The Delboeuf illusion occurs when two circles (test figures) of equal radius are placed side by side and surrounded by concentric circles (inducers) of varying radii, resulting in the test figure being misestimated depending on the size of the surrounding inducer. This study conducted three experiments to explore the impact of shape and the contour attraction and parallel attraction on the Delboeuf illusion for different shapes. In Experiment 1 (n = 64), the test figures remained as circles while the inducers varied in shape. Experiment 2 (n = 64) involved simultaneous changes in the shape of both the test figures and the inducers. Experiment 3 (n = 64) replicated Experiment 2, with the exception that the areas of the inducers were equal and the distances between the inducers and the test figures were also equal. We conclude that the shape of the inducer and the test figure had an impact on the visual size perception, and in the magnitude of the Delboeuf illusion, varied depending on contour attraction. Configurations with circles or shapes resembling circles exhibit contour attraction, while configurations with shapes possessing longer parallel lines shift toward parallel attraction, both attractions enhance the perceived magnitude of the Delboeuf illusion.

Vector analysis is used to determine the quantitative error in angle calibration using autoeollimators. This error is caused by tilt in the mount upon which the artifact is placed. For tilt angles that are less than 1°, the error can be simplified to be the product of a eoeffieient and three terms. The three terms are: (1) the square of the tilt, (2) the sine of the artifact\'s nominal angle, and (3) the eosine of the artifact\'s nominal angle plus two times the artifact\'s position angle. It is shown that the error can be eliminated by placing the artifact at designated periodic positions.

Fingerprints are unique patterns used as biometric keys because they allow an individual to be unambiguously identified, making their application in the forensic field a common practice. The design of a system that can match the details of different images is still an open problem, especially when applied to large databases or, to real-time applications in forensic scenarios using mobile devices. Fingerprints collected at a crime scene are often manually processed to find those that are relevant to solving the crime. This work proposes an efficient methodology that can be applied in real time to reduce the manual work in crime scene investigations that consumes time and human resources. The proposed methodology includes four steps: (i) image pre-processing using oriented Gabor filters; (ii) the extraction of minutiae using a variant of the Crossing Numbers method which include a novel ROI definition through convex hull and erosion followed by replacing two or more very close minutiae with an average minutiae; (iii) the creation of a model that represents each minutia through the characteristics of a set of polygons including neighboring minutiae; (iv) the individual search of a match for each minutia in different images using metrics on the absolute and relative errors. While in the literature most methodologies look to validate the entire fingerprint model, connecting the minutiae or using minutiae triplets, we validate each minutia individually using n-vertex polygons whose vertices are neighbor minutiae that surround the reference. Our method also reveals robustness against false minutiae since several polygons are used to represent the same minutia, there is a possibility that even if there are false minutia, the true polygon is present and identified; in addition, our method is immune to rotations and translations. The results show that the proposed methodology can be applied in real time in standard hardware implementation, with images of arbitrary orientations.

Anion templated assembly of supramolecular systems has been extensively explored in previous reports, whereas anions serve only as an auxiliary and spectator role. With the development of anion coordination chemistry in recent years, anion coordination-driven assembly (ACDA) has emerged as a new strategy for the construction of supramolecular self-assemblies. Anions are proved to exist as the main actors in the construction of supramolecular architectures, i. e., serve as the coordination center. This Review will focus on the recent progress in anion-coordination-driven assembly of discrete supramolecular architectures, such as helicates, polyhedrons and polygons, and the various applications of \'aniono\'-systems. At the end of this Review, we highlight current challenges and opportunities for future research of anion-coordination-driven self-assembly.

The grain boundary is an intrinsic defect within mono- and multi-layer polygonal graphene islands during the chemical vapor deposition growth process. It greatly influences their mechanical and electronic properties. However, the precise characterization and formation mechanism of grain boundaries still remain unclear. In this work, H2 etching experiments show that a polygonal etched hole originates from the natural location of a grain boundary beyond the nucleation site in polygonal monolayer graphene. Furthermore, colorful Raman mapping provides a visualized method to explore the distribution of grain boundaries in polygonal bilayer graphene. Therefore, a deep understanding of the growth kinetics of mono- and bi-layer polygonal graphene was obtained through etching engineering combined with Raman spectroscopy.

The Salzburg Database is a repository of polygonal areas of various classes and sizes, with and without holes. Positive weights are assigned to all edges of all polygons. We introduce this collection and describe the generators that produced its polygons. The source codes for all generators as well as the polygons generated are publicly available.

A synthetic strategy to construct large geodesic structures of phenine (1,3,5-trisubstituted benzene) was devised. In this strategy, five pentagons were assembled on an omphalos pentagon, and bridging peripheral pentagons furnished five additional hexagons. Thirty phenine units were synthetically assembled to afford a large C220 H180 molecule with a phenine framework isoreticular to a hemispherical, bisected segment of C60 . Although a hemispherical structure of the phenine framework was suggested by solution-phase NMR spectra, crystallographic analysis revealed an oval-like deformation of the molecular shape. In-depth structural analyses, including theoretical calculations, showed that structural fluctuations observed as variations in the biaryl torsion angles allowed structural deformations and, at the same time, that the dynamic fluctuations resulted in the spectroscopic observation of a hemisphere as a time-averaged structure.