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.

Kenji Ohmori and Tosiyasu L. Kunii, “Development of an Accounting System: Applying the Incrementally Modular Abstraction Hierarchy to a Complex System“

Abstract

The new methodology for software development is introduced and applied to an accounting system. The new method is called the incrementally modular abstraction hierarchy (IMAH). IMAH has an abstraction hierarchy from abstract to concrete levels. Invariants defined on an abstract level are kept on a concrete level, which allows adding modules incrementally on each hierarchical level and avoiding combinatorial explosion of the serious problem in software engineering, while climbing down abstraction hierarchy in designing and modeling a complex system. This paper shows how IMAH is applied in developing an accounting system, which is fundamental in enterprise systems and a suitable example of complex software systems. At first, very simple example recording only journal vouches to a database system is used to describe methodologies of IMAH. Then, it is described how this simple system is incrementally developed to a conventional complex accounting system.

In the Proceedings of CG International ‘96, Pohang, Korea, June 24-29, 1996, pp. 2-8, published by IEEE Computer Society Press, Los Alamitos, California, June 1996.

Abstract

As the key visual display- and processing- element of information super highway nodes, computer graphics is advancing into dynamic and higher dimensional visual worlds. So is visual algorithms to program visual worlds as the contents of information super highways. This research presents a drastic approach in designing visual algorithms to construct visual worlds. The address is on the most critical phase of conceptual design that has been conducted ad hoc in designers’ mind. Conceptual visual algorithms make mental design processes and design results explicitly represented in a computer executable form after interactive machine translation. Hence, they are explicitly validatable against the design requirements. Taking a popular case of human performance design including dramas, music performance and sporting, recreational skiing algorithm design in particular as an example of visual world design, we show a requirement-driven approach to conceptual visual human algorithm design produces a truly effective skiing method to meet wide varieties of recreational requirements.

Tosiyasu L. Kunii, “Cyberworlds Modeling –Integrating Cyberworlds, the Real World and Conceptual Worlds-“, Proceedings of International Conference on Cyberworlds (CW2005), 23-25 November 2005, Nanyang Executive Center, Singapore, IEEE Computer Society Press, Los Alamitos, California, USA

Abstract

The globalization of the real world we live has been almost exploding in its speed and scale spatiotemporally in all the key aspects including business, economy, industry, education and culture, making it hard for human beings to cognize what's going on and deal with them . Thus the links between the real world and conceptual world is getting weaker. The globalization is mainly driven by the Web-based activities in their cyberspaces creating cyberworlds as seen in e-business, e-commerce, e-manufacturing and cultural heritages through the Web and on the Web. Thus the links between the real world and cyberworlds are ever becoming tighter nonlinearly in time and space.

It is now crucial to find a way to automatically integrate the dynamically changing worlds, namely the real world, cyberworlds and conceptual worlds, fast enough to cope with the rapid changes. It is a hard task owing to the vast complexity of the worlds to be integrated, and it requires an advanced abstraction modeling. This is an interim progress report on it, presenting the outline based on the previous works on the abstraction hierarchy modeling of cyberworlds to realize an incrementally modular hierarchical modeling of cyberworlds via attaching spaces as quotient spaces and attaching maps. Attaching spaces are also for unique integration of the worlds that are real, cyber, and/or conceptual. They also guarantee liner interoperability of the integrated worlds to eliminate the combinatorial explosion of the computing in their complexity.

Tosiyasu L. Kunii, “Towards Open Education through Distributed and Networked Information Systems - An Experience-based Approach”, S. Bhalla (Ed.): DNIS 2005, LNCS 3433, pp. 204–212, 2005, Springer-Verlag, Heidelberg, Germany.

Abstract

To overcome overwhelming and global international struggles to secure limited resources such as oil and land, the potential role of open source education through networked and distributed information systems (DNIS) on the Web to create advanced IT experts as unlimited global resources is increasing rapidly. An experience-based summary of global open education is presented solely for promoting its practices. My life has been benefited from practicing open education, first at an elementary school and later at a graduate school. The openness has been local because of the lack of globalization mechanisms in education. It is fairly recent that we have effective global educations mechanisms for global interactivity and global two way communications such as the web and cyberspaces, distributed and networked information systems (DNIS) in particular. Compared to local open education, global open education removes the boundaries of ages, organizations, nations, sexes, and disciplines. Many unseen barriers exist to prevent global open education, mostly originating from survival intuitions and fights embodied in life itself. Since the barriers are rooted in the nature of life, it is hard to practice global openness in education. Hence it is important to cooperate for us to practice it to see real advances in our knowledge.

Tosiyasu L. Kunii, “Cyberworlds -Theory, Design and Potential-“, IEICE Trans. Fundamentals/Communications/Electronics/Information and Systems, Vol. E88-D, No. 5, May 2005, pp. 790-802

Abstract

Cyberworlds are being formed in cyberspaces as computational spaces. Now cyberspaces are rapidly expanding 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. The major key players of cyberworlds include e-finance that trades a GDP- equivalent a day and e-manufacturing that is transforming industrial production into Web shopping of product components and assembly factories. Lacking proper theory and design, cyberworlds have continued to grow chaotic and are now out of human understanding and control. This research first presents a generic theoretical framework and design based on algebraic topology, and also provides an axiomatic approach to theorize the potentials of cyberworlds.