In [Bi2] we defined connections on a parabolic principal bundle. While connections on usual principal bundles are defined as splittings of the Atiyah exact sequence, it was noted in [Bi2] that the Atiyah exact sequence does not generalize to the parabolic principal bundles. Here we show that a twisted version of the Atiyah exact sequence generalize to the context of parabolic principal bundles....

We now describe these groups briefly. To obtain T, divide the group of diffeomorphisms of the n — 1 sphere S" by the normal subgroup of those diffeomorphisms that are extendable to the w-ball. See [2] for details. The set 0 is the set of /-equivalence classes of closed, oriented, differentiable w-manifolds that are homotopy spheres. If M is an oriented manifold, let —If be the oppositely orient...

In this paper we address the problem of characterizing the RNA complement of a given cell type, that is, the set of RNA species and their relative copy number, from a large set of short sequence reads which have been randomly sampled from the cell’s RNA sequences through a sequencing experiment. We refer to this problem as the transcriptome reconstruction problem, and we specifically investigat...

The Birman exact sequence describes the effect on the mapping class group of a surface with boundary of gluing discs to the boundary components. We construct an analogous exact sequence for the automorphism group of a free group. For the mapping class group, the kernel of the Birman exact sequence is a surface braid group. We prove that in the context of the automorphism group of a free group, ...

Given a three-dimensional complex algebraic variety with isolated singular point and a sufficiently fine complete resolution of the singularity, we can make a careful choice of hyperplane that allows us to construct an exact sequence of weighted Nash complexes.

In recent years, there has been an increasing interest in planted (l, d) motif search (PMS) with applications to discovering significant segments in biological sequences. However, there has been little discussion about PMS over large alphabets. This paper focuses on motif stem search (MSS), which is recently introduced to search motifs on large-alphabet inputs. A motif stem is an l-length strin...

Time series motif discovery is important as the discovered motifs generally form the primitives for many data mining tasks. In this work, we examine the problem of discovering groups of motifs from different time series that exhibit some lag relationships. We define a new class of pattern called lagPatterns that captures the invariant ordering among motifs. lagPatterns characterize localized as...