Monochromatic Clique Decompositions of Graphs

Let $G$ be a graph whose edges are coloured with $k$ colours, and $\mathcal H=(H_1,\dots , H_k)$ be a $k$-tuple of graphs. A monochromatic $\mathcal H$-decomposition of $G$ is a partition of the edge set of $G$ such that each part is either a single edge or forms a monochromatic copy of $H_i$ in colour $i$, for some $1\le i\le k$. Let $\phi_{k}(n,\mathcal H)$ be the smallest number $\phi$, such that, for every order-$n$ graph and every $k$-edge-colouring, there is a monochromatic $\mathcal H$-decomposition with at most $\phi$ elements. Extending the previous results of Liu and Sousa ["Monochromatic $K_r$-decompositions of graphs", Journal of Graph Theory}, 76:89--100, 2014], we solve this problem when each graph in $\mathcal H$ is a clique and $n\ge n_0(\mathcal H)$ is sufficiently large.Comment: 14 pages; to appear in J Graph Theor

Asset Returns Under Model Uncertainty: Eveidence from the euro area, the U.K and the U.S

The goal of thes paper is to analyze predictability of future asset returns in the context of model uncertainty. Using data for the euro area, the US and the U.K., we show that one can improve the forecasts of stock returns using a Bayesian Model Averaging (BMA) approach, and there is a large amount of model uncertainty. The empirical evidence for the euro area suggests that several macroeconomic, financial and macro-financial variables are consistently among the most prominent determinants of risk premium. As for the U.S, only a few number of predictors play an important role. In the case of the UK, future stock returns are better forecasted by financial variables. These results are corroborated for both the M-open and the M-closed perspectives and in the context of "in-sample" and "out-of-sample" forescating. Finally, we highlight that the predictive ability of the BMA framework is stronger at longer periods, and clearly outperforms the constant expected returns and the autoregressive benchmark models.stock returns, model uncertainty, Bayesian Model Averaging

Sex and recombination in the H\"otzel aging model

Why sex evolved and it prevails in nature remains one of the great puzzles of evolution. Most biologists would explain that it promotes genetic variability, however this explanation suffers from several difficulties. What advantages might sex confer? The present communication aims at certain investigations related to this question, in this way we introduce sexual recombination on the H\"otzel model (with males and females) and we compare these results with those from asexual reproduction without recombination.Comment: 10 pages, 6 figure