Duality and separation theorems in idempotent semimodules

We consider subsemimodules and convex subsets of semimodules over semirings with an idempotent addition. We introduce a nonlinear projection on subsemimodules: the projection of a point is the maximal approximation from below of the point in the subsemimodule. We use this projection to separate a point from a convex set. We also show that the projection minimizes the analogue of Hilbert's projective metric. We develop more generally a theory of dual pairs for idempotent semimodules. We obtain as a corollary duality results between the row and column spaces of matrices with entries in idempotent semirings. We illustrate the results by showing polyhedra and half-spaces over the max-plus semiring.Comment: 24 pages, 5 Postscript figures, revised (v2

Variable elimination for building interpreters

In this paper, we build an interpreter by reusing host language functions instead of recoding mechanisms of function application that are already available in the host language (the language which is used to build the interpreter). In order to transform user-defined functions into host language functions we use combinatory logic : lambda-abstractions are transformed into a composition of combinators. We provide a mechanically checked proof that this step is correct for the call-by-value strategy with imperative features.Comment: 33 page

Multiple Production, Transport in Atmosphere and Detection of High Energy Cosmic Rays

We describe the general aspects of Monte Carlo Collision Generators suitable for cosmic ray nucleon-Air and nuclei-Air interactions, including accelerator and collider data. The problem of the extrapolation at 3 energy decades above the LHC of the main features of high energy collisions is discussed and under theoretical and phenomenological assumptions, the properties of the longitudinal and lateral development of giant extensive air showers simulated with the CORSIKA program are presented. The determination of the primary energy near $10^{20}$ eV is examined for different observables, total size, densities of charged particles interpolated at 600~m from shower core. The extensive air shower data collected around LHC energy is in better agreement with models of large multiplicities. Beyond this energy, the extrapolation carried assuming the diquark breaking mechanism can change the classic conversion to primary energy and such circumstance can have consequences on the validity of the GZK cut off. In those conditions, we have simulated large and giant air showers taking into account, in addition, new processes, such as diquark breaking, and topological problems involving adequate structure functions for lateral distributions, up to energies exceeding $10^{20}$ eV for P.AUGER and EUSO experiments.Comment: 10 pages, 8 figures (6 in eps, 2 in ps) talk given at XXXI International Symposium on Multiparticle Dynamics, Sep. 1-7, 2001, Datong China URL http://ismd31.ccnu.edu.cn

Decision under risk : The classical Expected Utility model

This chapter of a collective book aims at presenting the basics of decision making under risk. We first define notions of risk and increasing risk and recall definitions and classifications (that are valid independently of any representation) of behavior under risk. We then review the classical model of expected utility due to von Neumann and Morgenstern andd its main properties. Issues raised by this model are then discussed and two models generalizing the expected utility model are briefly discussed.Risk, risk aversion, expected utility, von Neumann and Morgenstern, Allais paradox.

Decision under Uncertainty : the Classical Models

This chapiter of a collective book is dedicated to classical decision models under uncertainty, i.e. under situations where events do not have "objective" probabilities with which the Decision Marker agrees. We present successively the two main theories, their axiomatic, the interpretation and the justification of their axioms and their main properties : first, the general model of Subjective Expected Utility due to Savage (Savage, 1954), second, the Anscombe-Aumann (1963) theory, in a different framework. Both theories enforce the universal use of a probabilistic representation. We then discuss this issue in connection with the experimental result known as the Ellsberg paradox.Uncertainty, subjective probability, Subjective Expected Utility, Savage, Anscombe and Aumann, Ellsberg paradox.

Asia-Europe: the third link

The report provides a comprehensive analysis of Europe-East Asia interdependences (in terms of relative economic weights, trade and financial integration, trade and financial flows, exchange rate and wealth transfers). The prime motivation of the paper is that linkages between Europe and East Asia remain frequently underestimated. While the “third link†between them is in many respects as important as the linkages between the two regions and North America, it is too often regarded only as of secondary importance.Regional integration, Financial integration, Trade integration, East Asia, European Monetary Union, Pisani-Ferry , Cohen-Setton

The use of colloquial words in advanced French interlanguage

This article addresses the issue of underrepresentation or avoidance of colloquial words in a cross-sectional corpus of advanced French interlanguage (IL) of 29 Dutch L1 speakers and in a longitudinal corpus of 6 Hiberno-Irish English L1 speakers compared with a control of 6 native speakers of French. The main independent variable analysed in the latter corpus is the effect of spending a year in a francophone environment. This analysis is supplemented by a separate study of sociobiographical and psychological factors that affect the use of colloquial vocabulary in the cross-sectional corpus. Colloquial words are not exceptionally complex morphologically and present no specific grammatical difficulties, yet they are very rare in our data. Multivariate regression analyses suggest that only active authentic communication in the target language (TL) predicts the use of colloquial lexemes in the cross-sectional corpus. This result was confirmed in the longitudinal corpus where a t-test showed that the proportion of colloquial lexemes increased significantly after a year abroad

Dynamic consistency for Stochastic Optimal Control problems

For a sequence of dynamic optimization problems, we aim at discussing a notion of consistency over time. This notion can be informally introduced as follows. At the very first time step $t_0$, the decision maker formulates an optimization problem that yields optimal decision rules for all the forthcoming time step $t_0, t_1, ..., T$; at the next time step $t_1$, he is able to formulate a new optimization problem starting at time $t_1$ that yields a new sequence of optimal decision rules. This process can be continued until final time $T$ is reached. A family of optimization problems formulated in this way is said to be time consistent if the optimal strategies obtained when solving the original problem remain optimal for all subsequent problems. The notion of time consistency, well-known in the field of Economics, has been recently introduced in the context of risk measures, notably by Artzner et al. (2007) and studied in the Stochastic Programming framework by Shapiro (2009) and for Markov Decision Processes (MDP) by Ruszczynski (2009). We here link this notion with the concept of "state variable" in MDP, and show that a significant class of dynamic optimization problems are dynamically consistent, provided that an adequate state variable is chosen