The FOOT (FragmentatiOn Of Target) experiment is an international project designed to carry out the fragmentation cross-sectional measurements relevant for charged particle therapy (CPT), a technique based on the use of charged particle beams for the treatment of deep-seated tumors. The FOOT detector consists of an electronic setup for the identification of fragments and an emulsion spectrometer for fragments. The first data taking was performed in 2019 at the GSI facility (Darmstadt, Germany). In this study, the charge identification of fragments induced by exposing an emulsion detector, embedding a target, to an oxygen ion beam of 200 MeV/n is discussed. The charge identification is based on the controlled fading of nuclear emulsions in order to extend their dynamic range in the ionization response.
Charged particles therapy (CPT) is an established therapy for cancer treatment. The advantages of CPT are due to the energy release occurring mainly at the end of the particle’s path, in the Bragg peak region, and to the enhanced biological effectiveness of hadron beams, measured in terms of the relative biological effectiveness (RBE). The RBE value, defined as the ratio of photons to charged particles dose producing the same biological effect, is assessed to an average value of 1.1 for proton beams . This value is affected by both physical (i.e. particle type, dose, linear energy transfer) and biological parameters (i.e. tissue type, cell cycle phase, oxygenation level) , and many recent studies highly support a comprehensive analysis to reduce uncertainties on the RBE value for the clinical practice [2,3,4]. Regarding physical parameters, target fragmentation plays a key role as low-energy secondary fragments contribute to increment the dose deposition in normal tissues along the entrance channel and in the region surrounding the tumor. Hence, the re-assessment of the proton RBE value due to secondary fragmentation is an important topic . The complexity of dedicated experiments makes this milestone challenging, and in fact, very few and limited experimental data are available in the literature regarding target fragmentation, and none of them fully describes secondary fragments induced by a proton beam. The fragmentation of carbon ions (400 MeV/n) in a polycarbonate target was studied in 2011 to determine the charge-changing cross-sections by exploiting the nuclear emulsion technology .
In this framework, the FragmentatiOn Of Target (FOOT) experiment [6,7] has been proposed to measure the target fragmentation induced by a proton beam in the human tissues in the energy range relevant for therapeutic applications (150–250 MeV for protons and 200–400 MeV/n for carbon ions). As fragments generated by a proton beam have few micrometers range, an inverse kinematic approach has been adopted in which a beam (carbon or oxygen) impinge on targets made of carbon- and hydrogen-enriched carbon materials ( ). Therefore, the cross-section of hydrogen is derived from its linear combination.
FOOT is based on two complementary setups: a magnetic spectrometer, covering a polar angle acceptance up to about with respect to the beam axis, for fragments , and an emulsion spectrometer, to measure light fragments ( ) up to with respect to the beam axis.
In this article, the charge identification performance of the secondary fragments generated by the interaction of O (200 MeV/n) beam on a target by the emulsion spectrometer is reported.
The method for the charge identification is based on an established technique already performed in previous studies [8,9,10], consisting of a controlled fading of nuclear emulsions by means of different thermal treatments that extend the emulsion response to a broader range and make them sensitive to particles with different ionization power and charge.
2 Experimental setup and track reconstruction
In April 2019, an emulsion spectrometer was exposed to a 200 MeV/n O ion beam at the GSI facility in Darmstadt (Germany). The spectrometer acts both as target and tracking device. The target, made of layers, was embedded in the detector structure. The exposure setup also included a counter and a beam monitor in order to measure the integrated particle density and its spatial distribution. The experimental apparatus is shown in Figure 1.
After the exposure, emulsions were first thermally treated, then developed and analyzed by fast-automated microscopes. Dedicated software algorithms were used to reconstruct tracks of impinging ions and produced fragments. In the following sections, nuclear emulsion characteristics, emulsion spectrometer exposure, structure, and the thermal treatment procedure are described.
2.1 Nuclear emulsion films
Nuclear emulsion films consist of two 70 m thick sensitive emulsion layers, called top and bottom layers, deposited on both sides of a 210 m thick plastic base, resulting in a total thickness of 350 m. A nuclear emulsion comprises a large number of small AgBr crystals, uniformly dispersed in gelatine. When a charged particle crosses the emulsion layer, a sequence of AgBr crystals is sensitized along its trajectory, producing a latent image. After a chemical development procedure, the latent images turn into a sequence of dark silver grains, which can be seen with an optical microscope . The darkness of these grains depends on the ionization of the particle.
Nuclear emulsion films used in the 2019 FOOT measurements were produced by the Nagoya University (Japan) and Slavich Company (Russia) (75% and 25%, respectively). Their sensitivity corresponds to 30 grains over a track length of for a minimum ionizing particle (MIP).
From the moment they are produced and until their chemical development, nuclear emulsion films are sensitive to charged particles. In particular, during their lifetime, they integrate all particle tracks from cosmic rays and environmental radioactivity. To avoid an unwanted background, before the detector assembly, films were transported in a random order, so that cosmic rays accumulated during that period have a different alignment and cannot be reconstructed as penetrating tracks. Nevertheless, they can still contribute to the background in case of random association of two or more aligned base-tracks.
2.2 Emulsion spectrometer exposure
The emulsion spectrometer was installed in cave A of the GSI facility. The incident beam flux was monitored by the start counter, made of a thin plastic scintillator, and by the beam monitor, consisting of a drift chamber that provides the beam spatial distribution.
The integrated flux in emulsion films was set at about 1,000 O ions/cm , a trade-off between the need to avoid the pile-up of interactions in emulsions and the requirement for large statistics. The corresponding number of triggered events in the start counter was 19,375. The beam had a Gaussian shape ( mm sigma), a fixed energy, and was used to scan a square area of 2.4 cm side (in a grid of points), starting from the center and following a squared spiral shape with 1 mm pitch.
2.3 Emulsion spectrometer structure
The emulsion spectrometer structure, shown in Figure 2, was built according to the emulsion cloud chamber (ECC) technique , which consists of nuclear emulsion films alternated with passive material layers. The emulsion spectrometer structure is organized in three main sections: Section I acts as target region and vertex determination, Section II for the charge identification, and Section III for the momentum measurement and, consequently, isotopic identification of fragments.
Section I consists of 30 emulsion films interleaved with 30 polyethylene layers (2 mm thick ) and is meant for the detection of beam interactions with the target (vertex detector). Its length is optimized so that about 33% of 200 MeV/n O ions interacts therein, according to Monte Carlo simulations based on FLUKA code [13,14]. At this energy, the Bragg peak is contained in this section and occurs after 26 layers.
Section II is made of a sequence of 36 emulsion films divided into nine cells, each consisting of four films. The four nuclear emulsions of each cell underwent an appropriate thermal treatment to extend the dynamic range of the emulsion sensitivity to ionization with the aim of measuring the charge of fragments. A detailed description of the thermal process is reported later.
Section III is made of a sequence of 55 nuclear emulsion films interleaved with lexan (C H O , 1.2 g/cm , 1 mm thick), tungsten (19.25 g/cm , 0.5 mm, and 0.9 mm thick) and lead (11.34 g/cm , 1 mm, and 2 mm thick) layers. It is designed to measure particle momenta taking into account the particle range and the multiple Coulomb scattering (MCS) .
2.4 Track reconstruction
Emulsion films were analyzed by fast-automated microscopes with high tracking efficiency ( ) and speed (up to 190 cm /h) [16,17,18]. The automated scanning system consists of a microscope equipped with a 3D motorized translation stage, a dedicated optical system and a CCD camera.
During the scanning, silver grains produced by the particle are recognized as aligned clusters of dark pixels and associated to form the so-called micro track in the emulsion layer, as shown in Figure 3. For each film, micro tracks on the top and bottom layers are then connected across the plastic base to form a base-track, with an accuracy of about 0.3 m in position and 1.2 mrad in angle. A sequence of base-tracks in different emulsion films allows to reconstruct the particle trajectory inside the detector called track .
The sum of all pixels corresponding to the same track is proportional to the specific ionization of the incident particle.
3 Charge identification
In nuclear emulsions, the grain density along particle trajectories is proportional to the particle energy loss over a certain dynamic range. For highly ionizing particles, such as the ion beam considered here and induced fragments, a saturation effect occurs due to the limited range of the grain density, thus preventing the charge measurement.
The dynamic range of the emulsion film response can be extended by keeping them for a certain amount of time, typically 24 h, at temperatures above C with a relative humidity around 95%: a controlled fading is induced, which can partially or totally erase base-tracks of less ionizing particles . The use of films that underwent different thermal treatments allows to recover the original ionization of the track, thus reconstructing the particle charge.
To exploit this technique, Section II was divided into nine cells of four emulsion films each, denoted as , with . Each of these films underwent a specific thermal treatment (see Figure 4): films did not undergo any treatment, , , and ones were kept for 24 h at relative humidity and at a temperature of C, C, and C, respectively. Applying these thermal treatments, the number of residual grains along the track will be progressively reduced, according to their ionization. For example, the erased fraction of base-tracks for cosmic rays has been measured to be larger than 99% in R1, while proton base-tracks are erased with an efficiency larger than 96% in R2.
For this analysis, Section II has been considered as a stand-alone detector. In Section II, 91,876 tracks were reconstructed. For each track, the following variables were evaluated:
: the tangent of the inclination of most upstream fitted track segment w.r.t. the -axis;
: the number of base-tracks belonging to the track for each set of thermal treatments , with ;
: for each base-track, a variable named “volume” is defined as the sum of the pixel brightness and expressed in arbitrary units related to particles’ ionization;
Combining these variables, the particle charge can be distinguished with two complementary methods: an analysis based on event selections, hereafter referred to as cut-based (CB) analysis, for MIP cosmic rays and , and the principal components analysis (PCA)  for fragments. Excluding the combinatorial background, the sample can be divided into three disjoint sets, according to the number of base-tracks ( ) survived to each thermal treatment.
Minimum ionizing particle tracks, such as muon cosmic rays, are expected to be erased from all thermal treatments; therefore, they are present only in films. The same happens for high energy ( MeV) protons, as shown in previous tests . Nevertheless, given intrinsic statistical fluctuations of the number of grains, distributed according to a Poisson function, and thermal treatments efficiency, a single base-track may be formed in films other than . Therefore, the criterion adopted for the identification of these particles requires the reconstruction of track segments in films and allows the presence of one track segment elsewhere: and . The number of tracks fulfiling this request is 78,905, and MIP cosmic rays and high energy protons can be separated through a cut-based analysis.
The cut based-analysis is applied also to fragments surviving thermal treatment ( and ) that do not have a statistically significant number of base-tracks in and ( and ) are 3,858.
Fragments not included in previous selections, whose base-tracks survived also to and/or thermal treatments, are 9,113, but for the PCA analysis, the presence of at least three is required. This condition is satisfied by 7,529 fragments. The remaining tracks, about of the whole sample (1,584), are due to the combinatorial background, which is formed by random association of spare base-tracks: 95% of these tracks, indeed, have less than four base-tracks without any specific correlation with . As an example, if a track has three base-tracks, two of them in and one in , this must be due to a random association of base-tracks, since it is not possible that a track has survived thermal treatment without leaving any base-track in and .
3.1 Identification of cosmic rays
First of all, we want to separate MIP cosmic rays from high energy ( MeV) protons, which are particles that are expected to be erased from all thermal treatments.
From the profile, shown in Figure 5(a) for all particles fulfiling the request and , it is possible to distinguish between two populations. These are well separated looking at , as in Figure 5(b). The particles at lower have angles which span over a wide range, mainly . This behavior is expected for cosmic rays integrated during all the detector lifetime. Indeed, the beam direction is orthogonal to the emulsion film surface and fragments produced by beam interactions are expected at smaller angles w.r.t. the beam direction, while cosmic rays impinge at wider angles. The distribution is truncated at due to limits used during data reconstruction.
To study the behavior of cosmic rays, a control sample has been taken in a region of the emulsion spectrometer outside the signal area, where only cosmic rays are present. The distribution of versus for these tracks is shown in Figure 6. These are mainly MIPs ( ), with a small component due to cosmic ray protons ( ), as expected by cosmic rays flux measurements .
Therefore, MIP cosmic rays can be identified by combining the information of , , and . The yellow line in Figure 5 is used to separate in the plane ( , ) cosmic rays and fragments, which have higher ionization. Green and red lines, instead, define the range of the boundary between the two populations and therefore have been used to evaluate the systematic uncertainty, given by half of the difference between the highest and lowest values obtained.
With this analysis condition, 60,126 particles out of 78,905 are identified as MIP cosmic rays and 18,779 as fragments. The systematic uncertainty due to the selection is estimated to be for cosmic rays and for fragments.
At this stage, only the charge is measured, while the isotopic discrimination task is addressed in Section III; therefore, we refer to these fragments as rather than protons. The same will apply to fragments.
3.2 Identification of fragments with a cut-based analysis
There are 3,858 fragments that have not been included in previous selection because of and that do not have a statistically significant number of base-tracks in and ( and ). These are shown in Figure 7, where the is plotted versus . One population is visible: tracks with below the yellow line in Figure 7 are due to fragments, but more ionizing than the ones already identified having . At equal charge, higher ionization corresponds to lower energy, so these tracks are identified as due to lower energy fragments. Light blue and magenta lines define possible choices in the definition of the boundary to select this population and therefore were used to evaluate systematic uncertainties.
Fragments with larger than the cut have been interpreted as belonging to the next atomic species, .
The hypothesis of two populations and their boundaries are confirmed by the same plot without any cut applied on and , as shown in Figure 8. The number of fragments below the straight line is almost stable in the two cases, demonstrating that those are particles which do not survive thermal treatments more aggressive than . On the contrary, tracks above the straight line show higher ionization and are thus fragments with . When and are missing, the higher energy component with equal to 2 is selected. Most of the tracks with will be analyzed in the next section with the PCA analysis.
From the information retrieved from and films, the charge has been measured for 3,858 particles: 2,420 fragments constitute the populations, while 1,438 have been recognized as fragments. The systematic uncertainty due to the selection is estimated to be for and for .
Excluding cosmic rays from the sample, with the cut-based analysis, the charge has been measured for of fragments. A summary of the charge measured is reported in Table 1. The distribution for cosmic rays is reported in Figure 9, compared with the distribution of other fragments whose charge was measured with the cut-based analysis.
|Z||Number of tracks||Syst. Err.|
|2 (high energy)||1,438||161|
3.3 Identification of fragments with the principal component analysis
To further distinguish fragments surviving also and/or thermal treatments, a cut-based analysis on and variables is not powerful enough due to saturation effects, as shown in Figure 10, where only cuts and were applied.
In order to disentangle different fragment tracks, the principal component analysis, a multidimensional technique, well established in the field of pattern recognition  was adopted. This technique is based on applying a linear transformation to the measured variables and is useful when these are not the most significant for data classification, while reducing the dimensionality of the problem results in an easier classification procedure. This transformation, described by an orthogonal matrix, is equivalent to a rotation of the original pattern space into a new set of coordinate vectors.
Being , the vector containing our measured values, the covariance matrix is defined as , where . matrix is real, positive definite, symmetric, and with non-null, positive eigenvalues.
The base formed by the eigenvectors of the matrix and belonging to the largest eigenvalues corresponds to the most significant features of the description of the original prototypes.
The PCA method was applied to all fragments with at least three measured , which are 7,529. For these fragments, four new variables called are defined. These variables are expressed in arbitrary units as .
The first principal component is calculated to account for the highest variance in the data.
Considering how have been evaluated, particles with higher ionization are expected to also have a higher .
Each of these variables was fitted with three Gaussian functions, as shown in Figure 11. To each Gaussian fit, the particle population with increasing was associated: violet for fragments, pink for , and green for ones. The fit model has been inferred by the study of a high-purity sample requiring tracks crossing at least 7 cells ( ). With the cut-based analysis, a fraction of fragments was already identified. Therefore, in the complementary sample, which survived after the more aggressive thermal treatment applied on and , the component of fragments with higher ionization (lower energy) is expected. For this reason, the Gaussian will be partially erased. The threshold value depends on the particle energy and on the statistical fluctuation in the number of sensitized grains along the track. These effects produced a smearing in the threshold that is not expected to be sharp. Therefore, the fit is not taking into account low values, where the behavior is not Gaussian. Another requirement is that the height of Gaussian peak must be higher than that of the Gaussian, which in turn has to be higher than or equal to the height of the Gaussian, since the number of fragments is expected to decrease as increases. Consequently, the mean value of the Gaussian is lower than the mean value of Gaussian, which in turn is lower than the mean value of Gaussian.
The charge is assigned to each fragment by generating a random number which takes into account probabilities given by the height of each Gaussian curve for its value with respect to the height of the overall fit distribution. As far as the evaluation of the relative contribution of each population is concerned, this method is equivalent to estimating the relative weight of each Gaussian distribution. Nevertheless, the procedure outlined above is meant to provide an additional feature to each track that could be useful for future analysis.
The variable is used if , , and are available. Especially for tracks with a small number of segments, it can happen that segments in a specific are not reconstructed or are not correctly associated with the track, so it is not possible to evaluate their . In this case, one of the other combinations applies. In Table 2, we report the number of fragments tagged with the corresponding variable.
|VP||Number of tracks||%|
Three error components have been identified: a systematic uncertainty due to the fit, which can differ because of plot binning or lower limit, the error due to uncertainties of the fit parameters and a statistical error due to the size of the available sample. All error components have been evaluated only for : the contribution of the error coming from the other , indeed, is negligible with respect to the one of , which is used for more than 90% of fragments.
To evaluate the systematic uncertainty, six fits have been applied, which differ from each other for the plot binning and lower limits. For each one of them, the error due to uncertainties of fit parameters was evaluated through the generation of fits, where mean values of the three Gaussian curves are normally distributed around their mean within . Only fits with a probability larger than 0.001 have been accepted. An example is shown in Figure 12.
For each of the six different fits, the average on the results obtained over the random generations gives a partial estimation of the number of particles with a given Z. The final result is obtained as the weighted average on these six partial results. The systematic uncertainty is given by the maximum error on the six results, while the statistical error is given by the standard deviation on the weighted average. The main contribution is due to the systematic uncertainty, while the statistical error and the one due to uncertainties of fit parameters are negligible.
The number of fragments for each is reported in Table 3, together with relative uncertainties. Combining the information through the PCA, the charge has been assigned also to fragments with . It is not possible to further distinguish particles with the current thermal treatments used.
|Number of tracks||Syst. Err.|
|2 (low energy)||3,506||370|
To crosscheck the results obtained with PCA, other two methods have been tried: the singular value decomposition (SVD) and the non-negative matrix factorization (NMF) . Both lead to compatible results within the errors.
The charge has been measured or assigned for 98.3% of reconstructed particles. Different fragments identified and corresponding fractions are reported in Table 4.
|CB||PCA||Total||%||Syst. Err. (%)||Stat. Err. (%)|
In this study, the charge identification of fragments produced in interactions of 200 MeV/n oxygen ions with a target has been reported. Thermal treatments inducing controlled fading of nuclear emulsion films were applied to the Section II of the emulsion spectrometer to distinguish the charge of fragments generated by oxygen interactions and separate them from cosmic rays integrated during the detector lifetime. The charge was measured or assigned for 99.4% of tracks reconstructed in Section II of the detector. The charge of these fragments was measured using two complementary methods: a cut-based analysis and the principal component analysis. Our aim was to identify fragments as heavy as lithium, and this goal was achieved. Within the FOOT experiment, identification of fragments is a task of the electronic detector setup. For future data takings, the systematic uncertainty, which is the dominant one, will be reduced by optimizing the thermal treatments to get a better separation between fragments with different charge.
We thank GSI for the successful operation of their facilities during the data taking. This paper is dedicated to the memory of Ennio Morricone, a source of inspiration for many of us.
Funding information: The FOOT Collaboration acknowledges the INFN for its support in building and running the detector. We would like to acknowledge all the personnel of the CNAO and GSI centres that provided us support during the operational tests performed using proton, 12C and 16O beams at their facilities. The GSI data were taken in the IBER 006 experiment, supported by the European Space Agency (ESA) – IBER17 717 project, in the frame of FAIR Phase-0. The paper underwent an internal collaboration-wide review process and all authors approved the final version of the manuscript.
Author contributions: All authors have contributed to the publication, being variously involved in the design and the construction of the detectors, in writing software, calibrating subsystems, operating the detectors, acquiring data and finally analysing the processed data. The FOOT Collaboration members discussed and approved the scientific results reported in the submitted document. The manuscript was prepared by a subgroup of authors appointed by the collaboration and subject to an internal collaboration-wide review process. All authors reviewed and approved the final version of the manuscript.
Conflict of interest: Authors state no conflict of interest.
 Paganetti H, Niemierko A, Ancukiewicz M, Gerweck LE, Goitein M, Loeffler JS, et al. Relative biological effectiveness (RBE) values for proton beam therapy. Int J Radiation Oncology Biol Phys. 2002;53(2):407–21. Search in Google Scholar
 Tommasino F and Durante M. Proton radiobiology. Cancers. 2015;7:353–81. Search in Google Scholar
 Durante M, Paganetti H. Nuclear physics in particle therapy: a review. Rep Prog Phys. 2016;79:096702. Search in Google Scholar
 Paganetti H. Relative Biological Effectiveness (RBE) values for proton beam therapy. Variations as a function of biological end-point, dose, and linear energy transfer. Phys Med Biol. 2014;59(22):R419. Search in Google Scholar
 De Lellis G, Buontempo S, Di Capua F, Di Crescenzo A, Migliozzi P, Petukhov Y, et al. Measurements of the fragmentation of carbon nuclei used in hadron therapy. Nucl Phys A. 2011;853:124–34. Search in Google Scholar
 G. Battistoni, Toppi Marco, Patera V, (FOOT collaboration). Measuring the impact of nuclear interaction in particle therapy and in radio protection in space: the foot experiment. Front Phys. 2021. 10.3389/fphy.2020.568242. Search in Google Scholar
 https://web.infn.it/f00t/index.php/it/public links. 2020. Search in Google Scholar
 De Lellis G, Buontempo S, Di Capua F, Marotta A, Migliozzi P, Petukhov Y, et al. Emulsion Cloud Chamber technique to measure the fragmentation of high-energy carbon beam. J Instrum. 2007;2:P06004. Search in Google Scholar
 Montesi MC, Lauria A, Alexandrov A, Alunni Solestizi L, Giovanni A, Argiró S, et al. (FIRST Collaboration). Ion charge separation with new generation of nuclear emulsion films. Open Phys. 2019;17(1):233–40. Search in Google Scholar
 Nakamura T, Ariga A, Ban T, Fukuda T, Fukuda T, Fujioka T, et al. The OPERA film: new nuclear emulsion for large-scale, high-precision experiments. NIMA-A. 2006;556:80–6. Search in Google Scholar
 A Ariga, T Ariga, G De Lellis, A Ereditato, K Niwa. Nuclear emulsions. Cham: Springer International Publishing; 2020. p. 383–438. Search in Google Scholar
 De Lellis G, Buontempo S, Di Capua F, Marotta A, Migliozzi P, Petukhov Y, et al. Emulsion cloud chamber technique to measure the fragmentation of a high-energy carbon beam. JINST. 2007;2:P06004. Search in Google Scholar
 Battistoni G, Bauer J, Boehlen T, Cerutti F, Chin M, Santos Augusto R, et al. The FLUKA code: An accurate simulation tool for particle therapy. Front Oncol. May 2016;6:116. 10.3389/fonc.2016.00116. Search in Google Scholar
 Ferrari A, Sala PR, Milan/CERN/INFN, Fasso A, /SLAC, Ranft J, Siegen U. FLUKA: A multi-particle transport code. 12 2005. Search in Google Scholar
 Agafonova N, Aleksandrov A, Altinok O, Anokhina A, Aoki S, Ariga A, et al. Momentum measurement by the multiple Coulomb scattering method in the OPERA lead emulsion target. New J Phys. 2012;14:013026. Search in Google Scholar
 Alexandrov A, Buonaura A, Consiglio L, D’Ambrosio N, De Lellis G, Di Crescenzo A, et al. A new fast scanning system for the measurement of large angle tracks in nuclear emulsions. J Instrum. 2015;10:P11006. Search in Google Scholar
 Alexandrov A, Buonaura A, Consiglio L, D’Ambrosio N, De Lellis G, Di Crescenzo A, et al. A new generation scanning system for the high-speed analysis of nuclear emulsions. J Instrum. 2016;11:P06002. Search in Google Scholar
 Alexandrov A, Buonaura A, Consiglio L, D’Ambrosio N, De Lellis G, Di Crescenzo A, et al. The continuous motion technique for a new generation of scanning systems. Sci Rep. 2017;7(1):7310. Search in Google Scholar
 Aleksandrov A, Consiglio L, De Lellis G, Di Crescenzo A, Lauria A, Montesi MC, et al. Measurement of large angle fragments induced by 400 MeV n−1 carbon ion beams. Meas Sci Technol. 2015;26(9):094001. Search in Google Scholar
 CERN-72-21. 1972 CERN Computing and Data Processing School, Pertisau, Austria, 10-24 Sep 1972: Proceedings, CERN Yellow Reports: School Proceedings, 12 1972. https://cds.cern.ch/record/186411. Search in Google Scholar
 Grieder PKF. Cosmic rays at Earth. Amsterdam: Elsevier Science; 2001. Search in Google Scholar
 Eldén L. Numerical linear algebra in data mining. Acta Numerica. May 2006;15:327–84. Search in Google Scholar
© 2021 Giuliana Galati et al., published by De Gruyter
This work is licensed under the Creative Commons Attribution 4.0 International License.