A preconditioning procedure is developed for the L2 and more general optimal transport problems. The procedure is based on a family of affine map pairs which transforms the original measures into two new measures that are closer to each other while preserving the optimality of solutions. It is proved that the preconditioning procedure minimizes the remaining transportation cost among all admiss...

Let G be a compact affine definable C group and let r be∞ or ω. We prove that the representative definable C functions on G is dense in the space of continuous functions on G. Moreover we compare the category of compact affine definable C groups D with that of compact real algebraic groups A.

We extend the knowledge compilation map introduced by Darwiche and Marquis with three influential propositional fragments, the Krom CNF one (also known as the bijunctive fragment), the Horn CNF fragment and the affine fragment (also known as the biconditional fragment) as well as seven additional languages based on them, and composed respectively of Krom or Horn CNF formulas, renamable Horn CNF...

Let D be an affine difference set of order n in an abelian group G relative to a subgroup N . Set H̃ = H \ {1, ω}, where H = G/N and ω = ∏ σ∈H σ. Using D we define a two-to-one map g from H̃ to N . The map g satisfies g(σ) = g(σ) and g(σ) = g(σ−1) for any multiplier m of D and any element σ ∈ H̃. As applications, we present some results which give a restriction on the possible order n and the grou...

Let G be an affine algebraic group over an algebraically closed field k of characteristic zero. In this paper, we consider finite G-equivariant morphisms F : X → Y of irreducible affine varieties. First we determine under which conditions on Y the induced map FG : X//G → Y//G of quotient varieties is also finite. This result is reformulated in terms of kernels of derivations on k-algebras A ⊂ B...

In this paper we focus on the identification of discrete-time hybrid systems in the Mixed-Logic Dynamical (MLD)/Piece-Wise Affine (PWA) form. This problem can be formulated as the reconstruction of a possibly discontinuous PWA map with a multi-dimensional domain. In order to achieve our goal, we propose an algorithm that exploits the combined use of clustering, linear identification, and classi...

A preconditioning procedure is developed for the L2 and more general optimal 3 transport problems. The procedure is based on a family of affine map pairs which transforms the 4 original measures into two new measures that are closer to each other, while preserving the optimality 5 of solutions. It is proved that the preconditioning procedure minimizes the remaining transportation 6 cost among a...

This paper presents extensions to Alpha, a language based upon the formalism of affine recurrence equations (AREs). These extensions address the need for parametric and structured systems of such AREs. Similar to, but more general as the map operator of classical functional languages, the Alpha structuration techniques provide a dense and powerful description of complex systems referencing each...

Background: Modified Atmosphere Packaging (MAP) is one of the most convenient packaging methods that could be useful in reducing the wastes and extending the crops’ shelf-life. This research aimed to assess the impact of MAP containing high concentrations of carbon dioxide on physicochemical, microbial, and sensorial properties of Iranian Mazafati date. Methods: Date samples were packed separa...

The affine synthesis operator Sc = P j>0 P k∈Zd cj,kψj,k is shown to map the mixed-norm sequence space `(`) surjectively onto L(R), 1 ≤ p < ∞, under mild conditions on the synthesizer ψ ∈ L(R) (say, having a radially decreasing L majorant near infinity) and assuming R Rd ψ dx = 1. Here ψj,k(x) = | det aj |ψ(ajx− k), for some dilation matrices aj that expand. Therefore the standard norm on f ∈ L...