Towards an understanding of tradeoffs between regional wealth, tightness of a common environmental constraint and the sharing rules

Consider a country with two regions that have developed differently so that their current levels of energy efficiency differ. Each region's production involves the emission of pollutants, on which a regulator might impose restrictions. The restrictions can be related to pollution standards that the regulator perceives as binding the whole country (e.g., imposed by international agreements like the Kyoto Protocol). We observe that the pollution standards define a common constraint Upon the joint strategy space of the regions. We propose a game theoretic model with a coupled constraints equilibrium as a solution to the regulator's problem of avoiding excessive pollution. The regulator can direct the regions to implement the solution by using a political pressure, or compel them to employ it by using the coupled constraints' Lagrange multipliers as taxation coefficients. We specify a stylised model of the Belgian regions of Flanders and Wallonia that face a joint constraint, for which the regulator wants to develop a sharing rule. We analytically and numerically analyse the equilibrium regional production levels as a function of the pollution standards and of the sharing rules. We thus provide the regulator with an array of equilibria that he (or she) can select for implementation. For the computational results, we use NIRA, which is a piece of software designed to min-maximise the associated Nikaido-Isoda function.

Towards an understanding of tradeoffs between regional wealth, tightness of a common environmental constraint and the sharing rules

Consider a country with two regions that have developed differently so that their current levels of energy efficiency differ. Each region's production involves the emission of pollutants, on which a regulator might impose restrictions. The restrictions can be related to pollution standards that the regulator perceives as binding the whole country (e.g., enforced by international agreements like the Kyoto Protocol). We observe that the pollution standards define a common constraint upon the joint strategy space of the regions. We propose a game theoretic model with a coupled constraints equilibrium as a solution to the regulator's problem of avoiding excessive pollution. The regulator can direct the regions to implement the solution by using a political pressure, or compel them to employ it by using the coupled constraints' Lagrange multipliers as taxation coefficients. We specify a stylised model that possesses those characteristics, of the Belgian regions of Flanders and Wallonia. We analytically and numerically analyse the equilibrium regional production levels as a function of the pollution standards and of the sharing rules for the satisfaction of the constraint. For the computational results, we use NIRA, which is a piece of software designed to min-maximise the associated Nikaido-Isoda function.coupled constraints, generalised Nash equilibrium, Nikaido-Isoda function, regional economics, environmental regulations.

Monetary policy as a source of uncertainty

This paper proposes a model in which control variations induce an increase in the uncertainty of the system. The aim of our paper is to provide a stochastic theoretical model that can be used to explain under which uncertainty conditions monetary policy rules should be less or more aggressive, or, simply, applied or not.

Towards an understanding of tradeoffs between regional wealth, tightness of a common environmental constraint and the sharing rules

Consider a country with two regions that have developed differently so that their current levels of energy efficiency differ. Each region's production involves the emission of pollutants, on which a regulator might impose restrictions. The restrictions can be related to pollution standards that the regulator perceives as binding the whole country (e.g., enforced by international agreements like the Kyoto Protocol). We observe that the pollution standards define a common constraint upon the joint strategy space of the regions. We propose a game theoretic model with a coupled constraints equilibrium as a solution to the regulator's problem of avoiding excessive pollution. The regulator can direct the regions to implement the solution by using a political pressure, or compel them to employ it by using the coupled constraints' Lagrange multipliers as taxation coefficients. We specify a stylised model that possesses those characteristics, of the Belgian regions of Flanders and Wallonia. We analytically and numerically analyse the equilibrium regional production levels as a function of the pollution standards and of the sharing rules for the satisfaction of the constraint. For the computational results, we use NIRA, which is a piece of software designed to min-maximise the associated Nikaido-Isoda function

On the Detection of Magnetic Helicity

Magnetic fields in various astrophysical settings may be helical and, in the cosmological context, may provide a measure of primordial CP violation during baryogenesis. Yet it is difficult, even in principle, to devise a scheme by which magnetic helicity may be detected, except in some very special systems. We propose that charged cosmic rays originating from known sources may be useful for this purpose. We show that the correlator of the arrival momenta of the cosmic rays is sensitive to the helicity of an intervening magnetic field. If the sources themselves are not known, the method may still be useful provided we have some knowledge of their spatial distribution.Comment: 5 pages, 1 figure, discussions and references added, submited to Phys. Rev.

Surjective H-Colouring over reflexive digraphs

The Surjective H-Colouring problem is to test if a given graph allows a vertex-surjective homomorphism to a fixed graph H. The complexity of this problem has been well studied for undirected (partially) reflexive graphs. We introduce endo-triviality, the property of a structure that all of its endomorphisms that do not have range of size 1 are automorphisms, as a means to obtain complexity-theoretic classifications of Surjective H-Colouring in the case of reflexive digraphs. Chen (2014) proved, in the setting of constraint satisfaction problems, that Surjective H-Colouring is NP-complete if H has the property that all of its polymorphisms are essentially unary. We give the first concrete application of his result by showing that every endo-trivial reflexive digraph H has this property. We then use the concept of endo-triviality to prove, as our main result, a dichotomy for Surjective H-Colouring when H is a reflexive tournament: if H is transitive, then Surjective H-Colouring is in NL; otherwise, it is NP-complete. By combining this result with some known and new results, we obtain a complexity classification for Surjective H-Colouring when H is a partially reflexive digraph of size at most 3

When stereotype threat does not impair performance, self-affirmation can be harmful

International audienc

An O(M(n) log n) algorithm for the Jacobi symbol

The best known algorithm to compute the Jacobi symbol of two n-bit integers runs in time O(M(n) log n), using Sch\"onhage's fast continued fraction algorithm combined with an identity due to Gauss. We give a different O(M(n) log n) algorithm based on the binary recursive gcd algorithm of Stehl\'e and Zimmermann. Our implementation - which to our knowledge is the first to run in time O(M(n) log n) - is faster than GMP's quadratic implementation for inputs larger than about 10000 decimal digits.Comment: Submitted to ANTS IX (Nancy, July 2010

A Number-Theoretic Error-Correcting Code

In this paper we describe a new error-correcting code (ECC) inspired by the Naccache-Stern cryptosystem. While by far less efficient than Turbo codes, the proposed ECC happens to be more efficient than some established ECCs for certain sets of parameters. The new ECC adds an appendix to the message. The appendix is the modular product of small primes representing the message bits. The receiver recomputes the product and detects transmission errors using modular division and lattice reduction