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Concept

Product (mathematics)

Related publications (24)

The first Grushin eigenvalue on cartesian product domains

Joachim Stubbe, Luigi Provenzano

In this paper, we consider the first eigenvalue.1(O) of the Grushin operator.G :=.x1 + |x1|2s.x2 with Dirichlet boundary conditions on a bounded domain O of Rd = R d1+ d2. We prove that.1(O) admits a unique minimizer in the class of domains with prescribed ...

WALTER DE GRUYTER GMBH2023

A mathematical theory for mass lumping and its generalization with applications to isogeometric analysis

Annalisa Buffa, Yannis Dirk Voet, Espen Sande

Explicit time integration schemes coupled with Galerkin discretizations of time-dependent partial differential equations require solving a linear system with the mass matrix at each time step. For applications in structural dynamics, the solution of the li ...

2023

Matrix product states with backflow correlations

Giuseppe Carleo

By taking inspiration from the backflow transformation for correlated systems, we introduce a tensor network Ansatz which extends the well-established matrix product state representation of a quantum many-body wave function. This structure provides enough ...

AMER PHYSICAL SOC2022

Quadratic serendipity element shape functions on general planar polygons

Xiaodong Wei

This paper proposes a method for the construction of quadratic serendipity element (QSE) shape functions on planar convex and concave polygons. Existing approaches for constructing QSE shape functions are linear combinations of the pair-wise products of ge ...

ELSEVIER SCIENCE SA2022

Neural tensor contractions and the expressive power of deep neural quantum states

Giuseppe Carleo

We establish a direct connection between general tensor networks and deep feed-forward artificial neural networks. The core of our results is the construction of neural-network layers that efficiently perform tensor contractions and that use commonly adopt ...

AMER PHYSICAL SOC2022

Poly-NL: Linear Complexity Non-local Layers With 3rd Order Polynomials

Grigorios Chrysos

Spatial self-attention layers, in the form of Non-Local blocks, introduce long-range dependencies in Convolutional Neural Networks by computing pairwise similarities among all possible positions. Such pairwise functions underpin the effectiveness of non-lo ...

IEEE2021

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

Learning (from) the Electron Density: Transferability, Conformational and Chemical Diversity

Anne-Clémence Corminboeuf, Alberto Fabrizio, Andrea Grisafi, Ksenia Briling

Machine-learning in quantum chemistry is currently booming, with reported applications spanning all molecular properties from simple atomization energies to complex mathematical objects such as the many-body wavefunction. Due to its central role in density ...

2020

Forward-Backward Splitting for Optimal Transport Based Problems

Pascal Frossard, Mireille El Gheche, Hermina Petric Maretic, Guillermo Ortiz Jimenez, Effrosyni Simou

Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When the entropy regula ...

IEEE2020

Recursive blocked algorithms for linear systems with Kronecker product structure

Daniel Kressner

Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to higher-dimensional variants of g ...

SPRINGER2020

Modeling spatially dependent functional data via regression with differential regularization

Fabio Nobile

We propose a method for modelling spatially dependent functional data, based on regression with differential regularization. The regularizing term enables to include problem-specific information about the spatio-temporal variation of phenomenon under study ...

2019

Extensive amenability and an application to interval exchanges

Nicolas Monod, Nicolas Matte Bon

Extensive amenability is a property of group actions which has recently been used as a tool to prove amenability of groups. We study this property and prove that it is preserved under a very general construction of semidirect products. As an application, w ...

2018

Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré

David Valentin Strütt

In this thesis, we study two distinct problems. The first problem consists of studying the linear system of partial differential equations which consists of taking a k-form, and applying the exterior derivative 'd' to it and add the wedge product with a 1- ...

EPFL2018

Quantum critical probing and simulation of colored quantum noise

Eduardo Carlo Mascarenhas Moraes

We propose a protocol to simulate the evolution of a non-Markovian open quantum system by considering a collisional process with a many-body system, which plays the role of an environment. As a result of our protocol, the environment spatial correlations a ...

Amer Physical Soc2017

Notions of affinity in calculus of variations with differential forms

Saugata Bandyopadhyay, Swarnendu Sil

Ext-int. one affine functions are functions affine in the direction of one-divisible exterior forms with respect to the exterior product in one variable and with respect to the interior product in the other. The purpose of this article is to prove a charac ...

Walter De Gruyter Gmbh2016

Existence and Uniqueness Theorems for the Two-Dimensional Ericksen-Leslie System

Tudor Ratiu

In this paper we study the two dimensional Ericksen-Leslie equations for the nematodynamics of liquid crystals if the moment of inertia of the molecules does not vanish. We prove short time existence and uniqueness of strong solutions for the initial value ...

Springer Verlag2016

Polynomials Vanishing On Cartesian Products: The Elekes-Szabo Theorem Revisited

Frank de Zeeuw

Let F 2 C[x; y; z] be a constant-degree polynomial, and let A; B; C subset of C be finite sets of size n. We show that F vanishes on at most O(n(11/6))points of the Cartesian product A X B X C, unless F has a special group-related form. This improves a the ...

Duke Univ Press2016

Extremal behavior of squared Bessel processes attracted by the Brown-Resnick process

Sebastian Engelke

The convergence of properly time-scaled and normalized maxima of independent standard Brownian motions to the Brown-Resnick process is well-known in the literature. In this paper, we study the extremal functional behavior of non-Gaussian processes, namely ...

Elsevier Science Bv2015

Reduction and Abstraction Techniques for BIP

Simon Bliudze

Reduction and abstraction techniques have been proposed to address the state space explosion problem in verification. In this paper, we present reduction and abstraction techniques for component-based systems modeled in BIP (Behavior, Interaction and Prior ...

Springer2014

Low-Rank Tensor Methods for Communicating Markov Processes

Daniel Kressner, Francisco Santos Paredes Quartin de Macedo

Stochastic models that describe interacting processes, such as stochastic automata networks, feature a dimensionality that grows exponentially with the number of processes. This state space explosion severely impairs the use of standard methods for the num ...

Springer-Verlag Berlin2014