Subgeometric rates of convergence for a class of continuous-time Markov process

Let (Phi(t))(t is an element of R+) be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure pi. We investigate the rates of convergence of the transition function P-t(x, (.)) to pi; specifically, we find conditions under which r(t) vertical bar vertical bar P-t (x, (.)) - pi vertical bar vertical bar -> 0 as t -> infinity, for suitable subgeometric rate functions r(t), where vertical bar vertical bar - vertical bar vertical bar denotes the usual total variation norm for a signed measure. We derive sufficient conditions for the convergence to hold, in terms of the existence of suitable points on which the first hitting time moments are bounded. In particular, for stochastically ordered Markov processes, explicit bounds on subgeometric rates of convergence are obtained. These results are illustrated in several examples.

Post-Fordism, the welfare state and the personal social services: A comparison of Australia and Britain

The Post-Fordist welfare state thesis locates contemporary social welfare change within a wider analysis of the transformation of capitalist accumulation regimes. Whilst this analysis is useful in directing attention to macro socio-economic change, it has for the most part contained three shortcomings. First, the Post-Fordist thesis has overemphasized the role of historical 'breaks' in the development of social welfare as it purportedly passes from Fordism to Post-Fordism. Second, the thesis has assumed a degree of convergence between welfare states as a result of global economic forces. In doing so, it has underemphasized the mediating impact of existing institutional arrangements within nations. Third, the thesis has assumed, rather than demonstrated, the specific changes which are alleged to be taking place in various fields of social welfare. As a consequence, aspects of continuity in social welfare have been neglected. These three lacunae are addressed through a comparative analysis of developments in the personal social services in Australia and Britain. Services to older people are employed as the specific context of comparison in relation to three dimensions of measuring transformation along a Post-Fordist trajectory: a shift from a unitary economy to a mixed economy of service provision; changes in the model of service delivery and consumption; and strengthening the governance function of the central state. This comparative analysis suggests the need for refinement of the Post-Fordist welfare state thesis concerning the restructuring of social welfare and its impact on the personal social services.

A Statistical Convergence Aplication for the Hopfield Networks

When Recurrent Neural Networks (RNN) are going to be used as Pattern Recognition systems, the problem to be considered is how to impose prescribed prototype vectors ξ^1,ξ^2,...,ξ^p as fixed points. The synaptic matrix W should be interpreted as a sort of sign correlation matrix of the prototypes, In the classical approach. The weak point in this approach, comes from the fact that it does not have the appropriate tools to deal efficiently with the correlation between the state vectors and the prototype vectors The capacity of the net is very poor because one can only know if one given vector is adequately correlated with the prototypes or not and we are not able to know what its exact correlation degree. The interest of our approach lies precisely in the fact that it provides these tools. In this paper, a geometrical vision of the dynamic of states is explained. A fixed point is viewed as a point in the Euclidean plane R2. The retrieving procedure is analyzed trough statistical frequency distribution of the prototypes. The capacity of the net is improved and the spurious states are reduced. In order to clarify and corroborate the theoretical results, together with the formal theory, an application is presented

Viability, Optimality and Stability of Dynamical Systems and Estimation of Convergence of Numerical Schemes

AMS subject classification: 49N35,49N55,65Lxx.

Effects of roadway geometric features on run-off road crashes on the Florida State Highway System

Run-off-road (ROR) crashes have increasingly become a serious concern for transportation officials in the State of Florida. These types of crashes have increased proportionally in recent years statewide and have been the focus of the Florida Department of Transportation. The goal of this research was to develop statistical models that can be used to investigate the possible causal relationships between roadway geometric features and ROR crashes on Florida's rural and urban principal arterials. ^ In this research, Zero-Inflated Poisson (ZIP) and Zero-Inflated Negative Binomial (ZINB) Regression models were used to better model the excessive number of roadway segments with no ROR crashes. Since Florida covers a diverse area and since there are sixty-seven counties, it was divided into four geographical regions to minimize possible unobserved heterogeneity. Three years of crash data (2000–2002) encompassing those for principal arterials on the Florida State Highway System were used. Several statistical models based on the ZIP and ZINB regression methods were fitted to predict the expected number of ROR crashes on urban and rural roads for each region. Each region was further divided into urban and rural areas, resulting in a total of eight crash models. A best-fit predictive model was identified for each of these eight models in terms of AIC values. The ZINB regression was found to be appropriate for seven of the eight models and the ZIP regression was found to be more appropriate for the remaining model. To achieve model convergence, some explanatory variables that were not statistically significant were included. Therefore, strong conclusions cannot be derived from some of these models. ^ Given the complex nature of crashes, recommendations for additional research are made. The interaction of weather and human condition would be quite valuable in discerning additional causal relationships for these types of crashes. Additionally, roadside data should be considered and incorporated into future research of ROR crashes. ^

Services growth and convergence: Getting India’s states together

India’s success story in services is well documented at the national level, but similar literature does not exist for India’s states. In this paper, we bridge this gap in research by looking at India’s services growth at the sub-national level and in doing so, also challenge existing literature by arguing that this growth has positive implications for income distribution. The first interesting finding is that even as per capita income is not converging across India’s states, per capita services are and we provide evidence for this both in terms of traditional measures of sigma- and beta-convergence and more recent panel unit root tests. Secondly, not only is external demand an important determinant of services value added at the state level, but this demand also emanates from all over the country rather than being concentrated in the neighbouring or richer states. This suggests that the benefits from services growth are being distributed more widely than may be perceived.

Evaluating tests for convergence of economic series using Monte Carlo methods with an application to real GDP's per head.

Doutoramento em Economia.

Convergence of gender roles in a globalized world: international comparison of family and gender roles

This paper examines emerging and changing gender roles in different regions of the world. Using data on 12 countries from last three ISSP Special Modules “Family and Changing Gender Roles” (1994, 2002 and 2012), we compare the evolution of gender roles about motherhood and fatherhood and its relation with the extension of women as breadwinners around the world: four Western Europe countries, representatives of different models of Welfare State (Germany, United Kingdom, Norway and Spain) plus United States, three former Soviet nations (Russia, Poland and Czech Republic), two Latin American countries (Chile and Mexico) and two Asian nations (Japan and Taiwan). Data show that family change (measured both in terms of attitudes and social practices) is spreading from Western contexts to other regions of the world, although the pace of this change varies from one country to another, depending on cultural, economic and political factors.

Time-Dependent Density Functional Molecular Orbital and Excited State Calculations on Bis(porphyrinyl)butadiynes in the Monocationic, Neutral, Monoanionic, and Dianionic Oxidation States

We report a theoretical study of the multiple oxidation states (1+, 0, 1−, and 2−) of a meso,meso-linked diporphyrin, namely bis[10,15,20-triphenylporphyrinatozinc(II)-5-yl]butadiyne (4), using Time-Dependent Density Functional Theory (TDDFT). The origin of electronic transitions of singlet excited states is discussed in comparison to experimental spectra for the corresponding oxidation states of the close analogue bis{10,15,20-tris[3‘,5‘-di-tert-butylphenyl]porphyrinatozinc(II)-5-yl}butadiyne (3). The latter were measured in previous work under in situ spectroelectrochemical conditions. Excitation energies and orbital compositions of the excited states were obtained for these large delocalized aromatic radicals, which are unique examples of organic mixed-valence systems. The radical cations and anions of butadiyne-bridged diporphyrins such as 3 display characteristic electronic absorption bands in the near-IR region, which have been successfully predicted with use of these computational methods. The radicals are clearly of the “fully delocalized” or Class III type. The key spectral features of the neutral and dianionic states were also reproduced, although due to the large size of these molecules, quantitative agreement of energies with observations is not as good in the blue end of the visible region. The TDDFT calculations are largely in accord with a previous empirical model for the spectra, which was based simplistically on one-electron transitions among the eight key frontier orbitals of the C4 (1,4-butadiyne) linked diporphyrins.