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Dynamical Approximation By Hierarchical Tucker And Tensor-Train Tensors

Related publications (31)

A new method for lattice reduction using directional and hyperplanar shearing

A geometric method of lattice reduction based on cycles of directional and hyperplanar shears is presented. The deviation from cubicity at each step of the reduction is evaluated by a parameter called 'basis rhombicity' which is the sum of the absolute val ...

INT UNION CRYSTALLOGRAPHY2022

Mutual information for low-rank even-order symmetric tensor estimation

Nicolas Macris, Jean François Emmanuel Barbier, Clément Dominique Luneau

We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tensor is of even order. The proof applies the adaptive interpolation method orig ...

OXFORD UNIV PRESS2021

Realizing doubles: a conjugation zoo

Jérôme Scherer

Conjugation spaces are topological spaces equipped with an involution such that their fixed points have the same mod 2 cohomology (as a graded vector space, a ring and even an unstable algebra) but with all degrees divided by two, generalizing the classica ...

CAMBRIDGE UNIV PRESS2021

Polarity Of Almost All Points For Systems Of Nonlinear Stochastic Heat Equations In The Critical Dimension

Robert Dalang

We study vector-valued solutions u(t, x) is an element of R-d to systems of nonlinear stochastic heat equations with multiplicative noise, ...

INST MATHEMATICAL STATISTICS-IMS2021

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How Lagrangian States Evolve Into Random Waves

Alejandro Rivera

In this paper, we consider a compact connected manifold (X, g) of negative curvature, and a family of semi-classical Lagrangian states f(h)(x) = a(x)e(i phi(x)/h) on X. For a wide family of phases phi, we show that f(h), when evolved by the semi-classical ...

ECOLE POLYTECHNIQUE2022

Continuation Methods For Riemannian Optimization

Daniel Kressner, Axel Elie Joseph Séguin

Numerical continuation in the context of optimization can be used to mitigate convergence issues due to a poor initial guess. In this work, we extend this idea to Riemannian optimization problems, that is, the minimization of a target function on a Riemann ...

SIAM PUBLICATIONS2022

A new method for lattice reduction using directional and hyperplanar shearing

Cyril Cayron

INT UNION CRYSTALLOGRAPHY2022

Mutual information for low-rank even-order symmetric tensor estimation

Nicolas Macris, Jean François Emmanuel Barbier, Clément Dominique Luneau

OXFORD UNIV PRESS2021

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

Matthew De Courcy-Ireland

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 ...

OXFORD UNIV PRESS2021

Realizing doubles: a conjugation zoo

Jérôme Scherer

CAMBRIDGE UNIV PRESS2021

Polarity Of Almost All Points For Systems Of Nonlinear Stochastic Heat Equations In The Critical Dimension

Robert Dalang

We study vector-valued solutions u(t, x) is an element of R-d to systems of nonlinear stochastic heat equations with multiplicative noise, ...

INST MATHEMATICAL STATISTICS-IMS2021

Slow-fast Dynamics of Strongly Coupled Adaptive Frequency Oscillators

Auke Ijspeert, Jonas Buchli, Ludovic Righetti

Oscillators have two main limitations: their synchronization properties are limited (i.e., they have a finite synchronization region) and they have no memory of past interactions (i.e., they return to their intrinsic frequency whenever the entraining signa ...

SIAM PUBLICATIONS2021

Ergodic Exploration Using Tensor Train: Applications in Insertion Tasks

Sylvain Calinon, Suhan Narayana Shetty

In robotics, ergodic control extends the tracking principle by specifying a probability distribution over an area to cover instead of a trajectory to track. The original problem is formulated as a spectral multiscale coverage problem, typically requiring t ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Bootstrapping Heisenberg magnets and their cubic instability

Alessandro Vichi, Ning Su

We study the critical O(3) model using the numerical conformal bootstrap. In particular, we use a recently developed cutting-surface algorithm to efficiently map out the allowed space of conformal field theory data from correlators involving the leading O( ...

American Physical Society2021

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