Finite to infinite steady state solutions, bifurcations of an integro-differential equation

We consider a bistable integral equation which governs the stationary solutions of a convolution model of solid--solid phase transitions on a circle. We study the bifurcations of the set of the stationary solutions as the diffusion coefficient is varied to examine the transition from an infinite number of steady states to three for the continuum limit of the semi--discretised system. We show how the symmetry of the problem is responsible for the generation and stabilisation of equilibria and comment on the puzzling connection between continuity and stability that exists in this problem

Two classes of nonlocal Evolution Equations related by a shared Traveling Wave Problem

We consider reaction-diffusion equations and Korteweg-de Vries-Burgers (KdVB) equations, i.e. scalar conservation laws with diffusive-dispersive regularization. We review the existence of traveling wave solutions for these two classes of evolution equations. For classical equations the traveling wave problem (TWP) for a local KdVB equation can be identified with the TWP for a reaction-diffusion equation. In this article we study this relationship for these two classes of evolution equations with nonlocal diffusion/dispersion. This connection is especially useful, if the TW equation is not studied directly, but the existence of a TWS is proven using one of the evolution equations instead. Finally, we present three models from fluid dynamics and discuss the TWP via its link to associated reaction-diffusion equations

Pushed traveling fronts in monostable equations with monotone delayed reaction

We study the existence and uniqueness of wavefronts to the scalar reaction-diffusion equations $u_{t}(t,x) = \Delta u(t,x) - u(t,x) + g(u(t-h,x)),$ with monotone delayed reaction term $g: \R_+ \to \R_+$ and $h >0$. We are mostly interested in the situation when the graph of $g$ is not dominated by its tangent line at zero, i.e. when the condition $g(x) \leq g'(0)x,$ $x \geq 0$, is not satisfied. It is well known that, in such a case, a special type of rapidly decreasing wavefronts (pushed fronts) can appear in non-delayed equations (i.e. with $h=0$). One of our main goals here is to establish a similar result for $h>0$. We prove the existence of the minimal speed of propagation, the uniqueness of wavefronts (up to a translation) and describe their asymptotics at $-\infty$. We also present a new uniqueness result for a class of nonlocal lattice equations.Comment: 17 pages, submitte

The "silver" Japanese quail and the MITF gene: causal mutation, associated traits and homology with the "blue" chicken plumage

<p>Abstract</p> <p>Background</p> <p>The <it>MITF </it>(<it>microphthalmia-associated transcription factor</it>) gene has been investigated in mice and various vertebrates but its variations and associated effects have not yet been explored much in birds. The present study describes the causal mutation <it>B </it>at the <it>MITF </it>gene responsible for the "silver" plumage colour in the Japanese quail (<it>Coturnix japonica</it>), and its associated effects on growth and body composition, and tests its allelism with the "blue" plumage colour mutation <it>Bl </it>in <it>Gallus gallus</it>.</p> <p>Results</p> <p>The semi dominant <it>B </it>mutation results from a premature stop codon caused by a 2 bp deletion in exon 11 of <it>MITF</it>. Homozygous "white" (<it>B/B</it>) quail which have a white plumage also show a slightly lower growth, lower body temperature, smaller heart, and lighter <it>pectoralis </it>muscles but more abdominal adipose tissue than the recessive homozygous "wild-type" (<it>+/+</it>) and heterozygous "silver" (<it>B/+</it>) quail. Similar observations on cardiac and body growth were made on mice (<it>Mus musculus</it>) homozygous for mutations at <it>MITF</it>. The production of chicken-quail hybrids with a white plumage obtained by crossing <it>Bl/+ </it>chicken heterozygous for the <it>blue </it>mutation with <it>B/B </it>white quail indicated that the mutations were allelic.</p> <p>Conclusion</p> <p>The "silver" Japanese quail is an interesting model for the comparative study of the effects of <it>MITF </it>in birds and mammals. Further investigation using a chicken family segregating for the "blue" plumage and molecular data will be needed to confirm if the "blue" plumage in chicken results from a mutation in <it>MITF</it>.</p

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead