) which are coupled via a mean field interaction on the underlying Erd\"os-R\'enyi graph. In this paper, we address the question of inferring the connectivity parameter $p$ based only on the observation of the interacting chains over $T$ time units. In our main result, we show that the connectivity parameter $p$ can be estimated with rate $N^{-1/2}+N^{1/2}/T+(\log(T)/T)^{1/2}$ through an easy-to-compute estimator. Our analysis relies on a precise study of the spatio-temporal decay of correlations of the interacting chains. This is done through the study of coalescing random walks defining a backward regeneration representation of the system. Interestingly, we also show that this backward regeneration representation allows us to perfectly sample the system of interacting chains (conditionally on each realization of the underlying Erd\"os-R\'enyi graph) from its stationary distribution. These probabilistic results have an interest in its own., Comment: 76 pages, 2 figures

Machine learning tasks are generally formulated as optimization problems, where one searches for an optimal function within a certain functional space. In practice, parameterized functional spaces are considered, in order to be able to perform gradient descent. Typically, a neural network architecture is chosen and fixed, and its parameters (connection weights) are optimized, yielding an architecture-dependent result. This way of proceeding however forces the evolution of the function during training to lie within the realm of what is expressible with the chosen architecture, and prevents any optimization across architectures. Costly architectural hyper-parameter optimization is often performed to compensate for this. Instead, we propose to adapt the architecture on the fly during training. We show that the information about desirable architectural changes, due to expressivity bottlenecks when attempting to follow the functional gradient, can be extracted from %the backpropagation. To do this, we propose a mathematical definition of expressivity bottlenecks, which enables us to detect, quantify and solve them while training, by adding suitable neurons when and where needed. Thus, while the standard approach requires large networks, in terms of number of neurons per layer, for expressivity and optimization reasons, we are able to start with very small neural networks and let them grow appropriately. As a proof of concept, we show results~on the CIFAR dataset, matching large neural network accuracy, with competitive training time, while removing the need for standard architectural hyper-parameter search.

Automated classification of electroencephalogram (EEG) signals is complex due to their high dimensionality, non-stationarity, low signal-to-noise ratio, and variability between subjects. Deep neural networks (DNNs) have shown promising results for EEG classification, but the above challenges hinder their performance. Euclidean Alignment (EA) and Data Augmentation (DA) are two promising techniques for improving DNN training by permitting the use of data from multiple subjects, increasing the data, and regularizing the available data. In this paper, we perform a detailed evaluation of the combined use of EA and DA with DNNs for EEG decoding. We trained individual models and shared models with data from multiple subjects and showed that combining EA and DA generates synergies that improve the accuracy of most models and datasets. Also, the shared models combined with fine-tuning benefited the most, with an overall increase of 8.41\% in classification accuracy., Comment: 8 pages, 4 figures, 2 tables, accepted at Eusipco 2024

In 1980, R. Tijdeman provided an on-line algorithm that generates sequences over a finite alphabet with minimal discrepancy, that is, such that the occurrence of each letter optimally tracks its frequency. In this article, we define discrete dynamical systems generating these sequences. The dynamical systems are defined as exchanges of polytopal pieces, yielding cut and project schemes, and they code tilings of the line whose sets of vertices form model sets. We prove that these sequences of low discrepancy are natural codings of toral translations with respect to polytopal atoms, and that they generate a minimal and uniquely ergodic subshift with purely discrete spectrum. Finally, we show that the factor complexity of these sequences is of polynomial growth order $n^{d-1}$, where $d$ is the cardinality of the alphabet.

Artificial intelligence (AI), based on deep-learning algorithm using high-quality reanalysis datasets, is showing enormous potential for weather forecasting. In this context, the European Centre for Medium-Range Weather Forecasts (ECMWF) is developing a new forecasting system based on AI. Verification results of deterministic forecast for now are promising. However, the realism of weather forecasts based on AI is often questioned. Here, different types of realism are identified and we discuss, in particular, the relationship between structural realism and predictability of weather events. Furthermore, a statistical analysis of deterministic forecasts based on AI points to a realism/performance dilemma that a probabilistic approach should help to solve. -- L'intelligence artificielle (IA) bouleverse aujourd'hui le monde de la pr\'evision m\'et\'eorologique avec l'utilisation d'algorithmes d'apprentissage profond nourris par des champs de r\'eanalyses. Dans ce contexte, le Centre Europ\'een pour les Pr\'evisions M\'et\'eorologiques \`a Moyen Terme (CEPMMT) a d\'ecid\'e de d\'evelopper un nouveau syst\`eme de pr\'evisions resposant sur l'IA. Ces pr\'evisions, pour le moment de type d\'eterministe, montrent des r\'esultats prometteurs. Toutefois, le r\'ealisme de ce type de pr\'evisions reposant sur l'IA est souvent questionn\'e. Ici, nous identifions diff\'erents types de r\'ealisme et interrogeons notamment le rapport entre r\'ealisme structurel et pr\'evisibilit\'e des \'ev\^enements m\'et\'eorologiques. Une analyse statistique de pr\'evisions d\'eterministes reposant sur l'IA laisse apparaitre un dilemme r\'ealisme/performance qu'une approche probabiliste devrait aider \`a r\'esoudre., Comment: 8 pages, in French

Objective. This study conduct an extensive Brain-computer interfaces (BCI) reproducibility analysis on open electroencephalography datasets, aiming to assess existing solutions and establish open and reproducible benchmarks for effective comparison within the field. The need for such benchmark lies in the rapid industrial progress that has given rise to undisclosed proprietary solutions. Furthermore, the scientific literature is dense, often featuring challenging-to-reproduce evaluations, making comparisons between existing approaches arduous. Approach. Within an open framework, 30 machine learning pipelines (separated into raw signal: 11, Riemannian: 13, deep learning: 6) are meticulously re-implemented and evaluated across 36 publicly available datasets, including motor imagery (14), P300 (15), and SSVEP (7). The analysis incorporates statistical meta-analysis techniques for results assessment, encompassing execution time and environmental impact considerations. Main results. The study yields principled and robust results applicable to various BCI paradigms, emphasizing motor imagery, P300, and SSVEP. Notably, Riemannian approaches utilizing spatial covariance matrices exhibit superior performance, underscoring the necessity for significant data volumes to achieve competitive outcomes with deep learning techniques. The comprehensive results are openly accessible, paving the way for future research to further enhance reproducibility in the BCI domain. Significance. The significance of this study lies in its contribution to establishing a rigorous and transparent benchmark for BCI research, offering insights into optimal methodologies and highlighting the importance of reproducibility in driving advancements within the field., Comment: 43 pages, 13 figures, 5 tables

We consider the problem of nonparametric density estimation under privacy constraints in an adversarial framework. To this end, we study minimax rates under local differential privacy over Sobolev spaces. We first obtain a lower bound which allows us to quantify the impact of privacy compared with the classical framework. Next, we introduce a new Coordinate block privacy mechanism that guarantees local differential privacy, which, coupled with a projection estimator, achieves the minimax optimal rates.

Objective: The integration of Deep Learning (DL) algorithms on brain signal analysis is still in its nascent stages compared to their success in fields like Computer Vision. This is particularly true for BCI, where the brain activity is decoded to control external devices without requiring muscle control. Electroencephalography (EEG) is a widely adopted choice for designing BCI systems due to its non-invasive and cost-effective nature and excellent temporal resolution. Still, it comes at the expense of limited training data, poor signal-to-noise, and a large variability across and within-subject recordings. Finally, setting up a BCI system with many electrodes takes a long time, hindering the widespread adoption of reliable DL architectures in BCIs outside research laboratories. To improve adoption, we need to improve user comfort using, for instance, reliable algorithms that operate with few electrodes. Approach: Our research aims to develop a DL algorithm that delivers effective results with a limited number of electrodes. Taking advantage of the Augmented Covariance Method and the framework of SPDNet, we propose the Phase-SPDNet architecture and analyze its performance and the interpretability of the results. The evaluation is conducted on 5-fold cross-validation, using only three electrodes positioned above the Motor Cortex. The methodology was tested on nearly 100 subjects from several open-source datasets using the Mother Of All BCI Benchmark (MOABB) framework. Main results: The results of our Phase-SPDNet demonstrate that the augmented approach combined with the SPDNet significantly outperforms all the current state-of-the-art DL architecture in MI decoding. Significance: This new architecture is explainable and with a low number of trainable parameters.

Combining electroencephalogram (EEG) datasets for supervised machine learning (ML) is challenging due to session, subject, and device variability. ML algorithms typically require identical features at train and test time, complicating analysis due to varying sensor numbers and positions across datasets. Simple channel selection discards valuable data, leading to poorer performance, especially with datasets sharing few channels. To address this, we propose an unsupervised approach leveraging EEG signal physics. We map EEG channels to fixed positions using field interpolation, facilitating source-free domain adaptation. Leveraging Riemannian geometry classification pipelines and transfer learning steps, our method demonstrates robust performance in brain-computer interface (BCI) tasks and potential biomarker applications. Comparative analysis against a statistical-based approach known as Dimensionality Transcending, a signal-based imputation called ComImp, source-dependent methods, as well as common channel selection and spherical spline interpolation, was conducted with leave-one-dataset-out validation on six public BCI datasets for a right-hand/left-hand classification task. Numerical experiments show that in the presence of few shared channels in train and test, the field interpolation consistently outperforms other methods, demonstrating enhanced classification performance across all datasets. When more channels are shared, field interpolation was found to be competitive with other methods and faster to compute than source-dependent methods.

We design variational pulse sequences tailored for neutral atom quantum simulators and show that we can engineer layers of single-qubit and multi-qubit gates. As an application, we discuss how the proposed method can be used to perform refocusing algorithms, SWAP networks, and ultimately quantum chemistry simulations. While the theoretical protocol we develop still has experimental limitations, it paves the way, with some further optimisation, for the use of analog quantum processors for variational quantum algorithms, including those not previously considered compatible with analog mode., Comment: 11 pages, 6 figures

Electroencephalography (EEG) signals are frequently used for various Brain-Computer Interface (BCI) tasks. While Deep Learning (DL) techniques have shown promising results, they are hindered by the substantial data requirements. By leveraging data from multiple subjects, transfer learning enables more effective training of DL models. A technique that is gaining popularity is Euclidean Alignment (EA) due to its ease of use, low computational complexity, and compatibility with Deep Learning models. However, few studies evaluate its impact on the training performance of shared and individual DL models. In this work, we systematically evaluate the effect of EA combined with DL for decoding BCI signals. We used EA to train shared models with data from multiple subjects and evaluated its transferability to new subjects. Our experimental results show that it improves decoding in the target subject by 4.33% and decreases convergence time by more than 70%. We also trained individual models for each subject to use as a majority-voting ensemble classifier. In this scenario, using EA improved the 3-model ensemble accuracy by 3.7%. However, when compared to the shared model with EA, the ensemble accuracy was 3.62% lower., Comment: 14 pages and 10 figures

Let $B=(B_t)_{t\geq 0}$ be a standard Brownian motion. The main objective is to find a uniform (in time) control of the modulus of continuity of $B$ in the spirit of what appears in (Kurtz, 1978). More precisely, it involves the control of the exponential moments of the random variable $\sup_{0\leq s\leq t} |B_t-B_s|/w(t,|t-s|)$ for a suitable function $w$. A stability inequality for diffusion processes is then derived and applied to two simple frameworks.

We report a study about the electrical response from a sliding contact made of a silver-graphite brush and a brass ring. This study focuses specifically on the voltage variations due to the mechanical interactions across the contact according to the rotational speed. This study is part of the research and the development about the monitoring of dynamical interfaces.

Electroencephalography (EEG) decoding is a challenging task due to the limited availability of labelled data. While transfer learning is a promising technique to address this challenge, it assumes that transferable data domains and task are known, which is not the case in this setting. This study investigates the transferability of deep learning representations between different EEG decoding tasks. We conduct extensive experiments using state-of-the-art decoding models on two recently released EEG datasets, ERP CORE and M$^3$CV, containing over 140 subjects and 11 distinct cognitive tasks. We measure the transferability of learned representations by pre-training deep neural networks on one task and assessing their ability to decode subsequent tasks. Our experiments demonstrate that, even with linear probing transfer, significant improvements in decoding performance can be obtained, with gains of up to 28% compare with the pure supervised approach. Additionally, we discover evidence that certain decoding paradigms elicit specific and narrow brain activities, while others benefit from pre-training on a broad range of representations. By revealing which tasks transfer well and demonstrating the benefits of transfer learning for EEG decoding, our findings have practical implications for mitigating data scarcity in this setting. The transfer maps generated also provide insights into the hierarchical relations between cognitive tasks, hence enhancing our understanding of how these tasks are connected from a neuroscientific standpoint., Comment: 19 pages, 9 figures

Data-driven modeling based on machine learning (ML) is showing enormous potential for weather forecasting. Rapid progress has been made with impressive results for some applications. The uptake of ML methods could be a game-changer for the incremental progress in traditional numerical weather prediction (NWP) known as the 'quiet revolution' of weather forecasting. The computational cost of running a forecast with standard NWP systems greatly hinders the improvements that can be made from increasing model resolution and ensemble sizes. An emerging new generation of ML models, developed using high-quality reanalysis datasets like ERA5 for training, allow forecasts that require much lower computational costs and that are highly-competitive in terms of accuracy. Here, we compare for the first time ML-generated forecasts with standard NWP-based forecasts in an operational-like context, initialized from the same initial conditions. Focusing on deterministic forecasts, we apply common forecast verification tools to assess to what extent a data-driven forecast produced with one of the recently developed ML models (PanguWeather) matches the quality and attributes of a forecast from one of the leading global NWP systems (the ECMWF IFS). The results are very promising, with comparable skill for both global metrics and extreme events, when verified against both the operational analysis and synoptic observations. Increasing forecast smoothness and bias drift with forecast lead time are identified as current drawbacks of ML-based forecasts. A new NWP paradigm is emerging relying on inference from ML models and state-of-the-art analysis and reanalysis datasets for forecast initialization and model training.

Animal-borne sensors (`bio-loggers') can record a suite of kinematic and environmental data, which are used to elucidate animal ecophysiology and improve conservation efforts. Machine learning techniques are used for interpreting the large amounts of data recorded by bio-loggers, but there exists no common framework for comparing the different machine learning techniques in this domain. This makes it difficult to, for example, identify patterns in what works well for machine learning-based analysis of bio-logger data. It also makes it difficult to evaluate the effectiveness of novel methods developed by the machine learning community. To address this, we present the Bio-logger Ethogram Benchmark (BEBE), a collection of datasets with behavioral annotations, as well as a modeling task and evaluation metrics. BEBE is to date the largest, most taxonomically diverse, publicly available benchmark of this type. Using BEBE, we compare the performance of deep and classical machine learning methods for identifying animal behaviors based on bio-logger data. As an example usage of BEBE, we test an approach based on self-supervised learning. To apply this approach to animal behavior classification, we adapt a deep neural network pre-trained with 700,000 hours of data collected from human wrist-worn accelerometers. We find that deep neural networks out-perform the classical machine learning methods we tested across all nine datasets in BEBE. We additionally find that the approach based on self-supervised learning out-performs the alternatives we tested, especially in settings when there is a low amount of training data available. In light of this, we are able to make concrete suggestions for designing studies that rely on machine learning to infer behavior from bio-logger data. Datasets and code are available at https://github.com/earthspecies/BEBE., Comment: For associated code repositories, see https://github.com/earthspecies/BEBE/ and https://github.com/earthspecies/BEBE-datasets/ . For data repository, see https://zenodo.org/record/7947104

Privacy enhancing technologies (PETs) have been proposed as a way to protect the privacy of data while still allowing for data analysis. In this work, we focus on Fully Homomorphic Encryption (FHE), a powerful tool that allows for arbitrary computations to be performed on encrypted data. FHE has received lots of attention in the past few years and has reached realistic execution times and correctness. More precisely, we explain in this paper how we apply FHE to tree-based models and get state-of-the-art solutions over encrypted tabular data. We show that our method is applicable to a wide range of tree-based models, including decision trees, random forests, and gradient boosted trees, and has been implemented within the Concrete-ML library, which is open-source at https://github.com/zama-ai/concrete-ml. With a selected set of use-cases, we demonstrate that our FHE version is very close to the unprotected version in terms of accuracy.