How to Intervene?
The Curious Case of Form and Function in Complex Systems
Casper van Elteren is born in pic-
turesque Amsterdam. The author em-
bodies the quintessential spirit of Dutch
creativity and wit. From a young age,
his insatiable curiosity and boundless
ingenuity have driven him to explore
the world through a unique lens. His
works, though not widely read, res-
onate deeply with a silent yet appre-
ciative audience who admire his abil-
ity to capture the essence of the hu-
man experience with subtle brilliance.
———————————————————————————
“Casper van Elteren has
a particular talent for
elucidating a complex
topic by tackling it from
multiple angles and
focusing on salient
details without losing
sight of the greater story
and context. He
naturally navigates the
issue at both macro and
micro levels of analysis,
and clearly articulates
how to reconcile the
two.”
‘The picture of Casper
on this book reminded
me that before he
started his PhD, Casper
was actually a healthy,
happy and skinny
person.”
“Casper’s work
exemplifies how someone
with broad interests can
still delve into the core
of their subject. This
thesis not only
demonstrates impressive
breadth and depth but
also excels in both form
and function.”
– J.D.A de Bouter – W.M. Rouwhorst – B. Chatel
University of Amsterdam
Casper van Elteren
How to Intervene?
University of
Amsterdam
How to Intervene?
The Curious Case of Form and Function in Complex
Systems
Casper van Elteren
University of Amste rdam
Promotiecommissie
ε
&
https://github.com/cvanelteren/template- uva-thesis
https://github
.
com/suchow/Dissertate
form function
Contents
v
vi
1
5
9
25
55
67
85
99
105
109
125
I(s
τ
i
; S
τ +t
)
139
149
165
Key Findings and Contributions
—
—
τὸ παν ἄλλο ἐστὶ τὸ ὂλον παρά τὰ μόρια
besides
Il faut imaginer Sisyphe heureux
Introduction
how
—
how to
intervene in complex systems
its
form its function
The Kanawa Tsugi (かなわつぎ) demonstrates how fundamental components interlock with precise geometric relationships, where
each part ts perfectly to create structural integrity. Like a complex system, its strength is derived from the thoughtful arrangement of
simple, interlocking elements.
Chapter 1
Complex Systems: a
Decomposition of Form and
Function
He who loves practice without theory is like the sailor who boards ship without a rudder
and compass and never knows where he may cast.
Abstract
— —
Three Myths in Complexity Science and How to Resolve Them
10.48550/arXiv.2407.01762 2407.01762
–
Myth 1
Myth 2
Myth 3
–
S = (P, R) P
R(P )
complexus
plectere
Figure 1.2. Complex systems across multiple scales of organization.
a
a
Figure 1.1. The Blind Men and the Elephant metaphor
illustrates the challenges in complex systems analysis.
Cartoon by G.
Renee Guzlas.
complex systems
its form
its function
explandum
how
Every resultant is either a sum or a dierence of the co-operant forces; their sum,
when their directions are the same –their dierence, when their directions are
contrary. Further, every resultant is clearly traceable in its components, because
these are homogeneous and commensurable. It is otherwise with emergents, when,
instead of adding measurable motion to measurable motion, or things of one kind
to other individuals of their kind, there is a co-operation of things of unlike kinds.
The emergent is unlike its components insofar as these are incommensurable, and
it cannot be reduced to their sum or their dierence.
Problems of Life and Mind
feels
Box 1 Explanations in Complex Systems: Reductionism, and Holism
Figure 1.3. The tension between reductionism and holism can be resolved by considering both approaches
in terms of the level of compression.
emergere
ex- mergere
hyle morphe
The whole is not merely the sum of its parts, but it is something more than this.
Science and Hypothesis
— —
dierent
—
Box 2 Complex Systems and Emergent Novelty
C
c
=
C C
Figure 1.4. Novelty can be understood of system C
by creating an augmented system C
′
, eectively creat-
ing a nested hierarchy
C
C
Q
Q
|C|
C
C
′
c ∈ C
(Q
′
)
|c|
all the way
down
Denition 1: Emergent property
Denition 2: Emergent behavior
Myth 1: The whole is more than the sum of its parts.
Myth 2: Emergent Systems Evade Reductionist Analysis.
Myth 3: Emergent Systems Requires Many Entities.
Killing Commendatore
—
The Koshikake Arigata (こしかけありがた) shows how structural form is achieved through its unique angle-bracing design, where
each brace is carefully positioned to create functional strength, illustrating the seamless integration of form and function.
Chapter 2
Does form imply function?
Form follows function –that has been misunderstood. Form and function should be one,
joined in a spiritual union.
Abstract
Physica A: Statistical Mechanics and its Applications
10.1016/j.physa.2022.126889
Figure 2.1. Driver node inference. This gure demonstrates how dierent methods identify driver nodes in a
system governed by kinetic Ising spin dynamics.
X Y
Y X Y
causal
how much
one single node entire
S =
{s
1
, s
2
, . . . , s
n
} E = {(s
i
, s
k
)|s
i
, s
k
∈ S} s
i
∈ S
A
s
i
∈ S
S
t
p(S
t
|S
t−1
, . . . , S
t
0
) = p(S
t
|S
t−1
),
s
i
∈ S
p(S
t
|S
t−1
, . . . , S
t
0
) = p(S
t
|S
t−1
) =
j
p(s
t
j
|S
t−1
) = p(s
t
i
|S
t−1
).
S
t+1
= X
′
S
t
= X
g(X
′
|X) X
′
A(S
t+1
= X
′
, S
t
= X) = min (1,
p(S
t+1
= X
′
)g(S
t+1
= X|S
t
= X
′
)
p(S
t
= X)g(S
t+1
= X
′
|S
t
= X)
)
= min (1,
p(s
t+1
i
= x
′
)g(s
t
i
= x|s
t
i
= x
′
)
p(s
t+1
i
= x)g(s
t
i
= x
′
|s
t
i
= x)
),
x
′
∈ A S
t+1
= X
S
t+1
s
i
∈ S
X
′
x
′
A g(x
′
|x) = g(x|x
′
) = g(x
′
) =
1
|A|
g (X
′
|X)
g (X|X
′
)
=
g (x
′
|x)
g (x | x
′
)
= 1
β
p( X
′
) =
p
(
X
′
)
p(X)
=
1 H(X
′
) − H(X) < 0
exp(−β(H(X
′
) − H(X))
H(S)
H(S) = −
i,j
J
ij
s
i
s
j
− h
i
s
i
.
β
1
k
b
T
k
b
J
ij
s
i
s
j
h
i
i J
s
i
, s
j
∈ S |J
ij
|> 0
J
|S|×|S| J
ij
∈ {0, 1}
β
β
p(s
i
= a), a ∈ A
β → 0 β
driver node
ϵ s
j
∈ S
p
′
s
j
(s
t
i
|S
t−1
) = p(s
t
i
|S
t−1
) + ϵδ
ij
,
δ
ij
(ϵ) = |A|
|A|
i=0
ϵ
i
= 0
|A|
i=0
|ϵ
i
|= c c ∈ (0, 1] ϵ
0 ≤ p
′
≤ 1
p(S
τ
) ϵ
p
′
(S
τ
)
t
t = τ
s
i
∈ S
Γ(s
i
) =
∞
t=τ
γ(s
t
i
)∆t
=
∞
t=τ
s
j
∈S
D
KL
(p
′
s
i
(s
t
j
)||p(s
t
j
))∆t
D
KL
∆t = 1
D
KL
(p||q)
p = q Γ(s
i
) =
0 i
s
i
∈S
(Γ(s
i
))
∆t
= τ − t
0
P
′
s
i
(S), ∀s
i
P (S) τ τ
Γ(s
i
)
τ
τ = 15
τ = 25
τ
τ
τ
Figure 2.2. Eect of intervention size on system magnetization ⟨M
t
⟩ =
1
n
∑
i
s
t
i
with kinetic Ising spin dynamics
(see 2.1.1). s
0
s
0
s
0
a priori
energy
H
s
k
(S) = −
i,j
J
ij
s
i
s
j
−
i
h
i
s
i
− ηs
i
δ
ik
.
s
k
η
η → ∞ s
k
s
j
η := {η :
η = 0.55+i, i ∈ {1, . . . , 10}}
η
s
i
H(s
i
) = −
s
i
=x
p(x) log p(x).
log
s
i
S
X Y
I(X : Y ) =
x∈X,y∈Y
p(x, y) log
p(x, y)
p(x)p(y)
= H(X) − H(X|Y ),
p(x) p(y) p(x, y) X Y H(X|Y )
30 25 20 15 10 5 0
0
0.2
0.4
0.6
0.8
1
0
1
2
3
Time (t)
I(
S
t
0
,
s
t
0
i
)
Figure 2.3. Example of non-causal ination of
mutual information decay.
X H(X|Y )
X Y
S = {s
i
, s
j
} s
j
s
i
s
i
s
j
downstream
t
0
+ t t > 0
t < 0
I(S
t
0
−t
; s
t
0
i
)
s
t
0
−ω
j
s
t
0
i
S
t
0
−t
s
t
0
I(s
t
0
−t
i
: s
t
j
)
s
i
S
t
0
t
0
s
t
0
−t
i
t
t = 0 I(s
t
0
i
; S
t
0
) = H(s
t
i
)
I(s
t
0
−t
i
; S
t
0
) = I(s
t
0
+t
i
; S
t
0
)
I(s
t
0
+t
i
; S
t
0
)
µ(s
i
) =
∞
t=t
0
I(s
t
0
−t
i
; S
t
0
)∆t,
I(s
t
0
−t
i
; S
t
0
)
always t → ∞
how fast this decay takes
place for each node informational impact
I(S
t+1
; s
t
i
)
I(s
t
0
+t
i
; S
t
0
)
r
β
−1
p(S
t
0
) p(S
t
0
+t
|S
t
0
)
N = 1.000 × 10
3
p( S
t
0
)
N
Figure 2.4. Experimental setup.
t
n
= 1000 t
n
= 1000
t I(s
t
0
+t
i
; S
t
0
)
τ
τ
p(s
t
0
+t
i
|S
t
0
) S
i
∈ S
t
0
n
= 20
t
s
t±1
i
S
t
[0, 1] y = a exp(−b(t − c)) +
d exp( − e ( t − f))
Λ ϕ
ϕ = 0.5
Λ
i j ϕ
ij
> 0.5
N = 1e4 M = n
= 20
N
Λ f
Λ
cent
= f
cent
(x) := {x ∈ S : f
cent
(s) ≤ f(x)∀s ∈ S}
f
f
deg
(a
i
) =
j
a
ij
a
ij
i j A
a
ij
> 0 i j
J =
A ∩ B
A ∪ B
.
R
cent
= J
IM I
− J
cent
J
cent
N =
1.000 00 × 10
5
α = 0.01
(0, ∞)
Figure 2.5. Jaccard score per system (see g. 2.4 D for the various network structures) as a function of intervention
size
η = ∞
J
(η
∗
) (η = ∞)
Figure 2.6. Example of typical experimental results.
η
∗
η = ∞
t = τ t > τ
p << 0.01
η = 0.1
Figure 2.7. Mutual information decay (I(s
t
0
+t
i
; S
t
0
+t
)) (top) and causal impact (γ(s
τ +t
i
) for minimal soft
intervention η
∗
(middle) and hard intervention (bottom).
η
∗
X
Figure 2.8. Comparative analysis of IMI and centrality-based driver node prediction.
R
cent
= J
IM I
− J
cent
α = 0.01
η = ∞
Figure 2.9. Driver Node Identication Analysis in Psychosymptom Networks Using IMI and Network Features.
α < .01
α < 0.05
not
η = c
η
∗
ϕ = 0.5 Λ
ϕ
I(s
t
0
+t
i
; S
t
0
) t → ∞
I(s
t
0
+t
i
; S
t
0
)
t
t → ∞
γ
I(s
t
0
+t
i
: S
t
0
)
s
i
(n = 12)
–
The Kawai Tsugite (かわいつぎて) demonstrates how functional requirements shape the form of the joint. Its assembly sequence
reveals how each component is meticulously aligned to meet specic functional needs, dening the structural possibilities within the
design.
Chapter 3
Does function imply form?
The aordances of the environment are what it oers the animal, what it provides or fur-
nishes, either for good or ill.
Abstract
—
Entropy 10 .
3390/e26121050 Nature Communications
initiator
stabilizing
0 2000 4000 6000 8000 10000
Time (
t
)
0
0.2
0.4
0.6
0.8
1
Instantaneous system macrostate (
S
t
)
1
2
a
Agent state
0 1
S
i
S
Stabilizing dynamics
Destabilizing dynamics
b
0 0.2 0.4 0.6 0.8 1
System macrostate (
S
)
0
0.1
0.2
P
(
S
)
c
20
0
Energy ( (
S
) )
0 0.25
P
(
S
)
Figure 3.1. A dynamical network governed by kinetic Ising dynamics produces multistable behavior.
β ≈ 0.534
S
i
∈ S
S
i
∈ S
p(S)
s
i
s
′
i
P (s
i
→ s
′
i
) =
1
1 + exp(−β∆E( s
i
, s
′
i
))
,
∆E(s
i
, s
′
i
) β
β
β
τ
s
t
i
t
S
t+τ
I(s
τ
i
: S
τ +t
) t
µ(s
i
) =
∞
t=0
(I(s
τ
i
: S
τ +t
) − ω
(
s
i
))∆t.
µ(s
i
)
ω(s
i
) ∈ R
≥0
ω(s
i
)
ω(s
i
)
ω(s
i
)
—
—
role
initiators
stabilizers
0 20 40 60 80 100120140
0
0.1
0.2
0.3
0.4
0.5
Information flow
I(s
i
:S
+t
| S )
S = 0.1
a
0 20 40 60 80 100120140
0
0.02
0.04
0.06
0.08
S = 0.2
b
0 20 40 60 80 100 120 140
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
S = 0.3
c
0 20 40 60 80 100120140
0
0.2
0.4
0.6
0.8
S = 0.4
d
0 20 40 60 80 100120140
0
0.2
0.4
0.6
0.8
1
Tipping point
S = 0.5
e
0 0.2 0.4 0.6 0.8 1
0
2.5
5
7.5
10
12.5
15
17.5
20
Integrated mutual information
( (s
i
))
f
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Asymptotic information ( )
g
Fraction of nodes in state +1
Time (t)
System macrostate ( S )
Figure 3.2. When networks fall like dominoes: an essential interaction between short-lived and long-lived correla-
tions.
n = 10
⟨S⟩ = 0.5
τ = 300
O(n) =
2
n
domino eect
initiators
stabilizers
S
γ
= {S
′
⊆ S|⟨S
′
⟩ = γ} γ ∈ [0, 1]
µ(s
i
|⟨S⟩) =
∞
t=0
(I(s
τ
i
: S
τ +t
|⟨S
τ
⟩) − ω
s
i
)∆t.
µ(s
i
|⟨S⟩)
S = {0, . . . , 0} t = 5
log p(S
t+1
|S
t
, S
0
= {0, . . . , 0}, ⟨S
5
⟩ = 0.5).
i
r
i
= max
⟨S⟩
µ
∗
(s
i
|⟨S⟩) − max
⟨S⟩
ω
∗
(s
i
) ∈ [−1, 1],
µ
∗
ω
∗
µ ω
0
1
2
3
4
5
6
7
8
9
0.00
0
1
2
3
4
5
6
7
8
9
0.10
0
1
2
3
4
5
6
7
8
9
0.20
0
1
2
3
4
5
6
7
8
9
0.30
0
1
2
3
4
5
6
7
8
9
0.40
0
1
2
3
4
5
6
7
8
9
0.50
Node state
0 1
Fraction of nodes in +1
Figure 3.3. The tipping point is initiated from the bottom up
∑
5
t=1
log p(S
t+1
|S
t
, S
0
= {0}, ⟨S
5
⟩) = 0.5)
0 0.2 0.4 0.6 0.8 1
Instantaneous macrostate S
+10
0
0.05
0.1
0.15
0.2
P( S
+10
|s
i
=0, S =0.5 )
a
Control
0 1 2 3 4 5 6 7 8 9
Intervention on node
0
0.0025
0.005
0.0075
0.01
0.0125
0.015
0.0175
Transition ratio (
p
succes
p
failure
)
b
Node
0
1
2
3
4
5
6
7
8
9
Figure 3.4. Conditional probabilities reveal source of shifting roles.
t = 10
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2
Time spent below tipping point (
T
T
control
)
0
2
4
6
8
10
12
14
Second moment (
control
)
a
1 1.5 2
0.25
0.5
0.75
1
1.25
S > 0.5
S < 0.5
0 2500 5000 7500 10000 12500 15000 17500
Time(t)
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
Fraction of nodes +1
b
1
0.75
0.5
0.25
0
0.25
0.5
0.75
1
Node role (r
i
)
Initiator
Stabilizer
1
0.75
0.5
0.25
0
0.25
0.5
0.75
1
Node role (r
i
)
Initiator
Stabilizer
Figure 3.5. Role duality in noise-induced tipping points
stabilizers
initiators
N = 100 p = 0.2
< 0.5
how
The Kakushi Domekata Sanmai Hozo (かくしどめかたさんまいほぞ) represents a delicate choreography of hidden connections
between revelation and concealment. Its hidden mechanism provides structural integrity while maintaining an outward simplicity.
Chapter 4
How to intervene?
All models are wrong, but some are useful.
Abstract
—
—
Scientic Reports
10.1038/s41598-024-68445-0
—
—
“”
Z a
i
= {r
i
, s
i
}, i ∈ {1, ..., Z}
R r
i
∈ {1, ..., R} s
i
∈ {0, 1}
z
r
= Z
r
/Z
R
r=1
z
r
= 1
R = 3
s
i
= 0 s
i
= 1
i
n a
i
a
j
g
ij
= 1 g
ij
= 0 G = [g
ij
]
a
i
R − 1 {a
k
: r
k
= r a
ik
= 1} r ∈ {1, ..., R } \ r
i
M
i
R − 1 a
i
M
i
b R
c
i s ∈ {0, 1}
π
(i)
s
= s
b
s
j
∈M
i
s
j
− c
.
n M
i
⟨π
(i)
s
⟩
i
s = 1 s = 0
s s
′
p
s→s
′
=
1
1 + e
−
1
ϵ
(
⟨π
(i)
s
′
⟩−⟨π
(i)
s
⟩
)
,
ϵ
ϵ → ∞
ϵ → 0
g
ij
= 1 i j
x
r
=
1
z
r
Z
i:r
i
=r
s
i
n → ∞
lim
n→∞
d
dt
x
r
=
1
1 + e
−
1
ϵ
b(
∏
R
q=0,q=r
x
q
−
c
b
)
− x
r
,
b c ϵ
c/b ϵ/b
R
R = 3
z
1
= z
2
= z
3
c/b ϵ/b b = 1 c ϵ
b
R
R ≥ 2 R
ϵ
ϵ = ∞ ϵ = 5
R
(c/b)
crit
= 1/2
R−1
ϵ
(c/b )
H
(c/b)
L
(c/b)
L
(c/b)
R
A → B
(c/b)
R
B → C
C → D
(c/b)
L
D → C
resilience
Figure 4.1. Modulating the decision error in-
duces hysteresis in the system’s behavior.
robustness
ϵ ≳ 40
ϵ = 5
A
c
b
≃ 0.56
B → C
B
Figure 4.2. The emergence of criminal organizations depends on the decision error, the cost-to-benet ratio, and
the initial fraction of criminals.
ϵ
resilience
resilience
Figure 4.3. Link density pro-
motes the resilience of criminal or-
ganizations.
ϵ = 10
C → D D → A
resilience robustness
ϵ
Figure 4.4. The robustness of criminal organizations is promoted by networks characterized by elevated density
and dissortativity.
c
∗
≈ 0.2
c
∗
t = 300
ϵ = 10 Z = 150
ϵ = 10
c
∗
N = 100 Z = 150
c
∗
c
∗
≃ 0.25
c
Figure 4.5. The stability of the system is af-
fected by the exploration rates of the agents and the
number of required roles
The Shihou Kama Tsugi (し ほ う か ま
つぎ) showcases the remarkable craftsman-
ship of Japanese carpentry, where the joint’s
complex three-dimensional form ts together
with geometric precision. This “impossible
joint” relies on carefully aligned angles and
interlocking components, seamlessly merging
mechanical strength with visual harmony in
architectural design.
Chapter 5
How Could Form and Function
Co-evolve?
Shape clay into a vessel; it is the space within that makes it useful. cut doors and windows
for a room; it is the holes which make it useful. therefore, benet comes from what is there;
usefulness from what is not there.
Abstract
The Paradox of Intervention:
Resilience in Adaptive Multi-Role Coordination Networks 10.48550/arXiv.2501.14637
2501.14637
γ
1
= 3.32
0 0.1 0.2 0.3
Fraction
Law Enforcement Related
Corruption and Extortion
Weapon-related Crimes
Informant Related
Violent Crimes
Financial Crimes
Drug-related Activities
A.
0 0.1 0.2 0.3
Fraction
Security guard
Front man
Robber
Supplier
Extraction broker
Coordinator
Gatekeeper
Financier
Distributor
Extractor
Broker
Stasher
Transporter
Exporter
Processor
Driver
Organizer
Importer
Owner
Trader
B.
Figure 5.1. The Netherlands is a strategic gateway for European distribution.
A
B
A.
0 20
Degree
0
0.1
0.2
0.3
0.4
Fraction
1
= 3.32
B.
1 0
Role Assortativity
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
C.
00.511.522.533.5
Ward Cluster Similarity (1
cos
(
x
))
Trader
Extractor
Stasher
Owner
Exporter
Extraction broker
Importer
Front man
Coordinator
Financier
Security guard
Driver
Processor
Supplier
Distributor
Transporter
Robber
Broker
Organizer
Gatekeeper
D.
Role-Role Network
Figure 5.2. Underworld connections: mapping organized crime networks in the Netherlands A
B
γ = 3.31 C
D
i s
π
(i)
s
= s
b
O∈O
i
O
j
s
r
j
− c|O
i
|
,
O
i
i
R s
r
j∈O
j O r ∈ R c
π
(i)
π
′
(i)
p
π
(i)
→π
′
(i)
=
1
1 + e
−
1
ϵ
(
π
(i)
s
′
−π
(i)
s
)
,
ϵ
λ
ϵ
c
b
ϵ
Figure 5.3. Emergence and
evolution of criminal organiza-
tions in a minimal adaptive net-
work model.
0
0.2
0.4
0.6
0.8
1
= 0.010,
c
b
= 0.010 = 0.010,
c
b
= 0.100 = 0.010,
c
b
= 1.000
0
0.2
0.4
0.6
0.8
1
= 0.100,
c
b
= 0.010 = 0.100,
c
b
= 0.100 = 0.100,
c
b
= 1.000
0 0.25 0.5 0.75 1
0
0.2
0.4
0.6
0.8
1
= 10.000,
c
b
= 0.010
0 0.25 0.5 0.75 1
= 10.000,
c
b
= 0.100
0 0.25 0.5 0.75 1
= 10.000,
c
b
= 1.000
Link density (
L
)
Criminality (
S
)
c
b
ϵ
L
t=0
= 1
L
t=0
= 0
⟨S
t=0
⟩ = 0
L
t=0
< 0.5
0 0.2 0.4 0.6 0.8 1
Link density (
L
t
)
0
0.2
0.4
0.6
0.8
1
Criminality (
S
t
)
0
0.1
Freq.
0 0.25
Freq.
0
0.2
0.4
0.6
0.8
1
0.0 2.0
Cost-Benefit Ratio (
c
b
)
0.0
10.0
Decision error ( )
Figure 5.4. Network equilibria
reveal how cost-benet ratios and un-
certainty shape organizational struc-
ture. t =
1000
c
b
> 1 L < 0.3
< 0.3
c
b
≪ 1
H(k) > 0.7 C > 0.8
L
t=0
< 0.5
Figure 5.5. The zoo of crimi-
nal networks
k = 20
30
3 10 , 800
10 5 0 5 10 15 20
15
10
5
0
5
10
15
PCA Component 1
PCA Component 2
c
b
> 1
L < 0.3 < 0.3
c
b
≪ 1
H(k) > 0.7
C > 0.8
ϵ = 11,
c
b
= 0.11 λ = 0. 5
L = 0.5
1.5 1 0.5 0 0.5 1 1.5
Impact Link Density
1.5
1
0.5
0
0.5
1
1.5
Impact Criminality
More Criminal
Organizations
Less Visible
More Criminal
Organizations
More Visible
Less Criminal
Organiztions,
More Social Cohesion
Less Criminal
Organizations,
Less Social Cohesion
1.5 1 0.5 0 0.5 1 1.5
Impact Link Density
1.5
1
0.5
0
0.5
1
1.5
Impact Criminality
1.5 1 0.5 0 0.5 1 1.5
Impact Link Density
1.5
1
0.5
0
0.5
1
1.5
Impact Criminality
0 200 400 600 800 1000
Time(t)
0
0.2
0.4
0.6
0.8
1
Criminality (
S
)
D.
0 200 400 600 800 1000
Time(t)
0
0.2
0.4
0.6
0.8
1
Link density (
L
)
E.
0
1
Freq.
Reintegration
A.
0 1
Freq.
0
1
Freq.
Arrests
B.
0 1
Freq.
0
1
Freq.
Cooperation
C.
0 1
Freq.
0 0.05
Freq.
00.25
Freq.
Betweenness Degree Random Role
Figure 5.6. Response to interventions (A) arrests, (B) reintegration, and (C) cooperation
t = 500
[1, 2, 10, 20] t = 500
—
The Juji Mechigai Tsugi (ジ ュ ウ ジ メ
チ ガ イ ツ ギ) embodies both literal and
metaphorical extension. As a splice joint,
its castle-like interlocking geometry enables
physical elongation of structural members,
while symbolically representing how knowl-
edge itself can be extended through new con-
tributions. The joint’s innovative form, with
its reciprocal castellated interfaces, demon-
strates how traditional woodworking princi-
ples can be carried forward into novel expres-
sions.
Chapter 6
The Curious Case of Complex
Systems
Der Fliege den Ausweg aus dem Fliegenglas zeigen.
how
— —
—
—
–
Ik snap er nog steeds helemaal niks van
Appendix A
Implications for Law
Enforcement
Appendix B
Does Form Imply Function?
Denition 1 X → Y → Z
Z Y X
X, Y, Z
p(x, y, z) = p(x)p(y|x)p(z|y)
Theorem 1 (Data-processing inequality) If X → Y → Z, then I(X; Y ) ≥ I(X; Z).
Proof:
I(X; Y ; Z) = I(X; Z) + I(X; Y |Z)
= I(X; Y ) + I(X; Z|Y )
X Z Y I(X; Z|Y ) = 0
I(X; Y |Z) ≥ 0
I(X; Y ) ≥ I(X; Z).
I(X; Y |Z) = 0
I(Y ; Z) ≥ I(X; Z)■
Corollary 1 If Z = g(Y ) → I(X; Y ) ≥ I(X; g(Y ))
Proof: X → Y → g(Y ) ■
g(Y ) X
Corollary 2 If X → Y → Z, then I(X; Y |Z) ≤ I(X; Y )
I(X; Z|Y ) = 0
I(X; Z) ≥ 0
I(X; Y |Z) ≤ I(X; Y )■
X Y
Z
X
t
0
→ X
t
0
+1
→ . . . → X
t
0
+∞
I(X
t
0
; X
t
0
+t
) t → ∞
p(s
t+1
j
|S
t
) = p(s
t+1
j
|s
t
i
).
s
i
, s
j
∈ S D
KL
(p(s
t+1
j
|s
t
i
)||p(s
t
j
))
I(s
t+1
i
; s
t
j
)
Theorem 2 E
s
i
[D
KL
(p(s
t+1
j
|s
t
i
)||p(s
t
j
)] = I(s
t+1
i
; s
t
j
) when s
i
and s
j
have no common
neighbors.
Proof
E
s
t
i
[D
KL
(p(s
t+1
j
|s
t
i
)||p(s
t
j
))]
=
E
s
t
i
E
s
t+1
j
|s
t
i
log
p(s
t+1
j
| s
t
i
)
p(s
t+1
j
)
=
s
t
i
p(s
t
i
)
s
t+1
j
p(s
t+1
j
| s
t
i
) log
p(s
t+1
j
| s
t
i
)
p(s
t+1
j
)
=
s
t
i
p(s
t
i
)
s
j
log p(s
t+1
j
| s
t
i
) log p(s
t+1
j
| s
t
i
) −
s
t+1
j
p(s
t+1
j
) log p(s
t+1
j
)
= H(s
t+1
j
) − H( s
t+1
j
| s
t
i
)
= I(s
t+1
j
: s
t
i
) ■.
t t
0
−40 −20 0 20 40
Time (t)
0.0
0.2
0.4
0.6
0.8
1.0
I
(
s
t
0
+
t
i
:
S
t
0
)
0
1 2
3
45
*
(a)
−40 −20 0 20 40
Time (t)
0.0
0.2
0.4
0.6
0.8
1.0
I
(
s
t
0
+
t
i
:
S
t
0
)
0
1 2
3
45
*
(b)
Figure B.II.1. Example of time symmetry in directed and undirected networks. B.II.1a
t < t
0
S
t
0
t > t
0
S
t
0
t < t
0
t > t
0
B.II.1b t
0
J
s
i
,s
j
= J
s
j
,s
i
∀s
i
, s
j
∈ S
S(t) = {s
1
(t), s
2
(t), σ(t)} σ(t) = {σ
1
(t −
1), σ
1
(t−1)} H(σ) = −J
s
1
,σ
1
s
1
σ
1
−J
s
2
,σ
2
σ
2
s
2
σ(t)
s
1
, s
2
J
J
i,j
= 1
J
i,j
→ ∞
σ
J
σ
1
,1
= J
σ
2
,2
= 0 J
σ
1
,1
=
J
σ
2
,2
→ ∞ σ
J
σ
1
,1
= J
1,σ
1
= 1, J
σ
2
,2
= J
2,σ
2
= 1
J
σ
i
,i
= J
i,σ
i
→ ∞
s
i
s
j
J
I(s
t
0
+t
i
: S
t
0
I(s
t+1
i
; S
t
) = I(s
t−1
i
; S
t
) p(S
t+1
∗
|S
t
∗
) =
p(S
t−1
∗
|S
t
)
{S
t
: t ∈ N}
P π {S
t
∗
: t ∈ N}
S
0
∼ π S
t
k ≥ 1
S S
t
∗
(k) = S
t−k
∗
0 ≤ k < ∞
S
t−k
∗
S
t
{S
t
∗
: t ∈ Z}
Figure B.II.2. IMI performance in identifying driver nodes: directed vs undirected integrator networks.
σ(t) = {σ
1
(t), σ
2
(t)}
J
1,σ
2
= J
σ
2
,2
→ ∞
{S
t
∗
: t ∈ Z}
P π
i j i → j
p(S
1
∗
= j|S
0
= i) = p(S
1
∗
(k = 1) = j|p(S
0
∗
(k = 1)) = i)
= p(S
0
∗
= j|S
−1
∗
= i)
=
p(S
−1
∗
= i|S
0
∗
= j)p(S
0
∗
= j)
p(S
−1
∗
= i)
=
π
j
π
i
P
i→j
P
i→j
π
i
= π
j
P
j→i
I(s
t+1
i
; S
t
) = I(s
t−1
i
; S
t
)
0 1 2 3 4 5 6 7 8 9 101112131415
System idx
0.00
0.01
0.02
0.03
0.04
0.05
Mean squared error
(a) Model t error analysis across dierent
systems. Average mean squared error ±2SEM per
system
depr
effort
sleep
happy
lonely
enjoy
appet
sad
dislike
getgo
loss
unfr
0.000000
0.000025
0.000050
0.000075
0.000100
0.000125
(b) Average mean squared error ±2SEM for
psychosymptom system.
Figure B.III.1. Model t error analysis.
Figure B.IV.1. Main results from Friend and colleagues [79].
D
X
etc
et al.
i j
i j
implicitly assume
D
c
i
=
j
a
ij
a
ij
i A
a
ij
c
i
=
j,k
σ(j, k|i)
σ(j, k)
σ(j, k) j k σ(j, k|i)
i
i
c
i
=
1
Z
j,k
σ(j, k|i)
σ(j, k)
Z =
((n − 1)(n − 2))
2
i j ∈ N
c
i
=
1
N
j
d(i, j)
.
A i
c
i
=
1
λ
j
a
ij
x
j
↔ Ax = λx
n n
x λ
A
x
1.0000 × 10
4
Λ ϕ
ϕ = 0.5
ϕ ≥ 0.5
ϕ
ϕ
η = 0 η > 0 x
Figure B.VII.1. Driver node detection algorithm in python.
Figure B.VII.2. Kernel density estimation of bootstrap distributions for network analysis.
η = 0 η > 0
x
η = 0 η > 0
Figure B.VII.3. Bootstrap distri-
bution for psychosymptom network.
https:
//github.com/cvanelteren/information
i
mpact
thefriendlyghost.nl
Appendix C
Does Function Imply Form?
how
information dynamics
how
Integrated mutual information
Asymptotic information
X Y
(S)
(s
i
∈ S) (t)
S = {s
1
, . . . , s
n
}
p(S) =
1
Z
exp(−βH(S)) ,
β =
1
T
H(S)
X
′
∈ S
p
(
X
′
) =
1
1 + exp(−β∆E)
,
∆E = H(X
′
) − H(X) X
X
′
S = {s
1
, . . . , s
n
}
H(S) = −
i,j
J
ij
s
i
s
j
− h
i
s
i
,
J
ij
s
i
, s
j
J
ij
how
X Y Y
Y X
S = {s
1
, . . . , s
n
}
S
t
t
S
H(S) = −
x∈S
p(x) log p(x),
log p(x) p(S = x)
S
s
i
S I(S; s
i
)
I(S; s
i
) =
S
i
∈S,s
′
∈s
i
p(S
i
, s
′
) log
p(S
i
, s
′
)
p(S
i
)p(s
′
)
= H(S) − H(S|s
i
).
S
s
i
s
i
S
infor-
mation s
τ
i
S
τ +t
I(S
τ +t
; s
τ
i
) = H(S
τ +t
) − H( S
τ +t
|s
τ
i
).
S
t
s
i
µ(s
i
) =
∞
τ =0
I(s
t−τ
i
; S
t
).
I(S
τ
: s
τ +t
i
)
I(S
τ
: s
τ +t
i
|⟨S⟩)
t = t
1
t = t
2
t
2
>
t
1
I
(
S
t+τ
: s
τ
i
|⟨S⟩)
β =
1
kT
T
k β
C
C =
¯
H(S)D(S),
¯
H(S) =
H(s)
− log
2
(|S|)
D(S)
2 4 6 8 10
Temperature (T)
0
0.2
0.4
0.6
0.8
1
A.
C
H
(S)
D(S)
0 0.2 0.4 0.6 0.8 1
Fraction of nodes in +1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
P(S)
B.
Figure C.II.1. Statistical complexity analysis for parameter optimization. C
H(S) D(S) T =
1
β
p(S)
D(S) =
i
(p(S
i
) −
1
|S|
)
2
.
β
optimize.minimize
I(s
τ
i
; S
τ +t
)
I( s
τ
i
: S
τ +t
) p(S
τ +t
|s
τ
i
) p(S
τ +t
)
⟨S⟩
n
S S
′
s
i
p(S
t
|s
i
) = P
p
ij
p
ij,i=j
=
1
|S|
1
1 + exp(−∆E)
,
p
ii
= 1 −
j,j=i
p
ij
,
∆E = H(S
j
) − H(S
i
) S
i
S
j
S
γ
= {S
′
⊆ S|⟨S
′
⟩ = γ}
p(S
t
|s
i
) s
i
p(S
t
)
p(S
τ +t
) =
s
i
p(S
τ +t
|s
τ
i
)p(s
τ
i
).
t = 500
t
T
1
T
2
T P
M(S
t
) = 0.5
t = 10
6
η
η =
1
α
2
|S
w
|
w
S
t
w
2
,
w ∈ {⟨S⟩ < 0.5, ⟨S⟩ > 0.5}
S
t
w
=
S
t
S
t
< 0.5
1 − S
t
S
t
> 0.5
α
s
i
1 −
1
n
n α
S
⟨S⟩>0.5
α
n
2
−
1
n
T
s
i
s
i
s
i
N {0, 1}
|N|
n
j
∈ N
s
i
s
i
M(S
t
) =
1
|S
t
|
i
s
t
i
.
s
i
E[p(s
i
= 1|N )]
p(N)
=
N
i
∈N
p(N
i
)p(s
i
= 1|N
i
)
=
N
i
∈N
|N
i
|
j
p(n
j
)p(s
i
= 1|N
i
)
=
N
i
∈N
n
k
f
k
(1 − f)
n−k
p(s
i
= 1|f ),
0.10 0.20 0.30 0.40 0.50
System stability
Fraction of nodes with state +1
Figure C.IV.1. Analysis of Alternative network structures beyond the Krackhardt kite graph.
f n
k
s
i
00.20.40.60.81
0
0.2
0.4
0.6
0.8
1
Tipping point
Degree (k)
1
2
3
4
5
6
7
8
9
10
Fraction of nodes being in +1
E[p(s
i
= + 1|N)]
Figure C.V.1. Tendency of a node
to ip.
k
β = 0.5
N
E[p(s
i
)|N] = 0.2
⟨S⟩
0.0 0.1 0.2 0.3 0.4 0.5
Fraction of nodes with state+1
Figure C.V.2. Path analysis reveals domino mechanism towards tipping points.
E[s
i
= 1]
S
t
,M(S
5
)
2
n
Figure C.VI.1. Erdős-Rényi
graphs generated from seed = 0 to
produce non-isomorphic connected
graphs.
2
|S|
×
2
|S|
I(s
τ
i
: S
τ +t
)
O(2
|S|
) O(2
t|S|
)
c ∈ [0, 1]
t − 2
12.5 12 11.5 11 10.5 10 9.5
Trajectory probability
(
5
t
=1
log
p
(
S
t
+1
|
S
t
,
S
0
={0},
S
5
)=0.5)
)
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Frequency
A.
0 1 2 3 4
Time(
t
)
B.
Figure C.VIII.1. Trajectory analysis and cascade patterns in network collapse.
0 50
0
0.5
1
0 50
0 50
0 50
0 50
0 50
0 50
S
= 0.1
S
= 0.17
S
= 0.23
S
= 0.3
S
= 0.37
S
= 0.43
S
= 0.5
Time (t)
I
(
s
t
+
i
:
S
t
)
Figure C.IX.1. Scaling analysis: information ow patterns in larger networks.
N = 15
⟨S⟩ = 0.1
I
min
Appendix D
How to Intervene?
Z = 150
Z
r
= 50∀r ∈ R = 1, . . . 3
f
∈ {
0
,
0
.
1
}
f = 1
n q
q
′
[0, 100]
[0, 10]
G
A
G
=
T r(M ) −
(M
2
)
1 −
M
2
M
Figure D.I.1. A typical output for increasing assorta-
tivity for xed link density; as the number swaps increase,
the associativity increases.
T = 1000
Z = 300
https://github.com/
cvanelteren/boiler
r
oom
n =
100
β
S
t
= {s
1
, s
2
, . . . , s
z
}
t robustness
0.2 0.4 0.6 0.8 1
0.2
0.4
0.6
0.8
1
a
0.2 0.4 0.6 0.8 1
b
0 0.5 1
Fraction of criminals
Cost/benefit ratios (
R
)
Decision error ( )
Figure D.I.2. Simulations were performed on a complete graph with Z = 150 agents. t = 300
T = 100 ϵ
(R)
c
∗
(ϵ, ⟨S
0
⟩ = 1) = max
c
⟨S
t
⟩ = 1.
c
∗
⟨S
0
⟩ = 1
β
ϵ = 10 c
∗
t = 300
O
t
=
Z
i=0
M
t
i
M
t
i
,
M
t
i
i t M
t
i
i t
x
r
r ∈ R r
π
r
= (1 − x
r
)
n
k=0
(
R
j=0,j=i
x
j
)
k
(1 −
R
j=0,j=i
x
j
)
n−k
1
1 + e
−
1
ϵ
(kb
∏
R
j=0,j=i
x
j
−cn)
.
x
r
d
dt
x
i
= E[x
+
i
] − E[x
−
i
]
= (1 − x
i
)
n
k=0
n
k
R
j=0
j=i
x
j
k
1 −
R
j=0
j=i
x
j
n−k
1
1 + e
−ϵ
(
k
n
b−c
)
− x
i
n
k=0
n
k
R
j=0
j=i
x
j
k
1 −
R
j=0
j=i
x
j
n−k
1
1 + e
−ϵ
(
k
n
b−c
)
=
n
k=0
n
k
R
j=0
j=i
x
j
k
1 −
R
j=0
j=i
x
j
n−k
1 − x
i
1 + e
−ϵ
(
k
n
b−c
)
−
x
i
1 + e
−ϵ
(
k
n
b−c
)
=
n
k=0
n
k
R
j=0
j=i
x
j
k
1 −
R
j=0
j=i
x
j
n−k
1
1 + e
−ϵb
(
k−
c
b
n
)
− x
i
.
n → ∞
lim
n→∞
d
dt
x
i
=
1
1 + e
−
1
ϵ
b(
∏
R
j=0,j=i
x
j
−
c
b
)
− x
i
,
{0, 1}
b
R ≥ 2
c
b
≈ 0.5
ϵ ϵ → 0
ϵ = 2
R = 4
R = i+1 R = i
x
∗
R = 0.2
R
Figure D.III.1. Bifurcation diagram of the system dynamics as a function of the number of roles.
Figure D.IV.1. Non-criminal groups can be comprimised by increased link density between the groups.
robustness
robustness
I shall not today attempt further to dene the kinds of material I understand to
be embraced within that shorthand description. But I know it when I see it, and
the motion picture involved in this case is not that I know it when I see it
it is organized
organized crime
embedded
Appendix E
How Could Form and Function
Co-evolve?
µ
µ
λ
µ = 1
Figure E.I.1. The system dynam-
ics show increased uctuations when
agents have access to global informa-
tion.
ϵ = 0
λ
i s
i
∈ {0, 1}
b
b c
i
i
π
(i)
s
= s
b
O∈O
i
O
j
s
j
− c|O
i
|
,
O
i
i
R s
r
j∈O
j O r ∈ R c
(⟨k ⟩ )
2
π
(i)
π
′
(i)
p
π
(i)
→π
′
(i)
=
1
1 + e
−
1
ϵ
(
π
(i)
s
′
−π
(i)
s
)
,
ϵ
λ
a
i
→ a
′
i
Z = 30
R = 3
≤ 0.1
t = 100 t = 100
tz = 30000
λ
λ = 0
λ =
λ → 0
c
1
Z−1
1
2
Z
M−1
M
Z
µ
mu = 1
µ = 0
µ → 0
µ = 0
µ = 1
µ
µ
D
t ∈ T D
I(D; T )
I(T ; D ) = H(D) − H(D|T )
=
t∈T
p(t|D)p(D)(H(D) − H(D|t)),
H(D) H(D|T )
t
a
i
= max
t∈T
I(t; D).
1 2 3 4 5 6 7 8 9
Number of roles per individual
0
0.1
0.2
0.3
0.4
Fraction
0 0.1 0.2 0.3
Frequency role occurence
Security guard
Front man
Straw man
Robber
Extraction broker
Coordinator
Financier
Supplier
Distributor
Gatekeeper
Extractor
Processor
Stasher
Transporter
Driver
Broker
Exporter
Owner
Importer
Organizer
Trader
Figure E.III.1. Distribution and frequency of criminal network roles in Dutch drug markets.
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
W
2
=0.02
Degree
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
W
2
=0.16
Closeness
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
W
2
=0.01
Betweenness
1 0.5 0 0.5 1
0
0.05
0.1
0.15
0.2
0.25
0.3
W
2
=0.28
Assortativity
Optimal Observed
Centrality value
Fraction
Figure E.IV.1. Comparison of
calibrated model to data
W
2
L = 0.05
L = 0.03
p ≪ 0.05
ϵ
c
b
λ = 0.5
c ∈ [0.001, 2] ϵ ∈ [0.001, 10] 500
1000 n = 10
F =
(⟨S
O
⟩ − ⟨S
M
⟩)
2
+
1
Z(Z − 1)
i,j
(a
O
i,j
− a
M
i,j
)
2
F O
M ⟨ S⟩
a
i,j
⟨S
O
⟩ = 1
1000
t = 1000
n ∈ {1, 5, 10, 20}
µ = 0 t = 1000
Reintegration
Arrests
Cooperation
z = 30
R
1 0.5 0 0.5 1
1
0.5
0
0.5
1
1 0.5 0 0.5 1
1 0.5 0 0.5 1
0
2
Reintegration
A.
0 1
Arresting
B.
0 1
Cooperating
C.
0 1
Betweenness Degree Random Role
Change in Link Density (
L
i
L
c
)
Change in Criminality (
S
i
S
c
)
Figure E.VI.1. Impact of law enforcement interventions on criminal network structure and dynamics.
{1, 2, 5, 20} z = 30
i c
h − 1 h
i
=
1
h − c
h−1
t=c
x
i,t
∆x
i,t
= x
i,t
−
i
t ≥ h
∆x
i
= max
t≥h
∆x
i,t
∆x
i
= min
t≥h
∆x
i,t
∆x
∗
i
=
k∈{,}
|∆x
k
i
|
∆x
i
=
∆x
∗
i
max
j
|∆x
∗
j
|
t ≥ h ∆x
i,t
∆x
i
∆x
i
∆x
∗
i
j ∆x
i
±1
t > 100
??
8.995 × 10
3
??
Z = 30
Z
i
= 10 i ∈ {0, 1, 2}
λ = 0.5
0 0.1 0.2 0.3
Corruption and Extortion
Weapons-related Crimes
Law Enforcement Related
Informant Related
Violent Crimes
Financial Crimes
Drug-related Activities
Frequency
Figure E.VII.1. Distribution of
criminal activities in Dutch organized
crime (2009-2023).
Z
= 30
k = 20 5.90±0.062σ
t = 1000
c
b
∈ {0.001, . . . , 2}
ϵ = {0.001, . . . , 40}
20
0 20 40 60 80 100
3
3.5
4
4.5
5
5.5
6
6.5
7
Cluster size
Gap score
Figure E.VIII.1. The network
properties of the synthetically gener-
ated was separated using the gap score.
k = 20 5.90 ±
0.062σ
0.001
5.0
10.0
Degree distribution entropy Average clustering coefficient
0.001 1.0 2.0
0.001
5.0
10.0
Link density
0.001 1.0 2.0
Number of nodes
0
0.2
0.4
0.6
0.8
1
Normalized value (
v
min((
v
)
max(
v
) min(
v
)
)
Cost-to-benefit ratio (
c
b
)
Decision error ( )
Figure E.VIII.2. Graphical prop-
erties of the synthetic networks
0 0.2 0.4 0.6 0.8 1
Link density (
L
)
0
0.2
0.4
0.6
0.8
1
Criminality (
S
)
A.
0 2 4 6
Iteration
0.2
0.4
0.6
0.8
1
1.2
Cost Function
B.
Observed Network
0 0.2 0.4 0.6 0.8 1
0
0.5
W
2
=0.02
Degree
C.
0 0.2 0.4 0.6 0.8 1
0
0.5
W
2
=0.16
Closeness
0 0.2 0.4 0.6 0.8 1
0
1
W
2
=0.01
Betweenness
1 0.5 0 0.5 1
0
0.25
W
2
=0.28
Assortativity
Centrality value
Fraction
Figure E.VIII.3. Optimization results using simulated annealing shows a clear convergence towards the optimal
solution. 0.995
Appendix F
References
4178 kilocoke onderschept in Rotterdam, grootste vangstvanafgelopen jaren https:
/ / nos . nl / artikel / 2403810 - 4178 - kilo - coke - onderschept - in -
rotterdam-grootste-vangst-van-afgelopen-jaren
Journal of Computational Science 10.1016/
j.jocs.2023.102063
Infor-
mation Processing & Management 10 . 1016 /
S0306-4573(02)00021-3
Illegal
Mining: Organized Crime, Corruption, and Ecocide in a Resource-Scarce World
10.1007/978-3-030-46327-
4_2
PNAS Nexus 10.1093/pnasnexus/pgae131
Nature Re-
views Genetics 10.1038/nrg2102
Nature
Communications 10.1038/s41467-018-03740-9
Science
10.1126/science.177.4047.393
Physica A: Statistical Mechanics and
its Applications 10.1016/j.physa.2021.125795
Advances in Com-
plex Systems 10.1142/S0219525908001465
International Journal of Law,
Crime and Justice 10.1016/j.ijlcj.2009.
10.003
NaturePhysics
10.1038/nphys2741
Emergence: Contemporary Readings in Phi-
losophyand Science
Noûs 2216138
Cognitive Science 10.1111/cogs.
12142
Frontiers
in Physiology 10.3389/fphys.2012.00163
PLOS ONE
10.1371/journal.pone.0085531
Communications de la Société Mathématique de Kharkov
Emergence: Com-
plexity and Organization
General System Theory : Foundations, Development, Applications
Predictive Information cond - mat /
9902341
Social Networks
10.1016/j.socnet.2004.11.008
Social Networks 10.1016/j.socnet.2005.11.
005
PLoS ONE
10.1371/journal.pone.0027407
Crime and Justice 10.1086/708435
Brainless Creature Solves Problems with Memories of Slime https : / / www.
nationalgeographic . com / science / article / brainless - creature -
solves-problems-with-memories-of-slime
Communications Biology 10 .
1038/s42003-022-03281-4
Global Crime
10.1080/17440572.2017.1377614
10.13140/RG.2.2.25024.58884
Scientic
Reports 10.1038/s41598-017-16982-2
Pro-
ceedings of the National Academy of Sciences
10.1073/pnas.2106140118
Review of
Law & Economics 10.2202/1555-5879.1206
Foundations of Physics 10.1007/s10701-011-
9549-0
Campbell Systematic Reviews
10.1002/cl2.1218
Journal of Quantitative Criminology
10.1007/s10940-020-09489-z
Philosophical Transactions of the Royal Society A:
Mathematical,PhysicalandEngineering Sciences
10.1098/rsta.2020.0236
Law, Democracy & Development
10.10520/EJC60323
IEMC ’03 Proceedings. Managing Technologically
Driven Organizations:TheHuman Side of Innovation and Change (IEEE Cat. No.03CH37502)
10 . 1109 / KIMAS . 2003 . 1245033
The SAGE Handbook of Social Network Analysis
Jour-
nal of Bioeconomics 10 .1007/s10818- 020 -
09295-4
Journal of Conscious-
ness Studies
NCA and Police Smash Thousandsof Criminal Conspiracies after Inltra-
tion of Encrypted Communication Platform in UK’s Biggest Ever Law Enforcement
Operation https : / / www . nationalcrimeagency . gov . uk / news /
operation-venetic
The Stanford Ency-
clopedia of Philosophy
Complex, Adj. Meanings, Etymology and More | Oxford English Dictionary
https://www.oed.com/dictionary/complex_adj
Handbook of Experimental Game Theory
Nature Ecology & Evolution
10.1038/s41559-018-0564-9
CoordinationGames: Complementarities and Macroeconomics
Elements of Information Theory
10.1002/047174882X
The Canadian Journal of Economics / Revue canadienne d’Economique
10.2307/136461 10.2307/136461
Street Crime in London: Deterrence, Disruption and Displacement
Scientic Reports 10.
1038/srep01223
Physics
of Life Reviews 10.1016/j.plrev.2014.11.001
Scientic Reports 10 . 1038 /
s41598-019-43033-9
The Four Oxen and The Lion https ://fablesofaesop . com/
the-four-oxen-and-the-lion.html
Area 10.1111/area.12724
Ecological Complexity
10.1016/j.ecocom.2007.02.003
Nachr. Ges. Wiss. Göt-
tingen, Math.-physik. Klasse
Journal of Experimental Criminology
10.1007/s11292-023-09563-z
Detecting and Disrupting Criminal Networks: A Data Driven Ap-
proach 978-90-77595-41-1
Scientic Reports
10.1038/srep04238
Scientic Reports
10.1038/srep04238
Criminology
10.1111/1745-9125.12203
Clean Technologies and Environmen-
tal Policy 10.1007/s10098-013-0687-2
Journal of transnational organized crime
Journal of Eco-
nomic Perspectives 10.1257/jep.10.1.43
Royal Society Open Science 10.1098/
rsos.160753
Behavior Research Methods
10.3758/s13428-017-0862-1
PLoS ONE 10.1371/
journal.pone.0179891 1604.08045
Foundations of Science
10.1007/s10699-023-09917-w
Decoding the EU’s Most
Threatening Criminal Networks.
Nature Reviews Neuroscience 10 . 1038 /
nrn2258
American Journal of Soci-
ology 10.1086/227352
Networks: From Biology to The-
ory
10.1007/978-1-84628-780-0
Mathematics 10.3390/math10162929
Trends
in Organized Crime 10 . 1007 / s12117 - 005 -
1038-4
SIAM Review 10 .
1137/17M1142028
Proceedings of The 35th Uncertainty in Articial In-
telligence Conference
SocialNetworks
10.1016/0378-8733(78)90021-7 cond-mat/0112110
Journal of Abnormal Psychology
10.1037/abn0000028
Sitzungsberichte
der Königlich Preussischen Akademie der Wissenschaften zu Berlin
Nature 10.1038/nature18019
Nature Food
10.1038/s43016-020-0097-7
Scientic Reports 10.1038/
srep24456
Journal of the Operational Re-
search Society 10 . 1057 / palgrave . jors .
2601520
Journal of Math-
ematical Physics 10.1063/1.1703954
American Journal of Sociology 2780199
Physica D: Nonlinear Phenomena
10.1016/j.physd.2008.12.016
Entropy 10.3390/e22020242
Handbook of Transdisciplinary Research
10.1007/978-1-4020-6699-3_2
Trends in Organized Crime
10.1007/s12117-006-1017-4
Crime and Justice
10.1086/449296
Physics of Fluids 10.1063/1.4820128
Nature Communications 10.1038/s41467-
017-01916-3
Proceedings of the Fourth European Conference on Ar-
ticial Life 10 . 1103 / PhysRevA . 84 . 041806
1104.0592
Biometrika 10 . 2307 / 2334940
2334940
San Jose
Mercury News
Nature Sustainability
10.1038/s41893-022-00866-z
The Stanford Encyclopedia of
Philosophy
Quantitative Sociodynamics: Stochastic Methods and Models of Social In-
teraction Processes
10.1007/978-3-642-11546-2
Journal of Statistical Physics
10.1007/s10955-014-1024-9
History | SantaFe Institute https://www.santafe.edu/about/history
Resilience
and Stability of Ecological Systems (1973)
10.12987/9780300188479- 023
Proceedings of the National Academy of Sciences
10.1073/pnas.79.8.2554
Journal for General Philos-
ophy of Science 10.1007/s10838-006-7153-3
Synthese 10.1007/
s11229-010-9721-7
Annals of Data Science 10.1007/s40745-
020-00311-y
Nature Sustainability 10.1038/
s41893-019-0351-x
Jacobellis v. Ohio,378 U.S. 184 https://casetext.com/case/jacobellis-
v-state-of-ohio
Physical Review Letters 10 .
1103/PhysRevLett.116.238701 1512.06479
Entropy 10 . 3390 / e19100531 1609 .
01233
Annalsof Statistics
10.1214/13-AOS1145 1203.6502v2
World Politics
10.2307/2009945
International
Journal of Parallel, Emergent and Distributed Systems
10.1080/17445760.2015.1085535
Multi-Chaos, Fractal and Multi-Fractional Articial Intelligence of Dierent Com-
plex Systems
10.1016/B978-0-323-90032-4.00003-1
Synthese
10.1007/s11229-006-9025-0
Proceedings of the National Academy of Sciences
10.1073/pnas.1309933111
The Oxford Hand-
book of Organized Crime
10.1093/oxfordhb/9780199730445.013.
005
When Brute Force Fails
10.1515/9781400831265
Entropy 10.3390/e24030403
Physica 10 . 1016 /
S0031-8914(40)90098-2
Euro-
pean Journal for Philosophy of Science 10 . 1007 /
s13194-012-0056-8
SIAM Review 10 . 1137 /
S0036144503424786
The Annals of Applied Statistics 10.1214/21-
AOAS1595
NatureCommunications 10.1038/s41467-
023-44609-w
Crime, Law and Social Change
10.1023/B:CRIS.0000039600.88691.af
Problems of Life and Mind : First Series : The Foundation of a Creed
Physical Review E
10.1103/PhysRevE.78.037101
Physical Review E 10 .
1103/PhysRevE.97.052216
Reviews
of Modern Physics 10.1103/RevModPhys.88.035006
1508.05384
National
Science Review 10.1093/nsr/nwaa229
IEEE Symposium on Articial Life (AL-
IFE) 10.1109/ALIFE.2013.6602430
1303.3440
Chaos: AnInterdisciplinary Journal
of Nonlinear Science 10.1063/1.3486801
Entropy
10.3390/e20040307
Scientic Re-
ports 10.1038/s41598-022-20025-w
Physics Letters A 10 . 1016 / 0375 -
9601(95)00867-5
Policing Contingencies
Vision: A Computational Investigation into the Human Representation and
Processing of Visual Information
Multivariate Behavioral Research
10.1080/00273171.2017.1379379
Nature Reviews Neuroscience
10.1038/nrn3061
The Stanford Encyclopedia of
Philosophy
Journal of Quantitative Criminology 10 .
1007/s10940-019-09426-9
Physical
Review A 10.1103/PhysRevA.39.4854
American Journal of
Sociology 10.1086/216745
Dynamics, Computation, and the
”Edge of Chaos”: A Re-Examination 10 . 48550 / arXiv . adap -
org/9306003 adap-org/9306003
Inside Criminal Networks
10.1007/978-0-387-09526-4
Inside Criminal Networks
10.1007/978-0-387-09526-4_4
Social Networks 10 . 1016 / j .
socnet.2006.05.001
Global Crime 10 . 1080 / 17440572 . 2011 .
589593
Organised Cime, Tracking, Drugs: Selected Papers Pre-
sented at the Annual Conference of the European Society of Criminology, Helsinki 2003
Computational Science – ICCS
2023
10 . 1007 /
978-3-031-35995-8_35
Physical Review E
10.1103/PhysRevE.67.026126
Foundations of Complex Systems: Emergence, Information
andPrediction
Entropy
10.3390/e18050172
Reviews of
Modern Physics 10.1103/RevModPhys.76.
663
Optimal Resilience of Modular Interacting Networks https://www.pnas.
org/doi/10.1073/pnas.1922831118 10.1073/pnas.1922831118
Journal of Theoretical Biology 10.
1016/j.jtbi.2006.06.027
Physical Review Letters
10.1103/PhysRevLett.97.258103
Journal of Theoretical Biology 10 . 1016 / j .
jtbi.2007.10.040
The Problem of
Emergence
10.1515/9781400845552-005
Journal of Neurophysiology 10.1152/
jn.00559.2007
Statistical Mechanics of
Complex Networks
Causality Second Edition
International Journal of Bi-
furcation and Chaos 10.1142/S0218127419300222
PLOS ONE 10.
1371/journal.pone.0076063
Scientic Reports
10.1038/srep11027
Emergence, A Journal of
Complexity Issues in Organizations and Management 10.1207/
S15327000EM0301_08
Science and Hypothesis
Competitive Advantage of Nations: Creating and Sustaining Superior
Performance
Tak-
ing Stock
10.4324/9781315130620-
14
Physical Re-
view E 10.1103/PhysRevE.84.041116
Journal of the Royal Society, Interface
/ the Royal Society 10.1098/rsif.2013.0568
24004558
Entropy 10.
3390/e19020085 1602.01265
Sci-
entic Reports 10.1038/srep01898
Stripping Syntax from Complexity: An Information-Theoretical Perspective
on Complex Systems 10 . 48550 / arXiv . 1603 . 03552
1603.03552
Scientic Reports 10.
1038/s41598-022-07195-3
Scientic Reports
10.1038/s41598-023-38589-6
Ecological Networks in the Tropics
10 . 1007 / 978 - 3 - 319 - 68228 - 0 _ 4
Supreme
Court Economic Review 10.1086/710158
PLOS ONE
10.1371/journal.pone.0021282
Disorganized Crime : The Economics of the Visible Hand
Crime and Justice 10.1086/708869
Software in the Natural World: A Computational Approach to Hierarchi-
cal Emergence 2402.09090
Noise and Ran-
domness in Living System
10 . 1007 / 978 - 981 -
16-9583-4_10
Na-
ture Communications 10.1038/s41467-019-10105-3
On Principles of Emergent Organization
2311.13749
Journal of Theo-
retical Biology 10.1016/j.jtbi.2023.111670
Entropy 10.3390/
e18040152
Entropy 10.3390/e22080854
Nature
10.1038/35098000
Nature
10.1038/nature08227
The American Scholar
New Ideas in Psychology
10.1016/j.newideapsych.2011.02.007
Reversible Destiny: Maa, Antimaa, and the
Struggle for Palermo
10.1525/j.ctt1pns8w
Volume 1 Edited by K. Krickeberg· R. C. Lewontin. J. NeymanM. Schreiber
PhysicalReview Letters
10.1103/PhysRevLett.85.461 nlin/0001042v1
Seizures of Drugs in England and Wales, Financial Year Ending 2022 https:
/ / www . gov . uk / government / statistics / seizures - of - drugs - in -
england- and - wales - financial - year - ending- 2022/seizures- of-
drugs-in-england-and-wales-financial-year-ending-2022
Chaos, Solitons& Fractals
10.1016/j.chaos.2014.08.007
European Physical Journal B
10.1140/epjb/e2013-31025-5 1110.2558
Exactly Solved Models: A Journey in Statistical Me-
chanics: Selected Papers with Commentaries (1963-2008) 10 .
1142/9789812813893_0004
Computers in Biology and Medicine 10.
1016/j.compbiomed.2016.10.010
Proceedings of the National Academy of Sciences
10.1073/pnas.1408618111
Proceedingsof theNational Academy
of Sciences 10.1073/pnas.1704663114
Nature Computational Science 10 . 1038 /
s43588-023-00509-z
Physica D: Nonlinear Phenom-
ena 10.1016/j.physd.2013.07.001
1504.03769
Physics Reports
10.1016/j.physrep.2007.04.004
Journal of Theoretical Biology
10.1016/j.jtbi.2006.07.015
Bulletin of Mathematical Biology
10.1007/BF02460618
Phenomenology and the Cognitive Sciences
10.1023/B:PHEN.0000048936.73339.dd
43 Visions For Complexity
Federal Probation
Transnational Crime Is a $1.6 Trillion to $2.2 Trillion Annual “Business”, Finds New
GFI Report
Trust in the Law: Encouraging Public Cooperation with the
Police and Courts
Nature 10.1038/s41586-
018-0422-6
Scientic Reports 10.1038/srep05918 1112.
5635
Crime, Law and Social Change
10.1007/s10611-006-9038-0
Three Myths in Complexity Science and How to Resolve Them
10 .48550/arXiv.2407.01762 2407.01762
Physica A: Statistical Mechanics
and its Applications 10.1016/j.physa.2022.
126889
Entropy
10.3390/e26121050
Sci-
entic Reports 10.1038/s41598-024-68445-0
The Paradox of Intervention: Re-
silience in Adaptive Multi-Role Coordination Networks 10.48550/
arXiv.2501.14637 2501.14637
Trends in Ecology & Evo-
lution 10.1016/j.tree.2016.09.011
Varieties of Emergence https://www . consc .net/papers/ granada .
html
Scientic Reports 10.1038/
s41598-017-13400-5
Grootste cocaïnevangst ooit in Nederland - Nieuwsbericht - Open-
baar Ministerie https://www.om.nl/actueel/nieuws/2023/08/
10 / grootste - vangst - ooit - in - rotterdamse - haven - 8000 - kilo -
ter- waarde- van- 600- miljoen-euro 10/
grootste - vangst - ooit - in - rotterdamse - haven - 8000 - kilo - ter -
waarde-van-600-miljoen-euro
Nature Methods
Illegal Entrepreneurship, OrganizedCrimeand SocialControl
10.1007/978-3-319- 31608-
6_2
Global Crime 10.1080/17440570500096734
Less Law, More Order: The Truth about Reducing Crime
PhysicsReports
10.1016/j.physrep.2016.06.004
Nature 10.1038/30918
Games 10.3390/g1040551
Journal of Arti-
cial Societies and Social Simulation 10.18564/jasss.5212
Nature Reviews Microbiology
10.1038/nrmicro.2016.111
Directed Information Measures in Neuro-
science 10.1007/978-3-642-54474-3
1004.2515
Famous Experiment Dooms Alternative to Quantum Weirdness
https : / / www . quantamagazine . org / famous - experiment - dooms -
pilot - wave - alternative - to - quantum - weirdness - 20181011/
Philosophy and Phenomeno-
logical Research 10.1111/phpr.12095
World Drug Report 2023 https://www.unodc.org/unodc/en/data-
and-analysis/world-drug-report-2023.html
Chaos: An Interdisci-
plinary Journal of Nonlinear Science 10.1063/1.
5142827
Earth System Dynamics
10.5194/esd-12-601-2021
Nature 10.1038/
nature24056
Physical Review Letters 10 . 1103 /
PhysRevLett.119.248302
Science
10.1126/science.aan3184
iScience 10.1016/j.
isci.2019.07.043
Nature
Machine Intelligence 10 . 1038 / s42256 - 018 -
0005-0
Scientic Reports
10.1038/s41598-017-10744-w
Publications
Three Myths in Complexity Science and How to Resolve Them
10 .48550/arXiv.2407.01762 2407.01762
Physica A: Statistical Mechanics
and its Applications 10.1016/j.physa.2022.
126889
Entropy
10.3390/e26121050
Sci-
entic Reports 10.1038/s41598-024-68445-0
The Paradox of Intervention: Re-
silience in Adaptive Multi-Role Coordination Networks 10.48550/
arXiv.2501.14637 2501.14637
Author Contributions
Casper van Elteren
Wiebe M. Rouwhorst
Jonathan
D.A. de Bouter
Casper van Elteren
Rick
Quax Peter
M.A. Sloot
Casper van Elteren
Rick Quax Pe-
ter M.A. Sloot
Casper van Elteren
Vítor V. Vasconcelos
Mike H. Lees
Casper van Elteren
Software Contributions
https://github.com/cvanelteren
https://thefriendlyghost.nl
Acknowledgments
Reections
—
