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Interestingly, the optimization formulation also reveals that maximally compact sequences are derived from Mathieu's harmonic cosine function of order zero.
In particular, we introduce an effective plane merging procedure with a global error guarantee in order to maximally compact the resulting models.
We show that, while extended forms of ligands are indeed common in ligand protein structures, instances of ligands in almost maximally compact arrangements can also be found.
We found that a common practice of restricting protein structure space to maximally compact lattice conformations results in (i.e., "designs in") many encodable (designable) structures that are not otherwise encodable in the corresponding unrestrained structure space.
For a chosen frequency variance, we formulate the search for "maximally compact sequences" as an exactly and efficiently solved convex optimization problem, thus providing a sharp uncertainty principle for sequences.
In general, restricting conformations to be maximally compact leads to larger changes in the model genotype-phenotype mapping than a moderate shifting of reference state energy of the model potential function to allow for more specific encoding via the "designing out" effects of repulsive interactions.
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A maximally compacted tree is obtained, generating smaller and more useful diagrams.
A three-step process is combined with an edge-lit hologram display system to provide a self-contained, maximally-compact 3-D holographic display.
"Our framework is a result of the analysis and synthesis of research on learning sciences, views from futurists and economists, standards around the world, and needs of employers and societies -- all organized to be maximally comprehensive, compact, appropriate, and globally relevant".
In particular such an embedding exists for the C∗-algebra of a second countable amenable locally compact maximally almost periodic group.
The paper addresses the design of compact and maximally permissive decentralized supervisors for Petri nets, based on generalized mutual exclusion constraints.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com