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Concept

Euclidean vector

Related publications (28)

Dynamical Low-Rank Approximation for Stochastic Differential Equations

Fabio Nobile, Yoshihito Kazashi, Fabio Zoccolan

In this paper, we set the mathematical foundations of the Dynamical Low-Rank Approximation (DLRA) method for stochastic differential equations (SDEs). DLRA aims at approximating the solution as a linear combination of a small number of basis vectors with r ...

American Mathematical Society (AMS)2025

Three-dimensional evaluation of the transverse rotator cuff muscle's resultant force angle in relation to scapulohumeral subluxation and glenoid vault morphology in nonpathological shoulders

Alexandre Terrier, Alain Farron, Patrick Goetti, Pezhman Eghbalishamsabadi, Matthieu Boubat

Background: Static posterior subluxation of the humeral head (SPSH) results in glenohumeral osteoarthritis. Treatment strategies for SPSH with or without resulting osteoarthritis remain challenging. There is growing interest in evaluating the rotator cuff ...

Mosby-Elsevier2024

Randomized low-rank approximation and its applications

Ulf David Persson

In this thesis we will present and analyze randomized algorithms for numerical linear algebra problems. An important theme in this thesis is randomized low-rank approximation. In particular, we will study randomized low-rank approximation of matrix functio ...

EPFL2024

Randomized flexible GMRES with deflated restarting

Laura Grigori

For a high-dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in terms of both computational cost and numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g., to the ge ...

Springer2024

Diversity of radial spin textures in chiral materials

Oleg Yazyev, Alberto Crepaldi, Daniel Gosalbez Martinez

We introduce a classification of the radial spin textures in momentum space that emerge at the high-symmetry points in crystals characterized by nonpolar chiral point groups (D2, D3, D4, D6, T, O). Based on the symmetry constraints imposed by these point g ...

Amer Physical Soc2023

DARE-GRAM : Unsupervised Domain Adaptation Regression by Aligning Inverse Gram Matrices

Olga Fink, Ismail Nejjar

Unsupervised Domain Adaptation Regression (DAR) aims to bridge the domain gap between a labeled source dataset and an unlabelled target dataset for regression problems. Recent works mostly focus on learning a deep feature encoder by minimizing the discrepa ...

IEEE2023

Overflow-free compute memories for edge AI acceleration

David Atienza Alonso, Giovanni Ansaloni, Alexandre Sébastien Julien Levisse, Flavio Ponzina, Marco Antonio Rios

Compute memories are memory arrays augmented with dedicated logic to support arithmetic. They support the efficient execution of data-centric computing patterns, such as those characterizing Artificial Intelligence (AI) algorithms. These architectures can ...

2023

Get the Best of Both Worlds: Improving Accuracy and Transferability by Grassmann Class Representation

Haoqi Wang

We generalize the class vectors found in neural networks to linear subspaces (i.e., points in the Grassmann manifold) and show that the Grassmann Class Representation (GCR) enables simultaneous improvement in accuracy and feature transferability. In GCR, e ...

Ieee Computer Soc2023

Traversing Time Dependent Light Fields for Daylight Glare Evaluation

Stephen William Wasilewski

To understand how daylight gives shape and life to architectural spaces, whether existing or imagined, requires quantifying its dynamism and energy. Maintaining these details presents a challenge to simulation and analysis methods that flatten data into di ...

EPFL2023

IMPROVED VARIANTS OF THE HUTCH plus plus ALGORITHM FOR TRACE ESTIMATION

Daniel Kressner, Alice Cortinovis, Ulf David Persson

This paper is concerned with two improved variants of the Hutch++ algorithm for estimating the trace of a square matrix, implicitly given through matrix-vector products. Hutch++ combines randomized low-rank approximation in a first phase with stochastic tr ...

SIAM PUBLICATIONS2022

Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning

Tommaso Vanzan

Iterative substructuring Domain Decomposition (DD) methods have been extensively studied, and they are usually associated with nonoverlapping decompositions. It is less known that classical overlapping DD methods can also be formulated in substructured for ...

2022

Collaborative Learning in the Jungle (Decentralized, Byzantine, Heterogeneous, Asynchronous and Nonconvex Learning)

Rachid Guerraoui, El Mahdi El Mhamdi, Sébastien Louis Alexandre Rouault, Le Nguyen Hoang, Arsany Hany Abdelmessih Guirguis, Sadegh Farhadkhani

We study Byzantine collaborative learning, where n nodes seek to collectively learn from each others' local data. The data distribution may vary from one node to another. No node is trusted, and f < n nodes can behave arbitrarily. We prove that collaborati ...

2021

Further results on latent discourse models and word embeddings

Youssef Allouah

We discuss some properties of generative models for word embeddings. Namely, (Arora et al., 2016) proposed a latent discourse model implying the concentration of the partition function of the word vectors. This concentration phenomenon led to an asymptotic ...

Microtome Publishing2021

Coarse graining and large-N behavior of the d-dimensional N-clock model

Matthias Benjamin Ruf

We study the asymptotic behavior of the N-clock model, a nearest neighbors ferromagnetic spin model on the d-dimensional cubic epsilon-lattice in which the spin field is constrained to take values in a discretization S-N of the unit circle S-1 consisting o ...

2021

Gaussian Process Regression for Materials and Molecules

Michele Ceriotti, David Mark Wilkins

We provide an introduction to Gaussian process regression (GPR) machinelearning methods in computational materials science and chemistry. The focus of the present review is on the regression of atomistic properties: in particular, on the construction of in ...

AMER CHEMICAL SOC2021

Locally supported tangential vector, n-vector, and tensor fields

Christopher Brandt

We introduce a construction of subspaces of the spaces of tangential vector, n-vector, and tensor fields on surfaces. The resulting subspaces can be used as the basis of fast approximation algorithms for design and processing problems that involve tangenti ...

2020

Coordinate Difference Matrices

Martin Vetterli, Gilles Baechler, Golnooshsadat Elhami, Miranda Krekovic

In many problems such as phase retrieval, molecular biology, source localization, and sensor array calibration, one can measure vector differences between pairs of points and attempt to recover the position of these points; this class of problems is called ...

SIAM PUBLICATIONS2020

On compact representations of Voronoi cells of lattices

Matthias Schymura, Christoph Hunkenschröder

In a seminal work, Micciancio and Voulgaris (SIAM J Comput 42(3):1364-1391, 2013) described a deterministic single-exponential time algorithm for the closest vector problem (CVP) on lattices. It is based on the computation of the Voronoi cell of the given ...

SPRINGER HEIDELBERG2020

Proximity Results and Faster Algorithms for Integer Programming Using the Steinitz Lemma

Friedrich Eisenbrand

We consider integer programming problems in standard form max{c(T)x : Ax = b, x >= 0, x is an element of Z(n)} where A is an element of Z(mxn), b is an element of Z(m), and c is an element of Z(n). We show that such an integer program can be solved in time ...

ASSOC COMPUTING MACHINERY2020

Rapid Analysis of Arbitrary-Shaped Conformal Beam-Scanning Arrays

Anja Skrivervik, Denys Nikolayev

Conformal antenna arrays are able to fit seamlessly on curved 3D-shaped surfaces, which are found ubiquitously on vehicles, aircraft, a human body, etc. In addition, conformal structures can overcome the scan loss limitations of conventional planar arrays. ...

IEEE2020