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How to Untangle Complex Systems?
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Philosophy
and
Geology
psychology
and
Engineering
astronomy
Social
sciences
Economy
Complexity
Medicine
Computer
science
Biology and
related
disciplines
Mathematics
Physics
Chemistry
FIGURE 13.27 A multidisciplinary approach to face Complexity.
• Humbleness and wisdom. In fact, science alone cannot furnish a code of morals or a basis
for aesthetics. Science cannot “furnish the yardstick for measuring, nor the motor for con-
trolling, man’s love of beauty and truth, his sense of value, or his convictions of faith”
(Weaver, 1948).
The polymath figures formed at the interdisciplinary academic degrees in Complexity should
work along with specialized scientists to build vibrant research teams. The lively multidisciplinary
research teams will have a much higher potential for facing the Complexity Challenges than the
potential of teams composed only of members specializing in one particular discipline. In fact, con-
nections among different disciplines will blossom new great ideas and spark flashes of brilliance.
However, a fundamental ingredient for success is the willingness of each member to sacrifice selfish
short-term interests to bring about improvements for all.
13.5 LAST MOTIVATING SENTENCES PRONOUNCED
BY “IMPORTANT PEOPLE”
I want to conclude this breathtaking journey exploring Complexity by citing some motivating sen-
tences pronounced by eminent philosophers, scientists, and writers.
He who knows the happiness of understanding
has gained an infallible friend for life.
Thinking is to man
what flying is to birds.
Don’t follow the example of a chicken
when you could be a lark.
Albert Einstein (1879–1955 AD)
Knowledge is like a sphere.
The greater it’s volume
the larger it’s contact with the unknown.
Blaise Pascal (1623–1662 AD)
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The scientific man does not aim at an immediate result.
He does not expect that his advanced ideas will be readily taken up.
His work is like that of the planter—for the future.
His duty is to lay the foundation for those who are to come, and point the way.
Nikola Tesla (1856–1943 AD)
Learn from yesterday,
live for today,
hope for tomorrow.
The important thing is not to stop questioning.
Albert Einstein (1879–1955 AD)
One doesn’t discover new lands
without consenting to lose sight of the shore.
André Gide (1869–1951 AD)
13.6 KEY QUESTIONS
• Which are the principal strategies to tackle the Complexity Challenges?
• Which are the fundamental elements of an electronic computer and how does it work?
• What is the future of the electronic computers?
• What is Natural Computing?
• Present the three-step methodology to study Complex Systems?
• Which are the essential attributes of a living being?
• Explain the basic idea of membrane computing.
• Explain the Adleman’s idea and procedure of using DNA hybridization reaction to solve
the Travelling Salesman Problem.
• Compare DNA with RNA computing.
• Which are the potentialities and limits of DNA as a memory?
• Which are the factors that rule biological evolution and are suitable to process information?
• Describe the essential features of the Human Immune System, which are used to make
computations.
• Why are Cellular Automata good models of Complex Systems?
• Indicate what distinguishes a brain from a Von Neumann computer as far as their compu-
tational capabilities are concerned.
• How does Fuzzy logic mimic human ability to compute with words?
• Which are the routes for developing Artificial Intelligence?
• How do proteins compute?
• Describe some methodologies to model phenomena involving Complex Systems.
• Discuss the potentialities of those algorithms that are based on Swarm Intelligence.
• Present the Prisoner’s dilemma and its usefulness.
• Which are the conditions required to compute with a particle in a force field that generates
a potential energy profile with two wells?
• Is any irreversible computation an irreversible transformation?
• Describe the story of mechanical computing.
• What kind of logic can be processed by using subatomic particles, atoms and molecules?
13.7 KEY WORDS
Big Data; Transistor; Von Neumann architecture; Natural Computing; Artificial life; Systems biol-
ogy; Systems chemistry; Synthetic biology; Artificial Intelligence; Agent; Prisoner’s dilemma;
Reversible and irreversible logical operations; Quantum logic; Fuzzy logic.
How to Untangle Complex Systems?
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13.8 HINTS FOR FURTHER READING
• For those who are interested particularly in Systems Biology, Kitano (2002) suggests visit-
ing two websites. First, the website of Systems Biology Markup Language (SBML) (http://
sbml.org/Main_Page) that offers a free and open interchange format for computer models of biological processes. Second, the website of the CellML project (https://www.cellml.
org/) whose purpose is to store and exchange computer-based mathematical models at a range of resolutions from the subcellular to organism level.
• For those interested in the theory of Complexity in Medicine, it is worthwhile reading the
book edited by Sturmberg (2016).
• A survey on nucleic acid-based devices is the review by Krishnan and Simmel (2011).
More about DNA origami and their use in chemical robots can be found in the review by
Hong et al. (2017).
• More about the thermodynamics of computation in the review by Parrondo et al. (2015).
• To learn more about Information and have more cues to develop the new theory for under-
standing Complexity, it is really useful to read the book by von Baeyer (2004).
• For learning more about the origin of great new ideas, it is nice to read Where Good Ideas
Come From: The Natural History of Innovation by Johnson (2010).
• For acquiring an interdisciplinary vision on Complex Systems, it is worthwhile reading
Humanity in a Creative Universe by the Kauffman (2016). Kauffman sorts through the
most significant questions and theories in biology, physics, and philosophy.
13.9 EXERCISES
13.1. According to the IBM website https://www.ibm.com/analytics/us/en/big-data/, Big Data will amount to 43 Trillion Gigabytes by 2020. If we imagine storing all these data in DNA,
how much DNA do we need? The data density in bacterial DNA is 1019 bits/cm3 (Extance
2016). The average density of DNA is 1.71 g/cm3 (Panijpan 1977). Remember that 1 byte
corresponds to 8 bits.
13.2. In Xenopus embryos, the cell cycle is driven by a protein circuit centered on the cyclin-
dependent protein kinase CDK1 and the anaphase-promoting complex APC (Ferrell et al.
2011). The activation of CDK1 drives the cell into mitosis, whereas the activation of APC
drives the cell back out of mitosis. A simple two-component model for the cell-cycle oscil-
lator is shown in Figure 13.28.
Use a Boolean analysis, to predict the dynamics of the system.
13.3. A more complex model to describe the cell cycle of Xenopus embryo (see the previous
exercise) consists of three components (Ferrell et al. 2011). Besides CDK1 and APC, there
is a third protein that is Polo-like kinase 1 (Plk1), as shown in Figure 13.29.
Plk1 (P) is activated by CDK1 (C), and, in turn, it activates APC (A). APC inhibits
CDK1. Use a Boolean analysis, to predict the dynamics of the system.
CDK1
APC
FIGURE 13.28 Mutual relationship between CDK1 and APC.
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Untangling Complex Systems
APC (A)
CDK1
Plk1 (P)
(C)
FIGURE 13.29 Model of the cell cycle for the Xenopus embryo.
13.4. Open NetLogo software (Wilensky 1999). Go to Models Library. Select Biology and
open the “Ants” Model (Wilensky 1997). Fix “Populations” to 200 and “Diffusion rate”
to 20.
For each pheromone “evaporation-rate” value reported below, run the model five times.
For each run, record the number of ticks it takes until all the food is eaten. Remember
to click “setup” before each run. Then, average these five numbers. The result is the
“average time taken” as a function of the evaporation rate value. What is the value of the
evaporation-rates, reported below, which makes the ants quickest (on average) to eat all
the food?
A: “evaporation-rate” = 0
B: “evaporation-rate” = 5
C: “evaporation-rate” = 20
13.5. This exercise is an ideal model of inductive reasoning (Arthur 2015). One hundred people
decide each week independently whether to go, or not to go, to a bar that offers enter-
tainment on a certain night. Space is limited. The night is enjoyable if the bar is not too
crowded, no more than sixty people. There is no sure way to tell the number of people
coming in advance. Therefore, every agent goes if he expects fewer than sixty to show up or
stays home if he expects more than sixty to go. There is no prior communication among the
agents. The only information available is the numbers who went in the past M weeks. This
model was inspired by the bar El Farol in Santa Fe, which offers Irish music on Thursday
nights (Wilensky and Rand 2015). Let N be the number of strategies (or mental models)
each agent has to make predictions. Let t be the current time (i.e., week). The previous
weeks are thus t − 1, t − 2, and so on. Let A( t − 1) be the attendance at time t − 1, A( t − 2) that at time t − 2, and so on. Each strategy predicts the attendance at time t, S( t), by the following equation:
S( t) = 100 w 1 A( t − )
1 + w 2 A( t − 2) +…+ w
M A( t − M) + c
where wi ∈[− ,
1 + ],
1
i
∀ = ,
1 …, M.
The
N strategies differ in the values of the coefficients wi. The values of the coefficients
wi are randomly initialized. The attendance history (previous M time steps) is initialized at
random, with values between 0 and 99. At each time step t, after making his decision and
learning the current attendance A( t), each agent evaluates his best current strategy S* as the one that minimizes the error:
Error( S) = S( t) − A( t) + S( t − )
1 − A( t − )
1 +…+ S( t − M) − A( t − M)
S* will be used by that agent to make his decision on the next round. If S*( t + 1) > 60 (i.e., the overcrowding threshold), the agent does not go; otherwise, he goes.
How to Untangle Complex Systems?
497
(I)
(II)
( i)
( f)
FIGURE 13.30 Mixing of two ideal gases (I) and free expansion of a perfect gas (II) where the state labeled
as ( i) and ( f) represent the initial and final states, respectively.
Open NetLogo software (Wilensky 1999). Go to Models Library; select Social Science
and open the “El Farol” Model (Rand and Wilensky 2007). Find a combination of
memory-size and number of strategies that reduce the frequency and the extent of over-
crowding. How does the attendance behave dynamically over time?
13.6. Determine the variation of the thermodynamic entropy and the information entropy for the
following two processes: (I) mixing of two ideal gases and (II) free expansion of a perfect
gas from volume Vi to Vf = V
2 i (see Figure 13.30).
13.10 SOLUTIONS OF THE EXERCISES
13.1. The Big Data will amount to 4 3×1022 bytes = 3 44 ×1023
.
.
bits. If we imagine storing all
these data in DNA, the volume needed would be
3.44 1023 bits
V ( DNA) =
×
= 3.44×104
3
cm
1019 bits/
3
cm
The mass of DNA would be
.
3 44 ×104
3
cm
m( DNA) =
= 2×104g = 20 kg
g
.
1 71
3
cm
It is worthwhile noticing that the Big Data are constantly manipulated to extract useful
information from them. Therefore, their storage in DNA is not the best choice because
writing and reading information in DNA is not a fast process, yet. However, DNA requires
much less volume than a hard disk and flash memory. In fact, the data density of a hard disk
(based on magnetism) and flash memory (based on electric charges; the name “flash” refers
to the fact that the data can be erased quickly) are one million and one thousand smaller
than that of DNA, respectively (Extance 2016).
13.2. According to the Boolean analysis, the two variables, CDK1 and APC, are either entirely
ON or entirely OFF. Then, the two-component system has four possible states, indicated in
Figure 13.31.
Let us imagine that the system starts from a state wherein it prepares for the process
of cell division: CDK1 and APC
(state 1 in Figure). In the first discrete time step,
OFF
OFF
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Untangling Complex Systems
(4)
(3)
CDK1: OFF
CDK1: ON
APC: ON
APC: ON
CDK1: OFF
CDK1: ON
APC: OFF
APC: OFF
(1)
(2)
FIGURE 13.31 Possible binary states of CDK1 and APC.
CDK1
APC
CDK1
0
−1
APC
+1
0
FIGURE 13.32 Connection matrix for the CDK1-APC system.
CDK1 turns ON because APC is OFF: the system moves from the state 1 to the state 2.
Then, the active CDK1 activates APC; thus, the system goes from the state 2 to the state 3.
Now, the active APC inactivates CDK1, and the system goes from the state 3 to the
state 4. Finally, in the absence of active CDK1, APC becomes inactive, and the system goes
from the state 4 to the state 1, completing the cycle. The system will oscillate indefinitely.
The transitions of the system can also be determined by using the “connection matrix”
reported in Figure 13.32 and representing the state of the two-component system through
2 × 1 vectors. Here, −1 corresponds to OFF, whereas +1 to ON.
Ferrell et al. (2011) have demonstrated that if we use ODEs to describe the dynamics
of this two-component system, we find that it gives damped oscillations to a stable steady
state.
13.3. For the three-component system, there are 23 possible states (see Figure 13.33). If we start with the variables in their OFF state (i.e., the state 1), we get periodic cycling of
six states (from 1 to 6). States 7 and 8 are not visited by the periodic cycle. However, they
feed into the cycle (see grey arrows) according to the relations existing between the vari-
ables. Thus, no matter where the system starts, it will converge to the cycle traced by the
black arrows. The cycle is stable.
The evolution of the system can also be calculated using the “connection matrix,” shown
in Figure 13.34, and 3 × 1 vectors to represent the states of the system.
The analysis of this three-component system by ODEs gives the same result: a stable
limit cycle (Ferrell et al., 2011).
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(5)
C: OFF
C: ON
P: ON
P: ON
A: ON
A: ON
(4)
(3)
C: ON
C: OFF
P: ON
P: ON
A: OFF
A: OFF
(7)
(6)
(8)
C: OFF
C: ON
P: OFF
P: OFF
A: ON
A: ON
(1)
(2)
C: OFF
C: ON
P: OFF
P: OFF
A: OFF
A: OFF
FIGURE 13.33 Possible states for the system consisting of CDK1 (C), Plk1 (P), and APC (A).
CDK1
PlK1
APC
CDK1
0
0
−1
PlK1
+1
0
0
APC
0
+1
0
FIGURE 13.34 Connection matrix for the CDK1-P-APC system.
13.4. The results are listed in Table 13.3.
