2. Etude du LASSO 2.1. Erreur de prédiction. Proposition 2.1. Soit ŵ ∈ Argmin(J). Si ∆ = ŵ−w∗, et ||Ω||∞ ≤ λ2 , alors ||∆Jc ||1 ≤ 3||∆J ||1, où on note J le support de w∗. Pour démontrer cette proposition on rappelle des résultats sur la norme duale. Définition 1. Soit N une norme sur R, ∀y,N∗(y) = supN(x)≤1 x>y Proposition 2.2. La norme duale est une norme, et vérifie N∗∗ = N . ∀(x, y), x>y ≤ ...

s e l e c t i o n o f a p p r o p r i a t e g r o u n d m o t i o n i s a k e y e l e m e n t w i t h i n a n y s e i s m i c a s s e s s m e n t o f s t r u c t u r e s. m a n y m e t h o d o l o g i e s h a v e b e e n d e v e l o p e d i n o r d e r t o s e l e c t a n d s c a l e g r o u n d m o t i o n r e c o r d s f o r t h e p u r p o s e o f r e s p o n s e h i s t o r y a n a l y s i ...

Introduction to (near-separable) NMF • NMF Problem: X ∈ Rm×n + is a matrix with nonnegative entries, and we want to compute a nonnegative matrix factorization (NMF) X = WH, where W ∈ Rm×r + and H ∈ Rr×n + . When r < m, this problem is NP-hard. • A separable matrix is one that admits a nonnegative factorization where W = X(:,K), i.e. W is just consists of some subset of the columns of X . A near...

In this paper, it is shown that the linearized Boltzmann-Enskog collision operator cannot be dissipative in the L2-space setting contrarily to the linearized Boltzmann operator. Some estimates useful for the spectral theory are given. The Enskog equation is a modification of the Boltzmann kinetic equation, in which each particle is considered as a hard sphere with nonzero diameter a > 0 (and th...

This paper consists of three parts. In the first part we prove a general theorem on the image of a language K under a substitution, in the second we apply this to the special case when K is the language of balanced words and in the third part we deal with recurrent Z-words of minimal block growth. Definitions and notation In this paper a word is a mapping w : I → {a, b} where I is a subinterval...

introduction one of the best methods in the diagnosis and control of breast cancer is mammography. the importance of mammography is directly related to its value in the detection of breast cancer in the early stages, which leads to a more effective treatment. the purpose of this article was to calculate the x-ray spectrum in a mammography system with monte carlo codes, including mcnpx and mcnp5...

Of concern are the minimal and maximal operators on L2(R") associated with the differential expression Te = J2{id/dxJ + qJ{x))2 + W{x) j=i where (q.#„) = gradQ for some real function W on R" and W satisfies ¿M-2 < W(Jf) < C|x|~2 . In particular, for Q = 0, Xq reduces to the singular Schrödinger operator -A+ W{x). Among other results, it is shown that the maximal operator (associated with the xq...

\begin{abstract} In this paper, we partly solve the generalized Khavinson conjecture in setting of hyperbolic harmonic mappings Hardy space. Assume that $u=\mathcal{P}_{\Omega}[\phi]$ and $\phi\in L^{p}(\partial\Omega, \mathbb{R})$, where $p\in[1,\infty]$, $\mathcal{P}_{\Omega}[\phi]$ denotes Poisson integral $\phi$ with respect to Laplacian operator $\Delta_{h}$ $\Omega$, $\Omega$ unit ball $\...

Stability of stationary Navier-Stokes flows in , n ≥ 3, is discussed in the function space L or H (Hardy space). It is shown that a stationary flow w is stable in H (resp. L) if sup |x| · |w(x)| + sup |x|2|∇w(x)| (resp. ‖w‖(n,1) + ‖∇w‖(n/2,1)) is small. Explicit decay rates of the form O(t−β/2), 0 < β ≤ 1, are deduced for perturbations under additional assumptions on w and on initial data. The ...