Agent Dynamics in Complex Multilevel Systems of Systems of Systems Jeffrey Johnson

Agent Dynamics in Complex Multilevel

Systems of Systems of Systems

Jeffrey Johnson

The Open University - UK

AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009


Complex systems – dynamics emerge from the

interaction of the parts

e.g. a conversation is emerges from interaction

e.g.

did you see the football ?





e.g.

did you see the football ?

no





e.g.

do you like Paris ?





e.g.

do you like Paris ?

yes, a lot





e.g.

I love the food …

and the wine





I love the food …

and the wine





Generally the interaction is computationally irreducible

I love the food …

and the wine

… unpredictable






I love the food …

and the wine






I love the food …

and the wine

… unpredictable – cannot make point predictions




More generally the behaviour of people depends on interaction with many other people.





in networks





in networks





in networks




nodes in networks can be anything




nodes in networks can be anything

e.g. countries

Taiwan

France

USA

JapanIceland

Ghana

Mexico

Peru

Australia




What is there between the micro and the macro level ?

Taiwan





Taiwan System

Sub-System





Taiwan System

Sub-System





Taiwan System

Sub-System




Taiwan is a system of systems of systems

Taiwan System

Sub-Systems

System of




Taiwan is a system of systems of systems

Taiwan System

Sub-Systems

System of


Complex systems

How can we:

- represent multilevel systems of system of systems ?

- model their dynamics at any level ?

- integrate their bottom-up and top down dynamics ?


Complex systems

How can we:

- represent multilevel systems of system of systems ?

- model their dynamics at any level ?

- integrate their bottom-up and top down dynamics ?

What role do agents play in all this ?


Relations give us networks of agents


Relations give us networks

Micro-level connectivity structure matters


3 binary relations one 3-ary relation

Binary relations are not rich enough


Relational Structure

Binary relation 3-ary relation 4-ary relation


Multilevel Systems & Hypernetworks for the dynamics of complex multilevel systems

Polyhedral Connectivity in Hypernetworks

0- near polyhedra

The intersection of two simplices is called their shared face.

They are q-near if their shared face has dimension q


1- near polyhedra

0- near polyhedra





0- near polyhedra



1- near polyhedra

(and also 0-near)



1- near polyhedra

2- near polyhedra

0- near polyhedra


Polyhedra can be q-connected

through shared faces





1-connected components





1-connected components

Q-analysis: listing q-components



Polyhedral Connectivity & q-transmission

The Bull The Dog The Ship The Royal Oak



My dog’s got

No nose

How does he smell ?




Terrible !

How does he smell ?




Terrible !

How does he smell ?




My dog’s got

No nose

How does he smell ?




My dog’s got

No nose

How does he smell ?




My dog’s got

No nose

How does he smell ?




Terrible!

How does he smell ?

The joke is q-transmitted through the backcloth


Hypernetworks for the dynamics of complex multilevel systems ISCTE Lisbon 12-Jan-2008

Polyhedral Structure

provides a new way of representing

& multilevel systems …


e.g. take a set of 3 blocks

Formation of simplices hierarchical structure

{ }AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

{ }R

R


e.g. take a set of 3 blocks assembled by a 3-ary relation


{ }R


e.g. take a set of 3 blocks assembled by a 3-ary relation R

The structure has an emergent property


{ }R


Level N+1

Level N

n-ary relation

assembles elements

into named

structures at a higher

level


{ }R


Archn-ary relation

assembles elements

into named

structures at a higher

level

R


Example:

gin, tonic, ice, lemon

gin

ice

tonic

lemon


Example:

gin, tonic, ice, lemon

Gin & Tonic is a Gestalt !

gin

ice

tonic

lemon


Example: Road Accidents

upset

rain

speed

tired



upset

rain

speed

tired


The accident is a whole

the individual parts may not cause an accident


upset

rain

speed

tired

can weight importance

of the vertices

0.6 contribution



upset

rain

speed

tired


of the vertices

0.6 contribution

0.8 contribution



rain

speed

tired


of the vertices

0.6 contribution

0.8 contribution

0.3 contribution


upset


upset

rain

speed

tired


of the vertices

0.6 contribution

0.8 contribution

0.9 contribution

0.3 contribution



upset

rain

speed

tired


of the vertices

0.6 contribution

0.8 contribution

0.9 contribution

0.3 contribution


Fuzzy 0.6 contribution

Example: robot soccer








‘scoring a goal’



‘the old 1-2 move’

‘scoring a goal’



‘The old 1-2’ as a trajectory in multidimensional space












‘The old 1-2’ as a polyhedral trajectory in multidimensional space



formation of a polyhedron is a structural event

Passing ball event

Goal scoring event



Multilevel Structure and Set Definition


Multilevel Structure and Set Definition

Complex systems generally have many ‘levels’

cells → organs → animals

chips → boards → computers

people → departments → institutions

nurses → … hospitals … → health trusts


Multilevel Structure in Human Systems

Clipboard challenge

you are studying a hospital, how many

things can you see ? € 1.00 for each !

e.g.

bandages, desks, nurses, uniforms, aspirin, light-switches, door knobs, beds, pencils, pills, doctors, trolleys, windows, doors, wards, flowers, canteens, children, teddy bears, waste bins, curtains, computers, car parks, cups, …



Clipboard challenge

bandages, desks, nurses, uniforms, aspirin, light-switches, door knobs, beds, pencils, pills, doctors, trolleys, windows, doors, wards, flowers, canteens, children, teddy bears, waste bins, curtains, computers, car parks, cups, …

This is a multilevel mess !



Sorting out the hierarchical mess …



Lifting coherent vocabulary from the soup








AND and OR aggregations in multilevel systems


Representing Complex Systems & Dynamics

Backcloth, Traffic & Type-1 Dynamics

Traffic on the multi-dimensional backcloth




Traffic on the multi-level backcloth




Traffic on the multi-level backcloth - coherence

Cannot look at just one level

Traffic must aggregate coherently over the structure


Unpacking High-level Structure in Human Systems



System time and System Events

System dynamics as traffic on a fixed multilevel backclothAESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009



Towards representing systems of systems of …

Cannot look at just one level

Traffic must aggregate coherently over the structure


Agents, Climate Change & Systems of Systems of Systems


Agents, Climate Change & Systems of Systems of Systems


Government Policy

?

?

Agents

Conclusions

- complex systems - systems of systems of systems


Conclusions


- need new multilevel mathematics to integrate

hypernetworks are necessary if not sufficient


Conclusions




- hypernetworks give a theory of aggregation

- mappings aggregate over hypernetworks


Conclusions






- governments think at the macrolevel (it’s easier!)


Conclusions







- agents are needed at the microlevel


Conclusions







- agents are needed at the microlevel

- new opportunities for agent based modelling !


Agent Dynamics in Complex Multilevel Systems of Systems of Systems Jeffrey Johnson

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