Cycle basisIn graph theory, a branch of mathematics, a cycle basis of an undirected graph is a set of simple cycles that forms a basis of the cycle space of the graph. That is, it is a minimal set of cycles that allows every even-degree subgraph to be expressed as a symmetric difference of basis cycles. A fundamental cycle basis may be formed from any spanning tree or spanning forest of the given graph, by selecting the cycles formed by the combination of a path in the tree and a single edge outside the tree.
M62 motorwayThe M62 is a west–east trans-Pennine motorway in Northern England, connecting Liverpool and Hull via Manchester, Bradford, Leeds and Wakefield; of the route is shared with the M60 orbital motorway around Manchester. The road is part of the unsigned Euroroutes E20 (Shannon to Saint Petersburg) and E22 (Holyhead to Ishim). The motorway, which was first proposed in the 1930s, and conceived as two separate routes, was opened in stages between 1971 and 1976, with construction beginning at Pole Moor near Huddersfield and finishing at that time in Tarbock on the outskirts of Liverpool.
Metropolitan areaA metropolitan area or metro is a region consisting of a densely populated urban agglomeration and its surrounding territories sharing industries, commercial areas, transport network, infrastructures and housing. A metro area usually comprises multiple principal cities, jurisdictions and municipalities: neighborhoods, townships, boroughs, cities, towns, exurbs, suburbs, counties, districts, as well as even states and nations like the euro districts.
Longest path problemIn graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph. A path is called simple if it does not have any repeated vertices; the length of a path may either be measured by its number of edges, or (in weighted graphs) by the sum of the weights of its edges. In contrast to the shortest path problem, which can be solved in polynomial time in graphs without negative-weight cycles, the longest path problem is NP-hard and the decision version of the problem, which asks whether a path exists of at least some given length, is NP-complete.
Urban historyUrban history is a field of history that examines the historical nature of cities and towns, and the process of urbanization. The approach is often multidisciplinary, crossing boundaries into fields like social history, architectural history, urban sociology, urban geography, business history, and archaeology. Urbanization and industrialization were popular themes for 20th-century historians, often tied to an implicit model of modernization, or the transformation of rural traditional societies.
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.
MycetozoaMycetozoa is a polyphyletic grouping of slime molds. It was originally thought to be a monophyletic clade, but recently it was discovered that protostelia are a polyphyletic group within Conosa. It can be divided into dictyostelid, myxogastrid, and protostelid groups. The mycetozoan groups all fit into the unikont supergroup Amoebozoa, whereas most other slime molds fit into various bikont groups (fonticulids are opisthokonts). The dictyostelids are used as examples of cell communication and differentiation, and may provide insights into how multicellular organisms develop.
Urban sociologyUrban sociology is the sociological study of cities and urban life. One of the field’s oldest sub-disciplines, urban sociology studies and examines the social, historical, political, cultural, economic, and environmental forces that have shaped urban environments. Like most areas of sociology, urban sociologists use statistical analysis, observation, archival research, U.S.
Measure (mathematics)In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events. These seemingly distinct concepts have many similarities and can often be treated together in a single mathematical context. Measures are foundational in probability theory, integration theory, and can be generalized to assume negative values, as with electrical charge.
Convergence of measuresIn mathematics, more specifically measure theory, there are various notions of the convergence of measures. For an intuitive general sense of what is meant by convergence of measures, consider a sequence of measures μn on a space, sharing a common collection of measurable sets. Such a sequence might represent an attempt to construct 'better and better' approximations to a desired measure μ that is difficult to obtain directly.
AmoebozoaAmoebozoa is a major taxonomic group containing about 2,400 described species of amoeboid protists, often possessing blunt, fingerlike, lobose pseudopods and tubular mitochondrial cristae. In traditional classification schemes, Amoebozoa is usually ranked as a phylum within either the kingdom Protista or the kingdom Protozoa. In the classification favored by the International Society of Protistologists, it is retained as an unranked "supergroup" within Eukaryota. Molecular genetic analysis supports Amoebozoa as a monophyletic clade.
