Related papers: Sur la lin\'earisation des tissus

This paper addresses the challenge of viewing and navigating Bayesian networks as their structural size and complexity grow. Starting with a review of the state of the art of visualizing Bayesian networks, an area which has largely been…

We use a generalization of Horrocks monads for arithmetic Cohen-Macaulay (ACM) varieties to establish a cohomological characterization of linear and Steiner bundles over projective spaces and quadric hypersurfaces. We also study resolutions…

The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…

We define a notion which contains numerous basic notions of Analysis as special cases, for example limit, continuity, differential, Riemann and Lebesgue integral, root and exponential functions. Properties like additivity or linearity of…

We apply recent advances in machine learning and computer vision to a central problem in materials informatics: The statistical representation of microstructural images. We use activations in a pre-trained convolutional neural network to…

We give a precise mathematical formulation for the notions of a parametric patch and linear precision, and establish their elementary properties. We relate linear precision to the geometry of a particular linear projection, giving necessary…

We propose the use of lattice field theory for the study of string field theory at the non-perturbative quantum level. We identify many potential obstacles and examine possible resolutions thereof. We then experiment with our approach in…

Bases, mappings, projections and metrics, natural for Neural network training, are introduced. Graph-theoretical interpretation is offered. Non-Gaussianity naturally emerges, even in relatively simple datasets. Training statistics,…

Text network analysis has received increasing attention as a consequence of its wide range of applications. In this work, we extend a previous work founded on the study of topological features of mesoscopic networks. Here, the geometrical…

In our article "A tree of linearisable second-order evolution equations by generalised hodograph transformations" [J. Nonlin. Math. Phys. {\bf 8} (2001), 342-362] we presented a tree of linearisable (C-integrable) second-order evolution…

Let X be a smooth projective variety of dimension n in P^r. We study the fibers of a general linear projection pi: X --> P^{n+c}, with c > 0. When n is small it is classical that the degree of any fiber is bounded by n/c+1, but this fails…

In this paper, we define the linear complexity for multidimensional sequences over finite fields, generalizing the one-dimensional case. We give some lower and upper bounds, valid with large probability, for the linear complexity and…

In this paper, the flexibility, versatility and predictive power of kernel regression are combined with now lavishly available network data to create regression models with even greater predictive performances. Building from previous work…

In this work, we investigate \textit{texture learning}: the identification of textures learned by object classification models, and the extent to which they rely on these textures. We build texture-object associations that uncover new…

Generalization is a central aspect of learning theory. Here, we propose a framework that explores an auxiliary task-dependent notion of generalization, and attempts to quantitatively answer the following question: given two sets of patterns…

Considered two linear regression models of a given response variable with some predictor set and its subset. It is shown that there is a linear relationship between coefficients of these models. Some corollaries of the proved theorem is…

Given a web (multi-foliation) and a linear system on a projective surface we construct divisors cutting out the locus where some element of the linear system has abnormal contact with the leaf of the web. We apply these ideas to reobtain a…

We define in a global manner the notion of a connective structure for a gerbe on a space X. When the gerbe is endowed with trivializing data with respect to an open cover of X, we describe this connective structure in two separate ways,…

In this paper, we provide constructions to enumerate large numbers of CI-liaison classes. To this end, we introduce a liaison invariant and prove several results concerning it, notably that it commutes with hypersurface sections. This…

We develop a unified framework for the study of properties involving diagonalizations of dense families in topological spaces. We provide complete classification of these properties. Our classification draws upon a large number of methods…