Motivated by isotropic fully developed turbulence, we define a theory of symmetric matrix valued isotropic Gaussian multiplicative chaos. Our construction extends the scalar theory developed by J.P. Kahane in 1985.

Support Vector Machines nd maximal margin hyperplanes in a high dimensional feature space, represented as a sparse linear combination of training points. Theoretical results exist which guarantee a high generalization performance when the margin is large or when the representation is very sparse. Multiplicative-Updating algorithms are a new tool for perceptron learning which are guaranteed to c...

We define a (chaotic) deterministic variant of random multiplicative cascade models of turbulence. It preserves the hierarchical tree structure , thanks to the addition of infinitesimal noise. The zero-noise limit can be handled by Perron-Frobenius theory, just as the zero-diffusivity limit for the fast dynamo problem. Random multiplicative models do not possess Kolmogorov 1941 (K41) scaling be...

Multiplicative backward stability results are presented for two algorithms which compute the singular value decomposition of dense matrices. These algorithms are the classical onesided Jacobi algorithm, with a stringent stopping criterion, and an algorithm which uses one-sided Jacobi to compute high accurate singular value decompositions of matrices given as rank-revealing factorizations. When ...

In this paper we present a theory of proof nets for full multiplicative linear logic, including the two units. It naturally extends the well-known theory of unit-free multiplicative proof nets. A linking is no longer a set of axiom links but a tree in which the axiom links are subtrees. These trees will be identified according to an equivalence relation based on a simple form of graph rewriting...

In this article, we consider the continuous analog of the celebrated Mandelbrot star equation with lognormal weights. Mandelbrot introduced this equation to characterize the law of multiplicative cascades. We show existence and uniqueness of measures satisfying the aforementioned continuous equation; these measures fall under the scope of the Gaussian multiplicative chaos theory developed by J....

We deene a (chaotic) deterministic variant of random multiplicative cascade models of turbulence. It preserves the hierarchical tree structure , thanks to the addition of innnitesimal noise. The zero-noise limit can be handled by Perron-Frobenius theory, just as the zero-diiusivity limit for the fast dynamo problem. Random multiplicative models do not possess Kolmogorov 1941 (K41) scaling becau...

We give a representation of the classical theory of multiplicative arithmetic functions (MF)in the ring of symmetric polynomials. The basis of the ring of symmetric polynomials that we use is the isobaric basis, a basis especially sensitive to the combinatorics of partitions of the integers. The representing elements are recursive sequences of Schur polynomials evaluated at subrings of the comp...

We study the model theory of (F;<χ) where the field F is an algebraic closure of a finite field and <χ is an ordering on the multiplicative group F× induced by a group embedding χ ∶ F× → C×. Using number-theoretic bounds on multiplicative character sums over finite fields and Weyl’s criterion for equidistribution, we establish a number of properties about the interaction between <χ and the unde...

In the case of a locally compact field K, the additive group (K,+) and the multiplicative group (K×, ·) play key roles in the theory. Each is a locally compact abelian group, hence amenable to the methods of Fourier analysis. Moreover, the additive group is self-Pontrjagin dual, and the multiplicative group K× is a target group for class field theory on K: that is, there is a bijective correspo...