Presented by Mohamed Fazeen Ruwan Nawarathna

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1 Δεκ 2013 (πριν από 3 χρόνια και 8 μήνες)

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Pablo
Cristian

Tissera
, Marcela
Printista
,
Marcelo Luis
Errecalde

Lab
. de
Investigacion

y Desarrollo en Inteligencia
Computacional (
LIDIC
)

Universidad Nacional de San Luis
-

Ej. de los Andes 950
-

(D5700HHW) San Luis,
Argentina

Presented by

Mohamed
Fazeen

Ruwan

Nawarathna

1


Introduction Cellular Automata


Formulation of Cellular Automata and Some
Examples


Introduction to the Evacuation Simulation


Model Description


Experiments


Conclusions & Future Work

2


CA is a result of,


The
joint work of
John
Von

Neumann
and
Stanislaw
Ulam
.


A study
related to machines
with
auto
-
replication

capabilities
.



Later popularized due the work proposed by
Jhon

H. Conway,
“the game of life”
in 1970.

3


The CA are mathematical systems with
discrete
values in
space
,
time

and
state
.



Have,


Auto
-
replication


Universal computation capabilities


The property of being able to perform

different tasks with the same underlying

construction just by being programmed in a different way



Auto
-
organization effects


Can
generate
extreme
ordered
behaviors from a total
disorder.

Brain’s Brain CA

4

Gosper's

Glider Gun

creating "gliders" in the cellular
automaton

Conway's Game of Life.

5


Let,

A


D dimensional array of cells with each element of
the array has
associated a
finite state

(Cellular
Space)

Q


A finite set of states (Ex: true, false , 0, 1 etc.)

c
i



An arbitrary cell of A, (
i
th

cell)




Input alphabet (input states)

δ



T
he transition function is given by,


6


Let,




is the set of cells considered as neighborhood of an
arbitrary cell
excluding

c
i
.



is the number of adjacent cells.

Then,





Thus,


is the specification of which cells
are included in a neighborhood

Ex: Moore's
Neighborhood

Because, ∑ is given by all possible
combination of the
cell states
of the
adjacent (neighboring) cells.

7


The transition function of states is a
mapping such that


If is the state of the cell
c
i

at the time
t



And, are the states of the
adjacent cells to
c
i
,

Then,





denotes the state of
c
i

in the time
t + 1.



i.e. state at t+1 of
c
i

is determined by considering the state
of the
c
i

and the neighboring cells

8


The
δ

function
is usually
represented
in tabular form
with rules:





There are many ways of specifying rules. (Ex:
Brian's
Brain
,
Wireworld
,
Rule 90
,
Rule 184
)



It is possible to specify
probabilistic transition

rules
, where an arbitrary probability p can be
associated to a transition rule.

9

The Cellular Automation is defined as 4
-
tuples



Implies that CA consist of


A D
-
Dimensional cell array


A set of finite states


A transition function


A neighborhood

10


Refers to a class of CA , studied by Stephen
Wolfram.


Definition
ECA
,


A
-

one
-
dimensional array


Q
-

set of states with elements {0, 1}


.





: Neighborhood


δ

-

Transition function (set of rules) defined as
follows (next slide),


11


If a cell at time
t

is
inactive

(0), is
activated

at time
t+1

if
some of the adjacent cells (left or right) are active (1).



An
active

cell at time
t
, is turned
inactive

at time
t+1

if its
adjacent cells are both actives or both
inactives
.



In other case a cell preserve its previous state.

Called
Rule 90

12


When above rules are evolved and arranged in consecutive
lines, this will generate the following “
Sierpinski

Triangle”.

13


Consists of a collection of cells based on a few mathematical
rules


Can live, Die, or Multiply, depending on the initial conditions.



Cells form various patterns throughout the game.



Transition Rules,


For a space that is
'populated'
:

Each cell with one or no neighbors dies, as if by loneliness.

Each cell with four or more neighbors dies, as if by overpopulation.

Each cell with two or three neighbors survives.

For a space that is
'empty'
or
'unpopulated'

Each cell with three neighbors becomes populated.

14


Computer Science


Cryptography


Fractal Generation


Computer Graphics


Image processing


Genetic Algorithm Calibration


Design of massively parallel hardware



Simulations of biology, chemistry, physics.


ferromagnetism according to
Ising

mode


forest fire propagation


nonlinear chemical reaction
-
diffusion systems


turbulent flow


biological pigmentation patterns


breaking of materials


growth of plants and animals


15


Dynamic system that represent a grid of locally
connected finite automata.


Finite Automata
:
describes
a class of models of computation
that
are characterized
by having a
finite
number of states
.



Each Automation,


produces an output
from several
inputs


modifies
its
state in
this process by means of a transition
function
.



The
state of a cell of a
CA in a particular
generation
only depends
on,


The states of
its neighboring
cells and


The state, the cell had in its previous
generation.

16


In this work CA is used in order to specify and implement a
simulation model called
EVAC

that allows to investigate
behavioral dynamics for pedestrians in an emergency evacuation.



Eg
: forced evacuation of a large number of people due to the
threat of the fire, within a building with a specific number of exits.



Due to real world experimental research has ethical, financial and
logical limitations, simulations are desired.



The simulation allows to specify,


different scenes with a large number of people and environmental
features


making easier to study the complex behaviors that arise when the
people interact.

17


To analyze the strengths and limitations of CA for
modeling this type of domains.



To present a simulation tool that allows to design,
construct, execute, visualize and analyze different
configurations of a building to be evacuated.



To evaluate the performance of a forced evacuation
under different fire conditions.



To identify relevant aspects that should be considered
in the design of new buildings.

18


A finite two
-
dimensional array with closed boundaries.



Each cell of the cellular space represents a 40 x 40 cm square.


This is the space usually occupied by a person in a crowd with maximal
density



So, one grid of 10 x 10 m will contain 25 x 25 cells




19


Cells can be one of the states of the set,


20


The neighborhood considered in the model is
Moore's Neighborhood that includes the
eight cells surrounding the central cell.






Individual has all possible movement
directions.

21


Before the simulation starts, the diverse
information related to,


outer walls, inner obstacles, individuals,
combustible locations, cells with fire, and
arrangement of the exits are defined.



In
EVAC

(a simulation system built by the
authors), this task can be realized by means
of its graphical interface.

22


Rules about the building:


a cell in state W or O (outer wall or obstacle)
will not change its state throughout the
simulation.



23


Rules about smoke propagation:


A cell with
smoke (in one of the following states: S, SF,
PS or PSF.) in time
t, also will have smoke in time t+1.


If at time t


central cell

no smoke,


some adjacent cells

have smoke,

Then the central cell also will have smoke at time t+1 with a
probability proportional to the number of adjacent cells with
smoke.



Ex: the central cell will have smoke in the next
time step with probability ½

24


Rules about fire propagation:


these rules are analogous to the rules for smoke
propagation as explained above.



However, they incorporate an additional
constraint: a non
-
zero combustion level of the cell
is required.

25


Rules about the people motion:



A cell with
out a person at time t, will have a
person at time t+1 if;

1.
At least one adjacent cell con
tains an individual

2.
.




In other cases, the cell does not change its
state.

The distance from
the
current cell to an exit

T
he distance from the cell occupied
by the individual to the exit

<

26


Two important aspects considered in people
motion simulation.

1.
Estimation of distances from the cells to an exit


Cellular space was represented in a weighted graph


Dijkstra's

algorithm was used to calculate the shortest
path.







27


Two important aspects considered, Cont…

2.
Handling of collisions between individuals.


To avoid collision the current cell will in charge of
selecting an individual among the neighbors.



Following rules use in selection

a)
Shorter to the exit will not be considered as a candidate.

b)
If more than one candidate, a person with minor number
of damage points will be selected.

c)
Still the conflict persists, a candidate selected randomly.


28


The experiments were carried out with
EVAC
, an
integrated simulation system based on cellular
automata.



The idea of the experiment is to verify their CA model
for simple evacuation scenarios.



The experiment conceptually divided in to three
groups



Each group correspond to environmental
configuration show in each row in the following figure

30


31


32

Exit Size (m)

Evacuation Time (s)

33


In this work CA were used for developing and
implementing a simulation model of emergency
evacuations due to the fire threat.



A software named
EVAC

was developed for the above
purpose.



These studies were intended to detect which
modifications that would improve the evacuation
processes in designing new buildings.



The authors claimed that CA are a very suitable tools
for modeling this class of problems.



34


Authors mentioned that they are developing
a hybrid model where the dynamics of fire
and smoke propagation are modeled by
means of CA.



In the future authors are planning to add
structural dynamic changes that could occur
during the evacuation process.


for instance, the creation of a new exit as
consequence of shattering window.

35


P. C.
Tissera
, M.
Printista
, M. L.
Errecalde
, “Evacuation Simulations using
Cellular Automata,” Journal of Computer Science & Technology,
Vol. 7, No.
1, pp. 14
-
20, 2007.



Finite automata by M. V. Lawson, Department of Mathematics, School
of Mathematical and Computer Sciences,
Heriot
-
Watt University.



http://en.wikipedia.org/wiki/Cellular_automaton



http://www.bitstorm.org/gameoflife/



http://en.wikipedia.org/wiki/Brian's_Brain






36