Publications associées à On long time behavior of solutions to nonlinear dispersive equations

Transportation-based functional ANOVA and PCA for covariance operators

Victor Panaretos, Yoav Zemel, Valentina Masarotto

We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an Analysis of Vari ...

Inst Mathematical Statistics-Ims2024

Extensions of Peer Prediction Incentive Mechanisms

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As large, data-driven artificial intelligence models become ubiquitous, guaranteeing high data quality is imperative for constructing models. Crowdsourcing, community sensing, and data filtering have long been the standard approaches to guaranteeing or imp ...

EPFL2024

Seeking the new, learning from the unexpected: Computational models of surprise and novelty in the brain

Alireza Modirshanechi

Human babies have a natural desire to interact with new toys and objects, through which they learn how the world around them works, e.g., that glass shatters when dropped, but a rubber ball does not. When their predictions are proven incorrect, such as whe ...

EPFL2024

Probabilistic and Deterministic Wellposedness for Low Regularity Dispersive Equations

Katie Sabrina Catherine Rosie Marsden

In this thesis we will present two results on global existence for nonlinear dispersive equations with data at or below the scaling regularity. In chapter 1 we take a probabilistic perspective to study the energy-critical nonlinear Schrödinger equation in ...

EPFL2024

Robust machine learning for neuroscientific inference

Steffen Schneider

Modern neuroscience research is generating increasingly large datasets, from recording thousands of neurons over long timescales to behavioral recordings of animals spanning weeks, months, or even years. Despite a great variety in recording setups and expe ...

EPFL2024

Generalization of Scaled Deep ResNets in the Mean-Field Regime

Volkan Cevher, Grigorios Chrysos, Fanghui Liu

Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate scaled ResNet in the limit of infinitely deep and wide neural networks, of wh ...

2024

Homogenization results for the generator of multiscale Langevin dynamics in weighted Sobolev spaces

Andrea Zanoni

We study the homogenization of the Poisson equation with a reaction term and of the eigenvalue problem associated to the generator of multiscale Langevin dynamics. Our analysis extends the theory of two-scale convergence to the case of weighted Sobolev spa ...

OXFORD UNIV PRESS2023

Towards a multiscale point cloud structural similarity metric

Touradj Ebrahimi, Davi Nachtigall Lazzarotto

Point clouds are effective data structures for the rep- resentation of three-dimensional media and hence adopted in a wide range of practical applications. In many cases, the portrayed data is expected to be visualized by humans. After acquisition, point c ...

IEEE2023

We Need Subject Matter Expertise to Choose and Identify Causal Estimands: Comment on "Estimands for Recurrent Event Endpoints in the Presence of a Terminal Event"

Matias Janvin, Mats Julius Stensrud

We summarize what we consider to be the two main limitations of the "Estimands for Recurrent Event Endpoints in the Presence of a Terminal Event" (Schmidli et al. 2022). First, the authors did not give detailed guidance on how to choose an appropriate esti ...

TAYLOR & FRANCIS INC2023

Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds

Le Chen, David Jean-Michel Candil, Cheuk Yin Lee

We consider nonlinear parabolic stochastic PDEs on a bounded Lipschitz domain driven by a Gaussian noise that is white in time and colored in space, with Dirichlet or Neumann boundary condition. We establish existence, uniqueness and moment bounds of the r ...

Springer2023