# Gray Level Co-Occurrence Matrix, Fractal and Wavelet Analyses of Discrete Changes in Cell Nuclear Structure following Osmotic Stress: Focus on Machine Learning Methods

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

## 3. Results

#### 3.1. Results of GLCM, Fractal, and DWT Analyses

#### 3.2. Machine Learning Models

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Saccharomyces cerevisiae yeast cells exposed to a hyperosmotic environment (right half of the image, 6 cells) and control cells (left half of the image, 6 cells). Although microscopically, no significant morphological differences can be observed, nuclear ROIs of these cells have different values of GLCM, fractal and wavelet indicators. For example, the first cell of the control group (upper left cell, marked with the black arrow) had a nuclear IDM of 0.163 and a fractal dimension of 1.551. The morphologically similar cell exposed to a hyperosmotic environment (right half of the image, marked with the white arrow) had an IDM value of 0.149 and a fractal dimension of 1.434.

**Figure 3.**The fractal dimension of ROIs was calculated based on the slope of the regression line of log(1/ε) versus log N(ε) for all scales. The value of the fractal dimension in this example is 1.6142. The standard deviations for the experimental and control groups of cells were 0.155 and 0.142, respectively.

**Figure 4.**Average values of nuclear GLCM indicators in cells exposed to hyperosmotic environment and controls.

**Table 1.**Average values of GLCM, fractal and DWT indicators of nuclear ROIs on cells exposed to hyperosmotic environment and controls. * p < 0.05 ** p < 0.01.

Osmotic Stress | Controls | |
---|---|---|

Angular second moment | 0.00076 ± 0.00092 ** | 0.0015 ± 0.0011 |

Inverse difference moment | 0.154 ± 0.012 ** | 0.167 ± 0.013 |

Contrast | 59.87 ± 8.78 ** | 51.03 ± 9.17 |

Correlation | 0.0019 ± 0.0023 ** | 0.0041 ± 0.0037 |

Variance | 799.39 ± 363.96 ** | 507.17 ± 434.37 |

Fractal dimension | 1.454 ± 0.155 ** | 1.538 ± 0.142 |

DWT coefficient energy | 0.369 ± 0.089 * | 0.250 ± 0.084 |

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**MDPI and ACS Style**

Pantic, I.; Valjarevic, S.; Cumic, J.; Paunkovic, I.; Terzic, T.; Corridon, P.R.
Gray Level Co-Occurrence Matrix, Fractal and Wavelet Analyses of Discrete Changes in Cell Nuclear Structure following Osmotic Stress: Focus on Machine Learning Methods. *Fractal Fract.* **2023**, *7*, 272.
https://doi.org/10.3390/fractalfract7030272

**AMA Style**

Pantic I, Valjarevic S, Cumic J, Paunkovic I, Terzic T, Corridon PR.
Gray Level Co-Occurrence Matrix, Fractal and Wavelet Analyses of Discrete Changes in Cell Nuclear Structure following Osmotic Stress: Focus on Machine Learning Methods. *Fractal and Fractional*. 2023; 7(3):272.
https://doi.org/10.3390/fractalfract7030272

**Chicago/Turabian Style**

Pantic, Igor, Svetlana Valjarevic, Jelena Cumic, Ivana Paunkovic, Tatjana Terzic, and Peter R. Corridon.
2023. "Gray Level Co-Occurrence Matrix, Fractal and Wavelet Analyses of Discrete Changes in Cell Nuclear Structure following Osmotic Stress: Focus on Machine Learning Methods" *Fractal and Fractional* 7, no. 3: 272.
https://doi.org/10.3390/fractalfract7030272