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White © 2005 All rights reserved 50 slides - also viewable on drw conference paper website version 1.3 of 11/12/2005 European Conference on Complex Systems Paris, 14-18 November 2005 Slide2: acknowledgements Thanks to the International Program of the Santa Fe Institute for support of the work on urban scaling with Nataša Kejžar and Constantino Tsallis, and thanks to the ISCOM project (Information Society as a Complex System) principal investigators David Lane, Geoff West, Sander van der Leeuw and Denise Pumain for ISCOM support of collaboration with Peter Spufford at Cambridge, and for research assistance support from Joseph Wehbe. Also thanks to David Krakauer and Luis Bettencourt at SFI in suggesting how our multilayered models of rise and fall of city networks could be guided by sufficient statistics modeling principles and to Lane and van der Leeuw for suggestions on the slides. This study is complemented by others within the ISCOM project concerned with urban scaling and innovation and draws several slides from those projects. Thanks to Peter Spufford for his generous support in providing systematic empirical data on intercity networks and industries in the medieval period to complement the data in his book, Dean Anuska Ferligoj, School of Social Sciences, University of Ljubljana, for five weeks of support for work carried out with Kejžar in Ljubljana in summer, 2005, Céline Rozenblat (ISCOM project) for providing the historical urban size data, and Camille Roth (Polytechnic, Paris) for collaborations on representing evolutions of multiple industries across city netwks. A jointly authored on this project is in draft with Spufford and possibly others.some main approaches and areas of findings: some main approaches and areas of findings 1 Urban scaling: distributional scaling and historical transitions City functions (Geoff West , Luis Bettencourt, José Lobo 2005) City growth and inequality parameters: From Zipf's rank size laws to power laws to a stronger scaling theory of q-exponentials Periodizing: Historical q-periods and their correlates Commercial vs. Financial capital and organization Market equilibrium vs. Structural Inflation 2 Rise and fall of intercity networks (e.g., trade and conflict) Key concept: structural cohesion and its effects, such as market zones and price equilibrium vs. inflation in cohesive cores versus peripheries (White and Harary 2002 SocMeth, Moody and White 2003 ASR) Similarly, effects of network betweenness versus flow centrality on commercial vs. financial capital and institutional organization 3 Interactive dynamics: world population, cities and hinterlands, polities economic growth versus sociopolitical conflict organizational change at macro level and micro level. Outline re: civilizations as dynamic networks General approach: interactive multi-nets, networks among and between different types of entities in time series with changing links and attributesSlide4: City Networks Routes, Capacities Velocities and Magnitudes of trade Organizational transformation of nodes STATES MARKETS from factions & coalitions from structurally cohesive to sovereignty - emergent k-components - emergent Spatiopolitical units Network units (overlap) Co-evolution time-series of Cities and City Networks Interference and attempts at regulation Sources of boundary conflicts begin periodizeSlide5: Geoff West, Luis Bettencourt, José Lobo. 2005 (Pace of City Life): Innovation-Dependent (Superlinear), Linear, and Scale-Efficient (Sublinear) Power Laws Urban Scaling: FunctionsSlide6: Superlinear ~ 1.67 Linear ~ 1 Sublinear ~ .85 ISCOM working paperSlide7: (White, Kejžar, Tsallis, and Rozenblat © 2005 working paper) the next few slides compare the scale K and α coefficients of the power-law y(x) ≈ K x-α (and Pareto β= α+1) with the q-exponential parameters for q slope and scale κ in y(x) ~ [1 + (1–q) x/κ)]1/(1–q), fitted to entire size curves Not a good fit to overall city size distributions Power laws and Zipf’s law might fit upper bin frequencies for city sizes but not the whole curve inset: y = cumulative number of people in these cities Dashed line = portion of distribution that is "power-law“ (but is exaggerated in the upper bins) Horizontal axis x = binned (logs of city size) Vertical axis y = cumulative number of cities at this log bin or higher Urban Scaling: City Sizes α=1β=2 Example: 1950 United Nations data for world cities Slide8: % Urban in Europe fitted q-exponential distributions, q, κ. power law coef. β = 1/(q-1) equals 2 for q = 1.5, thus more equality at the asymptote … more inequality α = 1 at the asymptote: α = 0.24 β = 2 β = 1.24 q = 1.5 q = 1.8 In this segment of the data series the upper bin slope is going from q ~ 2 in 1800 (inegalitarian, α = 1) to q ~ 1.5 (egalitarian) in 2000. If these distributions were actual power laws, they should straight line fits in this log-log graph. The x axis has the city size-bins, e.g., 20.0 = 200,000 people or more. The dotted lines show number of cities in multiples of two: 2,4,8,16,32,etc. The entire city-size distributions for these 18 time periods are fitted here by q and κ ( not just the Zipfian upper size bins) Dotted lines here are city numbers for each size bin. (for 1800) for 2005: City-size bins 1950 Units of 10K 9 Q-exponential scaling ~ .99+ fit to 18 post-1800 and 22 pre-1800 distributions At time t, population y(x) ≈ y(0) [1 + (1–q) x/κ)]1/(1–q), as function of q, κ, binned size x α = 1 β = 2 q = 1.5Slide9: Stylized contrasts and historical examples in unlogged graphs: β ~ 2 α ~ 1 (high) q ~ 1.5 (low) more egalitarian thin tail : like the standard Zipfian β < 2 α < 1 (low) q ~ 2 (high) Inegalitarian fat tail: possibly heterarchical with the Adamic effect Log city bin size Realistic critical feature different than power laws: city size truncation inegalitarian fat tail; e.g., industrial revolution pushes out to fatten smaller towns; hubs in average neighborhoods of average local nghbhood heterogeneity wrt hubs (L Adamic et al 2003) Log cumulative populations in cities at least this bin size egalitarian thin tail; few hubs (bigger towns) in average neighborhoods α ~ 1, high e.g., year 2005 α < 1, low e.g., year 1800 Stylized q-exponentials (note the connection here to networks: city links to other nearby cities)Slide10: β=2 (α=1) long thin tail; greater size equality The q-slopes for all periods are well bounded from β → 1 (inequality, i.e., fat tails) to β =2 (i.e., thin tails, equality) Tails truncate because the city numbers are discrete (dotted line = 1 city), with limits above which there are no larger cities. Truncation at a finite limit allows a power- law distribution to flatten as α (=β-1)→0. This is more realistic than a scale-free model. β → 1 (α → 0) thicker tail; greater size inequality 430 BCE to 1750 Slide11: Kappa detrended World city sizes scaled in 28 reliable-estimate periods, fitted slope q & scale κ (kappa) 2000 1750 1500 1250 1000 750 500 250 0 -250 At time t, population y(x) ≈ y(0) [1 + (1–q) x/κ)]1/(1–q), as function of q, κ, binned size x heterarchy Detrending method: κ increasing and headed to singularity post-2000Slide12: World city sizes scaled in 28 periods, fitted slope q, scale κ (kappa) 2000 1750 1500 1250 1000 750 500 250 0 -250 At time t, population y(x) ≈ y(0) [1 + (1–q) x/κ)]1/(1–q), as function of q, κ, binned size x Time is reversed in the two graphsSlide13: Contiguous time periods (verified by runs test), discrete (1-7) periods egalitarian hierarchy q inegalitarian hierarchy >1950 Mass urbanization World cities phase diagramSlide14: City attributes and distributions Pop. Size Hierarchy Urban Industries plus Commerce, Finance Hinterland Productivity City Networks Routes, Capacities, Markets Velocities and Magnitudes of trade Organizational transformation of nodes, periods; commercial, financial, religious Dynamics from Structural Cohesion Unit Formation (e.g. polities) Demography/Resources Conflicts Co-evolution of Cities and City Networks for the Circum-Mediterranean all major industries and their distributions across cities in the trading city networks are also coded in generational (25 year) intervals, and the capacities of transport routes are similarly coded in 25 year intervals. All-Eurasia coding incomplete. periodizeq-dependent variables: q-dependent variables historical q-correlates? (Circum-Mediterranean) Alternation in inflationary market trends? Evaluated with 13 datasets (near-equilibrium vs. inflation periods from Spufford 1982, Fischer 1996) Alternation of trade hegemony with new q-periods? Evaluated with dates of q-alternations and other periods (commercial vs. financial centers) Alternation of periods of organization forms? Evaluated with Arrighi data, 1994, 5 periods, 1100-1990 (commercial vs. financial capital) Slide16: Summary of historical correlates of hierarchy variable q Slide17: Euro-Hegemon examples (Arrighi 1994) Commercial Financial (hegemonic cities in historic order) Constantinople Venice Genoa Amsterdam London New York Amsterdam Slide18: Given its 13th C betweenness centrality, Genoa generated the most wealth Betweenness centrality in the trade network predicts accumulation of mercantile wealth and emergence of commercial hegemons. e.g., in the 13th century, Genoa has greatest betweeness, greatest wealth, as predicted. Later developments in the north shift the network betweeness center to England. Size of nodes adjusted to indicate differences in betweenness centrality of trading cities in the banking network Betweenness Centralities in the banking network Episodically, in 1298, Genoa defeated the Venetians at sea. Repeating the pattern, England later defeats the Dutch at sea Slide19: Flow centrality (how much total network flow is reduced with removal of a node) predicts the potential for profit-making on trade flows, emergence of financial centers, and (reflecting flow velocities, as Spufford argues) organizational transformations in different cities. Here, Bruges is a predicted profit center, prior to succession by Amsterdam. This type of centrality is conceptually very different. It maps out very differently than strategic betweenness centers like Genoa, which are relatively low in flow centrality. Slide20: Core towns Linking kaufmannskirchen (by Saint name) Distant towns Additional linking kaufmannskirchen Medieval Hanse trading towns had religious brotherhoods under a Patron Saint for a distant church of the same Saint (kaufmannskirch), which hosted the traders and protected their goods. The more distant the trading locations, into foreign lands, the more frequent the construction of matching kaufmannskirchen. Bipartite network cohesion in Hanse saintly brotherhood trade organizationSlide21: time-series data coded by 25 year periods, hegemonic economic organization: C = Commercial capital (e.g., colonizing or diaspora traders) F = Financial capital (e.g., corporate traders) supported propositions: initial C, F => L (low inflation), little or no time lag initial C => I (inegalitarian city hierarchy) initial F => E (egalitarian city hierarchy) L gives way to h (high inflation) within E(galitarian) and I(negalitarian) Inflation Lo/hi Financial Commercial Financial capitalSlide22: time-series data coded by 25 year periods, hegemonic economic organization: C = Commercial capital (e.g., colonizing or diaspora traders) F = Financial capital (e.g., corporate traders) supported propositions: initial C, F => L (low inflation), little or no time lag initial C => I (inegalitarian city hierarchy) initial F => E (egalitarian city hierarchy) L gives way to h (high inflation) within E, I Type of hegemony and inflation as q-correlated temporal variables Inflation Lo/hi Inflation Lo/hi Financial Commercial Financial capitalSlide23: Transaction costs, hegemony and inflation as q-correlated temporal variables Conflict on Land Sea trade routes safer than land, 1318-1453/4+ (Spufford:407) Inflation Lo/hi Landed Armies safe land routes 1500-1650 Maritime Conflicts (Jan Glete) Landed Trade Secure Dominant Routes Sea routes safe French Sov. Peace of Westphalia Baltic conflicts: connection to Novgorod and Russia (lost) Swedish hegemony European access Struggle for Empire: Sea Battles to 1815 Global Maritime Economy Industrial Rev. from 1760 Political Revolutions to 1814 Trade net (low cost) versus (high cost) Maritime (low cost) versus Land routes trade (pop. growth) Financial capital Commercial Slide24: Hierarchy (I) city distributions landed civil conflict, with multiple generation time lag Recode previous slide predict landed inter-national conflict Hegemony-type and inflation as q-correlated temporal variables Conflict on Land Sea trade routes safer than land, 1318-1453/4+ (Spufford:407) Inflation Lo/hi Landed Armies Land Routes safer than sea 1500-1650 Maritime Conflicts (Jan Glete) Landed Trade Secure Sea routes safe French Sov. Peace of Westphalia Baltic conflicts: connection to Novgorod and Russia (lost) Swedish hegemony European access Struggle for Empire: Sea Battles to 1815 Global Maritime Economy Industrial Rev. from 1760 Political Revolutions to 1814 Landed inter-national conflict is protracted (versus) Landed international peace (incl. WW I or II followed by peace) Land routes UNSAFE versus Land routes SAFE Financial capital Commercial Commercial capital competition landed inter-national conflict, with generational time lag Interactive Dynamics Hierarchy Heterarchy Land Routes From Dominant Routes to a Land Routes variable Sea unsafe star bank routesSlide25: Commercial and financial centers as q-correlated temporal variables Inflation Lo/hi Florence Venice Arras Bruges Antwerp Amsterdam London Champaign Fairs Constantinople Genoa Shift of financial center due to civil war of 1480 Industrial center Commerce center Commercial Finance =Blue Red = Financial profit center (Blue = Commercial Finance Red = Medici Bank & profits ; controlled by Florentines) Domestic Fustians (innov.: cotton-linen) Imported cotton, manuf. woven cotton Commercial Financial capital Industry Add: religious centered trade Sea unsafe star bank routes Sea unsafe star bank routes Underwarer star bank routes cohesive bank routes cohesive bank routes cohesive bank routesSlide26: Co-evolution of Cities and City Networks Analyzing cohesion in social groups (Cohesive Blocking): : (Structural) Cohesion is measured by the number of node-independent paths that hold two nodes together. Two nodes with k node-independent paths are k times as resistant to being pulled apart than if they are connected by a single path. A k-component of a graph, or a maximal subgraph that is k-connected (also called a cohesive block of connectivity k), is a maximal subgraph S in which no pair of nodes can be disconnected by removal of k or fewer other nodes in S. The 1-, 2-, and 3-components of a graph G are called, respectively, components, bicomponents and tricomponents of G. Menger’s Theorem: The minimum node cut set (connectivity) of a graph G equals the minimum of the maximum node-independent paths (cohesion) between any two nodes in G. This is one of the deepest theorems in graph theory. If the edges of a graph (network) are weighted (e.g., at unity), the node-independent flow between two nodes is the sum over node-independent paths of minimum weights on these paths. E.g., node-independent flow of 2 between a & b: a b (the graph is 2-connected) Analyzing cohesion in social groups (Cohesive Blocking): Slide28: For example, among medieval merchants and merchant cities of the 13th century, cohesive trade zones (gold nodes) and their potential for market pricing supported the creation of wealth, with states benefiting by marketplace taxation and loans. The Hanse League port of Lübeck at its peak had about 1/6th the trade of Genoa, 1/5th that of Venice; its network had a well documented colonial and religious-brotherhood trade organization. (early slide, merely illustrative, not to scale, network incomplete) Lübeck banking network cohesion Slide29: the banking network, main routes only (again, geographically). the spine of the exchange system is tree-like and thus centralized. It is land based. Linking the four parts was Alessandria, a small stronghold fortification built in 1164-1167 by the Lombard League and named for Pope Alexander III. At first a free commune, the city passed in 1348 to the duchy of Milan. Note again the closeness of Genoa to the center, and the exclusion of Venice. Control networks often rely on unambiguous centralized spines but their operation relies on feedback in cohesive networks. banking network hierarchySlide30: In Northern Europe the main Hanse League port of Lubeck had about 1/6th the trade of Genoa, 1/5th that of Venice. Red 3-components Middle East and its 3-component also With expanded coding and further road identification for the medieval network, 2nd- (gold) and 3rd-order cohesiveness (red nodes) reveals multiple cohesive zones such as those of Western Europe or the Russian plains. Again, this cohesion supported the creation of wealth among merchants and merchant cities, with states benefiting by taxation and loans. Slide31: RISE AND FALL Silk, Jade and Porcelain from China - Spice trade from India and SE Asia - Gold and Salt from Africa The lead-up to the 13th C world-system and its economy was a period of population expansion and then crisis as environmental carrying capacities were reached. In the 14th C, economic depression set in, inflation abated and population dropped, with famines beginning well before the Black Death. After closure of the Golden Horde/Mongol Corridor (1360s), the EurAsian network crashed. To illustrate the effects of structural cohesion in the trade route network on the development of market pricing versus structural inflation, we could start with the AfroEurasian world-system at the end of the pre-classical period in 500 BCE - What came before the medieval networks rise and fall? Slide32: These trade routes mostly form a tree, with a narrow structurally cohesive trading zone (with market potential) from India to Gibraltar Trade networks before 500 BCE were smaller, even more tree-like, and lacking cohesion(figures courtesy of Andrew Sherratt, ArchAtlas): (figures courtesy of Andrew Sherratt, ArchAtlas) Cohesive extension of trade routes leads to a host of other developments…Slide34: Multiconnected regions => structural cohesion variables During classical antiquity trade routes become much more structurally cohesive from China to FranceSlide35: Multiconnected regions => structural cohesion variablesSlide36: Multiconnected regions => structural cohesion variablesSlide37: Some changes in the medieval network from 1000 CE Multiconnected regions => structural cohesion variablesSlide38: to 1500 CE (note changes in biconnected zones of structural cohesion) Project mapping is proceeding for cities and trade networks for all of AfroEurasia and urban industries for Europe in 25-year intervals, 1150-1500 (our technology for cities / zones / trade networks / distributions of multiple industries across cities for each time period includes dynamic GIS overlays, flyover and zoomable web images) Multiconnected regions => structural cohesion variablesSlide39: Co-evolution of Cities and City Networks Scarcity; Inflation; Competition; Sociopolitical violence; Periods of: Slide40: Peter Spufford - in Power & Profit (2002) shows how rises in the velocity of trade in intercity networks causes transformations in organizations. Peter Turchin - in Structure & Dynamics (2005) demonstrates dynamic interactions between governance, conflicts, unraveling, on the one hand, and population oscillations on the other (structural demographic theory) Data sources and dynamic interaction analysesSlide41: Chinese phase diagram (Turchin 2005)Slide42: English sociopolitical violence cycles don’t directly correlate but lag population cycles. Detrended English population cycles, 1100-1900, occur every 300-200 years. (Turchin 2005)Slide43: Turchin tests statistically the interactive prediction versus the inertial prediction for England, Han China (200 BCE -300 CE), Tang China (600 CE - 1000) (Turchin 2005)Slide44: Geoff West, Luis Bettencourt, José Lobo. 2005 (Pace of City Life): Revisiting the Innovation-Dependent Superlinear Case Unsustainable superlinear growth superlinear growth crisis superlinear growth crisis superlinear growth crisis Resetting growth through costly innovation Resetting growth through costly innovation Resetting growth through costly innovationWorld population 'response' to power-law city growth: World population 'response' to power-law city growth Cities and hinterlands context variables Kremer data; Fitted Coefficients of Equation 1, Nt = CN / e(t0 – t) 1250q-dependent variables: q-dependent variables power-law population growth is unsustainable, generates decreasing lengths of oscillations, also general inflection points (e.g., flattening, crisis) World population growth rate is slower with q-flat city growth, but also tends to diminish at the end of each type of q-period. Possibly a failure of innovation rate because leading cities depend on innovation. Slide47: Geoff West, Luis Bettencourt, José Lobo. 2005 (Pace of City Life): Revisiting the Innovation Dependent Superlinear Case World pop. Downturn World urbanization inflections (I have added the correlations of world and NYC population shifts)Slide48: Economic macro variables Stylized facts: 1. Gross World Economic Product grows not in proportion to 1/(time to singularity), as does population, but 1/ /(time to singularity)2 2. Inflation, however, is more sensitive to global and local fluctuations of population above and below its superlinear trend-line, which also correlate with q-periods. (David Hackett Fischer 1996) (Turchin 2005)Slide49: Co-evolution of Cities and City Networks Effects of Inflation of Land on Monetization: Effects of Inflation of Land on Monetization The population and sociopolitical crisis dynamic that drove inflation in the 12th-15th centuries also drove monetization and trade in luxury goods. Inflation of land value created migration of impoverished peasants ejected from the land, demands of money rents for parts of rural estates, and substitution of salaries for payments in land to retainers. (Spufford 2002)Slide51: Adamic, Lada, et al. 2003. Local search in unstructured networks. In, Bornholdt and Schuster, eds., Handbook of Graphs and Networks. Wiley-VCH. Arrighi, Giovanni. 1994. The Long Twentieth Century. London: Verso. Fischer, David Hackett. 1996. The Great Wave: Price Revolutions and the Rhythm of History. Oxford University Press Sherratt, Andrew. (visited) 2005. ArchAtlas. http://www.arch.ox.ac.uk/ArchAtlas/ Spufford, Peter. 2002. Power and Profit: The Merchant in Medieval Europe. Cambridge U Press. Tsallis, Constantino. 1988. Possible generalization of Boltzmann-Gibbs statistics, J.Stat.Phys. 52, 479. Turchin, Peter. 2005. Dynamical Feedbacks between Population Growth and Sociopolitical Instability in Agrarian States. Structure and Dynamics 1(1):Art2. http://repositories.cdlib.org/imbs/socdyn/sdeas/ West, Geoff, Luis Bettencourt, José Lobo. 2005. The Pace of City Life: Growth, Innovation and Scale. Ms. Santa Fe Institute, Project ISCOM. Douglas R. White, Natasa Kejzar, Constantino Tsallis, Doyne Farmer, and Scott White. 2005. A generative model for feedback networks. Physica A forthcoming. http://arxiv.org/abs/cond-mat/0508028 White, Douglas R., Natasa Keyzar, Constantino Tsallis and Celine Rozenblat. 2005. Ms. Generative Historical Model of City Size Hierarchies: 430 BCE – 2005. Ms. Santa Fe Institute. White, Douglas R., and Peter Spufford. (Book Ms.) 2005. Medieval to Modern: Civilizations as Dynamic Networks. Cambridge: Cambridge University Press. ReferencesSlide52: City Networks Routes, Capacities Velocities and Magnitudes of trade Organizational transformation of nodes STATES MARKETS from factions & coalitions from structurally cohesive to sovereignty - emergent k-components - emergent Spatiopolitical units Network units (overlap) Co-evolution of Cities and City Networks Interference and attempts at regulation Sources of boundary conflictsCumulative population is used because by taking only the populations in each size bin in different growth periods differential city growth generates the dogs-eaten-by-snake phenomena:: Cumulative population is used because by taking only the populations in each size bin in different growth periods differential city growth generates the dogs-eaten-by-snake phenomena: Actual 1965 data on distribution at one time smoothed cumulative distributions A cumulative distribution has with more population in the lower bins requires curve fitting such as y ~ log (x) with lower bins weighted proportional to population. The upper bins show bias toward longer tails compared to semi-log but less than a power-law tendency, as in these data. “innovative bulges” in city sizes move thru timeSemilog y ~ log(x) scaling r2~.99 fits: Semilog y ~ log(x) scaling r2~.99 fits 1950 to 2005 Because the curves bend at the tails, but the Zipf parameter varies considerably around ~ 1, these data are be nicely modeled by q-exponentials with q and size parameters that are more comparable over time. 1950 and earlier Total number of people in cities at or above the city size bin city size bins, logged Which is an integral of Zifp's law, approximately a log if the exponents are exactly 1) Changes in slope over time are not directly comparable over historical periods: they tend to flatten further back in time but irregularly.Slide56: % Urban in Europe fitted q-exponential distributions, q, κ. power law coef. β = 1/(q-1) => (= 2 for q = 1.5) thus more equality at the asymptote q =1.81 q =1.61 q =1.70 q =1.57 q =1.50 q =2.01 q =2.08 q =2.01 q =1.84 q =2.1 q =1.9 more inequality α = 1 at the asymptote: α = 0.24 β = 2 β = 1.24 q = 1.5 q = 1.8 In this segment of the data series the upper bin slope is going from q ~ 2 in 1800 (inegalitarian, α = 1) to q ~ 1.5 (egalitarian) in 2000. If these distributions were actual power laws, they would be best-fitted by a straight line in this log-log graph. The x axis has the city size-bins, e.g., 20.0 = 200,000 people or more. The dotted lines show number of cities in multiples of two: 4, 8,16,32,etc. The entire city-size distributions for these 18 time periods are fitted by q and κ, not just the upper size bins Dotted lines here are city numbers for each size bin. (for 1800) (for 2005) City-size bins 1950 Units of 10K 9 Q-exponential scaling ~ .99+ fit At time t, population y(x) ≈ y(0) [1 + (1–q) x/κ)]1/(1–q), as function of q, κ, binned size x α = 1 β = 2 q = 1.5 You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.