This paper investigates the scaling of the surface roughness of coronavirus, including the SARS-nCoV based on fractal and spectral analyses of their published electron microscopy images. The box-counting fractal dimensions obtained are subjected to ANOVA tests for statistical significance. Results show that the SARS-nCoV particles could not statistically be resolved by their shape on the basis of the fractal dimension values, but they could be distinguished from the earlier SARS-CoV particles. MANOVA test results require interaction of factors used for classifying virions into different types. The topological entropies, a measure of randomness in a system, measured for the images of varying size show correlation with the fractal dimensions. Spectral analyses of our data show a departure from power-law self-similarity, suggesting an apparent scaling of surface roughness over a band of maximum an order of magnitude. The spectral crossover that corresponds to characteristic length scale may represent average viral size. Our results may be useful in inferring the nature of surface-contact between the viral and human cell, causing infection and also in providing clues for new drugs, although it is too early to say. In addition, limitations of this study, including possible ways to avoid the bias in scaling exponents due to the use of different techniques are discussed.

本文研究了冠状病毒表面粗糙度的标度，包括基于已发布电子显微镜图像的分形和光谱分析得出的SARS-nCoV。获得的盒计数分形维数经过ANOVA测试，以显示统计显着性。结果表明，SARS-nCoV粒子不能通过分形维数的形状来统计解析，但可以与早期的SARS-CoV粒子区分开。MANOVA测试结果需要用于将病毒粒子分类为不同类型的因素的相互作用。对于大小不同的图像，所测量的拓扑熵（系统中的随机性度量）与分形维数相关。我们数据的频谱分析表明，它与幂律自相似性背离，这表明表面粗糙度在最大一个数量级的带上有明显的缩放。对应于特征长度标度的光谱交叉可以代表平均病毒大小。我们的研究结果可能有助于推断病毒与人细胞之间的表面接触性质，从而引起感染，并且还可以为新药提供线索，尽管这还为时过早。此外，还讨论了这项研究的局限性，包括避免因使用不同技术而导致缩放指数出现偏差的可能方法。虽然现在说还为时过早，但它会导致感染并为新药提供线索。此外，还讨论了这项研究的局限性，包括避免因使用不同技术而导致缩放指数出现偏差的可能方法。虽然现在说还为时过早，但它会导致感染并为新药提供线索。此外，还讨论了这项研究的局限性，包括避免因使用不同技术而导致比例指数出现偏差的可能方法。