Cellular automata

chatventriloquistAI and Robotics

Dec 1, 2013 (3 years and 10 months ago)

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Università di Genova

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-

D. Ghersi

Cellular automata


They consist of a discrete lattice of sites called
CELLS
.


Each site takes on a finite set of possible values (red or white,0 or 1).


The value of each site evolves according to the same
deterministic

rules.


The rules for the evolution of a site depend only

on a local neighborhood of sites around it.


They evolve in discrete time steps.

Cellular Automata
consider discrete events and work from them to capture their consequences and
delineate the whole phenomenon.

Wolfram classical rules

Università di Genova

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Conway's Game of Life

Rules


Survivals

Every counter with two or three neighboring counters survives for the next generation.


Deaths

Each counter with four or more neighbors dies (is removed) from overpopulation. Every counter with one
neighbor or none dies from isolation.


Births

Each empty cell adjacent to exactly three neighbors
--
no more, no fewer
--
is a birth cell. A counter is placed on
it at the next move.


Università di Genova

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D. Ghersi

Conway's Game of Life (2)

Università di Genova

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Immsim: a modified cellular automaton

As classical cellular automata do, it consists of a discrete lattice of site,but it uses the grid only as the
playground
of the simulation.

The grid id populated by different entities, placed randomly in all the cells of the lattice.

More then one entity can be in a single sitee.

At every time step the entities in the same site can interact with each other according to probabilistic rules and
they move from site to site.





Università di Genova

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The grid

Università di Genova

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Immsim basic rules

Rules modified in Immsim


The value of each site evolves according to the same
probabilistic

rules.

The rules for the evolution of a site depend only

by the site itself.


Added rule


The entities move from site to site

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Interactions


Antibody
-

Antigen



B Cell (BCR)
-

Antigen



T Killer (TCR)
-

APC (MHC I)



T Helper (TCR)
-

APC (MHC II)



T Killer (TCR)
-

Infected Cell (MHC I)



B Cell (MHC II)
-

T Helper (TCR)

The entities represented in Immsim interact whith each other

Interactions can be divided in
specific

and
non specific

Specific

Non specific


APC
-
Antigen



Epithelial Cell
-
Antigen

Università di Genova

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Interactions (2)

Interactions activate specific programmes for both the entities involved

Epitope
Peptide


Peptide processing by B
cells


MHC loading and MPC

MPC


TCR
-
MPC interaction

B cell activation

Università di Genova

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Interactions and specificity

Receptors

are represented by bit strings

Bit strings

are 0' and 1' sequences

11001100

Since each bit can take one of two value we can say that two bit strings complement each other
(
perfect match
) if every 0 in one correspond to a 1 in the other and conversely.

11000110


00111001

Perfect match

11
1
00110


00
1
11001

Mismatch 1

Specific

interactions

use
specific

receptors

Università di Genova

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Bitstrings representation

Base
-
2

Base
-
10

11000110


00111001

198


57

11111111

255=2
8
-
1


How to calculate a best match
of a n
-
bits specificity
element(SE):


(2
n
-
1)
-

SE

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Interactions: overview

Università di Genova

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The core of the simulation

1) Load parameters

Cells (randomly on the grid)

Antigen Injection (randomly on the grid)

2) Populate the grid

3) Interactions between entities in a randomic order

4) Death

5) Birth

Age

T Killer

Virus

6) Diffusion

Università di Genova

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The Affinity Function

Affinity Slope

Weight coefficients

-

Calculates binding
-
probabilities according to the matching bits

-

Its slope can be modulated using weight coefficients

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Affinity and number of receptors

Matching

bits

No. of
Receptors

-

+

-

+

16 bits simulation

16/16

1

13/16

3360+240+16+1

15/16

14/16

16+1

240+16+1

17

257

3617

(65536 possible receptors)

Università di Genova

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IMMSIM and probability

IMMSIM is a
probabilistic

cellular automaton:



Every interaction is based on a probabilistic factor, usually proportional to affinity.


Every entitity diffuses on the grid in a stochastic way.


Many programs of differentiation are implemented according to probabilistic rules.


Simulations started with the same parameters set can lead to slightly different
results.


In IMMSIM, in order to study a phenomenon, we must perform statistical
analyses.

Università di Genova

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IMMSIM and probability (2)