On Singular Poisson Sternberg Spaces

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Axonal and Dendritic Morphology of Excitatory Neurons in Layer 2/3 Mouse Barrel Cortex Imaged Through Whole-Brain Two-Photon Tomography and Registered to a Digital Brain Atlas

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Communication between cortical areas contributes importantly to sensory perception and cognition. On the millisecond time scale, information is signaled from one brain area to another by action potentials propagating across long-range axonal arborizations. ...

FRONTIERS MEDIA SA2022

Self-Structuring Of Cellular And Channel Type In Complex System Dynamics In The Framework Of Scale Relativity Theory

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In the framework of Scale Relativity Theory, by analyzing dynamics of complex system structural units based on multifractal curves, both Schrodinger and Madelung approaches are functional and complementary. The Madelung selected approach involve synchronou ...

UNIV POLITEHNICA BUCHAREST, SCI BULL2022

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

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We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle: On a nonsmooth se ...

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Dynamical low rank approximation for uncertainty quantification of time-dependent problems

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The quantification of uncertainties can be particularly challenging for problems requiring long-time integration as the structure of the random solution might considerably change over time. In this respect, dynamical low-rank approximation (DLRA) is very a ...

EPFL2022

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

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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

Generalised Howe duality and injectivity of induction: the symplectic case

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We study the symplectic Howe duality using two new and independent combinatorial methods: via determinantal formulae on the one hand, and via (bi)crystals on the other hand. The first approach allows us to establish a generalised version where weight multi ...

2022

Local invertibility and sensitivity of atomic structure-feature mappings

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Background: The increasingly common applications of machine-learning schemes to atomic-scale simulations have triggered efforts to better understand the mathematical properties of the mapping between the Cartesian coordinates of the atoms and the variety o ...

2021

On The Singular Set In The Thin Obstacle Problem: Higher-Order Blow-Ups And The Very Thin Obstacle Problem

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We consider the singular set in the thin obstacle problem with weight vertical bar x(n +1)vertical bar(a) for a epsilon (-1, 1), which arises as the local extension of the obstacle problem for the fractional Laplacian (a nonlocal problem). We develop a ref ...

MATHEMATICAL SCIENCE PUBL2021

Structure-Preserving Reduced Basis Methods For Poisson Systems

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We develop structure-preserving reduced basis methods for a large class of nondissipative problems by resorting to their formulation as Hamiltonian dynamical systems. With this perspective, the phase space is naturally endowed with a Poisson manifold struc ...

AMER MATHEMATICAL SOC2021

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

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We prove equidistribution at shrinking scales for the monochromatic ensemble on a compact Riemannian manifold of any dimension. This ensemble on an arbitrary manifold takes a slowly growing spectral window in order to synthesize a random function. With hig ...