Yushkov, A V

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29th International Cosmic Ray Conference Pune (2005) 6, 8184Using of the analog complexing of parameters of space-temporaldistribution of the EAS Cherenkov light for the analysis of the masscomposition of cosmic raysA. V. Yushkov and O. V. ZhurenkovAltai State University, Lenin Ave. 61, Barnaul 656049, RussiaPresenter: A. V. Yushkov (yushkov@theory.dcn-asu.ru), rus-yushkov-AV-abs3-he11-posterThe space-temporal distribution of the EAS Cherenkov light initiated by p, O and Fe nuclei in the energy region10–200 TeV per nucleus is described by 11 parameters. The ALTAI Monte-Carlo code has been used to performsimulations of the hadronic and electromagnetic interactions and detector’s responses for real conditions. Weapplied analog complexing recognition method with optimization in relation to reference size for classificationof primary nuclei with “event by event” method. Some results of these researches are given. Particularly, forsome energies and distances the probability of true recognition of primary nuclei reaches value of 85%.1. IntroductionAt present, the elemental composition of primary cosmic rays above eV is studied by ground based ex-periments, generally equipped with a system of atmospheric Cherenkov telescopes (ACTs). Some parametersof the space-temporal distribution of Cherenkov light depend essentially on the atomic number of the primarynucleus [1]. The possibility of effective rejection of protons with the use of the same parameters set and cri-terion also was shown in [1]. Such approach can be applied in gamma-astronomical experiments (see e.g. [2]),but for classification of three and more groups of nuclei it is not suitable.50 mFigure 1. The installation geometryNeural nets, evolution and genetic algorithms maybe used for classification of complex multiparamet-ric objects. In our work we applied one of theGMDH (Group Method of Data Handling) algo-rithms, namely, the analog complexing method.2. SimulationIn our calculations we used the data on photoelec-trons time registration, obtained with Monte-Carlocode ALTAI. The detailed description of the com-puting program can be found in [3].For the data simulation we have chosen the installa-tion geometry in the form of the square lattice ( 	 )with the distance between adjacent telescopes equalto 50 m. The placement scheme of the telescopes ispresented in Fig. 1. The position of the shower axiswas simulated in the central quadrate of size 150 m	 150 m.The radius of each telescope mirror is taken equal to82 A. V. Yushkov and O. V. ZhurenkovTable 1. Structure of energy bins for different primary nucleiPrimary  , TeVnucleus 1 2 3 4 5 6 10  15 15  20 20  30 30  50 50  70 70  100O 15  20 20  30 30  50 50  70 70  100 100  150Fe 20  30 30  50 50  70 70  100 100  150 150  2001 m, focus distance   m, sight angle of a telescope  . The threshold of the detector was setequal to  Tresh  ph. e. and for the trigger condition the 16 telescopes must be fired simultaneously. Onlythe vertical showers were simulated for the observation level of 2200 m a.s.l. (800 g/cm). It is necessary tonote that the experimental setup, described above, does not represent a model of any real ACT array. However,for example AIROBICC [4], PACT [5] and TUNKA [6] installations have the similar technical characteristicsand regular placement of ACTs.We used three groups of primary nuclei: H, O and Fe. The sample sets were arranged by the following rules.EAS were simulated in energy range ﬁﬀTeV per primary nucleus. This energy range was divided into 6intervals, with numbers of simulated events for every particle type varying from 1500 to 100 for the lowest andthe highest energy bins correspondingly. The initial energy was picked with the equal probability inside theenergy bin. The bins borders for the different types of nuclei do not coincide (see Table 1). They were chosenfrom condition, that the primary nuclei from the bins with the same numbers must produce approximately thesame average numbers of Cherenkov photons.In the prospective experiment simulation the number of energy bin for particular nucleus was estimated fromaverage number of Cherenkov ﬂ -quants at the distance of ﬃ ! m."#%$&'('max'*),+'*),+f'*-+',./'*-+f'+ 'r'f'd'+f'widthFigure 2. The basic parameters of the temporal distributionIn the simulation of such experiment the additionalerrors are brought in the calculations not only by theevaluation of the incident particle energy, but also bythe definition of the shower axis position. We used asimple method to define the coordinates 0%132,465 of theshower axis in the installation plane. For this pur-pose the coordinates of 9 telescopes with maximumamplitudes were used to get 07132,45 in the followingway:189):,;<1::9):,;:and 4=9):,;<4::9):,;:2where 1?> , 4> — coordinates of the @ -th telescope, and*> — full number of the photoelectrons in the @ -thtelescope.The space-temporal distribution was reconstructedwith time step ACBD6ﬀ ns and step by distancefrom an axis AFE=ﬀ m. In Fig. 2 the form of tem-poral pulse and the basic parameters of temporal dis-tribution are shown: ' d — the arrival time of the firstphoton (in our calculations for all events is equal to 0); ' max — the position of the pulse maximum; '  + , '*- + ,Using of the analog complexing ... 83' )G+ — the arrival times of 10%, 50% and 90% of photons correspondingly; '  + f, '- + f, ' ),+ f — the arrival timesof 10%, 50% and 90% of photons on the pulse falling side correspondingly; ' ,./ — the FWHM time; ' r, ' f —the pulse rise and fall times; ' width — the width of the pulse at 10% level.3. Analog complexing algorithmThe principles of GMDH were developed by A. G. Ivakhnenko in 1967 [7]. The general idea — selection —was borrowed from nature. There are many GMDH algorithms and one of them is analog complexing [8].The aim of this algorithm is to choose from the basic sample the objects, lying at the closest distance inthe multidimension space to the investigated unknown object (the basic sample consists of the great number ofknown objects). This method is very often used for the linked objects (e.g. consecutive in time) in a forecastingtasks. However, when the size of pattern equals to unity the data can not be linked and ordered. Then the taskbecomes the task of classification. 0 20 40 60 80 100 120 0  200  400  600  800  1000  1200  1400  1600  1800210Calculation time for one event (s)Classification efficacyData set sizeCalculation timeClassification efficacy for oxygenFigure 3. Dependence of the average calculation time for oneevent and of the classication efcacy for the primary oxygennuclei on the basic set sizeThe characteristic property of the analog complex-ing is an absence of models, corresponding to everyclass of objects. This property is the advantage be-cause of absence of the time waste for the buildingof models for objects (this is the most essential whenthe basic set frequently changes). On the other hand,this property is drawback because the full calculationprocedure must be executed for the every checkedobject and the time of this calculations essentiallydepends on the size of the basic set (reference size)(see Fig. 3). We decided to reduce the influence ofthis drawback and therefore we had to solve the op-timization task in relation to the basic set size. Inthe solving of this task not only the calculation time,but also the classification efficacy (see below) weretaken into account. It is important, that the classi-fication efficacy will be always higher for the  andFe nuclei initiated EAS, than for EAS, initiated byoxygen nuclei.Hence, the classification efficacy for the oxygen nuclei initiated EAS was chosen as the main factor. In result ofthe optimization we determined the size of the basic set to be equal to 200 of the most characteristic events forevery type of primary particle (i.e. 600 in total). The most characteristic events correspond to the least valueof HI9/>;KJ>0'>3LNM'>5, where ' > and M' > — the parameters of temporal distribution, described above (seeFig. 2),J> — the weight of corresponding parameter. The values of the weights were taken from our resultsin [1] and were confirmed with the tests of the neural network model. If the number of the events ( O a) forsome type of the primary particles (a) is less than 200 and less than for the other types of the primary particles,we take ( O a) events for all particle types.4. Results of the classificationFor the basic set construction the temporal parameters (type and energy of a primary particle and coordinatesof a shower axis) for known events were used. We have performed the classification of the air showers gen-84 A. V. Yushkov and O. V. Zhurenkov 40 50 60 70 80 90 100 1  2  3  4  5  6Probability of true classification, %Energy binpOFea) 0 20 40 60 80 1002252001751501251007550250Probability of true classification, %r, mpOFeb)Figure 4. Probability of true classication: a)  distance from shower axis; b)  energy binerated by the different nuclei with the use of the analog complexing, as described above. Some results of theclassification are given in Fig. 4.Probabilities of true classification for every primary nucleus type for EPﬃ are represented in Fig. 4 a); forthe fifth bin energies ( RQFSTTeV,  O S TeV,  Fe   TeV) are given in Fig. 4 b).Recognition at the edges ( EFﬃUﬀ m and EFﬃNﬀVﬀﬀ m) is not provided with enough statistics and cannot be used for any conclusions in our simulation.We have introduced classification efficacy W nucl for a primary type nucl as W nucl Xnucl LXnucl2 whereXnucl —the probability of true classification. So, the classification efficacy for the 5-th energy bin at 100 m from theaxis is W QDY ﬀ , W O Y  Z, W Fe Y ﬀﬀ . This approach may be recommended for reliable classification fordistances EPﬃ![ ﬀ m. The average values of the efficacy for these distances for energies 10-200 TeV areWQﬃ [ , W O ﬃ   \, W Fe ﬃ ﬀ]\ \. The classification efficacy slowly increases with the energy.This behavior agrees with results of [9], obtained with neural networks on the basis of data on O_^%`a and O=b forPeV-region.We recommend to use the given “event by event” method of primary particle type determination in analysis ofspace-temporal characteristics of Cherenkov light from EAS.References[1] O. V. Zhurenkov and A. V. Plyasheshnikov, Nuclear Physics B 75A, 296 (1999).[2] V. R. Chitnis and P. N. Bhat, 26-th ICRC, Salt Lake City (1999), 5, 251.[3] A. K. Konopelko and A. V. Plyasheshnikov, J. Phys. G: Nucl. Part. Phys. 26, 183 (2000).[4] V. Fonseca, F. Arqueros, S. Bradbury et al., 24-th ICRC, Roma (1995), 1, 470.[5] P. N. Bhat, B. S. Acharya, V. R. Chitnis et al., 26-th ICRC, Salt Lake City (1999), 5, 191.[6] N. Budnev, D. Chernov, V. Galkin et al., 27-th ICRC, Hamburg (2001), 1, 581.[7] A. G. Ivakhnenko, IEEE Transactions on Systems, Man, and Cybernetics (1971), SMC-1, 4, 364.[8] Johann-Adolf Mueller and Frank Lemke, Self-Organising Data Mining. An Intelligent Approach ToExtract Knowledge From Data (Berlin, Dresden, 1999), 1. Edition.[9] M. Roth, T. Antoni, W.D. Apel et al., 27-th ICRC, Hamburg (2001), 1, 88.

Using of the analog complexing of parameters of space-temporal distribution of the EAS Cherenkov light for the analysis of the mass composition of cosmic rays

Using of the analog complexing of parameters of space-temporal distribution of the EAS Cherenkov light for the analysis of the mass composition of cosmic rays

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