The present disclosure provides systems and methods for path analysis using a homotopy method, for the purpose of computing. In particular, the present disclosure unifies path representations with the standard construction and formalizes synthetics and semantics of the paths. In this way, the present disclosure enables efficient representation and manipulation of paths in well forms of all dimensions, including in higher dimensions. This is critical and significant to computing, for example, when path representations need to be transformed to each other during cloud resource and service migrations. Keywords associated with the present disclosure include: path analysis; homotopy; homotopy path analytics; path constructions; path geometry; path representation; higher dimensions; cloud resource; service migration; cloud computing; big data.
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Liu, Lei, "A Homotopy Method of Path Analysis for the Purpose of Computing", Technical Disclosure Commons, (January 29, 2019)