### Abstract

The relation for the product of peak velocity and duration against saccadic amplitude was tightly correlated with correlation coefficient according to the previous study. Previous study described the velocity profile as triangular and referred to the saccadic amplitude as an integration of the profile that the amplitude is proportional to V _{m}D. From our observation and derivation, in addition to the triangular profile, the rational power function could also be applied to explain the linear relationship between the saccadic amplitude and the product of peak velocity and duration. The saccadic amplitude is proportional to the product of peak velocity and duration (V _{m}D) only when the velocity profile is symmetry. For greater amplitudes, the profiles become asymmetrical and it is more suitable for describing the saccadic amplitude as the sum of the acceleration and the deceleration amplitudes. Although the correlation coefficients, after fitting two rational power functions to the acceleration phase and the deceleration phase, were satisfactory, thist however cannot resolve the inflection points which divide two phases into four segments: two are located in the acceleration phase and the other two in the deceleration phase. In this study, the inflection points were obtained by differentiating the velocity profile. Rational power functions were then applied individually to fit these 4 separate segments. The results show that the rational power functions were fitted very well to velocity profiles for amplitudes 5°, 10°, 20°, and 30° with correlation coefficients greater than 0.999. A comparison for the shape parameters indicates that the curvature for segment 1 (n _{1}) and 2 (n _{2}) is significantly larger than segment 3 (n _{3}) and 4 (n _{4}). Also n _{3} is very close to 1, which mimics that it approximates to a line. In conclusion, rational power functions are efficient in piecewise fitting for the saccadic velocity profiles. The shape parameters are also illuminated for describing the velocity profile characteristics of saccades.

Original language | English |
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Title of host publication | Proceedings of the International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences, METMBS'04 |

Editors | F. Valafar, H. Valafar |

Pages | 486-489 |

Number of pages | 4 |

Publication status | Published - 2004 Dec 1 |

Event | Proceedings of the International Conference on Mathematics and Engineering Techniques in medicine and Biological Sciences, METMBS'04 - Las Vegas, NV, United States Duration: 2004 Jun 21 → 2004 Jun 24 |

### Publication series

Name | Proceedings of the International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences, METMBS'04 |
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### Other

Other | Proceedings of the International Conference on Mathematics and Engineering Techniques in medicine and Biological Sciences, METMBS'04 |
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Country | United States |

City | Las Vegas, NV |

Period | 04-06-21 → 04-06-24 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

*Proceedings of the International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences, METMBS'04*(pp. 486-489). (Proceedings of the International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences, METMBS'04).

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*Proceedings of the International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences, METMBS'04.*Proceedings of the International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences, METMBS'04, pp. 486-489, Proceedings of the International Conference on Mathematics and Engineering Techniques in medicine and Biological Sciences, METMBS'04, Las Vegas, NV, United States, 04-06-21.

**Piecewise fittings of the saccadic velocity profiles using the rational power functions.** / Lin, Hsuan Hung; Chen, Yung Fu; Chen, Tainsong; Tsai, Tze Tung.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Piecewise fittings of the saccadic velocity profiles using the rational power functions

AU - Lin, Hsuan Hung

AU - Chen, Yung Fu

AU - Chen, Tainsong

AU - Tsai, Tze Tung

PY - 2004/12/1

Y1 - 2004/12/1

N2 - The relation for the product of peak velocity and duration against saccadic amplitude was tightly correlated with correlation coefficient according to the previous study. Previous study described the velocity profile as triangular and referred to the saccadic amplitude as an integration of the profile that the amplitude is proportional to V mD. From our observation and derivation, in addition to the triangular profile, the rational power function could also be applied to explain the linear relationship between the saccadic amplitude and the product of peak velocity and duration. The saccadic amplitude is proportional to the product of peak velocity and duration (V mD) only when the velocity profile is symmetry. For greater amplitudes, the profiles become asymmetrical and it is more suitable for describing the saccadic amplitude as the sum of the acceleration and the deceleration amplitudes. Although the correlation coefficients, after fitting two rational power functions to the acceleration phase and the deceleration phase, were satisfactory, thist however cannot resolve the inflection points which divide two phases into four segments: two are located in the acceleration phase and the other two in the deceleration phase. In this study, the inflection points were obtained by differentiating the velocity profile. Rational power functions were then applied individually to fit these 4 separate segments. The results show that the rational power functions were fitted very well to velocity profiles for amplitudes 5°, 10°, 20°, and 30° with correlation coefficients greater than 0.999. A comparison for the shape parameters indicates that the curvature for segment 1 (n 1) and 2 (n 2) is significantly larger than segment 3 (n 3) and 4 (n 4). Also n 3 is very close to 1, which mimics that it approximates to a line. In conclusion, rational power functions are efficient in piecewise fitting for the saccadic velocity profiles. The shape parameters are also illuminated for describing the velocity profile characteristics of saccades.

AB - The relation for the product of peak velocity and duration against saccadic amplitude was tightly correlated with correlation coefficient according to the previous study. Previous study described the velocity profile as triangular and referred to the saccadic amplitude as an integration of the profile that the amplitude is proportional to V mD. From our observation and derivation, in addition to the triangular profile, the rational power function could also be applied to explain the linear relationship between the saccadic amplitude and the product of peak velocity and duration. The saccadic amplitude is proportional to the product of peak velocity and duration (V mD) only when the velocity profile is symmetry. For greater amplitudes, the profiles become asymmetrical and it is more suitable for describing the saccadic amplitude as the sum of the acceleration and the deceleration amplitudes. Although the correlation coefficients, after fitting two rational power functions to the acceleration phase and the deceleration phase, were satisfactory, thist however cannot resolve the inflection points which divide two phases into four segments: two are located in the acceleration phase and the other two in the deceleration phase. In this study, the inflection points were obtained by differentiating the velocity profile. Rational power functions were then applied individually to fit these 4 separate segments. The results show that the rational power functions were fitted very well to velocity profiles for amplitudes 5°, 10°, 20°, and 30° with correlation coefficients greater than 0.999. A comparison for the shape parameters indicates that the curvature for segment 1 (n 1) and 2 (n 2) is significantly larger than segment 3 (n 3) and 4 (n 4). Also n 3 is very close to 1, which mimics that it approximates to a line. In conclusion, rational power functions are efficient in piecewise fitting for the saccadic velocity profiles. The shape parameters are also illuminated for describing the velocity profile characteristics of saccades.

UR - http://www.scopus.com/inward/record.url?scp=11144255749&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=11144255749&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:11144255749

SN - 1932415432

SN - 9781932415438

T3 - Proceedings of the International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences, METMBS'04

SP - 486

EP - 489

BT - Proceedings of the International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences, METMBS'04

A2 - Valafar, F.

A2 - Valafar, H.

ER -