Implicit ODE solvers with good local error control for the transient analysis of Markov models

Obtaining the transient probability distribution vector of a continuous-time Markov chain (CTMC) using an implicit ordinary differential equation (ODE) solver tends to be advantageous in terms of run-time computational cost when the product of the maximum output rate of the CTMC and the largest time of interest is large. In this paper, we show that when applied to the transient analysis of CTMCs, many implicit ODE solvers are such that the linear systems involved in their steps can be solved by using iterative methods with strict control of the 1-norm of the error. This allows the development of implementations of those ODE solvers for the transient analysis of CTMCs that can be more efficient and more accurate than more standard implementations.Peer ReviewedPostprint (published version

A comparison of numerical splitting-based methods for Markovian dependability and performability models

Iterative numerical methods are an important ingredient for the solution of continuous time Markov dependability models of fault-tolerant systems. In this paper we make a numerical comparison of several splitting-based iterative methods. We consider the computation of steady-state reward rate on rewarded models. This measure requires the solution of a singular linear system. We consider two classes of models. The first class includes failure/repair models. The second class is more general and includes the modeling of periodic preventive test of spare components to reduce the probability of latent failures in inactive components. The periodic preventive test is approximated by an Erlang distribution with enough number of stages. We show that for each class of model there is a splitting-based method which is significantly more efficient than the other methods.Postprint (published version

A Parameterized multi-step Newton method for solving systems of nonlinear equations

We construct a novel multi-step iterative method for solving systems of nonlinear equations by introducing a parameter. to generalize the multi-step Newton method while keeping its order of convergence and computational cost. By an appropriate selection of theta, the new method can both have faster convergence and have larger radius of convergence. The new iterative method only requires one Jacobian inversion per iteration, and therefore, can be efficiently implemented using Krylov subspace methods. The new method can be used to solve nonlinear systems of partial differential equations, such as complex generalized Zakharov systems of partial differential equations, by transforming them into systems of nonlinear equations by discretizing approaches in both spatial and temporal independent variables such as, for instance, the Chebyshev pseudo-spectral discretizing method. Quite extensive tests show that the new method can have significantly faster convergence and significantly larger radius of convergence than the multi-step Newton method.Peer ReviewedPostprint (author's final draft

The impact of immigration on the wage structure : Spain 1995-2002

In this paper we estimate the impact of inward migration flows on the Spanish wage structure over the period 1995-2002 by constructing counterfactual wage distributions that provide the wages that would have been observed had individual and job characteristics remain constant over time. Hence, we compute the impact of immigration on the wage distribution from (i) the estimated wage gaps between similar immigrants and native workers and (ii) the changes in the composition of employment associated to the arrival of new immigrants. Overall, we find that (i) the effects of immigration on wage changes are small and only noticeable when job characteristics are included as determinants of wages, and (ii) the correlation between the incidence of immigration in each decile of the wage distribution and the change in native wages not explained by changes in their individual and job characteristics is positive. These results suggest that other factors, besides immigration, should be identified as the key determinants of the wage moderation observed since the early nineties in Spain

On the computation of poisson probabilities

The Poisson distribution is a distribution commonly used in statistics. It also plays a central role in the analysis of the transient behaviour of continuous-time Markov chains. Several methods have been devised for evaluating using floating-point arithmetic the probability mass function (PMF) of the Poisson distribution. Restricting our attention to published methods intended for the computation of a single probability or a few of them, we show that neither of them is completely satisfactory in terms of accuracy. With that motivation, we develop a new method for the evaluation of the PDF of the Poisson distribution. The method is intended for the computation of a single probability or a few of them. Numerical experimentation illustrates that the method can be more accurate and slightly faster than the previous methods. Besides, the method comes with guaranteed approximation relative error.Postprint (author's final draft

The effect of immigration on the employment opportunities of native-born workers : some evidence for Spain

Spain is one of the European countries where immigration flows during the last decade have increased noticeably. The Spanish labor market institutions and the Spanish immigration policy exhibit some peculiarities which may be relevant when analyzing the impact of immigration. This paper provides a first approximation to the labor market effects of immigrants in Spain during the second half of the 1990s, the period in which immigration flows to Spain have accelerated. By using alternative datasets, we estimate both the impact of legal and total immigration flows on the employment rates of native workers, accounting for the possible occupationa l and geographical mobility of immigrants and native-born workers. Using different samples and estimation procedures, we have not found a significant negative effect of immigration on the employment rates of native workers. The corresponding estimated elasticity is low, around -0.1, when considering only legal immigrants, and is not significant when considering both legal and illegal immigrants

Cumulative dominance and heuristic performance in binary multi-attribute choice

Working paper 895, Department of Economics and Business, Universitat Pompeu FabraSeveral studies have reported high performance of simple decision heuristics in multi-attribute decision making. In this paper, we focus on situations where attributes are binary and analyze the performance of Deterministic-Elimination-By-Aspects (DEBA) and similar decision heuristics. We consider non-increasing weights and two probabilistic models for the attribute values: one where attribute values are independent Bernoulli randomvariables; the other one where they are binary random variables with inter-attribute positive correlations. Using these models, we show that good performance of DEBA is explained by the presence of cumulative as opposed to simple dominance. We therefore introduce the concepts of cumulative dominance compliance and fully cumulative dominance compliance and show that DEBA satisfies those properties. We derive a lower bound with which cumulative dominance compliant heuristics will choose a best alternative and show that, even with many attributes, this is not small. We also derive an upper bound for the expected loss of fully cumulative compliance heuristics and show that this is moderate even when the number of attributes is large. Both bounds are independent of the values of the weights.Postprint (author’s final draft

Cumulative dominance and heuristic performance in binary multi-attribute choice

Several studies have reported high performance of simple decision heuristics multi-attribute decision making. In this paper, we focus on situations where attributes are binary and analyze the performance of Deterministic-Elimination-By-Aspects (DEBA) and similar decision heuristics. We consider non-increasing weights and two probabilistic models for the attribute values: one where attribute values are independent Bernoulli randomvariables; the other one where they are binary random variables with inter-attribute positive correlations. Using these models, we show that good performance of DEBA is explained by the presence of cumulative as opposed to simple dominance. We therefore introduce the concepts of cumulative dominance compliance and fully cumulative dominance compliance and show that DEBA satisfies those properties. We derive a lower bound with which cumulative dominance compliant heuristics will choose a best alternative and show that, even with many attributes, this is not small. We also derive an upper bound for the expected loss of fully cumulative compliance heuristics and show that this is moderate even when the number of attributes is large. Both bounds are independent of the values of the weights.Multi-attribute decision making, binary attributes, DEBA, cumulative dominance, performance bounds, Leex

Cortes y monarquía en el Reino de Navarra, siglos XII-XV

La erudición del siglo XIX tuvo también en Navarra su campo de actuación, centrada en el estudio de los orígenes y significado de los fueros o textos normativos que avalasen la naturaleza del poder monárquico. Yangüas y Miranda, en 1840, afirmaba “que hubo un contrato social entre los navarros y sus monarcas y que existía una representación nacional, aun que aristocrática y circunscrita a los doce ricos hombres”. De aquí que la posterior historiografía, con su acentuado carácter reduccionista, calificase a la monarquía navarra como pactista. Ceremonial de la coronación y juramento de sus reyes, asistidos por las asambleas representativas de los estamentos sociales:” deben levantar rey los ricos hombres, infanzones, caballeros e el pueblo de la tierra (Fuero General, lib. 2, tít.4, cap. 2). Las etapas más significativas para observar los fenómenos antes mencionados son: 1º. El reino de Pamplona bajo la dinastía aragonesa (1076-1134) 2º. Restauración de la monarquía: de rey de los Pamploneses a rey de Navarra (1134.1234) 3º. La Casa Condal de Champaña (1234-1274). El Fuero Antiguoy el juramento real.. 4º. El reino de Navarra bajo el gobierno de la Casa de Francia (1274-1328): De las Cortes o Cort General a los Tres Estados del reino. 5.º. Navarra entre Francia y España (1328-1425)Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec