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Intrinsic area near the origin for self-similar growth-fragmentations and related random surfaces

We study the behaviour of a natural measure defined on the leaves of the genealogical tree of some branching processes, namely self-similar growth-fragmentation processes. Each particle, or cell, is attributed a positive mass that evolves in continuous tim ...

2022

Conservation of Forces and Total Work at the Interface Using the Internodes Method

Simone Deparis

The Internodes method is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into disjoint subdomains. In this paper we are interested in measuring how much the Internodes ...

2022

A Characterisation Of The Continuum Gaussian Free Field In Arbitrary Dimensions

Juhan Aru

We prove that under certain mild moment and continuity assumptions, the d-dimensional continuum Gaussian free field is the only stochastic process satisfying the usual domain Markov property and a scaling assumption. Our proof is based on a decomposition o ...

ECOLE POLYTECHNIQUE2022

Quadrature-free immersed isogeometric analysis

Pablo Antolin Sanchez, Thibaut Hirschler

This paper presents a novel method for solving partial differential equations on three-dimensional CAD geometries by means of immersed isogeometric discretizations that do not require quadrature schemes. It relies on a newly developed technique for the eva ...

SPRINGER2022

ADAGRAD Avoids Saddle Points

Kimon Antonakopoulos, Xiao Wang

Adaptive first-order methods in optimization are prominent in machine learning and data science owing to their ability to automatically adapt to the landscape of the function being optimized. However, their convergence guarantees are typically stated in te ...

2022

Weakly nonlinear evolution of stochastically driven non-normal systems

François Gallaire, Edouard Boujo, Yves-Marie François Ducimetière

We consider nonlinear dynamical systems driven by stochastic forcing. It has been largely evidenced in the literature that the linear response of non-normal systems (e.g. fluid flows) may exhibit a large variance amplification, even in a linearly stable re ...

2022

A driven tagged particle in asymmetric exclusion processes

Zhe Wang

We consider the asymmetric exclusion process with a driven tagged particle on Z which has different jump rates from other particles. When the non-tagged particles have non-nearest-neighbor jump rates , we show that the tagged particle can have a speed whic ...

INST MATHEMATICAL STATISTICS-IMS2022

ADAGRAD Avoids Saddle Points

Kimon Antonakopoulos, Xiao Wang

JMLR-JOURNAL MACHINE LEARNING RESEARCH2022

Event-driven acquisition for content-enriched microscopy

Suliana Manley, Martin Weigert, Chen Zhang, Willi Leopold Stepp, Dora Mahecic, Juliette Griffie

Event-driven acquisition uses neural-network-based recognition of specific biological events to trigger switching between slow and fast super-resolution imaging, enriching the capture of interesting events with high spatiotemporal resolution. A common goal ...

NATURE PORTFOLIO2022

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Nicolas Boumal, Christopher Arnold Criscitiello

We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...

SPRINGER2022