Two decades after their invention, the IBM word-based translation models, widely available in the GIZA++ toolkit, remain the dominant approach to word alignment and an integral part of many statistical translation systems. Although many models have surpassed them in accuracy, none has supplanted them in practice. In this paper, we propose a simple extension to the IBM models: an l0 prior to enc...

In this paper, a fast algorithm for overcomplete sparse decomposition, called SL0, is proposed. The algorithm is essentially a method for obtaining sparse solutions of underdetermined systems of linear equations, and its applications include underdetermined Sparse Component Analysis (SCA), atomic decomposition on overcomplete dictionaries, compressed sensing, and decoding real field codes. Cont...

Two decades after their invention, the IBM word-based translation models, widely available in the GIZA++ toolkit, remain the dominant approach to word alignment and an integral part of many statistical translation systems. Although many models have surpassed them in accuracy, none have supplanted them in practice. In this paper, we propose a simple extension to the IBM models: an l0 prior to en...

INTRODUCTION: Compressed Sensing (CS) ([1], [2], [3], [4]) is a recently created algorithm which allows reconstructing a signal from a small portion of its Fourier coefficients if that signal is sparse in a suitable basis. It was first used by Lustig et al. [5] in MRI, and it has become a popular alternative for speeding up the MRI acquisition processes. In practice, CS has been implemented as ...

The p-adic description of Higgs mechanism in TGD framework provides excellent predictions for elementary particle and hadrons masses ([email protected] 9410058-62). The gauge group of TGD is just the gauge group of the standard model so that it makes sense to study the p-adic counterpart of the standard model as a candidate for low energy effective theory. Momentum eigen states can be constru...

We consider shape optimization problems governed by the unsteady Navier-Stokes equations by applying the method of mappings, where the problem is transformed to a reference domain Ωref and the physical domain is given by Ω = τ(Ωref) with a domain transformation τ ∈ W (Ωref). We show the Fréchet-differentiability of τ 7→ (v, p)(τ) in a neighborhood of τ = id under as low regularity requirements ...

Let E be an ideal of L0 over a σ-finite measure space (Ω,Σ, μ), and let E∼ stand for the order dual of E. For a real Banach space (X, ‖ · ‖X ) let E(X) be a subspace of the space L0(X) of μ-equivalence classes of strongly Σ-measurable functions f : Ω −→ X and consisting of all those f ∈ L0(X) for which the scalar function ‖f(·)‖X belongs to E. For a real Banach space (Y, ‖ · ‖Y ) a linear opera...

Theorem 1 (Exact Recovery of Outlier Pursuit). Suppose m = Θ(n), Range(L0) = Range(PI⊥ 0 L0), and [S0]:j 6∈ Range(L0) for ∀j ∈ I0. Then any solution (L0+H,S0−H) to Outlier Pursuit (1) with λ = 1/ √ log n exactly recovers the column space of L0 and the column support of S0 with a probability at least 1 − cn−10, if the column support I0 of S0 is uniformly distributed among all sets of cardinality...

Compressed sensing is a developing field aiming at reconstruction of sparse signals acquired in reduced dimensions, which make the recovery process under-determined. The required solution is the one with minimum l0 norm due to sparsity, however it is not practical to solve the l0 minimization problem. Commonly used techniques include l1 minimization, such as Basis Pursuit (BP) and greedy pursui...

We study the l0-Low Rank Approximation Problem, where the goal is, given anm×nmatrix A, to output a rank-k matrix A for which ‖A′ −A‖0 is minimized. Here, for a matrix B, ‖B‖0 denotes the number of its non-zero entries. This NP-hard variant of low rank approximation is natural for problems with no underlying metric, and its goal is to minimize the number of disagreeing data positions. We provid...