Mitochondrial Dna Replacement Versus Nuclear Dna Persistence

In this paper we consider two populations whose generations are not overlapping and whose size is large. The number of males and females in both populations is constant. Any generation is replaced by a new one and any individual has two parents for what concerns nuclear DNA and a single one (the mother) for what concerns mtDNA. Moreover, at any generation some individuals migrate from the first population to the second. In a finite random time $T$, the mtDNA of the second population is completely replaced by the mtDNA of the first. In the same time, the nuclear DNA is not completely replaced and a fraction $F$ of the ancient nuclear DNA persists. We compute both $T$ and $F$. Since this study shows that complete replacement of mtDNA in a population is compatible with the persistence of a large fraction of nuclear DNA, it may have some relevance for the Out of Africa/Multiregional debate in Paleoanthropology

Spot foreign exchange market and time series

We investigate high frequency price dynamics in foreign exchange market using data from Reuters information system (the dataset has been provided to us by Ols en & Associates). In our analysis we show that a na\"ive approach to the definition of price (for example using the spot midprice) may lead to wrong conclusions on price behavior as for example the presence of short term covariances for returns. For this purpose we introduce an algorithm which only uses the non arbitrage principle to estimate real prices from the spot ones. The new definition leads to returns which are i.i.d. variables and therefore are not affected by spurious correlations. Furthermore, any apparent information (defined by using Shannon entropy) contained in the data disappears

Bethe-Peierls Approximation for the 2D Random Ising Model

The partition function of the 2d Ising model with random nearest neighbor coupling is expressed in the dual lattice made of square plaquettes. The dual model is solved in the the mean field and in different types of Bethe-Peierls approximations, using the replica method.Comment: Plane TeX file, 21 pages, 5 figures available under request to [email protected]