A dd-dimensional Analyst's Travelling Salesman Theorem for subsets of Hilbert space

We are interested in quantitative rectifiability results for subsets of infinite dimensional Hilbert space $H$. We prove a version of Azzam and Schul's $d$-dimensional Analyst's Travelling Salesman Theorem in this setting by showing for any lower $d$-regular set $E \subseteq H$ that $$\text{diam}(E)^d + \beta^d(E) \sim \mathscr{H}^d(E) + \text{Error},$$ where $\beta^d(E)$ give a measure of the curvature of $E$ and the error term is related to the theory of uniform rectifiability (a quantitative version of rectifiability introduced by David and Semmes). To do this, we show how to modify the Reifenberg Parametrization Theorem of David and Toro so that it holds in Hilbert space. As a corollary, we show that a set $E \subseteq H$ is uniformly rectifiable if and only if it satisfies the so-called Bilateral Weak Geometric Lemma, meaning that $E$ is bi-laterally well approximated by planes at most scales and locations

Monitoring drainage water quality during green roof irrigation trials using synthetic greywater

Aims: To evaluate the potential for substituting green roof mains water irrigation by irrigation using lightly loaded synthetic greywater. Study Design: The planted green roof system was designed to be operated and tested within a glasshouse. Place and Duration of Study: Schools of Engineering, and Plant Sciences, The University of Reading, for 28 days commencing 28th of May 2012. Methodology: A trial was conducted for comparing two planting schemes using Sedum and Stachys Byzantina and a third unplanted control. The three sets of growing boxes were subdivided between substrate depths of 10cm and 20cm. By further subdivision, half of each set were watered using mains water, and half using a synthetic greywater. The soil composition and water quality of the drainage (filtrate) water were monitored. Statistical analysis of the results was conducted. Results: Consistency was observed in influent pH and EC, in both mains and greywater samples. Influent Na concentrations were higher in the greywater samples due to detergent content. The Na mass balance calculations for all boxes showed that some Na mass was unaccounted for when comparing aggregated concentrations in influent, plant tissue and soil with the aggregated Na mass in filtrate, plant tissue and soil water. It was concluded that this was likely to be due to retained/ponded irrigation water in the boxes, difficulties in attaining homogenous box flushing and the underestimation of soil Na. The variation in substrate depth affected all results. The plants themselves seemed to have little significant influence on the measured parameters, with the exception of the accumulation of Na mass in plants irrigated with greywater. Conclusion: No improvement was observed in the quality of the greywater following filtration through the soil matrix. For longer term watering using greywater, a choice of Na resistant species should be considered, although the Sedum species used in this trial showed no recorded adverse growth effects due to Na accumulation

The interferon-stimulated gene IFITM3 restricts infection and pathogenesis of arthritogenic and encephalitic alphaviruses

Host cells respond to viral infections by producing type I interferon (IFN), which induces the expression of hundreds of interferon-stimulated genes (ISGs). Although ISGs mediate a protective state against many pathogens, the antiviral functions of the majority of these genes have not been identified. IFITM3 is a small transmembrane ISG that restricts a broad range of viruses, including orthomyxoviruses, flaviviruses, filoviruses, and coronaviruses. Here, we show that alphavirus infection is increased in Ifitm3(−/−) and Ifitm locus deletion (Ifitm-del) fibroblasts and, reciprocally, reduced in fibroblasts transcomplemented with Ifitm3. Mechanistic studies showed that Ifitm3 did not affect viral binding or entry but inhibited pH-dependent fusion. In a murine model of chikungunya virus arthritis, Ifitm3(−/−) mice sustained greater joint swelling in the ipsilateral ankle at days 3 and 7 postinfection, and this correlated with higher levels of proinflammatory cytokines and viral burden. Flow cytometric analysis suggested that Ifitm3(−/−) macrophages from the spleen were infected at greater levels than observed in wild-type (WT) mice, results that were supported by experiments with Ifitm3(−/−) bone marrow-derived macrophages. Ifitm3(−/−) mice also were more susceptible than WT mice to lethal alphavirus infection with Venezuelan equine encephalitis virus, and this was associated with greater viral burden in multiple organs. Collectively, our data define an antiviral role for Ifitm3 in restricting infection of multiple alphaviruses. IMPORTANCE The interferon-induced transmembrane protein 3 (IFITM3) inhibits infection of multiple families of viruses in cell culture. Compared to other viruses, much less is known about the antiviral effect of IFITM3 on alphaviruses. In this study, we characterized the antiviral activity of mouse Ifitm3 against arthritogenic and encephalitic alphaviruses using cells and animals with a targeted gene deletion of Ifitm3 as well as deficient cells transcomplemented with Ifitm3. Based on extensive virological analysis, we demonstrate greater levels of alphavirus infection and disease pathogenesis when Ifitm3 expression is absent. Our data establish an inhibitory role for Ifitm3 in controlling infection of alphaviruses

Uniformly rectifiable metric spaces: Lipschitz images, Bi-Lateral Weak Geometric Lemma and Corona Decompositions

In their 1991 and 1993 foundational monographs, David and Semmes characterized uniform rectifiability for subsets of Euclidean space in a multitude of geometric and analytic ways. The fundamental geometric conditions can be naturally stated in any metric space and it has long been a question of how these concepts are related in this general setting. In this paper we prove their equivalence. Namely, we show the equivalence of Big Pieces of Lipschitz Images, Bi-lateral Weak Geometric Lemma and Corona Decomposition in any Ahlfors regular metric space. Loosely speaking, this gives a quantitative equivalence between having Lipschitz charts and approximations by nicer spaces. En route, we also study Reifenberg parameterizations.Comment: 125 pages. 4 Figure

Developments in the quality of treated greywater supplies for buildings, and associated user perception and acceptance

A manufactured aeration and nanofiltration MBR greywater system was tested during continuous operation at the University of Reading, to demonstrate reliability in delivery of high quality treated greywater. Its treatment performance was evaluated against British Standard criteria [BSI (Greywater Systems—Part 1 Code of Practice: BS8525-1:2010. BS Press, 2010); (Greywater Systems—Part 2 Domestic Greywater Treatment, Requirements and Methods: BS 8525-2:2011. BS Press, 2011)]. The low carbon greywater recycling technology produced excellent analytical results as well as consistency in performance. User acceptance of such reliably treated greywater was then evaluated through user perception studies. The results inform the potential supply of treated greywater to student accommodation. Out of 135 questionnaire replies, 95% demonstrated a lack of aversion in one or more attributes, to using treated, recycled greywater

Resource Management and Contingencies in Aerospace Concurrent Engineering

significant concern in designing complex systems implementing new technologies is that while knowledge about the system is acquired incrementally, substantial financial commitments, even make-or-break decisions, must be made upfront, essentially in the unknown. One practice that helps in dealing with this dichotomy is the smart embedding of contingencies and margins in the design to serve as buffers against surprises. This issue presents itself in full force in the aerospace industry, where unprecedented systems are formulated and committed to as a matter of routine. As more and more aerospace mission concepts are generated by concurrent design laboratories, it is imperative that such laboratories apply well thought-out contingency and margin structures to their designs. The first part of this publication provides an overview of resource management techniques and standards used in the aerospace industry. That is followed by a thought provoking treatise on margin policies. The expose presents the actual flight telemetry data recorded by the thermal discipline during several recent NASA Goddard Space Flight Center missions. The margins actually achieved in flight are compared against pre-flight predictions, and the appropriateness and the ramifications of having designed with rigid margins to bounding stacked worst case conditions are assessed. The second half of the paper examines the particular issues associated with the application of contingencies and margins in the concurrent engineering environment. In closure, a discipline-by-discipline disclosure of the contingency and margin policies in use at the Integrated Design Center at NASA s Goddard Space Flight Center is made

Predicting morphotropic phase boundary locations and transition temperatures in Pb- and Bi-based perovskite solid solutions from crystal chemical data and first-principles calculations

Using data obtained from first-principles calculations, we show that the position of the morphotropic phase boundary (MPB) and transition temperature at MPB in ferroelectric perovskite solutions can be predicted with quantitative accuracy from the properties of the constituent cations. We find that the mole fraction of PbTiO$_3$ at MPB in Pb(B$'$B$''$)O$_3$-PbTiO$_3$, BiBO$_3$-PbTiO$_3$ and Bi(B$'$B$''$)O$_3$-PbTiO$_3$ exhibits a linear dependence on the ionic size (tolerance factor) and the ionic displacements of the B-cations as found by density functional theory calculations. This dependence is due to competition between the local repulsion and A-cation displacement alignment interactions. Inclusion of first-principles displacement data also allows accurate prediction of transiton temperatures at the MPB. The obtained structure-property correlations are used to predict morphotropic phase boundaries and transition temperatures in as yet unsynthesized solid solutions.Comment: Accepted for publication in J. Appl. Phy