# Prediction of the Near-Infrared Absorption Spectrum of Single-Walled Carbon Nanotubes Using a Bayesian Regularized Back Propagation Neural Network Model

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## Abstract

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## 1. Introduction

_{2}O

_{2}, which is an oxidizing agent, is added to the DNA-SWCNTs’ dispersion [31]. (8,4)/(9,4) SWCNTs indicate that the absorption wavelengths for chirality (8,4) and (9,4) are almost the same. Matsukawa et al. have suggested the possibility of a biosensor that detects antioxidant activity because the peak amplitude is restored before oxidation when catechin, which has antioxidant properties, is added to oxidized DNA-SWCNTs, as shown in Figure 1. In order to put DNA-SWCNTs to practical use in biosensor applications, it is necessary to clarify the absorption spectra responses to detailed catechin concentration changes through more experiments. However, preparing many of these experiments is time consuming, costly and impractical. Thus, predictions with high accuracy, using machine learning from a small amount of experimental data, will contribute to efficient experiment planning in the future.

## 2. Materials and Methods

#### 2.1. Sample Data

_{2}O

_{2}that was diluted with sterilized water (with a final concentration of 0.03%) was added to the samples, followed by incubation for 30 min at 21 °C. The spectra of the samples were measured. Finally, 10 μL of catechin solution (with final concentrations at 15, 1.5, 0.15, 0.075, and 0.03 μg/mL) was added to the samples and the spectra were measured after 10 min incubation at 21 °C. Triplicate NIR measurements for each experiment were recorded in order to verify the reproducibility.

#### 2.2. Bayesian Regularized Backpropagation Neural Network

#### 2.3. Input/Output Data and the Verification Method

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Typical reaction example of experimental data targeted by the BRBPNN model. Blue line of step 1 is NIR spectrum in the initial state of DNA-SWCNTs. Red line is NIR spectrum with H

_{2}O

_{2}added to the initial state. Green line is NIR spectrum with catechin added in step 2.

**Figure 2.**Overview of the learned BRBPNN model. Initial (8,4)/(9,4) peak absorption and catechin concentration are used as input data I, II, and NIR spectra after catechin addition in (iii) state as output data.

**Figure 3.**Comparison of the results of prediction data and verification data in the spectrum waveform after catechin addition for each catechin concentration.

**Figure 4.**(

**a**) Comparison of prediction data and verification data of absorption peak of (8,4)/(9,4) DNA-SWCNTs. (

**b**) Comparison of prediction data and verification data of peak wavelength of (8,4)/(9,4) DNA-SWCNTs. Each value is expressed as mean ± standard deviation.

**Figure 5.**Prediction results of (8,4)/(9/4) absorption peaks for catechin concentration input using BRBPNN: The blue circles represent the BRBPNN model’s output from learned data. The orange circles represent the BRBPNN model’s outputs when the learned excluding the catechin 1.5 μg/mL. The light blue circles represent the BRBPNN model’s output when learned excluded the catechin 0.075 μg/mL. The green squares, black lines and gray dotted lines represent the validation data, the power approximation lines and the polynomial approximation lines (quadratic) for them, respectively.

Input Data | Output Data | |||
---|---|---|---|---|

Catechin Concentration [μg/mL] | (8,4)/(9,4) Peak | (8,4)/(9,4) Peak | ||

Absorption [a.u.] | Data Type | Absorption [a.u.] | Wavelength [nm] | |

15 | 0.513 | Verification | 0.502 ± 0.009 | 1135.0 ± 0.1 |

Prediction | 0.499 ± 0.000 | 1134.8 ± 0.3 | ||

1.5 | 0.499 | Verification | 0.491 ± 0.005 | 1133.5 ± 0.2 |

Prediction | 0.489 ± 0.001 | 1133.4 ± 0.2 | ||

0.15 | 0.500 | Verification | 0.461 ± 0.005 | 1133.0 ± 0.2 |

Prediction | 0.461 ± 0.001 | 1132.9 ± 0.2 | ||

0.075 | 0.498 | Verification | 0.457 ± 0.001 | 1133.0 ± 0.0 |

Prediction | 0.458 ± 0.001 | 1133.0 ± 0.0 | ||

0.030 | 0.500 | Verification | 0.457 ± 0.006 | 1133.0 ± 0.0 |

Prediction | 0.453 ± 0.002 | 1133.0 ± 0.0 |

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**MDPI and ACS Style**

Onishi, T.; Matsukawa, Y.; Yamazaki, Y.; Miyashiro, D.
Prediction of the Near-Infrared Absorption Spectrum of Single-Walled Carbon Nanotubes Using a Bayesian Regularized Back Propagation Neural Network Model. *C* **2021**, *7*, 80.
https://doi.org/10.3390/c7040080

**AMA Style**

Onishi T, Matsukawa Y, Yamazaki Y, Miyashiro D.
Prediction of the Near-Infrared Absorption Spectrum of Single-Walled Carbon Nanotubes Using a Bayesian Regularized Back Propagation Neural Network Model. *C*. 2021; 7(4):80.
https://doi.org/10.3390/c7040080

**Chicago/Turabian Style**

Onishi, Takao, Yuji Matsukawa, Yuto Yamazaki, and Daisuke Miyashiro.
2021. "Prediction of the Near-Infrared Absorption Spectrum of Single-Walled Carbon Nanotubes Using a Bayesian Regularized Back Propagation Neural Network Model" *C* 7, no. 4: 80.
https://doi.org/10.3390/c7040080