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1,098 Research products

  • Neuroinformatics
  • 2023-2023
  • arXiv.org e-Print Archive

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    Authors: Alain Durmus; Andreas Eberle; Arnaud Guillin; Katharina Schuh;

    We develop a new approach to study the long time behaviour of solutions to nonlinear stochastic differential equations in the sense of McKean, as well as propagation of chaos for the corresponding mean-field particle system approximations. Our approach is based on a sticky coupling between two solutions to the equation. We show that the distance process between the two copies is dominated by a solution to a one-dimensional nonlinear stochastic differential equation with a sticky boundary at zero. This new class of equations is then analyzed carefully. In particular, we show that the dominating equation has a phase transition. In the regime where the Dirac measure at zero is the only invariant probability measure, we prove exponential convergence to equilibrium both for the one-dimensional equation, and for the original nonlinear SDE. Similarly, propagation of chaos is shown by a componentwise sticky coupling and comparison with a system of one dimensional nonlinear SDEs with sticky boundaries at zero. The approach applies to equations without confinement potential and to interaction terms that are not of gradient type. 46 pages

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    Stochastic Partial Differential Equations Analysis and Computations
    Article . 2023 . Peer-reviewed
    License: CC BY
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    Other literature type . Preprint . 2022
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    https://doi.org/10.48550/arxiv...
    Article . 2022
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ Stochastic Partial D...arrow_drop_down
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      Stochastic Partial Differential Equations Analysis and Computations
      Article . 2023 . Peer-reviewed
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    Authors: Tomasevic, Milica;

    International audience; In this work, we prove the well-posedness and propagation of chaos for a stochastic particle system in mean-field interaction under the assumption that the interacting kernel belongs to a suitable $L_t^q-L_x^p$ space. Contrary to the large deviation principle approach recently proposed in [2], the main ingredient of the proof here are the \textit{Partial Girsanov transformations} introduced in [3] and developed in a general setting in this work.

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    Electronic Communications in Probability
    Article . 2023 . Peer-reviewed
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    https://doi.org/10.48550/arxiv...
    Article . 2023
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    Authors: Majhi, Snehashis; Dai, Rui; Kong, Quan; Garattoni, Lorenzo; +2 Authors

    Video anomaly detection in surveillance systems with only video-level labels (i.e. weakly-supervised) is challenging. This is due to, (i) the complex integration of human and scene based anomalies comprising of subtle and sharp spatio-temporal cues in real-world scenarios, (ii) non-optimal optimization between normal and anomaly instances under weak supervision. In this paper, we propose a Human-Scene Network to learn discriminative representations by capturing both subtle and strong cues in a dissociative manner. In addition, a self-rectifying loss is also proposed that dynamically computes the pseudo temporal annotations from video-level labels for optimizing the Human-Scene Network effectively. The proposed Human-Scene Network optimized with self-rectifying loss is validated on three publicly available datasets i.e. UCF-Crime, ShanghaiTech and IITB-Corridor, outperforming recently reported state-of-the-art approaches on five out of the six scenarios considered.

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    Other literature type . 2023
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    https://doi.org/10.48550/arxiv...
    Article . 2023
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      https://doi.org/10.48550/arxiv...
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    Authors: Abdolmahdi Bagheri; Mahdi Dehshiri; Yamin Bagheri; Alireza Akhondi-Asl; +1 Authors

    Neuroscientific studies aim to find an accurate and reliable brain Effective Connectome (EC). Although current EC discovery methods have contributed to our understanding of brain organization, their performances are severely constrained by the short sample size and poor temporal resolution of fMRI data, and high dimensionality of the brain connectome. By leveraging the DTI data as prior knowledge, we introduce two Bayesian causal discovery frameworks -the Bayesian GOLEM (BGOLEM) and Bayesian FGES (BFGES) methods- that offer significantly more accurate and reliable ECs and address the shortcomings of the existing causal discovery methods in discovering ECs based on only fMRI data. Moreover, to numerically assess the improvement in the accuracy of ECs with our method on empirical data, we introduce the Pseudo False Discovery Rate (PFDR) as a new computational accuracy metric for causal discovery in the brain. Through a series of simulation studies on synthetic and hybrid data (combining DTI from the Human Connectome Project (HCP) subjects and synthetic fMRI), we demonstrate the effectiveness of our proposed methods and the reliability of the introduced metric in discovering ECs. By employing the PFDR metric, we show that our Bayesian methods lead to significantly more accurate results compared to the traditional methods when applied to the Human Connectome Project (HCP) data. Additionally, we measure the reproducibility of discovered ECs using the Rogers-Tanimoto index for test-retest data and show that our Bayesian methods provide significantly more reliable ECs than traditional methods. Overall, our study’s numerical and visual results highlight the potential for these frameworks to significantly advance our understanding of brain functionality.

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    PLoS ONE
    Article . 2023 . Peer-reviewed
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    https://doi.org/10.48550/arxiv...
    Article . 2023
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      https://doi.org/10.48550/arxiv...
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    Authors: Adam Rançon; Nicolas Dupuis;

    We determine the two-body contact in a planar Bose gas confined by a transverse harmonic potential, using the nonperturbative functional renormalization group. We use the three-dimensional thermodynamic definition of the contact where the latter is related to the derivation of the pressure of the quasi-two-dimensional system with respect to the three-dimensional scattering length of the bosons. Without any free parameter, we find a remarkable agreement with the experimental data of Zou {\it et al.} [Nat. Comm. {\bf 12}, 760 (2021)] from low to high temperatures, including the vicinity of the Berezinskii-Kosterlitz-Thouless transition. We also show that the short-distance behavior of the pair distribution function and the high-momentum behavior of the momentum distribution are determined by two contacts: the three-dimensional contact for length scales smaller than the characteristic length $\ell_z=\sqrt{\hbar/m\omega_z}$ of the harmonic potential and, for length scales larger than $\ell_z$, an effective two-dimensional contact, related to the three-dimensional one by a geometric factor depending on $\ell_z$. Comment: v1) 6+10 pages, 2+1 figures; v2) 6+12 pages, 2+4 figures, published version

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    Physical Review Letters
    Article . 2023 . Peer-reviewed
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      Physical Review Letters
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    Authors: Daniele De Gennaro; Anna Kubin;

    We show that the discrete approximate volume preserving mean curvature flow in the flat torus $\mathbb{T}^N$ starting near a strictly stable critical set $E$ of the perimeter converges in the long time to a translate of $E$ exponentially fast. As an intermediate result we establish a new quantitative estimate of Alexandrov type for periodic strictly stable constant mean curvature hypersurfaces. Finally, in the two dimensional case a complete characterization of the long time behaviour of the discrete flow with arbitrary initial sets of finite perimeter is provided. 38 pages, 2 figure. arXiv admin note: text overlap with arXiv:2004.04799 by other authors

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    Calculus of Variations and Partial Differential Equations
    Article . 2023 . Peer-reviewed
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      Calculus of Variations and Partial Differential Equations
      Article . 2023 . Peer-reviewed
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    Authors: Pablo Lemos; Niall Jeffrey; Miles Cranmer; Shirley Ho; +1 Authors

    We present an approach for using machine learning to automatically discover the governing equations and hidden properties of real physical systems from observations. We train a "graph neural network" to simulate the dynamics of our solar system's Sun, planets, and large moons from 30 years of trajectory data. We then use symbolic regression to discover an analytical expression for the force law implicitly learned by the neural network, which our results showed is equivalent to Newton's law of gravitation. The key assumptions that were required were translational and rotational equivariance, and Newton's second and third laws of motion. Our approach correctly discovered the form of the symbolic force law. Furthermore, our approach did not require any assumptions about the masses of planets and moons or physical constants. They, too, were accurately inferred through our methods. Though, of course, the classical law of gravitation has been known since Isaac Newton, our result serves as a validation that our method can discover unknown laws and hidden properties from observed data. More broadly this work represents a key step toward realizing the potential of machine learning for accelerating scientific discovery. 12 pages, 6 figures, under review

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    Machine Learning: Science and Technology
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    https://doi.org/10.48550/arxiv...
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      Machine Learning: Science and Technology
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    Authors: Wang, Yinghao; Nahon, Rémi; Tartaglione, Enzo; Mozharovskyi, Pavlo; +1 Authors

    Electroencephalography has been widely used to study mental processes such as attention, perception, and emotion. This is because mental state classification has important applications in many fields, including healthcare, human-computer interaction, and education.In this paper, we present a new approach to mental state classification from EEG signals by combining signal processing techniques and machine learning (ML) algorithms. We evaluate the performance of the proposed method on a dataset of EEG recordings collected during a cognitive load task. The results show that the proposed method achieves high accuracy in classifying mental states and outperforms state-of-the-art methods in terms of classification accuracy and computational efficiency

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    https://doi.org/10.1109/ssp532...
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      https://doi.org/10.1109/ssp532...
      Conference object . 2023 . Peer-reviewed
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    Authors: Quentin Vigneron; Boudewijn F. Roukema;

    We study the properties of the Newtonian gravitational potential in a spherical Universe for different topologies. For this, we use the non-Euclidean Newtonian theory developed in Vigneron [2022, Class. & Quantum Gravity, 39, 155006] describing Newtonian gravitation in a spherical or hyperbolic Universe. The potential is calculated for a point mass in all the globally homogeneous regular spherical topologies, i.e. whose fundamental domain is unique and is a platonic solid. We provide the exact solution and the Taylor expansion series of the potential at a test position near the point mass. We show that the odd terms of the expansion can be interpreted as coming from the presence of a non-zero spatial scalar curvature, while the even terms relate to the closed nature of the topological space. A consequence is that, compared to the point mass solution in a 3-torus, widely used in Newtonian cosmological simulations, the spherical cases all feature an additional attractive first order term dependent solely on the spatial curvature. The choice of topology only affects the potential at second order and higher. For typical estimates of cosmological scales (curvature and topology), the strongest topological effect occurs in the case of the Poincaré dodecahedral space, but in general the effect of curvature dominates over topology. We also provide the set of equations that can be used to perform $N$-body simulations of structure formation in spherical topologies. Accepted in Physical Review D, 12 pages, 4 tables, calculation source code at https://codeberg.org/boud/topoaccel

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    https://doi.org/10.1103/physre...
    Article . 2023 . Peer-reviewed
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      https://doi.org/10.1103/physre...
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    Authors: Sidharth Pancholi; Amita Giri; Anant Jain; Lalan Kumar; +1 Authors

    The ability to reconstruct the kinematic parameters of hand movement using noninvasive electroencephalography (EEG) is essential for strength and endurance augmentation using exoskeleton/exosuit. For system development, the conventional classification-based brain-computer interface (BCI) controls external devices by providing discrete control signals to the actuator. A continuous kinematic reconstruction from EEG signal is better suited for practical BCI applications. The state-of-the-art multivariable linear regression (mLR) method provides a continuous estimate of hand kinematics, achieving a maximum correlation of up to 0.67 between the measured and the estimated hand trajectory. In this work, three novel source aware deep learning models are proposed for motion trajectory prediction (MTP). In particular, multilayer perceptron (MLP), convolutional neural network-long short-term memory (CNN-LSTM), and wavelet packet decomposition (WPD) for CNN-LSTM are presented. In addition, novelty in the work includes the utilization of brain source localization (BSL) [using standardized low-resolution brain electromagnetic tomography (sLORETA)] for the reliable decoding of motor intention. The information is utilized for channel selection and accurate EEG time segment selection. The performance of the proposed models is compared with the traditionally utilized mLR technique on the reach, grasp, and lift (GAL) dataset. The effectiveness of the proposed framework is established using the Pearson correlation coefficient (PCC) and trajectory analysis. A significant improvement in the correlation coefficient is observed when compared with the state-of-the-art mLR model. Our work bridges the gap between the control and the actuator block, enabling real-time BCI implementation.

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    IEEE Transactions on Cybernetics
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      IEEE Transactions on Cybernetics
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    Authors: Alain Durmus; Andreas Eberle; Arnaud Guillin; Katharina Schuh;

    We develop a new approach to study the long time behaviour of solutions to nonlinear stochastic differential equations in the sense of McKean, as well as propagation of chaos for the corresponding mean-field particle system approximations. Our approach is based on a sticky coupling between two solutions to the equation. We show that the distance process between the two copies is dominated by a solution to a one-dimensional nonlinear stochastic differential equation with a sticky boundary at zero. This new class of equations is then analyzed carefully. In particular, we show that the dominating equation has a phase transition. In the regime where the Dirac measure at zero is the only invariant probability measure, we prove exponential convergence to equilibrium both for the one-dimensional equation, and for the original nonlinear SDE. Similarly, propagation of chaos is shown by a componentwise sticky coupling and comparison with a system of one dimensional nonlinear SDEs with sticky boundaries at zero. The approach applies to equations without confinement potential and to interaction terms that are not of gradient type. 46 pages

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    Stochastic Partial Differential Equations Analysis and Computations
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      Stochastic Partial Differential Equations Analysis and Computations
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    Authors: Tomasevic, Milica;

    International audience; In this work, we prove the well-posedness and propagation of chaos for a stochastic particle system in mean-field interaction under the assumption that the interacting kernel belongs to a suitable $L_t^q-L_x^p$ space. Contrary to the large deviation principle approach recently proposed in [2], the main ingredient of the proof here are the \textit{Partial Girsanov transformations} introduced in [3] and developed in a general setting in this work.

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    Electronic Communications in Probability
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    https://doi.org/10.48550/arxiv...
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