THE NEW DYNAMICS OF SCIENCE AND EUROPEAN...

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DIMETIC DOctoral School Pecs, July 11-12, 2007 THE NEW DYNAMICS OF SCIENCE AND EUROPEAN SCIENTIFIC INSTITUTIONS Prof Andrea Bonaccorsi University of Pisa

Transcript of THE NEW DYNAMICS OF SCIENCE AND EUROPEAN...

DIMETIC DOctoral School

Pecs, July 11-12, 2007

THE NEW DYNAMICS OF SCIENCE

AND EUROPEAN SCIENTIFICINSTITUTIONS

Prof Andrea Bonaccorsi

University of Pisa

Outline

1. Informational vs search models in economics ofscience

2. The dynamics of search in new leading sciences

• Rate of growth

• Diversity

• Nature of complementarity

3. The performance of European science in the lastthree decades

4. Better institutions vs better policies in Europeanscience

Theoretical background: Economics of science

Nelson (1959), Arrow (1962): information as public good.

Non rivalry and non appropriability responsible forunderinvestment.

Economic implications are derived from intrinsiccharacteristics of information (“science as a good” vs “scienceas a process”)

Informational model

E.g. Search models (Stigler, Marschack, Radner; Evensonand Kislev; David, Mowery, Steinmuller)

Dasgupta and David (1995, 1996): add to the properties ofinformation the dimension of information asymmetry

Informational model plus information asymmetry

- scientists are more informed than any others on the contentof experiments (e.g. other scientists that may want to controland replicate the experiment)

- scientists are agents that work for principals

- norms of science (Mertonian “Republic of science”) solve forthe information asymmetry and incentive problem:

- priority rule (winner takes all)

- full disclosure of the procedures of experimentation

- open science

Main focus on the explanation of general scientific institutionsafter Galileo

Problems with informational model

- difficult to articulate other dimensions of informationasymmetry:

- government, funding agencies- civil society, accountability issues

- the public and/or private nature of knowledge cannot bederived from intrinsic properties of the good produced(coevolution of institutions and type of knowledge produced)

- impossible to address issues of direction and rate ofchange of scientific knowledge

- informational models of topics selection (David, Dalle,Carayol) are an exception

Structural or topological models

- Simon (1962): in order to understand the behavior of agentsin a complex system, there are two possible strategies:

- make very detailed assumptions on agents’ rationalityand build models that predict their behavior on thebasis of an objective function

- make simple assumptions on cognitive abilities ofagents and concentrate on environmental constraints,or the structure of the search space

The ant metaphor.

Topological models in science

- scientists are the best possibly informed people in anygiven field- it is impossible for the modeler to build up arepresentation of the problem which is close (or evenbetter) to the one held by scientists- consequently, predictive models of the informational typewill not be able to add anything to the simple observationof scientists’ behavior- trying to represent the structure of the problem spacethey are searching in is an interesting alternative(Bonaccorsi, 2005)

Models of search dynamics in the problemspace

Dynamics of science

The problem of characterizing the growth of knowledge inscience is an old one in philosophy and sociology of science:

- Popper’s notion of growth via conjectures and confutation

- distinction between context of discovery and context ofjustification

- Kuhnian scientific paradigms

- De Solla Price: the ideal of quantitative laws of growth

- Campbell’s model of evolutionary cultural change (variation,selection, retention)

- Peirce, Rescher: economic laws in growth of knowledge,diminishing returns

- debate on the limits of growth of knowledge (Casti)

New leading sciences

Sciences born in XX century, grown after Second WorldWar, exploded in the last quarter of XX century:

Life sciences

Information sciences

Materials sciences (including Nanoscience)

All these sciences deal with complex, hierarchicalsystems (human body, mind, computer, multilayeredmaterials) and with their intersections (e.g. biorobotics,neurosciences, bioninformatics)

All these sciences share an approach based onmethodological reductionism

Stylized facts in late XX century- early XXIcentury science

Acceleration in the rate of growth of production ofscientific results

Proliferation of diversity in scientificprogrammes

New forms of complementarity in research

Evidence from Nanopublications

0

20000

40000

60000

80000

100000

120000

140000

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Cumulate arrivial of publications Cumulate entry of authors Cumulate entry of affiliations

Source: Bonaccorsi and Thoma (2005)

High rate of growth

Average rate of growth of scientific production is 1-2% peryear. Fast moving fields grow 5-15% per year. A growth rateof 5% for many years means destabilisation.

These fields are most likely found in new sciences (information, life, materials,nano).

Implications

• Mechanisms for rapid growth of research labs orinstitutes (funding, staff)

• Formalized postgraduate education and post-doc positions

• Extremely high opportunity costs for junior scientists

• High mobility in research careers

• Need for rapidity of decisions in priority setting atgovernment level

Dynamics of growth

Theoretical background on variety/ diversity in science

Professional norms of science (Merton)

Reduction of variety as a result of internal professionaldynamics (Callon)

Variety and diversity in science mainly comes fromparadigmatic uncertainty (Kuhn)

Within normal science there is limited variety:convergence towards a common framework

Dynamics of growth

Notion of divergent dynamics (or proliferation)

Large intra-paradigmatic diversity

Research programmes sharing fundamentalexplanations but diverging on lower level hypothesesor experimental techniques/ objects

Main reasons:A. reductionism in explanation vs systemicintegration

B. observation vs manipulation

C. new forms of combination between science andengineering

Reductionism in explanation vs systemicintegration

Experimental advancements make it possible to explainphenomena by making reference to variables at lowerlevel of resolution of matter (i.e. molecular and atomiclevel).

Reductionist approach: explaining higher levels oforganization of matter using knowledge of lowerlevels. “One gene, one disease” programme.

Interestingly, when applied to complex objects orsystems (i.e. proteins, or cells, tissues, organs) andtheir behavior (e.g. disease) the reductionist approachdoes not lead to complete explanation- it does notreduce but rather increases epistemic uncertainty.

HIV-1

The case of HIV research

The search for a causal explanation of the AIDS diseasewas solved with the discovery of HIV virus.

However, this fundamental explanation (“the cause of thediseases lies in the agent HIV”) over which the scientificconsensus was almost universal, did not reduce theuncertainty over:- the specific biochemical mechanisms of interaction of thevirus with the cell- the entry points of the virus in the cell- the patterns of mutation of HIV, etc.

The reductionist approach did not produce a reduction adunum, but rather opened the way for a proliferation ofdiverse (even competing) sub-hypotheses.

Uncertainty about basicequations

A schematic representation of the degree of uncertainty that exists in theunderlying mathematical equations describing various phenomenarelative to the intrinsic complexity of the phenomena

Complexity of phenomena

QuantumGravity

ParticlePhysics

Chemicalreactions

Dynamics of Meteorology Turbulencesolar system

Appliedsciences

Living systems

Climate

Social scienceEconomicsFinance

Source: Barrow (1998) after Ruelle

Observation vs manipulation

In the development of science there has always beenseparation between the level of resolution at which itcould be possible at any date:- make predictions- observe- manipulate

New experimental technologies, e.g.- scanning tunneling microscope (1981)- polymerase chain reaction (1985)- atomic force microscope (1986)

These technologies make it possible to manipulatebefore observing, or to observe before makingpredictions

Science-driven engineering

New sciences make it possible new combinationsbetween scientific explanation (knowing theproperties of nature) and engineering (manipulatingnature for a purpose)

New relations between natural and artificial, discoveryand invention:- the fundamental properties of matter cannot bediscovered unless a specific configuration is designed- design is an artificial activity oriented towards goals- design goals can be achieved following manypossible directions (design theory)-“scientists become engineers”

Large scale exploration through manipulation

Measuring the dynamics of proliferation

Experimental workNew measure of variety derived from bipartite graphtheory

Dataset:- >100,000 publications in Nano S&T- query from ISI Fraunhofer Karlsruhe expert selection- part of a larger data construction exercise (PRIMEproject)- period 1990-2001- extraction of all keywords- isolation of new keywords per year of birth

References:- Bonaccorsi & Thoma, Research Policy, 2007- Bonaccorsi & Vargas, in progress

1990199119921993199419951996199719981999200020010

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Num

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of k

eyw

ords

Occurrence year

Birth year

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000

0 250 500 750 1000 1250 1500 1750 2000 2250 2500

1990

1991

1992

1993

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1995

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1997

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Num

ber o

f keyw

ord

s

[11983]

[1601]

[1662]

[1473]

[1568]

[1486]

[1449]

[1350]

[1486]

[1750]

[3181]

[716]

Birth

year

Degree k

150

300

450

600

Degree hW

(Occurrencesin 2001)

FILM

Atomic Force Microscopy

Nanoparticles

Ion Channel

thin film

system

Particleprotein

Biosensor

Nanostructures

FULLERENE

Limit case 1: all new articles share the same set of keywords > no correlationbetween number of articles and degree. Limit case 2: all articles share only onekeyword: perfect correlation between number of articles and degree.

0 100 200 300 400 500 600 700 800

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ree k

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Class A Class B Class A curve

Class B curve

Limit case 1 Limit case 2

Birth year1992≤

Birth year1992≤Class A =

0 50 100 150 200 250 300 350 400 450 500 550 600

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Degree hW (occurrences)

Deg

ree k

Proliferation pattern

• Large cognitive distance between senior scientists andjunior scientists- doctoral education based on competitiveallocation of resources and proposals

• Impossibility to decide research directions in a centralizedway- multilayer governance and funding systems

• Need to finance competing research projects- variety offunding sources (but mainly grant-like)

• Need to mobilize research projects in parallel- welldeveloped post doc system with possibility to apply asprincipal investigators

• Strong epistemic uncertainty- premium given to topquality universities (signaling effect)

An ant model of science

In the paper by Solé et al. (Artificial Life, 2000)“Pattern formation and optimization in Army AntRaids” a model of food search behavior for ants isdeveloped, based on findings from etology.

There are two levels:1. A behavioral model (search algorythms)2. A macromodel, that evaluates the search

strategies through a macroevolutionary algorythm

The ant model of scienceAt each step the ant must evaluate environmental factors P (D, i, j)(=probability to find food of size D in cell i,j) and pheromon signals φ leftby other ants in order to decide whether to move and where.

First of all the ant must decidewhether to move; the probabilityto move Pm depends on theoverall concentration of pheromonin cells ahead.

In moving the ant releasespheromon on the ground. If theant is looking for food, it releasesone unit of pheromon. If the ant isgoing back to the colony it releasesq units.

The threshold of release ofpheromon in the journey forwardis

The threshold in the journey backis

These thresholds govern the trade-off between exploration eexploitation.

1σ2σ

Variables(deterministic part of the model).

The environment is represented by a grid.•P(D,i,j) : probability to find food of size D in the cell(i,j).• 1 , if the ant is searching food;

=

0 , if the ant is going back to the colony• δ : rate of decay of pheromon left by ants

)(tSk

• φ(i,j) : concentration of pheromon in the cell (i,j).The quantity is updated at each step : φ(i,j) (1-δ)φ(i,j).

• : threshold of release of pheromon in the wayforward.• : threshold of release of pheromon in the wayback to the colony.• µ : attractiveness of the empty cells.

• q : quantity of pheromon released at each step inthe way back (in the way forward the quantity isalways 1)

Probabilistic aspects

Probability that an ant in the cell (i,j) decides to move.

Probability that the ant decides to move left.

Probability that the ant decides to move right.

•Probability that the ant decides to move centre.

Normalization constant.

2. The evolutionary model

.

.

Search space . .

200200×

Enviromental variables

Search strategy 5-tuple

Search grid

Initialization

Un Modello di Ricerca nella Rete delle Keywords Andrea Bonaccorsi, Juan Sebastian Vargas

For each a simlation of T = 1000 steps is launched,using the criteria defined in the search strategy

For each solution

we can define an efficiency score given by

The macroevolutionary algorythm is run on theefficiency scores.

Quantità di cibo che entranella tana al tempo t.

Numero di formichepresenti nel reticolo altempo t.

Pattern 1 Pattern 2

Two patterns are dominant

(a) convergent or focused search

In environments where the food is concentratedin large quantities in a few places, the optimalstrategy is to focus the search

• pheromon is released in high quantities inthe way back• the decay of pheromon is slow• the attractiveness of empty cells is very low

All ants walk in the same direction and go backto the colony reinforcing the quantity ofpheromon along the path

Two patterns are dominant

(b) proliferation or divergent search

In environments where the food is scattered in smallquantities across the grid the optimal strategy is aproliferation in the directions of search

• pheromon is released in small quantities in theway back so that reinforcing mechanisms are notexceedingly strong• the decay of pheromon is rapid• the attractiveness of empty cells is moderate tohigh

Ants explore in many different directions, branchingon the right or the left after a number of nodes with agiven probability.

Institutional and cognitive complementarity

• Need for rapidly mobilizing heterogeneouscompetences

• Combinatorial opportunities- high mobility ofscientists along their career

• New professional roles (e.g. transfer roles inbiomedical research)

• Flexibility in arranging collaboration betweenacademia and other institutions (industry, hospitals,regulatory agencies, public administration).

New relations between science, technology andinnovation

A recent study on knowledge flows from academic research to firms

Dataset (1981-1999)

- more than 7.000 scientific journals

- approx. 230.000 papers published by top 200 firms(raniking by total expenditure in R&D)

- approx. 2.430.000 papers published by top 110universities

- top 200 firms make approx. 1 million citations topublications of top 110 universities and 600.000citations to industrial publications

Fonte: Adams e Clemmons (2006)

Knowledge flows

% citations

Number Chemistry Computer Engineering Physicsscience

Communications services 26,292 12.1 10.8 22.2 51.4

Software & Businessservices 25,272 15.1 17.7 17.1 46.3

Electrical equipment 22,896 8.2 9.1 50.3 27.9

Computers 9,210 15.3 13.6 26.5 40.5

Totale Industrial sector 217,623 17.7 5.5 22.4 22.4

Slow tomoderate

Rapid

Turbulent/exponential

Focused/ predictable Divergent/proliferating

Rate of change of scientific knowledge

Dynamics of change of scientific knowledge and type of complementarity

Weak complementarityStrong complementarity(facilities) Weak complementarity

Strongcomplementarity(institutional)

Traditionalchemistry

Particlephysics

Astrophysics Mathematics

Slow tomoderate

Rapid

Turbulent/exponential

Focused/ predictable Divergent/proliferating

Rate of change of scientific knowledge

Dynamics of change of scientific knowledge and type of complementarity

Weak complementarityStrong complementarity(facilities) Weak complementarity

Strongcomplementarity(institutional)

Traditionalchemistry

Particlephysics

Astrophysics Mathematics

Computerscience

Materials scienceLife science

Nanotechnology

Implications for institutional change in science

European science has developed separateinstitutions at national, intergovernmental andEuropean level, for dealing with search regimes withstrong physical infrastructure complementarities

(e.g. high energy physics, astronomy, space research,oceanography, nuclear technology).

It is much more difficult to provide rapidly emergingfields the required complementarities in terms ofhuman capital within the common institutionalframework.

There are few rapid growth mechanisms inEuropean science.

Slow tomoderate

Rapid

Turbulent/exponential

Focused/ convergent Divergent/proliferating

Rate of change of scientific knowledge

Dynamics of change of scientific knowledge and type of complementarity

Weak complementarityStrong complementarity(facilities) Weak complementarity

Strongcomplementarity(institutional)

Traditionalchemistry

Particlephysics

Astrophysics Mathematics

European science is historically strong in fields characterizedby convergent dynamics, or divergent dynamics but weakforms of complementarity

European model of university

Dedicated intergovernmental institutions

Slow tomoderate

Rapid

Turbulent/exponential

Focused/ predictable Divergent/proliferating

Rate of change of scientific knowledge

Dynamics of change of scientific knowledge and type of complementarity

Weak complementarityStrong complementarity(facilities) Weak complementarity

Strongcomplementarity(institutional)

Traditionalchemistry

Particlephysics

Astrophysics Mathematics

Computerscience

Materials science

Life scienceEuropean science has proved weak in promoting fastmoving fields (new leading sciences)

Difficult to mobilize resources and growrapidly

Difficult to build new formsof complementarity

Nanotechnology

The scientific tradition of XX century

• European academic institutions are perfectly adaptedto scientific fields characterized by:

• moderate rate of growth (controlability, limited cognitive distance betweensenior and junior scientists)

• proliferation pattern only if coupled with low degree of complementarity and/ormoderate rate of growth

• convergent pattern of search

• The European system has performed extremely well inXX century science, while has found it more difficult toadapt to late century new search regimes.

Forecasting the position of Europein the Nobel prize competition

Cesare Marchetti, The Nobel saga, Technology Review, September 1989

• “Actions of society are consequences of culturaldiffusion processes, that can be represented bymeans of epidemiologic mechanisms.

• Lotka-Volterra equations fully represent theseprocesses, although logistics equations areappropriate in most cases, including our own.

• A long experience with this tool shows that theseequations are robustly predictive”.

• “It is possible to calculate how many Nobelprizes Europeans and Americans will win.

• The Americans will be in minority.

• To give an idea, Europeans should receive 20prizes in the period between 1998 and 2000,and Americans only 13”.

And finally:

• “In ten years time we will meet to check thisprediction” (p.11).

8,83

21

17,85

46

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Fractional count

Full count

Premi Nobel Europa Premi Nobel USA

E

Distribution of Nobel prizes in Physics, Chemistry, Medicine.Year 1990-2000

Distribution of Nobel prizes in Physics, Chemistry, Medicine. Year 2001-2006

2,5

7

12,5

31

0 5 10 15 20 25 30 35

Fractional count

Full count

Premi Nobel Europa Premi Nobel USA

Commonly held beliefs in European S&T policy

Proposition 1. European science is quantitatively andqualitatively comparable to US science.

Proposition 2. The technological position of Europe in hightechnology is, on the contrary, much weaker than US.

Hence, the European paradox: European science is good,but the translation of knowledge into commerciallyapplicable solutions is poor.

A number of policy measures are therefore needed, fromuser-based or application-oriented European research to thefunding of technology transfer or intermediaries bodies atregional or local level.

Another look at European science

• European science is only quantitatively comparable to USscience but is weaker in the overall quality and isseverely under-represented in the upper tail of scientificquality;

(b) European science is strong in fields characterized by slowgrowth and weak in fields characterized by turbulentgrowth;

(c) European science is strong in fields characterized byconvergent search regimes and weak in fieldscharacterized by divergent search regimes;

(d) European science is strong in fields characterized by highlevels of infrastructural complementarities while it ismuch less prepared in fields characterized by humancapital and institutional complementarities.

Upper tail in quality of research. Piece of evidence # 1

Data on the most cited scientists worldwide have beenrecently made available by ISI on the basis of the analysis of19 million papers in the period 1981-1999, authored by 5million scientists.They refer to around 5,000 scientists worldwide in all fields, selected asthose 250 that receive the largest number of total citations in any subjectarea (0.1% of the total).In all 21 fields US scientists largely dominate, with aproportion of highly cited scientists ranging from 40% inpharmacology and agricultural sciences to over 90% ineconomics/business and social sciences and an averagearound 60-70% of the total.Among the 21 areas, only in other three areas non-UScountries represent more than 40% of the total: physics,chemistry and plant and animal science

Countrywise distribution of Highly Cited Scientists

0% 20% 40% 60% 80% 100%

Mathematics

Physics

Geosciences

Space Sciences

Materials Science

Engineering

Computer Science

Chemistry

Pharmacology

Biology & BioChemistry

Plant & Animal Science

Molecular Biology & Genetics

Microbiology

Immunology

Clinical medicine

Psychology/ Psychiatry

Neuroscience

Ecology/Environment

Agricultural Sciences

Social Sciences

Economics/Business

US

UK

Germany

Japan

Canada

France

Australia

Switzerland

Netherlands

Italy

Sweden

Israel

Belgium

Denmark

New Zealand

Spain

Austria

PR China

India

Finland

Norway

S. Africa

Russia

Taiwan

US scientists dominate in each of the 21 subject areas of science

USA

Piece of evidence # 2

We examined (with non-ISI sources) the publications oftop 1,000 scientists by citations received along all theirscientific career in

- Computer science- High energy physics

and all publications in nanotechnology for the period1990-2001 (ISI source).We identified the most productive institutions interms of total number of publications in the periodand ranked the first 100.

Share in the list of top 100 affiliations

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Computer science High energyphysics

Nanotechnology

Scientific field

%

NAFTA

Europe

East Asia

An examination of the professional career of top 1000scientists in computer science

• Excellence measured by total number of citationsreceived in all published articles in the field (source:www. citeseer. com)

• Well recognized source in the scientific community

• Identify top 1,010 scientists by number of citations

• Download CVs from individual websites, or search CVson the web

• Codify CV data and build the dataset

• Analysis: (a) overall career pattern (b) by cohort of age.

MIT University of California University of CaliforniaUniversity of California MIT Stanford University

Indian Institute ofTechnology Stanford University MIT

National TaiwanUniversity Harvard University Harvard UniversityHarvard University University of Massachusetts University of Illinois

Cambridge University Cornell University Carnegie-Mellon University

Yale University Carnegie-Mellon University Cornell UniversityUniversity of Michigan University of Illinois University of Michigan

Seoul NationalUniversity Purdue University University of WisconsinCalifornia Institute of University of Michigan University of TexasTechnology

Bachelor Master PhD

Piece of evidence # 3

Institutions awarding degrees of the top 1,000 scientists inComputer science. Top 10 list

Prof career Count position

University 2620

University-director 497

Industry 463

Consulting 332

Industry-director 323

Government 183

Professional positions over the career oftop scientists in Computer scienceNumber of scientists: 1010.Number of different positions: 4418.Mean 4,36

More than3,000changes incareerpositions

Institution Count Massachusetts Institute of Technology 174

Stanford University 166

University of California at Berkeley 102

Carnegie-Mellon University 102

University of Illinois 59

University of Maryland 58

Cornell University 52

University of Washington 45

University of Pennsylvania 44

Harvard University 44

Princeton University 44

University of Texas 44

University of Massachusetts 42

Brown University 41

University of Toronto 34

Ranking of top 15 affiliations in the total number ofpositions over the career. Academic positions

Source: Bonaccorsi (2006)

More than 1/6 of thesemobility paths areaccounted for by thetop 4 universities

First, the US system is better able to attract the besttalents worldwide, benefiting from a larger pool of people.In abstract terms, a system like this has superiorsampling properties. Furthermore, the US system hassuperior selection properties.

Second, European countries do not play a great role inthis international competition.

Third, Asian countries seem to have understoodmuch better the rules of the game. By sending theirbrightest students to US, they position themselves to thefrontier of scientific research.

SSpecialisation patterns(Revealed Comparative Advantages, 1981-1994)

oNo European country is specialised in Computer sciencenNo European country is specialised in Engineering;iIn biology and biochemistry small European countries (Netherlands, Sweden,

Denmark, Norway, Finland) exhibit strong specialisation while large countrieshave an index lower than unity;

IIn molecular biology several large countries (United Kingdom, Germany andFrance) and small countries (Netherlands, Finland, in addition to Switzerland) arespecialised

EEurope as a whole is specialised in a few biomedical areas (pharmacology,immunology, microbiology) and in the large traditional disciplines of chemistry,physics and astronomy.

RRate of growth of broad disciplines Over the period 1995-1999 the fastest growing area has been

computer science with a growth rate of almost 10% Earth sciences, engineering and mathematics also show high growth

rates, varying between 4.2 and 4.6% Biology and agriculture have the lowest growth rates with 1.4 and

1.6% respectively The broad field of life sciences as a whole experienced a growth

rate of 2.33% The growth rate for the broad field of engineering was 4.5%, of

which 35% was materials science, that grew at 1.9% per year.EEuropean science is strong in fields characterized by slow

growth and weak in fields characterized by turbulent growth

In materials science EU-15 produce 40,108 papersand receive 83,748 citations, while NAFTA produce31,620 papers but receive 106,841 citations

In the life sciences EU-15 produce 616,212 papersand US 529,608 in the period 1995-1999, but thecitation impact (1993-1999) is 1.35 in USA and only0.90 in EU-15

In computer science the citation impact (1993-1999) is1.33 for Israel, 1.17 for US, but only in the rangebetween 0.81 (Germany) and 0.95 (Italy) for the fourlargest countries

Source: Third European Report on S&T Indicators

European science has developed separateinstitutions at national, intergovernmental andEuropean level, for dealing with search regimes withstrong physical infrastructure complementarities

(e.g. high energy physics, astronomy, space research,oceanography, nuclear technology).

It is much more difficult to provide emerging fields therequired complementarities in terms of human capitalwithin the common institutional framework.

There are few rapid growth mechanisms.

TPERS/INSTAG

543210

T_PERS120

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60

40

20

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Plot of rate of growth (average number of personnel pereach year of life, T_PERS/INSTAG) against size (number

of personnel, T_PERS). CNR 1957-1997

Source: Bonaccorsi and Daraio (2003)

TRES/INSTAG

3.02.52.01.51.0.50.0

T_RES

50

40

30

20

10

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Plot of rate of growth (average number of researchers pereach year of life, T_RES/INSTAG) against size (number of

researchers, T_RES). CNR 1957-1997

Source: Bonaccorsi and Daraio (2003)