Weak Lie Symmetry and extended Lie algebra

The concept of weak Lie motion (weak Lie symmetry) is introduced through ${\cal{L}}_{\xi}{\cal{L}}_{\xi}g_{ab}=0,$ (${\cal{L}}_{\xi}{\cal{L}}_{\xi}f=0$). Applications are given which exhibit a reduction of the usual symmetry, e.g., in the case of the the rotation group. In this context, a particular generalization of Lie algebras is found ("extended Lie algebras") which turns out to be an involutive distribution or a simple example for a tangent Lie algebroid. Riemannian and Lorentz metrics can be introduced on such an algebroid through an extended Cartan-Killing form. Transformation groups from non-relativistic mechanics and quantum mechanics lead to such tangent Lie algebroids and to Lorentz geometries constructed on them (1-dimensional gravitational fields).Comment: A summary of this article has been presented at the "90th Encounter between Mathematicians and Theoretical Physicists" at the Institut de Recherche Math\'ematique Avanc\'ee (University of Strasbourg and CNRS), September 20-22, 201

Mutagenesis of the conserved 51-nucleotide region of Sindbis virus

We have constructed 25 site-specific mutations in a domain of 51 nucleotides in Sindbis virus that is highly conserved among all alphaviruses sequenced to date. These 51 nucleotides are capable of forming two hairpin structures and are found from nucleotides 155 to 205 in Sindbis virus within the region encoding nsP1. Of the mutations, 21 were silent and did not lead to a change in the amino acid sequence encoded. These silent mutations changed not only the linear sequence but also the stability of the hairpins in most cases. Two double mutants that were constructed led to the replacement of one base pair by another so that the linear sequence was altered but the nature of the hairpins was not. All of the mutants with silent mutations were viable, but 19 of the 21 mutants were severely impaired for growth in both chicken and mosquito cells. Compared with the parental virus, they grew slowly and produced virus at rates of 10(-1) to 10(-4) times the parental rate. Surprisingly, however, the plaques produced by these mutants were indistinguishable from those produced by the parental virus. Two of the silent mutations, found within the first hairpin structure, produced virus at a faster rate than the parental virus. It is clear that the exact sequence of this region is important for some aspect of virus replication. We suggest that one or more proteins, either virus encoded or cellular, bind to the hairpin structures in a sequence-specific fashion in a step that promotes replication of the viral RNA. Of the mutations that resulted in a change of coding, only one of four was viable, suggesting that the amino acid sequence encoded in this domain is essential for virus replication

Rational invariants of even ternary forms under the orthogonal group

In this article we determine a generating set of rational invariants of minimal cardinality for the action of the orthogonal group $\mathrm{O}_3$ on the space $\mathbb{R}[x,y,z]_{2d}$ of ternary forms of even degree $2d$. The construction relies on two key ingredients: On one hand, the Slice Lemma allows us to reduce the problem to dermining the invariants for the action on a subspace of the finite subgroup $\mathrm{B}_3$ of signed permutations. On the other hand, our construction relies in a fundamental way on specific bases of harmonic polynomials. These bases provide maps with prescribed $\mathrm{B}_3$-equivariance properties. Our explicit construction of these bases should be relevant well beyond the scope of this paper. The expression of the $\mathrm{B}_3$-invariants can then be given in a compact form as the composition of two equivariant maps. Instead of providing (cumbersome) explicit expressions for the $\mathrm{O}_3$-invariants, we provide efficient algorithms for their evaluation and rewriting. We also use the constructed $\mathrm{B}_3$-invariants to determine the $\mathrm{O}_3$-orbit locus and provide an algorithm for the inverse problem of finding an element in $\mathbb{R}[x,y,z]_{2d}$ with prescribed values for its invariants. These are the computational issues relevant in brain imaging.Comment: v3 Changes: Reworked presentation of Neuroimaging application, refinement of Definition 3.1. To appear in "Foundations of Computational Mathematics

Defined mutations in the 5' nontranslated sequence of Sindbis virus RNA

We have constructed 24 deletion mutants which contain deletions of from 1 to 15 nucleotides in the 5' nontranslated region of Sindbis virus RNA and tested the effect of these mutations on virus replication. The results showed that the first 44 nucleotides, which are capable of forming a hairpin structure, are important for virus replication, as all deletions tested in this region were either lethal or resulted in virus that grew poorly in comparison to the parental virus. Many of these deletions had different effects in mosquito cells than in chicken cells, suggesting that cellular factors, presumably proteins, bind to this region. This domain may function in at least two processes in viral replication. It seems likely that in the minus strand, this sequence element is bound by the viral replicase and promotes RNA replication. In the plus strand, this element may modulate initiation of translation of the nonstructural proteins. The results suggest that the hairpin structure itself is important. All deletions within it had deleterious effects on virus replication, and in particular, deletion of one of the G residues at nucleotide 7 or 8 or of one of the C residues at nucleotide 36 or 37 which are theoretically base-paired with these G's resulted in temperature-sensitive viruses that behaved very similarly. In contrast, large deletions between the 44-nucleotide hairpin and the translation start site at nucleotides 60 to 62 resulted in virus that grew as well as or better than the parental virus in both chicken and mosquito cells. The A residue at position 5 of the HRSP strain used was examined in more detail. Deletion of this A was lethal, whereas substitution by G resulted in a virus that grew poorly, despite the fact that G is present at position 5 in the AR339 parent of HRSP. U at position 5 resulted in a virus that grew less well than the A5 strain but better than the G5 mutant

Surface properties of ocean fronts

Background information on oceanic fronts is presented and the results of several models which were developed to study the dynamics of oceanic fronts and their effects on various surface properties are described. The details of the four numerical models used in these studies are given in separate appendices which contain all of the physical equations, program documentation and running instructions for the models

Roughening and preroughening in the six vertex model with an extended range of interaction

We study the phase diagram of the BCSOS model with an extended interaction range using transfer matrix techniques, pertaining to the (100) surface of single component fcc and bcc crystals. The model shows a 2x2 reconstructed phase and a disordered flat phase. The deconstruction transition between these phases merges with a Kosterlitz-Thouless line, showing an interplay of Ising and Gaussian degrees of freedom. As in studies of the fully frustrated XY model, exponents deviating from Ising are found. We conjecture that tri-critical Ising behavior may be a possible explanation for the non-Ising exponents found in those models.Comment: 25 pages in RevTeX 3.0, seven uuencoded postscript figures, REPLACED because of submission error (figures were not included