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Act Talk - Diego Garlaschelli: Complex networks and econophysics
 

Act Talk - Diego Garlaschelli: Complex networks and econophysics

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Over the last decades, an interdisciplinary community of scientists, especially physicists, has carried out both empirical and theoretical investigations aimed at understanding economic and financial ...

Over the last decades, an interdisciplinary community of scientists, especially physicists, has carried out both empirical and theoretical investigations aimed at understanding economic and financial systems within the framework of complex systems. This approach, which defines the so-called field of Econophysics, differs from the one traditionally adopted in mainstream economics in various respects. First of all, emphasis is put on induction from empirical evidence to theoretical models, rather than deduction from strict and often ureasonable mathematical assumptions about the expected behaviour of individuals. Second, the preferred objects of analysis are large socio-economic systems with many uderlying units, which often interact with each other forming intricate networks with a complex topology. In this talk, I will briefly introduce various examples of complex networks encountered in Econophysics, and then focus in particular on the World Trade Web formed by the import-export relationships among all world countries. I will conclude with a discussion of the implications that recent results about the properties of the World Trade Web have for international macroeconomics

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    Act Talk - Diego Garlaschelli: Complex networks and econophysics Act Talk - Diego Garlaschelli: Complex networks and econophysics Presentation Transcript

    • Interdisciplinary challenges:Complex Networks and EconophysicsDiego GarlaschelliAssistant ProfessorLorentz Institute for Theoretical PhysicsLeiden Institute of Physicsgarlaschelli@lorentz.leidenuniv.nl
    • Econophysics and networksVertices = assets traded in the stock marketLinks = equal-time correlationsFrom synchronouscorrelationsto distances:↑Minimum Spanning Tree
    • Vertices = assets traded in the stock marketLinks = delayed correlationsDelayed correlationsDirected network of influenceEconophysics and networks
    • Italian Stock Market (2002)Vertices = companiesLinks = shareholdings (who owns whom)Econophysics and networks
    • Vertices = boards of directorsLinks = interlock (shared directors)Econophysics and networks
    • Austrian Banks (2000-2003)Vertices = banksLinks = liabilityEconophysics and networks
    • The World Trade WebVertices = world countriesLinks = trade relationshipsEconophysics and networks
    • Product space of worldeconomyVertices = commoditiesLinks = similar trade patterns by countriesEconophysics and networks
    • Network description: added value?Example (WTW):1) Does the network approach add nontrivial information to traditional international-economics analyses that explain trade in terms of country-specific variables only?2) In network jargon: are higher-order topological properties (indirect interactions,n-steps-away) explained by local ones (direct interactions, 1-step-away)?Fix degrees(1st order)Study effect on degree correlations(2nd order)Study effect on clustering properties(3rd order)
    • Rewiring the WTW: 4 choices of local constraintsdegreein-degree &out-degreestrengthin-strength &out-strengthWe employ a maximum-entropy method:Squartini, Garlaschelli – arxiv:1103.0701Squartini, Fagiolo, Garlaschelli – arxiv:1103.1243Squartini, Fagiolo, Garlaschelli – arxiv:1103.1249
    • (average number of trade partners of country i’s trade partners)- Both the observed disassortativity and the temporal evolution of ANNDare fully explained by the degree sequence (red=real, blue=randomized).- Focusing on local properties captures higher-order patterns.Binary undirected WTW (constraint = degrees)Degree-degree correlations:
    • (fraction of country i’s trade partners that are mutually connected)- Both the observed profile and the temporal evolution of clusteringare fully explained by the degree sequence (red=real, blue=randomized).- The degree sequence is maximally informative and should be reproduced by models!Binary undirected WTW (constraint = degrees)Clustering Coefficient:
    • Arms Coffee & TeaPlastics Optical inst.Nuclear react. Top 14Arms Coffee & TeaPlastics Optical inst.Nuclear react. Top 14Binary undirected WTW – disaggregated commoditiesDegree correlations vs Degree: Clustering vs Degree:- Note: from a) to f), the volume of trade and level of aggregation increases.- The results obtained in the aggregated case are robust to disaggregation.- Commodity-specific degree sequences are still maximally informative!
    • Same as in the binary undirected case: perfect accordance (red=real, blue=randomized).Binary directed WTW (constraint = in & out degrees)Average Nearest Neighbour Degree (ANND, 4 types):
    • Same as in the binary undirected case: perfect accordance (red=real, blue=randomized).Binary directed WTW (constraint = in & out degrees)Clustering Coefficients (4 types, see Fagiolo PRE 2007):
    • Binary directed WTW – disaggregated commoditiesTot.ANND vs Tot.Degree: Tot.Clustering vs Tot.Degree:- Note: from a) to f), the volume of trade and level of aggregation increases.- The results obtained in the aggregated case are robust to disaggregation.- Commodity-specific degree sequences are still maximally informative!Arms Coffee & TeaPlastics Optical inst.Nuclear react. Top 14Arms Coffee & TeaPlastics Optical inst.Nuclear react. Top 14
    • (average bidirectional trade intensity of country i’s trade partners)Scatter plot: ANNS vs strength (2002); ANNS mean & 95% conf. int. (1992-2002)- Both the observed disassortativity and the temporal evolution of ANNSare not explained by the strength sequence (red=real, blue=randomized).- Focusing on local properties only (strength sequence = total trade of countries)does not capture higher-order patterns.- As the formula shows, deviations are in the topology (real sparser than random)Weighted undirected WTW (constraint = strengths)Strength-strength correlations (ANNS):
    • (relative intensity of interconnections among country i’s trade partners)Scatter plot: clustering vs strength (2002); Clust. mean & 95% conf. int. (1992-2002)- Partial accordance, improving over time (red=real, blue=randomized).- However deviations in the topology (denominator) and in the weigths (numerator)are both large, but largely compensate each other.- Deviations from the null model are more evident when disaggregating (see next).Weighted undirected WTW (constraint = strengths)Weighted Clustering Coefficient:
    • Weighted undirected WTW – disaggregated commoditiesStrength correlations vs Strength: W.Clustering vs Strength:- Note: from a) to f), the volume of trade and level of aggregation increases.- Sparser and less aggregated commodities are more scattered.- Local properties become less informative as sparseness and resolution increase.Arms Coffee & TeaPlastics Optical inst.Nucl.react. Top 14Arms Coffee & TeaPlastics Optical inst.Nucl.react. Top 14
    • Scatter plots: ANNS vs strength (2002); ANNS mean & 95% conf. int. (1992-2002)Same as in the weighted undirected case: no accordance (red=real, blue=randomized).Weighted directed WTW (constraint = in & out strengths)Strength correlations (ANNS, 4 types):
    • Scatter plots: clustering vs strength (2002); Clust. mean & 95% conf. int. (1992-2002)Improved accordance with respect to the undirected case (red=real, blue=randomized).Weighted directed WTW (constraint = in & out strengths)Clustering Coefficients (4 types, see Fagiolo PRE 2007):
    • Arms Coffee & TeaPlastics Optical inst.Nucl.react. Top 14Weighted directed WTW – disaggregated commoditiesTot.ANNS vs Tot.Strength: Tot.W.Clustering vs Tot.Strength:- Note: from a) to f), the volume of trade and level of aggregation increases.- Sparser and less aggregated commodities are more scattered.- Local properties become less informative as sparseness and resolution increase.Arms Coffee & TeaPlastics Optical inst.Nucl.react. Top 14
    • InterpretationThe WTW as a binary network:1) Local constraints (direct interactions) fully explain higher-order properties (indirectinteractions);2) This finding holds for both directed and undirected representations, and over time;3) It also holds for disaggregated commodities with different volume and resolution;4) Two consequences:3a) country-specific properties (number of trade partners) fully capture the WTW;3b) theories and models of trade should aim at explaining the degree sequence,which is maximally informative and encodes all the observed topology.The WTW as a weighted network:1) Local constraints (direct interactions) do not completely explain higher-orderproperties (indirect interactions);2) The real WTW is sparser and more disassortative than explained by local trade;3) This finding holds for both directed and undirected representations, and over time;4) Deviations from the null model increase as sparser and less aggregated commodityclasses are considered;5) Two consequences:4a) country-specific properties (total trade of countries) do not capture the WTW;4b) again, the topology deserves more attention in models of trade, as it isresponsible for most of the empirical deviations from the expected behavior.
    • The binary topology of the World Trade Web can be completely reproducedusing only the knowledge of the GDP of each country (“fitness model”)• Garlaschelli, Loffredo Physical Review Letters 93, 188701 (2004)• Garlaschelli, Loffredo Physica A 355, 138 (2005)• Garlaschelli, Di Matteo, Aste, Caldarelli, Loffredo European Physical Journal B 57,159 (2007)• Garlaschelli, Loffredo Physical Review E 78, 015101(R) (2008)GDP data  connection probability expected topologyWTW data  test the modelLooking back at previous results from a new perspectiveDirectionality and reciprocity can also be taken into account and reproduced.
    • • Garlaschelli, Battiston, Castri, Servedio, Caldarelli, Physica A 350, 491 (2005).• Caldarelli, Battiston, Garlaschelli, Catanzaro, Lecture Notes in Physics 650, 399 (2004).• Battiston, Garlaschelli, Caldarelli, in Nonlinear Dynamics and Heterogeneous Interacting Agents (2005).• Caldarelli, Battiston, Garlaschelli, in Practical Fruits of Econophysics (Springer, 2006).(links are drawn from ownedcompanies to shareholders)Italian Stock Market(MIB) 2002Effects of wealth on topology: Shareholding Networks
    •  ijijiijjijiii (t)wJ(t)wJ(t)(t)wη(t)wEffects of topology on wealth: Transaction networksReal GDP distributions:Bouchaud-Mézard model:Empty graph: Complete graph:PajekMixed (log-normal + power-law)Core-periphery network:• Garlaschelli, Loffredo, Physica A 338, 113 (2004)• Garlaschelli, Loffredo, Journal of Physics A 41, 224018 (2008)
    • ‘Food webs’: Networks of interactions among biological speciesFood Webs• Garlaschelli, Caldarelli, Pietronero, Nature 423, 165 (2003)• Garlaschelli, Caldarelli, Pietronero, Nature 435, E1 (2005)• Garlaschelli, Sapere 6, year 69 (2003)• Garlaschelli, European Physical Journal B 38(2), 277 (2004)• Caldarelli, Garlaschelli, Pietronero, Lecture Notes in Physics 625, 148 (2003)St. Martin St. Mark Grassland SilwoodYthan 1 LittleRockYthan 2Similar allometric scaling lawsfound in Mimimal Spanning Treesobtained from real food webs(common organising principle?):C(A) Aηη = 1.13  0.03
    • Analytical solution:Interplay between topology and dynamics:coupling Extremal Dynamics (Bak-Sneppen model) with the Fitness Model.Naturally generates scale-free networks with clustering and correlations.Self-Organized Adaptive Network EvolutionDynamical processTopological evolutionx1 x2x3x4x5x6x7x8x9x10• Garlaschelli, Capocci, Caldarelli, Nature Physics 3, 813-817 (2007)• Caldarelli, Capocci, Garlaschelli, Eur. Jour. of Physics B 64, 585-591 (2008).
    • • Garlaschelli, Loffredo, Physical Review Letters 93, 268701 (2004)• Garlaschelli, Loffredo, Physical Review E 73, 015101(R) (2006)Reciprocity of Directed NetworksReciprocity = tendency to form mutual connections.Traditional measure of reciprocity in social network analysis:Problem:networks with different link densities havedifferent null values of r: rnull=L/N(N-1)(so they cannot be compared with each other)Our new measure of reciprocity (correlation coefficient):This unbiased quantity allows cross-network comparisons126453
    • Comparing thereciprocity ofreal networksWTWWWWNeuralEmailMetabolicFood WebsWordsFinancialResults:-Real networks alwaysdisplay a nontrivial degreeof reciprocity,while models do not.- Networks of the same kinddisplay similar values of thereciprocity, so thatreciprocity classifies realnetworks.-For some networks, it ispossible to characterize thereciprocity structure moreaccurately.Garlaschelli, Loffredo Phys. Rev. Lett. 93,268701(2004)