Isotopic tiling theory for hyperbolic surfaces

In this paper, we develop the mathematical tools needed to explore isotopy classes of tilings on hyperbolic surfaces of finite genus, possibly nonorientable, with boundary, and punctured. More specifically, we generalize results on Delaney-Dress combinatorial tiling theory using an extension of mapping class groups to orbifolds, in turn using this to study tilings of covering spaces of orbifolds. Moreover, we study finite subgroups of these mapping class groups. Our results can be used to extend the Delaney-Dress combinatorial encoding of a tiling to yield a finite symbol encoding the complexity of an isotopy class of tilings. The results of this paper provide the basis for a complete and unambiguous enumeration of isotopically distinct tilings of hyperbolic surfaces

Towards a combinatorial algorithm for the enumeration of isotopy classes of symmetric cellular embeddings of graphs on hyperbolic surfaces

Based on the recent mathematical theory of isotopic tilings, we present the, to the best of our knowledge, first algorithm for the enumeration of isotopy classes of cellular embeddings of graphs invariant under a given symmetry group on hyperbolic surfaces. To achieve this, we substitute the isotopy classes with combinatorial objects and propose different techniques, guided by structural results on the mapping class group of an orbifold and notions from computational group theory that ensure that the algorithm is computationally tractable. Furthermore, we extend data structures of combinatorial tiling theory to isotopy classes that lead to an actual implementation of the algorithm for symmetry groups generated by rotations. \\From the enumerated combinatorial objects, we produce a range of simple graphs on hyperbolic surfaces represented as symmetric tilings in the hyperbolic plane, illustrating the enumeration with examples and experimentally demonstrating the feasibility of the approach. These tilings are finally projected onto a family of triply-periodic surfaces that are relevant for the natural sciences

Computing a Dirichlet Domain for a Hyperbolic Surface

This paper exhibits and analyzes an algorithm that takes a given closed orientable hyperbolic surface and outputs an explicit Dirichlet domain. The input is a fundamental polygon with side pairings. While grounded in topological considerations, the algorithm makes key use of the geometry of the surface. We introduce data structures that reflect this interplay between geometry and topology and show that the algorithm runs in polynomial time, in terms of the initial perimeter and the genus of the surface

Design Science Research in Green IS - Analyzing the Past to Guide Future Research

The field of Green IS research addresses the environmental challenges of our rapidly growing economy. IS-based solutions are valuable tools for emissions reduction and waste mitigation. The development of novel sustainable IS artifacts falls in the domain of Design Science Re-search. Applying the Design Science Research paradigm helps to design, develop, improve and implement IS related artifacts to solve prevailing problems or challenges. Hence, regarding sustainability, it acts as an aid to the goals of Green IS. Thus, the development of novel sustain-able artifacts falls in the intersection of Green IS and Design Science Research. We analyze the relationship between Design Science Research and Green IS by providing a deeper understanding of current research knowledge and opportunities at the intersection of these two important IS topics. Based on these findings, we present five directions for future re-search that aim to facilitate further contributions to theoretical knowledge, Design Science Re-search, and sustainable solution development in the field of Green IS

Towards a Taxonomy of Platforms for Conversational Agent Design

Software that interacts with its users through natural language, so-called conversational agents (CAs), is permeating our lives with improving capabilities driven by advances in machine learning and natural language processing. For organizations, CAs have the potential to innovate and automate a variety of tasks and processes, for example in customer service or marketing and sales, yet successful design remains a major challenge. Over the last few years, a variety of platforms that offer different approaches and functionality for designing CAs have emerged. In this paper, we analyze 51 CA platforms to develop a taxonomy and empirically identify archetypes of platforms by means of a cluster analysis. Based on our analysis, we propose an extended taxonomy with eleven dimensions and three archetypes that contribute to existing work on CA design and can guide practitioners in the design of CA for their organizations

On Conversational Agents in Information Systems Research: Analyzing the Past to Guide Future Work

Conversational agents (CA), i.e. software that interacts with its users through natural language, are becoming increasingly prevalent in everyday life as technological advances continue to significantly drive their capabilities. CA exhibit the potential to support and collaborate with humans in a multitude of tasks and can be used for innovation and automation across a variety of business functions, such as customer service or marketing and sales. Parallel to the increasing popularity in practice, IS researchers have engaged in studying a variety of aspects related to CA in the last few years, applying different research methods and producing different types of theories. In this paper, we review 36studies to assess the status quo of CA research in IS, identify gaps regarding both the studied aspects as well as applied methods and theoretical approaches, and propose directions for future work in this research area

Designing Anthropomorphic Enterprise Conversational Agents

The increasing capabilities of conversationalagents (CAs) offer manifold opportunities to assist users ina variety of tasks. In an organizational context, particularlytheir potential to simulate a human-like interaction vianatural language currently attracts attention both at thecustomer interface as well as for internal purposes, often inthe form of chatbots. Emerging experimental studies onCAs look into the impact of anthropomorphic design ele-ments, so-called social cues, on user perception. However,while these studies provide valuable prescriptive knowl-edge of selected social cues, they neglect the potentialdetrimental influence of the limited responsiveness ofpresent-day conversational agents. In practice, many CAsfail to continuously provide meaningful responses in aconversation due to the open nature of natural languageinteraction, which negatively influences user perceptionand often led to CAs being discontinued in the past. Thus,designing a CA that provides a human-like interactionexperience while minimizing the risks associated withlimited conversational capabilities represents a substantialdesign problem. This study addresses the aforementionedproblem by proposing and evaluating a design for a CAthat offers a human-like interaction experience while mit-igating negative effects due to limited responsiveness.Through the presentation of the artifact and the synthesis ofprescriptive knowledge in the form of a nascent designtheory for anthropomorphic enterprise CAs, this researchadds to the growing knowledge base for designing human-like assistants and supports practitioners seeking to intro-duce them into their organizations