Tracking using Cellular Automaton Algorithm for CBM experiment Arkadiusz Bubak University of Silesia, Katowice, Poland

Arek Bubak, XXXI MLCOP, Piaski /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, John von Neumann, 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 if CA is “The Game of Life” - devised by British mathematician John Horton Conway in 1970

Arek Bubak, XXXI MLCOP, Piaski /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, John von Neumann,

Arek Bubak, XXXI MLCOP, Piaski /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, John von Neumann, John Conway 1937

Arek Bubak, XXXI MLCOP, Piaski /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 /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 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 on 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 :() IMPORTANT: All births and deaths occur simultaneously in given time step 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 /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 cause of diarrhea in the Poland

Arek Bubak, XXXI MLCOP, Piaski /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 /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 /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 /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 /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 /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 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 on 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 :() IMPORTANT: All births and deaths occur simultaneously in given time step 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 /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 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 on 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 :() IMPORTANT: All births and deaths occur simultaneously in given time step Such game based on the cellular automata could be viewed as kind of parallel computers

Arek Bubak, XXXI MLCOP, Piaski /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 /23 CBM detection system → e + e - TRD Transition Radiation Detector RICH Ring Imaging Cherenkov Detector STS Silicon Tracking System MVD Micro Vertex Detector Dipol Magnet ECAL Electromagnetic Calorimeter Projectile Spectator Detector (Calorimeter) RPC (TOF) Resistive Plate Chamber

Arek Bubak, XXXI MLCOP, Piaski /23 CBM detection system → μ + μ - Tracking Detector Much Muon Detector System STS Silicon Tracking System MVD Micro Vertex Detector Dipol Magnet Projectile Spectator Detector (Calorimeter) RPC (TOF) Resistive Plate Chamber

Arek Bubak, XXXI MLCOP, Piaski /23 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)

Arek Bubak, XXXI MLCOP, Piaski /23 Transition Radiation Detector: TRD 4m7.25m9.5m Y X Z Y X

Arek Bubak, XXXI MLCOP, Piaski /23 Transition Radiation Detector: TRD XYXY XYXY 1 st station 2 nd station 3 rd station

Arek Bubak, XXXI MLCOP, Piaski /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) 2 Nd & 3 rd loops Standalone TRD tracking: algorithm 1 st Loop: ~50% total time 2 nd Loop: ~ 30% of tt 3 rd Loop: ~ 20% of tt

Arek Bubak, XXXI MLCOP, Piaski /23 CA → Results Efficiency CentralMbias Primary reference fast (p > 1 GeV/c) Primary reference slow (p < 1GeV/c) Ghost level Clones 00 Time* (s/event) * at 2x3GHz, 1GB RAM Au+Au 25AGeV → ~700 tracks

Arek Bubak, XXXI MLCOP, Piaski /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. Koeiec