Objective: We report
the results of nuclear DNA analyses of Napoléon the First (Napoléon Bonaparte; 1769-1821).
Design: His genomic DNA was extracted from dandruff adherent to his hair, coming
from a lock of his hair dating from the year of 1811. Results: We obtained the complete
STR (short tandem repeats) profile of Napoléon, based on fifteen autosomal loci.
On this profile, ten loci (D8S1179, D21S11, D7S820, D3S1358, TH01, D16S539, D2S1338,
vWa, D18S51 and FGA) are heterozygous; the most frequent alleles in Caucasians are
present for only seven (allele 8 for TPOX and allele 11 for D5S818, allele 13 for
D8S1179, allele 10 for D7S820, allele 9.3 for THO1, allele 12 for D16S539 and allele
24 for FGA) of the homozygous and heterozygous loci. Conclusions: So the discriminating
power of this sort of genetic profile is elevated, permitting useful comparisons
to other STR profiles in the future. Finally, an analysis of fifteen Y chromosomal
STRs from the dandruff of this lock of hair confirms allele values of Napoléon already
obtained or deduced for the corresponding loci in previous determinations.

Abstract:
In this paper we use the theory of viscosity solutions for Hamilton-Jacobi equations to study propagation phenomena in kinetic equations. We perform the hydrodynamic limit of some kinetic models thanks to an adapted WKB ansatz. Our models describe particles moving according to a velocity-jump process, and proliferating thanks to a reaction term of monostable type. The scattering operator is supposed to satisfy a maximum principle. When the velocity space is bounded, we show, under suitable hypotheses, that the phase converges towards the viscosity solution of some constrained Hamilton-Jacobi equation which effective Hamiltonian is obtained solving a suitable eigenvalue problem in the velocity space. In the case of unbounded velocities, the non-solvability of the spectral problem can lead to different behavior. In particular, a front acceleration phenomena can occur. Nevertheless, we expect that when the spectral problem is solvable one can extend the convergence result.

Abstract:
In this paper, we study propagation in a nonlocal reaction-diffusion-mutation model describing the invasion of cane toads in Australia. The population of toads is structured by a space variable and a phenotypical trait and the space-diffusivity depends on the trait. We use a Schauder topological degree argument for the construction of some travelling wave solutions of the model. The speed $c^*$ of the wave is obtained after solving a suitable spectral problem in the trait variable. An eigenvector arising from this eigenvalue problem gives the flavor of the profile at the edge of the front. The major difficulty is to obtain uniform $L^\infty$ bounds despite the combination of non local terms and an heterogeneous diffusivity.

Abstract:
We analyse the linear kinetic transport equation with a BGK relaxation operator. We study the large scale hyperbolic limit $(t,x)\to (t/\eps,x/\eps)$. We derive a new type of limiting Hamilton-Jacobi equation, which is analogous to the classical eikonal equation derived from the heat equation with small diffusivity. We prove well-posedness of the phase problem and convergence towards the viscosity solution of the Hamilton-Jacobi equation. This is a preliminary work before analysing the propagation of reaction fronts in kinetic equations.

Abstract:
We study a non-local parabolic Lotka-Volterra type equation describing a population structured by a space variable x 2 Rd and a phenotypical trait 2 . Considering diffusion, mutations and space-local competition between the individuals, we analyze the asymptotic (long- time/long-range in the x variable) exponential behavior of the solutions. Using some kind of real phase WKB ansatz, we prove that the propagation of the population in space can be described by a Hamilton-Jacobi equation with obstacle which is independent of . The effective Hamiltonian is derived from an eigenvalue problem. The main difficulties are the lack of regularity estimates in the space variable, and the lack of comparison principle due to the non-local term.

Abstract:
Background Food security is an issue that has come under renewed scrutiny amidst concerns that substantial yield increases in cereal crops are required to feed the world’s booming population. Wheat is of fundamental importance in this regard being one of the three most important crops for both human consumption and livestock feed; however, increase in crop yields have not kept pace with the demands of a growing world population. In order to address this issue, plant breeders require new molecular tools to help them identify genes for important agronomic traits that can be introduced into elite varieties. Studies of the genome using next-generation sequencing enable the identification of molecular markers such as single nucleotide polymorphisms that may be used by breeders to identify and follow genes when breeding new varieties. The development and application of next-generation sequencing technologies has made the characterisation of SNP markers in wheat relatively cheap and straightforward. There is a growing need for the widespread dissemination of this information to plant breeders. Description CerealsDB is an online resource containing a range of genomic datasets for wheat (Triticum aestivum) that will assist plant breeders and scientists to select the most appropriate markers for marker assisted selection. CerealsDB includes a database which currently contains in excess of 100,000 putative varietal SNPs, of which several thousand have been experimentally validated. In addition, CerealsDB contains databases for DArT markers and EST sequences, and links to a draft genome sequence for the wheat variety Chinese Spring. Conclusion CerealsDB is an open access website that is rapidly becoming an invaluable resource within the wheat research and plant breeding communities.

Abstract:
We perform the analysis of a hyperbolic model which is the analog of the Fisher-KPP equation. This model accounts for particles that move at maximal speed $\epsilon^{-1}$ ($\epsilon>0$), and proliferate according to a reaction term of monostable type. We study the existence and stability of traveling fronts. We exhibit a transition depending on the parameter $\epsilon$: for small $\epsilon$ the behaviour is essentially the same as for the diffusive Fisher-KPP equation. However, for large $\epsilon$ the traveling front with minimal speed is discontinuous and travels at the maximal speed $\epsilon^{-1}$. The traveling fronts with minimal speed are linearly stable in weighted $L^2$ spaces. We also prove local nonlinear stability of the traveling front with minimal speed when $\epsilon$ is smaller than the transition parameter.

Abstract:
In this paper, we show super-linear propagation in a nonlocal reaction-diffusion-mutation equation modeling the invasion of cane toads in Australia that has attracted attention recently from the mathematical point of view. The population of toads is structured by a phenotypical trait that governs the spatial diffusion. In this paper, we are concerned with the case when the diffusivity can take unbounded values, and we prove that the population spreads as $t^{3/2}$. We also get the sharp rate of spreading in a related local model.

Abstract:
In this paper, we study the existence and stability of travelling wave solutions of a kinetic reaction-transport equation. The model describes particles moving according to a velocity-jump process, and proliferating thanks to a reaction term of monostable type. The boundedness of the velocity set appears to be a necessary and sufficient condition for the existence of positive travelling waves. The minimal speed of propagation of waves is obtained from an explicit dispersion relation. We construct the waves using a technique of sub- and supersolutions and prove their \eb{weak} stability in a weighted $L^2$ space. In case of an unbounded velocity set, we prove a superlinear spreading. It appears that the rate of spreading depends on the decay at infinity of the velocity distribution. In the case of a Gaussian distribution, we prove that the front spreads as $t^{3/2}$.

Abstract:
This paper examines the significance of spatial externalities for youths’
school-to-training transitions in Germany. For this purpose, it is necessary to
address the methodological question of how an individual’s spatial context has
to be operationalized with respect to both its extent and the problem of
spatial autocorrelation. Our analyses show that the “zone of influence”
comprises of the whole of Germany, not only close-by districts, and that these
effects differ between structurally weak and strong regions. Consequently,
assuming that only close proximity affects individual outcomes may disregard
relevant contextual influences, and for spatial models that require an a priori
definition of the weights for spatial units, it may be erroneous to make a decision
based on this assumption. Concerning spatial autocorrelation, we found that
neglecting local spatial autocorrelation at the context level causes
considerable bias to the estimates, especially for districts that are close to
the home district.