On periodic solutions of 2-periodic Lyness difference equations

We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n} is a cycle with positive values a,b and with positive initial conditions. It is known that for a=b=1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a,b) different from (1,1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a is not equal to b, then any odd period, except 1, appears.

Integro-difference equations for interacting species and the Neolithic transition

We introduce a set of sequential integro-difference equations to analyze the dynamics of two interacting species. Firstly, we derive the speed of the fronts when a species invades a space previously occupied by a second species, and check its validity by means of numerical random-walk simulations. As an example, we consider the Neolithic transition: the predictions of the model are consistent with the archaeological data for the front speed, provided that the interaction parameter is low enough. Secondly, an equation for the coexistence time between the invasive and the invaded populations is obtained for the first time. It agrees well with the simulations, is consistent with observations of the Neolithic transition, and makes it possible to estimate the value of the interaction parameter between the incoming and the indigenous populations

RiskDiff: A web tool for the analysis of the difference due to risk and demographic factors for incidence or mortality data.

Background Analysing the observed differences for incidence or mortality of a particular disease between two different situations (such as time points, geographical areas, gender or other social characteristics) can be useful both for scientific or administrative purposes. From an epidemiological and public health point of view, it is of great interest to assess the effect of demographic factors in these observed differences in order to elucidate the effect of the risk of developing a disease or dying from it. The method proposed by Bashir and Estève, which splits the observed variation into three components: risk, population structure and population size is a common choice at practice. Results A web-based application, called RiskDiff has been implemented (available at http://rht.iconcologia.net/riskdiff.htm webcite), to perform this kind of statistical analyses, providing text and graphical summaries. Code from the implemented functions in R is also provided. An application to cancer mortality data from Catalonia is used for illustration. Conclusions Combining epidemiological with demographical factors is crucial for analysing incidence or mortality from a disease, especially if the population pyramids show substantial differences. The tool implemented may serve to promote and divulgate the use of this method to give advice for epidemiologic interpretation and decision making in public health.

Mergers and difference-in-difference estimator : why firms do not increase prices?

Difference-in-Difference (DiD) methods are being increasingly used to analyze the impact of mergers on pricing and other market equilibrium outcomes. Using evidence from an exogenous merger between two retail gasoline companies in a specific market in Spain, this paper shows how concentration did not lead to a price increase. In fact, the conjectural variation model concludes that the existence of a collusive agreement before and after the merger accounts for this result, rather than the existence of efficient gains. This result may explain empirical evidence reported in the literature according to which mergers between firms do not have significant effects on prices.

The Dialogic Turn in Educational Psychology

The increasing presence of and claim for dialogue in today"s society has already had an impact on the theory and practice of learning. Whereas in the past individual and cognitive elements were seen as crucial to learning, since about two decades ago, scientific literature indicates that culture, interaction and dialogue are the key factors. In addition, the research project of highest scientific rank and with most resources dedicated to the study of school education in the Framework Program of the European Union: INCLUD-ED shows that the practices of successful schools around Europe are in line with the dialogic approach to learning. This article presents the dialogic turn in educational psychology, consisting of moving from symbolic conceptions of mind and internalist perspectives that focus on mental schemata of previous knowledge, to theories that see intersubjectivity and communication as the primary factors in learning. The paper deepens on the second approach.