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Concept

Metric tensor

Related publications (28)

Spatiotemporal energy‐density distribution of time‐reversed electromagnetic fields

Farhad Rachidi-Haeri, Marcos Rubinstein, Nicolas Mora Parra, Hamidreza Karami, Elias Per Joachim Le Boudec

Time reversal exploits the invariance of electromagnetic wave propagation in reciprocal and lossless media to localize radiating sources. Time-reversed measurements are back-propagated in a simulated domain and converge to the unknown source location. The ...

2024

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

A Gapless Post-quantum Hash Proof System in the Hamming Metric

Serge Vaudenay, Bénédikt Minh Dang Tran

A hash proof system (HPS) is a form of implicit proof of membership to a language. Out of the very few existing post-quantum HPS, most are based on languages of ciphertexts of code-based or lattice-based cryptosystems and inherently suffer from a gap cause ...

2023

Learning Dynamics of Spring-Mass Models with Physics-Informed Graph Neural Networks

Olga Fink, Vinay Sharma

We propose a physics-informed message-passing graph neural network (GNN) for learning the dynamics of springmass systems. The proposed method embeds the underlying physics directly into the message-passing scheme of the GNN. We compare the new scheme with ...

Research Publishing2023

Learning a QoE Metric from Social Media and Gaming Footage

Aikaterini Argyraki, Catalina Paz Alvarez Inostroza

Defining a universal metric for Quality of Experience (QoE) is notoriously hard due to the complex relationship between low-level performance metrics and user satisfaction. The most common metric, the Mean Opinion Score (MOS), has well-known biases and inc ...

2023

A new method for lattice reduction using directional and hyperplanar shearing

Cyril Cayron

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

Covariant formulation of relativistic mechanics

Miguel Alexandre Ribeiro Correia

Accretion disks surrounding compact objects, and other environmental factors, deviate satellites from geodetic motion. Unfortunately, setting up the equations of motion for such relativistic trajectories is not as simple as in Newtonian mechanics. The prin ...

American Physical Society2022

Coupling metric-affine gravity to a Higgs-like scalar field

Sebastian Zell

General relativity (GR) exists in different formulations. They are equivalent in pure gravity but generically lead to distinct predictions once matter is included. After a brief overview of various versions of GR, we focus on metric-affine gravity, which a ...

American Physical Society2022

Learning to Represent and Reconstruct 3D Deformable Objects

Jan Bednarík

Representing and reconstructing 3D deformable shapes are two tightly linked problems that have long been studied within the computer vision field. Deformable shapes are truly ubiquitous in the real world, whether be it specific object classes such as human ...

EPFL2022

Fast and accurate decoding of finger movements from ECoG through Riemannian features and modern machine learning techniques

Mahsa Shoaran, Bingzhao Zhu

Objective. Accurate decoding of individual finger movements is crucial for advanced prosthetic control. In this work, we introduce the use of Riemannian-space features and temporal dynamics of electrocorticography (ECoG) signal combined with modern machine ...

IOP Publishing Ltd2022

On Linear Interpolation in the Latent Space of Deep Generative Models

Quentin Christian Becker

The underlying geometrical structure of the latent space in deep generative models is in most cases not Euclidean, which may lead to biases when comparing interpolation capabilities of two models. Smoothness and plausibility of linear interpolations in lat ...

2021

Geodesic flows on real forms of complex semi-simple Lie groups of rigid body type

Tudor Ratiu

The geodesic flows are studied on real forms of complex semi-simple Lie groups with respect to a left-invariant (pseudo-)Riemannian metric of rigid body type. The Williamson types of the isolated relative equilibria on generic adjoint orbits are determined ...

SPRINGER INTERNATIONAL PUBLISHING AG2020

Kinetic Euclidean Distance Matrices

Martin Vetterli, Ivan Dokmanic

Euclidean distance matrices (EDMs) are a major tool for localization from distances, with applications ranging from protein structure determination to global positioning and manifold learning. They are, however, static objects which serve to localize point ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Tits Buildings And K-Stability

Giulio Codogni

A polarized variety is K-stable if, for any test configuration, the Donaldson-Futaki invariant is positive. In this paper, inspired by classical geometric invariant theory, we describe the space of test configurations as a limit of a direct system of Tits ...

CAMBRIDGE UNIV PRESS2019

A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities

Adrien Giuliano Marcone

The purpose of this thesis is to provide an intrinsic proof of a Gauss-Bonnet-Chern formula for complete Riemannian manifolds with finitely many conical singularities and asymptotically conical ends. A geometric invariant is associated to the link of both ...

EPFL2019

On The Move: Localization With Kinetic Euclidean Distance Matrices

Martin Vetterli, Ivan Dokmanic

In this paper, we propose kinetic Euclidean distance matrices (KEDMs) a new algebraic tool for localization of moving points from spatio temporal distance measurements. KEDMs are inspired by the well-known Euclidean distance matrices (EDM) which model stat ...

IEEE2019

Dimensionality Reduction and Network Inference for Climate Data Using delta-MAPS: Application to the CESM Large Ensemble Sea Surface Temperature

Athanasios Nenes

A framework for analyzing and benchmarking climate model outputs is built upon delta-MAPS, a recently developed complex network analysis method. The framework allows for the possibility of highlighting quantifiable topological differences across data sets, ...

2019

Procrustes Metrics and Optimal Transport for Covariance Operators

Valentina Masarotto

Covariance operators play a fundamental role in functional data analysis, providing the canonical means to analyse functional variation via the celebrated Karhunen-Loève expansion. These operators may themselves be subject to variation, for instance in con ...

EPFL2019

Smooth Shapes with Spherical Topology: Beyond Traditional Modeling, Efficient Deformation, and Interaction

Michaël Unser, Daniel Andreas Schmitter

Existing shape models with spherical topology are typically designed either in the discrete domain using interpolating polygon meshes or in the continuous domain using smooth but non-interpolating schemes such as subdivision or NURBS. Both polygon models a ...

2017

Scale-invariant alternatives to general relativity. II. Dilaton properties

Mikhail Chapochnikov, Georgios Karananas

In the present paper, we revisit gravitational theories which are invariant under TDiffs-transverse (volume-preserving) diffeomorphisms and global scale transformations. It is known that these theories can be rewritten in an equivalent diffeomorphism-invar ...

American Physical Society2016