Medial/skeletal linking structures for multi-region configurations

We consider a generic configuration of regions, consisting of a collection of distinct compact regions $\{\Omega_i\}$ in $\mathbb{R}^{n+1}$ which may be either smooth regions disjoint from the others or regions which meet on their piecewise smooth boundaries $\mathcal{B}_i$ in a generic way. We introduce a skeletal linking structure for the collection of regions which simultaneously captures the regions' individual shapes and geometric properties as well as the "positional geometry" of the collection. The linking structure extends in a minimal way the individual "skeletal structures" on each of the regions, allowing us to significantly extend the mathematical methods introduced for single regions to the configuration. We prove for a generic configuration of regions the existence of a special type of Blum linking structure which builds upon the Blum medial axes of the individual regions. This requires proving several transversality theorems for certain associated "multi-distance" and "height-distance" functions for such configurations. We show that by relaxing the conditions on the Blum linking structures we obtain the more general class of skeletal linking structures which still capture the geometric properties. In addition to yielding geometric invariants which capture the shapes and geometry of individual regions, the linking structures are used to define invariants which measure positional properties of the configuration such as: measures of relative closeness of neighboring regions and relative significance of the individual regions for the configuration. These invariants, which are computed by formulas involving "skeletal linking integrals" on the internal skeletal structures, are then used to construct a "tiered linking graph," which identifies subconfigurations and provides a hierarchical ordering of the regions.Comment: 135 pages, 36 figures. Version to appear in Memoirs of the Amer. Math. So

Challenges facing green space: is statute the answer?

Against a backdrop of austerity, characterised by public-sector funding cuts and a devolutionary agenda, this paper explores how legislation might address two, inter-related challenges which face public urban green space ('greenspace') in England and Wales; namely, responsibility for provision, and identification of supporting funds. It focuses on two proposals; first, the introduction of legislative powers to enable local authorities to create user-charging schemes, and secondly, the imposition of a local authority statutory duty to provide greenspace

Regulation of the hrp Type III Secretion System in Pseudomonas syringae pv. tomato DC3000

Pseudomonas syringae pv. DC3000 is a gram-negative bacterium that infects the model plant Arabidopsis thaliana. Pathogenicity is achieved via secretion of effector proteins into the host cytoplasm through a Type III Secretion System (T3SS). In Ps. DC3000 the T3SS (and associated effector proteins) are dependent on HrpL for their transcription. hrpL transcription is sigma54-dependent and requires two co-dependent enhancer binding proteins, HrpR and HrpS (HrpRS), for activation. HrpRS are regulated by two hrpL-dependent proteins, HrpV and HrpG, where HrpV negatively affects HrpRS activity and HrpG relieves this repression. Here the mechanism of HrpV and HrpG’s action on HrpRS activity was tested in vivo and in vitro; and the molecular determinants of HrpV and HrpG functionality were characterised by in silico and mutational analysis. Whole-gene deletion mutants of hrpV and hrpG in Ps. DC3000 revealed complications associated with inserting marker cassettes in transcriptionally-antagonistic orientations. Truncation mutants of HrpV and HrpG showed that C-terminal helices in both proteins play a functional and/or structural role. Alanine mutants indicated a structural role for residues 108-110 in HrpV and a functional role for residues 111-113 in HrpG (NQR motif). HrpV was demonstrated to form a dimer and represses the activity of HrpRS (in vivo and in vitro) but not via inhibiting ATPase activity or destabilising open promoter complexes. HrpG was shown to destabilise the HrpV dimer (potentially via the C-terminal NQR motif). Findings from this study were used to propose a revised model of hrpL regulation in which an active dimer of HrpV binds two adjacent HrpS subunits of a HrpRS hexamer to “lock” the hexamer in an unfavourable conformation. HrpG acts by destabilising the HrpV dimer into an inactive monomeric form. Additional experiments to confirm this model include creating an artificially linked dimer of HrpV and testing its repressive action on HrpRS in the presence or absence of HrpG

The alphaviruses: gene expression, replication, and evolution

The alphaviruses are a genus of 26 enveloped viruses that cause disease in humans and domestic animals. Mosquitoes or other hematophagous arthropods serve as vectors for these viruses. The complete sequences of the +/- 11.7-kb plus-strand RNA genomes of eight alphaviruses have been determined, and partial sequences are known for several others; this has made possible evolutionary comparisons between different alphaviruses as well as comparisons of this group of viruses with other animal and plant viruses. Full-length cDNA clones from which infectious RNA can be recovered have been constructed for four alphaviruses; these clones have facilitated many molecular genetic studies as well as the development of these viruses as expression vectors. From these and studies involving biochemical approaches, many details of the replication cycle of the alphaviruses are known. The interactions of the viruses with host cells and host organisms have been exclusively studied, and the molecular basis of virulence and recovery from viral infection have been addressed in a large number of recent papers. The structure of the viruses has been determined to about 2.5 nm, making them the best-characterized enveloped virus to date. Because of the wealth of data that has appeared, these viruses represent a well-characterized system that tell us much about the evolution of RNA viruses, their replication, and their interactions with their hosts. This review summarizes our current knowledge of this group of viruses

The island of Kauai, Hawaii's progressive shoreline setback and coastal protection ordinance

Approximately two-thirds of coastal and Great Lakes states have some type of shoreline construction setback or construction control line requiring development to be a certain distance from the shoreline or other coastal feature (OCRM, 2008). Nineteen of 30 coastal states currently use erosion rates for new construction close to the shoreline. Seven states established setback distances based on expected years from the shoreline: the remainder specify a fixed setback distance (Heinz Report, 2000). Following public hearings by the County of Kauai Planning Commission and Kauai County Council, the ‘Shoreline Setback and Coastal Protection Ordinance’ was signed by the Mayor of Kauai on January 25, 2008. After a year of experience implementing this progressive, balanced shoreline setback ordinance several amendments were recently incorporated into the Ordinance (#887; Bill #2319 Draft 3). The Kauai Planning Department is presently drafting several more amendments to improve the effectiveness of the Ordinance. The intent of shoreline setbacks is to establish a buffer zone to protect shorefront development from loss due to coastal erosion - for a period of time; to provide protection from storm waves; to allow the natural dynamic cycles of erosion and accretion of beaches and dunes to occur; to maintain beach and dune habitat; and, to maintain lateral beach access and open space for the enjoyment of the natural shoreline environment. In addition, a primary goal of the Kauai setback ordinance is to avoid armoring or hardening of the shore which along eroding coasts has been documented to ultimately eliminate the fronting beach. (PDF contains 4 pages

Maintenance and repair: too big to ignore

Most models of aggregate economic activity, like the standard neoclassical growth model, ignore the fact that equipment and structures are maintained and repaired. Once physical capital is purchased in these models, there are typically no more decisions made regarding its use. The theme of this article is that there is evidence to suggest that incorporating expenditures on the maintenance and repair of physical capital into models of aggregate economic activity will change the quantitative answers to some key questions that have been addressed with these models. This evidence is primarily from a little-used economywide survey in Canada. The survey shows that the activity of maintaining and repairing equipment and structures is an activity that is generally both large relative to investment and a substitute for investment to some extent—and to a large extent during some episodes.Econometric models