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Engineers can calculate the maximum stiffness of a given material in a given shape; for instance, they know how to give airplane wings their maximum strength using a given alloy.
However, current efforts on modeling porous structures in a given shape either consider uniform pore distributions, or regard the physical constraints as an underlying scalar field, both generating pores in an isotropic manner.
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Among the transitional Hamiltonian a specially interesting case occurs when it describes a critical point in the transition from a given shape to another.
Each dot provides a small amount of information about the location of the shape boundary and one must combine the information from many dots in order to identify a given shape.
These results are consistent with the concept that the rate of decline in hit rate for a given shape depends on the degree to which neighboring dots are redundant.
In this chapter we study the problem of finding tile systems of minimum size that assemble a given shape in the Tile Assembly Model, defined by Rothemund and Winfree [Paul W.K. Rothemund, Erik Winfree, The program-size complexity of self-assembled squares (extended abstract), in: Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing , ACM Press 2000, pp. 459 468].
This review perhaps poses more questions than answers, and sets the stage for future investigations by highlighting, for instance, the question of possible benefits of a given shape in a particular environment.
As described in Methods, each subject saw a given shape only once, and provided a response that was classified as recognition (1) or no recognition (0).
For a given shape, the order in which pairs were displayed was chosen at random.
He was a writer who, as one Times critic noted, in 1963, "has given shape to the fantasies of millions of children — an awful responsibility".
In "The Art of Living" (University of California, 1998), he argued that the philosophical quest for a worthwhile life does not involve the application of universal principles; each life is given shape in a particular and idiosyncratic manner.
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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