Polynomial Functions and the Riesz Interpolation Property

Building on a proof by D. Handelman of a generalisation of an example due to L. Fuchs, we show that the space of real-valued polynomials on a non-empty set X of reals has the Riesz Interpolation Property if and only if X is bounded.

An updated moraine map of Far NE Russia

Barr and Clark published a series of maps depicting the distribution of end moraines across Far NE Russia. These
moraines outlined the former distribution and dimensions of glaciers, and were identified through the analysis of
Landsat ETM+ satellite images (15- and 30-m resolution). Now, a number of freely available digital elevation
model (DEM) datasets are available, which cover the entire 4 million km2 of Far NE Russia. These include
the 30-m resolution ASTER GDEM and the 90-m resolution Viewfinder Panorama DEM. Here we use these
datasets, in conjunction with Landsat ETM+ images, to complete the process of systematically and
comprehensively mapping end moraines. With the aid of the DEMs described above, here we present a total
dataset of 8414 moraines, which almost quadruples the inventory of Barr and Clark. This increase in the
number of moraines is considered to reflect the utility of the DEMs for mapping glacial landforms. In terms of
moraine distribution, the Barr and Clark map and the one presented here are comparable, with moraines found
to cluster in highland regions and upon adjacent lowlands, attesting to the former occupation of the region by
mountain-centred ice masses. This record is considered to reflect palaeoclimatic and topographic controls upon
the extent and dynamics of palaeoglaciers, as well as spatial variability in moraine preservation.

An Impact Of Various Shroud Bleed Slot Configurations And Cavity Vanes On Compressor Map Width And The Inducer Flow Field

This paper describes an investigation of map width enhancement and a detailed analysis of the inducer flow field due to various bleed slot configurations and vanes in the annular cavity of a turbocharger centrifugal compressor. The compressor under investigation is used in a turbocharger application for a heavy duty diesel engine of approximately 400 hp. This investigation has been undertaken using a computational fluid dynamics (CFD) model of the full compressor stage, which includes a manual multiblock-structured grid generation method. The influence of the bleed slot flow on the inducer flow field at a range of operating conditions has been analyzed, highlighting the improvement in surge and choked flow capability. The impact of the bleed slot geometry variations and the inclusion of cavity vanes on the inlet incidence angle have been studied in detail by considering the swirl component introduced at the leading edge by the recirculating flow through the slot. Further, the overall stage efficiency and the nonuniform flow field at the inducer inlet have been also analyzed. The analysis revealed that increasing the slot width has increased the map width by about 17%. However, it has a small impact on the efficiency, due to the frictional and mixing losses. Moreover, adding vanes in the cavity improved the pressure ratio and compressor performance noticeably. A detail analysis of the compressor with cavity vanes has also been presented.

Map Width Enhancement Technique for a Turbocharger Compressor

This paper presents an investigation of map width enhancement and the performance improvement of a turbocharger compressor using a series of static vanes in the annular cavity of a classical bleed slot system. The investigation has been carried out using both experimental and numerical analysis. The compressor stage used for this study is from a turbocharger unit used in heavy duty diesel engines of approximately 300 kW. Two types of vanes were designed and added to the annular cavity of the baseline classical bleed slot system. The purpose of the annular cavity vane technique is to remove some of the swirl that can be carried through the bleed slot system, which would influence the pressure
ratio. In addition to this, the series of cavity vanes provides a better guidance to the slot recirculating flow before it mixes with the impeller main inlet flow. Better guidance of the flow improves the mixing at the inducer inlet in the circumferential direction. As a consequence, the stability of the compressor is improved at lower flow rates and a wider map can be achieved. The impact of two cavity vane designs on the map width and performance of the compressor was highlighted through a detailed analysis of the impeller flow field. The numerical and experimental study revealed that an effective vane design can improve the map width and pressure ratio characteristic without an efficiency penalty compared to the classical bleed slot system without vanes. The comparison study between the cavity vane and noncavity vane configurations presented in this paper showed that the map width was improved by 14.3% due to a significant reduction in surge flow and the peak pressure ratio was improved by 2.25% with the addition of a series of cavity vanes in the annular cavity of the bleed slot system.

MAP kinase pathway signalling is essential for extracellular matrix determined mammary epithelial cell survival

Mammary epithelial cells in primary cell culture require both growth factors and specific extracellular matrix (ECM)-attachment for survival. Here we demonstrate for the first time that inhibition of the ECM-induced Erk 1/Erk 2 (p42/44 MAPK) pathway, by PD 98059, leads to apoptosis in these cells. Associated with this cell death is a possible compensatory signalling through the p38 MAP kinase pathway the inhibition of which, by SB 203580, leads to a more rapid onset of apoptosis. This provides evidence for a hitherto undescribed Erk 1/Erk 2 to p38 MAP kinase pathway 'cross-talk' that is essential for the survival of these cells. The cell death associated with inhibition of these two MAP kinase pathways however, occurred in the presence of insulin that activates the classical PI-3 kinase-dependent Akt/PKB survival signals and Akt phosphorylation. Cell death induced by inhibition of the MAP kinase pathways did not affect Akt phosphorylation and may, thus, be independent of PI-3 kinase signalling.

Defending the Irish Border: The Map of Watchful Architecture

This chapter offers an analysis of a map of the Irish border. The Map of Watchful Architecture charts the history of defensive structures in the border region.

Demonstrating the Transferability and the Descriptive Power of Sketch-Map

Increasingly, it is recognized that new automated forms of analysis are required to understand the high-dimensional output obtained from atomistic simulations. Recently, we introduced a new dimensionality reduction algorithm, sketch-map, that was designed specifically to work with data from molecular dynamics trajectories. In what follows, we provide more details on how this algorithm works and on how to set its parameters. We also test it on two well-studied Lennard-Jones clusters and show that the coordinates we extract using this algorithm are extremely robust. In particular, we demonstrate that the coordinates constructed for one particular Lennard-Jones cluster can be used to describe the configurations adopted by a second, different cluster and even to tell apart different phases of bulk Lennard-Jonesium.

Using sketch-map coordinates to analyze and bias molecular dynamics simulations

When examining complex problems, such as the folding of proteins, coarse grained descriptions of the system drive our investigation and help us to rationalize the results. Oftentimes collective variables (CVs), derived through some chemical intuition about the process of interest, serve this purpose. Because finding these CVs is the most difficult part of any investigation, we recently developed a dimensionality reduction algorithm, sketch-map, that can be used to build a low-dimensional map of a phase space of high-dimensionality. In this paper we discuss how these machine-generated CVs can be used to accelerate the exploration of phase space and to reconstruct free-energy landscapes. To do so, we develop a formalism in which high-dimensional configurations are no longer represented by low-dimensional position vectors. Instead, for each configuration we calculate a probability distribution, which has a domain that encompasses the entirety of the low-dimensional space. To construct a biasing potential, we exploit an analogy with metadynamics and use the trajectory to adaptively construct a repulsive, history-dependent bias from the distributions that correspond to the previously visited configurations. This potential forces the system to explore more of phase space by making it desirable to adopt configurations whose distributions do not overlap with the bias. We apply this algorithm to a small model protein and succeed in reproducing the free-energy surface that we obtain from a parallel tempering calculation.

Simplifying the representation of complex free-energy landscapes using sketch-map

A new scheme, sketch-map, for obtaining a low-dimensional representation of the region of phase space explored during an enhanced dynamics simulation is proposed. We show evidence, from an examination of the distribution of pairwise distances between frames, that some features of the free-energy surface are inherently high-dimensional. This makes dimensionality reduction problematic because the data does not satisfy the assumptions made in conventional manifold learning algorithms We therefore propose that when dimensionality reduction is performed on trajectory data one should think of the resultant embedding as a quickly sketched set of directions rather than a road map. In other words, the embedding tells one about the connectivity between states but does not provide the vectors that correspond to the slow degrees of freedom. This realization informs the development of sketch-map, which endeavors to reproduce the proximity information from the high-dimensionality description in a space of lower dimensionality even when a faithful embedding is not possible.

Invariant Information Local Sub-map Filter (IILSF) for Efficient Simultaneous Localisation and Mapping of Large Environments

This paper presents an Invariant Information Local Sub-map Filter (IILSF) as a technique for consistent Simultaneous Localisation and Mapping (SLAM) in a large environment. It harnesses the benefits of sub-map technique to improve the consistency and efficiency of Extended Kalman Filter (EKF) based SLAM. The IILSF makes use of invariant information obtained from estimated locations of features in independent sub-maps, instead of incorporating every observation directly into the global map. Then the global map is updated at regular intervals. Applying this technique to the EKF based SLAM algorithm: (a) reduces the computational complexity of maintaining the global map estimates and (b) simplifies transformation complexities and data association ambiguities usually experienced in fusing sub-maps together. Simulation results show that the method was able to accurately fuse local map observations to generate an efficient and consistent global map, in addition to significantly reducing computational cost and data association ambiguities.