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Bi-Jacobi Fields And Riemannian Cubics For Left-Invariant SO(3)

Publications associées (31)

Multiplicity-free Representations of Algebraic Groups

Let K be an algebraically closed field of characteristic zero, and let G be a connected reductive algebraic group over K. We address the problem of classifying triples (G, H, V ), where H is a proper connected subgroup of G, and V is a finitedimensional ir ...

Amer Mathematical Soc2024

From low-rank retractions to dynamical low-rank approximation and back

Daniel Kressner, Axel Elie Joseph Séguin, Gianluca Ceruti

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

Springer2024

Touch and Closeness in Naturally Organized Activities

Countless aspects of touch and closeness have been questioned in an unprecedented way during the recent Covid epidemic. Social practices as banal as greetings were both reflexively and practically challenged and sometimes deeply altered, resulting in painf ...

2024

Hybrid ground-state quantum algorithms based on neural Schrödinger forging

Giuseppe Carleo, Sofia Vallecorsa

Entanglement forging based variational algorithms leverage the bipartition of quantum systems for addressing ground-state problems. The primary limitation of these approaches lies in the exponential summation required over the numerous potential basis stat ...

Amer Physical Soc2024

A structured prediction approach for robot imitation learning

Aude Billard, Iason Batzianoulis, Anqing Duan

We propose a structured prediction approach for robot imitation learning from demonstrations. Among various tools for robot imitation learning, supervised learning has been observed to have a prominent role. Structured prediction is a form of supervised le ...

Sage Publications Ltd2023

Lie groups in the symmetric group: Reducing Ulam's problem to the simple case

Nicolas Monod

Ulam asked whether all Lie groups can be represented faithfully on a countable set. We establish a reduction of Ulam's problem to the case of simple Lie groups. In particular, we solve the problem for all solvable Lie groups and more generally Lie groups w ...

Academic Press Inc Elsevier Science2023

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Axel Elie Joseph Séguin

The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...

EPFL2023

A geometric optimal control approach for imitation and generalization of manipulation skills

Sylvain Calinon, Amirreza Razmjoo Fard, Jie Zhao

Daily manipulation tasks are characterized by regular features associated with the task structure, which can be described by multiple geometric primitives related to actions and object shapes. Only using Cartesian coordinate systems cannot fully represent ...

Elsevier2023

RMAML: Riemannian meta-learning with orthogonality constraints

Soumava Kumar Roy

Meta-learning is the core capability that enables intelligent systems to rapidly generalize their prior ex-perience to learn new tasks. In general, the optimization-based methods formalize the meta-learning as a bi-level optimization problem, that is a nes ...

ELSEVIER SCI LTD2023

Floyd's manifold is a conjugation space

Jérôme Scherer

E. E. Floyd showed in 1973 that there exist only two nontrivial cobor-dism classes that contain manifolds with three cells, and that they lie in dimen-sions 10 and 5. We prove that there is an action of the cyclic group C2 on the 10-dimensional Floyd manif ...

Scuola Normale Superiore2023

Cohomology in singular blocks of parabolic category O

Jonathan Gruber

We determine the dimensions of Ext -groups between simple modules and dual generalized Verma modules in singular blocks of parabolic versions of category O for complex semisimple Lie algebras and affine Kac-Moody algebras. ...

2023

Tangent functional connectomes uncover more unique phenotypic traits

Mingkui Wang, Enrico Amico

Functional connectomes (FCs) containing pairwise estimations of functional couplings between pairs of brain regions are commonly represented by correlation matrices. As symmetric positive definite matrices, FCs can be transformed via tangent space projecti ...

CELL PRESS2023

Unlikely intersections on the p-adic formal ball

Vlad Serban

We investigate generalizations along the lines of the Mordell-Lang conjecture of the author's p-adic formal Manin-Mumford results for n-dimensional p-divisible formal groups F. In particular, given a finitely generated subgroup (sic) of F(Q(p)) and a close ...

SPRINGER INT PUBL AG2023

Critical Schrodinger Cat Qubit

Vincenzo Savona, Luca Gravina, Fabrizio Minganti

Encoding quantum information onto bosonic systems is a promising route to quantum error correc-tion. In a cat code, this encoding relies on the confinement of the dynamics of the system onto the two-dimensional manifold spanned by Schrodinger cats of oppos ...

AMER PHYSICAL SOC2023

Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups

Nicolas Monod

We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the polynomial ring g ...

SPRINGER HEIDELBERG2023

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

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

A b-symplectic slice theorem

Anna Kiesenhofer

In this article, motivated by the study of symplectic structures on manifolds with boundary and the systematic study of b-symplectic manifolds started in Guillemin, Miranda, and Pires Adv. Math. 264 (2014), 864-896, we prove a slice theorem for Lie group a ...

WILEY2022

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

Nicolas Boumal

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 ...

SPRINGER HEIDELBERG2022

Lie groups as permutation groups: Ulam's problem in the nilpotent case

Nicolas Monod

Ulam asked whether every connected Lie group can be represented on a countable structure. This is known in the linear case. We establish it for the first family of non-linear groups, namely in the nilpotent case. Further context is discussed to illustrate ...

WALTER DE GRUYTER GMBH2022