Unsupervised Machine Learning for Improved Delaunay Triangulation

Physical oceanography models rely heavily on grid discretization. It is known that unstructured grids perform well in dealing with boundary fitting problems in complex nearshore regions. However, it is time-consuming to find a set of unstructured grids in specific ocean areas, particularly in the case of land areas that are frequently changed by human construction. In this work, an attempt was made to use machine learning for the optimization of the unstructured triangular meshes formed with Delaunay triangulation in the global ocean field, so that the triangles in the triangular mesh were closer to equilateral triangles, the long, narrow triangles in the triangular mesh were reduced, and the mesh quality was improved. Specifically, we used Delaunay triangulation to generate the unstructured grid, and then developed a K-means clustering-based algorithm to optimize the unstructured grid. With the proposed method, unstructured meshes were generated and optimized for global oceans, small sea areas, and the South China Sea estuary to carry out data experiments. The results suggested that the proportion of triangles with a triangle shape factor greater than 0.7 amounted to 77.80%, 79.78%, and 79.78%, respectively, in the unstructured mesh. Meanwhile, the proportion of long, narrow triangles in the unstructured mesh was decreased to 8.99%, 3.46%, and 4.12%, respectively.

Informational Measure of Symmetry vs. Voronoi Entropy and Continuous Measure of Entropy of the Penrose Tiling. Part II of the “Voronoi Entropy vs. Continuous Measure of Symmetry of the Penrose Tiling”

The notion of the informational measure of symmetry is introduced according to: Hsym(G)=−∑i=1kP(Gi)lnP(Gi), where P(Gi) is the probability of appearance of the symmetry operation Gi within the given 2D pattern. Hsym(G) is interpreted as an averaged uncertainty in the presence of symmetry elements from the group G in the given pattern. The informational measure of symmetry of the “ideal” pattern built of identical equilateral triangles is established as Hsym(D3)= 1.792. The informational measure of symmetry of the random, completely disordered pattern is zero, Hsym=0. The informational measure of symmetry is calculated for the patterns generated by the P3 Penrose tessellation. The informational measure of symmetry does not correlate with either the Voronoi entropy of the studied patterns nor with the continuous measure of symmetry of the patterns. Quantification of the “ordering” in 2D patterns performed solely with the Voronoi entropy is misleading and erroneous.

Informational Measure of Symmetry vs. Voronoi Entropy and Continuous Measure of Entropy of the Penrose Tiling. Part II of the “Voronoi Entropy vs. Continuous Measure of Symmetry of the Penrose Tiling”.

The notion of the informational measure of symmetry is introduced according to: HsymG=-i=1kPGilnPGi, where PGi is the probability of appearance of the symmetry operation Gi within the given 2D pattern. HsymG is interpreted as an averaged uncertainty in the presence of symmetry elements from the group G in the given pattern. The informational measure of symmetry of the “ideal” pattern built of identical equilateral triangles is established as HsymD3=1.792. The informational measure of symmetry of the random, completely disordered pattern is zero, Hsym=0. Informational measure of symmetry is calculated for the patterns generated by the P3 Penrose tessellation. Informational measure of symmetry does not correlate neither with the Voronoi entropy of the studied patterns nor with the continuous measure of symmetry of the patterns.

Oncoplastic breast surgery combining partial mastectomy with resection of double equilateral triangular skin flaps

The treatment of early breast cancer using oncoplastic breast surgery (OBS) has been gradually increasing in popularity and is recognized for its efficacy in local control and excellent cosmetic results. We herein report a useful technique for obtaining symmetry of the breast shape for an early breast lesion located in an outer area, close to the nipple-areola, in a Japanese patient with ptotic, fatty breasts. We designed two equilateral triangles: one just upon the resected area and the other on the axilla. They were located on a straight line, with one top pointed to the cranial side and one to the caudal side. A crescent area around the areola was de-epithelialized in the 12 o’clock and 6 o’clock directions. Columnar-shaped breast tissue and an equilateral triangular skin flap and fatty tissue were removed together. To fill the defect, a skin-glandular flap was slid horizontally after suturing the inframammary line. Although an incision scar was formed on the breast and lateral chest wall in a Z-shape, this new technique was able to achieve not only cancer control but also excellent cosmetic results.

Algorithms for Delivery of Data by Drones in an Isolated Area Divided into Squares

Drones are frequently used for the delivery of materials or other goods, and to facilitate the capture and transmission of data. Moreover, drone networks have gained significant interest in a number of scenarios, such as in quarantined or isolated areas, following technical damage due to a disaster, or in non-urbanized areas without communication infrastructure. In this context, we propose a network of drones that are able to fly on a map covered by regular polygons, with a well-established mobility schedule, to carry and transfer data. Two means exist to equidistantly cover an area with points, namely, grouping the points into equilateral triangles or squares. In this study, a network of drones that fly in an aerial area divided into squares was proposed and investigated. This network was compared with the case in which the area is divided into equilateral triangles. The cost of the square drone network was lower than that of the triangular network with the same cell length, but the efficiency factors were better for the latter. Two situations related to increasing the drone autonomy using drone charging or battery changing stations were analyzed. This study proposed a Delay Tolerant Network (DTN) to optimize the transmission of data. Multiple simulation studies based on experimental flight tests were performed using the proposed algorithm versus five traditional DTN methods. A light Wi-Fi Arduino development board was used for the data transfer between drones and stations using delivery protocols. The efficiency of data transmission using single-copy and multiple-copy algorithms was analyzed. Simulation results showed a better performance of the proposed Time-Dependent Drone (TD-Drone) Dijkstra algorithm compared with the Epidemic, Spray and Wait, PRoPHET, MaxProp, and MaxDelivery routing protocols.

The effect of pore shape on the Poisson ratio of porous materials

A brief review is given of the effect of porosity on the Poisson ratio of a porous material. In contrast to elastic moduli such as K, G, or E, which always decrease with the addition of pores into a matrix, the Poisson ratio [Formula: see text] may increase, decrease, or remain the same, depending on the shape of the pores, and on the Poisson ratio of the matrix phase, [Formula: see text]. In general, for a given pore shape, there is a unique critical Poisson ratio, [Formula: see text], such that the addition of pores into the matrix will cause the Poisson ratio to increase if [Formula: see text], decrease if [Formula: see text], and remain unchanged if [Formula: see text]. The critical Poisson ratio for spherical pores is 0.2, for prolate spheroidal pores is close to 0.2, and tends toward zero for thin cracks. For two-dimensional materials, [Formula: see text] for circular pores, 0.306 for squares, 0.227 for equilateral triangles, and again approaches 0 for thin cracks. The presence of a “trapped” fluid in the pore space tends to cause [Formula: see text] to increase, and for the range of parameters that may occur in rocks or concrete, this increase is more pronounced for thin crack-like pores than for equi-dimensional pores. Measurements of the Poisson ratio therefore may allow insight into pore geometry and pore fluid. If the matrix phase is strongly auxetic, small amounts of porosity will generally not cause the Poisson ratio to become positive.

New Geometric Constants in Banach Spaces Related to the Inscribed Equilateral Triangles of Unit Balls

Geometric constant is one of the important tools to study geometric properties of Banach spaces. In this paper, we will introduce two new geometric constants JL(X) and YJ(X) in Banach spaces, which are symmetric and related to the side lengths of inscribed equilateral triangles of unit balls. The upper and lower bounds of JL(X) and YJ(X) as well as the values of JL(X) and YJ(X) for Hilbert spaces and some common Banach spaces will be calculated. In addition, some inequalities for JL(X), YJ(X) and some significant geometric constants will be presented. Furthermore, the sufficient conditions for uniformly non-square and normal structure, and the necessary conditions for uniformly non-square and uniformly convex will be established.

Analysis of reachable workspace for spatial 3-cable under-constrained suspended cable driven parallel robots

Workspace is an important reference for design of cable-driven parallel robots (CDPRs). Most current researches focus on calculating the workspace of redundant CDPRs. However, few literatures study the workspace of under-constrained CDPRs. In this paper, the static equilibrium reachable workspace (SERW) of spatial 3-cable under-constrained CDPRs is solved numerically since expressions describing workspace boundaries cannot be obtained in closed form. The analysis steps to solve the SERW are as follows. First, expressions which describe the SERW and its boundaries are proposed. Next, these expressions are instantiated through the novel anchor points model composed of linear equations, quadratic equations and limits of tension in cables. Then, based on the reformulated linearization technique (RLT), the constraint system is transformed into a system containing only linear equality constraints and linear inequality constraints. Finally, the framework of branch-and-prune (BP) algorithm is adopted to solve this system. The effect of the algorithm is verified by 2 examples. One is a special 3-cable CDPR in which the anchor points layouts both on the moving platform (MP) and on the base are equilateral triangles, followed by the method to extract the SERW boundary where cables do not interfere with each other. The other is a general case with randomly selected geometry arrangement. The presented method in this paper is universal for spatial 3-cable CDPRs with arbitrary geometry parameters.