Binary Matrices under the Microscope: A Tomographical Problem

A binary matrix can be scanned by moving a fixed rectangular window (submatrix) across it, rather like examining it closely under a microscope. With each viewing, a convenient measurement is the number of 1s visible in the window, which might be thought of as the luminosity of the window. The rectangular scan of the binary matrix is then the collection of these luminosities presented in matrix form. We show that, at least in the technical case of a smooth m x n binary matrix, it canbe reconstructed from its rectangular scan in polynomial time in the parameters m and n, where the degree of the polynomial depends on the size of the window of inspection. For an arbitrary binary matrix, we then extend this result by determining the entries in its rectangular scan that preclude the smoothness of the matrix.Comment: 25 pages, 15 figures, submitte

French outward and inward foreign direct investment in 2009 - New presentation.

France’s direct investment flows drawn up according to the future international standards produce different results from those compiled using the current methodology. Inflows and outflows are on average EUR 30 billion lower from 1999 onwards and recent developments are signifi cantly altered.foreign direct investment, FDI, International Group, balance of payments, international investment position.

On Certain Subshifts and their Associated Monoids

Within a subclass of monoids (with zero) a structural characterization is given of those that are associated to topologically transitive subshifts with Property (A).Comment: 11 page

On subshift presentations

We consider partitioned graphs, by which we mean finite strongly connected directed graphs with a partitioned edge set ${\mathcal E} ={\mathcal E}^- \cup{\mathcal E}^+$. With additionally given a relation $\mathcal R$ between the edges in ${\mathcal E}^-$ and the edges in $\mathcal E^+$, and denoting the vertex set of the graph by ${\frak P}$, we speak of an an ${\mathcal R}$-graph ${\mathcal G}_{\mathcal R}({\frak P},{\mathcal E}^-,{\mathcal E}^+)$. From ${\mathcal R}$-graphs ${\mathcal G}_{\mathcal R}({\frak P},{\mathcal E}^-,{\mathcal E}^+)$ we construct semigroups (with zero) ${\mathcal S}_{\mathcal R}({\frak P}, {\mathcal E}^-,{\mathcal E}^+)$ that we call ${\mathcal R}$-graph semigroups. We describe a method of presenting subshifts by means of suitably structured labelled directed graphs $({\mathcal V}, \Sigma,\lambda)$ with vertex set ${\mathcal V}$, edge set $\Sigma$, and a label map that asigns to the edges in $\Sigma$ labels in an ${\mathcal R}$-graph semigroup ${\mathcal S}_{\mathcal R}({\frak P}, {\mathcal E}^-, {\mathcal E}^-)$. We call the presented subshift an ${\mathcal S}_{\mathcal R}({\frak P}, {\mathcal E}^-, {\mathcal E}^-)$-presentation. We introduce a Property $(B)$ and a Property (c), tof subshifts, and we introduce a notion of strong instantaneity. Under an assumption on the structure of the ${\mathcal R}$-graphs ${\mathcal G}_{\mathcal R}({\frak P},{\mathcal E}^-, {\mathcal E}^-)$ we show for strongly instantaneous subshifts with Property $(A)$ and associated semigroup ${\mathcal S}_{\mathcal R}({\frak P},{\mathcal E}^-,{\mathcal E}^-)$, that Properties $(B)$ and (c) are necessary and sufficient for the existence of an ${\mathcal S}_{\mathcal R}({\frak P}, {\mathcal E}^-,{\mathcal E}^-)$-presentation, to which the subshift is topologically conjugate,Comment: 33 page

Metric interpretations of infinite trees and semantics of non deterministic recursive programs

AbstractIn order to define semantics of non deterministic recursive programs we are led to consider infinite computations and to replace the structure of cpo on computation domain by the structure of complete metric space. In this setting we prove the two main theorems of semantics: 1.(i) equivalence between operational and denotational semantics, where this last one is defined2.as a greatest fixed point for inclusion,3.(ii) the one-many function computed by a program is the image of the set of trees computed by4.the scheme associated with it

Les investissements directs français à l’étranger et étrangers en France en 2009.

Présentés selon la prochaine norme internationale, les investissements directs de la France affichent des résultats différents de ceux établis suivant la méthodologie actuelle. Les flux entrants et sortants sont ainsi réduits en moyenne de 30 milliards par an depuis 1999 et leur évolution récente se modifie significativement.investissements directs, ID, groupe international, balance des paiements, position extérieure.

La position extérieure de la France à fin 2005.

L’augmentation rapide des avoirs et des engagements de la position extérieure reflète l’internationalisation de l’économie française. L’amélioration de la position nette résulte essentiellement de l’évolution des devises.Position extérieure, investissements directs, investissements de portefeuille.

Les flux d’investissements directs de la France en 2008.

Une présentation détaillée des statistiques traditionnelles sur les flux d’investissements directs de la France, entrants et sortants, en 2008.Investissements directs, IDE, fusions-acquisitions, balance des paiements.