Comments on selected fundamental aspects of microarray analysis

Microarrays are becoming a ubiquitous tool of research in life sciences. However, the working principles of microarray-based methodologies are often misunderstood or apparently ignored by the researchers who actually perform and interpret experiments. This in turn seems to lead to a common over-expectation regarding the explanatory and/or knowledge-generating power of microarray analyses. In this note we intend to explain basic principles of five (5) major groups of analytical techniques used in studies of microarray data and their interpretation: the principal component analysis (PCA), the independent component analysis (ICA), the t-test, the analysis of variance (ANOVA), and self organizing maps (SOM). We discuss answers to selected practical questions related to the analysis of microarray data. We also take a closer look at the experimental setup and the rules, which have to be observed in order to exploit microarrays efficiently. Finally, we discuss in detail the scope and limitations of microarray-based methods. We emphasize the fact that no amount of statistical analysis can compensate for (or replace) a well thought through experimental setup. We conclude that microarrays are indeed useful tools in life sciences but by no means should they be expected to generate complete answers to complex biological questions. We argue that even well posed questions, formulated within a microarray-specific terminology, cannot be completely answered with the use of microarray analyses alone.     

Differential growth and instability in elastic shells

Differential growth in elastic materials can produce stress either through incompatibility of growth or by interaction with the surrounding medium. In many situations, this stress can be sufficient to induce shape instability in the growing medium. To gain better insight in growth-induced instabilities, the growth of an elastic shell loaded with hydrostatic pressure or embedded in an elastic medium is studied. The residual stress arising from the incompatibility of growth and the contact stress arising from the interaction with the surrounding medium are computed with respect to growth and geometric parameters and critical values for instability are obtained. Depending on these parameters, different modes of instability can be obtained.     

Two-dimensional numerical simulation of acoustic wave phase conjugation in magnetostrictive elastic media

The effect of parametric wave phase conjugation (WPC) in application to ultrasound or acoustic waves in magnetostrictive solids has been addressed numerically by Ben Khelil et al. [J. Acoust. Soc. Am. 109, 75-83 (2001)] using 1-D unsteady formulation. Here the numerical method presented by Voinovich et al. [Shock waves 13(3), 221-230 (2003)] extends the analysis to the 2-D effects. The employed model describes universally elastic solids and liquids. A source term similar to Ben Khelil et al.'s accounts for the coupling between deformation and magnetostriction due to external periodic magnetic field. The compatibility between the isotropic constitutive law of the medium and the model of magnetostriction has been considered. Supplementary to the 1-D simulations, the present model involves longitudinal/transversal mode conversion at the sample boundaries and separate magnetic field coupling with dilatation and shear stress. The influence of those factors in a 2-D geometry on the potential output of a magneto-elastic wave phase conjugator is analyzed in this paper. The process under study includes propagation of a wave burst of a given frequency from a point source in a liquid into the active solid, amplification of the waves due to parametric resonance, and formation of time-reversed waves, their radiation into liquid, and focusing. The considered subject is particularly important for ultrasonic applications in acoustic imaging, nondestructive testing, or medical diagnostics and therapy.     

Exact maximal height distribution of fluctuating interfaces

We present an exact solution for the distribution P(h(m),L) of the maximal height h(m) (measured with respect to the average spatial height) in the steady state of a fluctuating Edwards-Wilkinson interface in a one dimensional system of size L with both periodic and free boundary conditions. For the periodic case, we show that P(h(m),L)=L(-1/2)f(h(m)L(-1/2)) for all L>0, where the function f(x) is the Airy distribution function that describes the probability density of the area under a Brownian excursion over a unit interval. For the free boundary case, the same scaling holds, but the scaling function is different from that of the periodic case. Numerical simulations are in excellent agreement with our analytical results. Our results provide an exactly solvable case for the distribution of extremum of a set of strongly correlated random variables.     

Surface modification of several carbon-based materials: comparison between CF4 rf plasma and direct F2-gas fluorination routes

Due to their extreme reactivity, fluorine and fluorinated gases may be used to modify the surface properties of numerous materials. In the following, the surface fluorination of some carbon-based compounds (graphite, graphitised carbon fibres, carbon blacks and elastomers) using CF₄ rf plasma technique and direct F₂-gas fluorination is proposed. From XPS studies, the different types of CF bonding obtained in the materials after treatment have been correlated either to the physico-chemical characteristics of the pristine material or to the experimental parameters of the fluorination. Reaction mechanisms are proposed.     

Une Conjecture de Lebesgue

Let A > 0 be an integer. The equation x⁵–y⁵ = Az⁵ wasfirst studied by Dirichlet and Lebesgue. Lebesgue conjecturedin 1843 that if A has no prime divisors of the form 10k+1, theequation has no solutions except the visible ones. Partial resultswere obtained by Lebesgue and by Terjanian in 1987. The purposeof the paper is to prove Lebesgue's conjecture. The main toolused is the method known as the elliptic Chabauty method.