Person:
Morán Cabré, Manuel

First Name

Manuel

Last Name

Morán Cabré

Affiliation

Universidad Complutense de Madrid

Faculty / Institute

Ciencias Económicas y Empresariales

Area

Fundamentos del Análisis Económico

Identifiers

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Now showing 1 - 10 of 28

Convergence of the Eckmann and Ruelle algorithm for the estimation of Liapunov exponents
(Cambridge University Press, 2000) Mera Rivas, Maria Eugenia; Morán Cabré, Manuel
We analyze the convergence conditions of the Eckmann and Ruelle algorithm (E.R.A. for the sequel) used to estimate the Liapunov exponents, for the tangent map, of an ergodic measure, invariant under a smooth dynamical system. We find sufficient conditions for this convergence which are related to those ensuring the convergence to the tangent map of the best linear L^{p}-fittings of the action of a mapping f on small balls. Under such conditions, we show how to use E.R.A. to obtain estimates of the Liapunov exponents, up to an arbitrary degree of accuracy. We propose an adaptation of E.R.A. for the computation of Liapunov exponents in smooth manifolds which allows us to avoid the problem of detecting the spurious exponents. We prove, for a Borel measurable dynamics f, the existence of Liapunov exponents for the function Sr(x), mapping each point x to the matrix of the best linear Lp-fitting of the action of f on the closed ball of radius r centered at x, and we show how to use E.R.A. to get reliable estimates of the Liapunov exponents of Sr. We also propose a test for checking the differentiability of an empirically observed dynamics.
Modeling the stochastic dynamics of the aggregate stock in collapsed fisheries: The case of the Northern cod stock
(2013-09) Maroto Fernández, José María; Morán Cabré, Manuel
Motivated by the evidence that many collapsed stocks have failed to recover despite the fact that fishing mortality has been reduced, or even when a moratorium is in effect, we develop a methodological approach using splines to analyze the stochastic population dynamics of fish stocks at low stock levels. Considering the aggregate Northern cod stock by way of illustration, we find that the species’ lack of recovery, despite the moratorium which still remains in force, is consistent with the hypothesis of depensatory population dynamics at low population sizes, as opposed to the compensation estimated by the conventional regression methods used in classic bioeconomic models.
A bridge between continuous and discrete-time bioeconomic models: Seasonality in fisheries
(2016) Kvamsdal, Sturla; Maroto Fernández, José María; Morán Cabré, Manuel; Sandal, Leif K.
Wedevelopadiscretizationmethodto construct adiscretefinite-time bioeconomicmodel, corresponding to bioeconomic models with continuous-time growth function, but allowing the analysis of seasonality in fisheries. The discretization method consists ofthree steps: first, we estimate a proper growth function for the continuous-time model with the Ensemble Kalman Filter. Second, we use the Runge-Kutta method to discretize the growth function. Third, we use the Bellman approach to analyze the optimal management of seasonal fisheries in a discrete-time setting. We analyze both the case of quarterly harvest and the case of monthly harvest, and we compare these cases with the case of annual harvest. We find that seasonal harvesting is a win–win optimal solution that provides higher harvest, higher optimal steady state equilibrium, and higher economic value than annual harvesting. We also demonstrate that the discretization method overcomes the errors and preserves the strengths of both continuous and discretetime bioeconomic models.
Singularity of self-similar measures with respect to Hausdorff measures
(Facultad de Ciencias Económicas y Empresariales. Decanato, 1995) Morán Cabré, Manuel; Rey Simo, José Manuel
Besicoviteh (1941) and Egglestone (1949) analyzed subsets of points of the unit interval with given frequencies in the figures of their base-p expansions. We extend this analysis to self-similar sets, by replacing the frequencies of figures with the frequencies of the generating similitudes. We focus on the interplay among such sets, self-similar measures, and Hausdorff measures. We give a fine-tuned classification of the Hausdorff measures according to the singularity of the self-similar measures with respect to those measures. We show that the self-similar measures are concentrated on sets whose frequencies of similitudes obey the law of the iterated logarithm
Noise reduction by recycling dynamically coupled time series
(American Institute of Physics, 2011) Mera Rivas, Maria Eugenia; Morán Cabré, Manuel
We say that several scalar time series are dynamically coupled if they record the values of measurements of the state variables of the same smooth dynamical system. We show that much of the information lost due to measurement noise in a target time series can be recovered with a noise reduction algorithm by crossing the time series with another time series with which it is dynamically coupled. The method is particularly useful for reduction of measurement noise in short length time series with high uncertainties.
Detection of chaos in time series. Application to spanish sea swell
(Facultad de Ciencias Económicas y Empresariales. Decanato, 1995) Mera Rivas, María Eugenia; Rey Simo, José Manuel; Morán Cabré, Manuel
En esta memoria se revisan tres herramientas complementarias para el Análisis No-Lineal de Series Temporales: dimensión fractal, entropía, y exponentes de Liapunov. Se hace una revisión crítica del estado de la cuestión en el área, señalando el fundamento teórico de las técnicas aplicadas cuando éste existe, el campo de aplicación admitido por los especialistas cuando no existe base teórica, las limitaciones, etc. En ocasiones se aportan pruebas rigurosas, o razonamientos heurísticos, nuevos en la literatura.
Attainable values for upper porosities of measures
(Michigan State University Press, 2000) Mera Rivas, Maria Eugenia; Morán Cabré, Manuel
In this paper we introduce two definitions of upper porosity of a measure which range from 0 to (1/2) and from 0 to 1 respectively, and prove that actually the first porosity only can take the extreme values 0 or (1/2), and the second one takes either the value 0 or the values (1/2) or 1. The other main result of this paper says that any measure μ which does not satisfy the doubling condition μ-a.e. has a maximal porosity.
Porosity, σ-porosity and measures
(American Physical Society, 2003) Mera Rivas, Maria Eugenia; Morán Cabré, Manuel; Preiss, David; Zajicek, Ludik
We show that given a σ-finite Borel regular measure μ in a metric space X, every σ-porous subset of X of finite measure can be approximated by strongly porous sets. It follows that every σ-porous set is the union of a σ-strongly porous set and a μ-null set. This answers in the positive the question whether a measure which is absolutely continuous with respect to the σ-ideal of all σ-strongly porous sets is absolutely continuous with respect to the σ-ideal of all σ-porous sets. Using these results, we obtain a natural decomposition of measures according to their upper porosity and obtain detailed information on values that upper porosity may attain almost everywhere.
Tangent measures and Lp estimation of tangent maps
(Facultad de Ciencias Económicas y Empresariales. Decanato, 1996) Mera Rivas, María Eugenia; Morán Cabré, Manuel
We analyze under what conditions the best Lp- linear fittings of the action of a mapping f on small balls give reliable estimates of the tangent map Df. We show that there is an inverse relationslúp between the conditions on the regularity, in terms of local densities, of the underlying measure and the smoothness of the mapping f which are required to ensure the goodness of the estimates. The above results can be applied to the estimation of tangent maps in two empirical settings: from fiuite samples of a given probability distribution on mn and from fiuite orbits of smooth dynamical systems.
General dynamics in overlapping generations models
(Facultad de Ciencias Económicas y Empresariales. Instituto Complutense de Análisis Económico (ICAE), 1993) Carrera Calero, Carmen; Morán Cabré, Manuel
Se analiza en este trabajo las dinámicas generadas por las soluciones de equilibrio en un modelo de generaciones sucesivas con producción. El punto de vista adoptado es el inverso. Es decir, se parte de una dinámica dos veces diferenciable cualquiera, y se caracterizan y se construyen las clases de economías que generan esta dinámica. Se prueba que dinámicas arbitrariamente caóticas pueden ser generadas por modelos convencionales. Para conseguir estos resultados, se introduce una técnica basada en las ecuaciones diferenciales en derivadas parciales.