The connected components of the space of Alexandrov surfaces

Denote by $\mathcal{A}(\kappa)$ the set of all compact Alexandrov surfaces with curvature bounded below by $\kappa$ without boundary, endowed with the topology induced by the Gromov-Hausdorff metric. We determine the connected components of $\mathcal{A}(\kappa)$ and of its closure

Star Unfolding Convex Polyhedra via Quasigeodesic Loops

We extend the notion of star unfolding to be based on a quasigeodesic loop Q rather than on a point. This gives a new general method to unfold the surface of any convex polyhedron P to a simple (non-overlapping), planar polygon: cut along one shortest path from each vertex of P to Q, and cut all but one segment of Q.Comment: 10 pages, 7 figures. v2 improves the description of cut locus, and adds references. v3 improves two figures and their captions. New version v4 offers a completely different proof of non-overlap in the quasigeodesic loop case, and contains several other substantive improvements. This version is 23 pages long, with 15 figure

Orientation and symmetries of Alexandrov spaces with applications in positive curvature

We develop two new tools for use in Alexandrov geometry: a theory of ramified orientable double covers and a particularly useful version of the Slice Theorem for actions of compact Lie groups. These tools are applied to the classification of compact, positively curved Alexandrov spaces with maximal symmetry rank.Comment: 34 pages. Simplified proofs throughout and a new proof of the Slice Theorem, correcting omissions in the previous versio

The Serret-Andoyer Riemannian metric and Euler-Poinsot rigid body motion

The Euler-Poinsot rigid body motion is a standard mechanical system and is the model for left-invariant Riemannian metrics on SO(3). In this article, using the Serret-Andoyer variables we parameterize the solutions and compute the Jacobi fields in relation with the conjugate locus evaluation. Moreover the metric can be restricted to a 2D surface and the conjugate points of this metric are evaluated using recent work [4] on surfaces of revolution

Universal curvature identities II

We show that any universal curvature identity which holds in the Riemannian setting extends naturally to the pseudo-Riemannian setting. Thus the Euh-Park-Sekigawa identity also holds for pseudo-Riemannian manifolds. We study the Euler-Lagrange equations associated to the Chern-Gauss-Bonnet formula and show that as in the Riemannian setting, they are given solely in terms of curvature (and not in terms of covariant derivatives of curvature) even in the pseudo-Riemannian setting.Comment: 15 page

DGCR8 HITS-CLIP reveals novel functions for the Microprocessor

The Drosha-DGCR8 complex (Microprocessor) is required for microRNA (miRNA) biogenesis. DGCR8 recognizes the RNA substrate, whereas Drosha functions as the endonuclease. High-throughput sequencing and crosslinking immunoprecipitation (HITS-CLIP) was used to identify RNA targets of DGCR8 in human cells. Unexpectedly, miRNAs were not the most abundant targets. DGCR8-bound RNAs also comprised several hundred mRNAs as well as snoRNAs and long non-coding RNAs. We found that the Microprocessor controls the abundance of several mRNAs as well as of MALAT-1. By contrast, DGCR8-mediated cleavage of snoRNAs is independent of Drosha, suggesting the involvement of DGCR8 in cellular complexes with other endonucleases. Interestingly, binding of DGCR8 to cassette exons, acts as a novel mechanism to regulate the relative abundance of alternatively spliced isoforms. Collectively, these data provide new insights in the complex role of DGCR8 in controlling the fate of several classes of RNAs

Regulation of MicroRNA Biogenesis: A miRiad of mechanisms

microRNAs are small, non-coding RNAs that influence diverse biological functions through the repression of target genes during normal development and pathological responses. Widespread use of microRNA arrays to profile microRNA expression has indicated that the levels of many microRNAs are altered during development and disease. These findings have prompted a great deal of investigation into the mechanism and function of microRNA-mediated repression. However, the mechanisms which govern the regulation of microRNA biogenesis and activity are just beginning to be uncovered. Following transcription, mature microRNA are generated through a series of coordinated processing events mediated by large protein complexes. It is increasingly clear that microRNA biogenesis does not proceed in a 'one-size-fits-all' manner. Rather, individual classes of microRNAs are differentially regulated through the association of regulatory factors with the core microRNA biogenesis machinery. Here, we review the regulation of microRNA biogenesis and activity, with particular focus on mechanisms of post-transcriptional control. Further understanding of the regulation of microRNA biogenesis and activity will undoubtedly provide important insights into normal development as well as pathological conditions such as cardiovascular disease and cancer

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead