COMPUTATIONAL SOCIAL SCIENCE I - geza.kzoo.edugeza.kzoo.edu/~erdi/leckek/lec1.pdf · 6.Earthquakes,...

COMPUTATIONAL SOCIAL SCIENCEI : SOCIODYNAMICS: FROM CONCEPTS

TO DATA AND BACK

Peter Erdi1,2

1Center for Complex Systems Studies, Kalamazoo College, Kalamazoo, Michigan

2Dept. Biophysics, KFKI Res. Inst. Part. Nucl. Phys. Hung. Acad. Sci. Budapest,Hungary

Content

1. Towards a computational social science: from data mining

via social simulations to prediction

2. Sociodynamics: from concepts to data and back

3. Oscillations and chaos

4. War dynamics, drug propagation and control, economic cy-

cles and chaos, biological and social epidemics

5. Dynamic threshold modeling of budget changes

6. Earthquakes, Epilepsy, Stock Market Crashes: Predicting and

Managing Extreme Events

7. Conclusions

3

Towards a computational social science: from datamining via social simulations to prediction

Computational social science is the interdisci-plinary studies of complex social systems by com-bining

• social theories

• data mining

• dynamical modeling techniques

4


New challenges

• to predict, control and management of socio-economic crises and political insabilites

• to avoid ”pathological” collective behavior: panic, extremism, breakdown of trust ...

• to understand and manage demographic changes

• to control of spreading epidemics

• to ensure security and peace

• to understand the structure and dynamics of different social networks

• to defend intellectual property rights

• to understand the relationship between individual and institutional decision makingmechanism

5


Figure 1: Instabilities, collective phenomena, social networks

Political instability in-dex. Vulnerability to so-cial and political unrest.From Economist Intelli-gence Unit

Panic: stadium collapsesin Abidjan

Patent citation net-work: Chemistry:molecular biologyand microbiology:from Steve Borgatti

6

Data, Rules, Prediction:Lessons from Tycho de Brahe, Kepler and Newton

The world of Tycho Brahe: DATA COLLECTION

7

Data, Rules, Prediction: Lessons from Tycho deBrahe, Kepler and Newton

Kepler: MATHEMATICAL but not predictive

Newton’s laws: PREDICTIVE

8


Figure 2: Visioneer is a European project aiming to reach a better, quantitative under-standing of complex socio-economic systems: Dirk Helbing: ETH, Zurich

9


NEW SOURCES of DATA

Figure 3: Everywhere you look, the quantity of information in the world is soaring.According to one estimate, mankind created 150 exabytes (billion gigabytes) of data in2005. This year, it will create 1,200 exabytes. Economist 2010 February

• internet

• sensor networks

• government databases

10

Sociodynamics: from concepts to data and back

GROWTH PROCESSES

Figure 4: Unbounded growth processes: infinite and finite-time singularities

11

The dynamic laws behind rises and falls, periodicityand irregular changes

• boundless growth

• equilibrium dynamics|

• rise-and-fall (boom and bust)

• periodicity

• chaos

Historical dynamics: Peter Turchin

12


From finite-time singularity to crash

• unbalanced (higher-than-linear) positive feedback -> finite-time singularities

• infinite value during finite time: (chemical) explosion and ”explosion”

• earthquakes, volcano, epilepsy stock prices ...

• super-exponential increase (due to the irrational expectations) cannot be continued for “ever” due to

the unstable nature of this process

• followed by a compensatory process (i.e. stock market crash)

Figure 5: Stock market crashes

14

Oscillations and Chaos

Oscillations

• harmonic oscillation

• Belousov - Zhabotinsky reaction: nonlinear chemical oscillator

• predator - prey systems

• neural oscillation

• circadian rhythms

• female hormonal cycle

• business cycle

15

Oscillation and Chaos

Temporal complexity

Chaotic patterns

Lorenz: unpredictability

Lorenz attractor

16

War dynamics, drug propagation and control, economic cycles and chaos,biological and social epidemics

A) war dynamics

dR

dt= −kBRB + αR

(1− R

K

)(1)

dB

dt= −kRBR+ βB

(1− B

L

), (2)

where α, β, K and L are positive constants.

Generalized Lotka-Volterra equation: a famous model of competition of the strugglefor existence

Georgyi Frantsevitch Gause (1910-1986)

17

Temporal dynamics: interacting variables: equilibrium, oscillation, chaos

A) war dynamics

principle of competitive exclusion vs. “permanent war”,Gause, Strogatz, Epstein

PSfrag replacements

L

R = 0

B = 0

K

B = 0

B = 0

B = 0

R = 0 R = 0

R = 0

K

KK

L

L

L

R

B

R

RR

B

B

B

Figure 6: Phase planes of the possible outcomes of bilateral wars

18


B) drug propagation and control

(adapted from Behrens et. al, 2004)

Figure 7: Simple dynamic models of drug propagation

19




At+1 = (1− α)At + af(At, Dt), A0 = A(0), (3a)

Dt+1 = (1− β)Dt + bf(At, Dt), D0 = D(0), (3b)

a, b > 0, and α, β ∈ [0, 1]. The positive and negative feedback effects should beexpressed in the form of the function f .

A rather general form for the function is

f(A,D) =1

1 + e−c(A−D), c > 0. (4)

20




Figure 8: Drug market might be chaotic

Since a chaotic drug market is interpreted as unpredictable, there is a natural questionwhether it is possible to control the system to stable cycles or even (low level)

equilibrium.

21


C) economic cycles and chaos

Business Cycles: Kaldor model

2

1

−1

1 2 3 4 5 6 7 8

ye

k = ke

I, S, dy

y

S

I

Figure 9: Kaldor model: y:income, k:capital, I :investment, S: saving

22




Assuming time-independent investment and saving the dynamics is given as:

y(t) = a[I(k(t), y(t))− S(k(t), y(t))] (5a)

k(t) = I(k(t), y(t))− δk(t). (5b)

23




4

3

2

1

1 2 3 4 5 6 7 8

k

y

dk/dt = 0

dy/dt = 0

Figure 10: Limit cycle behavior of the Kaldor model

24


D) biological and social epidemics

Figure 11: The standard epidemic model with three sub-populations:S(t) – Susceptible, I(t) – Infectious, R(t) – Recovered

25


A) war dynamicsPSfrag replacements

L

R = 0

B = 0

K

B = 0

B = 0

B = 0

R = 0 R = 0

R = 0

K

KK

L

L

L

R

B

R

RR

B

B

B



4

3

2

1

1 2 3 4 5 6 7 8

k

y

dk/dt = 0

dy/dt = 0

D) biological and social epidemics

Figure 12: Summary of some low-dimensional sociodynamic models

26

Spatiotemporal processesclosed systems: homogenization

open systems: pattern formation

spatial: as urban (racial) segregation (ThomasSchelling: Micromotives and Macrobehavior)

• propagation of matter, energy: Physics,virus: Biology

• propagation of matter: goods, money etc.:Economics

• propagation of drugs: Criminology

• propagation of “information” (knowledge,opinion, gossip, fear, trust) among humans:Behavioral Social sciences

Figure 13: A spatial pattern

Real world models: coupling!!

27


” All models are wrong, but some are useful.”

Concept-driven, low-dimensional, single-scale models give insights

//////The///////End////of////////////Theory:///////The/////////Data///////////Deluge//////////Makes//////the//////////////Scientific////////////Method

////////////Obsolete//////////(Chris//////////////Anderson,//////////Wired/////////2008)

Correlation (and brute force) is not enough: we need causal (maybecircular and network causal, but causal) explanations even in the peta-computing age.

It is time to combine concept-driven and data-driven models

• to determine governing rules of the dynamics

• to extend to High-dimensional, Multi-Scale, Multi-Level systems

• to obtain realistic parameter values with data mining

• equation-based AND (not XOR) agent-based simulations

28


• The difficulties in social sciences: from Kepler to Newton

• Kepler’s laws: data-driven, inductive, global, integral

• Newton’s laws: data-motivated and concepts driven, deduc-

tive, local, differential

• The a priori knowledge of the forcing functions, which ba-

sically governs the dynamic evolution of the systems, is

difficult: social dynamics is in the post-Keplerian and pre-

Newtonian age (and maybe it remains there).

29

Dynamic Threshold Modeling of Budget Changes

30

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32

Lessons from Political Science

• the budget is a scalar number annually (the sum of many elements, i.e categories)

• each year a new point is generated -> budget changes

• traditional pure incremental model of budget changes leads to Gaussian distribution.

• comparative statistics: budget change distribution deviates from the Gaussian (double-

Pareto? generalized extreme distribution?)0 2000 4000 6000 8000 10000

0.0

0000

0.0

0010

0.0

0020

Value

Pro

bability

• SKEW distributions? probably due to the existence of institutional friction.

33


US real outlays, percentage change

Jones et al, 2007: A General Empirical Law of Public Budgets: A Comparative Analysis. Figure 2a.

34


US total outlays, histogram

Jones et al, 2007: A General Empirical Law of Public Budgets: A Comparative Analysis. Figure 3a.

� leptokurtic

� asymmetric

� bounded

� peak close tozero

35

Dynamic Modeling of Public Policy DecisionMaking Processes

We are building a macroscopic and microscopicmodels to explain how institutionalmechanisms transform Gaussian to power law distributions by assuming:

• limited attention of political institutions

• friction by collective decision rules

• resistance to change

• error accumulation

• prioritized preferences, reprioritize

36

Dynamic Modeling of Public Policy DecisionMaking Processes

• Deterministic versus stochastic process

• incremental model versus ”avalanches”

• is the initial distribution really Gaussian?

• why and how to get SKEW distributions?

• probably due to the existence of institutional friction.

37

Error-accumulation: Single Threshold Models

A dynamic stimulus-response threshold model:

• Rt: response variable

• St: input signal, (Gaussian random variable)

• C: threshold

• λ : efficiency parameter or friction

• β: amplification parameter

Rt =

{βSt if

∑t−1t′=1 St′ > C,

λβSt otherwise

38

Error-accumulation: Single Threshold Models

A simulation result:

Figure 14: A leptokurtic distribution as a simulated response, comparing to a Gaussian distribution

.

39

Multiple Threshold Models

• C1 = 3; upper threshold

• C2 = 1.2; middle threshold

• C3 = −4; lower threshold

• λ1p = 0.03; efficiency for the region of positive accumulated sum

• λ1n = 0.02; efficiency for the region of negative accumulated sum

• λ2p = 0.3; efficiency between the two positive threshold

• β = 1;

• T denotes the time of last resetting to 0 of accumulated signal.

40

Multiple Threshold Models

Rt =

βSt if∑t−1t′=T St′ > C1, T = t

λ2pβSt if C1 >∑t−1t′=T St′ > C2

λ1nβSt if∑t−1t′=T St′ < 0 ∧ St < 0

λ1nβSt if∑t−1t′=T St′ < C3, T = t

λ1pβSt if C2 >∑t−1t′=T St′ > 0 ∨ 0 >

∑t−1t′=T St′ > C3 ∧ St > 0

41

Multiple Threshold Models:Simulation results

0

1

2

3

4

5

6

7

8

σ

−3 −2 −1 0 1 2 3

1.2−0.6 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.00

1

2

3

4

5

6

7

8(1820−2002) and fitted model distribution

input Gauss (*10), =1 and French budget distribution

French total budget distribution

Figure 15: Transformation of the Gaussian input signals to skew distribution fitted to the French budget

data. The upper figure shows the tenfold enlarged input Gaussian sample distribution and the budget

distribution histogram. The lower figure shows the measured data histogram and the fitted model output

histogram (solid line). Parameters of the fit: C1 = −3; C2 = 1.6; C3 = 4.6; λ1n = 0.07;

λ1p = 0.04; λ2p = 0.3.

42

Multiple Threshold Models:Simulation results

σ

(1947−2003) and fitted model distribution

−3 −2 −1 0 1 2 30

2

4

6

8

10

12

−0.4 −0.2 0.0 0.2 0.4 0.6 0.80

4

8

12

16

20

input Gauss (*10), =1 and USA budget distribution

USA total budget distribution

Figure 16: Transformation of the Gaussian input signals to skew distribution fitted to the US budget data.

The upper figure shows the tenfold enlarged input Gaussian sample distribution and the budget distribution

histogram. The lower figure shows the measured data histogram and the fitted model output histogram

(solid line). Parameters of the fit: C1 = −12; C2 = 0; C3 = 3; λ1n = 0.01; λ1p = 0.04;

λ2p = 0.3.

43

Conclusions and Some Open Problems

• Government budgets seem to be skew distributions

• Multiple threshold models should be better justified

• Can we design institutions that are more efficient? Do we want to?

• Can we get direct measurements of decision making costs?

• Why do budgets produce power laws but virtually all other distributions (such as GDP)are less extreme?

44

Earthquakes, Epilepsy, Stock Market Crashes:Predicting and Managing Extreme Events

Scope and limits of predictability

• Surprising events: no rule?

• Self-organized criticality (P. Bak) → inherently unpredictable

• Intermittent criticality (D. Sornette) → there are precursors

45

PhenomenologyEarthquake eruption

Gutenberg-Richter law

logN(M) = −bM (6)

b ∼ 1 N(M): number of earthquakes of magnitude greater than M

46

PhenomenologyEarthquake eruption

Omori’s law

n(t) =K

(c+ t)p(7)

where:

• n(t) is the number of earthquakes

n measured in a certain time t,

• K is the decay rate,

• c is the “time offset” parameter;

and

• the parameter p typically falls in

the range 0.75–1.5.

47

PhenomenologyEpilepsy

• epileptic seizures may begin hours earlier than their clinical onset

• definiton of different measures

• relative self-excitation is a control paramater to induce/suppress epilepsy

• our own lab in Budapest: Zoltan Somogyvari

48

PhenomenologyEpilepsy

Psp

(t+ ) t

t=1time step

0 100 200 300 400 500 600 700 800 900 1000

18001600140012001000

800600400200

Pos

t−sy

napt

ic p

oten

tial

Time

10 20 30 40 50 60 70 80 90 100 110

110

100

90

80

70

60

50

40

30

20

10

t=1time step

Psp

(t+ ) t

1400

1200

1000

800

600

400

200

0

0 200 400 600 800 1000 1200 1400Psp(t)Psp(t)

complexity decrease

0

Somogyvari et al : Slow dynamics of epileptic seizure: analysis and model

49

PhenomenologyMarket crash

50

Statistical analysis of extreme eventsOutliers vs extreme value statistics

• What is the probabilty of having big earthquake in California

within a year?

• How large might a possible stock market crash be tomorrow?

- lowest daily return (the minimum)

- highest daily return (the maximum) over a given period

- not normally distributed

51

Statistical analysis of extreme eventsGeneralized extreme value distribution

52

Statistical analysis of extreme eventsGumbel distribution

f(x;µ, σ) = exp(−(exp(−x− µ))/σ) (8)

for

−∞ < x <∞ (9)

• forest fires

• earthquakes

• financial loss

• epileptic

seizures

53

Statistical analysis of extreme eventsPower law distributions

P (ξ > x) = ax−k; (10)

k is the shape parameter

100

101

102

103

102

10 1

100

101

102

103

104

105

1994 2003 / M>1.5 / 5km / 1 day expos= 2.6

Number of events

Num

ber

of bin

s

Empirical probability density

functions of the number r

of earthquakes in the space–

time [5×5 km2 – 1 day]

California SCEC catalog

(Saichev and Sornette)

log-normal for the initial part

and power law heavy tail

54

Power law distributions

100 102 104

word frequency

100

102

104

100 102 104

citations

100

102

104

106

100 102 104

web hits

100

102

104

106 107

books sold

1

10

100

100 102 104 106

telephone calls received

100

103

106

2 3 4 5 6 7earthquake magnitude

102

103

104

0.01 0.1 1

crater diameter in km

10-4

10-2

100

102

102

103

104

105

peak intensity

101

102

103

104

1 10 100intensity

1

10

100

109

1010

net worth in US dollars

1

10

100

104

105

106

name frequency

100

102

104

103

105 10

7

population of city

100

102

104

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

(j) (k) (l)

55

Towards prediciting seizuresDynamical characteristics of pre-epileptic seizures in rats with recurrence quantifica-

tion analysisXiaoli Li, Gaoxiang Ouyang, Xin Yao, Xinping GuanPhysics Letters A 333(2004) 164–171

measures based on recurrence pointsX. Li et al. / Physics Letters A 333 (2004) 164–171 169

Fig. 2. The long-term EEG recordings of rat 1 and their three RQA measures. The gray vertical bar marked represents the interval from injectiontime to seizure time. Visual inspections of the signals (A) show no visible changes during the pre-ictal phase. Three RQA measures clearlyshow the dynamic changes of EEG signal preceding the seizures (B, C, D), e.g., %REC (B), %DET (C), and ENTR (D) progressively decreasefrom the inter-ictal to ictal phases.

To follow the changes of these RQA measures overtime, a moving-window technique is applied to a long-term rat EEG data. EEG signal firstly is divided intosegments of 5 seconds (1000 points), then the RP iscomputed after embedding the EEG segment with adimension of m = 15, a delay of τ = 11 [28], and aradius of ε = 1.5 (in units of the standard deviation σ ).Finally, three RQA measures are calculated to discoverthe EEG dynamics over time. Herein, two case studieswere shown, since the results of others ten cases weresimilar with ones of two cases.

Figs. 2(A) and 3(A) showed the long-term EEGrecordings of two rats, respectively. A gray verticalbar marked the extended pre-ictal phase. From the ob-servation of %REC, %DET, and ENTR over the en-tire EEG recordings (seeing Figs. 2(B)–(D) and 3(B)–(D)), it is found that these three measures can trackthe complexity changes of brain electrical activity overtime. As can be seen in Figs. 2 and 3, three RQA mea-sures reveal a progressive decrease during the pre-ictalphase, then reach a minimum value before the onset ofa seizure.

High %REC represents high probabilities of the oc-currence of the same state at the different time. %RECin Figs. 2(B) and 3(B) appears in the higher level dur-

ing the inter-ictal phase, which indicated that the brainelectrical activity share a similar underlying dynamicin this period. During the extended pre-ictal phase,%REC decreases to a minimum value prior to the on-set of the seizures. However, an altered state of thebrain dynamics is hard to be observable from EEGtime series itself. In Figs. 2(C) and 3(C), %DET aresensitive to quickly and highly the fluctuating EEG,the values of the %DET fluctuate but still remain inrelatively small bounds during the inter-ictal phase,from 0.8 to 0.9. It is found that %DET decreases fromthe inter-ictal to ictal phase, the dynamics of brainelectrical activity experienced changes prior to theepileptic seizure. Also, ENTR in Figs. 2(D) and 3(D)are high during the inter-ictal phase (large diversity inthe diagonal line lengths), but lowered during the ic-tal phase (small diversity in the diagonal line lengths),which indicate the loss of recurrence complexity.

5. Discussions and conclusions

Up to now the seizure-generating mechanisms isnot very clear [29]. Some methods are being exploredto discover the mechanism of the phase transition from

comlexity reduction

seizure initation: lower signal complexity (higher synchrony)

56

Towards prediciting seizuresSimilarities in precursory features in seismic shocks and epileptic seizures

P. G. Kapiris, J. Polygiannakis, X. Li, X. Yao and K. A. Eftaxias Europhys. Lett., 69(657–663) 2005

P. G. Kapiris et al.: Common precursory feat ures 659

0 2 4 6 8 10 12 14 16 18 20−500

0

500

Time (min)

(mV)

41 2 3

a25/08/99 28/08/99 31/08/99 03/09/99 06/09/99 09/09/99

0

500

1000

1500

2000

(mV)

EQ

41 2 3

a’

0.8 10

0.2

0.4

0.6

ρ

Pro

babi

lity

1

0.8 1ρ

2

0.8 1ρ

3

0.8 1ρ

4

b0.5 1

0

0.1

0.2

0.3

0.4

ρ

Pro

babi

lity

1

0.5 1ρ

2

0.5 1ρ

3

0.5 1ρ

4

b’

0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4 53%r > 0.97

β

Pro

babi

lity

1

0.5 1 1.5 2 2.5

75%r > 0.97

β

2

0.5 1 1.5 2 2.5

93%r > 0.97

β

3

0.5 1 1.5 2 2.5

93%r > 0.97

β

4

c0.5 1 1.5 2 2.5

0

0.1

0.2

0.3

0.4 05%r > 0.85

β

Pro

babi

lity 1

0.5 1 1.5 2 2.5

50%r > 0.85

β

2

0.5 1 1.5 2 2.5

73%r > 0.85

β

3

0.5 1 1.5 2 2.5

06%r > 0.85

β

4

c’

H∈[0,0.5)

H0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

H∈[0.5,1]

Time (min)

d0 2 4 6 8 10 12 14 16 18 20

H∈[0,0.5)

H0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

H∈[0.5,1]

d’25/08/99 28/08/99 31/08/99 03/09/99 06/09/99 09/09/99

0 2 4 6 8 10 12 140

1

2

3

4

5x 10

8

Seizure

Σ A

(t i )2

Time (min)

e24/08/99 27/08/99 30/08/99 02/09/99 05/09/99 08/09/99

0

5

10

15x 10

10

EQ

Σ A

(t i )2

e’

dB−10 −8 −6 −4

Per

iod

(s)

pre−ictal period

f

Time (min)0 2 4 6 8 10 12 14 16 18 20

0.1

dB−20 −15 −10 −5

Per

iod

(s)

EQ

f’29/08 30/08 31/08 01/09 02/09 03/09 04/09 05/09 06/09 07/09 08/09

10

100

1000

Fig. 1 – (a) R at EEG time series. The sampling rate was 200Hz. Bicuculline i.p. injection was usedto induce the rat epileptic seizures. The green, red and ochre epochs show the normal state, thepre-epileptic phase, and the stage of the epileptic seizure, respectively. (a′) EM anomalies recordedat magnetic loop antennas during the last days before the A thens EQ. The consecutive green, redand green epochs show the normal state, the pre-seismic phase, and the aftershock state (new normalstate), respectively. The sampling rate was 1Hz. (b)/(b′) Histograms of probability distribution ofthe correlation coefficient r calculated on 1024 measurements segments for the four consecutive timeintervals mark ed in (a)/(a′). (c)/(c′) Histograms of probability distribution of the exponent β calcu-lated on 1024 measurements segments for the four consecutive time intervals mark ed in (a)/(a′). Theinsets show the percentage of segments with r > 0.97 and r > 0.85, respectively. (d)/(d′) Decom-position of time series into sub-sets, each characterized by a different local Hurst exponent H. Thebehaviour of the pre-ictal/pre-seismic signal becomes persistent in the tail of the precursory phase.(e)/(e′) depict the cumulative energy release, in arbitrary units, as a function of time. (f)/(f′) Thewavelet power spectrum of the time series. The intensity scale on the top shows colours correspondingto the values of the square spectral amplitudes in arbitrary units.

The gradual increase of r-values with time suggests that the fractal character of the underlyingprocesses and structures b ecomes clearer with time.

Signatures indicating the approach to the global instability. – The β-exponent lies b etween1 and 3 during the precursory epochs (red epochs in figs. 1a, a′). This evidence implies that the

57

Towards prediciting seizures

Transiton from pre-epileptic and pre-seizmic

states toward critical states:

gradually increased spatial and temporal correla-

tions more dramatic change in energy release

better supports the“intermitten ciriticality”than

the “self-organzied criticality” hypothesis

58

Dynamical models of extreme events

Model of self-organized criticality: Sandpile model

The same effect may lead to small, but also to very large avalanches

(not predictable)

Toy model: Bak, Tang, and Wiesenfeld 1987

59

Each point z(x, y) in the grid has a number n associated

with it.

(say, average slope of the sand pile at that point)

for a randomly selected point: z(x, y)→ z(x, y) + 1

if z(x, y) > threshold, than

z(x, y) = z(x, y)− 4

z(x± 1, y)→ z(x± 1, y) + 1

z(x, y ± 1)→ z(x, y ± 1) + 1

If this redistribution causes n to be too big for any nearby

grid points → iteration

else stop and take randomly another point z(x, y)

60

Dynamical models of extreme eventsModel of self-organized criticality: Sandpile model

Perturbation of different points→avalanches with different size

small events which don’t stop → unpre-

dictability?

61

Dynamical models of extreme events“Explosions”: Finite time singularities

intermittent criticality

The simplest representative dynamical evolution equation leading to a

finite-time singularity is:dE

dt= Em, its solution is: E(t) = E(0)

(tc − ttc

)− 1m−1

10

20

30

40

50

60

70

80

90

0 1 2 3 4 5 6

0 < m ≤ 1

1.0 1.5 2.0 2.5

020

040

060

080

0

m > 1

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Earthquakes, Epilepsy, Stock Market Crashes:Predicting and Managing Extreme Events

E I+−

+ −

Figure 17: An excitatory-inhibitory networks supplemented with self-excitatory and self--inhibitory connections

• Uncompensated positive feedback: epilepsy and financial crisis

• Onset of two types of financial crisis

• Stock market crash and hyperinflation: generated by the positive feedback between the Actual and the

Expected Growth Rate

• Large stock market crashes are social analogues of epileptogenesis

• Unsustainable velocity of price increase resembles to over-excitation of the epileptic brain

• Disinhibition: systems without having the ability to ”cool down” are subject of explosion

• Seizure prediction?

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Grand conclusions

• Newton’ dynamical model: predictions led to the discovery of Neptune and Pluto

• What to do with this dynamical approach to social sciences?

• Social sciences: the overwhelming majority of data has been evaluated and interpretedin static or equilibrium perspective

• Something should be done with social data deluge

• The a priori knowledge of the rules, which basically govern the dynamic evolution ofthe systems, is difficult;

• By combining inductive and deductive strategies and using high-performance comput-ing: we hope to predict our social Neptunes and Plutos

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Cooperation

Hungarian students:Kinga Makovi (now: Columbia Univ.)Peter Volf (lionshare of the work)Anett Szabo

Seniors in Budapest:Zoltan SomogyvariLaszlo Zalanyi (Budapest)

Seniors in the US:Katherine Strandburg (NYU)Jan Tobochnik (Kzoo)Bryan D Jones (Austin)Frank Baumgartner (Chapel Hill)

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COMPUTATIONAL SOCIAL SCIENCE I - geza.kzoo.edugeza.kzoo.edu/~erdi/leckek/lec1.pdf · 6.Earthquakes,...

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