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- W2042317009 abstract "Using fractal self-similarity and functional-expectation relations, the classical theory of box integrals – being expectations on unit hypercubes – is extended to a class of fractal “string-generated Cantor sets” (SCSs) embedded in unit hypercubes of arbitrary dimension. Motivated by laboratory studies on the distribution of brain synapses, these SCSs were designed for dimensional freedom – a suitable choice of generating string allows for fine-tuning the fractal dimension of the corresponding set. We also establish closed forms for certain statistical moments on SCSs, develop a precision algorithm for high embedding dimensions, and report various numerical results. The underlying numerical quadrature issues are in themselves quite challenging." @default.
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- W2042317009 date "2013-09-01" @default.
- W2042317009 modified "2023-09-27" @default.
- W2042317009 title "Expectations on fractal sets" @default.
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- W2042317009 doi "https://doi.org/10.1016/j.amc.2013.06.078" @default.
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