Toshio Kodama, Tosiyasu L. Kunii and Yoichi Seki, "A Continuous Quantity Factor in the Condition Formula Search", Proceedings of Fourth International Conference on Next Generation Mobile Applications, Services and Technologies (NGMAST 2010), Amman, Jordan, 26-29 July, 2010, IEEE Computer Society Press.

Abstract

Cyberworlds in the era of ’cloud’ computing are being created on the Web where data and its dependencies are constantly changing and evolving. The problem of combinatorial explosion in system development inevitably arises when dealing with cyberworlds. To solve the problem, we have developed a data processing system called the Cellular Data System (CDS), based on the Incrementally Modular Abstraction Hierarchy (IMAH) in the cellular model, which offers powerful mathematical reason. In this paper, we design and implement a continuous quantity factor to deal with objects that express continuous quantity and integrate it into the condition formula search, which is the effective data search function of CDS, used to analyze data in cyberworlds without limitation by defining schema. If you take advantage of continuous quantity factors with the condition formula search in business application development, application logic development is made much simpler. In addition, we verify the effectiveness of a continuous quantity factor by taking up examples of core logic development of business applications.

Yoshihisa Shinagawa and Tosiyasu L. Kunii "Designing and Modeling Cyberworlds using the Incrementally Modular Abstraction Hierarchy based on Homotopy Theory", The Visual Computer: Volume 26, Issue 5 (2010), Page 297-309.

Abstract

For designing and modeling complicated and sophisticated systems such as cyberworlds, their mathematical foundation is critical. To realize it, two important properties called the homotopy lifting property (HLP) and homotopy extension property (HEP) are applied for designing and modeling a system in a bottom-up way and a top-down way, respectively. In this paper, an enterprise system and a real-time embedded system are considered as important socially emerging cases of cyberworlds, where the π-calculus processes for describing these behaviors formally, a Petri net for explaining process interactions, and XMOS XC programs are modeled and designed by our approach. The spaces in both properties are specified by the incrementally modular abstraction hierarchy by climbing down the abstraction hierarchy from the most abstract homotopy level to the most specific view level, while keeping invariants such as homotopy equivalence and topological equivalence.

Tosho Kodama, Tosiyasu L. Kunii and Yoichi Seki, "An Example of a Tracking Function Using the Cellular Data System", Proceedings of the 9th WSEAS International Conference on Artificial Intelligence, Knowledge Engineering and Databases (AIKED'10), Murray Edwards College, University of Cambridge, UK, February 20-22, 2010 , pp. 372-377.

Abstract

In the era of cloud computing, where data and data dependencies constantly change, a mechanism within system development that can correspond to those changes in user requirements is needed. The Incrementally Modular Abstraction Hierarchy (IMAH) offers the most appropriate mathematical background to model dynamically changing information worlds by descending from the abstract level to the specific, while preserving invariants. In this paper, we have applied the Cellular Data System (CDS), based on IMAH, to the development of core logic for a budget tracking function, and verified that using CDS makes the data modeling simpler.

Tosho Kodama, Tosiyasu L. Kunii, Yoichi Seki, "A Data Modeling Example of File Permission Management Using the Cellular Data System", Proceedings of 4th WSEAS International Conference on COMPUTER ENGINEERING and APPLICATIONS (CEA '10) Harvard University, Cambridge, Boston, USA, January 27-29, 2010, pp.90-95.

Abstract

In the era of cloud computing, data is processed within "the cloud", and data and its dependencies between systems or functions progress and change constantly within "the cloud", as user requirements change. Such information worlds are called cyberworlds. In designing cyberworlds, the Incrementally Modular Abstraction Hierarchy (IMAH) gives a most appropriate mathematical background to model dynamically changing cyberworlds by descending from the abstract level to the specific one, while preserving invariants. An attaching function is defined on the adjunction space level to model attachment of spaces by an equivalence relation in IMAH. In this paper, we have improved the attaching function to the Cellular Data System (CDS) that we developed based on IMAH. The function is quite effective in business application development when a system user recognizes an equivalence relation in business objects. We have also shown an example of the use of CDS for file permission information management under an unexpected situation, such as when an organizational structure or its staff assignments change, using CDS. In the example, we design and take advantage of spaces on three of the seven levels of IMAH, in order of abstractness: the set theoretical level, the topological space level and the adjunction space level.

Toshio Kodama, Tosiyasu L. Kunii, and Yoichi Seki, “A Product Control System using the Cellular Data System”, Proceedings of The 8th WSEAS International Conference on E-Activities (E-Learning, E-Communities, E-Commerce, E-Management, E-Marketing, E-Governance, Tele-Working / E-Activities '09), Puerto De La Cruz, Canary Islands, Spain, December 14-16, 2009, pp. 57-64.

Abstract

In the era of cloud computing, data is processed within "the cloud", and data and its dependencies between systems or functions progress and change constantly within "the cloud", as user requirements change. Such information worlds are called cyberworlds. Now we need a more powerful mathematical background which can model the cyberworlds in "cloud" as they are. We consider the Incrementally Modular Abstraction Hierarchy (IMAH), with its ability to descend from the most abstract homotopy level to the most specific view level while preserving invariants, to be appropriate to model dynamically changing cyberworlds. We have developed a data processing system called the Cellular Data System (CDS) based on IMAH. In this paper, we introduce a numerical value identifier and processing maps as a function on the presentation level of IMAH. This function is very effective in a business application, in which, in most cases, numerical values defined in information spaces are calculated while data is managed. We have shown its effectiveness through examples of core processing of a product control system in the manufacturing industry using a numerical value identifier.

Tosiyasu L. Kunii “Algebraic Modeling for Cyberworld Design“

Abstract

Cyberworlds are being formed on the web either intentionally or spontaneously, with or without design. Widespread and intensive local activities are melting each other on the web globally to create cyberworlds. What is called e-business including electronic financing has been conducted in cyberworlds and has gone beyond a national finance level in its scale. Without proper modeling, cyberworlds have continued to grow chaotic and are now out of human understanding and control. A novel information model we named “an adjunction space model” serves to globally integrate local models. As an information model, it is also applicable to the category of irregular data models that capture spatio- temporal aspects of information worlds. Mathematically it is based on an incrementally modular abstraction hierarchy including cellular spatial structures in a homotopy theoretical framework.

Allan J. Sieradski, “An Introduction to Topology and Homotopy“,

Introduction

Geometry uses the notions of distance, length, area and volume to express certain properties of objects in space. There are, however, features of objects that are not based upon rigid measurements.

For example, when a spherical balloon is inflated, it may lose the geometric property that all its points are equidistant from a central point in space. But all its deformed versions, whether ellipsoid?like or whatever, retain the feature that they divide space into a bounded region and an unbounded region, and that it is impossible to travel within space from one region to the other region without passing thuough the deformed sphere. In addition, if the balloon is punctured by the removal of a single point, it ceases to divide space into two regions.

Stretching and shrinking objects are examples of continuous functions. Puncturing and tearing objects are examples of discontinuous functions. These distinctions can be made only when the objects under consideration are sets of points in which it is known which subsets are near which points. The fundamental requirement for continuity is that the function respect all the nearness relationships between subsets and points of the object.

The features of the object that are preserved by continuous functions with continuous inverses are called topological properties. There are enough such features to warrant their own study in the discipline of topology.

Tosiyasu L. Kunii, "The Potentials of Cyberworlds -An Axiomatic Approach-", International Workshop on Information & Health Technology, Joint Lab of Health Information Technology, High Performance Computing Center, Shanghai University, April 24-25, 2009

Anatoly T. Fomenko and Tosiyasu L. Kunii, “Topological Modeling for Visualization“

Preface

Flooding of information on the Earth through various computer networks such as the Internet characterizes the world situation we live. Information worlds often called virtual spaces and cyber spaces have been formed on computer networks. The complexity of information worlds has been increasing almost exponentially through the exponential growth of computer networks. Such non-linearity in growth and in span characterizes information worlds. In other words, the characterization of nonlinearity is the key to understand, utilize and live through the flooding of information. The characterization approach is by characteristic points such as peaks, pits and passes according to the Morse theory. Another approach is by singularity signs such as folds and cusps. Atoms and molecules are the other fundamental characterization approach. Topology and geometry including differential topology serve as the framework of the characterization. Topological Modeling for Visualization is a textbook for people interested in the characterization to understand how to do it and what it is. Understanding is the key to utilize information worlds and to live through the changes of the real world on the Earth.

Writing this textbook paused the authors careful preparation. There are heavy mathematical stuff that requires the design of writing style for easy un- derstanding and for strong attraction. To realize the style, we set the main goal of this book to establish a link between the theoretical aspects of modern geometry and topology, on the one hand, and experimental computer geometry, on the other. There are many excellent books on modern geometry and topology (roughly speaking, “theory”), and many excellent books on modern computer and experimental geometry. But as far as we know, there is no book that bridges the gap between these two branches of modern science, that is, between “theory” and “practice”. We have tried to fill this gap. Our intention was to write a book that will be useful to both communities of scientists. Of course, we realize that this separation between “theoretical science” and “experimental science” is not clear-cut, and we use this language and images only for faster description of our main idea. We collect in the book some basic elements of theoretical geometry and topology that are used today in different branches of experimental computer geometry. We do not give detailed proofs because of lack of space, but we give references that can help the reader find the proofs. The advantage of such a style is this: We collect in one book a short description of the most powerful theoretical tools, and experts in experimental science can use this material in their concrete work. Certainly, as we know from our own experience, modern topological methods can improve the results of experimental computer geometry. On the other hand, experts in theoretical geometry and topology can find in our book possible applications of those fields to very interesting computer experiments in the world of geometrical computer methods, medicine, cars industry, architecture, and so on. Many pure mathematicians will also find here material for development of a new theoretical ideas. Each chapter consists of two layers: first theoretical ideas, then applications to the different branches of modern experimental computer geometry. We’ve tried to make chapters as independent as possible, to help to the reader use each chapter as an individual research tool, without a complete study of other sections of the book. As a consequence, sometimes we repeat in some chapters a summary of material from another section, to recall important notions.

Tosiyasu L. Kunii, "Independent Administrative Institutions and Roles of Universities ‐Past, Present, and Future‐", The University of Aizu Distinguished Lecture, November 16, 2007, Aizu, Japan