During the course -Network Types (Small World, Scale Free, Random) -Network Models (Erdos-Renyi,...

During the course-Network Types (Small World, Scale Free, Random)-Network Models (Erdos-Renyi, Scale-Free, Hierarchical Networks, Duplication Divergence)-Network Properties (Degree, Degree Distribution, Clustering, Degree Correlations, Rich Club Phenomena, Average Path Length, Diameter, Community Structure etc…)-Dynamical Properties (Failure and attack tolerance, epidemic thresholds, etc..)-Social Systems Team assembly and the invisible college, the dynamics of social ties and groups-Biological Systems Molecular Networks (PPI, Metabolic), Disease Networks.

We discovered that it was a bit too much for only seven sessions

Networks, Complexity and Economic Development

How can we describe the economic development of nations?

GDP per capita

Labor, Land, Capital, Technological Sophistication

Production Function

Robinson, J. (1953) The production function and the theory of capital, Review of Economic Studies, vol XXI, 1953, pp. 81-106

Technical Change and the Aggregate Production Function

RM Solow - The Review of Economics and Statistics, 1957

Designer Programmer Hardware Knowledge

Webpage

Mechanic

FashionableElectronic

Southern CaliforniaRich people toys

CA Hidalgo, B Klinger, A-L Barabasi, R Hausmann.Science (2007)

Building the ForestBuilding the Forest

d()=F(C,N,N,N)

corr()=(CN-NN)/sqrt((N-N) (N-N) NN)M.I.()=H()+H()-H()R.R.()= CN/NN

Proximity()= min(C/N, C/N)

Product

Maximum Spanning Tree (MST)

Threshold = 0.5

Number of Links = 2850

Threshold = 0.55

Threshold = 0.6

Threshold = 0.7

Threshold = 0.55

Patterns of Comparative Advantage

How do monkeys jump?

Malaysia 1975

Malaysia 1980

Malaysia 1985

Malaysia 1990

Malaysia 1995

Malaysia 2000

1975 1985 2000

High density ofMonkeys around this tree

Low density ofMonkeys around this tree

Countries are more likely to jump towards products that are close by

Malaysia 1990Chile 1990

High Densityin Malaysia

Low DensityChile

High Densityin Chile

Low Densityin Malaysia

Malaysia 2000Chile 2000

Exported byMalaysia

Not ExportedBy Chile

Exported byChile

Not exportedby Malaysia

H=Average Density in Countries that transitioned into the Product / Average Density in Countries that did not transition into the product

Society Products

A similar story….

What is matter made of?

Dimitri Mendeleev

Johann Döbereiner

John Newlands

Alexandrede Chancourtois

How good is your neighborhood?

First economic quantification

Country A

Country B

E=- Salog(Sa)

H= S2a

D= Sa F(Sa)

1006 product categories

sQuantifying Economic Complexity

Ma= 1 if country a exports product

Method of Reflections

Product 1

Country C1

Country C2

Country C3

Product 2

Product 3

Product

Degree (Countries) Degree (Products)

Diversification Ubiquity

Product 1

Country C1

Country C2

Country C3

Product 2

Product 3

Product

Country C1

Country C2

Country C3

k1,1=7/3

k2,1=2

k3,1=3

k1= Standardness: Average ubiquity of products exported by a country

Mirror

Product 1

Product 2

Product 3

Product

Country C1

Country C2

Country C3

Product 1

Product 2

Product 3

Product

1= Complexity: Average diversification of a products’ exporters

Country Variables Product Variables

Diversification k

Standardness k1

Poorly Diversified& Producing Common

Products

Highly Diversified& Producing Common

Products

Highly Diversified& Producing

Exclusive Products

Poorly Diversified& Producing Rare

Products

Method of Reflections: k-k1 diagram

Ubiquity

Produced in Few,Highly Diversified,

Countries

Produced in ManyHighly Diversified

Countries

Produced in ManyNon Diversified

Countries

Produced in FewNon-Diversified

Countries

Method of Reflections: diagram

Complexity

Method of Reflections: diagram

Method of Reflections: Null Models

Method of Reflections: k-k1 diagram and null models

Method of Reflections: k-k2, k1-k2 diagrams and null models

Method of Reflections: diagram and null models

Method of Reflections: diagrams and null models

Method of Reflections: k, k1 and GDP per capita (ppp)

Method of Reflections: and PRODY

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)PredictedVariable

Growth(85,95)

PredictorsGDP per capita

ppp(1985)

-0.00176 0.000993 -0.00206 -0.00154 -0.00249 -0.00223 -0.00470 -0.00233 -0.00244 -0.00238 -0.00242

(-0.794) (0.533) (-0.882) (-0.497) (-0.735) (-0.688) (-1.478) (-0.758) (-0.849) (-0.804) (-0.831)Entropy(1985)

0.00660*** 0.00828** 0.00200 0.00322

(3.650) (2.600) (0.931) (0.896)Herfindahl

(1985)-0.0273*** 0.0116 -0.00414 0.00723

(-2.765) (0.760) (-0.406) (0.454)k

(1985)6.62e-05**

(2.080)k1

(1985)

-0.000612

(-0.749)k4

(1985)

0.00169***

(2.866)k5

(1985)

0.0321*

(1.737)k8

(1985)

0.0338***

(3.075)k9

(1985)

0.890***

(2.713)k18

(1985)

0.401*** 38.88*** 35.05** 37.26*** 35.57***

(3.453) (2.952) (2.618) (2.849) (2.643)k19

(1985)

1127*** 1017** 1080*** 1033***

(2.928) (2.603) (2.829) (2.632)Constant 0.0114 0.0137 0.00650 0.0338 -0.735* -19.29*** -69.21*** -23801*** -21475** -22808*** -21801***

(0.751) (0.776) (0.437) (0.922) (-1.883) (-2.807) (-3.454) (-2.940) (-2.610) (-2.834) (-2.633)N 97 97 97 97 97 97 97 97 97 97 97

Adjusted R2 0.195 0.115 0.192 0.118 0.206 0.247 0.202 0.274 0.274 0.268 0.268

Method of Reflections: 20 year Growth

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)

PredictedVariable

Growth(85-95--05)

Growth(85-95-05)

PredictorsGDP per capita

ppp(85,95)

-0.00235 0.000334 -0.00246 0.00112 -0.00395** -0.00311* 0.00310** -0.00119 -0.00346* -0.00229 -0.00343*

(-1.322) (0.209) (-1.349) (0.595) (-2.062) (-1.695) (2.188) (-0.707) (-1.899) (-1.327) (-1.850)Entropy(85,95)

0.00699*** 0.00759*** 0.00458*** 0.00434

(4.962) (2.985) (3.002) (1.648)Herfindahl

(85,95)-0.0325*** 0.00422 -0.0210** -0.00162

(-3.890) (0.285) (-2.494) (-0.112)k

(85,95)9.75e-05***

(3.967)k1

(85,95)0.000916**

(2.543).k4

(85,95)0.00102***

(5.577)k5

(85,95)0.00329***

(5.971)k8

(85,95)0.00577***

(5.056)k9

(85,95)0.0152***

(5.594)k18

(85,95)-0.000660*** 0.455*** 0.310*** 0.375*** 0.311***

(-3.577) (4.306) (2.705) (3.428) (2.695)k19

(85,95)1.158*** 0.789*** 0.954*** 0.792***

(4.312) (2.709) (3.433) (2.699)Constant 0.0171 0.0226 0.0153 -0.0186 -0.168*** -1.178*** 0.102*** -96.21*** -65.48*** -79.20*** -65.78***

(1.356) (1.602) (1.087) (-0.971) (-6.137) (-5.215) (3.107) (-4.308) (-2.705) (-3.428) (-2.695)Observations 221 221 221 221 221 221 221 221 221 221 221Adjusted R2 0.113 0.077 0.109 0.085 0.170 0.160 0.068 0.137 0.168 0.158 0.164

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)

Predicted Variable

Growth(85-90-95-00-

05)Predictors

GDP per capita ppp

(85,90,95,00)-0.00269* 0.000292 -0.00286* 0.000361 -0.00393** 0.00224* 0.00326** 0.00310** -0.00257* 0.000281 -0.00275*

(-1.732) (0.211) (-1.785) (0.220) (-2.431) (1.767) (2.553) (2.479) (-1.686) (0.207) (-1.749)Entropy

(85,90,95,00) 0.00798*** 0.00885*** 0.00759*** 0.00851***

(6.280) (3.760) (6.060) (3.680)Herfindahl

(85,90,95,00) -0.0373*** 0.00602 -0.0351*** 0.00636

(-4.970) (0.440) (-4.765) (0.474)k

(85,90,95,00) 0.000121***

(5.351)k1

(85,90,95,00) 0.000953***

(2.853)k4

(85,90,95,00) 0.00113***

(7.074)k5

(85,90,95,00) 0.00260***

(5.694)k8

(85,90,95,00)0.00102***

(3.474)k9

(85,90,95,00)0.00312***

(5.504)k18

(85,90,95,00) -0.000265 0.000632** 0.000673** 0.000647** 0.000676**

(-1.147) (2.131) (2.359) (2.234) (2.365)k19

(85,90,95,00) 0.00280*** 0.00259*** 0.00265*** 0.00260***

(4.671) (4.494) (4.523) (4.493)Constant 0.0166 0.0236* 0.0142 -0.0160 -0.173*** -0.224*** 0.0349 -0.163*** -0.142** -0.132** -0.145***

(1.497) (1.910) (1.144) (-0.933) (-7.646) (-4.198) (0.889) (-2.846) (-2.576) (-2.355) (-2.611)

Observations 451 451 451 451 451 451 451 451 451 451 451

Adjusted R2 0.090 0.062 0.089 0.071 0.136 0.071 0.013 0.057 0.127 0.101 0.125

Method of Reflections: 5 year growth, fixed country effects(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)

Predicted Variables

Growth(85-90-95-00-

05)Predictors

GDP per capita ppp

(85,90,95,00)

-0.0585*** -0.0581*** -0.0595*** -0.0773*** -0.0863*** -0.0891*** -0.0651*** -0.0899*** -0.0868*** -0.0884*** -0.0867***

(-7.911) (-7.721) (-8.072) (-10.11) (-11.28) (-11.78) (-8.337) (-11.89) (-11.39) (-11.58) (-11.40)Entropy

(85,90,95,00)0.0134*** 0.0247*** 0.00706** 0.0142**

(4.478) (4.037) (2.453) (2.435)Herfindahl

(85,90,95,00)-0.0390*** 0.0585** -0.0181 0.0360

(-2.842) (2.117) (-1.435) (1.410)k

(85,90,95,00)0.000223***

(3.710)k1

(85,90,95,00)0.00238***

(6.549)k4

(85,90,95,00)0.000537***

(2.922)k5

(85,90,95,00)0.00366***

(9.287)k8

(85,90,95,00)0.000611***

(2.801)k9

(85,90,95,00)0.00410***

(8.998)k18

(85,90,95,00)-0.000535*** 0.000601*** 0.000653*** 0.000618*** 0.000673***

(-2.808) (2.801) (3.051) (2.879) (3.141)k19

(85,90,95,00)0.00419*** 0.00395*** 0.00410*** 0.00389***

(8.799) (8.164) (8.521) (8.031)Constant 0.467*** 0.514*** 0.429*** 0.594*** 0.588*** 0.589*** 0.651*** 0.596*** 0.543*** 0.585*** 0.511***

(7.427) (8.147) (6.592) (9.546) (8.165) (8.070) (8.203) (8.310) (7.315) (8.133) (6.583)Observations 451 451 451 451 451 451 451 451 451 451 451

Within R2 0.2071 0.1784 0.2179 0.2991 0.3379 0.3373 0.1779 0.3372 0.3494 0.3415 0.3535

Method of Reflections: Predicts network properties of future products

TheTheLegoLego

TheoryTheoryofof

DevelopmentDevelopment

Lego World

Real World

Countries

How many different pieces you have?

How rare are your pieces?

Many different pieces

If you have:

We might expect you to build manyproducts, including those requiringmany different pieces and rare pieces.

Few different pieces

We expect you to build few products, thatare made by many others, as it is likely to have those few pieces

High Diversification (k0), Low Standardness (k1)

Low Diversfication (k0), High Standardness (k1)

Many different piecesIf a product requires:

We might expect you to find that productIn few countries that have many pieces andtherefore build many products

Few different pieces

We expect to find that products in manyCountries, including those with few pieces

Low ubiquity (k0), High complexity (k1)

High ubiquity (k0), Low complexity (k1)

Few rare pieces

We expect to find that products in few countries

Low Ubiquity (k0)

Concluding RemarksINTRODUCTION:

1.- The product space is heterogeneous and can be approximated by studying export data using network methods.2.- The heterogeneity of the product space matters for development.(The location of a country in the product space determines their ability to diversify)

MAIN BODY

1.- We can quantify the productive structure of countries and the sophistication of products by studying exports as a bipartite network.2.- This network characterization of productive structure is associated with income and growth, suggesting that it is able to capture some fundamental properties of production.

FINALE

1.- We can explain some of this observations using the Lego Theory of Development

During the course -Network Types (Small World, Scale Free, Random) -Network Models (Erdos-Renyi,...

Documents

Transcript of During the course -Network Types (Small World, Scale Free, Random) -Network Models (Erdos-Renyi,...

Some analyses of Erdos collaboration graphvlado.fmf.uni-lj.si/vlado/papers../erdos.pdf · 2006-06-06 · Some analyses of Erdos collaboration graph˝ Vladimir Batagelj), Andrej Mrvar

A Model-based Adaptive Motion Estimation Scheme Using Renyi

(A) E(X (B) X (C) t€¦ · The Annals of Probability 1987, Vol. 15, No. 4, 1363-1386 LIMIT LAWS OF ERDOS-RENYI-SHEPP TYPE BY PAUL DEHEUVELS AND LUC DEVROYE University Paris VI …

Computer-Aided Proof of Erdos Discrepancy˝ Properties

Edges Detection Based on Renyi Entropy with Split/Merge

BEYOND PHYSICS: THE EMERGENCE AND EVOLUTION OF LIFE...Erdos and Renyi studied the evolution of “random graphs” where N nodes are connected by E edges, as the ratio of Edge to Nodes,

Social Networks VisualizerSocial Network Visualizer Software Requirements Specification Page 5 random networks (Erdos-Renyi, Watts-Strogatz, ring lattice, etc) can be created with

Structural Properties of Networks: Introductionmkearns/teaching/Networked... · 2013-09-05 · – Erdos numbers : distance to Paul Erdos – Erdos was definitely a hub or connector;

FINITE LINEAR SPACES AND PROJECTIVE PLANES P. ERDOS

The Erdos-Heilbronn Conjecture} Math (Additive Combinatorics) …af1p/Teaching/AdditiveCombinat... · 2009-02-20 · The Erdos-Heilbronn Conjecture} Math 21¡801 (Additive Combinatorics)

“Erdos and the Internet”

Topological Phase Transitions - Mathématiques · Linial-Meshulam model • X(d,n,p ): A generalization of the Erdos-Renyi graph G(n,p • Start with a full (d − 1)-dimensional

Paul Erdos and Egyptian Fractions}

Open-World Probabilistic Databasesguyvdb/slides/FLAIRS17.pdfQ2 = ∃x Coauthor(Bieber,x) ∧ Coauthor(Erdos,x) Q3 = Coauthor(Einstein,Straus) ∧ Coauthor(Erdos,Straus) ... Open-World

ERDOS P - On Random Graphs I

The Mathematics of Paul Erdos - American Mathematical Society

The Erdos-Ko-Rado Theorem for Permutationscanadam.math.ca/2009/pdf/meagher.pdf · 2009. 6. 22. · Erdos-Ko-Rado Theorem˝ Theorem (Erdos, Ko and Rado (1961))˝ Let Fbe a t-intersecting

Generalizing one of the De Bruijn – Erdos theorems

Estimation of Renyi Entropy and Mutual Information´ Based ...david.palenica.com/papers/nn/Renyi-rates.pdf · analysis. 1 Introduction We consider the nonparametric problem of estimating

RENYI ENTROPY AND CAUCHY-SCHWARTZ MUTUAL INFORMATION ... · RENYI ENTROPY AND CAUCHY-SCHWARTZ MUTUAL INFORMATION APPLIED´ TO MIFS-U VARIABLE SELECTION ALGORITHM: A COMPARATIVE STUDY