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Polygon triangulation. In computational geometry, polygon triangulation is the partition of a polygonal area (simple polygon) P into a set of triangles, [1] i.e., finding a set of triangles with pairwise non-intersecting interiors whose union is P. Triangulations may be viewed as special cases of planar straight-line graphs.
For a hole-free polygon with vertices, a triangulation can be calculated in time (). For a polygon with holes , there is a lower bound of Ω ( n log n ) {\displaystyle \Omega (n\log n)} . A related problem is partitioning to triangles with a minimal total edge length, also called minimum-weight triangulation .
Secondary structure is the set of interactions between bases, i.e., which parts of strands are bound to each other. In DNA double helix, the two strands of DNA are held together by hydrogen bonds. The nucleotides on one strand base pairs with the nucleotide on the other strand. The secondary structure is responsible for the shape that the ...
The two base-pair complementary chains of the DNA molecule allow replication of the genetic instructions. The "specific pairing" is a key feature of the Watson and Crick model of DNA, the pairing of nucleotide subunits. [5] In DNA, the amount of guanine is equal to cytosine and the amount of adenine is equal to thymine. The A:T and C:G pairs ...
The DNA "tile" structure in this image consists of four branched junctions oriented at 90° angles. Each tile consists of nine DNA oligonucleotides as shown; such tiles serve as the primary "building block" for the assembly of the DNA nanogrids shown in the AFM micrograph. Quadruplex DNA may be involved in certain cancers.
A simple polygon may be easily cut into monotone polygons in O(n log n) time. However, since a triangle is a monotone polygon, polygon triangulation is in fact cutting a polygon into monotone ones, and it may be performed for simple polygons in O(n) time with a complex algorithm. [6]
Nucleic acids consist of a chain of linked units called nucleotides. Each nucleotide consists of three subunits: a phosphate group and a sugar (ribose in the case of RNA, deoxyribose in DNA) make up the backbone of the nucleic acid strand, and attached to the sugar is one of a set of nucleobases.
The double-helix model of DNA structure was first published in the journal Nature by James Watson and Francis Crick in 1953, [6] (X,Y,Z coordinates in 1954 [7]) based on the work of Rosalind Franklin and her student Raymond Gosling, who took the crucial X-ray diffraction image of DNA labeled as "Photo 51", [8] [9] and Maurice Wilkins, Alexander Stokes, and Herbert Wilson, [10] and base-pairing ...