Valid path-based graph vertex numbering

A labelling of a graph is an assignment of labels to its vertex or edge sets (or both), subject to certain conditions, a well established concept. A labelling of a graph G of order n is termed a numbering when the set of integers {1,...,n} is used to label the vertices of G distinctly. A 2-path (a path with three vertices) in a vertex-numbered graph is said to be valid if the number of its middle vertex is smaller than the numbers of its endpoints. The problem of finding a vertex numbering of a given graph that optimises the number of induced valid 2-paths is studied, which is conjectured to be in the NP-hard class. The reported results for several graph classes show that apparently there are not one or more numbering patterns applicable to different classes of graphs, which requires the development of a specific numbering for each graph class under study

DP-EM: Differentially Private Expectation Maximization

The iterative nature of the expectation maximization (EM) algorithm presents a challenge for privacy-preserving estimation, as each iteration increases the amount of noise needed. We propose a practical private EM algorithm that overcomes this challenge using two innovations: (1) a novel moment perturbation formulation for differentially private EM (DP-EM), and (2) the use of two recently developed composition methods to bound the privacy “cost” of multiple EM iterations: the moments accountant (MA) and zero-mean concentrated differential privacy (zCDP). Both MA and zCDP bound the moment generating function of the privacy loss random variable and achieve a refined tail bound, which effectively decrease the amount of additive noise. We present empirical results showing the benefits of our approach, as well as similar performance between these two composition methods in the DP-EM setting for Gaussian mixture models. Our approach can be readily extended to many iterative learning algorithms, opening up various exciting future directions

Multipartite entanglement measures via Bell basis measurements

We show how to estimate a broad class of multipartite entanglement measures from Bell basis measurement data. In addition to lowering the experimental requirements relative to previously known methods of estimating these measures, our proposed scheme also enables a simpler analysis of the number of measurement repetitions required to achieve an $\epsilon$-close approximation of the measures, which we provide for each. We focus our analysis on the recently introduced Concentratable Entanglements [Beckey et al. Phys. Rev. Lett. 127, 140501 (2021)] because many other well-known multipartite entanglement measures are recovered as special cases of this family of measures. We extend the definition of the Concentratable Entanglements to mixed states and show how to construct lower bounds on the mixed state Concentratable Entanglements that can also be estimated using only Bell basis measurement data. Finally, we demonstrate the feasibility of our methods by realistically simulating their implementation on a Rydberg atom quantum computer.Comment: 5+19 pages. 4+3 figure

Constructing Policy Success for UK Energy Feedback

Energy feedback tools are commonly used to promote energy saving. In the UK, energy feedback provision (currently via an In-Home Display) is part of the government-mandated roll-out of smart meters to all homes by 2020. A core assumption underlying this widespread provision is that information, or evidence, can lead to positive changes in action. This is analogous to assumptions underlying the notion of ‘Evidence-Based Policy’, which raises questions about how users, researchers and policymakers go about using evidence in aiming for a ‘successful’ outcome. In addition the ‘policy feedback’ research agenda has asked how policies alter the landscapes within which they operate by, for example, affecting relationships between actors. Via an in-depth review of DECC (now BEIS) policy literature over 2010-2016, the UK smart meter roll-out was analysed in terms of how its energy feedback focussed measures may be deemed as ‘successful’. Findings include that direct energy savings played a smaller role than might be expected, and translation from one success measure to another was repeatedly observed. A key conclusion is that acting on feedback requires an assessment of success, but such assessment is highly contextual, for consumers and policymakers alike. Ways to increase reflexivity in this area are discussed

In Situ Contaminated Sediments Project – Work Package 1A Report

Project aims Defra is seeking to understand the magnitude of risks (e.g. to aquatic ecology and human health) or impacts (e.g. on the way that water bodies are managed) posed by contaminated sediment in England, as part of its work towards meeting its environmental objectives. In the context of this project, in-situ contaminated sediment is defined as: Chemically contaminated sediment within the water column, bed, banks and floodplain of a surface water body that has been transported alongside the normal sediment load and deposited by fluvial or coastal processes. This project considers the risk posed by non-agricultural diffuse pollution sources in England that result in the contamination of in-situ sediments (for example, contamination from toxic metals, hydrocarbons and surfactants). The scope encompasses both freshwater and marine sediments in England and extends to one nautical mile off-shore (the seaward limit of coastal waters under the Water Framework Directive (WFD) in England). Previous national strategies, including the 2007 Defra UK Strategy for Managing Contaminated Marine Sediments (CDMS), focussed on characterising the risks associated with contaminated sediments in the marine environment. However, while extensive research has been carried out in many locations (including as part of WFD implementation studies) and for particular sources of contamination (e.g. historical metal mining; Environment Agency, 2008) there has not been a comprehensive overview of sediment contamination on a national scale. This project seeks to build on the existing evidence base, drawing together information on the freshwater environment to complement that already gathered for marine waters. This project’s overall aim is to provide a sound evidence base on the contamination of in-situ sediments, which can underpin the development of tools and methods that will help Defra, the Environment Agency and other bodies engaged in regulation and protection of water quality