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We study variational systems for space curves, for which the Lagrangian or action principle has a Euclidean symmetry, using the Rotation Minimising frame, also known as the Normal, Parallel or Bishop frame. Such systems have previously been studied using the Frenet-Serret frame. The Rotation Minimising frame has many advantages, however, and can be used to study a wider class of examples. We achieve our results by extending the powerful symbolic invariant calculus for Lie group based moving frames, to the Rotation Minimising frame case. To date, the invariant calculus has been developed for frames defined by algebraic equations. By contrast, the Rotation Minimising frame is defined by a differential equation. In this paper, we derive the recurrence formulae for the symbolic invariant differentiation of the symbolic invariants. We then derive the syzygy operator needed to obtain Noether's conservation laws as well as the Euler-Lagrange equations directly in terms of the invariants, for variational problems with a Euclidean symmetry. We show how to use the six Noether laws to ease the integration problem for the minimising curve, once the Euler-Lagrange equations have been solved for the generating differential invariants. Our applications include variational problems used in the study of strands of proteins, nucleid acids and polymers., Comment: 28 pages, 22 figures

In this second part of the paper, we consider finite difference Lagrangians which are invariant under linear and projective actions of $SL(2)$, and the linear equi-affine action which preserves area in the plane. We first find the generating invariants, and then use the results of the first part of the paper to write the Euler--Lagrange difference equations and Noether's difference conservation laws for any invariant Lagrangian, in terms of the invariants and a difference moving frame. We then give the details of the final integration step, assuming the Euler Lagrange equations have been solved for the invariants. This last step relies on understanding the Adjoint action of the Lie group on its Lie algebra. We also use methods to integrate Lie group invariant difference equations developed in Part I. Effectively, for all three actions, we show that solutions to the Euler--Lagrange equations, in terms of the original dependent variables, share a common structure for the whole set of Lagrangians invariant under each given group action, once the invariants are known as functions on the lattice.

We used a combination of cDNA selection, exon amplification, and computational prediction from genomic sequence to isolate transcribed sequences from genomic DNA surrounding the familial Mediterranean fever (FMF) locus. Eighty-seven kb of genomic DNA around D16S3370, a marker showing a high degree of linkage disequilibrium with FMF, was sequenced to completion, and the sequence annotated. A transcript map reflecting the minimal number of genes encoded within the approximately 700 kb of genomic DNA surrounding the FMF locus was assembled. This map consists of 27 genes with discreet messages detectable on Northerns, in addition to three olfactory-receptor genes, a cluster of 18 tRNA genes, and two putative transcriptional units that have typical intron-exon splice junctions yet do not detect messages on Northerns. Four of the transcripts are identical to genes described previously, seven have been independently identified by the French FMF Consortium, and the others are novel. Six related zinc-finger genes, a cluster of tRNAs, and three olfactory receptors account for the majority of transcribed sequences isolated from a 315-kb FMF central region (between D16S468/D16S3070 and cosmid 377A12). Interspersed among them are several genes that may be important in inflammation. This transcript map not only has permitted the identification of the FMF gene (MEFV), but also has provided us an opportunity to probe the structural and functional features of this region of chromosome 16.

International audience; Nanomaterials are versatile materials with a vast repertoire of properties and potential applications. It is expected that they will be used in progressively incremental quantities in the future, giving rise to concerns about to their potential impact on living beings and the environment. The science of studying these effects of nanomaterials can be termed as “Nanotoxicology.” Nanotoxicology has evolved to date based on a combination of several in vitro, in silico, and in vivo experimental studies. Epidemiological information on nanomaterials is still lacking, rendering our understanding of these new materials, incomplete. This chapter makes a case for taking this field one step further in terms of combining in vitro, in vivo, and in silico methods to obtain an in-depth understanding of safety aspects associated with broad classes of nanomaterials in a manner never tried before. This combined approach is especially necessary in light of evolving regulations pertaining to nanomaterials, and the possibility of avoiding epidemiological challenges through in silico predictions (also known as computer-based simulations of complex biological phenomena). An overview of approaches to characterize nanomaterials, and the regulations associated with them will also be presented in this chapter.