Generative models have been shown to provide a powerful mechanism for anomaly detection by learning to model healthy or normal reference data which can subsequently be used as a baseline for scoring anomalies. In this work we consider denoising diffusion probabilistic models (DDPMs) for unsupervised anomaly detection. DDPMs have superior mode coverage over generative adversarial networks (GANs) and higher sample quality than variational autoencoders (VAEs). However, this comes at the expense of poor scalability and increased sampling times due to the long Markov chain sequences required. We observe that within reconstruction-based anomaly detection a full-length Markov chain diffusion is not required. This leads us to develop a novel partial diffusion anomaly detection strategy that scales to high-resolution imagery, named AnoDDPM. A secondary problem is that Gaussian diffusion fails to capture larger anomalies; therefore we develop a multi-scale simplex noise diffusion process that gives control over the target anomaly size. AnoDDPM with simplex noise is shown to significantly outperform both f-AnoGAN and Gaussian diffusion for the tumorous dataset of 22 T1weighted MRI scans (CCBS Edinburgh) qualitatively and quantitatively (improvement of +25.5% Sørensen-Dice coefficient, +17.6% IoU and +7.4% AUC).

The relationship between international environmental law and international humanitarian law, like relationships between many other subsystems of contemporary international law, has not yet been articulated. The problem of environmental damage in international armed conflict lies at the intersection of these two branches and thus provides an ideal opportunity to investigate this relationship. Rather than simply evaluating the applicable international law rules in their context, we break them into elements that we separately assess from both (international) environmental law and international humanitarian/international criminal law perspectives. By doing so, we identify how international law rules for cross-sectoral problems may appropriately combine the existing expertise and institutional strengths of simultaneously applicable branches of international law, and also discover how an evaluation of the ultimate appropriateness of the cross-sectoral rules adopted may be substantially affected by the different frames of reference that are used by those working within the different fields.

The field of international trade law, often highlighted for its unity and the strength of its dispute settlement and remedies systems, is itself no stranger to the phenomenon of the so-called 'proliferation' of dispute settlement mechanisms. Regional trade agreements (RTAs) are increasingly prevalent and set up more and more solid and far-reaching dispute settlement systems, some of which are likely to come into direct contact with the multilateral system of the World Trade Organization (WTO). This article focuses on one particular type of such interaction between RTAs and the WTO: how should we address the issue of a trade countermeasure taken in the context of an RTA when such retaliatory action can be considered a breach of a WTO rule? A proper answer to this question requires an analysis of the flexibilities provided by the General Agreement on Tariffs and Trade and General Agreement on Trade in Services exception provisions allowing Members to maintain certain RTAs and of the nature of countermeasures often explicitly authorized by RTA dispute settlement mechanisms. The range of issues, relevant international law rules and potential solutions discussed are set to become only more pertinent both within the changing field of international trade law and, as international legal regimes become more robust and increasingly come into contact with one another, in contemporary international law in general.

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