Fast Locality-Sensitive Hashing Frameworks for Approximate Near Neighbor Search

The Indyk-Motwani Locality-Sensitive Hashing (LSH) framework (STOC 1998) is a general technique for constructing a data structure to answer approximate near neighbor queries by using a distribution $\mathcal{H}$ over locality-sensitive hash functions that partition space. For a collection of $n$ points, after preprocessing, the query time is dominated by $O(n^{\rho} \log n)$ evaluations of hash functions from $\mathcal{H}$ and $O(n^{\rho})$ hash table lookups and distance computations where $\rho \in (0,1)$ is determined by the locality-sensitivity properties of $\mathcal{H}$. It follows from a recent result by Dahlgaard et al. (FOCS 2017) that the number of locality-sensitive hash functions can be reduced to $O(\log^2 n)$, leaving the query time to be dominated by $O(n^{\rho})$ distance computations and $O(n^{\rho} \log n)$ additional word-RAM operations. We state this result as a general framework and provide a simpler analysis showing that the number of lookups and distance computations closely match the Indyk-Motwani framework, making it a viable replacement in practice. Using ideas from another locality-sensitive hashing framework by Andoni and Indyk (SODA 2006) we are able to reduce the number of additional word-RAM operations to $O(n^\rho)$.Comment: 15 pages, 3 figure

Evaluation of Existing Models to Estimate Sorption Coefficients for Ionisable Pharmaceuticals in Soils and Sludge

In order to assess the environmental risk of a pharmaceutical, information is needed on the sorption of the compound to solids. Here we use a high-quality database of measured sorption coefficients, all determined following internationally recognised protocols, to evaluate models that have been proposed for estimating sorption of pharmaceuticals from chemical structure, some of which are already being used for environmental risk assessment and prioritization purposes. Our analyses demonstrate that octanol-water partition coefficient (Kow) alone is not an effective predictor of ionisable pharmaceutical sorption in soils. Polyparameter models based on pharmaceutical characteristics in combination with key soil properties, such as cation exchange capacity, increase model complexity but yield an improvement in the predictive capability of soil sorption models. Nevertheless, as the models included in this analysis were only able to predict a maximum of 71% and 67% of the sorption coefficients for the compounds to within one log unit of the corresponding measured value in soils and sludge, respectively, there is a need for new models to be developed to better predict the sorption of ionisable pharmaceuticals in soil and sludge systems. The variation in sorption coefficients, even for a single pharmaceutical across different solid types, makes this an inherently difficult task, and therefore requires a broad understanding of both chemical and sorbent properties driving the sorption process

Trust, negotiation, and communication: young adults' experiences of primary care services.

BACKGROUND: Young adulthood is an important transitional period during which there is a higher risk of individuals engaging in behaviours which could have a lasting impact on their health. Research has shown that young adults are the lowest responders to surveys about healthcare experiences and are also the least satisfied with the care they receive. However, the factors contributing to this reduced satisfaction are not clear. The focus of our research was to explore the needs and experiences of young adults around healthcare services with an aim of finding out possible reasons for lower satisfaction. METHODS: Twenty young adults were interviewed at GP surgeries and at a local young adult advice agency, exploring their experiences and use of primary care services. Interviews were analysed using thematic analysis. RESULTS: The use of primary care services varied amongst the young adult interviewees. Many interviewees reported positive experiences; those who did not linked their negative experiences to difficulties in negotiating their care with the health care system, and reported issues with trust, and communication difficulties. Most of the interviewees were unaware of the use of patient surveys to inform healthcare planning and delivery and were not inclined to take part, mainly because of the length of surveys and lack of interest in the topic area. CONCLUSIONS: In order to effectively address the health needs of young adults, young adults need to be educated about their rights as patients, and how to most efficiently use primary care services. GPs should be alert to effective means of approaching and handling the healthcare needs of young adults. A flexible, varied approach is needed to gathering high quality data from this group in order to provide services with information on the changes necessary for making primary care services more accessible for young adults

Novel critical point drying (CPD) based preparation and transmission electron microscopy (TEM) imaging of protein specific molecularly imprinted polymers (HydroMIPs)

We report the transmission electron microscopy (TEM) imaging of a hydrogel-based molecularly imprinted polymer (HydroMIP) specific to the template molecule bovine haemoglobin (BHb). A novel critical point drying based sample preparation technique was employed to prepare the molecularly imprinted polymer (MIP) samples in a manner that would facilitate the use of TEM to image the imprinted cavities, and provide an appropriate degree of both magnification and resolution to image polymer architecture in the <10 nm range. For the first time, polymer structure has been detailed that clearly displays molecularly imprinted cavities, ranging from 5-50 nm in size, that correlate (in terms of size) with the protein molecule employed as the imprinting template. The modified critical point drying sample preparation technique used may potentially play a key role in the imaging of all molecularly imprinted polymers, particularly those prepared in the aqueous phase

Lectures on Linear Stability of Rotating Black Holes

These lecture notes are concerned with linear stability of the non-extreme Kerr geometry under perturbations of general spin. After a brief review of the Kerr black hole and its symmetries, we describe these symmetries by Killing fields and work out the connection to conservation laws. The Penrose process and superradiance effects are discussed. Decay results on the long-time behavior of Dirac waves are outlined. It is explained schematically how the Maxwell equations and the equations for linearized gravitational waves can be decoupled to obtain the Teukolsky equation. It is shown how the Teukolsky equation can be fully separated to a system of coupled ordinary differential equations. Linear stability of the non-extreme Kerr black hole is stated as a pointwise decay result for solutions of the Cauchy problem for the Teukolsky equation. The stability proof is outlined, with an emphasis on the underlying ideas and methods.Comment: 25 pages, LaTeX, 3 figures, lectures given at first DOMOSCHOOL in July 2018, minor improvements (published version