Dynamic density

Abstract: For Smile Durkheim, crime and punishment were integral features of organized social life. He considered the study of crime and punishment essential to the sociological enterprise precisely because these "social facts" revealed the inner workings of society and the mechanism through which societies change. In The Rules of Sociological Method Durkheim argues (1938:70) that "crime is ... necessary, it is bound up with the fundamental conditions of all social life," and that "it is no longer possible . . to dispute the fact that law and morality vary from one social type to the next, nor that they change within the same type if the conditions of life are modified." Because he viewed law as a reflection of basic social arrangements, Durkheim grounded his theory of social change in an analysis of comparative legal types. He assumed (1933:68) that "since law reproduces the principal forms of social solidarity, we have only to classify the different types of law to find therefrom the different types of social solidarity which correspond to it." In his central theoretical work, The Division of Labor in Society (1933), Durkheim linked the changing nature of legal controls (repressive to restitutive) to transformations in the nature of social solidarity (mechanical to organic). Durkheim's assertion that repressive controls were dominant in simple societies and restitutive controls in complex societies has been criticized by sociologists and anthropologists alike (cf. Merton, 1934; Schwartz and Miller, 1964; Barnes, 1966; Diamond, 1971; Lukes, 1972; Dubow, 1974). Restitution clearly represents an important principle in many undifferentiated (mechanical) societies (cf. Malinowski, 1926; Kuper, 1965), and the decline of repressive sanctions has not been as general or systematic as Durkheim (1933: 152-168) implied. Although many questions

Abstract: © L p i Until the fall of 2015 although the toll of migrants who drowned daring to cross the Mediterranean appeared in headlines, most of those who survived the crossing were kept in their hundreds of thousands from much of Europe. Then those dispossessed by war or by the neoliberal agendas inflicted on their countries began walking into Europe with the goal of settling in the wealthiest states, which were also those countries— along with the United States–that have been manufacturing the instruments of war, participating in various “coalitions of the willing” and benefiting from contemporary forms of accumulation through dispossession. In demanding the right to settle and rebuild their lives, migrants challenged the political narratives that excluded them from belonging to Europe and claiming the wealth and social benefits concentrated in a handful of European states. And as migrants began to enter Europe in large numbers and make these claims, a large number of Europeans began to welcome these migrants (Kermani, 2015; Mount, 2015). Through a host of convivial practices these Europeans demonstrated that they repudiated the dominant anti-refugee discourse and policies of their political leaders and identified with the refugees. At railroad stations from Budapest to Munich, along roads, in temporary shelters, and through demonstrations, those who extended welcomes repeatedly stated that they saw migrants and nonmigrants as bound together by their common humanity. To note this embrace is not to deny that recently and increasingly, there has been a rise of racism and a repudiation of cultural and religious diversity across Europe, North America, and around the world. Both political tendencies require explanation. Will Kymlicka’s essay serves as a useful entry point into these contemporary crosscurrents by raising the question of how scholars, activists, and policy makers can understand as well as speak to our times. Currently, we find ourselves challenged by a persisting contradiction: even as the world is ever more tightly and unequally woven together through economic, political, military, and cultural networks of unequal power, increasing numbers of intellectuals as well as political leaders are embracing nation-state building narratives that portray the world as a set of independent states with their own discrete economies and welfare regimes. Unfortunately, Kymlicka has joined the ranks of those who perpetuate the Westphalian fantasy of a world of separate and politically equal nation-states and embrace nationalism as a progressive force at this moment of history.

Abstract: The impact of population size, physical density, social density, and age of 600 communities upon the extent of their industrial diversification was analyzed. Hypotheses concerning each independent variable were generated from the theory of the development of the division of labor proposed by Durkheim and subsequently adopted by human ecologists. Regression analysis was employed to test the hypotheses. The standardized partial regression coefficients indicated that only social density exerts a significant impact upon industrial diversification. In addition, it was discovered that the combined influence of the independent variables fails to account for the bulk of the variation in industrial diversification. Factors which may be responsible for these results, as well as directions for future research, are presented and discussed. One of the areas in human ecology where the gap between theory and research is most apparent is in the study of the division of labor. Although the concept itself has received relatively extensive treatment at the theoretical level (Durkheim, 1933; Hawley, 1950; Simmel, 1959:52-62; Smith, 1963:3-17; Spencer, 1921; Stigler, 1951), attempts at operationalization have been rare (Gibbs and Martin, 1962:669). The few studies which have attempted to delineate empirical components of the "division of labor" (e.g., Olsen, 1968:703) generally employ ad hoc operational definitions whose utility is limited to the specific research problem under consideration. One exception to this trend is a series of studies by Gibbs and Martin (1962), Labovitz and Gibbs (1964), Gibbs and Browning (1966), and Browning and Gibbs (1971), endeavoring to measure the division of labor at the national or international level. Unfortunately, beyond these efforts virtually no work has been done to formulate an empirically based theory of functional differentiation. This article attempts to further the development of a grounded theory of the division of labor by testing a series of hypotheses derived from the conceptual scheme proposed by Durkheim (1933) and subsequently adopted by human ecologists. We are cognizant of the many difficulties involved in attempting to provide empirical linkage to the theoretical work of someone like Durkheim (Land, 1970:262; Merton, 1934). Because of the level of generality of Durkheim's explanation it is impossible to give attention to all possible meanings of all constructs and all their implications. What must be done is to extract a logically consistent piece from the more global scheme and empirically examine that statement. Perhaps Land (1970:262) best states the nature of this epistemological problem as well as a possible resolution: "The modern social theorist... can rarely claim to have captured the 'complete' meaning of a classic in his more rigorous restatements of classical social theory. At best, he can choose the goals of his formalization and attempt to show how the classic implies his restatement...." THEORETICAL STATEMENT While a variety of theorists have attempted to delineate the factors involved in the development of the division of labor, the explanation that is most generally accepted today was first proposed by Durkheim (1933) in 1893. Ac[ 176 ] * Paper presented at the annual meeting of the Southern Sociological Society, New Orleans, 1972. We are indebted to John Stoeckel and two unidentified readers for their helpful comments on an earlier version. This content downloaded from 207.46.13.101 on Thu, 21 Apr 2016 05:49:15 UTC All use subject to http://about.jstor.org/terms Division of Labor / 177 cording to this approach, functional heterogeneity is the consequence of increased physical and social density. With an increase in population size and social interaction, the struggle for existence becomes acute. This intensification of competition stimulates the development of the division of labor. For, with the rise of functional differentiation, homogeneity of demands upon the sustenance supply is minimized and competition is more or less resolved (Lampard, 1955:91; see also Simmel, 1959:53). In explaining the role of competition in stimulating the development of the division of labor, Durkheim drew many of his ideas from the work of Darwin (1958:84-86). Consequently, much of his presentation is exemplified through organic analogies (e.g., 1933: 266). From Durkheim's discussion, however, Hawlcy (1950:202-203) has outlined four general stages that competition follows in the formation of community structure: (1) the demand for sustenance exceeds the supply, (2) there is an increasing degree of homogeneity among competitors, (3) the weakest competitors are eliminated, and (4) organization occurs since competition differentiates and multiplies functions. Hawley's statement lays the groundwork for referring to one of Durkheim's (1933:262) major propositions: The division of labor develops, as there are more individuals in contact to . . . act and react upon one another . . . the division of labor is in direct ratio to moral or dynamic density . . . and, if it progresses in a continuous manner in the course of social development, it is because societies regularly become denser and more voluminous. That the general constellation of variables within which Durkheim worked is essentially the same as that employed by human ecologists (e.g., Hawley, 1950: 192-203; Park, 1936) has been demonstrated by Schnore (1958). In addition, this overlap extends to the more specific conception of the development of the division of labor since Durkheim's propositions have, for the most part, found uncritical acceptance within the theory of ecological organization (Gibbs and Martin, 1962:669). Independent Variables In his discussion of the development of the division of labor Durkheim (1933:262) delineates three major determining factors-population size, physical density, and social density. Because he sets his argument in an evolutionary perspective, a fourth factor-time-can also be said to possess causal implications. While the impact of these four variables has been frequently discussed (Coste, 1899:95-103; McKenzie, 1933:316; Spencer, 1921:471; Stigler, 1951:185; Thompson, 1965:147), it has not been empirically verified although several studies (Keyes, 1958; Marden, 1966; Rogers, 1957) have found a direct association between size and the number of different services or industries extant in a population. And in regard to size, Clemente and Sturgis (1971) discovered a moderate correlation between city population size and one dimension of industrial diversification. Although there has been little other empirical research in the area, on the basis of the theoretical explanations proposed by Durkheim and subsequent human ecologists the following general conceptual hypothesis can

Abstract: Large-scale agent systems have foreseeable applications in the near future. Estimating their macroscopic density is critical for many density-based optimization and control tasks, such as sensor deployment and city traffic scheduling. In this letter, we study the problem of estimating their dynamically varying probability density, given the agents’ individual dynamics (which can be nonlinear and time-varying) and their states observed in real-time. The density evolution is shown to satisfy a linear partial differential equation uniquely determined by the agents’ dynamics. We present a density filter which takes advantage of the system dynamics to gradually improve its estimation and is scalable to the agents’ population. Specifically, we use kernel density estimators (KDE) to construct a noisy measurement and show that, when the agents’ population is large, the measurement noise is approximately “Gaussian”. With this important property, infinite-dimensional Kalman filters are used to design density filters. It turns out that the covariance of measurement noise depends on the true density. This state-dependence makes it necessary to approximate the covariance in the associated operator Riccati equation, rendering the density filter suboptimal. The notion of input-to-state stability is used to prove that the performance of the suboptimal density filter remains close to the optimal one. Simulation results suggest that the proposed density filter is able to quickly recognize the underlying modes of the unknown density and automatically ignore outliers, and is robust to different choices of kernel bandwidth of KDE.