Opening (morphology)In mathematical morphology, opening is the dilation of the erosion of a set A by a structuring element B: where and denote erosion and dilation, respectively. Together with closing, the opening serves in computer vision and as a basic workhorse of morphological noise removal. Opening removes small objects from the foreground (usually taken as the bright pixels) of an image, placing them in the background, while closing removes small holes in the foreground, changing small islands of background into foreground.
Comparative anatomyComparative anatomy is the study of similarities and differences in the anatomy of different species. It is closely related to evolutionary biology and phylogeny (the evolution of species). The science began in the classical era, continuing in the early modern period with work by Pierre Belon who noted the similarities of the skeletons of birds and humans. Comparative anatomy has provided evidence of common descent, and has assisted in the classification of animals.
Zariski topologyIn algebraic geometry and commutative algebra, the Zariski topology is a topology which is primarily defined by its closed sets. It is very different from topologies which are commonly used in real or complex analysis; in particular, it is not Hausdorff. This topology was introduced primarily by Oscar Zariski and later generalized for making the set of prime ideals of a commutative ring (called the spectrum of the ring) a topological space.
Topological indexIn the fields of chemical graph theory, molecular topology, and mathematical chemistry, a topological index, also known as a connectivity index, is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. Topological indices are used for example in the development of quantitative structure-activity relationships (QSARs) in which the biological activity or other properties of molecules are correlated with their chemical structure.
Dilation (morphology)Dilation (usually represented by ⊕) is one of the basic operations in mathematical morphology. Originally developed for , it has been expanded first to grayscale images, and then to complete lattices. The dilation operation usually uses a structuring element for probing and expanding the shapes contained in the input image. In binary morphology, dilation is a shift-invariant (translation invariant) operator, equivalent to Minkowski addition. A binary image is viewed in mathematical morphology as a subset of a Euclidean space Rd or the integer grid Zd, for some dimension d.
Class (biology)In biological classification, class (classis) is a taxonomic rank, as well as a taxonomic unit, a taxon, in that rank. It is a group of related taxonomic orders. Other well-known ranks in descending order of size are life, domain, kingdom, phylum, order, family, genus, and species, with class ranking between phylum and order. The class as a distinct rank of biological classification having its own distinctive name (and not just called a top-level genus (genus summum)) was first introduced by the French botanist Joseph Pitton de Tournefort in his classification of plants that appeared in his Eléments de botanique, 1694.
Ventricular zoneIn vertebrates, the ventricular zone (VZ) is a transient embryonic layer of tissue containing neural stem cells, principally radial glial cells, of the central nervous system (CNS). The VZ is so named because it lines the ventricular system, which contains cerebrospinal fluid (CSF). The embryonic ventricular system contains growth factors and other nutrients needed for the proper function of neural stem cells.
Islamic geometric patternsIslamic geometric patterns are one of the major forms of Islamic ornament, which tends to avoid using figurative images, as it is forbidden to create a representation of an important Islamic figure according to many holy scriptures. The geometric designs in Islamic art are often built on combinations of repeated squares and circles, which may be overlapped and interlaced, as can arabesques (with which they are often combined), to form intricate and complex patterns, including a wide variety of tessellations.
Golgi's methodGolgi's method is a silver staining technique that is used to visualize nervous tissue under light microscopy. The method was discovered by Camillo Golgi, an Italian physician and scientist, who published the first picture made with the technique in 1873. It was initially named the black reaction (la reazione nera) by Golgi, but it became better known as the Golgi stain or later, Golgi method. Golgi staining was used by Spanish neuroanatomist Santiago Ramón y Cajal (1852–1934) to discover a number of novel facts about the organization of the nervous system, inspiring the birth of the neuron doctrine.
Conjugacy classIn mathematics, especially group theory, two elements and of a group are conjugate if there is an element in the group such that This is an equivalence relation whose equivalence classes are called conjugacy classes. In other words, each conjugacy class is closed under for all elements in the group. Members of the same conjugacy class cannot be distinguished by using only the group structure, and therefore share many properties. The study of conjugacy classes of non-abelian groups is fundamental for the study of their structure.
