Tracking using Cellular Automaton Algorithm for CBM experiment Arkadiusz Bubak University of...

Tracking using Cellular Automaton Algorithm

for CBM experiment

Arkadiusz Bubak

University of Silesia, Katowice, Poland

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

2/23

Cellular automata

Proposed in forties of 20th century by Stanisław Ulam

At the same time John von Neumann who tried to develop hypothetical self-

reproduction machine realized that CA, which reflect, simplified physical model of the

real world, is solution of his search

Stanisław Ulam, 1909-1984

John von Neumann, 1903-1957

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

3/23

Cellular automata

Proposed in forties of 20th century by Stanisław Ulam

At the same time John von Neumann who tried to develop hypothetical self-

reproduction machine realized that CA, which reflect, simplified physical model of the

real world, is solution of his search

In early 1950s CA was also studied as possible model for biological systems

At present CA are numbered among wide and fashionable domains like artificial

intelligence

Stanisław Ulam, 1909-1984

John von Neumann, 1903-1957

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

4/23

Cellular automata

Proposed in forties of 20th century by Stanisław Ulam

At the same time John von Neumann who tried to develop hypothetical self-

reproduction machine realized that CA, which reflect, simplified physical model of the

real world, is solution of his search

In early 1950s CA was also studied as possible model for biological systems

At present CA are numbered among wide and fashionable domains like artificial

intelligence

The best-known example and implementation of CA is “The Game of Life” -

devised by British mathematician John Horton Conway in 1970

Stanisław Ulam, 1909-1984

John von Neumann, 1903-1957

John Conway 1937

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

5/23

The Game of Life

Non-player game – needing no input from human players

Further evolution of game is only determined by: Initial state Conditions – give particular forms of repetitive or other behavior

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

6/23

The Game of Life

Non-player game – needing no input from human players

Further evolution of game is only determined by: Initial state Conditions – give particular forms of repetitive or other behavior

In the game of life one can imagine a world as a matrix of cells Each cells has 8 neighboring cells

4 adjacent orthogonally 4 adjacent diagonally

Each cell may or may not be occupied by “life” Picture of the world changes in given time steps

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

7/23

The Game of Life

Non-player game – needing no input from human players

Further evolution of game is only determined by: Initial state Conditions – give particular forms of repetitive or other behavior

In the game of life one can imagine a world as a matrix of cells Each cells has 8 neighboring cells

4 adjacent orthogonally 4 adjacent diagonally

Each cell may or may not be occupied by “life” Picture of the world changes in given time steps

Salmonella Clostridium difficile is the leading causeof diarrhea in the Poland

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

8/23

The Game of Life

Non-player game – needing no input from human players

Further evolution of game is only determined by: Initial state Conditions – give particular forms of repetitive or other behavior

In the game of life one can imagine a world as a matrix of cells Each cells has 8 neighboring cells

4 adjacent orthogonally 4 adjacent diagonally

Each cell may or may not be occupied by “life” Picture of the world changes in given time steps

In the game are in force very simple set of rules:

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

9/23

The Game of Life

Non-player game – needing no input from human players

Further evolution of game is only determined by: Initial state Conditions – give particular forms of repetitive or other behavior

In the game of life one can imagine a world as a matrix of cells Each cells has 8 neighboring cells

4 adjacent orthogonally 4 adjacent diagonally

Each cell may or may not be occupied by “life” Picture of the world changes in given time steps

In the game are in force very simple set of rules: At each time step, life persists in any location where it is also present in 2 || 3 of the 8 neighboring locations

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

10/23

The Game of Life

Non-player game – needing no input from human players

Further evolution of game is only determined by: Initial state Conditions – give particular forms of repetitive or other behavior

In the game of life one can imagine a world as a matrix of cells Each cells has 8 neighboring cells

4 adjacent orthogonally 4 adjacent diagonally

Each cell may or may not be occupied by “life” Picture of the world changes in given time steps

In the game are in force very simple set of rules: At each time step, life persists in any location where it is also present in 2 || 3 of the 8 neighboring locations Life in each cell with 4 or more neighbors dies from overcrowding

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

11/23

The Game of Life

Non-player game – needing no input from human players

Further evolution of game is only determined by: Initial state Conditions – give particular forms of repetitive or other behavior

In the game of life one can imagine a world as a matrix of cells Each cells has 8 neighboring cells

4 adjacent orthogonally 4 adjacent diagonally

Each cell may or may not be occupied by “life” Picture of the world changes in given time steps

In the game are in force very simple set of rules: At each time step, life persists in any location where it is also present in 2 || 3 of the 8 neighboring locations Life in each cell with 4 or more neighbors dies from overcrowding Life in cells with 1 or none dies from isolation (or solitude :()

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

12/23

The Game of Life

Non-player game – needing no input from human players

Further evolution of game is only determined by: Initial state Conditions – give particular forms of repetitive or other behavior

In the game of life one can imagine a world as a matrix of cells Each cells has 8 neighboring cells

4 adjacent orthogonally 4 adjacent diagonally

Each cell may or may not be occupied by “life” Picture of the world changes in given time steps

In the game are in force very simple set of rules: At each time step, life persists in any location where it is also present in 2 || 3 of the 8 neighboring locations Life in each cell with 4 or more neighbors dies from overcrowding Life in cells with 1 or none dies from isolation (or solitude :() Birth occurs when cell has 3 neighbors (partners?)

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

13/23

The Game of Life

Non-player game – needing no input from human players

Further evolution of game is only determined by: Initial state Conditions – give particular forms of repetitive or other behavior

In the game of life one can imagine a world as a matrix of cells Each cells has 8 neighboring cells

4 adjacent orthogonally 4 adjacent diagonally

Each cell may or may not be occupied by “life” Picture of the world changes in given time steps

In the game are in force very simple set of rules: At each time step, life persists in any location where it is also present in 2 || 3 of the 8 neighboring locations Life in each cell with 4 or more neighbors dies from overcrowding Life in cells with 1 or none dies from isolation (or solitude :() Birth occurs when cell has 3 neighbors (partners?)

IMPORTANT: All births and deaths occur simultaneously in given time step

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

14/23

The Game of Life

Such game based on the cellular automata could be viewed as kind of parallel computers

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

15/23

The Game of Life

Such game based on the cellular automata could be viewed as kind of parallel computers

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

16/23

CBM detection system → e+e-

TRDTransition Radiation Detector

RICHRing Imaging Cherenkov Detector

STSSilicon Tracking System

MVDMicro Vertex Detector

Dipol Magnet

ECALElectromagnetic Calorimeter

Projectile Spectator Detector(Calorimeter)

RPC (TOF)Resistive Plate Chamber

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

17/23

CBM detection system → μ+μ-

Tracking Detector

MuchMuon Detector System

STSSilicon Tracking System

MVDMicro Vertex Detector

Dipol Magnet

Projectile Spectator Detector(Calorimeter)

RPC (TOF)Resistive Plate Chamber

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

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Software

Software

Package FairRoot (CbmRoot): Root + Virtual Monte Carlo

Geant 3 & 4, Fluka Particle generators: UrQMD, HSD, Pluto, ...

Serves both simulation & analysis Fully Root based → good support, easy maintenance, low newcomer threshold Object oriented Configurable via Root macros Prepared to run on the Grid Portable (compiles on many Linux platforms and with many compilers)

http://fairroot.gsi.de

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

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Transition Radiation Detector: TRD

4m 7.25m 9.5m

Y X Y X Z

Y

X

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

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Transition Radiation Detector: TRD

X Y

X Y

1st station 2nd station 3rd station

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

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Steps

(1) Creation Space Points (SP)

(2) Creation Tracklets

(3) Finding neighbours

(4) Tagging

(5) Creation tracks candidates

(6) Tracks competition

(7) Removing used points

(8) 2Nd & 3rd loops

Standalone TRD tracking: algorithm

1st Loop: ~50% total time2nd Loop: ~ 30% of tt3rd Loop: ~ 20% of tt

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

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CA → Results

Efficiency

Central Mbias

Primary reference fast (p > 1 GeV/c)

91.4 92.5

Primary reference slow (p < 1GeV/c)

81.3 80.4

Ghost level 8.3 6.2

Clones 0 0

Time* (s/event) 0.8 0.14

* at 2x3GHz, 1GB RAM

Au+Au 25AGeV → ~700 tracks

Arek Bubak, XXXI MLCOP, Piaski 2009.08.02

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Thank you for your attention

Dziękuję za uwagę [Pronunciation: Jenkooyen (Dzhienkooien) zza oovahgen]

The end. Eind. Extrémité. Ende. Τέλος. Estremità. Koniec. Extremidade. Конец. Extremo.