the many facets of natural computinglkari/natural_2015.pdf · 2015. 1. 20. · lila kari,...

The Many Facets of Natural Computing

Lila Kari Dept. of Computer Science

University of Western Ontario London, ON, Canada http://www.csd.uwo.ca/~lila/

[email protected]

Lila Kari, University of Western Ontario

Natural Computing •  Investigates models and computational

techniques inspired by nature •  Attempts to understand the world around us

in terms of information processing •  Interdisciplinary field that connects

computer sciences with natural sciences


Natural Computing

•  (i) Nature as Inspiration •  (ii) Nature as Implementation Substrate •  (iii) Nature as Computation


(i) Nature as Inspiration

•  Cellular Automata – self-reproduction •  Neural Computation – the brain •  Evolutionary Computation – evolution •  Swarm Intelligence – group behaviour •  Immunocomputing – immune system •  Artificial Life – properties of life •  Membrane Computing – cells and membranes •  Amorphous Computing - morphogenesis


1.Cellular Automata

•  Cellular automaton = dynamical system consisting of a regular grid of cells

•  Space and time and discrete •  Each cell can be in a finite number of states •  Each cell changes its state according to a list of

transition rules, based on its current state and the states of its neighbours

•  The grid updates its configuration synchronously


CA Example: Rule 30

111 110 101 100 011 010 001 000 0 0 0 1 1 1 1 0

CA Classification •  Class 1: Initial patterns evolve into a stable state;

Any randomness disappears. •  Class 2: Initial patterns evolve into stable or

oscillating states; Some randomness remains. •  Class 3: Initial patterns evolve into a pseudo-

random or chaotic manner; Stable structures are destroyed.

•  Class 4: Initial patterns evolve into structures that interact in complex ways, with local patterns surviving for a long time; Wolfram conjectured that many Class 4 CA (Rule 110, Game of Life) are capable of universal computation

Rule 110


Conway’s Game of Life •  Neighbourhood – 8 neighbours •  Any live cell with less than 2 live neighbours dies

(under-population) •  Any live cell with 2 or 3 live neighbours lives •  Any live cell with more than 3 live neighbours

dies (overcrowding) •  Any dead cell with exactly 3 live neighbours

becomes live cell (reproduction) •  Patterns: Still lives, Oscillators, Space ships



Conus Textile pattern


2.Neural Computation •  Artificial Neural Network: a network of

interconnected artificial neurons •  Neuron A : * n real- valued inputs x1,…, xn * weights w1,…,wn

* computes fA(w1x1 + w2x2 + …+ wnxn) •  Network Function = vectorial function that, for n input values, associates the outputs of the m

pre-selected output neurons


Applications to Human Cognition [T.Schultz, www.psych.mcgill.ca/labs/lnsc]


3.Evolutionary Computation

•  Constant or variable-sized population •  A fitness criterion according to which

individuals are evaluated •  Genetically inspired operators (mutation or

recombination of parents) that produce the next generation from the current one


Genetic Algorithms

•  Individuals = fixed-length bit strings •  Mutation = cut-and-paste of a prefix of a parent

with a suffix of another •  Fitness function is problem-dependent •  If initial population encodes possible solutions to a

given problem, then the system evolves to produce a near-optimal solution to the problem

•  Applications: real-valued parameter optimization

Cross-over


Example: Max of f(x) = x^2 x = 0,…, 31


Cross-over and 1st generation offspring



Using Genetic Algorithms to Create Evolutionary Art [M.Gold]


4.Swarm Intelligence

•  Swarm: group of mobile biological organisms (bacteria, ants, bees, fish, birds)

•  Each individual communicates with others either directly or indirectly by acting on its environment

•  These interactions contribute to collective problem solving = collective intelligence


Particle Swarm Optimization •  Inspired by flocking behaviour of birds •  Start with a swarm of particles (each

representing a potential solution) •  Particles move through a multidimensional

space and positions are updated based on * previous own velocity * tendency towards personal best * tendency toward neighbourhood best


Ant Algorithms

•  Model the foraging behaviour of ants •  In finding the best path between nest and a

source of food, ants rely on indirect communication by laying a pheromone trail on the way back (if food is found) and by following concentration of pheromones (if food is sought)


5.Immunocomputing

•  Immune system’s function = protect our bodies against external pathogens

•  Role of immune system: recognize cells and categorize them as self or non-self

•  Innate (non-specific) immune system •  Adaptive (acquired) immune system


Artificial Immune Systems

•  Computational aspects of the immune system: distinguishing self from non-self, feature extraction, learning, immunological memory, self-regulation, fault-tolerance

•  Applications: computer virus detection, anomaly detection in a time-series of data, fault diagnosis, pattern recognition


6.Artificial Life

•  ALife attempts to understand the very essence of what it means to be alive

•  Builds ab initio, within in silico computers, artificial systems that exhibit properties normally associated only with living organisms


Lindenmayer Systems

•  Parallel rewriting systems •  Start with an initial word •  Apply the rewriting rules in parallel to all

letters of the word •  Used, e.g., for modelling of plant growth

and morphogenesis

L systems

•  G = (V, a, P) •  V = the alphabet (set of symbols) •  a = axiom (string of symbols from V) •  P = set of production rules


Example: Growth of Algae

•  Variables : A, B •  Axiom: A •  Rules: A à AB, B à A •  Length of each string: Fibonacci sequence


Example: Pythagoras Tree

•  Variables: 0, 1 •  Constants: [, ] •  Axiom: 0 •  Rules: 1à 11, 0 à 1[0]0 •  2nd recursion 11[1[0]0]1[0]0 •  3rd recursion 1111[11[1[0]0]1[0]0]11[1[0]0]1[0]0 Lila Kari, University of Western Ontario

Turtle Graphics

•  0 – draw a line segment (ending in a leaf) •  1 – draw a line segment •  [ - push position and angle, turn left 45

degrees •  ]- pop position and angle, turn right 45

degrees


Pythagoras Tree 7th Recursion


Fractal Weeds (3D)


L-system Trees



L-Systems Applications •  Plant growth [Fuhrer, Wann Jensen, Prusinkiewicz 2004-05] •  Architecture and design [J.Bailey, Archimorph]


Mechanical Artificial Life

•  Evolving populations of artificial creatures in simulated environments

•  Combining the computational and experimental approaches and using rapid manufacturing technology to fabricate physical evolved robots that were selected for certain abilities (to walk or get a cube)


•  How to insert pdf file


7.Membrane Computing

•  Inspired by the compartmentalized internal structure of cells

•  Membrane System = a nested hierarchical structure of regions delimited by “membranes”

•  Each region contains objects and transformation rules + transfer rules

9-region “membrane computer”


P-system which outputs square numbers



8.Amorphous Computing •  Inspired by developmental biology •  Consist of a multitude of irregularly placed,

asynchronous, locally interacting computing elements

•  The identically programmed “computational particles” communicate only with others situated within a small radius

•  Goal: engineer specified coherent computational behaviour from the interaction of large quantities of such unreliable computational particles.


Amorphous Computing [Generating patterns: Abelson, Sussman, Knight, Ragpal]


(ii) Nature as Implementation Substrate

•  Molecular Computing (DNA Computing) Uses biomolecules, e.g., DNA, RNA •  Quantum Computing Uses, e.g., ion traps, superconductors, nuclear magnetic resonance


(ii-1) Molecular Computing

•  Data can be encoded as biomolecules (DNA, RNA)

•  Arithmetic/logic operations are performed by molecular biology tools

•  The proof-of-principle experiment was Adleman’s bio-algorithm solving a Hamiltonian Path Problem (1994)


Molecular (DNA) Computing •  Single-stranded DNA is a string over the

four-letter alphabet, {A, C, G, T}


Power of DNA Computing

Data: DNA single and double strands •  Watson–Crick Complementarity: W(C) = G, W(A) = T •  Bio-operations: cut-and-paste by enzymes,

extraction by pattern, copy, read-out •  R.Freund, L.Kari, G.Paun. DNA computing based on

splicing: the existence of universal computers. Theory of Computing Systems, 32 (1999).


DNA-Encoded Information

•  DNA strands interact with each other in programmed but also undesirable ways

•  The information has no fixed location •  The results of a biocomputation are not

deterministic, as they depend e.g. on concentration of populations of DNA strands, diffusion reactions, statistical laws


DNA-Motivated Concepts

•  θ-periodicity w = u1u2…un where ui is in {u, θ(u)} and θ is an antimorphic involution •  Generalize Lyndon-Schutzenberger u^n v^m = w^m •  θ-prefix, θ-infix, θ-compliant codes


Our DNA Information Research •  L. Kari, S. Seki, On pseudoknot-bordered words and their

properties, Journal of Computer and System Sciences, (2008)

•  L.Kari, K.Mahalingam, Watson-Crick Conjugate and Commutative Words, Proc. DNA Computing 13, LNCS 4848 (2008)

•  L. Kari, K. Mahalingam, S. Seki, Twin-roots of words and their properties, Theoretical Computer Science (2008)

•  E.Czeizler, L.Kari, S.Seki. On a Special Class of Primitive Words. MFCS (2008)

•  M. Ito, L. Kari, Z. Kincaid, S. Seki, Duplication in DNA sequences. Proc. of Developments in Language Theory (2008)


Computing by Self-Assembly

•  Self-Assembly = The process by which objects autonomously come together to form complex structures

•  Examples § Atoms bind by chemical bonds to form molecules § Molecules may form crystals or

macromolecules §  Cells interact to form organisms


Motivation for Self-Assembly

Nanotechnology: miniaturization in medicine, electronics, engineering, material science, manufacturing

•  Top-Down techniques: lithography (inefficient in creating structures with size of molecules or atoms)

•  Bottom-Up techniques: self-assembly


Computing by Self-Assembly of Tiles

•  Tile = square with the edges labelled from a finite alphabet of glues

•  Tiles cannot be rotated •  Two adjacent tiles on the plane stick if they

have the same glue at the touching edges


Computation by DNA Self-Assembly [Mao, LaBean, Reif, , Seeman, Nature, 2000]


Our Self-Assembly Research •  L.Adleman, J.Kari, L.Kari, D.Reishus, P.Sosik. The Undecidability of the Infinite Ribbon Problem:

Implications for Computing by Self-Assembly (SIAM Journal of Computing, 2009) •  This solves an open problem formerly known as the

“unlimited infinite snake problem” •  Undecidability of existence of arbitrarily large

supertiles that can self-assemble from a given tile set (starting from an arbitrary “seed”)

•  E.Czeizler, L.Kari, Geometrical tile design for complex neighbourhoods (2008)

•  L.Kari, B.Masson, Simulating arbitrary neighbourhoods by polyominoes (2008)


DNA Clonable Octahedron [Shih, Joyce, Nature, 2004]


Nanoscale DNA Tetrahedra [Goodman, Turberfield, Science, 2005]


DNA Origami [Rothemund, Nature, 2006]


(ii-2) Quantum Computing

•  A qubit can hold a “0”, a “1” or a quantum superposition of these

•  Quantum mechanical phenomena such as superposition and entanglement are used to perform operations on qubits

•  Shor’s quantum algorithm for factoring integers (1994)


Quantum Crytography •  “Unbreakable encryption unveiled” (BBC News,

Oct 2008) •  “Perfect secrecy has come a step closer with the

launch of the world's first computer network protected by unbreakable quantum encryption.”

•  The network connects six locations across Vienna and in the nearby town of St Poelten, using 200 km of standard commercial fibre optic cables.


(iii) Nature as Computation

Understand nature by viewing natural processes as information processing •  Systems Biology •  Synthetic Biology •  Cellular Computing


(iii-1) Systems Biology

•  Attempt to understand complex interactions in biological systems by taking a systemic approach and focusing on the interaction networks themselves and on the properties that arise because of these interactions

* gene regulatory networks * protein-protein interaction networks * transport networks


The Genomic Computer [Istrail, De Leon, Davidson, 2007]

•  Molecular transport replaces wires •  Causal coordination replaces imposed temporal

synchrony •  Changeable architecture replaces rigid structure •  Communication channels are formed on an as-needed basis •  Very large scale •  Robustness is achieved by rigorous selection


(iii-2) Synthetic Biology

•  TIMES best inventions 2008 : #21 The Synthetic Organism [C.Venter et al.]

•  Generate a synthetic genome (5,386bp) of a virus by self-assembly of chemically synthesized short DNA strands


(iii-3) Cellular Computing

Computation in living cells: ciliated protozoa


Ciliates: Gene Rearrangement

Photo courtesy of L.F. Landweber


Our Cellular Computing Research

§  L.Landweber, L.Kari. The evolution of cellular computing: nature's solution to a computational problem. Biosystems 52(1999)

§  L.Kari, L.F.Landweber. Computational power of gene rearrangement. Proc. DNA Computing 5, DIMACS Series, 54(2000)

§  L.Kari, J.Kari, L.Landweber. Reversible molecular computation in ciliates. In Jewels are Forever, Springer-Verlag (1999)


Natural Computing

•  Nature as inspiration: cellular automata, neural networks, evolutionary computation, swarm intelligence, immunocomputing, ALife, membrane computing, amorphous computing

•  Nature as implementation substrate: molecular (DNA) computing*, quantum computing

•  Nature as computation: systems biology, synthetic biology, cellular computing*

* Research interests of the UWO Biocomputing Lab


Natural Sciences, Ours to Discover

•  “Biology and computer science – life and computation – are related. I am confident that at their interface great

discoveries await those who seek them” [Leonard Adleman, Scientific American, August 1998]

the many facets of natural computinglkari/natural_2015.pdf · 2015. 1. 20. · lila kari,...

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