# Algorithm for Enhancing Event Reconstruction Efficiency by Addressing False Track Filtering Issues in the SPD NICA Experiment

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## Abstract

**:**

## 1. Introduction

## 2. Related Works and the Problem Formulation

## 3. Methodology

#### 3.1. The Solution of a Nonlinear Problem for the Estimation of Helical Line Parameters

#### 3.2. Dataset Description

- Number of events: 1000;
- Numbering of events: from 1 to 1000;
- Number of tracks in each event: from 5 to 61.

#### 3.3. The Data Processing Strategy

#### 3.4. Boosting Algorithm Efficiency for Accurate Track Elimination through Parallelization Techniques

Algorithm 1 Track Reconstruction |

Require: DataFrame D containing hit coordinates $(x,y,z)$, event and station identifiers, and track number |

Ensure: Labeled tracks T |

1: Load TrackNETv2.1 model |

2: function GenerateCandidates(D) |

3: Candidate tracks $C\leftarrow $ [] |

4: for $i\leftarrow 1$ to $\mathrm{length}\left(D\right)$ do |

5: $h\leftarrow {D}_{i}$ |

6: $c\leftarrow $ TrackNetv2.1(h) |

7: add c to C |

8: end for |

9: return C |

10: end function |

11: $C\leftarrow $GenerateCandidates(D) |

12: function LabelTracks(C) |

13: Labeled tracks $T\leftarrow $ [] |

14: for c in C do |

15: fit helix to c |

16: calculate ${\chi}^{2}$ value for fitted helix |

17: if ${\chi}^{2}$ < threshold then |

18: label c as correct |

19: else |

20: label c as false |

21: end if |

22: add c to T |

23: end for |

24: return T |

25: end function |

26: $T\leftarrow $LabelTracks(C) |

## 4. Results and Discussion

Algorithm 2 Polynomial Fit Method |

Require: All Tracks Table with x, y, z, N, s, d, and T |

1: for each track in All Tracks Table do |

2: Compute initial parametrization u using centripetal method |

3: Define polynomials ${f}_{x}\left(u\right)$, ${f}_{y}\left(u\right)$, ${f}_{z}\left(u\right)$ of degree k |

4: for each parameter ${u}_{i}$ in u do |

5: Compute n using Equation (12) |

6: Initialize search interval $[a,b]$ around ${u}_{i}$ |

7: repeat |

8: Apply Golden Ratio search on interval $[a,b]$ |

9: Update a and b based on Golden Ratio search |

10: Compute residuals and update ${f}_{x}\left(u\right)$, ${f}_{y}\left(u\right)$, ${f}_{z}\left(u\right)$ |

11: until convergence criterion is met or maximum iterations are reached |

12: end for |

13: Compute final polynomials ${f}_{x}\left(u\right)$, ${f}_{y}\left(u\right)$, ${f}_{z}\left(u\right)$ |

14: end for |

Ensure: Fitted polynomial parameters for each track |

#### 4.1. Parallel Algorithm 2

#### 4.2. Comparison of Performances for Two Algorithms

#### 4.3. Neural Network Algorithm for Track Recognition and Its Performance Results with False Tracks before and after Applying the Track Rejection Criterion

#### 4.4. False Track Rejection with Contaminated Data

- The input data in the form of a DataFrame containing hit coordinates $(x,y,z)$, event and station identifiers, and the track number are fed into the neural network.
- The network generates candidate tracks using the TrackNETv2.1 model.
- A thresholding procedure is applied to cluster the track candidates based on the chi-squared values obtained from fitting a helix to each trajectory. The tracks are then labeled as either false or correct.

## 5. Conclusions and Outlook

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

HEP | High-Energy Physics |

JINR | Joint Institute for Nuclear Research |

CERN | Conseil Europeen pour la recherche Nucleaire (fr.) or The European Organization |

for Nuclear Research | |

BNL | Brookhaven National Laboratory |

LHC | The Large Hadron Collider of CERN |

NICA | Nuclotron-based Ion Collider fAcility of JINR |

RHIC | The Relativistic Heavy Ion Collider of BNL |

EIC | The Electron-Ion Collider |

SPD | Spin Physics Detector on NICA Collider |

BM@N | Baryonic Matter at Nuclotron—the fixed-target experiment on NICA collider |

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**Figure 1.**General layout of the SPD setup [1].

Cluster ID | Mean | Std | Number of Elements |
---|---|---|---|

0 | 4.5178 | 0.3570 | 121 |

1 | 0.0006 | 0.0016 | 16,839 |

2 | 0.0225 | 0.0080 | 1091 |

3 | 0.0585 | 0.0131 | 277 |

4 | 0.1210 | 0.0233 | 419 |

5 | 0.2260 | 0.0378 | 277 |

6 | 0.3811 | 0.5841 | 259 |

7 | 0.6182 | 0.0807 | 211 |

8 | 0.9419 | 0.1005 | 182 |

9 | 1.3246 | 0.1326 | 161 |

10 | 1.8650 | 0.1732 | 144 |

Number of Iterations | Computational Complexity | Memory Consumption | |
---|---|---|---|

Algorithm 1 | Small | High | High |

Algorithm 2 | Average | Average | Average |

**Table 3.**Center cluster chi-squared depending on zero level of noise, 100 false hits, 1000 false hits.

0 Noise Level (0 False Hits) | 1st Noise Level (100 False Hits) | 2nd Noise Level (1000 False Hits) | |
---|---|---|---|

Mean value of the center cluster | 0.0005 | 0.0011 | 0.0071 |

Standard deviation value of the center cluster | 0.0012 | 0.0065 | 0.0142 |

Number of elements | 16,422 | 12,319 | 10,343 |

Recall | Precision | Calculation Time for 1 Event (s) | |
---|---|---|---|

With fake hits (100 points) | 90.2 | 92.2 | 0.00154 |

With fake hits (1000 points) | 89.6 | 91.5 | 0.00211 |

Without fake hits | 93.5 | 94.5 | 0.00127 |

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## Share and Cite

**MDPI and ACS Style**

Amirkhanova, G.; Mansurova, M.; Ososkov, G.; Burtebayev, N.; Shomanov, A.; Kunelbayev, M.
Algorithm for Enhancing Event Reconstruction Efficiency by Addressing False Track Filtering Issues in the SPD NICA Experiment. *Algorithms* **2023**, *16*, 312.
https://doi.org/10.3390/a16070312

**AMA Style**

Amirkhanova G, Mansurova M, Ososkov G, Burtebayev N, Shomanov A, Kunelbayev M.
Algorithm for Enhancing Event Reconstruction Efficiency by Addressing False Track Filtering Issues in the SPD NICA Experiment. *Algorithms*. 2023; 16(7):312.
https://doi.org/10.3390/a16070312

**Chicago/Turabian Style**

Amirkhanova, Gulshat, Madina Mansurova, Gennadii Ososkov, Nasurlla Burtebayev, Adai Shomanov, and Murat Kunelbayev.
2023. "Algorithm for Enhancing Event Reconstruction Efficiency by Addressing False Track Filtering Issues in the SPD NICA Experiment" *Algorithms* 16, no. 7: 312.
https://doi.org/10.3390/a16070312