Multi-layered perceptron, a kind of neural network, is suitable for modeling complex phenomena in a noisy and restricted data environment. In spatial interaction modeling, Openshaw (1993) and Fisher and Gopal (1994) verified better performance of perception than classical models. Openshaw wrote “If the dependent variable is binomial or Poisson then the net will deduce this from the training data, there is no need to be explict”. However, both residual patterns of perceptrons and a log-linear gravity model were similar in the results of Fisher and Gopal (1994). They performed log-transform for output data, and trained networks by the least square criterion, which is normal for most perceptrons. If we regard each output of perceptrons as probabilistic expectation, then both of their trained perceptrons and log-linear gravity models would be assumed as log-normal distributions for error term. The similarity of residual patterns (under-prediction in large flows) could be caused by the same assumption of error distribution. To overcome such well-known features of log-normal models, we might use the Poisson regression technique (Flowerdew and Aitkin, 1982).
In this paper, I specified PR-perceptron, which is a special type of two-layered perceptrons (Fig. 1). Its features are as follows. 1) By sigmoid hidden-units, PR-perceptrons can approximate any continuous mapping. 2) An exponential output-unit produces a positive real number with no upper limits, and 3) it also brings formal similarities between PR-perceptron and Poisson regression models. 4) Its training criteria is the maximum likelihood in the Poisson distribution. The PR-perceptron shares not simply the estimation process of parameters but also theories of undergoing process of spatial interaction with the Poisson regression, the family of maximum-entropy models, and discrete choice models, e. g. the multinominal logit model.
I applied the PR-perceptron to 1990 inter-prefectural migration data for Japan and compared results with those of Poisson regression models (un-constrained, singly-constrained, and doubly-constrained models). The following results were obtained: 1) the PR-perceptron, which is non-constrained, showed the same level of goodness-of-fit as singly-constrained Poisson regression models (Tables 1 and 2). We recognized the superiority of the PR-perceptron even if we consider the trade-off relation between the number of parameters and generality of training results. 2) There were similarities in residual distribution between the PR-perceptron and Poisson regression model (un-constrained type) (Fig. 5) and no observed underprediction in large flows as log-linear models. This could indicate that the assumption of error distribution affects outcomes of the perceptrons. 3) Visualization of contents of trained PR-perceptron was carried out (Figs. 6 and 7). It enables us to a) verify assumptions about forms of utility functions, e. g. distance-decay function, and b) investigate exploratory non-linear relations and interdependency among variables. In this case study, we recognized intermediate distance-decay effects between power and exponential function, and non-monotonic non-linear relations according to characteristics of origins and destinations.

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Since the 1950's, the studies dealing with swidden agriculture or its society have developed in various disciplines including geography, cultural anthropology, agronomy, forest ecology and soil science. Though the themes handled are varied, their approaches can roughly be classified as follows: (1) an ecological approach focused on environmental change or carrying capacity, (2) a socio-economic approach focused on analysis of subsistence economy and social structure, (3) an approach from the viewpoint of ethno-science, which aims to analyze folk knowledge systems or their cosmology, and (4) a comparative approach associated with a genealogical perspective.
On the other hand, there has been literature which investigates tropical swidden agricultural systems in comparison with other agricultural systems (for example, intensive irrigation agriculture). Geertz (1963) explained the difference between Inner and Outer Indonesia from their contrastive subsistence economies based on environmental factors. Taking notice of the difference of labor productivity and land productivity, Dove (1985) has developed this idea: based on the quantitative data of Indonesian agriculture, he has proposed that the swidden agricultural system has an advantage over the intensive rice irrigation system in terms of labor productivity, although the former may be inferior to the latter in land productivity. This implies that, in low population density areas, it may be rational to choose the swidden agriculture instead of intensive agriculture which the central government has recommended. His argument is considered to be important because it may offer a solution to the problem of underdeveloping countries' rural development plans propelled by the central governments and international aid organs for sustainable use.
Keeping such a viewpoint in mind, I intend to discuss the economic rationality of swidden agricultural people in Southwest Ethiopia where an ethnic group (the Majangir) maintains a relatively self-sufficient subsistence economy and might be put into a critical situation by political interaction with the central government in the near future. They are living in the dense forest of the southwestern escarpment of the Ethiopian Plateau, engaging in swidden agriculture and honey collecting activity. Crops are produced for self-consumption, while they sell honey in the local market for cash. Their traditional settlements are very small: a settlement consists of only several domestic groups. They move their houses according to abandonment of their swidden fields every few years. Since the Ethiopian socialist revolution in 1974, however, sedentarization has been encouraged by the central government. At almost the same time, Christianity was introduced to them by a Protestant missionary. Sedentarization and Christianity have had a great impact on the society.
From December 1992 through March 1994, I stayed in a village called Kumi which contains about 470 people. In this village, sedentarization and introduction of Christianity influenced them from a relatively early time. During my stay I made participant observations of their everyday life including agricultural practices, and I especially paid attention to the quantitative aspect of labor input and its seasonal allocation.
I observed technological features of their farming system which can be summarized as follows:
(1) Diversity of field types: I classified field types into five: (a) main fields cleared in the dry season (b) main fields cleared in the rainy season (c) sweet potato fields (d) fruit garden (e) backyard garden. Among them, worthy of note is (b) type, kate fields. Majangir adopts a peculiar way of farming, in which they first sow maize and sorghum directly in the bush, and then clear the grasses and shrubs. They cover the ground with them instead of burning. This farming technique allow them to prepare main fields at the height of the rainy season.

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1. GIS studies and the quantitative revolution in geography
The early development of GIS studies originated at the University of Washington in which the quantitative revolution in geography took place in the late 1950's. Garrison's students including Bunge, W., Tobler, W. R. and Marble, D. F. had the original leadership in GIS study and have driven the top level initiatives for GIS development. The Garrison School was divided into two parties by different analytical concepts and approaches. One was a quantitative statistical geography whose conceptual keywords were spatial structure, spatial process and spatial interaction in Newtonian space, and the other was GIS studies based on topological space concepts.
By the early 1970's, GIS studies were not dominant when compared with statistical analysis in geography because of the lack of technology in graphical facilities. But from the late 1970's GIS studies have been increasing by the development of some computer graphics technologies.
2. GIS studies in the 1960's and 1970's
In the late 1960's, the development of DIME files had a special influence in terms of topological data structure, geocoding and addressmatching. Fisher, H. made an important contribution to GIS study from the late 1960's to the middle 1970's and established the Harverd Laboratory for Computer Graphics and Spatial Analysis in which ODES-SEY as Vector GIS was desigend. A significant symposium about topological data structure was held in 1977 at this laboratory. The results of the symposium were published as Harvard Papers on Geographic Information System edited by Dutton, G. in 1978.
A vector GIS model was traced to CGIS (Canada Geographic Information System) which Tomlinson, H. R. designed in the early 1960's. This vector model means that the space was defined by the set of spatial objects such as points, lines, and polygons with topological linkage and connection.
A Raster GIS model also was developed in the 1970's in the field of grobal environmental studies such as environmental monitoring systems and resource management using remote sensing technology and Landsat data in large national projects.
3. Systematization of GIS studies in the 1980's and 1990's and the concept of topological space
We can recognize the spatial patterns and shapes of geographic entities on a map which represents what we see and know about the real world as one of models of the surface of the earth. The nature of a map as a model of the real world that depends on the concept of space demonstrates a variety of underlying conceptual frameworks. Geographical spatial models are based on the concepts of absolute space or Newtonian space. In particular, since quantitative geography was advocated, it has been important to measure distance between geographical entities and to make a distance based spatial model using Euclidean geometry.
But with the progress in GIS studies, spatial data structure stored as a database in a computer has been drastically shifted from a Euclidean space concept to a topological space concept. The concepts of topological space and topologically spatial analysis were made clear in the context of GIS Spatial Data Models in the 1980's and 1990's.

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Until the 1960s, geography was taught as a core subject in Swedish high schools. However in 1966, geography as a school subject was dismantled and combined with science and social studies. After about 30 years of non-existence as a discipline, geography was restored as an independent subject in 1993 with the introduction of a new, comprehensive high school system.
Despite the fact that the unification of geography with social studies and science in 1966 spelled the dismantling of geography as an independent discipline, academic geography at that time was already divided into human and natural branches, and many human geographers who had been working to establish their field as a subfield of social studies welcomed the merger into social studies.
With the merger of human geography into social studies, descriptive content in geography was removed and replaced with the scientific concepts and theories of the day. However, the status of geography within social studies began to decline. Reasons for this decline include 1) as geography was riding the wave toward applied social science, no consideration from an educational perspective was given of the results of geography as it was incorporated into social science, 2) almost no theoretical or practical research was conducted in geography as a sub-field of social studies, 3) academic geography and geography education became increasingly estranged from one another, and 4) geography became, in effect, irrelevant in the training of social studies teachers, with the result that their understanding and awareness of geography declined, and they themselves did not deal with geography within the subject of social studies. It can be said that in the 1970s and 1980s, geography education in social studies was essentially non-functional.
In 1991, when the Swedish high school system was completely reformed, it was decided to restore geography as a school subject. However, this would not have been possible without the existence of geographers who had struggled to restore their discipline to the school curriculum. At the same time, a quantitative reform in education was called for to deal with the diversification of the social demands of a deindustrializing and information-oriented society, the gravity of environmental problems, internationalization, and other issues. Geography which dealt with the relationship between man and nature apparently played an important role environmental education and international studies. One thing is for certain: there was a demand for its revival as a new type of geography education.
It cannot be denied that geography is the foundation of geography education, but it should also be stressed that emphasizing only the uniqueness of geography in geography education is behind the times. Therefore, as we look toward the development of a new type of geography education, geography itself, not only in Sweden but elsewhere, is being asked to reevaluate its significance in geography education.

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