Remarks on navier-stokes equations with measures as data

AbstractWe show the existence of a solution to the Navier-Stokes equation taking the vorticity ω as the unknown: ωt + Aω + Bω = μ, ω(0) = ω0. Here, ω0 and μ are bounded Radon measures. This study is motivated by a numerical approximation which will be given in a forthcoming work [1]

Finite-time synchronization of tunnel diode based chaotic oscillators

This paper addresses the problem of finite-time synchronization of tunnel diode based chaotic oscillators. After a brief investigation of its chaotic dynamics, we propose an active adaptive feedback coupling which accomplishes the synchronization of tunnel diode based chaotic systems with and without the presence of delay(s), basing ourselves on Lyapunov and on Krasovskii-Lyapunov stability theories. This feedback coupling could be applied to many other chaotic systems. A finite horizon can be arbitrarily established by ensuring that chaos synchronization is achieved at a pre-established time. An advantage of the proposed feedback coupling is that it is simple and easy to implement. Both mathematical investigations and numerical simulatioComment: 11 pages, 43 figure

Post-glacial colonisation of Europe by the wood mouse, Apodemus sylvaticus : evidence of a northern refugium and dispersal with humans

The wood mouse Apodemus sylvaticus is an opportunistic rodent that is found throughout most of the European mainland. It is present on many islands around the margins of the continent and in northern Africa. The species has been the subject of previous phylogeographic studies but these have focussed on the more southerly part of its range. A substantial number of new samples, many of them from the periphery of the species’ range, contribute to an exceptional dataset comprising 981 mitochondrial cytochrome b sequences. These new data provide sufficient resolution to transform our understanding of the species’ survival through the last glaciation and its subsequent re-colonisation of the continent. The deepest genetic split we found is in agreement with previous studies and runs from the Alps to central Ukraine, but we further distinguish two separate lineages in wood mice to the north and west of this line. It is likely that this part of Europe was colonised from two refugia, putatively located in the Iberian peninsula and the Dordogne or Carpathian region. The wood mouse therefore joins the growing number of species with extant populations that appear to have survived the Last Glacial Maximum in northern refugia, rather than solely in traditionally recognised refugial locations in the southern European peninsulas. Furthermore, the existence of a northern refugium for the species was predicted in a study of mitochondrial variation in a specific parasite of the wood mouse, demonstrating the potential value of data from parasites to phylogeographic studies. Lastly, the presence of related haplotypes in widely disparate locations, often on islands or separated by substantial bodies of water, demonstrates the propensity of the wood mouse for accidental human-mediated transport

Origin and putative colonization routes for invasive rodent taxa in the democratic Republic of Congo

The threat posed by biological invasions is well established. An important consideration in preventing the spread of invasives and also subsequent introductions lies in understanding introduction pathways. The Democratic Republic of the Congo (DRC) houses a large percentage of the world's biodiversity, yet no national strategy exists to deal with the growing number of invasive alien species. Amongst these are the house mouse and ship and Norwegian rats. By comparing our result to published data, we show that species were possibly introduced into the DRC via two routes. The first is via the western seaport at Kinshasa where specimens of M. m. domesticus and R. rattus on the western and northwestern side of the DRC show ties with European haplotypes. The second is via the east where specimens of R. rattus appear linked to Arab and southeast Asian haplotypes. Future work should consider more comprehensive sampling throughout the DRC to more accurately investigate the occurrence of invasive species throughout the country as well as extend sampling to other African countries

Vietnamese chickens: a gate towards Asian genetic diversity

BACKGROUND: Chickens represent an important animal genetic resource and the conservation of local breeds is an issue for the preservation of this resource. The genetic diversity of a breed is mainly evaluated through its nuclear diversity. However, nuclear genetic diversity does not provide the same information as mitochondrial genetic diversity. For the species Gallus gallus, at least 8 maternal lineages have been identified. While breeds distributed westward from the Indian subcontinent usually share haplotypes from 1 to 2 haplogroups, Southeast Asian breeds exhibit all the haplogroups. The Vietnamese Ha Giang (HG) chicken has been shown to exhibit a very high nuclear diversity but also important rates of admixture with wild relatives. Its geographical position, within one of the chicken domestication centres ranging from Thailand to the Chinese Yunnan province, increases the probability of observing a very high genetic diversity for maternal lineages, and in a way, improving our understanding of the chicken domestication process. RESULTS: A total of 106 sequences from Vietnamese HG chickens were first compared to the sequences of published Chinese breeds. The 25 haplotypes observed in the Vietnamese HG population belonged to six previously published haplogroups which are: A, B, C, D, F and G. On average, breeds from the Chinese Yunnan province carried haplotypes from 4.3 haplogroups. For the HG population, haplogroup diversity is found at both the province and the village level (0.69).The AMOVA results show that genetic diversity occurred within the breeds rather than between breeds or provinces. Regarding the global structure of the mtDNA diversity per population, a characteristic of the HG population was the occurrence of similar pattern distribution as compared to G. gallus spadiceus. However, there was no geographical evidence of gene flow between wild and domestic populations as observed when microsatellites were used. CONCLUSIONS: In contrast to other chicken populations, the HG chicken population showed very high genetic diversity at both the nuclear and mitochondrial levels. Due to its past and recent history, this population accumulates a specific and rich gene pool highlighting its interest and the need for conservation

Flavour Issues in Leptogenesis

We study the impact of flavour in thermal leptogenesis, including the quantum oscillations of the asymmetries in lepton flavour space. In the Boltzmann equations we find different numerical factors and additional terms which can affect the results significantly. The upper bound on the CP asymmetry in a specific flavour is weaker than the bound on the sum. This suggests that -- when flavour dynamics is included -- there is no model-independent limit on the light neutrino mass scale,and that the lower bound on the reheat temperature is relaxed by a factor ~ (3 - 10).Comment: 19 pages, corrected equations for flavour oscillation

Evolutionary history and species delimitations: a case study of the hazel dormouse, Muscardinus avellanarius

Robust identification of species and significant evolutionary units (ESUs) is essential to implement appropriate conservation strategies for endangered species. However, definitions of species or ESUs are numerous and sometimes controversial, which might lead to biased conclusions, with serious consequences for the management of endangered species. The hazel dormouse, an arboreal rodent of conservation concern throughout Europe is an ideal model species to investigate the relevance of species identification for conservation purposes. This species is a member of the Gliridae family, which is protected in Europe and seriously threatened in the northern part of its range. We assessed the extent of genetic subdivision in the hazel dormouse by sequencing one mitochondrial gene (cytb) and two nuclear genes (BFIBR, APOB) and genotyping 10 autosomal microsatellites. These data were analysed using a combination of phylogenetic analyses and species delimitation methods. Multilocus analyses revealed the presence of two genetically distinct lineages (approximately 11 % cytb genetic divergence, no nuclear alleles shared) for the hazel dormouse in Europe, which presumably diverged during the Late Miocene. The phylogenetic patterns suggests that Muscardinus avellanarius populations could be split into two cryptic species respectively distributed in western and central-eastern Europe and Anatolia. However, the comparison of several species definitions and methods estimated the number of species between 1 and 10. Our results revealed the difficulty in choosing and applying an appropriate criterion and markers to identify species and highlight the fact that consensus guidelines are essential for species delimitation in the future. In addition, this study contributes to a better knowledge about the evolutionary history of the species