Hierarchical Diffusion

5 Key excerpts on "Hierarchical Diffusion"

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  eBook - ePub

  Modeling Urban Dynamics

  Mobility, Accessibility and Real Estate Value

  • Marius Thériault, François Des Rosiers, Marius Thériault, François Des Rosiers(Authors)
  • 2013(Publication Date)
  • Wiley-ISTE

    (Publisher)

  These phases, which are continuous in time, are classically represented (on a Cartesian graph with a cumulative number of elements attained placed in ordinate and time in abscissa) by an S curve. This curve is generally modeled by a logistic function, but can also be modeled by other types of functions.

  8.4.2. The spatiotemporal diffusion process

  The chronological approach implicitly implies reducing the importance of the spatial conditions and nature of the diffusion and that which they can modify in the process. From a geographical point of view, we can differentiate diverse forms of diffusion: through expansion (i.e. the progression of a forest fire), migration (i.e. the relocalization of production), or contagion of proximity (spatial surroundings or Hierarchical Diffusion).

  Hägerstrand [HÄG 67] was the first to build a formal model of the spatiotemporal diffusion of an innovation. It was a question of the progressive adoption of a public grant by farmers to transform a forest into pasture, observed and simulated in the Asby district in Sweden between 1928 and 1932. The zone was cut evenly into square grids of 5 km on each side, and each cell contained

  ni

  farmers. At one given moment, each cell contained

  ki

  adopters and

  ni - ki

  potential adopters. A “spatial field of contact ” is defined thus: from each cell i , the probability of drawing a cell j at random decreases with its distance to i . The sending of a message between cells i and j takes place as many times as there are adopters in the cell i (

  ki

  times). The procedure is applied to all the cells in the zone and iterated. At the end of the iterations, we are left with a map of the numbers of adopters and chronology of the adoption process.

  In a study of the diffusion of AIDS in the USA, Gould [GOU 92, GOU 93] pointed out two spatial modalities: hierarchical diffusion (from the large centers along the urban hierarchy toward smaller centers); and diffusion by contagion

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  Spatial Simulation

  Exploring Pattern and Process

  • David O'Sullivan, George L. W. Perry(Authors)
  • 2013(Publication Date)
  • Wiley-Blackwell

    (Publisher)

  Chapter 5

  Percolation and Growth: Spread in Heterogeneous Spaces

  ‘Spread’ encompasses a wide range of environmental and social processes and ensuing patterns, occurring across a wide range of spatial and temporal scales. For example, wildfire spread, spread of forest into grassland habitats, encroachment of urban environments into the wildland interface, the movement of invasive species, the spread of epidemics such as the black death and the movement of gossip through social networks are all processes that can be represented using simple spatial models. In this chapter we will look at two broad types of spatial model that have been used to represent these types of dynamics: percolation and growth (or aggregation) models. These two approaches provide a broad framework for discussing issues relating to the dynamics of spread processes and the patterns formed by them. We will conclude by considering how we might apply these general approaches to more targeted questions about specific environmental and social systems.

  5.1 Motivating examples

  Soetaert and Herman (2009 ) recognise two fundamental spread processes: advection and diffusion. Advection is the directed movement of a substance in a fluid (for example transport of pollutants in groundwater), whereas diffusion is the random movement of materials from regions of high concentration to regions of low concentration (for example the movement of oil from a ruptured tank on a ship to the surrounding environment). Soetaert and Herman (2009 , pages 82ff.) consider the formulation of models of advective and diffusive fluxes in one, two and three dimensions in continuous and discrete space in detail. While there are fundamental differences in the physico-chemical mechanisms that underpin advection and diffusion, pragmatically, in environmental and social settings it may be difficult to distinguish them (similarly, it is hard to distinguish bias and localised correlation in random walks, see Section 4.2.4). Thus, it is probably more useful to think about the processes that drive spread per se

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  The Diffusion of Information and Communication Technologies

  • Ewa Lechman(Author)
  • 2017(Publication Date)
  • Routledge

    (Publisher)

  Also, it may be defined as the ‘mechanism that spreads successful varieties of products and processes throughout an economic structure and displaces wholly or partially the existing inferior varieties’ (Sarkar, 1998, p. 131). This time-related and dynamic process allows for putting into extensive use predominantly radical innovations (the process of emergence of invention, by definition, is prior to diffusion), which as claimed by Freeman (1991) are mainly discontinues events, but actually they are in the very center of a wide variety of diffusion studies. The process of technology diffusion preconditions how fast ‘pioneering technologies’ are being adopted and used by economic agents, spread among individuals and hence put to productive and organizational use. Technology diffusion reflects the process of spreading new inventions across individuals and companies. Also, it may be defined as the process of spreading innovations through the population and potential adopters (Rogers, 1983). Grübler and Nakićenović (1991) argue that the process of diffusion translates the enormous potential encapsulated in radical innovations into real economic change. In a similar vein, Peres et al. (2010) consider the process in the wider socio-economic context and write that ‘innovation diffusion is the process of market penetration of new products and services, which is driven by social influence. Such influences include all of the interdependencies among consumers that affect various players with or without their explicit knowledge’ (ibid., p. 92). Such an approach to the process of technology diffusion goes far beyond its purely mechanical aspects and emphasizes that the process of propagation of new ideas and knowledge embodied in innovations is, first, socially and economically driven and preconditioned, and, second, to a large extent, it is endogenously led. Many claim that the process of technology diffusion is—to a large extent—deterministic and mechanical in its nature (see, inter alia, works of Geroski, 2000 or Ismail, 2015) and may occur unintended by individuals. However, when going deeper, detailed study of the process of technology diffusion unveils its complexity, temporal and unique characteristics, as well as multiple interdependencies that it generates across societies and economies. Undeniably, technology diffusion results in multilevel adaptation of technological novelties and thus underlines social, organizational and, overall, economic processes. Ausubel (1991) notes that diffusion in itself demonstrates some countervailing effects, as it forces homogenization (as similar technologies are used by increasing the number of users) and, reversely, it drives heterogenization of individuals and/or companies, which, because of adoption of new technologies, diversify their economic activities.

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  High Dimensional Space to Formulate Marriage and Birth Functions

  • Shuichirou Ike(Author)
  • 2022(Publication Date)
  • CRC Press

    (Publisher)

  It must be emphasized that diffusion dynamics are fundamentally the stochastic fluctuation of some spatial state from a space to its neighborhood. In this fundamental schema, there is no scope for the interchange of information or ideas.

  Figure 1.2 The normal gradient of telephone traffic for outgoing exchange located within Kinda-Ydre.

  T. Hägerstrand, Innovation Diffusion as a Spatial Process [30 ], p. 210.

  The transmission of information is generally imagined as ideas flying past each other, such as in transmission control protocol/internet protocol (TCP/IP) packets on the Internet. However, this idea is not adequate for explaining sociological objects. True information transmission is a precise alteration of the state of destinations. For example, however enthusiastically teachers address their students, if the state of the students brains does not change, no information is transmitted at all.

  It was natural that, in his study of innovation diffusion, Hägerstrand assumed that there exists something that spreads in space. The process of diffusion of phones and automobiles in geographical segments is increasing. Everybody assumes that innovative goods diffuse in space.

  However, this postulation is too homespun to effectively analyze human behavior. Is it true that automobiles diffuse in space during the diffusion process? Even in Fisher’s theory, advantageous genes do not strictly transfer in space. In terms of social phenomena, no single entity moves from human to human. In any case, social diffusion is not a bucket brigade of ideas, meaning, and information. It is entirely untrue that some infectious information is transmitted from one brain to another; this is only a metaphor.

  Nothing spreads precisely in space. Hägerstrand emphasized the “neighborhood effect,” but he failed to capture the actual principles of diffusion. The most essential concept is that at the next sequential time point, neighboring spaces either do or do not have the goods in question (such as phones). These probabilities are highly essential and are theoretical objects of the reaction-diffusion theory. They are governed by the previous neighboring state of diffusion. Based on this, a mapping can be used to form a mathematical definition of social diffusion.

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  Interaction and Connectivity in the Greater Southwest

  • Karen Harry, Barbara J. Roth(Authors)
  • 2019(Publication Date)
  • University Press of Colorado

    (Publisher)

  chapter 5 , this volume for diffusion resulting from the movement of people).

  Social network analysis, currently being applied by a number of archaeologists, especially in the Southwest, also has much to contribute to understanding the diffusion of cultural practices. A broad field of study initially developed in sociology, archaeological studies have used material culture distributions to examine networks of social relationships and their influence on cultural developments (Borck et al. 2015; Crabtree 2015; Mills and Peeples, chapter 3 , this volume). Social network analysis uses data that are similar to those used in studies of trade and exchange, but within a theoretical framework that considers many aspects of the nature of connections among actors in the network, such as strength of ties between and among “nodes,” the prestige of innovators, and how innovators are related to one another (through direct ties or structurally similar social positions). Mills and Peeples (chapter 3 , this volume) provide an illustration of the power of network analysis for understanding how cultural practices were transmitted.

  Dissecting Diffusion

  Intergroup transmission processes similar to diffusion have been studied in other fields such as biology (exploring gene flow), linguistics (“contact-induced language change”; Thomason and Kaufman 1988:47), sociology (Rogers 2003; Mills and Peeples , this volume), and geography. The basic linking concept is the flow of genes, language, or cultural practices through contact among interacting groups of people (a similar concept in epidemiology involves the spread of disease [Fass 2003; see also Jones 2014]). Each of these fields has recognized barriers to transmission or conditions that encourage transmission. In the social sciences and linguistics, barriers often consist of attitudes toward the donor group or toward the introduced practice. Transmission can be accelerated when practices are introduced by people of higher status or when they are seen as particularly advantageous. Linguists have examined social factors that condition language change and identified a number of factors that affect the diffusion of culture traits: the intensity of contact between groups, group size, the role of prestige (languages with higher prestige predominate over those of lower prestige), the influence of colloquial usage, and positive or negative attitudes among speakers about potential donor languages and culture (Kroskrity 1993; Thomason and Kaufman 1988). Sociology has developed a somewhat different set of factors that include how easy the practice is to observe and experiment with (Mills and Peeples, chapter 3

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