SOCIAL NETWORKS AND THE CONVERGENCE OF POPULATION ATTRIBUTES: A GENERALIZATION

ABSTRACT.  Analysis of social interactions has recently become an important area of economic research, and the focus of researchers in this area has increasingly shifted toward dynamic models. In one recent contribution, Brueckner and Smirnov (2007) analyze the evolution of population attributes in an exceedingly simple model, where an agent's attributes at time t are equal to the average attribute value among his acquaintances. The pattern of acquaintances in the population is determined by the social network, and Brueckner and Smirnov (BS) explore the effect of network characteristics on the convergence of population attributes over time. They show that some simple sufficient conditions on the network structure ensure convergence to a "melting-pot" equilibrium where attributes are uniform across agents. The present paper provides a generalization of BS's analysis, allowing for a more general form of the rule governing the evolution of population attributes. The analysis shows that BS's previous conclusions continue to hold under this generalization, while also providing a result that can be applied more generally to other models.     

Intentional human burial: Middle Paleolithic (last glaciation) beginnings

This paper analyzes intentional burial as a historical phenomenon. Mortuary practices are viewed as a particular sphere of human activity, involving the transfer of the physical remains from one natural environment to another. The general and specific laws governing mortuary treatment and its development are discussed, and the earliest known deliberate burials—those of the Middle Paleolithic—are examined against this theoretical background. Middle Paleolithic groups invented almost all the basic ways of treating a corpse before burial and almost all the ways of burial itself. They seem to have developed a cult of the dead, based upon dualities such as concealment vs exposure of the body, burial of the body intact vs disarticulated, burial of the whole body vs parts of it only, and so on. It is shown that, in the Middle Paleolithic, there were centers of taphological activity, that inhumation was selectively practiced on only a small minority of the population, that men were buried much more often than women, and that the patterns of burial seem to have been independent of identifiable factors such as human physical type or level of technology.     

The Role and Significance of Objective (Mathematical) Methods in Geographic Research

A staff member of Leningrad University's Cartography Department reviews the introduction of quantitative methods into geography and offers a classification of physical and mathematical models used in geography. The increasing use of objective methods, including physical and chemical techniques, is expected inevitably to affect the nature of geography as a scientific discipline, just as the use of aerial photography changed the theory and practice of topographic mapping.     

General Geographic Concepts

Following are fragments of a book devoted to theoretical geography on which Professor Smirnov, head of the Department of Economic Geography of Odessa University, was working at the time of his death in July, 1969. An attempt is made to formulate a system of general geographic concepts that would constitute the axiomatic foundation of geography. Several types of fundamental concepts are distinguished: spatial concepts; concepts of the structure and functions of geographical formations; concepts of simple and complex formations, etc. The present paper is limited to an examination of spatial concepts associated with geographical space, which is viewed as one of the general properties of geographical formations. Three basic spatial concepts are discussed: (a) the concept of group space, meaning the space occupied by a set of interrelated objects, as opposed to the individual space of a single object; (b) the concept of spatial integration of phenomena, implying causal relationships; (c) the concept of geographical commonality of phenomena, as opposed to the theory of uniqueness or local exclusiveness. The interplay of general laws and purely local relationships gives rise to a spatial field of interaction known as the geographical field. A geographical formation and its field of interaction may be centered, as in urban settlement, industry and other nodal phenomena, or they may be noncentered, as in rural settlement, agriculture and other spatially continuous phenomena. Other concepts are the area, shape, orientation and spatial dynamics of development of geographical formations.     

Study of the Shape of Rural Communities

Recent research on the configuration of populated communities is found to suffer from the fact that it seeks to isolate shape from size and orientation. The authors dispute the view, underlying central-place theory, that minimum-distance or minimum-energy concepts are fundamental to spatial relations. An equally basic tendency in geographic phenomena, it is suggested, is a disregard for efficiency criteria at various stages of development. Shape, size, and spatial orientation are viewed as representing a unity that reflects the interaction of these two opposed tendencies. Accordingly a technique is proposed for the analysis of community shapes, seeking to establish the magnitude of deviation from an equal-area circle. The method is applied to 203 communities in Ukrainian and Siberian areas, representing different physical and economic conditions. In both situations a predominant tendency toward southward expansion of communities is observed, and configurational deviations from the equal-area circle are found to increase in middle and upper size classes. (The senior author, A. M. Smirnov, died in July, 1969.)     

Cognitive Value and Numerical Accuracy in Geocomputation: Choosing a Method to Compute the Log‐Jacobian Term

This article addresses the importance of cognitive value, numerical accuracy, and technical feasibility for geospatial models and methods. Researchers pursue large spatial data in an analysis to improve the statistical efficiency of parameter estimates and the cognitive value of the results. The critical requirement for this strategy is the availability of numerically accurate computational methods, without which parameter estimates lose their cognitive value. This article illustrates the relationship between cognitive value and numerical accuracy by establishing properties of popular polynomial schemes for approximating the log‐Jacobian term in spatial autoregressive models. It shows that numerical inaccuracies might be more misleading than is commonly assumed. En este artículo se aborda la importancia del valor cognitivo, la precisión numérica, y la viabilidad técnica de los modelos y métodos geoespaciales. Los investigadores interesados en análisis espacial tienden a preferir el uso de bases de datos de gran tamaño con el fin de mejorar la eficiencia estadística de sus estimaciones de parámetros y el valor cognitivo de los resultados. El requisito crítico para esta estrategia es la disponibilidad de métodos computacionales numéricamente precisos, sin los cuales las estimaciones de parámetros pierden su valor cognitivo. En este artículo se ilustra la relación entre el valor cognitivo y precisión numérica mediante la determinante jacobiano tipo log en modelos espaciales autorregresivos (spatial autorregresive models‐SAR). El estudio demuestra que las imprecisiones numéricas pueden ser más engañosas de lo que se asume comúnmente. 本文描述了地理空间模型和方法中认知价值、数值精度、技术可行性的重要性。研究者一般倾向于通过追求大规模空间数据,来提升参数估计的统计有效性和结果的认知价值。这一策略的关键是有实用的精确数值计算方法,否则参数估计将失去其认知价值。本文通过建立普遍使用的多项式方案来逼近空间自回归（SAR）模型中的Log‐Jacobian,从而说明认知价值和数值精度间的关系。结果表明数值不确定性可能比通常假设的误导性更大。     

WORKINGS OF THE MELTING POT: SOCIAL NETWORKS AND THE EVOLUTION OF POPULATION ATTRIBUTES*

ABSTRACT This paper links the two nascent economic literatures on social networks and cultural assimilation by investigating the evolution of population attributes in a simple model where agents are influenced by their acquaintances. The main conclusion of the analysis is that attributes converge to a melting‐pot equilibrium, where everyone is identical, provided the social network exhibits a sufficient degree of interconnectedness. When the model is extended to allow an expanding acquaintance set, convergence is guaranteed provided a weaker interconnectedness condition is satisfied, and convergence is rapid. If the intensity of interactions with acquaintances becomes endogenous, convergence (when it occurs) is slowed when agents prefer to interact with people like themselves and hastened when interaction with dissimilar agents is preferred.     

Geosystems and Geostructures

An attempt is made to distinguish geosystems and geostructures as the two basic objects of study in geography. Geosystems and geostructures are interdependent but different spatial formations. Geosystems are defined by direct, reverse, and transformed relationships among such relatively autonomous components as natural environment, population, and economy. Geosystems tend to be superimposed on one another and are relatively flexible and stochastic. Geostructures, on the other hand, are distinguished by a unity of heterogeneous components, by comparatively clearly defined boundaries, and by considerable rigidity of construction. (One of the authors, A. M. Smirnov, died in July, 1969.)     

EFFICIENT ALGORITHMS FOR CONSTRUCTING PROPER HIGHER ORDER SPATIAL LAG OPERATORS*

ABSTRACT. This paper extends the work of Blommestein and Koper (1992)–BK–on the construction of higher-order spatial lag operators without redundant and circular paths. For the case most relevant in spatial econometrics and spatial statistics, i.e., when contiguity between two observations (locations) is defined in a simple binary fashion, some deficiencies of the BK algorithms are outlined, corrected and an improvement suggested. In addition, three new algorithms are introduced and compared in terms of performance for a number of empirical contiguity structures. Particular attention is paid to a graph theoretic perspective on spatial lag operators and to the most efficient data structures for the storage and manipulation of spatial lags. The new forward iterative algorithm which uses a list form rather than a matrix to store the spatial lag information is shown to be several orders of magnitude faster than the BK solution. This allows the computation of proper higher-order spatial lags “on the fly” for even moderately large data sets such as 3,111 contiguous U. S. counties, which is not practical with the other algorithms.