A lifting and recombination algorithm for rational factorization of sparse polynomials

We propose a new lifting and recombination scheme for rational bivariate polynomial factorization that takes advantage of the Newton polytope geometry. We obtain a deterministic algorithm that can be seen as a sparse version of an algorithm of Lecerf, with now a polynomial complexity in the volume of the Newton polytope. We adopt a geometrical point of view, the main tool being derived from some algebraic osculation criterions in toric varieties.Comment: 22 page

OCA theory and EMU Eastern enlargement: An empirical application

The accession of several Central and Eastern European Countries to Euroland is likely to be realised within the next years. Some studies aim at analysing the suitability of these Euro aspirants for currency union with EMU by evaluating the related macroeconomic costs. Still, they are prone to the Lucas critique since they do not consider endogeneity of the relevant criteria. We build on methodologies developed with regard to the theory of optimum currency areas in the context of present EMU and use a structural VAR approach to evaluate EMU suitability of the candidate countries. To correct for the widespread flaw of previous studies we use lagged time series to account for endogeneities. An evaluation of the changing country characteristics within the process of integration in Western Europe confirms the importance of this approach. --OCA,EMU,shock analysis,Eastern enlargement

OCA theory and EMU eastern enlargement: An empirical application

Already before the final introduction of the single European currency there have been negotiations on a further enlargement of the Eurozone to the East. The accession of 10 Central and Eastern European Countries (CEEC) to Euroland is likely to be realised within the next 10 years and it is an important issue to assess whether these candidates are better or worse suitable for EMU membership than the current participants. The theory of optimum currency areas provides several criteria and econometric tools for analysing a prospective monetary union. Building on methodologies developed with regard to the current EMU we use a structural VAR approach in order to identify economic shocks that hit the countries to be analysed in the past. Correlations of the shocks disclosed do shed light on the question whether a common monetary policy may be suitable for the respective economies. The few already existing studies on this issue for the region are all prone to the Lucas critique since they compare contemporaneous correlations in East and West. In order to correct for this flaw we use lagged time series instead. --OCA,EMU,Eastern enlargement,Shock analysis

Using approximate roots for irreducibility and equi-singularity issues in K[[x]][y]

We provide an irreducibility test in the ring K[[x]][y] whose complexity is quasi-linear with respect to the valuation of the discriminant, assuming the input polynomial F square-free and K a perfect field of characteristic zero or greater than deg(F). The algorithm uses the theory of approximate roots and may be seen as a generalization of Abhyankhar's irreducibility criterion to the case of non algebraically closed residue fields. More generally, we show that we can test within the same complexity if a polynomial is pseudo-irreducible, a larger class of polynomials containing irreducible ones. If $F$ is pseudo-irreducible, the algorithm computes also the valuation of the discriminant and the equisingularity types of the germs of plane curve defined by F along the fiber x=0.Comment: 51 pages. Title modified. Slight modifications in Definition 5 and Proposition 1

Computing Puiseux series : a fast divide and conquer algorithm

Let $F\in \mathbb{K}[X, Y ]$ be a polynomial of total degree $D$ defined over a perfect field $\mathbb{K}$ of characteristic zero or greater than $D$. Assuming $F$ separable with respect to $Y$ , we provide an algorithm that computes the singular parts of all Puiseux series of $F$ above $X = 0$ in less than $\tilde{\mathcal{O}}(D\delta)$ operations in $\mathbb{K}$, where $\delta$ is the valuation of the resultant of $F$ and its partial derivative with respect to $Y$. To this aim, we use a divide and conquer strategy and replace univariate factorization by dynamic evaluation. As a first main corollary, we compute the irreducible factors of $F$ in $\mathbb{K}[[X]][Y ]$ up to an arbitrary precision $X^N$ with $\tilde{\mathcal{O}}(D(\delta + N ))$ arithmetic operations. As a second main corollary, we compute the genus of the plane curve defined by $F$ with $\tilde{\mathcal{O}}(D^3)$ arithmetic operations and, if $\mathbb{K} = \mathbb{Q}$, with $\tilde{\mathcal{O}}((h+1)D^3)$ bit operations using a probabilistic algorithm, where $h$ is the logarithmic heigth of $F$.Comment: 27 pages, 2 figure

Approximating the Diameter of Planar Graphs in Near Linear Time

We present a $(1+\epsilon)$-approximation algorithm running in $O(f(\epsilon)\cdot n \log^4 n)$ time for finding the diameter of an undirected planar graph with non-negative edge lengths

Competition as a Coordination Device. Experimental Evidence from a Minimum Effort Coordination Game

The problem of coordination failure, particularly in 'team production' situations, is central to a large number of mircroeconomic as well as macroeconomic models. As this type of inefficient coordination poses a severe economic problem, there is a need for institutions that foster efficient coordination of individual economic plans. In this paper, we introduce such a rather classical economic institution: competition. In a series of laboratory experiments, we reveal that the true reason for coordination failure is strategic uncertainty, which can be reduced almost completely by introducing a appropriately designed mechanism of (inter-group) competition.coordination failure, team production, competition