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The different possible notions of convergence relate to how such a behavior can be characterized: two readily understood behaviors are that the sequence eventually takes a constant value, and that values in the sequence continue to change but can be described by an unchanging probability distribution.
Convergence can be defined in terms of sequences in first-countable spaces. Nets are a generalization of sequences that are useful in spaces which are not first countable. Filters further generalize the concept of convergence. In metric spaces, one can define Cauchy sequences. Cauchy nets and filters are generalizations to uniform spaces.
Technological convergence is the tendency for technologies that were originally unrelated to become more closely integrated and even unified as they develop and advance. For example, watches, telephones, television, computers, and social media platforms began as separate and mostly unrelated technologies, but have converged in many ways into an interrelated telecommunication, media, and ...
Described in an informal way, if converges to uniformly, then how quickly the functions approach is "uniform" throughout in the following sense: in order to guarantee that () differs from () by less than a chosen distance , we only need to make sure that is larger than or equal to a certain , which we can find without knowing the value of in ...
In formal mathematics, rates of convergence and orders of convergence are often described comparatively using asymptotic notation commonly called "big O notation," which can be used to encompass both of the prior conventions; this is an application of asymptotic analysis.
Convergence spaces generalize the notions of convergence that are found in point-set topology, including metric convergence and uniform convergence. Every topological space gives rise to a canonical convergence but there are convergences, known as non-topological convergences , that do not arise from any topological space. [ 1 ]
Whole protein structural convergence is not thought to occur but some convergence of pockets and secondary structural elements have been documented. Some secondary structure convergence occurs due to some residues favouring being in α-helix (helical propensity) and for hydrophobic patches or pocket to be formed at the ends of the parallel sheets.
Convergence research aims to solve complex problems employing transdisciplinarity. [1] While academic disciplines are useful for identifying and conveying coherent bodies of knowledge , some problems require collaboration among disciplines, including both enhanced understanding of scientific phenomena as well as resolving social issues .