Quantitative Foundations for Resource Theories

Considering resource usage is a powerful insight in the analysis of many phenomena in the sciences. Much of the current research on these resource theories focuses on the analysis of specific resources such quantum entanglement, purity, randomness or asymmetry. However, the mathematical foundations of resource theories are at a much earlier stage, and there has been no satisfactory account of quantitative aspects such as costs, rates or probabilities. We present a categorical foundation for quantitative resource theories, derived from enriched category theory. Our approach is compositional, with rich algebraic structure facilitating calculations. The resulting theory is parameterized, both in the quantities under consideration, for example costs or probabilities, and in the structural features of the resources such as whether they can be freely copied or deleted. We also achieve a clear separation of concerns between the resource conversions that are freely available, and the costly resources that are typically the object of study. By using an abstract categorical approach, our framework is naturally open to extension. We provide many examples throughout, emphasising the resource theoretic intuitions for each of the mathematical objects under consideration

No-Go Theorems for Distributive Laws

Monads are commonplace in computer science, and can be composed using Beck's distributive laws. Unfortunately, finding distributive laws can be extremely difficult and error-prone. The literature contains some general principles for constructing distributive laws. However, until now there have been no such techniques for establishing when no distributive law exists. We present three families of theorems for showing when there can be no distributive law between two monads. The first widely generalizes a counterexample attributed to Plotkin. It covers all the previous known no-go results for specific pairs of monads, and includes many new results. The second and third families are entirely novel, encompassing various new practical situations. For example, they negatively resolve the open question of whether the list monad distributes over itself, reveal a previously unobserved error in the literature, and confirm a conjecture made by Beck himself in his first paper on distributive laws. In addition, we establish conditions under which there can be at most one possible distributive law between two monads, proving various known distributive laws to be unique.Comment: arXiv admin note: text overlap with arXiv:1811.0646

Nonholonomic constraints in classical field theories

A multisymplectic setting for classical field theories subjected to non-holonomic constraints is presented. The infinite dimensional setting in the space of Cauchy data is also given.Comment: 14 pages; 1 figur

A new fireworm (Amphinomidae) from the Cretaceous of Lebanon identified from three-dimensionally preserved myoanatomy

© 2015 Parry et al. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. The attached file is the published version of the article

Rapid model-guided design of organ-scale synthetic vasculature for biomanufacturing

Our ability to produce human-scale bio-manufactured organs is critically limited by the need for vascularization and perfusion. For tissues of variable size and shape, including arbitrarily complex geometries, designing and printing vasculature capable of adequate perfusion has posed a major hurdle. Here, we introduce a model-driven design pipeline combining accelerated optimization methods for fast synthetic vascular tree generation and computational hemodynamics models. We demonstrate rapid generation, simulation, and 3D printing of synthetic vasculature in complex geometries, from small tissue constructs to organ scale networks. We introduce key algorithmic advances that all together accelerate synthetic vascular generation by more than 230-fold compared to standard methods and enable their use in arbitrarily complex shapes through localized implicit functions. Furthermore, we provide techniques for joining vascular trees into watertight networks suitable for hemodynamic CFD and 3D fabrication. We demonstrate that organ-scale vascular network models can be generated in silico within minutes and can be used to perfuse engineered and anatomic models including a bioreactor, annulus, bi-ventricular heart, and gyrus. We further show that this flexible pipeline can be applied to two common modes of bioprinting with free-form reversible embedding of suspended hydrogels and writing into soft matter. Our synthetic vascular tree generation pipeline enables rapid, scalable vascular model generation and fluid analysis for bio-manufactured tissues necessary for future scale up and production.Comment: 58 pages (19 main and 39 supplement pages), 4 main figures, 9 supplement figure