8,695 research outputs found

    A Unifying Theory for Graph Transformation

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    The field of graph transformation studies the rule-based transformation of graphs. An important branch is the algebraic graph transformation tradition, in which approaches are defined and studied using the language of category theory. Most algebraic graph transformation approaches (such as DPO, SPO, SqPO, and AGREE) are opinionated about the local contexts that are allowed around matches for rules, and about how replacement in context should work exactly. The approaches also differ considerably in their underlying formal theories and their general expressiveness (e.g., not all frameworks allow duplication). This dissertation proposes an expressive algebraic graph transformation approach, called PBPO+, which is an adaptation of PBPO by Corradini et al. The central contribution is a proof that PBPO+ subsumes (under mild restrictions) DPO, SqPO, AGREE, and PBPO in the important categorical setting of quasitoposes. This result allows for a more unified study of graph transformation metatheory, methods, and tools. A concrete example of this is found in the second major contribution of this dissertation: a graph transformation termination method for PBPO+, based on decreasing interpretations, and defined for general categories. By applying the proposed encodings into PBPO+, this method can also be applied for DPO, SqPO, AGREE, and PBPO

    Why should we study plant sex chromosomes?

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    Understanding plant sex chromosomes involves studying interactions between developmental and physiological genetics, genome evolution, and evolutionary ecology. We focus on areas of overlap between these. Ideas about how species with separate sexes (dioecious species, in plant terminology) can evolve are even more relevant to plants than to most animal taxa because dioecy has evolved many times from ancestral functionally hermaphroditic populations, often recently. One aim of studying plant sex chromosomes is to discover how separate males and females evolved from ancestors with no such genetic sex-determining polymorphism, and the diversity in the genetic control of maleness vs femaleness. Different systems share some interesting features, and their differences help to understand why completely sex-linked regions may evolve. In some dioecious plants, the sex-determining genome regions are physically small. In others, regions without crossing over have evolved sometimes extensive regions with properties very similar to those of the familiar animal sex chromosomes. The differences also affect the evolutionary changes possible when the environment (or pollination environment, for angiosperms) changes, as dioecy is an ecologically risky strategy for sessile organisms. Dioecious plants have repeatedly reverted to cosexuality, and hermaphroditic strains of fruit crops such as papaya and grapes are desired by plant breeders. Sex-linked regions are predicted to become enriched in genes with sex differences in expression, especially when higher expression benefits one sex function but harms the other. Such trade-offs may be important for understanding other plant developmental and physiological processes and have direct applications in plant breeding

    Homotopical Combinatorics

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    Polynomial time and dependent types

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    We combine dependent types with linear type systems that soundly and completely capture polynomial time computation. We explore two systems for capturing polynomial time: one system that disallows construction of iterable data, and one, based on the LFPL system of Martin Hofmann, that controls construction via a payment method. Both of these are extended to full dependent types via Quantitative Type Theory, allowing for arbitrary computation in types alongside guaranteed polynomial time computation in terms. We prove the soundness of the systems using a realisability technique due to Dal Lago and Hofmann. Our long-term goal is to combine the extensional reasoning of type theory with intensional reasoning about the resources intrinsically consumed by programs. This paper is a step along this path, which we hope will lead both to practical systems for reasoning about programs’ resource usage, and to theoretical use as a form of synthetic computational complexity theory

    Topological Quantum Teleportation and Superdense Coding Without Braiding

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    We present the quantum teleportation and superdense coding protocols in the context of topological qudits, as realised by anyons. The simplicity of our proposed realisation hinges on the monoidal structure of Tambara-Yamagami categories, which readily allows for the generation of maximally entangled qudits. In particular, we show that both protocols can be performed without any braiding of anyons. Our exposition makes use of the graphical calculus for braided fusion categories, a medium in which the protocols find a natural interpretation. We also find a braid-free realisation of the Pauli gates using Ising anyons

    Semi-simplicial Set Models for Distributed Knowledge

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    In recent years, a new class of models for multi-agent epistemic logic has emerged, based on simplicial complexes. Since then, many variants of these simplicial models have been investigated, giving rise to different logics and axiomatizations. In this paper, we present a further generalization, where a group of agents may distinguish two worlds, even though each individual agent in the group is unable to distinguish them. For that purpose, we generalize beyond simplicial complexes and consider instead simplicial sets. By doing so, we define a new semantics for epistemic logic with distributed knowledge. As it turns out, these models are the geometric counterpart of a generalization of Kripke models, called "pseudo-models". We identify various interesting sub-classes of these models, encompassing all previously studied variants of simplicial models; and give a sound and complete axiomatization for each of them

    Preventing Object-centric Discovery of Unsound Process Models for Object Interactions with Loops in Collaborative Systems: Extended Version

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    Object-centric process discovery (OCPD) constitutes a paradigm shift in process mining. Instead of assuming a single case notion present in the event log, OCPD can handle events without a single case notion, but that are instead related to a collection of objects each having a certain type. The object types constitute multiple, interacting case notions. The output of OCPD is an object-centric Petri net, i.e. a Petri net with object-typed places, that represents the parallel execution of multiple execution flows corresponding to object types. Similar to classical process discovery, where we aim for behaviorally sound process models as a result, in OCPD, we aim for soundness of the resulting object-centric Petri nets. However, the existing OCPD approach can result in violations of soundness. As we will show, one violation arises for multiple interacting object types with loops that arise in collaborative systems. This paper proposes an extended OCPD approach and proves that it does not suffer from this violation of soundness of the resulting object-centric Petri nets. We also show how we prevent the OCPD approach from introducing spurious interactions in the discovered object-centric Petri net. The proposed framework is prototypically implemented

    Categorical entropies on symplectic manifolds

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    In this paper, being motivated by symplectic topology, we study categorical entropy. Specifically, we prove inequalities between categorical entropies of functors on a category and its localization. We apply the inequalities to symplectic topology to prove equalities between categorical entropies on wrapped, partially wrapped, and compact Fukaya categories if the functors are induced by the same compactly supported symplectic automorphisms. We also provide a practical way to compute the categorical entropy of symplectic automorphisms by using Lagrangian Floer theory if their domains satisfy a type of Floer-theoretical duality. Our main examples of symplectic manifolds satisfying the duality conditions are the plumbings of cotangent bundles of sphere along a tree. Moreover, for symplectic automorphisms of Penner type, we prove that our computation of categorical entropy becomes a computation by simple linear algebra.Comment: 38 page

    Posthuman Creative Styling can a creative writer’s style of writing be described as procedural?

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    This thesis is about creative styling — the styling a creative writer might use to make their writing unique. It addresses the question as to whether such styling can be described as procedural. Creative styling is part of the technique a creative writer uses when writing. It is how they make the text more ‘lively’ by use of tips and tricks they have either learned or discovered. In essence these are rules, ones the writer accrues over time by their practice. The thesis argues that the use and invention of these rules can be set as procedures. and so describe creative styling as procedural. The thesis follows from questioning why it is that machines or algorithms have, so far, been incapable of producing creative writing which has value. Machine-written novels do not abound on the bookshelves and writing styled by computers is, on the whole, dull in comparison to human-crafted literature. It came about by thinking how it would be possible to reach a point where writing by people and procedural writing are considered to have equal value. For this reason the thesis is set in a posthuman context, where the differences between machines and people are erased. The thesis uses practice to inform an original conceptual space model, based on quality dimensions and dynamic-inter operation of spaces. This model gives an example of the procedures which a posthuman creative writer uses when engaged in creative styling. It suggests an original formulation for the conceptual blending of conceptual spaces, based on the casting of qualities from one space to another. In support of and informing its arguments are ninety-nine examples of creative writing practice which show the procedures by which style has been applied, created and assessed. It provides a route forward for further joint research into both computational and human-coded creative writing
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