The process of macromolecular crystallisation almost always begins by setting up crystallisation trials using commercial or other premade screens, followed by cycles of optimisation where the crystallisation cocktails are focused towards a particular small region of chemical space. The screening process is relatively straightforward, but still requires an understanding of the plethora of commercially available screens. Optimisation is complicated by requiring both the design and preparation of the appropriate secondary screens. Software has been developed in the C3 lab to aid the process of choosing initial screens, to analyse the results of the initial trials, and to design and describe how to prepare optimisation screens.
Divisiveness appears to be increasing in much of the world, leading to concern about political violence and a decreasing capacity to collaboratively address large-scale societal challenges. In this working paper we aim to articulate an interdisciplinary research and practice area focused around what we call bridging systems: systems which increase mutual understanding and trust across divides, creating space for productive conflict, deliberation, or cooperation. We give examples of bridging systems across three domains: recommender systems on social media, software for conducting civic forums, and human-facilitated group deliberation. We argue that these examples can be more meaningfully understood as processes for attention-allocation (as opposed to "content distribution" or "amplification"), and develop a corresponding framework to explore similarities-and opportunities for bridging-across these seemingly disparate domains. We focus particularly on the potential of bridging-based ranking to bring the benefits of offline bridging into spaces which are already governed by algorithms. Throughout, we suggest research directions that could improve our capacity to incorporate bridging into a world increasingly mediated by algorithms and artificial intelligence.
Spatial models of preference, in the form of vector embeddings, are learned by many deep learning and multiagent systems, including recommender systems. Often these models are assumed to approximate a Euclidean structure, where an individual prefers alternatives positioned closer to their "ideal point", as measured by the Euclidean metric. However, previous work has shown there are ordinal preference profiles that cannot be represented with this structure if the Euclidean space has two fewer dimensions than there are individuals or alternatives. We extend this result, showing that there are situations in which almost all preference profiles cannot be represented with the Euclidean model, and derive a theoretical lower bound on the expected error when using the Euclidean model to approximate non-Euclidean preference profiles. Our results have implications for the interpretation and use of vector embeddings, because in some cases close approximation of arbitrary, true ordinal relationships can be expected only if the dimensionality of the embeddings is a substantial fraction of the number of entities represented.
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