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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
An Evolutionary Algorithm Approach to Guiding the Evolution of
Self-Organised Nanostructured Systems
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Natalio KrasnogorInterdisciplinary Optimisation LaboratoryAutomated Scheduling, Optimisation & Planning Research GroupSchool of Computer Science
Centre for Integrative Systems BiologySchool of Biology
Centre for Healthcare Associated InfectionsInstitute of Infection, Immunity & Inflammation
University of Nottingham
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Overview• Motivation
• Towards “Dial a Pattern” in Complex Systems
• Methodological Overview
• Virtual Complex Systems
• Physical Complex Systems
• Nanoparticle Simulation Details
• Results
• Conclusions & Further work
Au
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
This work was done in collaboration with Prof. P. Moriarty and his group at the School of Physics and Astronomy at the University of Nottingham
Based on the paper:
P.Siepmann, C.P. Martin, I. Vancea, P.J. Moriarty, and N. Krasnogor. A genetic algorithm approach to probing the evolution of self-organised nanostructured systems. Nano Letters, 7(7):1985-1990, 2007.
http://dx.doi.org/10.1021/nl070773m
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59ACDM 200625th April 2006
- Automated design and optimisation of complex systems’ target behaviour
- cellular automata/ ODEs/ P-systems models
- physically/chemically/biologically implemented
-present a methodology to tackle this problem
-supported by experimental illustration
Motivation
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Major advances in the rational/analytical design of large and complex systems have been reported in the literature and more recently the automated design and optimisation of these systems by modern AI and Optimisation tools have been introduced.
It is unrealistic to expect every large & complex physical, chemical or biological system to be amenable to hand-made fully analytical designs/optimisations.
We anticipate that as the number of research challenges and applications in these domains (and their complexity) increase we will need to rely even more on automated design and optimisation based on sophisticated AI & machine learning
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Major advances in the rational/analytical design of large and complex systems have been reported in the literature and more recently the automated design and optimisation of these systems by modern AI and Optimisation tools have been introduced.
It is unrealistic to expect every large & complex physical, chemical or biological system to be amenable to hand-made fully analytical designs/optimisations.
We anticipate that as the number of research challenges and applications in these domains (and their complexity) increase we will need to rely even more on automated design and optimisation based on sophisticated AI & machine learning
This has happened before in other research and industrial disciplines,e.g:
•VLSI design•Space antennae design•Transport Network design/optimisation•Personnel Rostering•Scheduling and timetabling
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Major advances in the rational/analytical design of large and complex systems have been reported in the literature and more recently the automated design and optimisation of these systems by modern AI and Optimisation tools have been introduced.
It is unrealistic to expect every large & complex physical, chemical or biological system to be amenable to hand-made fully analytical designs/optimisations.
We anticipate that as the number of research challenges and applications in these domains (and their complexity) increase we will need to rely even more on automated design and optimisation based on sophisticated AI & machine learning
This has happened before in other research and industrial disciplines,e.g:
•VLSI design•Space antennae design•Transport Network design/optimisation•Personnel Rostering•Scheduling and timetabling
That is, complex systems are plagued with NP-Hardness, non-approximability, uncertainty, undecidability, etc results
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Major advances in the rational/analytical design of large and complex systems have been reported in the literature and more recently the automated design and optimisation of these systems by modern AI and Optimisation tools have been introduced.
It is unrealistic to expect every large & complex physical, chemical or biological system to be amenable to hand-made fully analytical designs/optimisations.
We anticipate that as the number of research challenges and applications in these domains (and their complexity) increase we will need to rely even more on automated design and optimisation based on sophisticated AI & machine learning
This has happened before in other research and industrial disciplines,e.g:
•VLSI design•Space antennae design•Transport Network design/optimisation•Personnel Rostering•Scheduling and timetabling
That is, complex systems are plagued with NP-Hardness, non-approximability, uncertainty, undecidability, etc results
Yet, they are routinely solved by sophisticated optimisation and design techniques, like evolutionary algorithms, machine learning, etc
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Automated Design/Optimisation is not only good because it can solve larger problems but also because this approach gives access to different regions of the space of possible designs (examples of this abound in the literature)
AnalyticalDesign
AutomatedDesign
(e.g. evolutionary)
Space of all possible designs/optimisations
A distinct view of the space of possible designs couldenhance the understanding of underlying system
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
The research challenge :
For the Engineer, Chemist, Physicist, Biologist :
To come up with a relevant (MODEL) SYSTEM M*
For the Computer Scientist:
To develop adequate sophisticated algorithms -beyond exhaustive search- to automatically design or optimise existing designs on M* regardless of computationally (worst-case) unfavourable results of exact algorithms.
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Towards “Dial a Pattern” in Complex Systems
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
D
iscr
ete
Lexi
cal S
truct
ures
Towards “Dial a Pattern” in Complex Systems
How do we program?
Distributed Disc
rete C.S
Continuous (simulated) CS
Discrete/Contin. (physical) CS
Discrete/Continuos (Biological)
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Dial a Pattern requires:
Parameter Learning/Evolution Technology
Structural Learning/Evolution Technology
Integrated Parameter/Structural Learning/Evolution Tech.
Methodological Overview
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Initial Attempts at a “Dial a Pattern” Methodology
Evolutionaryalgorithms
behaviouremergent vs target
Parameters/model
CA-based / Real complex system
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
- infinite, regular grid of cells- each cell in one of a finite number of states- at a given time, t, the state of a cell is a function of the states of its neighbourhood at time t-1.
Example- infinite sheet of graph paper - each square is either black or white- in this case, neighbours of a cell are the eight squares touching it- for each of the 28 possible patterns, a rules table would state whether the center cell will be black or white on the next time step.
?
- Self-organising processes
- Modelled using cellular automata, gass latice, ODEs, etc
Parameter Learning/Evolution Technology Example
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
CA continuous Turbulence
Gas Lattice
Gas Lattice
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
CA continuous Turbulence
Gas Lattice
Gas Lattice
globals[ row ;; current row we are now calculating done? ;; flag used to allow you to press the go button multiple times]
patches-own[ value ;; some real number between 0 and 1]
to setup-general set row screen-edge-y ;; Set the current row to be the top set done? false cp ctend
;; ]end……..
Given
Evolve
d
Given
Evolve
d
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Wang Tiles Models
Glue Strength Matrix
Temperature T
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Structural Learning/Evolution Technology Example
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Wang Tiles Models
Glue Strength Matrix
Temperature T Given
Evolve
d
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Structural Learning/Evolution Technology Example
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Parameter Learning/Evolution Technology Example
mvaT-PAO1lecA-
Env.Params
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Parameter Learning/Evolution Technology Example
mvaT-PAO1lecA-
Env.Params
Evolve
d
Evolve
d15
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Evolutionaryalgorithms
behaviouremergent vs target
parameters
Complex System
How do we measure this?
How similar is to ?
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How Do We Program These Complex Systems?
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
The Universal Similarity Metric (USM)
- Is the USM a good objective function for evolving target spacio-temporal behaviour in a CA system?
- methodology for answering this question
- experimental results
CA model USM
Fitness Distance Correlation
Clustering
GENOTYPE PHENOTYPE FITNESS
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Data set
For each CA system:
• Keep all but one parameter the same
• Produce 10 behaviour patterns through the variable parameter
• Repeat for other parameters
EXAMPLE
turb_c4 refers to the spacio-temporal pattern produced by the fourth variation in parameter c of a Turbulence CA system
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Produced by MODEL(p1,p2,…,pn)
p1 p2 pn
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Clustering
• does the USM detect similarity of phenotype with a target pattern?
• if yes, it should be able to correctly cluster spatio-temporal patterns that look similar together
• and, those similar patterns should be related to a specific family of images arising from the variation of a single parameter
• calculate a similarity matrix filled with the results of the application of the USM to a set of objects
• during the clustering process, similar objects should be grouped together
CA model USM
Fitness Distance Correlation
Clustering
GENOTYPE PHENOTYPE FITNESS
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Fitness Distance Correlation
• correlation analyses of a given fitness function versus parametric (genotype) distance.
• larger numbers indicate the problem could be optimised by a GA
• numbers around zero [-0.15, 0.15] indicate bad correlation
• scatter plots are helpful
1 2 3
1 4 3
Fitness = USM (T,D)distance = 2
CA model USM
Fitness Distance Correlation
Clustering
GENOTYPE PHENOTYPE FITNESS
Target
Designoid
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
The Evolutionary Engine“we will implement an object-oriented, platform-independent, evolutionary engine (EE). The EE will have a user-friendly interface that will allow the various platform users to specify the platform with which the EE will interact”
Evolvable CHELLware grant application
generic GA resultsspecialisedGA
XML
web-based configuration
module
Java servlet
web-based executionmodule
- no data types- no evaluation module- no parameters
- data types and bounds - evaluation module (‘plug in’) - GA parameters
Evaluationmodule
problem-specific
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Results on CAs
.
e5
f3
Target Designoid
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Target usm(F,T) e(i) e(c) e(r) Ep 0.91980 0.26843 0.35314 0.05552 0.22569
.
Target Designoid
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Au
~3nm
Gold core
Thiol groups
Sulphur ‘head’
Alkane ‘tail’, e.g. octane
Dispersed in toluene, and spin castonto native-oxide-terminated silicon
Thiol-passivated Au nanoparticles
Self-Organised Nanostructured Systems
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
AFM images taken by Matthew O. Blunt, Nottingham
Au nanoparticles: Morphology
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Solvent is represented as a two-dimensional lattice gas
Each lattice site represents 1nm2
Nanoparticles are square, and occupy nine lattice sites
Based on the simulations of Rabani et al. (Nature 2003, 426, 271-274). Includes modifications to include next-nearest neighbours to remove anisotropy.
Nanoparticle Simulations
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http://www.nottingham.ac.uk/physics/research/nano/
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
• The simulation proceeds by the Metropolis algorithm:
– Each solvent cell is examined and an attempt is made to convert from liquid to vapour (or vice-versa) with an acceptance probability pacc = min[1, exp(-ΔH/kBT)]
– Similarly, the particles perform a random walk on wet areas of the substrate, but cannot move into dry areas.
– The Hamiltonian from which ΔH is obtained is as follows:
Nanoparticle Simulations
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Nanoparticle Simulations
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Nanoparticle Simulations
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Nanoparticle Simulations
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Nanoparticle Simulations
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Nanoparticle Simulations
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Nanoparticle Simulations
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Motivation
- optimisation problems
- large search space
- inspired by Darwinian evolution
global optimum
A brief overview of Genetic Algorithms
22 0.25 1.0 4.5
phenotype
genotype
simulator fitness function1.05
fitness
- area covered?- degree of order?- similarity to target pattern?
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
The Universal Similarity Metric (USM)
is a measure of similarity between two given objects in terms of information distance:
where K(o) is the Kolmogorov complexity
Prior Kolmogorov complexity K(o): The length of the shortest program for computing o by a Turing machine
Conditional Kolmogorov complexity K(o1|o2):How much (more) information is needed to produce object o1 if one already knows object o2 (as input)
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
TIME
A brief overview of Genetic Algorithms
Evolution- Recombination (mating) e.g. exchanging parameters ‘combine the best bits of each parent’
- Mutation e.g. altering the value of a parameter at random with some small probability
GENERATION 0
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
TIME
A brief overview of Genetic Algorithms
Evolution- Recombination (mating) e.g. exchanging parameters ‘combine the best bits of each parent’
- Mutation e.g. altering the value of a parameter at random with some small probability
GENERATION 1
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
TIME
A brief overview of Genetic Algorithms
Evolution- Recombination (mating) e.g. exchanging parameters ‘combine the best bits of each parent’
- Mutation e.g. altering the value of a parameter at random with some small probability
GENERATION 1
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
TIME
A brief overview of Genetic Algorithms
Evolution- Recombination (mating) e.g. exchanging parameters ‘combine the best bits of each parent’
- Mutation e.g. altering the value of a parameter at random with some small probability
GENERATION 2
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
TIME
A brief overview of Genetic Algorithms
Evolution- Recombination (mating) e.g. exchanging parameters ‘combine the best bits of each parent’
- Mutation e.g. altering the value of a parameter at random with some small probability
GENERATION 2
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
TIME
A brief overview of Genetic Algorithms
Evolution- Recombination (mating) e.g. exchanging parameters ‘combine the best bits of each parent’
- Mutation e.g. altering the value of a parameter at random with some small probability
GENERATION 3
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
TIME
A brief overview of Genetic Algorithms
Evolution- Recombination (mating) e.g. exchanging parameters ‘combine the best bits of each parent’
- Mutation e.g. altering the value of a parameter at random with some small probability
GENERATION 3
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
TIME
A brief overview of Genetic Algorithms
Evolution- Recombination (mating) e.g. exchanging parameters ‘combine the best bits of each parent’
- Mutation e.g. altering the value of a parameter at random with some small probability
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
TIME
A brief overview of Genetic Algorithms
Evolution- Recombination (mating) e.g. exchanging parameters ‘combine the best bits of each parent’
- Mutation e.g. altering the value of a parameter at random with some small probability
FITN
ES
S
converges to optimum solution
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
• Selected a target image from simulated data set
• Initialised GA- Roulette Wheel selection- Uniform crossover (probability 1)- Random reset mutation (probability 0.3)
- Population size: 10- Offspring: 5- µ + λ replacement
• Ran the GA for 200 iterations- on a single processor server, run time ≈ 5 days- using Nottingham’s cluster (up to 10 nodes), run time ≈ 12 hours
Target:
Evolving towards a target pattern (simulated)
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
0.900
0.915
0.930
0.945
0.960
02468 11 15 19 23 27 31 35 39 43 47 51 55 59 63 67 71 75 79 83 87 91 95 99 104 110 116 122 128 134 140 146 152 158 164 170 176 182 188 194 200
Evolving to a simulated target
Fitness
Generations
Average
Best
Target:
Evolving towards a target pattern (simulated)
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
0.900
0.925
0.950
0.975
1.000
0 3 6 9 13 18 23 28 33 38 43 48 53 58 63 68 73 78 83 88 93 98 104 111 118 125 132 139 146 153 160 167 174 181 188 195
Evolving to a experimental target
Fitness
Generations
AverageBest
Target:
Evolving towards a target pattern (experimental)
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Using only the same fitness function as for the CAs was not sufficient for matching simulation to experimental data
We extended the image analysis, i.e. fitness function, to Minkowsky functionals, namely, area, perimeter and euler characteristic
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Self-organising nanostructuresMinkowski Functionals
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Self-organising nanostructuresEvolved design: Minkowski functionals
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Self-organising nanostructuresEvolved design: Minkowski functionals Robustness checking
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Self-organising nanostructuresEvolved design: Minkowski functionals Robustness checking: i) Clustering
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Self-organising nanostructuresEvolved design: Minkowski functionals Robustness checking: ii) Fitness Distance Correlation
1/Fi
tnes
s
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Self-organising nanostructuresEvolved design: Minkowski functionals Robustness checking: ii) Fitness Distance Correlation
1/Fi
tnes
s
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Self-organising nanostructuresEvolved design: Minkowski functionals Robustness checking: ii) Fitness Distance Correlation
1/Fi
tnes
s
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Self-organising nanostructuresExperimental target set
Cell Island Labyrinth Worm
Evolved set
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Self-organising nanostructuresExperimental target set
Cell Island Labyrinth Worm
Evolved set
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Self-organising nanostructuresExperimental target set
Cell Island Labyrinth Worm
Evolved set
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Self-organising nanostructuresExperimental target set: Results
P.Siepmann, C.P. Martin, I. Vancea, P.J. Moriarty, and N. Krasnogor. A Genetic Algorithm for Evolving Patterns in Nanostructured systems.Nano Letters (to appear)
The analysis of the designability of specific patterns is important as some patterns are more evolvable (multiple solutions) than others and
Smart surface design
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
• We can evolve target simulated behaviour using a GA with the USM but the USM is not enough
•For evolving target experimental designs we used Minkowsky functionals (e.g. Area, Perimeter, Euler Characteristics)
• Using Fitness Distance Correlation and Clustering, we can show whether a given fitness function is/isn’t an appropriate objective function for a given domain.
• Can we generate a target spatio-temporal behaviour in a CA/Real system? YES - GA generates very convincing designoid patterns
Conclusions
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
use of more problem-specific fitness functions open ended (multiobjective) evolution
e.g. “evolve a pattern with as many large spots as possible in as ordered a fashion as possible”
parameter investigations larger populations full fitness landscape analysis Noisy, expensive, multiobjective fitness functions Datamining the results
Future Work (I)
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Future Work (II)
Physical, Chemical, BiologicalSystem
Expensive, noisy, Stochastic, etc
Model
EvolutionaryDesign
Evolve parameters toapproximate target behaviour of desired system
Try best estimates from model parameters
EvolutionaryDesign
Collect Data Evolve models using“reality runs (RR)” results as targetsfor the models themselves
Abstracted intoa model, e.g.,ODE, NN, “cook book”,etc
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Applications (in design and manufacture) and further work
- Many, many systems can be modelled using CAs/Monte Carlos
-Many complex physical/chemical systems need to be programmed
- Research into chemical ‘design’
and self-organising nanostructured systems
e.g. designoid patterns in the BZ reaction
We are actively working towards these practical goals in the context of the EPSRC grant CHELLnet (EP/D023343/1), which comprises Evolvable CHELLware (EP/D021847/1), vesiCHELL (EP/D022304/1), brainCHELL (EP/D023645/1) and wellCHELL (EP/D023807/1).
CHELLNethttp://www.chellnet.org
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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59
Acknowledgements
My colleagues in Physics, specially Prof. P. Moriarty
EPSRC, BBSRC for funding
Thanks To Prof. R. Bartak for inviting me here!
Any questions?
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