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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
18/23
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
19/23
Transition Radiation Detector: TRD
4m 7.25m 9.5m
Y X Y X Z
Y
X
Arek Bubak, XXXI MLCOP, Piaski 2009.08.02
20/23
Transition Radiation Detector: TRD
X Y
X Y
1st station 2nd station 3rd station
Arek Bubak, XXXI MLCOP, Piaski 2009.08.02
21/23
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
22/23
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
23/23
Thank you for your attention
Dziękuję za uwagę [Pronunciation: Jenkooyen (Dzhienkooien) zza oovahgen]
The end. Eind. Extrémité. Ende. Τέλος. Estremità. Koniec. Extremidade. Конец. Extremo.