Search results for "vector space"
showing 10 items of 287 documents
Dual attachment pairs in categorically-algebraic topology
2011
[EN] The paper is a continuation of our study on developing a new approach to (lattice-valued) topological structures, which relies on category theory and universal algebra, and which is called categorically-algebraic (catalg) topology. The new framework is used to build a topological setting, based in a catalg extension of the set-theoretic membership relation "e" called dual attachment, thereby dualizing the notion of attachment introduced by the authors earlier. Following the recent interest of the fuzzy community in topological systems of S. Vickers, we clarify completely relationships between these structures and (dual) attachment, showing that unlike the former, the latter have no inh…
Removing the saturation assumption in Bank-Weiser error estimator analysis in dimension three
2020
International audience; We provide a new argument proving the reliability of the Bank-Weiser estimator for Lagrange piecewise linear finite elements in both dimension two and three. The extension to dimension three constitutes the main novelty of our study. In addition, we present a numerical comparison of the Bank-Weiser and residual estimators for a three-dimensional test case.
The Spatial Dimension in Population Fluctuations
1997
Theoretical research into the dynamics of coupled populations has suggested a rich ensemble of spatial structures that are created and maintained either by external disturbances or self-reinforcing interactions among the populations. Long-term data of the Canadian lynx from eight Canadian provinces display large-scale spatial synchrony in population fluctuations. The synchronous dynamics are not time-invariant, however, as pairs of populations that are initially in step may drift out of phase and back into phase. These observations are in agreement with predictions of a spatially-linked population model and support contemporary population ecology theory.
Interrogating witnesses for geometric constraint solving
2012
International audience; Classically, geometric constraint solvers use graph-based methods to decompose systems of geometric constraints. These methods have intrinsic limitations, which the witness method overcomes; a witness is a solution of a variant of the system. This paper details the computation of a basis of the vector space of free infinitesimal motions of a typical witness, and explains how to use this basis to interrogate the witness for dependence detection. The paper shows that the witness method detects all kinds of dependences: structural dependences already detectable by graph-based methods, but also non-structural dependences, due to known or unknown geometric theorems, which…
Robust Mean Field Games with Application to Production of an Exhaustible Resource
2012
International audience; In this paper, we study mean field games under uncertainty. We consider a population of players with individual states driven by a standard Brownian motion and a disturbance term. The contribution is three-fold: First, we establish a mean field system for such robust games. Second, we apply the methodology to an exhaustible resource production. Third, we show that the dimension of the mean field system can be significantly reduced by considering a functional of the first moment of the mean field process.
Variable Ranking Feature Selection for the Identification of Nucleosome Related Sequences
2018
Several recent works have shown that K-mer sequence representation of a DNA sequence can be used for classification or identification of nucleosome positioning related sequences. This representation can be computationally expensive when k grows, making the complexity in spaces of exponential dimension. This issue effects significantly the classification task computed by a general machine learning algorithm used for the purpose of sequence classification. In this paper, we investigate the advantage offered by the so-called Variable Ranking Feature Selection method to select the most informative k − mers associated to a set of DNA sequences, for the final purpose of nucleosome/linker classifi…
Interpretability of Recurrent Neural Networks in Remote Sensing
2020
In this work we propose the use of Long Short-Term Memory (LSTM) Recurrent Neural Networks for multivariate time series of satellite data for crop yield estimation. Recurrent nets allow exploiting the temporal dimension efficiently, but interpretability is hampered by the typically overparameterized models. The focus of the study is to understand LSTM models by looking at the hidden units distribution, the impact of increasing network complexity, and the relative importance of the input covariates. We extracted time series of three variables describing the soil-vegetation status in agroe-cosystems -soil moisture, VOD and EVI- from optical and microwave satellites, as well as available in si…
Visible parts of fractal percolation
2009
We study dimensional properties of visible parts of fractal percolation in the plane. Provided that the dimension of the fractal percolation is at least 1, we show that, conditioned on non-extinction, almost surely all visible parts from lines are 1-dimensional. Furthermore, almost all of them have positive and finite Hausdorff measure. We also verify analogous results for visible parts from points. These results are motivated by an open problem on the dimensions of visible parts.
Isometric embeddings of snowflakes into finite-dimensional Banach spaces
2016
We consider a general notion of snowflake of a metric space by composing the distance by a nontrivial concave function. We prove that a snowflake of a metric space $X$ isometrically embeds into some finite-dimensional normed space if and only if $X$ is finite. In the case of power functions we give a uniform bound on the cardinality of $X$ depending only on the power exponent and the dimension of the vector space.
On the Almost Everywhere Convergence of Multiple Fourier-Haar Series
2019
The paper deals with the question of convergence of multiple Fourier-Haar series with partial sums taken over homothetic copies of a given convex bounded set $$W\subset\mathbb{R}_+^n$$ containing the intersection of some neighborhood of the origin with $$\mathbb{R}_+^n$$ . It is proved that for this type sets W with symmetric structure it is guaranteed almost everywhere convergence of Fourier-Haar series of any function from the class L(ln+L)n−1.