Sales restriction, quality selection and the mode of competition

A regulator imposing “sales restrictions” on firms competing in oligopolistic markets may enhance quality provision by the firms. Moreover, for most restrictions levels, the impact on quality selection is invariant to the mode of competition

Variétés CR polarisées et G-polarisées, partie I

Polarized and G-polarized CR manifolds are smooth manifolds endowed with a double structure: a real foliation &em&F&/em& (given by the action of a Lie group G in the G-polarized case) and a transverse CR distribution. Polarized means that (E,J) is roughly speaking invariant by&em&F&/em&. Both structures are therefore linked up. The interplay between them gives to polarized CR-manifolds a very rich geometry. In this paper, we study the properties of polarized and G-polarized manifolds, putting special emphasis on their deformations.

N-dimensional dynamical systems exploiting instabilities in full

We report experimental and numerical results showing how certain N-dimensional dynamical systems are able to exhibit complex time evolutions based on the nonlinear combination of N-1 oscillation modes. The experiments have been done with a family of thermo-optical systems of effective dynamical dimension varying from 1 to 6. The corresponding mathematical model is an N-dimensional vector field based on a scalar-valued nonlinear function of a single variable that is a linear combination of all the dynamic variables. We show how the complex evolutions appear associated with the occurrence of successive Hopf bifurcations in a saddle-node pair of fixed points up to exhaust their instability capabilities in N dimensions. For this reason the observed phenomenon is denoted as the full instability behavior of the dynamical system. The process through which the attractor responsible for the observed time evolution is formed may be rather complex and difficult to characterize. Nevertheless, the well-organized structure of the time signals suggests some generic mechanism of nonlinear mode mixing that we associate with the cluster of invariant sets emerging from the pair of fixed points and with the influence of the neighboring saddle sets on the flow nearby the attractor. The generation of invariant tori is likely during the full instability development and the global process may be considered as a generalized Landau scenario for the emergence of irregular and complex behavior through the nonlinear superposition of oscillatory motions

La teoría de Morales-Ramis y el algoritmo de Kovacic

La teor\'\ı a de Morales–Ramis es la teor\'\ı a de Galois en el contextode los sistemas din\'amicos y relaciona dos tipos diferentes de integrabilidad:integrabilidad en el sentido de Liouville de un sistema hamiltonianoe integrabilidad en el sentido de la teor\'\ı a de Galois diferencial deuna ecuaci\'on diferencial. En este art\'\i culo se presentan algunas aplicacionesde la teor\'\i a de Morales–Ramis en problemas de no integrabilidadde sistemas hamiltonianos cuya ecuaci\'on variacional normal a lo largode una curva integral particular es una ecuaci\'on diferencial lineal desegundo orden con coeficientes funciones racionales. La integrabilidadde la ecuaci\'on variacional normal es analizada mediante el algoritmode Kovacic.

Experimental design on the simplex

Optimum experimental designs depend on the design criterion, the model andthe design region. The talk will consider the design of experiments for regressionmodels in which there is a single response with the explanatory variables lying ina simplex. One example is experiments on various compositions of glass such asthose considered by Martin, Bursnall, and Stillman (2001).Because of the highly symmetric nature of the simplex, the class of models thatare of interest, typically Scheff´e polynomials (Scheff´e 1958) are rather differentfrom those of standard regression analysis. The optimum designs are also ratherdifferent, inheriting a high degree of symmetry from the models.In the talk I will hope to discuss a variety of modes for such experiments. ThenI will discuss constrained mixture experiments, when not all the simplex is availablefor experimentation. Other important aspects include mixture experimentswith extra non-mixture factors and the blocking of mixture experiments.Much of the material is in Chapter 16 of Atkinson, Donev, and Tobias (2007).If time and my research allows, I would hope to finish with a few comments ondesign when the responses, rather than the explanatory variables, lie in a simplex.ReferencesAtkinson, A. C., A. N. Donev, and R. D. Tobias (2007). Optimum ExperimentalDesigns, with SAS. Oxford: Oxford University Press.Martin, R. J., M. C. Bursnall, and E. C. Stillman (2001). Further results onoptimal and efficient designs for constrained mixture experiments. In A. C.Atkinson, B. Bogacka, and A. Zhigljavsky (Eds.), Optimal Design 2000,pp. 225–239. Dordrecht: Kluwer.Scheff´e, H. (1958). Experiments with mixtures. Journal of the Royal StatisticalSociety, Ser. B 20, 344–360.1

Ratio maps and correspondence analysis

We compare two methods for visualising contingency tables and developa method called the ratio map which combines the good properties of both.The first is a biplot based on the logratio approach to compositional dataanalysis. This approach is founded on the principle of subcompositionalcoherence, which assures that results are invariant to considering subsetsof the composition. The second approach, correspondence analysis, isbased on the chi-square approach to contingency table analysis. Acornerstone of correspondence analysis is the principle of distributionalequivalence, which assures invariance in the results when rows or columnswith identical conditional proportions are merged. Both methods may bedescribed as singular value decompositions of appropriately transformedmatrices. Correspondence analysis includes a weighting of the rows andcolumns proportional to the margins of the table. If this idea of row andcolumn weights is introduced into the logratio biplot, we obtain a methodwhich obeys both principles of subcompositional coherence and distributionalequivalence.

Computing congruences of modular forms and Galois representations modulo prime powers

This article starts a computational study of congruences of modular forms and modular Galoisrepresentations modulo prime powers. Algorithms are described that compute the maximum integermodulo which two monic coprime integral polynomials have a root in common in a sensethat is defined. These techniques are applied to the study of congruences of modular forms andmodular Galois representations modulo prime powers. Finally, some computational results withimplications on the (non-)liftability of modular forms modulo prime powers and possible generalisationsof level raising are presented.

On the robustness of least-squares Monte Carlo (LSM) for pricing American derivatives

This paper analyses the robustness of Least-Squares Monte Carlo, a techniquerecently proposed by Longstaff and Schwartz (2001) for pricing Americanoptions. This method is based on least-squares regressions in which theexplanatory variables are certain polynomial functions. We analyze theimpact of different basis functions on option prices. Numerical resultsfor American put options provide evidence that a) this approach is veryrobust to the choice of different alternative polynomials and b) few basisfunctions are required. However, these conclusions are not reached whenanalyzing more complex derivatives.

Multiple filtering devices for the estimation of cyclical DSGE models

We propose a method to estimate time invariant cyclical DSGE models using the informationprovided by a variety of filters. We treat data filtered with alternative procedures as contaminated proxies of the relevant model-based quantities and estimate structural and non-structuralparameters jointly using a signal extraction approach. We employ simulated data to illustratethe properties of the procedure and compare our conclusions with those obtained when just onefilter is used. We revisit the role of money in the transmission of monetary business cycles.

Macaulay style formulas for sparse resultants

We present formulas for computing the resultant of sparse polyno- mials as a quotient of two determinants, the denominator being a minor of the numerator. These formulas extend the original formulation given by Macaulay for homogeneous polynomials.

On the motive of a quotient variety

We show that the motive of the quotient of a scheme by a finite group coincides with the invariant submotive.

A numerical characterization of hypersurface singularities

In this note we give a numerical characterization of hypersurface singularities in terms of the normalized Hilbert-Samuel coefficients, and we interpret this result from the point of view of rigid polynomials.

Multiple edges of a quantum Hall system in a strong electric

In this paper we show that if the electrons in a quantum Hall sample are subjected to a constant electric field in the plane of the material, comparable in magnitude to the background magnetic field on the system of electrons, a multiplicity of edge states localized at different regions of space is produced in the sample. The actions governing the dynamics of these edge states are obtained starting from the well-known Schrödinger field theory for a system of nonrelativistic electrons, where on top of the constant background electric and magnetic fields, the electrons are further subject to slowly varying weak electromagnetic fields. In the regions between the edges, dubbed as the "bulk," the fermions can be integrated out entirely and the dynamics expressed in terms of a local effective action involving the slowly varying electromagnetic potentials. It is further shown how the bulk action is gauge noninvariant in a particular way, and how the edge states conspire to restore the U(1) electromagnetic gauge invariance of the system. In the edge action we obtain a heretofore unnoticed gauge-invariant term that depends on the particular edge. We argue that this term may be detected experimentally as different edges respond differently to a monochromatic probe due to this term

Critical review of K- ppn bound states

We make a thorough study of the process of three-body kaon absorption in nuclei, in connection with a recent FINUDA experiment which claims the existence of a deeply bound kaonic state from the observation of a peak in the Lambdad invariant mass distribution following K- absorption on 6Li. We show that the peak is naturally explained in terms of K- absorption from three nucleons leaving the rest as spectators. We can also reproduce all the other observables measured in the same experiment and used to support the hypothesis of the deeply bound kaon state. Our study also reveals interesting aspects of kaon absorption in nuclei, a process that must be understood in order to make progress in the search for K- deeply bound states in nuclei.