- Email: [email protected]
Application of a cellular automaton for recognition of straight tracks in the spectrometer DISTO
Computers Math. Applic. Vol. 34, No. 7/8, pp. 695-701, 1997
Pergamon
Copyright(~)1997 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0898-1221/97 $17.00 + O.00 PII: S0898-1221(97)00170-3
Application of a Cellular A u t o m a t o n for Recognition of Straight Tracks in the Spectrometer D I S T O M. P. BUSSA, L. FAVA, L. FERRERO AND A. GRASSO Instituto Nazionale di Fisica Nucleate, Sezione di Torino Via Pietro Giuria n. 1, 10125 Torino, Italy bussa@to, infn. it
V. V. IVANOV, I. V. KISEL E. V. KONOTOPSKAYA AND G. B. PONTECORVO Laboratory of Computing Techniques and Automation, Laboratory of Nuclear Physics Joint Institutefor Nuclear Research, 141980 Dubna, Russia ivanovhainl, j inr. dubna, su A b s t r a c t - - A model of the cellular automaton for recognition of straight tracks has been developed. The program realization of this algorithm has shown high efficiency and speed for the simulated data for the experiment DISTO. Its working speed provides for the processing of approximately 1000 events/sec using the 50 MIPS RISC processor. This makes suitable its application for track recognition in the second-level trigger of the DISTO spectrometer. K e y w o r d s - - N u c l e a r physics, Trigger, Track recognition, Cellular automaton.
1. I N T R O D U C T I O N Cellular a u t o m a t a arose from numerous a t t e m p t s to create a simple mathematical model describing complex biological structures and processes [1]. A cellular a u t o m a t o n is a most simple discrete dynamical system, the behaviour of which is totally dependent upon the local interconnections between its elementary parts [2]. Schematically, a cellular a u t o m a t o n m a y be visualized as a regular spatial net, each cell of which is capable of assuming a number of discrete states. T i m e is varied in discrete steps, and evolution of the system obeys certain a p r i o r i fixed rules determining the new state of each individual cell at each successive step in accordance with the states of its nearest neighbours. Such a simple model has turned out to be very fruitful and has been widely applied in describing various complex structures and processes in physics, biology, chemistry, etc. At present, two different kinds of application of cellular a u t o m a t a are known in high energy physics: 1. revealing clusters in a honeycomb calorimeter [3], and 2. track filtration in cylindrical multiwire proportional chambers [4]. In the present work, a cellular a u t o m a t o n model is proposed for the recognition of straight tracks. T h e structure of the a u t o m a t o n is described, and the results of its application in handling simulated d a t a for the D I S T O experiment are analyzed [5]. W I and IVK acknowledge the support of the Commission of the European Community within the framework of the EU-RUSSIA Collaboration under the ESPRIT contract P9282-ACTCS. Typeset by A~q-TEX 695
696
M . P . Bossn et al.
2. E X P E R I M E N T
DISTO
At present, an experiment is being prepared by the DISTO (Dubna-Indiana-Saclay-TOrino) collaboration for studying spin effects in the reaction
T~
>PK +Y
with the polarized proton beam of Saturne (Saclay, France) [5]. The aim of this experiment is a detailed study of the reactions pp ~ pK+A °, pp ----* pK+E °, and pp ~ ppC0. The layout of the experiment is presented in Figure 1. The DISTO spectrometer has a cylindrical geometry and consists of two arms situated symmetrically about the beam direction. In each arm there are five detectors: two scintillation fiber chambers, two multiwire proportional chambers (MWPC), and an outer detector, which consists of two planes, vertical and horizontal, of scintillation hodoscope counters.1 They cover a scattering angle of 45 ° in the horizontal plane and a dip angle of +20 °. The detectors and the liquid-hydrogen target are situated in the magnetic field, which is perpendicular to the incident beam.
Hodoscope ^ ~ C e r e n k o v
\
\ Figure 1. The layout of the DISTO experiment.
1At present, the possibilityof placing Cherenkovcounters behind the scintillation hodoscopeis investigated [6].
• Application of a Cellular Automaton
697
For effective on-line selection of useful events in the presence of a dominant background, mainly due to pp , p p r + r - processes, a two-level trigger will be used. The first-level trigger is for selection of events by their multiplicity: only four-prong events are selected. For producing the trigger pulse, the signals from the scintillation fiber chambers and from the scintillation hodoscopes are used (see details in the workshop proceedings [7]). Events accepted by the first-level trigger are examined for the presence of a secondary vertex. At present, two different approaches to searching for the secondary vertex, based on RISC-processors, are under development: 1. the dual algorithm [8], 2. the method of invariant moment variables together with application of a multilayer perceptron [9,10]. In the second approach, calculation of moment variables requires knowledge of the track parameters for the event analyzed (see details in [9,10]). To this end, the coordinate information arriving from the scintillation fiber chambers and from the multiwire proportional chambers 2 is taken into account. Only coordinates corresponding to the vertical plane are used. This is due to the influence of the magnetic field on the charged particle trajectories in this projection being negligible, and to the possibility of approximating tracks by straight lines and thus speeding up their reconstruction. The actual track recognition is done applying the cellular automaton, the algorithm of which is described below. 3. A L G O R I T H M
OF CELLULAR
AUTOMATON
A typical cellular automaton is constructed in accordance with the following algorithm: 1. cells and their possible discrete states are defined; usually, each cell may assume one of two states, 0 or 1; however, there may be cellular automata with more states; 2. interconnections between cells are defined; usually, each cell can only communicate with neighbour cells; 3. rules determining evolution of the cellular automaton are fixed; they depend on the actual problem considered and usually have a simple functional form; 4. the cellular automaton is a timed system, in which all cells change states simultaneously. In our case, it is convenient to identify a cell with the straight-line segment connecting two hits in neighbouring detectors. To take into account the inefficiency of the coordinate chambers, one must also consider the segments connecting hits skipping one chamber. At each step, a cell can assume one of two possible states: 1, if the segment can be considered a part of the track, and 0 otherwise. Clearly, only such segments can be considered neighbours which have a common point serving as the end of one segment and the beginning of the second. We shall now consider the rules determining the evolution of the cellular automaton. Taking into account the geometry of the spectrometer DISTO, it is convenient to utilize a cylindrical coordinate system and to conduct track recognition in the vertical R O Z plane, where charged particle trajectories may be approximated by straight lines. Here, the OR axis coincides with the radius, and the OZ axis is perpendicular to the beam. For the criterion in assigning segments to a track, it is convenient to use the angle ~0 between two adjacent segments. Owing to the coordinate detectors having a discrete structure and to multiple scattering in the material of the experimental apparatus, the angles between track segments in the real experiment are not zero, but an upper limit can be imposed. In Figure 2 the distribution of the angles ~o for tracks simulated with the aid of the LACYL code3 is presented. From this figure, it follows that for most of the tracks the angles to satisfy the 2The coordinate detectors are located at 20 cm, 40 cm, 90 cm, and 120 cm from the center of the target, respectively. 3For simulating the physical processes and operation of the experimental apparatus, a computer program termed LACYLbased on the GEANT package [11] has been developed.
698
M.P. BUSSA
et al.
inequality ko[ < 2.0°. This value can be used as a criterion for the selection of useful segments. It must be noted here, that a notable part of particles are scattered in the coordinate chambers through large angles, which hinders their recognition. Figure 3 shows the distribution of tracks over the m a x i m u m angle ~o for each individual track. 3500 ........................................................... 3000 2500 2000 i 15oo
I000 5OO o -a
........ -4 -3 -2
~ -1.
0
..... k._ 1
-
.
~
2
. . . . . . . .
3
4
5
Figure 2. Distribution of angles ~ for simulated tracks. ~', 5O tJ 4J
v
40 30 20 l0 0
0.0
1.0
2.0
3.0
4.0
Figure 3. Distribution of tracks over the maximum angle ~o in the track.
Upon completion of the work of the cellular automaton, additional testing of the quality of reconstructed tracks (for instance, for the presence of at least two hits belonging only to each individual track) is carried out. This permits rejecting "phantom" tracks, which were accidentally constructed from hits belonging to different tracks.
4. A N A L Y S I S
OF THE RESULTS
Let us consider the work of the cellular automaton with a typical simulated event. Figures 4 and 5 present the respective initial and resultant configurations of the cellular automaton. One can note the absence of hits in the first chamber and the presence of one noise hit in the third chamber. In Table 1, the total numbers of generated and reconstructed events are presented versus the number of tracks in the individual events. In all, 1000 events were simulated. A simple comparison of the figures reveals the high efficiency of the cellular automaton. The difference between the
Application of a Cellular Automaton
699
m
l
u
1
Z
3
1
4
Figure 4. Initial configuration of the cellular automaton for a typical Monte-Carlo event in the spectrometer DISTO.
~
3
.
4
Figure 5, Resultant configuration of the cellular automaton for the event presented in Figure 4.
Table 1. Distribution of the number of simulated and reconstructed events depending o n t h e number of tracks in the event (total number of generated events was equal
to 1000). Number of Tracks in Event
Number of Generated Events
Number of Reconstructed Events
1
0
48
57
447
478
502
463
2
2
numbers is due to the large-angle scattering of secondary particles that occurs in the coordinate chambers and which may result in the multiplicity of a reconstructed event being wrong. A detailed analysis of the cellular automaton functioning and examination of the generated events making use of graphical computer images of the events have shown that tracks containing large scattering angles ~0 are lost. Some of such tracks can still be reconstructed in the case when the break of the track happens in the first three chambers and it has hits in all the chambers. In this case, the track is reconstructed using the information from the three chambers. An event containing a track that cannot be fully reconstructed is usually assigned fictitious tracks and may be lost. The analysis of these situations is presented in Figure 6, where the upper curve shows the fraction (in %) of lost tracks versus the chosen upper limit for the angle ~Oma~. Comparison of this figure with Figure 3 shows that a certain fraction of tracks with large breaks can actually be recognised. The lower curve shows the contribution (in %) of added "phantom" tracks. Such tracks are mostly constructed from points belonging to lost tracks. Figure 7 shows the efficiency of event reconstruction versus the upper limit for the angle ~Om=. The maximum efficiency of event reconstruction is achieved at I~Om~x[= 2.5°. It equals 79% and represents the limit value, determined by the fraction of tracks with large breaks--approximately 18% of the events contain such broken tracks, given this boundary angle.
5. C O N C L U S I O N An algorithm for recognition of straight tracks based on the cellular automaton has been developed. It has shown a high efficiency for simulated events. Its working speed provides
700
M. P. BUSSA et al. 50 ~t
4o .~ 3O
2o
10 0 0.0
2.0
1.0
3.0
4.0
Figure 6. Fraction (in %) of lost (upper curve) and "phantom" (bottom curve) tracks versus boundary angle ~max. I00 ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
755:0" ~ 25 0
. . . . . . . . .
0.0
'
.
1.0
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
2.0
.
.
.
' ' ' ' '
3.0
. . . . .
4.0
Figure 7. Efficiency of event reconstruction versus boundary angle ~Omax. for t h e processing o f a p p r o x i m a t e l y 1000 e v e n t s / s e c using t h e 50 M I P S R I S C processor. T h i s m a k e s s u i t a b l e its a p p l i c a t i o n for t h e t r a c k r e c o g n i t i o n in t h e second-level t r i g g e r o f t h e D I S T O spectrometer.
REFERENCES 1. S. Wolfram, Editor, Theory and Applications of Cellular Automata, Worm Scientific, (1986). 2. T. Toffoli and N. Margolus, Cellular Automata Machines: A New Environment for ModeUing, MIT Press, Cambridge, MA, (1987). 3. B. Denby, Neural networks and cellular automata in experimental high energy physics, Comp. Phys. Commun. 49, 429 (1988). 4. A. Ginzov, I. Kieel, E. Konotopskaya and G. Ososkov, Filtering tracks in discrete detectors using a cellular automaton, Nucl. Instr. and Meth. A329, 262 (1993). 5. DISTO collaboration, J. Arvieux et al., Proposal 213 at Saturne, (1991). 6. D.R. Gill et al., ~b production and OZI role, Experience NO. 281, Laboratoire National SATURNE, (November 29, 1993). 7. DISTO experiment trigger, DISTO meeting, Torino, Italy, (September 24, 1992). 8. E. Calligarich et al., A fast algorithm for vertex estimation, Nucl. Instr. and Meth. in Phys. Res. A311, 151-155 (1992). 9. V.V. Ivanov and G.B. Pontecorvo, An algorithm for identifying secondary vertices, In Proc. of the Third International Workshop on Software Engineering, Artificial Intelligence and Expert Systems for High Energy and Nuclear Physics, Oberammergau, Oberbayern, Germany, October 4-8, 1993.
Application of a Cellular Automaton
701
10. V.V. Ivanov and G.B. Pontecorvo, New Computing Techniques in Physics Research Ill, (Edited by K.-H. Becks and D. Perret-Gallix), pp. 321-326, World Scientific, (1994). 11. R. Brunet al., GEANT3 Reference Manual, CERN Program Library Long Writeup W5013, DD/EE/84-1, (1987).
Pergamon
Copyright(~)1997 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0898-1221/97 $17.00 + O.00 PII: S0898-1221(97)00170-3
Application of a Cellular A u t o m a t o n for Recognition of Straight Tracks in the Spectrometer D I S T O M. P. BUSSA, L. FAVA, L. FERRERO AND A. GRASSO Instituto Nazionale di Fisica Nucleate, Sezione di Torino Via Pietro Giuria n. 1, 10125 Torino, Italy bussa@to, infn. it
V. V. IVANOV, I. V. KISEL E. V. KONOTOPSKAYA AND G. B. PONTECORVO Laboratory of Computing Techniques and Automation, Laboratory of Nuclear Physics Joint Institutefor Nuclear Research, 141980 Dubna, Russia ivanovhainl, j inr. dubna, su A b s t r a c t - - A model of the cellular automaton for recognition of straight tracks has been developed. The program realization of this algorithm has shown high efficiency and speed for the simulated data for the experiment DISTO. Its working speed provides for the processing of approximately 1000 events/sec using the 50 MIPS RISC processor. This makes suitable its application for track recognition in the second-level trigger of the DISTO spectrometer. K e y w o r d s - - N u c l e a r physics, Trigger, Track recognition, Cellular automaton.
1. I N T R O D U C T I O N Cellular a u t o m a t a arose from numerous a t t e m p t s to create a simple mathematical model describing complex biological structures and processes [1]. A cellular a u t o m a t o n is a most simple discrete dynamical system, the behaviour of which is totally dependent upon the local interconnections between its elementary parts [2]. Schematically, a cellular a u t o m a t o n m a y be visualized as a regular spatial net, each cell of which is capable of assuming a number of discrete states. T i m e is varied in discrete steps, and evolution of the system obeys certain a p r i o r i fixed rules determining the new state of each individual cell at each successive step in accordance with the states of its nearest neighbours. Such a simple model has turned out to be very fruitful and has been widely applied in describing various complex structures and processes in physics, biology, chemistry, etc. At present, two different kinds of application of cellular a u t o m a t a are known in high energy physics: 1. revealing clusters in a honeycomb calorimeter [3], and 2. track filtration in cylindrical multiwire proportional chambers [4]. In the present work, a cellular a u t o m a t o n model is proposed for the recognition of straight tracks. T h e structure of the a u t o m a t o n is described, and the results of its application in handling simulated d a t a for the D I S T O experiment are analyzed [5]. W I and IVK acknowledge the support of the Commission of the European Community within the framework of the EU-RUSSIA Collaboration under the ESPRIT contract P9282-ACTCS. Typeset by A~q-TEX 695
696
M . P . Bossn et al.
2. E X P E R I M E N T
DISTO
At present, an experiment is being prepared by the DISTO (Dubna-Indiana-Saclay-TOrino) collaboration for studying spin effects in the reaction
T~
>PK +Y
with the polarized proton beam of Saturne (Saclay, France) [5]. The aim of this experiment is a detailed study of the reactions pp ~ pK+A °, pp ----* pK+E °, and pp ~ ppC0. The layout of the experiment is presented in Figure 1. The DISTO spectrometer has a cylindrical geometry and consists of two arms situated symmetrically about the beam direction. In each arm there are five detectors: two scintillation fiber chambers, two multiwire proportional chambers (MWPC), and an outer detector, which consists of two planes, vertical and horizontal, of scintillation hodoscope counters.1 They cover a scattering angle of 45 ° in the horizontal plane and a dip angle of +20 °. The detectors and the liquid-hydrogen target are situated in the magnetic field, which is perpendicular to the incident beam.
Hodoscope ^ ~ C e r e n k o v
\
\ Figure 1. The layout of the DISTO experiment.
1At present, the possibilityof placing Cherenkovcounters behind the scintillation hodoscopeis investigated [6].
• Application of a Cellular Automaton
697
For effective on-line selection of useful events in the presence of a dominant background, mainly due to pp , p p r + r - processes, a two-level trigger will be used. The first-level trigger is for selection of events by their multiplicity: only four-prong events are selected. For producing the trigger pulse, the signals from the scintillation fiber chambers and from the scintillation hodoscopes are used (see details in the workshop proceedings [7]). Events accepted by the first-level trigger are examined for the presence of a secondary vertex. At present, two different approaches to searching for the secondary vertex, based on RISC-processors, are under development: 1. the dual algorithm [8], 2. the method of invariant moment variables together with application of a multilayer perceptron [9,10]. In the second approach, calculation of moment variables requires knowledge of the track parameters for the event analyzed (see details in [9,10]). To this end, the coordinate information arriving from the scintillation fiber chambers and from the multiwire proportional chambers 2 is taken into account. Only coordinates corresponding to the vertical plane are used. This is due to the influence of the magnetic field on the charged particle trajectories in this projection being negligible, and to the possibility of approximating tracks by straight lines and thus speeding up their reconstruction. The actual track recognition is done applying the cellular automaton, the algorithm of which is described below. 3. A L G O R I T H M
OF CELLULAR
AUTOMATON
A typical cellular automaton is constructed in accordance with the following algorithm: 1. cells and their possible discrete states are defined; usually, each cell may assume one of two states, 0 or 1; however, there may be cellular automata with more states; 2. interconnections between cells are defined; usually, each cell can only communicate with neighbour cells; 3. rules determining evolution of the cellular automaton are fixed; they depend on the actual problem considered and usually have a simple functional form; 4. the cellular automaton is a timed system, in which all cells change states simultaneously. In our case, it is convenient to identify a cell with the straight-line segment connecting two hits in neighbouring detectors. To take into account the inefficiency of the coordinate chambers, one must also consider the segments connecting hits skipping one chamber. At each step, a cell can assume one of two possible states: 1, if the segment can be considered a part of the track, and 0 otherwise. Clearly, only such segments can be considered neighbours which have a common point serving as the end of one segment and the beginning of the second. We shall now consider the rules determining the evolution of the cellular automaton. Taking into account the geometry of the spectrometer DISTO, it is convenient to utilize a cylindrical coordinate system and to conduct track recognition in the vertical R O Z plane, where charged particle trajectories may be approximated by straight lines. Here, the OR axis coincides with the radius, and the OZ axis is perpendicular to the beam. For the criterion in assigning segments to a track, it is convenient to use the angle ~0 between two adjacent segments. Owing to the coordinate detectors having a discrete structure and to multiple scattering in the material of the experimental apparatus, the angles between track segments in the real experiment are not zero, but an upper limit can be imposed. In Figure 2 the distribution of the angles ~o for tracks simulated with the aid of the LACYL code3 is presented. From this figure, it follows that for most of the tracks the angles to satisfy the 2The coordinate detectors are located at 20 cm, 40 cm, 90 cm, and 120 cm from the center of the target, respectively. 3For simulating the physical processes and operation of the experimental apparatus, a computer program termed LACYLbased on the GEANT package [11] has been developed.
698
M.P. BUSSA
et al.
inequality ko[ < 2.0°. This value can be used as a criterion for the selection of useful segments. It must be noted here, that a notable part of particles are scattered in the coordinate chambers through large angles, which hinders their recognition. Figure 3 shows the distribution of tracks over the m a x i m u m angle ~o for each individual track. 3500 ........................................................... 3000 2500 2000 i 15oo
I000 5OO o -a
........ -4 -3 -2
~ -1.
0
..... k._ 1
-
.
~
2
. . . . . . . .
3
4
5
Figure 2. Distribution of angles ~ for simulated tracks. ~', 5O tJ 4J
v
40 30 20 l0 0
0.0
1.0
2.0
3.0
4.0
Figure 3. Distribution of tracks over the maximum angle ~o in the track.
Upon completion of the work of the cellular automaton, additional testing of the quality of reconstructed tracks (for instance, for the presence of at least two hits belonging only to each individual track) is carried out. This permits rejecting "phantom" tracks, which were accidentally constructed from hits belonging to different tracks.
4. A N A L Y S I S
OF THE RESULTS
Let us consider the work of the cellular automaton with a typical simulated event. Figures 4 and 5 present the respective initial and resultant configurations of the cellular automaton. One can note the absence of hits in the first chamber and the presence of one noise hit in the third chamber. In Table 1, the total numbers of generated and reconstructed events are presented versus the number of tracks in the individual events. In all, 1000 events were simulated. A simple comparison of the figures reveals the high efficiency of the cellular automaton. The difference between the
Application of a Cellular Automaton
699
m
l
u
1
Z
3
1
4
Figure 4. Initial configuration of the cellular automaton for a typical Monte-Carlo event in the spectrometer DISTO.
~
3
.
4
Figure 5, Resultant configuration of the cellular automaton for the event presented in Figure 4.
Table 1. Distribution of the number of simulated and reconstructed events depending o n t h e number of tracks in the event (total number of generated events was equal
to 1000). Number of Tracks in Event
Number of Generated Events
Number of Reconstructed Events
1
0
48
57
447
478
502
463
2
2
numbers is due to the large-angle scattering of secondary particles that occurs in the coordinate chambers and which may result in the multiplicity of a reconstructed event being wrong. A detailed analysis of the cellular automaton functioning and examination of the generated events making use of graphical computer images of the events have shown that tracks containing large scattering angles ~0 are lost. Some of such tracks can still be reconstructed in the case when the break of the track happens in the first three chambers and it has hits in all the chambers. In this case, the track is reconstructed using the information from the three chambers. An event containing a track that cannot be fully reconstructed is usually assigned fictitious tracks and may be lost. The analysis of these situations is presented in Figure 6, where the upper curve shows the fraction (in %) of lost tracks versus the chosen upper limit for the angle ~Oma~. Comparison of this figure with Figure 3 shows that a certain fraction of tracks with large breaks can actually be recognised. The lower curve shows the contribution (in %) of added "phantom" tracks. Such tracks are mostly constructed from points belonging to lost tracks. Figure 7 shows the efficiency of event reconstruction versus the upper limit for the angle ~Om=. The maximum efficiency of event reconstruction is achieved at I~Om~x[= 2.5°. It equals 79% and represents the limit value, determined by the fraction of tracks with large breaks--approximately 18% of the events contain such broken tracks, given this boundary angle.
5. C O N C L U S I O N An algorithm for recognition of straight tracks based on the cellular automaton has been developed. It has shown a high efficiency for simulated events. Its working speed provides
700
M. P. BUSSA et al. 50 ~t
4o .~ 3O
2o
10 0 0.0
2.0
1.0
3.0
4.0
Figure 6. Fraction (in %) of lost (upper curve) and "phantom" (bottom curve) tracks versus boundary angle ~max. I00 ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
755:0" ~ 25 0
. . . . . . . . .
0.0
'
.
1.0
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
2.0
.
.
.
' ' ' ' '
3.0
. . . . .
4.0
Figure 7. Efficiency of event reconstruction versus boundary angle ~Omax. for t h e processing o f a p p r o x i m a t e l y 1000 e v e n t s / s e c using t h e 50 M I P S R I S C processor. T h i s m a k e s s u i t a b l e its a p p l i c a t i o n for t h e t r a c k r e c o g n i t i o n in t h e second-level t r i g g e r o f t h e D I S T O spectrometer.
REFERENCES 1. S. Wolfram, Editor, Theory and Applications of Cellular Automata, Worm Scientific, (1986). 2. T. Toffoli and N. Margolus, Cellular Automata Machines: A New Environment for ModeUing, MIT Press, Cambridge, MA, (1987). 3. B. Denby, Neural networks and cellular automata in experimental high energy physics, Comp. Phys. Commun. 49, 429 (1988). 4. A. Ginzov, I. Kieel, E. Konotopskaya and G. Ososkov, Filtering tracks in discrete detectors using a cellular automaton, Nucl. Instr. and Meth. A329, 262 (1993). 5. DISTO collaboration, J. Arvieux et al., Proposal 213 at Saturne, (1991). 6. D.R. Gill et al., ~b production and OZI role, Experience NO. 281, Laboratoire National SATURNE, (November 29, 1993). 7. DISTO experiment trigger, DISTO meeting, Torino, Italy, (September 24, 1992). 8. E. Calligarich et al., A fast algorithm for vertex estimation, Nucl. Instr. and Meth. in Phys. Res. A311, 151-155 (1992). 9. V.V. Ivanov and G.B. Pontecorvo, An algorithm for identifying secondary vertices, In Proc. of the Third International Workshop on Software Engineering, Artificial Intelligence and Expert Systems for High Energy and Nuclear Physics, Oberammergau, Oberbayern, Germany, October 4-8, 1993.
Application of a Cellular Automaton
701
10. V.V. Ivanov and G.B. Pontecorvo, New Computing Techniques in Physics Research Ill, (Edited by K.-H. Becks and D. Perret-Gallix), pp. 321-326, World Scientific, (1994). 11. R. Brunet al., GEANT3 Reference Manual, CERN Program Library Long Writeup W5013, DD/EE/84-1, (1987).