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The Hofstadter butterfly is a quantum fractal with a highly complex nested set of gaps, where each gap represents a quantum Hall state whose quantized conductivity is characterized by topological invariants known as the Chern numbers.
They developed a multi-item conceptual model of service quality based on a set of gaps so that the fifth gap (the gap between expected service and perceived service) is a function of the gaps related to the service provider side.
The outcome of this evaluation highlights a set of gaps as they relate to the coverage and applicability of current methods for sociotechnical systems thinking and safety.
The set of network gaps was compared to the set of gaps in the original model to determine if any gaps were eliminated.
The outcomes from the evaluation highlight a set of gaps relating to the coverage and applicability of current methods for sociotechnical systems theory and safety.
The outcomes from the evaluation highlight a set of gaps relating to the coverage and applicability of current methods for STS and safety (e.g. coverage of external influences on system functioning; method usability).
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The drag varies with the two gap ratios; it has the minimum value at a certain set of gap ratios for each Reynolds number.
A set of gap equations was derived by symmetrizing the self energy, Σ ( i ω n ) ≈ iℏ ω n ( 1 − Z n A ) + Δ ̄ n A 0 0 iℏ ω n ( 1 − Z n B ) − Δ ̄ n B. The local approximation used here is a good starting point because the modulated potential Δ is large, and electrons are well localized.
We found that this limited set of gap insertion effectively helps to capture composite motifs with multiple functional elements.
It is therefore possible that the performance of PSI-BLAST with a better set of gap opening and extension penalties would more closely match the performance of HMMs.
It turned out that at least for one scoring matrix and one set of gap-cost parameters, the distribution deviates from the Gumbel form in the biologically relevant rare-event tail, where simple sampling methods fail.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com