Open Petri Nets

The reachability semantics for Petri nets can be studied using open Petri nets. For us an "open" Petri net is one with certain places designated as inputs and outputs via a cospan of sets. We can compose open Petri nets by gluing the outputs of one to the inputs of another. Open Petri nets can be treated as morphisms of a category $\mathsf{Open}(\mathsf{Petri})$, which becomes symmetric monoidal under disjoint union. However, since the composite of open Petri nets is defined only up to isomorphism, it is better to treat them as morphisms of a symmetric monoidal double category $\mathbb{O}\mathbf{pen}(\mathsf{Petri})$. We describe two forms of semantics for open Petri nets using symmetric monoidal double functors out of $\mathbb{O}\mathbf{pen}(\mathsf{Petri})$. The first, an operational semantics, gives for each open Petri net a category whose morphisms are the processes that this net can carry out. This is done in a compositional way, so that these categories can be computed on smaller subnets and then glued together. The second, a reachability semantics, simply says which markings of the outputs can be reached from a given marking of the inputs.Comment: 30 pages, TikZ figure

Embroidery and artistic taste

Every aspect of art requires from a person the beauty of the heart, the elegance. One of the most ancient and unique types of applied decorative art is embroider

UCL (University College London) Libraries Masterplan: Masterplanning Report

BDP were appointed to undertake a Masterplan for the UCL Main Library and the UCL Science Library and to identify how these buildings could be re-ordered to significantly improve the quality of the library environment and to facilitate the delivery of library services. An initial brief was agreed with UCL’s Estates Management Committee and a Masterplan Steering Group established including academic representatives, library staff and design consultants. To inform the development of this brief, UCL Library Services undertook a number of consultation exercises with users of the Library; students, academic staff and external users, together with Library staff. A number of visits to exemplar library buildings in the UK and continental Europe were also undertaken to inform the development of options for the buildings. Following the development and review of initial options for both the Main Library and Science Library, it was agreed a further, hypothetical New Build Central Library Option should be reviewed, to accommodate a relocated and consolidated library service encompassing 7 of the 16 existing libraries currently distributed across the UCL Estate

Translating and Evolving: Towards a Model of Language Change in DisCoCat

The categorical compositional distributional (DisCoCat) model of meaning developed by Coecke et al. (2010) has been successful in modeling various aspects of meaning. However, it fails to model the fact that language can change. We give an approach to DisCoCat that allows us to represent language models and translations between them, enabling us to describe translations from one language to another, or changes within the same language. We unify the product space representation given in (Coecke et al., 2010) and the functorial description in (Kartsaklis et al., 2013), in a way that allows us to view a language as a catalogue of meanings. We formalize the notion of a lexicon in DisCoCat, and define a dictionary of meanings between two lexicons. All this is done within the framework of monoidal categories. We give examples of how to apply our methods, and give a concrete suggestion for compositional translation in corpora.Comment: In Proceedings CAPNS 2018, arXiv:1811.0270