Exploration of RNA structure spaces

In order to understand the structure of real structure spaces, we are studying the 5S rRNA structure space experimentally. A plasmid containing a synthetic 5S rRNA gene, two rRNA promoters, and transcription terminators has been assembled. Assays are conducted to determine if the foreign 5S rRNA is expressed, and to see whether or not it is incorporated into ribosomes. Evolutionary competition is used to determine the relative fitness of strains containing the foreign 5S rRNA and a control 5S rRNA. By using site directed mutagenesis, a number of mutants can be made in order to study the boundaries of the structure space and how sharply defined they are. By making similar studies in the vicinity of structure space, it will be possible to determine how homogeneous the 5S rRNA structure space is. Useable experimental protocols have been developed, and a number of mutants have already been studied. Initial results suggest an explanation of why single stranded regions of the RNA are less subject to mutation than double stranded regions

Higher Whitehead torsion and the geometric assembly map

We construct a higher Whitehead torsion map, using algebraic K-theory of spaces, and show that it satisfies the usual properties of the classical Whitehead torsion. This is used to describe a "geometric assembly map" defined on stabilized structure spaces in purely homotopy theoretic terms.Comment: 46 pages. Revised version following the referee's suggestions. To appear in Journal of Topolog

The block structure spaces of real projective spaces and orthogonal calculus of functors

Given a compact manifold X, the set of simple manifold structures on X x \Delta^k relative to the boundary can be viewed as the k-th homotopy group of a space \S^s (X). This space is called the block structure space of X. We study the block structure spaces of real projective spaces. Generalizing Wall's join construction we show that there is a functor from the category of finite dimensional real vector spaces with inner product to the category of pointed spaces which sends the vector space V to the block structure space of the projective space of V. We study this functor from the point of view of orthogonal calculus of functors; we show that it is polynomial of degree <= 1 in the sense of orthogonal calculus. This result suggests an attractive description of the block structure space of the infinite dimensional real projective space via the Taylor tower of orthogonal calculus. This space is defined as a colimit of block structure spaces of projective spaces of finite-dimensional real vector spaces and is closely related to some automorphisms spaces of real projective spaces.Comment: corrected version, 32 pages, published in Transactions of the AMS at http://www.ams.org/tran/2007-359-01/S0002-9947-06-04180-8

Normal structure spaces of groups

Can we do a topological study of various classes of normal subgroups endowed with a hull-kernel-type topology? In this paper, we have provided an answer to this question. We have introduced as well a new class of normal subgroups called primitive subgroups. Separation axioms, compactness, connectedness, and continuities of these spaces have been studied. We have concluded with the question of determining spectral spaces among them

Contra continuity on weak structure spaces

We introduce some contra continuous functions in weak structure spaces such as contra (M,w)-continuous functions, contra (alpha(m),w)-continuous functions, contra (sigma(m),w)-continuous functions, contra (pi(m),w)-continuous functions and contra (beta(m),w)-continuous functions. We investigate their characterization and relationships among such functions

Noncommutative Lattices and Their Continuum Limits

We consider finite approximations of a topological space $M$ by noncommutative lattices of points. These lattices are structure spaces of noncommutative $C^*$-algebras which in turn approximate the algebra \cc(M) of continuous functions on $M$. We show how to recover the space $M$ and the algebra \cc(M) from a projective system of noncommutative lattices and an inductive system of noncommutative $C^*$-algebras, respectively.Comment: 22 pages, 8 Figures included in the LaTeX Source New version, minor modifications (typos corrected) and a correction in the list of author

Flux Vacua Attractors in Type II on SU(3)xSU(3) Structure

We summarize and extend our work on flux vacua attractors in generalized compactifications. After reviewing the attractor equations for the heterotic string on SU(3) structure manifolds, we study attractors for N=1 vacua in type IIA/B on SU(3)xSU(3) structure spaces. In the case of vanishing RR flux, we find attractor equations that encode Minkowski vacua only (and which correct a previous normalization error). In addition to our previous considerations, here we also discuss the case of nonzero RR flux and the possibility of attractors for AdS vacua.Comment: 10 pages, contribution to the proceedings of the 4th RTN workshop "Forces Universe", Varna, September 200

Strongly Minimal Generalized Closed Set in Biminimal Structure Spaces

AbstractIn this paper, we introduce the concept of smg-closed sets in biminimal structure space and a new notion of a pair wise smg-closed set is defined and studied some of its properties