Topic
Adjunction space
About: Adjunction space is a research topic. Over the lifetime, 23 publications have been published within this topic receiving 186 citations.
Papers
Journal Article•
TL;DR: This paper presents a model of Conceptual Multiresolution Analysis by an Incrementally Modular Abstraction Hierarchy and its Applications in Digital Media Science.
Abstract: Summary Recent advances of Web information systems such as e- commerce and e-learning have created very large but hidden demands on conceptual multiresolution analysis for more generalized information analysis, cognition and modeling. To meet the demands in a general way, its modeling is formulated based on modern algebraic topology. To be specific, the modeling formulation is worked out in an incrementally modular abstraction hierarchy with emphasis on the two levels of the hierarchy appropriate for conceptual modeling: the adjunction space level and the cellular structured space level. Examples are shown to demonstrate the usefulness of the presented model as well as an implementation of a flower structure case.
19 citations
TL;DR: An incrementally modular abstraction hierarchy, which specifies, models and visualizes the architecture of cyberworlds from general to specific, is presented and results in a fault-free reduction of time and cost.
Abstract: An incrementally modular abstraction hierarchy, which specifies, models and visualizes the architecture of cyberworlds from general to specific, is presented. The hierarchy, consisting of a homotopy level with fiber bundles, a set theoretical space level, a topological space level, an adjunction space level, a cellular space level, and presentation and view-levels, is described theoretically with examples of online book shopping such as e-commerce, seat assembling as such e-manufacturing, and accounting such as e-economy. Sharing invariants defined at each level contributes to robust architecture and modeling for designing, analyzing, implementing and visualizing cyberworlds, which results in a fault-free reduction of time and cost.
19 citations
16 Dec 2002
TL;DR: The nature of Web information is clarified and modeled as the adjunction space model, which has adopted algebraic topology, cellular spatial structures in the homotopic framework and adjunction spaces in particular to validate the advantages of this Web information modeling over the popular relational model, the entity relationship model, UML, and XML.
Abstract: The nature of Web information is clarified and modeled as the adjunction space model. Practical Web information management requires Web information to be modeled in such a way that the model captures the dynamic changes, present the dynamism visually, and validate the results formally. As the mathematical ground of the model, we have adopted algebraic topology, cellular spatial structures in the homotopic framework and adjunction spaces in particular. The results have been applied successfully to typical Web information systems such e-finance and e-manufacturing to validate the advantages of our Web information modeling over the popular relational model, the entity relationship model, UML, and XML.
12 citations
1 Feb 1983
9 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2016 | 1 |
| 2011 | 1 |
| 2010 | 1 |
| 2009 | 2 |
| 2007 | 1 |