I Sistemi Complessi sono sistemi naturali di cui la scienza non è in grado di fornire una descrizione esaustiva. Esempi di Sistemi Complessi sono gli esseri viventi sia unicellulari che multicellulari, il cervello ed il sistema immunitario umano, gli ecosistemi, le società umane, l’economia globale, il clima e la geologia del nostro pianeta. Questo libro è un racconto di un meraviglioso viaggio interdisciplinare che l’autore ha compiuto per comprendere le proprietà dei Sistemi Complessi.

1. Untangling Complex
Systems: A Grand
Challenge for Science
A Marvelous Interdisciplinary Journey towards the
Comprehension of the Natural Complexity
Complexity Literacy Meeting
23-25 November, 2018
Pier Luigi Gentili

2. The two most relevant driving forces
of the Scientific Knowledge
To satisfy the epistemic curiosity: Which is the origin of the beauty in nature?

3. The two most relevant driving forces
of the Scientific Knowledge
To solve practical problems and improve the psyco-physical well-being of humans
http://www.science20.com/curious_cub/new_way_change_genetic_code-80059

4. CHALLENGES
Incurable
diseases
(Cancer, Leukemia,
AIDS, Diabete,
Alzheimer,…)
Unpredictable
Catastrophic
events on Earth
(Earthquakes, Volcanic
erupstions)
Climate
Change
Exploitation of the
energy and food
resources without
deteriorating natural
ecosystems and
biodiversity
Unpredictable
economic crisis
Poverty
reduction
Unpredictable
political crisis
Climate
Ecosystems
Economy
Human
societies
COMPLEX SYSTEMS
Geology
Living Beings
Human Immune System
Human Nervous System

5. Which are the common features of the
COMPLEX SYSTEMS?
1) Networks (n° nodes and edges)

6. Which are the common features of the
COMPLEX SYSTEMS?
2) Out-of-Equilibrium
Inanimate Matter is driven by force-fields
The interactions between living beings are information-based

7. Which are the common features of the
COMPLEX SYSTEMS?
3) Emergent Properties
Integration of the nodes originates properties that belong to the whole.
The whole is more than the sum of its parts (by Aristotle)
Plato Aristotle
By Raffaello

8. SELF-ORGANIZATION IN TIME
A living being is like «a house with
clocks in every room and every
corner, yet in one way or another,
they work in a organized way.»

9. SELF-ORGANIZATION IN TIME
In Ecosystems: «Everything is related to everything»
else»
http://durun.ugrasgrup.com/predator-prey-relationship/

10. SELF-ORGANIZATION IN TIME
In Economy
EXOGENOUS FACTORS
Technological innovations;
Wars;
Natural catastrophic events;
Political decisions;…
ENDOGENOUS FACTORS
Competition between employment rate (𝜇)
and wage share (𝜈).
𝜇 =
𝐿
𝑁
𝜈 =
𝑤𝐿
𝑌

11. SELF-ORGANIZATION IN TIME
In a Chemical Laboratory
𝐼𝑂 + 2𝐻 𝑂 + 𝐶𝐻 (𝐶𝑂 𝐻) +𝐻 ICH 𝐶𝑂 𝐻 + 2𝑂 + 3𝐻 𝑂
https://www.youtube.com/watch?v=-RFb8T2ED5E
𝐼
𝐼
𝐼 + 𝑠𝑡𝑎𝑟𝑐ℎ
𝐻𝐼𝑂2

12. SELF-ORGANIZATION IN SPACE
Chemical Waves
Calcium Waves;
cAMP waves in Dictyostelium Discoideum;…
2𝐵𝑟𝑂 + 3𝐶𝐻 (𝐶𝑂 𝐻) +2𝐻 2BrCH 𝐶𝑂 𝐻 + 3𝐶𝑂 + 3𝐻2 𝑂

13. SELF-ORGANIZATION IN SPACE
Turing Patterns
PhyllotaxisAnimal markings
Development of embryos Dunes

14. SELF-ORGANIZATION IN SPACE
Periodic Precipitations
𝐴𝑔 𝐶𝑟𝑂
Malachite Agate
Fungal colony on an apple.
http://www.insilico.hu/liesegang/effects/effects.html

15. REALLY BIG QUESTION
Do the Complex Systems violate the II Law of Thermodynamics?
II Law of Thermodynamics
Non-equilibrium Thermodynamics
SdSddS ie
diS
deS
0Sdi

16. CHAOS IN TIME
Logistic Map: 𝒙 𝒏 𝟏 = 𝒓𝒙 𝒏(𝟏 − 𝒙 𝒏)
Features of Chaotic Dynamics:
Aperiodic;
Extremely sensitive to the initial conditions;
Unpredictable in the long term;
Positive Lyapunov exponent;
Dimension of the Strange Attractors;…
r
x

17. CHAOS IN SPACE: FRACTALS
The Chaos in Time generates Chaos in Space, i.e., Fractals
In nature, we find many fractal-like structures
Attributes of the Fractal Structures
Self-similarity;
Their Dimensions are not necessarily integer
numbers;

18. Which are the common features of the
COMPLEX SYSTEMS?
4) Their behaviour cannot be
predicted, especially in the
long term.

19. 1) COMPUTATIONAL COMPLEXITY REASONS
We cannot solve accurately and in reasonable time,
exponential problems having large dimensions.

20. 2) RECOGNITION OF VARIABLE PATTERNS
signal
time
Recognition of handwritten
cursive words or numbers
Recognition of human faces, voices and
fingerprints
Patterns in data
Patterns in medical
diagnosis
Deterministic Chaos
or Stochastic process?

21. 3) THE DETERMINATIONS OF THE INITIAL
CONDITIONS ARE ALWAYS AFFECTED BY
UNCERTAINTIES AND ERRORS
If the Complex System exhibits chaotic behavior, its dynamics is
unpredictable in the long term, by definition.
0 4 8 12 16 20
-10
0
10
20
X(t)
time
Real trend
Prediction

22. How can we tackle the Complexity
Challenges?
We need to improve the ways
we collect, store, and process data
STRATEGIES
IMPROVE CURRENT
COMPUTERS
(1)
NATURAL COMPUTING
(2)

23. NATURAL COMPUTING
NEW ALGORITHMS
NEW MATERIALS and
ARCHITECTURES
to COMPUTE
NEW METHODOLOGIES and MODELS
to INTERPRET
NATURAL COMPLEXITY
Draw inspiration from nature to propose
Rationale: information is encoded through the states of natural systems

24. NATURAL COMPUTING
1° PROGRAM

25. NATURAL COMPUTING
INITIAL
STATE OF
THE SYSTEM
CAUSE
INPUT OUTPUT
EFFECT FINAL STATE
OF THE
SYSTEM
2° PROGRAM

26. ~3x106 BC
Stone
Age
3x103 BC
1x103 BC
Bronze
Age
Iron Age
PRACTICAL
PERIOD
COMPUTATIONAL
PERIOD
21st century AD
PHYLOSOPHICAL
PERIOD
VI secolo BC
The first
philosophers in
Greece and its
colonies
EXPERIMENTAL
PERIOD
G. Galilei
e I. Newton
XVII
century AD
THE HUMANKIND JOURNEY TO DISCOVERING THE SECRETS OF NATURE

27. Untangling Complex Systems
A Grand Challenge for Science
Learn from yesterday,
Live for today,
Hope for tomorrow.
The important thing is
not to stop questioning
Albert Einstein

28. Index of the book
Chapter 1: Introduction.
Chapter 2: Reversibility or Irreversibility? That is the Question!
Chapter 3: Out-of-Equilibrium Thermodynamics.
Chapter 4: An amazing scientific voyage: from equilibrium up to self-organization through bifurcations.
Chapter 5: The emergence of temporal order in ecosystems.
Chapter 6: The emergence of temporal order in economy.
Chapter 7: The emergence of temporal order within a living being.
Chapter 8: The emergence of temporal order in a chemical laboratory.
Chapter 9: The emergence of order in space.
Chapter 10: The emergence of chaos in time.
Chapter 11: Chaos in space: The Fractals.
Chapter 12: Complex Systems
Chapter 13: How to untangle Complex Systems?
Appendix A: Numerical Solutions of Differential Equations
Appendix B: The Maximum Entropy Method
Appendix C: Fourier Transform of Waveforms
Appendix D: Errors and Uncertainties in Laboratory Experiments
Appendix E: Errors in Numerical Computation

29. Supporting Information

30. Chemical Waves

31. 1) COMPUTATIONAL COMPLEXITY REASONS
𝑖ℏ
𝜕
𝜕𝑡
|Ψ >= ℋ|Ψ >
Schrödinger Equation
N 2N time
10 1024 ≈10 fs
20 1x106 ≈20 ps
500 3.3 × 10 1 ×
10 years
IBM Summit
122 PFlop/s
Much longer than the
age of the Universe:
14 × 10 years.
8 ps
https://www.top500.org/