Riemannian geometry of Grassmann manifolds with a view on algorithmic computation

We give simple formulas for the canonical metric, gradient, Lie derivative, Riemannian connection, parallel translation, geodesics and distance on the Grassmann manifold of p-planes in ℝn. In these formulas, p-planes are represented as the column space of n × p matrices. The Newton method on abstract Riemannian manifolds proposed by Smith is made explicit on the Grassmann manifold. Two applications - computing an invariant subspace of a matrix and the mean of subspaces - are worked out.

Insulin-like growth factor-binding protein-3 plays an important role in regulating pharyngeal skeleton and inner ear formation and differentiation

Insulin-like growth factor-binding protein (IGFBP)-3 is the major insulin-like growth factor (IGF) carrier protein in the bloodstream. IGFBP-3 prolongs the half-life of circulating IGFs and prevents their potential hypo-glycemic effect. IGFBP-3 is also expressed in many peripheral tissues in fetal and adult stages. In vitro, IGFBP-3 can inhibit or potentiate IGF actions and even possesses IGF-independent activities, suggesting that local IGFBP-3 may also have paracrine/autocrine function(s). The in vivo function of IGFBP-3, however, is unclear. In this study, we elucidate the developmental role of IGFBP-3 using the zebrafish model. IGFBP-3 mRNA expression is first detected in the migrating cranial neural crest cells and subsequently in pharyngeal arches in zebrafish embryos. IGFBP-3 mRNA is also persistently expressed in the developing inner ears. To determine the role of IGFBP-3 in these tissues, we ablated the IGFBP-3 gene product using morpholino-modified antisense oligonucleotides (MOs). The IGFBP-3 knocked down embryos had delayed pharyngeal skeleton morphogenesis and greatly reduced pharyngeal cartilage differentiation. Knockdown of IGFBP-3 also significantly decreased inner ear size and disrupted hair cell differentiation and semicircular canal formation. Furthermore, reintroduction of a MO-resistant form of IGFBP-3 "rescued" the MO-induced defects. These findings suggest that IGFBP-3 plays an important role in regulating pharyngeal cartilage and inner car development and growth in zebrafish.

The unique skeleton of siliceous sponges (Porifera; Hexactinellida and Demospongiae) that evolved first from the Urmetazoa during the Proterozoic: a review

Sponges (phylum Porifera) had been considered as an enigmatic phylum, prior to the analysis of their genetic repertoire/tool kit. Already with the isolation of the first adhesion molecule, galectin, it became clear that the sequences of sponge cell surface receptors and of molecules forming the intracellular signal transduction pathways triggered by them, share high similarity with those identified in other metazoan phyla. These studies demonstrated that all metazoan phyla, including Porifera, originate from one common ancestor, the Urmetazoa. The sponges evolved prior to the Ediacaran-Cambrian boundary (542 million years ago [myr]) during two major "snowball earth events", the Sturtian glaciation (710 to 680 myr) and the Varanger-Marinoan ice ages (605 to 585 myr). During this period the ocean was richer in silica due to the silicate weathering. The oldest sponge fossils (Hexactinellida) have been described from Australia, China and Mongolia and are thought to have existed coeval with the diverse Ediacara fauna. Only little younger are the fossils discovered in the Sansha section in Hunan (Early Cambrian; China). It has been proposed that only the sponges possessed the genetic repertoire to cope with the adverse conditions, e.g. temperature-protection molecules or proteins protecting them against ultraviolet radiation. The skeletal elements of the Hexactinellida (model organisms Monorhaphis chuni and Monorhaphis intermedia or Hyalonema sieboldi) and Demospongiae (models Suberites domuncula and Geodia cydonium), the spicules, are formed enzymatically by the anabolic enzyme silicatein and the catabolic enzyme silicase. Both, the spicules of Hexactinellida and of Demospongiae, comprise a central axial canal and an axial filament which harbors the silicatein. After intracellular formation of the first lamella around the channel and the subsequent extracellular apposition of further lamellae the spicules are completed in a net formed of collagen fibers. The data summarized here substantiate that with the finding of silicatein a new aera in the field of bio/inorganic chemistry started. For the first time strategies could be formulated and experimentally proven that allow the formation/synthesis of inorganic structures by organic molecules. These findings are not only of importance for the further understanding of basic pathways in the body plan formation of sponges but also of eminent importance for applied/commercial processes in a sustainable use of biomolecules for novel bio/inorganic materials.

Skeleton-rearranged pentacyclic diterpenoids possessing a cyclobutane ring from Euphorbia wallichii

Two novel rearranged trachylobane diterpenoids, designated as wallichanol A (2) and wallichanol B (3), consisting of an unprecedented pentacyclic skeleton named wallichane with a cyclobutane ring, and a new ent-trachylobane diterpenoid, 3-oxo-ent-trachyloban-17-oic acid (1), were isolated from the roots of Euphorbia wallichii. Their structures were elucidated by comprehensive analysis of 2D-NMR spectroscopic data, with the stereochemistry of 1 confirmed by X-ray crystallographic study. All of these compounds potently block osteoclastogenesis in vitro, suggesting a potential therapeutic application in prevention of osteoporosis.

Revised Report on the Algorithmic Language Scheme

Data and procedures and the values they amass, Higher-order functions to combine and mix and match, Objects with their local state, the message they pass, A property, a package, the control of point for a catch- In the Lambda Order they are all first-class. One thing to name them all, one things to define them, one thing to place them in environments and bind them, in the Lambda Order they are all first-class. Keywords: Scheme, Lisp, functional programming, computer languages.

Algorithmic derivation of isochronicity conditions

Hill, Joe M., Lloyd, Noel G., Pearson, Jane M., 'Algorithmic derivation of isochronicity conditions', Nonlinear Analysis (2007) 67, 52-69.

WIMU instrumentation of assassin trainer & skeleton sled

Skeleton is a high‐speed Winter Olympic sport performed on the same twisting, downhill ice tracks used for Bobsleigh & Luge. The single rider sprints and pushes their sled for 20‐30m on a level start section before loading and going through a twisting course of over 1km, at speeds up to 140km/h, experiencing up to 5g. In competition, the top athletes can be within a fraction of a second of each other. The initial short pushing period is believed to be critical to overall performance but it is not well understood. A collaborative project between University of Bath, UK Sport and Tyndall National Institute is instrumenting skeleton athletes, training equipment and test tracks with Tyndall’s Wireless Inertial Measurement Unit technology in order to investigate and improve understanding of this phase of a skeleton run. It is hoped this will lead to improved training regimes and better performance of such elite, Olympic level athletes. This work presents an initial look at the system as implemented and data recorded.

WIMU instrumentation of assassin trainer & skeleton sled – initial data capture

Science Foundation Ireland (CSET - Centre for Science, Engineering and Technology, Grant No. 07/CE/11147)

To tremble the zero: art in the age of algorithmic reproduction

'To Tremble the Zero: Art in the Age of Algorithmic Reproduction' is a philosophic, political and sensuous journey playing with (and against) Benjamin's 'Art in the Age of Mechanical Reproduction'. In an age inundated by the 'post-': postmodernity, posthuman, post art, postsexual, post-feminist, post-society, post-nation, etc, 'To Tremble the Zero' sets out to re/present the nature of what it means to do or make 'art', as well as what it means to be or have 'human/ity' when the ground is nothing other than the fractal, and algorithmically infinite, combinations of zero and one. The work will address also the unfortunate way in which modern forms of metaphysics continue to creep 'unsuspectingly' into our understanding of contemporary media/electronic arts, despite (or perhaps even because of) the attempts by Latour, Badiou, or Agamben especially when addressing the zero/one as if a contradictory 'binary' rather than as a kind of 'slice' or (to use Deleuze and Guattari) an immanent plane of immanence. This work argues that by retrieving Benjamin, Einstein, Gödel, and Haraway, a rather different story of art can be told.