Generating Physically-Realistic Tertiary Protein Structures with Deep Latent Variable Models Learning Over Experimentally-available Structures
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Abstract In this paper, generalizing our previous construction, we equip the relative moduli stack of complexes over a Calabi–Yau fibration (possibly with singular fibers) with a shifted Poisson structure. Applying this construction to the anticanonical linear systems on surfaces, we get examples of compatible Poisson brackets on projective spaces extending Feigin–Odesskii Poisson brackets. Computing explicitly the corresponding compatible brackets coming from Hirzebruch surfaces, we recover the brackets defined by Odesskii–Wolf.
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Abstract In recent years, computability theorists have extensively studied generically and coarsely computable sets. This study of approximate computability was originally motivated by asymptotic density problems in combinatorial group theory. We generalize the notions of generic and coarse computability of sets, introduced by Jockusch and Schupp, to arbitrary structures by defining generically and coarsely computable and computably enumerable structures. There are two directions in which these notions could potentially trivialize: either all structures could have a densely computable copy or only those having a computable (or computably enumerable) copy. We show that some particular classes of structures realize each of these extremal conditions, while other classes realize neither of them. To further explore these concepts, we introduce a graded family of elementarity conditions for substructures, in which we require that the dense sets under consideration be ‘strong’ substructures of the original structure. Here, again, for a given class, the notion could trivialize in the same two directions and we show that both are possible. For each class that we investigate, there is some natural number $n$ such that requiring $\varSigma _{n}$ elementarity of substructures is enough to trivialize the class of generically or densely computable structures, witnessing the essentially structural character of these notions.more » « less
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Functional (aka immutable) data structures are used extensively in data management systems. From distributed systems to data persistence, immutability makes complex programs significantly easier to reason about and implement. However, immutability also makes many runtime optimizations like tree rebalancing, or adaptive organizations, unreasonably expensive. In this paper, we propose Fluid data structures, an approach to data structure design that allows limited physical changes that preserve logical equivalence. As we will show, this approach retains many of the desirable properties of functional data structures, while also allowing runtime adaptation. To illustrate Fluid data structures, we work through the design of a lazy-loading map that we call a Fluid Cog. A Fluid Cog is a lock-free data structure that incrementally organizes itself in the background by applying equivalence-preserving structural transformations. Our experimental analysis shows that the resulting map structure is flexible enough to adapt to a variety of performance goals, while remaining competitive with existing structures like the C++ standard template library map.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/BIBM52615.2021.9669584
