Abstract The canonical description of structures comprises two aspects: (1) basic structural elements and (2) arrangement pattern between those elements. This tidy description has been very successful and facilitates the development of structural physics tremendously, enabling the classification, comparison and analysis of an extremely wide range of structures, including crystals, quasi-crystals, liquid crystals, semi-crystalline materials and so on. However, it has been gradually realized that many novel materials and devices exhibit random structures in which either basic elements or arrangement patterns may not exist. With the rapid development of modern advanced materials, this type of apparently random structure pops up frequently, leaving researchers struggling with how to describe, classify and quantitatively compare them. This paper proposes the utilization of statistical characteristics as the major indicators for the description of apparently random structures. Specifically, we have explored many statistical properties, including power spectral density, histograms, structural complexity, entropic complexity, autocorrelation, etc., and found that autocorrelation may serve as a promising statistical proxy to distinguish similar-looking random structures. We discuss eight atomic force microscope images of random structures, demonstrating that autocorrelation can be used to distinguish them. In addition, 14 more diverse datasets are used to support this conclusion, including atomic force microscopy images of polymers and non-polymers, transmission electron microscopy images of nanocomposite layers and scanning electron microscopy images of non-polymers.
Fund: This work is supported by the School Important Direction Project Cultivation Fund and Key Fund Project for Youth Innovation (Grant Nos. WK2310000101, YD2310002006, and BJ2310000055).
Mei Xie(解梅), Fei Xie(谢飞), Baoyu Song(宋宝玉), Qiaoyu Guo(郭桥雨), and Xuechen Jiao(焦学琛) Exploring the proper statistical proxy to distinguish random structures 2025 Chin. Phys. B 34 058902
[1] Gidas B 1989 IEEE Transactions on Pattern Analysis and Machine Intelligence 11 164 [2] Lindeberg T 1998 International Journal of Computer Vision 30 79 [3] Buccigrossi RWand Simoncelli E P 1999 IEEE Transactions on Image Processing 8 1688 [4] Jinggang H and Mumford D 1999 IEEE Xplore 1 541 [5] Srivastava A, Lee A B, Simoncelli E P and Zhu S C 2003 Journal of Mathematical Imaging and Vision 18 17 [6] Munn B and Gong P L 2018 Phys. Rev. Lett. 121 058101 [7] Sinno Z, Caramanis C and Bovik A C 2018 IEEE Transactions on Image Processing. 27 3194 [8] Graham D J and Field D J 2008 Perception 37 1341 [9] Koch M, Denzler J and Redies C 2010 Plos One 5 8 [10] Foreman S, Giedt J, Meurice Y and Unmuth-Yockey J 2018 Phys. Rev. E 98 052129 [11] Crist B and Cohen J B 1979 Journal of Polymer Science Part B-Polymer Physics 17 1001 [12] Wilke W 1983 Colloid and Polymer Science 261 656 [13] Hindeleh A M and Hosemann R 1988 J. Phys. C-Solid State Phys. 21 4155 [14] Somashekar R and Somashekarappa H 1997 Journal of Applied Crystallography 30 147 [15] Haji-Akbari A, Engel M, Keys A S, Zheng X Y, Petschek R G, Palffy- Muhoray P and Glotzer S C 2009 Nature 462 773 [16] Keen D A and Goodwin A L 2015 Nature 521 303 [17] Carrasquilla J and Melko R G 2017 Nat. Phys. 13 431 [18] Oganov A R, Pickard C J, Zhu Q and Needs R J 2019 Nature Reviews Materials 4 331 [19] LeSar R 2014 Annual Review of Condensed Matter Physics 5 375 [20] Sólyom J 2007 Fundamentals of the Physics of Solids (Heidelberg: Springer Berlin) 13 [21] Böer K W and Pohl U W 2020 Semiconductor Physics (Cham: Springer) 59 [22] Jiao X C, Ye L and Ade H 2017 Advanced Energy Materials 7 1700084 [23] Rivnay J, Noriega R, Kline R J, Salleo A and Toney M F 2011 Phys. Rev. B 84 045203 [24] Keil P, Lützenkirchen-Hecht D, Novikov D V, Hahn U and Frahm R 2001 Nuclear Instruments and Methods in Physics Research Section a- Accelerators Spectrometers Detectors and Associated Equipment 467 275 [25] Liu F, Gu Y, Shen X B, Ferdous S, Wang H W and Russell T P 2013 Progress in Polymer Science 38 1990 [26] Fradler C, Rath T, Dunst S, Letofsky-Papst I, Saf R, Kunert B, Hofer F, Resel R and Trimmel G 2014 Solar Energy Materials and Solar Cells 124 117 [27] Hernández-Lemus E 2021 Frontiers in Physics 9 641859 [28] Lee J Y, Song K W, Ku J R, Sung T H and Moon D K 2011 Solar Energy Materials and Solar Cells 95 3377 [29] Bies A J, Boydston C R, Taylor R P and Sereno M E 2016 Journal of Environmental Psychology 47 155 [30] Knill D C, Field D and Kersten D 1990 J. Opt. Soc. Am. A 7 1113 [31] Adami C 2002 Bioessays 24 1085 [32] Stephens G J, Mora T, Tkacik G and Bialek W 2013 Phys. Rev. Lett. 110 018701 [33] Bolzani V D 2013 Planta Medica 79 10 [34] Crutchfield J P and Young K 1989 Phys. Rev. Lett. 63 105 [35] LopezRuiz R, Mancini H L and Calbet X 1995 Phys. Lett. A 209 321 [36] Cha S H 2007 International Journal of Mathematical Models and Methods in Applied Sciences 1 300-307 [37] Zanette D H 2018 Plos One 13 11 [38] Wolpert D H and Macready W 2007 Complexity 12 77 [39] Wolpert D H and Macready W G 1997 IEEE Transactions on Evolutionary Computation 1 67 [40] Bagrov A A, Iakovlev I A, Iliasov A A, KatsnelsonMI and Mazurenko V V 2020 Proc. Natl. Acad. Sci. USA 117 30241 [41] Aaronson S, Carroll S and Ouellette L 2014 arXiv: Statistical Mechanics CALT-68-2927 [42] Kolin D L and Wiseman P W 2007 Cell Biochemistry and Biophysics 49 141 [43] Robertson C and George S C 2012 Journal of Biomedical Optics 17 080801 [44] Rubin D M 2004 Journal of Sedimentary Research 74 160
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
