Modelling of complex systems

8/12/2019 Modelling of complex systems

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Definition of a system:A set of units with relationships among them that connect to form a

whole. set" implies that the units or elements contain similar characteristics and that each unitor element is controlled, influenced, or dependent upon the state of other units. Systems have

input, output, control, and feedback processes.

Open systems exchange matter or information with the environment. (ex: every living

organism, people, corporations, organisations, groups, families, interpersonal relationships and

computer-based information systems).

Closed systemshave clear boundaries prohibiting exchange of energy or information - isolated

from their environment.

General system Theory:

- Heirarchies (systems within systems)- Boundaries (define system by drawing boundaries)- Dynamic (Change over time and internal relationships change as well)- Synergistic (the whole > sum of parts)-

Feedback & Control (homeostasis)- Autopoesis (self-regulating)- Equifinality (same goal achieved via different paths)- Entropy (measure of disorder)

Life:a property of improbable complexity possessed by an entity that works to keep itself out of

equilibrium with its environment. R. Dawkins (1986)

Characteristics of all living things:are organized, work together to create increasingly higher

levels of complexity, metabolize, maintain internal environment, grow, respond, reproduce,

evolve. Process->Form->Structure->Process.

Living systems learn constantly (are adaptive) Living systems are self-organizing Life is systems-thinking Living systems are webbed with feedback (reciprocal modification) Living systems are interconnected Living systems are self-referential Living systems are autopoetic (self-regulating)

First Law of Thermodynamics:Total energy in the universe is constant. (Energy can neither be

created nor destroyed). You cant win, you can only break even.Second Law of Thermodynamics: Total entropy (randomness) in the universe is increasing.

You cant even break even.Organisms vs. Machines: Open versus closed, Dynamic versus static, Fluid versus bounded,

Adaptive versus rigid, Complex versus simple, Quantum versus Newtonian.

Chaos Theory:Systems described as "chaotic" are extremely susceptible to changes in initial

conditions. As a result, small uncertainties in measurement are magnified over time, making

chaotic systems predictable in principle but unpredictable in practice. Attempts to uncover the

statistical regularity hidden in processes that otherwise appear random, such as turbulence in


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fluids, weather patterns, predator-prey cycles, the spread of disease, and even the onset of war.

Chaos refers to an apparent lack of order in a system that nevertheless obeys particular laws or

rules that can cause very complex behaviours or events. Emphasize the interconnectedness of

everything. Connectedness generates order from disorder.

Quantum Universe:There are fields of energy flooding the entire universe, containing all the

information that ever was, is and will be. At the sub-atomic level of the universe, and, therefore,

at the very core of human make-up, the physical nature of the universe is a dance of energy. It

stands to reason that as a part of this celestial dance, we can have access to nature's wealth of

information, and we can be influenced by it.

The Vision of Leadership:Equilibrium is death to the quantum organization. A little creative

chaos will continue to drive human creativity.

Doctrines:

- The whole is greater than the sum of the parts.- Complex systems are best managed from the bottom up. Today's top-down command and

control management styles are complicated, inefficient, and problematic.- We must manage to recognize the tremendous individual potential in the workplace.

The Vision:Our leadership mission is to create a setting in which human beings can flourish and

are valued and recognized as the key to success. We will view employees as holistic versatile

partners in the creation of enterprise.

Characteristics of Successful Organisations: Self-organizing or self-renewing; Adaptive;

Flexible to internal and external change; Feedback loops, reflection, self-awareness, information;

Globally stable with local fluctuations; Open system; Self-referential.

Learning Organisations: Respond to environmental changes; Tolerate stress; Compete

effectively; Exploit new niches; Take risks; Develop symbiotic relationships; Evolve or perish.

Organisational Change: When the system is far from equilibrium, individual creativity canhave a huge impact: amplification of feedback loop and presence of lone fluctuation is amplified.

Organisations = Self Organising Systems = Complex Adaptive Systems:

Portfolio of skills--not portfolio of business units. Many levels of autonomy. Need strong competency, identity, and vision. Strong frame of reference (Self-referent). Capacity for spontaneously emerging structures that best fit present need. Strong relationship to environment - as matures, more efficient, more adaptive. Co-evolution with environment: establishes basic structure facilitates insulation that

protects system from constant, reactive changes.

Chaos forces organization to seek new points of view. Organizations and their environments are evolving simultaneously toward better fitness

for each other.

Flexible response to changes.


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Transformational Leadership: Organizational beliefs (genetic code); Feedback loop:

reciprocal modification; Guiding principles, shared vision; Straddle both continuity and

discontinuity; Adaptable; Aware of environment; Reflective; Self-transcendent; Adhocracy.

Entrepreneurial; Visionary; Build sustainable niche in emergent economic / political systems:

The Leaders task is to communicate shared values and guiding principles, keep them in the

forefront, and allow individuals in the system random, chaotic-looking meanderings. (Wheatley,

p. 133).

Interconncted-ness Conclusion:...Whatever befalls the earth, befalls the sons and daughters

of the earth. Man did not weave the web of life; he is merely a strand in it. Whatever he does to

the web, he does to himself F. Capra, The Web of Life, 1996.Characteristics of the computational methods

Computational

approach

Characteristics

Boolean

networks

The cell can be modeled as a network of two state components interacting

between them. The state of each component depends of a particular

boolean function.

Expert systems The interactions (activation, phosphorylation, etc.) between signaling

network components are modeled using production rules

Differential-

algebraic equations

An ODE equation is built or each molecule x describing its relationship

with all relevant moleculesy

Cellular

automata

The interaction between cells or molecules is modeled as a matrix, where

the state of an element of the matrix depends on the states of the

neighbouring elements.

Petri nets The cell is seen as a connected graph with two types of nodes. One type

represents elements, such as signaling molecules, the other type represents

transitions.

Artificial neural

networks

The proteins in signaling networks are seen as artificial neurons in ANN.

Like an artificial neuron, a protein receives weighted inputs, produces an

output, and has an activation value.

Distributed

systems (agents)

The cell is seen as a collection of agents working in parallel. The agents

communicate between them through messages.

SFG: Scale-free Graphs

The original presentation of scale-free (SF) graphs describes them in terms of a constructionmechanism based on incremental growth (i.e. nodes are added one at a time) and preferential

attachment (i.e. nodes are more likely to attach to nodes that already have many connections).


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Cellular processes and associated computational schemes

Process type Dominant phenomena Computation schemes

Metabolism Enzymatic reaction DAE, FBA

Signal transduction inSepsis

Molecular binding DAE, StAl,Scale-free networks

Gene expression Molecular binding,

polymerization, degradation

OOM, DAE, Boolean

networks, StAl

DNA replication Molecular binding,

polymerization

OOM, DAE

Cytoskeletal Polymerization,

depolymerization

DAE, particle dynamics

Cytoplasmic streaming Streaming Finite-element method

Membrane transport Osmotic pressure, membrane

potential

DAE, electrophysiology

Unstructured VS Structured networks

Unstructured Networks Structured Networks

No specific topology Predetermined topology

Random connections Predetermined connections (DHT)

Offer better resilience to network dynamics

(nodes joining and leaving, node failure andnetwork attacks)

Degraded performance during node removals

(needs much maintenance), node failures andnetwork attacks

Bad performance, node reachability, responsetime and no diameter quarantee

Better performance, faster response time andlow diameter

Lack of scalability, network partitioning More scalable, but problem in generic keywordsearches

Resilient in attacks Vulnerable in attacks

Examples: Gnutella, KaZaA Examples: Chord, CAN (DHT)Network Resiliency

- Power-law networks often collapse under targeted attacks in nodes with high degrees(network partitioning).

- Guidelines for resiliency: Hide the identity of high connected nodes. Node maintenance,rearrange connections under attack.

- Assume that attacker can force a node to drop out of network (e.g. DOS attack) when itknows the nodes IP.

- Goal of resilience is a network graph close to a strongly connected graph as possible.


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Organized complexity

Requires highly organized interactions, by design or evolution Completely different theory and technology from emergence

Simple answers: Predictable results; Short proofs; Simple outcomes.

Complex, uncertain, hostile environments Unreliable, uncertain, changing components Limited testing and experimentation

Yet predictable, robust, reliable, adaptable, evolvable systems

Complexity and Post-Modern Solution Themes

The dominant model has become complex adaptive systems (CAS), which focuses on the holistic

patterns. Underlying self-organizing systems are simple design principles. Organizational

practices turn into rules so keep them few, and to try small-scale experiments instead of fast,

large-scale interventions.

SCALE FREE NETWORKS !SFN are complex networks!Dorogovtsev and Mendes provide a standard programme of empirical research of a complexnetwork. For the case of undirected graphs, these steps consist of finding1. the degree distribution;

2. the clustering coefficient;

3. the average shortest-path length

SFN and the power law:

Barabasi and Albert consider that many large random networks share the common feature that

the distribution of their localconnectivity is free of scale, following a power law.

Properties of SFN:

1. SF networks have scaling (power law) degree distribution.2. SF networks can be generated by various random growth processes.

3. SF networks have highly connected, centrally located nodes (hubs), which give the robustyet fragile feature of error tolerance but attack vulnerability.4. SF networks are generic in the sense of being preserved under random degree preserving

rewiring.

5. SF networks are universal in the sense of not depending on domain-specific details.

6. SF networks are self-similar.

Power-Law Properties:

- Power-law (or scale-free) networks: their degree distribution follows a power law,p(K)=K

- , where K=degree, p(K)=the number of nodes with degree K and is theexponent, in most networks it tends to be close to 2.

- This means that in power-law networks many nodes have low degree and few nodes havea very high degree.

- These high connected nodes act as hubs for the rest nodes.


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- Every new node that joins the network wants to connect to a preferred node (with highdegree) for better visibility.

- This approach guarantees power-law for degree distribution.Scale-free Networks vs. Random Networks:

- SFN displays high tolerance to random node failures; but is fragile against attacks.- Random networks: insensitive to random attacks.

Generation of Robust (SFN) Networks

Robustness Complex systems maintain their basic functions even under errors and failures

(cellmutations; Internetrouter breakdowns)

- Incremental addition of nodes (agents).- A fixedEnumber of links per agent. Initially:Efully connected nodes.- Agents maximize their connectivity by linking to the nodes with the highest degrees.

Preferential Attachment Model (for the generation of scale-free networks):

incremental addition of nodes. Each node has a fixed number of links. Newcomers attach to existing nodes with probability proportional to the nodes

connectivity.

The Robustness of Internet:

Random failures of nodes have little effect on the overall connectivity.

The networks of Internet have a characteristic (scale-free) structure.The distribution of the #links per node follows a power law #nodes[#links = k] = k

-

(a)Hierarchical scale-free (HSF) network: the construction combines scale-free structure andinherent modularity in the sense of exhibiting an hierarchical architecture that starts with

a small 3-pronged cluster and build a 3-tier network a adding edge routers roughly in a

preferential manner.(b)Random network: This network is obtained from the HSF network in (a) by performing a

number of pairwise random degree-preserving rewiring steps.

(c)Poor design: In this heuristic construction, we arrange the non-edge routers in a line, picka node towards the middle to be the high-degree, low bandwidth bottleneck, and establish

connections between high-degree and low-degree nodes.

(d)HOT network: The construction mimics the build-out of a network by a hypothetical ISP.It produces a 3-tier network hierarchy in which the high-bandwidth, low-

connectivityrouters live in the network core while routers with low-bandwidth and high-

connectivity reside at the edge of the network.

Topological characterization of SFN

Heterogeneous networks: The Internet and the World-Wide-Web Protein networks Metabolic networks Social networks Food-webs and ecological networks


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SFG: Scale-free Graphs: The original presentation of scale-free (SF) graphs describes themin terms of a construction mechanism based on incremental growth (i.e. nodes are added one at a

time) andpreferential attachment (i.e. nodes are more likely to attach to nodes that already have

many connections).

Scale-free model

GROWTH : At every timestep we add a new node with m edges (connected to the nodes already

present in the system).

(2) PREFERENTIAL ATTACHMENT : The probability that a new node will be connected tonode idepends on the connectivity kiof that node

Tools for characterizing the various models

- Connectivity distribution P(k) => Homogeneous vs. Scale-free- Clustering- Assortativity

Random Graph Theory

Developed in the 1960s by Erdos and RenyiDiscusses the ensemble of graphs with N vertices and M edges (2M links). Distribution of connectivity per vertex is Poissonian (exponential), where k is the number of

links :

,

Distance d=log N -- SMALL WORLDCritical Exponents

Using the properties of power series (generating functions) near a singular point

(Abelian methods), the behavior near the critical point can be studied.For random breakdown the behavior near criticality in scale-free networks is different than for

random graphs or from mean field percolation. For intentional attack-same as mean-field.

Optimal Distance - Disorder

Weak disorder (WD)all contribute to the sum (narrow distribution)Strong disorder (SD)a single term dominates the sum (broad distribution)

Generalized percolation , >4Erdos-Renyi, 4) scale free Scale Free networks (2


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Node Maintenance Mechanism

- A state probing mechanism for node failure or attack cases:- The number of neighbors of a node i (h i) is: hi = hir + hip +hib, where hir, hip, hibrepresent

random, preferential (standard and highly) and backward neighbors

- If hir + hip < threshold, node i runs a maintenance procedure- If a node leaves gracefully it informs neighbors but if it leaves forcefully a neighbor node

can be informed only through probing

- Probing: message M2= is send to all neighbors bya node i waiting for response in a timeout if neighbor is alive

Preferential Nodes

- Is normal to encourage the use of nodes with higher degree than the average (preferrednodes)

- If is the average number of neighbors a new node will connect to /2 nodes fromGrandom,iand to /2 nodes from Gcandidates,ithat appears most (Gpreferred,i) since ai(t0)=1

-

Probability that a preferred node appears (a node that appears at least twice in candidateslist) versus the average number of neighbors for different values of N (number of nodes

in the initial network)

Attack Analysis

- Three different types of attacks: Modest attack: a user that acquires host cache information and candidates list like

a normal user and then attacks to the nodes that appears most, removing them

from the network

Group Type I attack:add a number of nodes to network that only point to eachother for increasing the possibility to emerge as preferred nodes and then create

anomalies and suddenly disconnect all at the same time for partitioning thenetwork

Group Type II attack: add a number of nodes to network that behaves likenormal nodes and then create anomalies and suddenly disconnect all at the same

time for partitioning the network

- Last two attacks are possible as network is open without any authentication orauthorization

- Simulations in network with 2000 nodes (starting with 20), each node chooses a numberof neighbors between 5 and 8

- Metric: percentage of unique reachable nodes in the network vs. the number of hops(TTL)

Giant Component

- Giant component: the largest portion of network that remains strongly connected underattacks

- Metric: percentage of nodes in giant component vs. percentage of malicious users (groupattack)


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Alpha behavior

- parameter contributes in creating highly connected nodes when it decreases, so it helpsfor fast recovery

- Simulation with hybrid attack 10% Group Type I and 20% Group Type II, behaviorstudied

Betweenness

measures the centrality of a node i:for each pair of nodes (l,m) in the graph, there are

slm

shortest paths between l and m

silm

shortest paths going through i

biis the sum of silm

/ slm

over all pairs (l,m)

SIS model on SF networks: SIS = Susceptible Infected Susceptible. Mean-Field usualapproximation: all nodes are equivalent (same connectivity) => existence of an epidemic

threshold 1/ for the order parameter r (density of infected nodes). Scale-free structure =>necessary to take into account the strong heterogeneity of connectivities => rk=density of

infected nodes of connectivity k.

Important characteristics of SFN: Noticeable resilience to random connection failure; Very

sensitive to selective damage ( the attack against highly connected nodes).

Immunization strategy:The network will increase its tolerance to infections at the price of a

tiny number of immune individuals. Design of more robust networks; Improved routing

algorithms; Prevention of epidemic broadcast (both human and computer viruses).

Examples of Complex Adaptive Systems: Living organisms. Nervous systems. Immune

systems. Insect colonies. Human societies. Cities. Economies. Markets. The WWW.

Characteristics of Complex Systems:

- Multiple Logics (contradictory rules)- Non-Linear (formally unpredictable)- Dynamical (not in equilibrium)- Not Deterministic (but not completely random)- Often Not Well-Behaved (exhibiting sudden large changes of behavior)- Open With Permeable Boundaries, Produce Effects Disproportional To Their Causes

Types of complexity:

Static Complexity: Fixed structures, frozen in time. Dynamic Complexity: Systems with time regularities. They have cyclic attractors. Evolving Complexity: Open ended mutation, innovation. Related are diffusion

aggregation and similar branching tree structures.

Self-Organizing Complexity: Self-maintaining systems, aware.Build artificial complex adaptive system:

Complex Adaptive System --Observation--> Experimental Data --Modelling--> Computational

Model --Design--> New Complex Adaptive System.


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Some Key Attributes of complex adaptive systems:

Self-Organized Order: Order emerges from the interaction of simple entities. Minimalpre-design, low cost, adaptivity, versatility.

Decentralization: All sensing, information processing, communication and control is local, with minimal central guidance. Scalability, robustness, flexibility,

expandability.

Multiple Scales: Entities and processes at many spatiotemporal scales. Depth ofrepresentation and information processing.

Self-Similarity (in many cases): The same structural motifs are present at many scales.Algorithmic economy, expandability

Self-Organization:

- The spontaneous emergence of large-scale spatial, temporal, or spatiotemporal order in asystem of locally interacting, relatively simple components.

- Self-organization is a bottom-up process where complex organization emerges at multiplelevels from the interaction of lower-level entities. The final product is the result ofnonlinear interactions rather than planning and design, and is not known a priority.

- Contrast this with the standard, top-down engineering design paradigm where planningprecedes implementation, and the desired final system is known by design.

Main features of complex self-organizing structures:

Uncontrolled - Autonomous agents, no executive or directing node (power symmetry). Nonlinear - Outputs are not proportional to input (superposition does not hold) Emergence - Properties are not describable in part terms (meta-system transitions) Coevolution - Part structure correlates to an external environment (contextual fitness) Attractors - Each occupies a small area of state space (concurrent options) Non-Equilibrium - System operates far from equilibrium (dissipative). Energy flows

drive the system away from equilibrium and establish semi-stable modes as dynamic

attractors. This relates to metabolic self-sustaining activity which in living systems is

usually called autopoiesis.

Non-Standard - System contains structures in space and time (heterogeneous); initiallyhomogenous systems will develop self-organising structures dynamically.

Non-Uniform - Parts are non-equivalent (different rules or local laws) Phase Changes - Edge of chaos states maintained (power law distributions of properties

occurs in both space and time) .

Unpredictability - Sensitivity to initial conditions (chaos) Instability - Stepped evolution or catastrophes exist (punctuated equilibria) Mutability - Random internal changes or innovations occur (dynamic state space); new

configurations are possible due to part creation, destruction or modification.

Self-Reproduction - Ability to clone identical or edited copies (growth) Self-Modification - Ability to change connectivity at will (redesign)

Elements of Self-Organization:


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Interacting components provide the substrate for organization of higher-level structures.

Interaction/communication is necessary for creating linkages to assemble larger structures.

Example components are molecules, cells, agents, etc. Example interactions are excitation,

inhibition, sensing, attraction, repulsion, etc.

Constructive processes needed to build larger structures from the components, e.g., reproduction,

aggregation, crystallization, copying, growth, recombination, ramification, etc.

Destructive processes needed to tear down existing (possibly suboptimal or unwanted) structures

to make room for new ones, (death, fragmentation, division, mixing, turbulence, noise).

Autocatalysis/positive feedback needed to reinforce and drive the construction of useful

structures, e.g., splits encouraging more splitting to create a complex branching structure.

Homeostasis/negative feedback needed to prevent runaway structure formation, e.g., structures

beyond a certain size becoming non-receptive to further addition or even unstable.

Nonlinearity needed to magnify some effects and squelch others in order to produce complex

structure. Examples include thresholds, unimodal and multimodal dependencies, saturation, and

amplification underlying the constructive, destructive and feedback processes.What is Emergence?

The appearance of large-scale collective order that cannot be described completely in terms of

the individual system components.e.g., meaning from a collection of words, a society from acollection of individuals, a wave from a collection of particles, a picture from a collection of

pixels. Emergence seeks to move beyond pure reductionism without resorting to metaphysical

explanations, e.g., in explaining phenomena such as intelligence and life. Complex adaptive

systems exhibit spontaneous emergence at many levels of description.

Why do we need to build complex adaptive systems?

To control other complex adaptive systems (communication networks, biological systems).

To obtain systems with attributes such as intelligence, adaptivity, robustness, scalability, andflexibility for operation in complex, dynamic and uncertain environments ( battlefields, disaster

areas, hazardous regions, ocean floors, outer space).

To create very large-scale or fine-grained systems where standard design, control, and analysis

methods break down for capacity reasons (sensor networks with millions of nodes).

Design approaches: Traditional Top-Down Approach; Self-Organized Bottom-Up Approach;

Heterarchical Holistic Approach.

Examples of Complex Adaptive Systems:

Living organisms. Nervous systems (brains). Immune systems. Ecosystems. Insect colonies. Human societies. Cities. Economies.


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Markets. The world-wide web.

Examples of Engineered Complex Adaptive Systems:

Self-organized sensor networks. Smart matter / smart structures. Smart paint. Smart dust. Amorphous computers. Evolvable hardware. Self-shaping, self-repairing materials. Self-reconfiguring robots. Kilorobot or megarobot swarms.

Self-Organized Traditional Top-Down Approach:

Consider all possibilities.

Develop a very careful design. Thoroughly test the design to verify performance. Implement and test a prototype. Carefully replicate the verified design to ensure reliability.

This top-down approach relies on anticipation of all eventualities, meticulous design, thorough

testing, and exact replication to obtain the desired level of performance. It works best in well-

understood, predictable and relatively simple environments --- no surprises please!

Self-Organized Bottom-Up Approach:

Provide the basic elements/components needed. Let the components interact among themselves and with the environment to organize

through an iterative process of creative exploration and selective destruction.This approach produces good designs by multi-scale, parallel, intelligent random search through

the space of possibilities. It is appropriate -- necessary -- for large-scale complex systems

operating in complex, dynamic, unpredictable environments, e.g., the real world.

Holistic Complexity View: We can summarise the structure of complex systems in an overall

heterarchical view where successively higher levels show a many to many (N:M) structure,

rather than the top down (1:N) tree structure common to conventional thought.

Key Difference between Top-Down, Bottom-Up and Hierarchical

- Top-DownEvery aspect of the system at all levels is carefully designed and evaluated.Critically dependent on component reliability. Non-scalable in cost, time, effort,

reliability. Inflexible in response to novel conditions.

- Bottom-UpOnly the basic simple and cheap components are designed; the rest of thesystem organizes itself. Inherently scalable. Flexible, robust, versatile, expandable,

evolvable.

- Hierarchical The components at each level also connect horizontally to form anhierarchy - an evolving web like network of associations which generates the


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autocatalysis or self-production aspect of the system. The 'part' interactions will createemergent modules with new properties. The groups of interlaced networks are

coevolutionary constrained by downward causalities.

What do complex adaptive systems buy us?

Scalability: The system can grow much larger because no one needs to keep track ofeverything.

Flexibility: The system can change as needed simply by individual agents changing theirbehavior.

Versatility: The system can be used in many different situations without redesign. Expandability: More agents can be added to the system without redesign. Robustness: The system can withstand changes and even loss of individual agents.

In complex environments that change all the time, we cannot anticipate all situations, so we

cannot pre-design a system that is always guaranteed to work.

However, engineered complex systems are also: Unpredictable; Open-ended; Opaque;Imperfect; Imprecise; Uncertain.

Engineering Self Organizing Systems - Key Features:

In our approach complex systems are described in terms of self-organization processes ofprime integer relations.

A prime integer relation is an indivisible element built from integers as the basicconstituents following a single organizing principle.

Prime integer relations can characterize correlation structures of complex systems andmay describe complex systems in a strong scale covariant form.

Determined by arithmetic only, the self-organization processes of prime integer relationsmay describe complex systems by information not requiring further explanations.

Some Enabling Technologies: MEMS (Micro-Electro-Mechanical Systems). Nanotechnology.Miniaturized wireless devices. Miniaturized power sources. Ad-hoc wireless networks. Very

high-speed digital circuits. FPGAs. Micro-robots. Neural networks. Evolutionary algorithms.

Cellular Automata:are discrete-time, lattice-based dynamical systems where the next state of

each cell depends on the current state of its neighborhood. Cellular automata provide a simple

but powerful way to study many fundamental features of biological systems, e.g.: Pattern

formation. Growth and morphogenesis. Spatial interactions and organization. Spreading

activation and signaling. Self-replication. etc.

Cellular Automata as Simple Self-Organizing SystemsAn ``elementary'' cellular automaton

consists of a sequence of sites carrying values 0 or 1 arranged on a line. The value at each site

evolves deterministically with time according to a set of definite rules involving the values of its

nearest neighbours. 2^8 = 256 possible rules. Only the 32 rules of the form abcdbed0 satisfy

reflection symmetry and leave the ``quiescent'' configuration -000000- unchanged, and are

therefore considered ``legal''. All ``complex'' cellular automaton rules yield asymptotically self-

similar patterns. All give the same fractal dimension Log23 ~1.59 except for rule 150 which

gives a fractal dimension 1+ Log2f~1.69 where f is the ``golden ratio (1+5)/2.


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Evolution of Development: Growth and development of an organism, or in this case a

genetically-controlled complex system, determine its form and function.

Over the course of its life history, the 'organism' goes through:

* an embryonic stage

* an ontogenetic (juvenile) stage, and

* an adulthood stage

In each stage of development, the 'organism' progressively develops the more specialized pieces

of its functional anatomy and behavior. This process has been described by the phrase 'ontogeny

recapitulating phylogeny', meaning that a developing 'organism' will resemble its ancestors

before its species-distinct characteristics are expressed.

From the biological to the artificial: Most importantly, the length of each developmental stage

is the primary driving force behind morphological growth and development (morphogenesis).

The process of changes in the length of growth during development and the rate of that growth is

called heterochrony. DeGaris: models embryogenesis, or the development of distinct shapes

from an undifferentiated blob. Rust et al: models neural morphogenesis, or the development ofneurons in the brain from an undifferentiated mass of cells.

Rule-Based Development:

* molecular interactions regulation and expression of hormones and genes, influence self-organization of neural structures.

* formation of neuron morphology different patterns of connectivity, differentiation into celltypes.

* neural systems several cell types all functionally integrated but structurally modular,plasticity allows for pruning and reconfiguration of connections based on function.

Evo-devo and complexity The evolution of development provides us with two problems

relevant to Evolutionary Computation:1) self-assembly

2) applying evolutionary techniques to the 'complexity' problem

DeGaris discusses building 'hyper-complex' systems by

a) using embryological algorithms to evolve shapes

b) shapes are self-assembled at several scales, which allows for the construction of systems of

which the inner workings cannot be easily understood.

Issues in modeling Evo-Devo: Variation- development produces variety using a hierarchical

system of regulatory systems and controls. Adaptation- different systems can be built through

adjusting 'genes' that modulate development. Regulation- multiple interactions and relations can

be controlled by a relatively small number of genes and input parameters. Modularity- creates

repeated structures and functional modules. Robustness- robust to variations in the

developmental environment (complex systems can be created without an complete blueprint).

Optimization- a process involving a search of an n-dimensional space of all developmental

parameters, which determine when or whether or not a rule is activated, in addition to the


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frequency of its use. In these cases, some traditional GA/GP concepts of optimization are

utilized, but get applied in novel ways.

Two models of digital morphogenesis

Rust et al (2002) use an attraction/repulsion model, while DeGaris (1992) uses 2-D and 3-D

cellular automata (CA's).

Attraction/repulsion:

* the Genesis GA system was used to evolve connectivity in a three layer neural network system

* intrinsic branchingoccurs in the first phase of development. This growth is mediated in the

second stage by local 'chemical' gradients

* interactive splitting occurs in the second stage as 'chemical' sources are encountered in a

manner congruent with current growth of the neuronal structures,

* the first two stages of the attraction/repulsion model lead to an overgrowth of synaptic

connections between neurons.

* growth rates are regulated over time by switching from one phase of growth to another.

* in the third stage of development, these extra synapses are pruned to optimize localfunctionality in space and time.* this is similar to what happens naturally in the visual system.

2-D and 3-D Cellular Automata: Segev and Ben-Jacob (1998) also use CA's to model

embryogenesis.

DeGaris starts by defining a subset of cells in the automata grid as a target shape. A small

number ofparent cells are inserted and allowed to evolve using uniform crossover and mutation

until the target shape is acquired. The interaction rules are:

1) a parent cell 'pushes' the grid in a given direction, while the internal state of a parent cell

determines that direction,

2) a finite number of iterations should be allowed for each colony to self-organize into thedesired shape, and

3) the final shape will produce a fitness that can be measured.

'Fitness' criterion in digital morphogenesis

DeGaris defines "fitness" as the degree to which the colony of parent cells and their children

conform to initially desired shape.

De Garis Embryo Loop algorithm//calculate cellular NEWS number (CNNs) of each cell

//from CNNs, calculate ranking pattern (RPN) of each cell

//use ranking pattern number to see if each cell reproduces or dies

//find reproduction and death directions for selected cells

//perform reproductions, perform deaths

* based on the NEWS number and the ranking, a matrix is calculated for each cell as operators

for the reproduction instructions (i) and death instructions (j).

This chromosome is divided into:

* the number of iterations required to achieve the desired shape (N1)


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* the rules for reproduction (REPRO1 -- 75 loci long) for the first iteration

* the direction in which the initial blob can spread (R DIRNS1 75 loci long) for the firstiteration.

Retele booleene:

Mijloace informatice de simulare a comportarii sistemelor dinamice RB: Retele de unitati binare

Se justifica deoarece:

Reprezinta o idealizare a unei tendinte naturale Numeroase fenomene celulare si biochimice tind spre o stare tot sau nimic

Pot reproduce structura logica a sistemelor biologice continue Majoritatea genelor au doua alele (variante): ca atare putem reprezenta o alela cu

(0) si cealalta cu (1).

2 parametri N: numarul de unitati binare

K: numarul de intrari la fiecare unitate Mecanism simplu: Intrare (0,1)Functie booleanaIesire (0,1)

2N stari posibile Cu cat creste K, cu atat avem mai multe functii booleene posibile Starea la momentul T+1 depinde de starea la momentul T Numar finit de stari:

Reteaua trebuie sa fie capabila sa repete o anumita traiectorie in spatiul starilor Exista atractori

Random Boolean networks (RBNs):

Classic algorithm nnodes with kincoming links per node Each node can be either on (1) or off (0) at any given time Updating is synchronous Update rule is a random Boolean function of inputs, assigned when the network is

created, different for each node

For each node there will be 22kpossible functions Each node has n!/(n-k)! Possible ordered combinations for k links

RBN dynamics:

Low connectivity -> Freeze to a single state (point attractor) Moderate connectivity (~2) -> Limit cycle behaviour High connectivity -> Chaotic dynamics Edge of chaos at the transition between ordered and chaotic dynamics It has been suggested that complex systems evolve to the edge of chaos because this

combines optimal robustness and flexibility

Advantages of Artificial Genome models:

More biologically plausible Genome / phenotype representation Development could be modelled

Network characteristics can be selected via appropriate parameterization


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Genome is a convenient representation for EC modelling Genetic operators applied at the genome level act differently from those applied at

the network level

Evolutionary algorithm:

f = n(l/2) each run 100 times with different random number seed n = number of times a previous state was revisited l = number of states before revisiting

Random Boolean genetic network model:

Genetic network inside a cell Random Boolean network

First proposed by Kauffman Kauffman, S. A. (1969). Metabolic stability and epigenesis in randomly

constructed genetic nets.Journal of Theoretical Biology, 22:437467. Consist of N nodes which have K random connections and randomly assigned

Boolean functions.

Canalyzing Rule: Canalyzing function has at least one input, such that for at least one input value, the

output value is fixed.

Ex) AND, ORRobustness:

The average effect, after a single time step, of a small perturbation at the equilibriumdistribution.

Total Sensitivity, S (R) The sum of the probabilities that a single flipped input will alter the output of R.

Tissue Simulations:

- Each cell communicates with its four nearest neighbours.- All cells have identical internal network architecture and rules (with N=50).- Each connection in network represents how a gene influences the transcription of another

gene.

- The value of a fraction, k, of genes is decided by intercellular connections it is true ifany of the four neighbours is true.

Goals of Network Biology Approach

1. From the elementary interactions among the participating models, explain the complexbehavior of a cellular function.

The Alliance for Cellular Signaling has identified over 600 molecules involved inG-protein coupled signal transduction.

2. By comparing networks from many organisms, deducing the engineering principles bywhich cell perform particular functions and deal with uncertainty in their environment.

The System of Linear Equations and Correlation Structures of Complex Systems: It is

shown that the correlation structures underlying the conservation of the quantities are built in

accordance with the hierarchical structures of prime integer relations associated with the system

of equations and inequality.


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Prime Integer Relations, a New Irreducible form of Information:

Prime integer relations give information in an irreducible form.

- we can be confident in an arithmetic statement as we can easily check it.- we know how the prime integer relation is built and may observe symmetry in its

corresponding geometric pattern.

- we can associate with the prime integer relation a correlation structure of a complexsystem.

How Prime Integer Relations Describe Complex Systems: In our approach a complex system

is described in terms of prime integer relations. A prime integer relation describes a correlation

structure of the complex system. In this capacity it encodes:the parts of the correlation structure;

the relationships between them, i.e., how the parts are correlated; the strength of the correlations,

i.e., how the dynamics of some parts of a relationship determine the dynamics of the other parts.

Search for an Optimality Condition of Complex Systems: A complex system S demonstratesthe optimal performance for a problem P, if its complexity C(S) is in a certain relationship C(S)

= F(C(P)) with the complexity C(E) of the problem P.Itsproposed to measure complexity interms of self-organization processes of prime integer relations.The Optimality Condition as a Possible Way to Manage Complex Systems Efficiently:

The optimality condition suggests the complexity of a system as a key to its optimization. It tells us that as long as we properly relate the complexity of the system with the

complexity of the problem, the optimal result is guaranteed.

Moreover, given the complexity of a problem, we may calculate then the complexity ofthe system needed to obtain the optimal result.

L-Systems:

- A model of morphogenesis, based on formal grammars (set of rules and symbols).- Introduced in 1968 by the Swedish biologist A. Lindenmayer.- Originally designed as a formal description of the development of simple multi-cellular

organisms.

- Later on, extended to describe higher plants and complex branching structures.Self-Similarity: When a piece of a shape is geometrically similar to the whole, both the shapeand the cascade that generate it are called self-similar (Mandelbrot, 1982).The recursive nature of the L-system rules leads to self-similarity and thereby fractal-like forms

are easy to describe with an L-system.

Self-Similarity in Fractals: Exact; Example Koch snowflake curve; Starts with a single line

segment; On each iteration replace each segment by; As one successively zooms in the resulting

shape is exactly the same.

Self-similarity in Nature:Approximate; Only occurs over a few discrete scales (3 in this Fern);

Self-similarity in plants is a result of developmental processes, since in their growth process

some structures repeat regularly. (Mandelbrot, 1982).


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- fMove forward a step of length dwithout drawing a line. The state of the turtle changesas above.

- + Turn left by angle . The next state of the turtle is (x, y, + ).- - Turn left by angle . The next state of the turtle is(x, y, -b).

w: F+F+F+F; p: F F+F-F-FF+F+F-F; Angle () = 90;Bracketed L-systems

To represent branching structures, L-systems alphabet is extended with two new symbols: [, ], to

delimit a branch. They are interpreted as follows:

[ Push the current state of the turtle onto a pushdown stack.

] Pop a state from the stack and make it the current state of the turtle. No line is drawn, in

general the position of the turtle changes.

Turtle Interpretation of Bracketed Strings: w: F;p: F F[-F]F[+F][F]; Angle () = 60;Generative Encodings for Evolutionary Algorithms:

- EAs has been applied to design problems. Past work has typically used a direct encodingof the solution

- Alternative: Generative encoding, i.e. an encoding that specifies how to construct thegenotype

- Greater scalability through self-similar and hierarchical structure and reuse of parts- Closer to Natural DNA encoding

Examples of Generative Encoding for EAs:

- Biomorphs, The Blind Watchmaker(R. Dawkins)- Graph encoding for animated 3D creatures (K. Sims)- L-Systems: plant-like structures, architectural floor design, tables, locomoting robots

(C.Jacob, G. Ochoa, G. Hornby & J. Pollack, and others)

- Cellular automata rules to produce 2D shapes (H. de Garis)- Context rules to produce 2D tiles (P. Bentley and S. Kumar)- Cellular encoding for artificial neural networks (F. Gruau)- Graph generating grammar for artificial neural networks (H. Kitano)

Evolving Plant-like Structures:

- Alife system for simulating the evolution of artificial plants- Genotype: single ruled bracketed D0L-systems.

L-system: w: F, p: F F[-F]F[+F][F] Chromosome: F[-F]F[+F][F]

- Phenotype: 2D branching structures, resulting from derivation and graphic interpretationof L-systems

- Genetic Operators: Recombination and mutation operators that preserve the syntacticstructure of rules

- Selection Automated: fitness Function inspired by evolutionary hypothesis concerning the

factors that have had the greatest effect on plant evolution.


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Interactive: allowing the user to direct evolution towards preferred phenotypesIt is difficult of automatically measuring the aesthetic visual success of simulated objects or

images. In most previous work the fitness is provided through visual inspection by a human.

Automated Selection

- Hypotheses about plant evolution (K.Niklas, 1985): Plants with branching patterns that gather the most light can be predicted to be the

most successful (photosynthesis).

Evolution of plants was driven by the need to reconcile the ability to supportvertical branching structures

- Analytic procedure, components: (a) phototropism (growth movement of plants in response to stimulus of light), (b) bilateral symmetry, (c) proportion of branching points.

Developmental rules for Neural Networks

Firstly,biological neural networks:- there is simply not enough information in all our DNA to specify all the architecture, the

connections within our nervous systems.

- so DNA (with other factors) must provide a developmental 'recipe' which in some sense(partially) determines nervous system structure and hence contributes to our behaviour.

Secondly, artificial neural networks (ANNs):

- we build robots or software agents with ANNs which act as their nervous system orcontrol system.

- Alternatives: (1) Design, (2) Evolve ANN architecture.- Evolving: (2.1) Direct encoding, (2.2) Generative encoding- Early References: Frederick Gruau, and Hiroaki Kitano.- Gruau invented 'Cellular Encoding', with similarities to L-Systems, and used this for

evolutionary robotics.

- Kitano invented a 'Graph Generating Grammar.: A Graph L-System that generates not a'tree', but a connectivity matrix for a network.

Evolutionary Approach Conclusions (based on Hornby et. al):

- Main criticism for the use of evolutionary approaches for design: it is doubtful whether itwill reach the high complexities necessary for real applications.

- Since the search space grows exponentially with the size of the problem, evolutionaryapproaches with direct encoding will not scale to large designs.

- Generative encoding (i.e. a grammatical encoding that specifies how to construct adesign) can achieve greater scalability through self-similar and hierarchical structure.

- Trough reuse of parts generative encoding is a more compact encoding of a solution.The logical depth of a system:A system should be called complex, or logically deep, if that

system can be generated by a few simple rules, but those rules require a long time to run. If the

definition of logical depth uses a classical computer then the list of factors has high logical depth


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Modelling Sequential Data (time series):

Classic approaches to time-series prediction

- Linear models: ARIMA(auto-regressive integrated moving average),ARMAX(autoregressive moving average exogenous variables model)

- Nonlinear models: neural networks, decision treesProblems with classic approaches

- prediction of the future is based on only a finite window- its difficult to incorporate prior knowledge- difficulties with multi-dimensional inputs and/or outputs

State-space models

- Assume there is some underlying hidden state of the world(query) that generates theobservations(evidence), and that this hidden state evolves in time, possibly as a function

of our inputs

- The belief state: our belief on the hidden state of the world given the observations up tothe current time y1:tand our inputs u1:tto the system, P( X | y1:t, u1:t)

- Two most common state-space models: Hidden Markov Models(HMMs) and KalmanFilter Models(KFMs)

- a more general state-space model: dynamic Bayesian networks(DBNs)State-space Models: Representation

Any state-space model must define a prior P(X1) and a state-transition function, P(Xt| Xt-1) , and

an observation function, P(Yt| Xt).

Assumptions:

- Models are first-order Markov, i.e., P(Xt| X1:t-1) = P(Xt| Xt-1)- observations are conditional first-order Markov P(Yt| Xt, Yt-1) = P(Yt| Xt)- Time-invariant or homogeneous

Representations:

- HMMs: Xtis a discrete random variables- KFMs: Xtis a vector of continuous random variables- DBNs: more general and expressive language for representing state-space models

State-space Models: Inference

A state-space model defines how Xtgenerates Yt and Xt. The goal of inference is to infer the

hidden states(query) X1:tgiven the observations(evidence) Y1:t.

Inference tasks:

- Filtering(monitoring): recursively estimate the belief state using Bayes rule predict: computing P(Xt| y1:t-1) updating: computing P(Xt| y1:t) throw away the old belief state once we have computed the prediction(rollup)

- Smoothing: estimate the state of the past, given all the evidence up to the current time Fixed-lag smoothing(hindsight): computing P(Xt-l| y1:t) where l > 0 is the lag

- Prediction: predict the future


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Lookahead: computing P(Xt+h| y1:t) where h > 0 is how far we want to look ahead- Viterbi decoding: compute the most likely sequence of hidden states given the data

MPE(abduction): x*1:t= argmax P(x1:t| y1:t)State-space Models: Learning

Parameters learning(system identification) means estimating from data these parameters that are

used to define the transition model P( Xt| Xt-1 ) and the observation model P( Yt| Xt )

The usual criterion is maximum-likelihood(ML)

The goal of parameter learning is to compute

- *ML= argmax P( Y| ) = argmax log P( Y| )- Or *MAP= argmax log P( Y| ) + logP() if we include a prior on the parameters- Two standard approaches: gradient ascent and EM(Expectation Maximization)- Structure learning: more ambitious

HMM: Hidden Markov Model

One discrete hidden node and one discrete or continuous observed node per time slice. X: hidden variables Y: observations Structures and parameters remain same over time Three parameters in a HMM:

The initial state distribution P( X1 ) The transition model P( Xt| Xt-1) The observation model P( Yt| Xt)

HMM is the simplest DBN a discrete state variable with arbitrary dynamics and arbitrary measurements

KFL: Kalman Filter Model

KFL has the same topology as an HMM all the nodes are assumed to have linear-Gaussian distributions

x(t+1) = F*x(t) + w(t),

- w ~ N(0, Q) : process noise, x(0) ~ N(X(0), V(0))

y(t) = H*x(t) + v(t),

- v ~ N(0, R) : measurement noise

Also known as Linear Dynamic Systems(LDSs) a partially observed stochastic process with linear dynamics and linear observations: f( a + b) = f(a) + f(b)

both subject to Gaussian noise KFL is the simplest continuous DBN

a continuous state variable with linear-Gaussian dynamics and measurementsDBN: Dynamic Bayesian networks

DBNs are directed graphical models of stochastic process DBNs generalize HMMs and KFLs by representing the hidden and observed state in

terms of state variables, which can have complex interdependencies


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The graphical structure provides an easy way to specify these conditional independencies A compact parameterization of the state-space model An extension of BNs to handle temporal models Time-invariant: the term dynamic means that we are modeling a dynamic model, not

that the networks change over time

Definition: a DBN is defined as a pair (B0, B), where B0defines the prior P(Z1), and is a

two-slice temporal Bayes net(2TBN) which defines P(Zt | Zt-1) by means of a DAG(directed

acyclic graph) as follows:

Z(i,t) is a node at time slice t, it can be a hidden node, an observation node, or a controlnode(optional)

Pa(Z( i, t)) are parent nodes of Z(i,t), they can be at either time slice t or t-1 The nodes in the first slice of a 2TBN do not have parameters associated with them But each node in the second slice has an associated CPD(conditional probability

distribution)

Representation of DBN in XML format

//a static BN(DAG) in XMLBIF format defining the//state-space at time slice 1

// a transition network(DAG) including two time slices t and t+1;

// node has an additional attribute showing which time slice it

// belongs to

// only nodes in slice t+1 have CPDs

The Semantics of a DBN

- First-order markov assumption: the parents of a node can only be in the same time sliceor the previous time slice, i.e., arcs do not across slices

- Inter-slice arcs are all from left to right, reflecting the arrow of time- Intra-slice arcs can be arbitrary as long as the overall DBN is a DAG- Time-invariant assumption: the parameters of the CPDs dont change over time-

The semantics of DBN can be defined by unrolling the 2TBN to T time slices

- The resulting joint probability distribution is then defined byDBN, HMM, and KFM

- HMMs state space consists of a single random variable; DBN represents the hidden state interms of a set of random variables

- KFM requires all the CPDs to be linear-Gaussian; DBN allows arbitrary CPDs

N

i

i

t

i

ttt ZZPZZP

1

1 ))(|()|(


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- HMMs and KFMs have a restricted topology; DBN allows much more general graphstructures

- DBN generalizes HMM and KFM; has more expressive powerDBN: Inference: The goal of inference in DBNs is to compute: Filtering: r = t; Smoothing: r > t;

Prediction: r < t; Viterbi: MPE.

DBN inference algorithms

DBN inference algorithms extend HMM and KFMs inference algorithms, and call BNinference algorithms as subroutines

DBN inference is NP-hard Exact Inference algorithms:

Forwards-backwards smoothing algorithm (on any discrete-state DBN) The frontier algorithm(sweep a Markov blanket, the frontier set F, across the DBN,

first forwards and then backwards)

The interface algorithm (use only the set of nodes with outgoing arcs to the next timeslice to d-separate the past from the future) Kalman filtering and smoothing

Approximate algorithms: The Boyen-Koller(BK) algorithm (approximate the joint distribution over the

interface as a product of marginals)

Factored frontier(FF) algorithm Loopy propagation algorithm(LBP) Kalman filtering and smoother Stochastic sampling algorithm:

importance sampling or MCMC(offline inference) Particle filtering(PF) (online)

DBN: Learning

The techniques for learning DBN are mostly straightforward extensions of the techniques forlearning BNs;

Parameter learning Offline learning: Parameters must be tied across time-slices; The initial state of the

dynamic system can be learned independently of the transition matrix

Online learning: Add the parameters to the state space and then do onlineinference(filtering).

Structure learning The intra-slice connectivity must be a DAG Learning the inter-slice connectivity is equivalent to the variable selection problem,

since for each node in slice t, we must choose its parents from slice t-1.

Learning for DBNs reduces to feature selection if we assume the intra-sliceconnections are fixed

Learning uses inference algorithms as subroutines


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DBN Learning Applications

Learning genetic network topology using structural EM Gene pathway models

Inferring motifs using HHMMs Motifs are short patterns which occur in DNA and have certain biological

significance; {A, C G, T}*

Inferring peoples goals using abstract HMMs Inferring peoples intentional states by observing their behavior

Modeling freeway traffic using coupled HMMsSummary

DBN is a general state-space model to describe stochastic dynamic system HMMs and KFMs are special cases of DBNs DBNs have more expressive power DBN inference includes filtering, smoothing, prediction; uses BNs inference as subroutines

DBN structure learning includes the learning of intra-slice connections and inter-sliceconnections

DBN has a broad range of real world applications, especially in bioinformatics.Engineering Biomorphic Systems: Discussions on morphogenesis

Theoretical/Mathematical/Computational Biology Developing a theoretical and/or

quantitative model for the structures and processes of a biological system.

Biomorphic EngineeringApplying methods (structures and processes) of a biological system to

design artificial systems with a similar or related functionality.

Attributes of Biological SystemsComplexity. Organization at many scales/levels. Adaptation.

Growth and development. Reproduction. Evolution.

Levels of Organization for Biological Systems- Molecules (DNA, RNA, proteins, amino acids, messengers, etc.)- Subcellular structures (membranes, channels, organelles, etc.)- Cells (neurons, blood cells, skin cells, bone cells, etc.)- Cell Assemblies (pancreatic islets, central pattern generatrs, etc.)- Sub-organs and Sub-systems (cortex, spinal cord, arteries, etc.)- Organs (skin, brain, heart, stomach, liver, etc.)- Systems (nervous system, digestive system, immune system, etc.)- Organisms (plants, animals)- Populations- Ecosystems- BiosphereLevels of Plasticity in Biological Systems:

Adaptation Rapid change to accommodate variations in the environment.

e.g., change in pupil size with light.


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Learning Gradual change in parameters to optimize behavior with respect to regularities in the

environment. e.g., classical conditioning.

Development Change in the structure and processes of a single organism over its lifetime.

Evolution Change in structures and processes over successive generations to maintain and

enhance fitness. e.g., invertebrate to vertebrate, reptile to bird.

Aspects of Biomorphicity:

Function: inference, pattern-recognition, locomotion, conversation, adaptation, learning. Behavior: homing, obstacle-avoidance, walking, mating, seeking sustenance, trail-

following, chemotaxis, phototaxis, etc.

Processes: signaling, cell-division, synaptic modification, excitation, inhibition, reaction,catalysis, recombination, mutation, etc.

Structure: limbed robots, neural networks, artificial limbs, robot bugs, swarms, etc. Information Structure: genes, spike trains, pheromone trails, etc. Development: morphogenesis, pattern-formation, growth, synaptogenesis, differentiation.

Inception: by copying, splitting, recombination, etc. Evolution: genetic algorithms, artificial life, etc.Examples of Biomorphic Systems:

Cellular Automata: Discrete cellular lattices where the next state of each cell depends on the

current states of its neighbors. CAs are used to study self-replication, pattern formation, fluiddynamics, traffic patterns, and in many other applications

Neural Networks: Adaptive systems based on networks of neurons (brain cells) that comprise the

nervous system and collectively perform all sensory, cognitive, motor, and control functions in

multicellular organisms. Neural networks are used in applications such as pattern recognition,

computer vision, classification, robot control, optimization, and many others.

Genetic Algorithms: Optimization algorithms that follow the selection-based approach ofevolution.

Swarms: Systems with large numbers of relatively simple mobile agents, interacting in limited

ways, with significant and nontrivial group-level order in the system. Modeled after insect

colonies and bird swarms, these systems have been applied to such problems as network

optimization, self-assembling or emergent structures, collective transport, etc.

Animats: Artificial organisms, implemented in software or hardware.

Artificial Life: The attempt to simulate, design, and implement artificial systems that mimic

living systems in some nontrivial sense.

Artificial Worlds: Detailed simulated environments with computationally specified rules,

mimicking real or imaginary environments inhabited by agents.

What is Artificial Life?

- collection of methods for building discrete event simulations with evolving multiple agents- study of the dynamics of living systems, regardless of substrate

BiologyStudy of CARBON-based life.


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- Artificial life (A-Life) uses informational concepts and computer modeling to study life ingeneral, and terrestrial life in particular. (Freeman quoting Langton)

- form of mathematical biologyCharacteristics of Artificial Life:

- Synthetic Approach: Synthesizes life-like behaviour within computers (or robots)- Emergence: A property of the system as a whole is not contained in any of its parts, but

results from interaction of the parts. The whole of the system being greater than the sum of

the parts

- Self-organization: The spontaneous formation of complex patterns or complex behaviouremerging from the interaction of simple lower-level elements

Modelling of complex systems

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