Finding the Kraus decomposition from a master equation and vice versa

For any master equation which is local in time, whether Markovian, non-Markovian, of Lindblad form or not, a general procedure is reviewed for constructing the corresponding linear map from the initial state to the state at time t, including its Kraus-type representations. Formally, this is equivalent to solving the master equation. For an N-dimensional Hilbert space it requires (i) solving a first order N^2 x N^2 matrix time evolution (to obtain the completely positive map), and (ii) diagonalising a related N^2 x N^2 matrix (to obtain a Kraus-type representation). Conversely, for a given time-dependent linear map, a necessary and sufficient condition is given for the existence of a corresponding master equation, where the (not necessarily unique) form of this equation is explicitly determined. It is shown that a `best possible' master equation may always be defined, for approximating the evolution in the case that no exact master equation exists. Examples involving qubits are given.Comment: 16 pages, no figures. Appeared in special issue for conference QEP-16, Manchester 4-7 Sep 200

From flood science to flood policy: The Foresight Future Flooding Project, seven years on.

Purpose: The Foresight Future Flooding (FFF) project researched flood risk in the UK to the year 2100 for central government, using scenarios and a national risk assessment model backed by qualitative analysis from panels of some 45 senior scientists. The purpose of this paper is to assess the impact of the project, both nationally and internationally. Design/methodology/approach: This paper assesses the impact of the FFF project, both nationally and internationally, using web searches, document analysis, and a questionnaire survey of key actors in the flood risk management policy field. Findings: It was found that the penetration of the project into professionals' consciousness was high in relation to other comparable projects and publications, and its impact on policy - both immediately and continuing - was profound. The FFF initiative did not create policy change, however, but facilitated its legitimation, adding impetus to what was already there, as one element of a part-catalytic and part-incremental process of policy evolution. Research limitations/implications: Special circumstances, internal and external to the project, mean that this cannot be a simple model for matching research to policymakers' needs in the future. Practical implications: Important lessons may be learnt from this project about both the methods of forward-looking foresight-type research, and the way that its results are disseminated to its target audiences. Originality/value: This is an innovative attempt to assess the impact of a new type of foresight project. © Emerald Group Publishing Limited

Measuring the Impact of the ‘Two Hours/Two Periods of Quality Physical Education’ Programme

No abstract available

Combining deep generative models with extreme value theory for synthetic hazard simulation: a multivariate and spatially coherent approach

Climate hazards can cause major disasters when they occur simultaneously as compound hazards. To understand the distribution of climate risk and inform adaptation policies, scientists need to simulate a large number of physically realistic and spatially coherent events. Current methods are limited by computational constraints and the probabilistic spatial distribution of compound events is not given sufficient attention. The bottleneck in current approaches lies in modelling the dependence structure between variables, as inference on parametric models suffers from the curse of dimensionality. Generative adversarial networks (GANs) are well-suited to such a problem due to their ability to implicitly learn the distribution of data in high-dimensional settings. We employ a GAN to model the dependence structure for daily maximum wind speed, significant wave height, and total precipitation over the Bay of Bengal, combining this with traditional extreme value theory for controlled extrapolation of the tails. Once trained, the model can be used to efficiently generate thousands of realistic compound hazard events, which can inform climate risk assessments for climate adaptation and disaster preparedness. The method developed is flexible and transferable to other multivariate and spatial climate datasets.Comment: Accepted at NeurIPS 2023 Workshop: Tackling Climate Change with Machine Learning (CCAI