A Fixed Parameter Tractable Approximation Scheme for the Optimal Cut Graph of a Surface

Given a graph $G$ cellularly embedded on a surface $\Sigma$ of genus $g$, a cut graph is a subgraph of $G$ such that cutting $\Sigma$ along $G$ yields a topological disk. We provide a fixed parameter tractable approximation scheme for the problem of computing the shortest cut graph, that is, for any $\varepsilon >0$, we show how to compute a $(1+ \varepsilon)$ approximation of the shortest cut graph in time $f(\varepsilon, g)n^3$. Our techniques first rely on the computation of a spanner for the problem using the technique of brick decompositions, to reduce the problem to the case of bounded tree-width. Then, to solve the bounded tree-width case, we introduce a variant of the surface-cut decomposition of Ru\'e, Sau and Thilikos, which may be of independent interest

Silsesquioxane polymer as a potential scaffold for laryngeal reconstruction

Cancer, disease and trauma to the larynx and their treatment can lead to permanent loss of structures critical to voice, breathing and swallowing. Engineered partial or total laryngeal replacements would need to match the ambitious specifications of replicating functionality, outer biocompatibility, and permissiveness for an inner mucosal lining. Here we present porous polyhedral oligomeric silsesquioxane-poly(carbonate urea) urethane (POSS-PCUU) as a potential scaffold for engineering laryngeal tissue. Specifically, we employ a precipitation and porogen leaching technique for manufacturing the polymer. The polymer is chemically consistent across all sample types and produces a foam-like scaffold with two distinct topographies and an internal structure composed of nano- and micro-pores. Whilst the highly porous internal structure of the scaffold contributes to the complex tensile behaviour of the polymer, the surface of the scaffold remains largely non-porous. The low number of pores minimise access for cells, although primary fibroblasts and epithelial cells do attach and proliferate on the polymer surface. Our data show that with a change in manufacturing protocol to produce porous polymer surfaces, POSS-PCUU may be a potential candidate for overcoming some of the limitations associated with laryngeal reconstruction and regeneration

Aerated blast furnace slag filters for enhanced nitrogen and phosphorus removal from small wastewater treatment plants

Rock filters (RF) are a promising alternative technology for natural wastewater treatment for upgrading WSP effluent. However, the application of RF in the removal of eutrophic nutrients, nitrogen and phosphorus, is very limited. Accordingly, the overall objective of this study was to develop a lowcost RF system for the purpose of enhanced nutrient removal from WSP effluents, which would be able to produce effluents which comply with the requirements of the EU Urban Waste Water Treatment Directive (UWWTD) (911271lEEC) and suitable for small communities. Therefore, a combination system comprising a primary facultative pond and an aerated rock filter (ARF) system-either vertically or horizontally loaded-was investigated at the University of Leeds' experimental station at Esholt Wastewater Treatment Works, Bradford, UK. Blast furnace slag (BFS) and limestone were selected for use in the ARF system owing to their high potential for P removal and their low cost. This study involved three major qperiments: (1) a comparison of aerated vertical-flow and horizontal-flow limestone filters for nitrogen removal; (2) a comparison of aerated limestone + blast furnace slag (BFS) filter and aerated BFS filters for nitrogen and phosphorus removal; and (3) a comparison of vertical-flow and horizontal-flow BFS filters for nitrogen and phosphorus removal. The vertical upward-flow ARF system was found to be superior to the horizontal-flow ARF system in terms of nitrogen removal, mostly thiough bacterial nitrification processes in both the aerated limestone and BFS filter studies. The BFS filter medium (whieh is low-cost) showed a much higher potential in removing phosphortls from pond effluent than the limestone medium. As a result, the combination of a vertical upward-flow ARF system and an economical and effective P-removal filter medium, such as BFS, was found to be an ideal optionfor the total nutrient removal of both nitrogen and phosphorus from wastewater. In parallel with these experiments, studies on the aerated BFS filter effective life and major in-filter phosphorus removal pathways were carried out. From the standard batch experiments of Pmax adsorption capacity of BFS, as well as six-month data collection of daily average P-removal, it was found that the effective life of the aerated BFS filter was 6.5 years. Scanning electron microscopy and X-ray diffraction spectrometric analyses on the surface of BFS, particulates and sediment samples revealed that the apparent mechanisms of P-removal in the filter are adsorption on the amorphous oxide phase of the BFS surface and precipitation within the filter

Preparation and characterization of self assembled polymer nanocomposites

Polymerní nanokompozity na bázi polyhedrálních oligomerních silsesquioxanů (POSS) představují slibnou oblast výzkumu, která potenciálně může využít samouspořádávní při navrhování nových materiálů. Tato diplomová práce popisuje postup přípravy oktafenyl-POSS/PS, oktafenyl-POSS/PMMA a oktamethyl-POSS/PS systémů a charakterizaci jejich termomechanických vlastností v pevné fázi a reologických vlastností v roztoku. Získané výsledky jsou diskutovány s přihlédnutím k teoriím zabývajících se stavem disperze nanočástic.Polymer nanocomposites based on polyhedral oligomeric silsesquioxanes (POSS) are promising field which could potentially utilize self-assembly approach in designing new materials. In this thesis, a preparation protocol of octaphenyl-POSS/PS, octamethyl-POSS/PMMA and octamethyl-POSS/PS systems was described and thermomechanic properties in solid state and rheological properties in solution were investigated. The obtained results are discussed with focus on nanoparticles dispersion state theories.

Machine learning reveals orbital interaction in crystalline materials

We propose a novel representation of crystalline materials named orbital-field matrix (OFM) based on the distribution of valence shell electrons. We demonstrate that this new representation can be highly useful in mining material data. Our experiment shows that the formation energies of crystalline materials, the atomization energies of molecular materials, and the local magnetic moments of the constituent atoms in transition metal--rare-earth metal bimetal alloys can be predicted with high accuracy using the OFM. Knowledge regarding the role of coordination numbers of transition-metal and rare-earth metal elements in determining the local magnetic moment of transition metal sites can be acquired directly from decision tree regression analyses using the OFM.Comment: 10 page

Simple and Robust Boolean Operations for Triangulated Surfaces

Boolean operations of geometric models is an essential issue in computational geometry. In this paper, we develop a simple and robust approach to perform Boolean operations on closed and open triangulated surfaces. Our method mainly has two stages: (1) We firstly find out candidate intersected-triangles pairs based on Octree and then compute the inter-section lines for all pairs of triangles with parallel algorithm; (2) We form closed or open intersection-loops, sub-surfaces and sub-blocks quite robustly only according to the cleared and updated topology of meshes while without coordinate computations for geometric enti-ties. A novel technique instead of inside/outside classification is also proposed to distinguish the resulting union, subtraction and intersection. Several examples have been given to illus-trate the effectiveness of our approach.Comment: Novel method for determining Union, Subtraction and Intersectio