Search results for "Embedding"
showing 10 items of 175 documents
Abstract and concrete tangent modules on Lipschitz differentiability spaces
2020
We construct an isometric embedding from Gigli's abstract tangent module into the concrete tangent module of a space admitting a (weak) Lipschitz differentiable structure, and give two equivalent conditions which characterize when the embedding is an isomorphism. Together with arguments from a recent article by Bate--Kangasniemi--Orponen, this equivalence is used to show that the ${\rm Lip}-{\rm lip}$ -type condition ${\rm lip} f\le C|Df|$ implies the existence of a Lipschitz differentiable structure, and moreover self-improves to ${\rm lip} f =|Df|$. We also provide a direct proof of a result by Gigli and the second author that, for a space with a strongly rectifiable decomposition, Gigli'…
The Fatou coordinate for parabolic Dulac germs
2017
We study the class of parabolic Dulac germs of hyperbolic polycycles. For such germs we give a constructive proof of the existence of a unique Fatou coordinate, admitting an asymptotic expansion in the power-iterated log scale.
Unifying vectors and matrices of different dimensions through nonlinear embeddings
2020
Complex systems may morph between structures with different dimensionality and degrees of freedom. As a tool for their modelling, nonlinear embeddings are introduced that encompass objects with different dimensionality as a continuous parameter $\kappa \in \mathbb{R}$ is being varied, thus allowing the unification of vectors, matrices and tensors in single mathematical structures. This technique is applied to construct warped models in the passage from supergravity in 10 or 11-dimensional spacetimes to 4-dimensional ones. We also show how nonlinear embeddings can be used to connect cellular automata (CAs) to coupled map lattices (CMLs) and to nonlinear partial differential equations, derivi…
The Poisson embedding approach to the Calderón problem
2020
We introduce a new approach to the anisotropic Calder\'on problem, based on a map called Poisson embedding that identifies the points of a Riemannian manifold with distributions on its boundary. We give a new uniqueness result for a large class of Calder\'on type inverse problems for quasilinear equations in the real analytic case. The approach also leads to a new proof of the result by Lassas and Uhlmann (2001) solving the Calder\'on problem on real analytic Riemannian manifolds. The proof uses the Poisson embedding to determine the harmonic functions in the manifold up to a harmonic morphism. The method also involves various Runge approximation results for linear elliptic equations.
Renewable energy for sustainable rural development: synergies and mismatches
2020
Abstract Energy transition is increasingly regarded as a promising opportunity for the economic development of rural areas. This possibility is associated with the siting and (co-)ownership of decentralized (small-scale) renewable energy facilities. The underlying productive link, however, has been taken for granted, rather than conceptually and practically cultivated. Thus, while renewable energy-based rural development has been stated as a desired by-product of energy transitions, its potential has remained largely unfulfilled. This review aims to illuminate the ambiguous interplay between renewable energy and rural development in the context of the current trajectories of the energy tran…
Contribution à l’apprentissage de représentation de données à base de graphes avec application à la catégorisation d’images
2020
Graph-based Manifold Learning algorithms are regarded as a powerful technique for feature extraction and dimensionality reduction in Pattern Recogniton, Computer Vision and Machine Learning fields. These algorithms utilize sample information contained in the item-item similarity and weighted matrix to reveal the intrinstic geometric structure of manifold. It exhibits the low dimensional structure in the high dimensional data. This motivates me to develop Graph-based Manifold Learning techniques on Pattern Recognition, specially, application to image categorization. The experimental datasets of thesis correspond to several categories of public image datasets such as face datasets, indoor and…
Embedding Evolution in Epidemic-Style Forwarding
2007
International audience; In this work, we introduce a framework to let forwarding schemes evolve in order to adapt to changing and a priori unknown environments. The framework is inspired by genetic algorithms: at each node a genotype describes the forwarding scheme used, a selection process fosters the diffusion of the fittest genotypes in the system and new genotypes are created by combining existing ones or applying random changes. A case study implementation is presented and its performance evaluated via numerical simulations.
Positionless aspect based sentiment analysis using attention mechanism.
2021
Abstract Aspect-based sentiment analysis (ABSA) aims at identifying fine-grained polarity of opinion associated with a given aspect word. Several existing articles demonstrated promising ABSA accuracy using positional embedding to show the relationship between an aspect word and its context. In most cases, the positional embedding depends on the distance between the aspect word and the remaining words in the context, known as the position index sequence. However, these techniques usually employ both complex preprocessing approaches with additional trainable positional embedding and complex architectures to obtain the state-of-the-art performance. In this paper, we simplify preprocessing by …
Testing Independence: A New Approach
2000
In time series analysis and modelling, testing for independence allows us to determine if the estimated model is correctly specified. In this work, we present a very simple method to test for serial independence, based on the two-dimensional embedding vectors (the so-called “2-histories”), and we analyse the power and size of such a procedure against a wide set of linear and nonlinear alternatives.
EMBER—Embedding Multiple Molecular Fingerprints for Virtual Screening
2022
In recent years, the debate in the field of applications of Deep Learning to Virtual Screening has focused on the use of neural embeddings with respect to classical descriptors in order to encode both structural and physical properties of ligands and/or targets. The attention on embeddings with the increasing use of Graph Neural Networks aimed at overcoming molecular fingerprints that are short range embeddings for atomic neighborhoods. Here, we present EMBER, a novel molecular embedding made by seven molecular fingerprints arranged as different “spectra” to describe the same molecule, and we prove its effectiveness by using deep convolutional architecture that assesses ligands&…