Characterization of Self-Assembled 2D Patterns with Voronoi Entropy

Bormashenko, Edward; Frenkel, Mark; Vilk, Alla; Fedorets, Alexander A.; Aktaev, Nurken E.; Dombrovsky, Leonid A.; Nosonovsky, Michael

doi:10.20944/preprints201811.0535.v1

2018

DOI: 10.20944/preprints201811.0535.v1

|View full text |Cite

Preprint

Characterization of Self-Assembled 2D Patterns with Voronoi Entropy

Edward Bormashenko¹,

Mark Frenkel²,

Alla Vilk³

et al.

Abstract: The Voronoi entropy is a mathematical tool for quantitative characterization of the orderliness of points distributed on a surface. The tool is useful to study various surface self-assembly processes. We provide the historical background, from Kepler and Descartes to our days, and discuss topological properties of the Voronoi tessellation, upon which the entropy concept is based, and its scaling properties, known as the Lewis and Aboav-Weaire laws. The Voronoi entropy has been successfully applied to recently … Show more

Help me understand this report

View published versions

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2019

2023

Publication Types

Select...

Article5

Relationship

Self Cite0

Independent5

Authors

Journals

Cited by 20 publications

References 46 publications

(80 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

Shannon (Information) Measures of Symmetry for 1D and 2D Shapes and Patterns

et al. 2022

View full text Add to dashboard Cite

In this paper, informational (Shannon) measures of symmetry are introduced and analyzed for patterns built of 1D and 2D shapes. The informational measure of symmetry Hsym(G) characterizes the averaged uncertainty in the presence of symmetry elements from group G in a given pattern, whereas the Shannon-like measure of symmetry Ωsym(G) quantifies the averaged uncertainty of the appearance of shapes possessing a total of n elements of symmetry belonging to group G in a given pattern. Hsym(G1)=Ωsym(G1)=0 for the patterns built of irregular, non-symmetric shapes, where G1 is the identity element of the symmetry group. Both informational measures of symmetry are intensive parameters of the pattern and do not depend on the number of shapes, their size, and the entire area of the pattern. They are also insensitive to the long-range order (translational symmetry) inherent for the pattern. Additionally, informational measures of symmetry of fractal patterns are addressed, the mixed patterns including curves and shapes are considered, the time evolution of Shannon measures of symmetry are examined, the close-packed and dispersed 2D patterns are analyzed, and an application of the suggested measures of symmetry for the analysis of the chemical reaction is demonstrated.

show abstract

Shannon (Information) Measures of Symmetry for 1D and 2D Shapes and Patterns

et al. 2022

View full text Add to dashboard Cite

show abstract

Structure-Based Analysis of Protein Cluster Size for Super-Resolution Microscopy in the Nervous System

2022

View full text Add to dashboard Cite

To overcome the diffraction limit and resolve target structures in greater detail, far-field super-resolution techniques such as stochastic optical reconstruction microscopy (STORM) have been developed, and different STORM algorithms have been developed to deal with the various problems that arise. In particular, the effect of the local structure is an important issue. For objects with closely correlated distributions, simple Gaussian-based localization algorithms often used in STORM imaging misinterpret overlapping point spread functions (PSFs) as one, which limits the ability of super-resolution imaging to resolve nanoscale local structures and leads to inaccurate length measurements. The STORM super-resolution images of biological specimens from the cluster-forming proteins in the nervous system were reconstructed for localization-based analysis. Generally, the localization of each fluorophore was determined by two-dimensional Gaussian function fitting. Further, the physical shape of the cluster structure information was incorporated into the size parameter of the localization structure analysis in order to generate structure-based fitting algorithms. In the present study, we proposed a novel, structure-based, super-resolution image analysis method: structure-based analysis (SBA), which combines a structural function and a super-resolution localization algorithm. Using SBA, we estimated the size of fluorescent beads, inclusion proteins, and subtle synaptic structures in both wide-field and STORM images. The results show that SBA has a comparable and often superior performance to the commonly used full width at half maximum (FWHM) parameter. We demonstrated that SBA is able to estimate molecular cluster sizes in far-field super-resolution STORM images, and that SBA was comparable and often superior to FWHM. We also certified that SBA provides size estimations that corroborate previously published electron microscopy data.

show abstract

Fibonacci Sequences, Symmetry and Order in Biological Patterns, Their Sources, Information Origin and the Landauer Principle

Bormashenko

2022

Biophysica

View full text Add to dashboard Cite

Physical roots, exemplifications and consequences of periodic and aperiodic ordering (represented by Fibonacci series) in biological systems are discussed. The physical and biological roots and role of symmetry and asymmetry appearing in biological patterns are addressed. A generalization of the Curie–Neumann principle as applied to biological objects is presented, briefly summarized as: “asymmetry is what creates a biological phenomenon”. The “top-down” and “bottom-up” approaches to the explanation of symmetry in organisms are presented and discussed in detail. The “top-down” approach implies that the symmetry of the biological structure follows the symmetry of the media in which this structure is functioning; the “bottom-up” approach, in turn, accepts that the symmetry of biological structures emerges from the symmetry of molecules constituting the structure. A diversity of mathematical measures applicable for quantification of order in biological patterns is introduced. The continuous, Shannon and Voronoi measures of symmetry/ordering and their application to biological objects are addressed. The fine structure of the notion of “order” is discussed. Informational/algorithmic roots of order inherent in the biological systems are considered. Ordered/symmetrical patterns provide an economy of biological information, necessary for the algorithmic description of a biological entity. The application of the Landauer principle bridging physics and theory of information to the biological systems is discussed.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

hi@scite.ai

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Characterization of Self-Assembled 2D Patterns with Voronoi Entropy

Cited by 20 publications

References 46 publications

Shannon (Information) Measures of Symmetry for 1D and 2D Shapes and Patterns

Shannon (Information) Measures of Symmetry for 1D and 2D Shapes and Patterns

Structure-Based Analysis of Protein Cluster Size for Super-Resolution Microscopy in the Nervous System

Fibonacci Sequences, Symmetry and Order in Biological Patterns, Their Sources, Information Origin and the Landauer Principle

Contact Info

Product

Resources

About