Publications related to Clifford algebra

Holography and localization of information in quantum gravity

Kyriakos Papadodimas, Alexandre Mathieu Frédéric Belin

Within the AdS/CFT correspondence, we identify a class of CFT operators which represent diff-invariant and approximately local observables in the gravitational dual. Provided that the bulk state breaks all asymptotic symmetries, we show that these operator ...

Springer2024

UNDERGRAD: A Universal Black-Box Optimization Method with Almost Dimension-Free Convergence Rate Guarantees

Volkan Cevher, Kimon Antonakopoulos

Universal methods for optimization are designed to achieve theoretically optimal convergence rates without any prior knowledge of the problem’s regularity parameters or the accurarcy of the gradient oracle employed by the optimizer. In this regard, existin ...

2022

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

Linear Lipschitz and C-1 extension operators through random projection

Federico Stra

We construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and C-1 functions. This way we prove more directly a result by Lee and Naor [5] and we generalize the C-l extension theorem by ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2021

Admissibility of Uncertain Injections in Quadratic Algebraic Systems

Jean-Yves Le Boudec, Cong Wang, Eleni Stai

We study the admissibility problem in multivariate algebraic systems, such as ac electrical networks, where the power injection is quadratic in the state. The goal of such systems is to ensure that the state stays in some security set (e.g., magnitudes of ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Sensing soft robot shape using imus: An experimental investigation

Josephine Anna Eleanor Hughes, Francesco Stella

Shape estimation of soft robotic systems is challenging due to the range of deformations that can be achieved, and the limited availability of physically compatible sensors. We propose a method of reconstruction using Inertial Measurement Units (IMUs), whi ...

Springer Verlag2021

Rapid measurement and correction of spatiotemporal B-0 field changes using FID navigators and a multi-channel reference image

Tobias Kober

Purpose To measure spatiotemporal B-0 field changes in real time using FID navigators (FIDnavs) and to demonstrate the efficacy of retrospectively correcting high-resolution T2*-weighted images using a novel FIDnav framework. Methods A forward model of the ...

2019

Type II solutions Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on $\R^{3+1}$

Joachim Krieger, Stefano Francesco Burzio

We show that the finite time type II blow up solutions for the energy critical nonlinear wave equation [ \Box u = -u^5 ] on

\R^{3+1}

constructed in \cite{KST}, \cite{KS1} are stable along a co-dimension one Lipschitz manifold of data perturbations in a ...

2018

Traces on reduced group C-*-algebras

Sven Raum

In this short note we prove that the reduced group C-*-algebra of a locally compact group admits a non-zero trace if and only if the amenable radical of the group is open. This completely answers a question raised by Forrest, Spronk and Wiersma. ...

Wiley2017

Rationally isomorphic hermitian forms and torsors of some non-reductive groups

Eva Bayer Fluckiger

Let R be a semilocal Dedekind domain. Under certain assumptions, we show that two (not necessarily unimodular) hermitian forms over an R-algebra with involution, which are rationally isomorphic and have isomorphic semisimple coradicals, are in fact isomorp ...

Academic Press Inc Elsevier Science2017

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Holography and localization of information in quantum gravity

UNDERGRAD: A Universal Black-Box Optimization Method with Almost Dimension-Free Convergence Rate Guarantees

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

Linear Lipschitz and C-1 extension operators through random projection

Admissibility of Uncertain Injections in Quadratic Algebraic Systems

Sensing soft robot shape using imus: An experimental investigation

Rapid measurement and correction of spatiotemporal B-0 field changes using FID navigators and a multi-channel reference image

Type II solutions Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on $\R^{3+1}$

Traces on reduced group C-*-algebras

Rationally isomorphic hermitian forms and torsors of some non-reductive groups

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

UNDERGRAD: A Universal Black-Box Optimization Method with Almost Dimension-Free Convergence Rate Guarantees

Traces on reduced group C-*-algebras

Holography and localization of information in quantum gravity

Linear Lipschitz and C-1 extension operators through random projection

Rationally isomorphic hermitian forms and torsors of some non-reductive groups

Rapid measurement and correction of spatiotemporal B-0 field changes using FID navigators and a multi-channel reference image

Type II solutions Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on $\R^{3+1}$

Sensing soft robot shape using imus: An experimental investigation

Admissibility of Uncertain Injections in Quadratic Algebraic Systems