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 ?

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 ? no

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. do you like Paris ?

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. do you like Paris ? yes, a lot

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. I love the food … and the wine

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 I love the food … and the wine

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 Generally the interaction is computationally irreducible I love the food … and the wine … unpredictable

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 Generally the interaction is computationally irreducible I love the food … and the wine

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 Generally the interaction is computationally irreducible I love the food … and the wine … unpredictable – cannot make point predictions

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

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

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

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

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 nodes in networks can be anything

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 nodes in networks can be anything e.g. countries Taiwan France USA Japan Iceland Ghana Mexico Peru Australia

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 What is there between the micro and the macro level ? Taiwan

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 What is there between the micro and the macro level ? Taiwan System Sub-System

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 What is there between the micro and the macro level ? Taiwan System Sub-System

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 What is there between the micro and the macro level ? Taiwan System Sub-System

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 Taiwan is a system of systems of systems Taiwan System Sub-Systems System of

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 Taiwan is a system of systems of systems Taiwan System Sub-Systems System of

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

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

AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009 Relations give us networks of agents

AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009 Relations give us networks Micro-level connectivity structure matters

AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, binary relations  one 3-ary relation Binary relations are not rich enough

AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009 Relational Structure Binary relation 3-ary relation 4-ary relation

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

1- near polyhedra 0- near polyhedra The intersection of two simplices is called their shared face. They are q-near if their shared face has dimension  q AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009 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 (and also 0-near) AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009 Polyhedral Connectivity in Hypernetworks

1- near polyhedra 2- near polyhedra 0- near polyhedra Polyhedral Connectivity in Hypernetworks

Polyhedra can be q-connected through shared faces AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009 Polyhedral Connectivity in Hypernetworks

Polyhedra can be q-connected through shared faces 1-connected components AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009 Polyhedral Connectivity in Hypernetworks

Polyhedra can be q-connected through shared faces 1-connected components Q-analysis: listing q-components AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009 Polyhedral Connectivity in Hypernetworks

Polyhedral Connectivity & q-transmission The Bull The Dog The Ship The Royal Oak AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Polyhedral Connectivity & q-transmission My dog’s got No nose How does he smell ? The Bull The Dog The Ship The Royal Oak AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Polyhedral Connectivity & q-transmission Terrible ! How does he smell ? The Bull The Dog The Ship The Royal Oak AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Polyhedral Connectivity & q-transmission Terrible ! How does he smell ? The Bull The Dog The Ship The Royal Oak AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Polyhedral Connectivity & q-transmission My dog’s got No nose How does he smell ? The Bull The Dog The Ship The Royal Oak AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Polyhedral Connectivity & q-transmission My dog’s got No nose How does he smell ? The Bull The Dog The Ship The Royal Oak AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Polyhedral Connectivity & q-transmission My dog’s got No nose How does he smell ? The Bull The Dog The Ship The Royal Oak AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Polyhedral Connectivity & q-transmission Terrible! How does he smell ? The joke is q-transmitted through the backcloth The Bull The Dog The Ship The Royal Oak Hypernetworks for the dynamics of complex multilevel systems ISCTE Lisbon 12-Jan-2008

Polyhedral Structure provides a new way of representing & multilevel systems … AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

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 Formation of simplices  hierarchical structure e.g. take a set of 3 blocks assembled by a 3-ary relation AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

{} R Formation of simplices  hierarchical structure e.g. take a set of 3 blocks assembled by a 3-ary relation R The structure has an emergent property AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

{} R Formation of simplices  hierarchical structure Level N+1 Level N n-ary relation assembles elements into named structures at a higher level AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

{} R Formation of simplices  hierarchical structure Arch n-ary relation assembles elements into named structures at a higher level R AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Example: gin, tonic, ice, lemon gin ice tonic lemon AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Example: gin, tonic, ice, lemon Gin & Tonic is a Gestalt ! gin ice tonic lemon AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Example: Road Accidents upset rain speed tired AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Example: Road Accidents upset rain speed tired AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009 The accident is a whole the individual parts may not cause an accident

Example: Road Accidents upset rain speed tired can weight importance of the vertices 0.6 contribution AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Example: Road Accidents upset rain speed tired can weight importance of the vertices 0.6 contribution 0.8 contribution AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Example: Road Accidents rain speed tired can weight importance of the vertices 0.6 contribution 0.8 contribution 0.3 contribution AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009 upset

Example: Road Accidents upset rain speed tired can weight importance of the vertices 0.6 contribution 0.8 contribution 0.9 contribution 0.3 contribution AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Example: Road Accidents upset rain speed tired can weight importance of the vertices 0.6 contribution 0.8 contribution 0.9 contribution 0.3 contribution AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009 Fuzzy 0.6 contribution

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

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

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

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

‘scoring a goal’ Example: robot soccer AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

‘the old 1-2 move’ ‘scoring a goal’ Example: robot soccer AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

‘The old 1-2’ as a trajectory in multidimensional space Example: robot soccer AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

‘The old 1-2’ as a trajectory in multidimensional space Example: robot soccer AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

‘The old 1-2’ as a trajectory in multidimensional space Example: robot soccer AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

‘The old 1-2’ as a trajectory in multidimensional space Example: robot soccer AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

‘The old 1-2’ as a polyhedral trajectory in multidimensional space Example: robot soccer AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

formation of a polyhedron is a structural event Passing ball event Goal scoring event Example: robot soccer AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

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

Multilevel Structure and Set Definition Complex systems generally have many ‘levels’ cells → organs → animals chips → boards → computers people → departments → institutions nurses → … hospitals … → health trusts AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

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

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

Multilevel Structure in Human Systems Sorting out the hierarchical mess … AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Multilevel Structure in Human Systems Lifting coherent vocabulary from the soup AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Multilevel Structure in Human Systems Lifting coherent vocabulary from the soup AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Multilevel Structure in Human Systems Lifting coherent vocabulary from the soup AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

AND and OR aggregations in multilevel systems AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Representing Complex Systems & Dynamics Backcloth, Traffic & Type-1 Dynamics Traffic on the multi-dimensional backcloth AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Representing Complex Systems & Dynamics Backcloth, Traffic & Type-1 Dynamics Traffic on the multi-level backcloth AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Representing Complex Systems & Dynamics Backcloth, Traffic & Type-1 Dynamics Traffic on the multi-level backcloth - coherence Cannot look at just one level Traffic must aggregate coherently over the structure AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

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

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

Representing Complex Systems & Dynamics Backcloth, Traffic & Type-1 Dynamics Towards representing systems of systems of … Cannot look at just one level Traffic must aggregate coherently over the structure AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

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

Agents, Climate Change & Systems of Systems of Systems AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009 Government Policy ? Agents

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

Conclusions - complex systems - systems of systems of systems - need new multilevel mathematics to integrate hypernetworks are necessary if not sufficient AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Conclusions - complex systems - systems of systems of systems - need new multilevel mathematics to integrate hypernetworks are necessary if not sufficient - hypernetworks give a theory of aggregation - mappings aggregate over hypernetworks AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Conclusions - complex systems - systems of systems of systems - need new multilevel mathematics to integrate hypernetworks are necessary if not sufficient - hypernetworks give a theory of aggregation - mappings aggregate over hypernetworks - governments think at the macrolevel (it’s easier!) AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Conclusions - complex systems - systems of systems of systems - need new multilevel mathematics to integrate hypernetworks are necessary if not sufficient - hypernetworks give a theory of aggregation - mappings aggregate over hypernetworks - governments think at the macrolevel (it’s easier!) - agents are needed at the microlevel AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009

Conclusions - complex systems - systems of systems of systems - need new multilevel mathematics to integrate hypernetworks are necessary if not sufficient - hypernetworks give a theory of aggregation - mappings aggregate over hypernetworks - governments think at the macrolevel (it’s easier!) - agents are needed at the microlevel - new opportunities for agent based modelling ! AESCS'09 Pacific-Asian Association for Agent-based Approach in Social Systems Sciences November 13-14, 2009