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A foundational problem in kernel-based learning is how to design suitable kernels.
I will acknowledge systemic racism as a foundational problem in America and devote myself to support those who are working to change the system so that people of color can someday have the same benefits that my children have received as white Americans.
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The groundwork was a study of the four foundational problems in axiomatic formulations of pure logic.
They continue to pose foundational problems in semantics and set theory.
In (Wallace 2006) unitarily inequivalent representations are not considered a foundational problem for QFT, while in (Ruetsche 2003) and (Kronz and Lupher 2005) unitarily inequivalent representations are considered physically significant.
Projective geometry has its own foundational problem, akin to that of distance in Euclidean geometry, which concerns the concept of cross-ratio, and we need to follow the moves to create projective geometry as an independent subject, to define cross-ratio in this setting, and to resolve the epistemological issues that are raised (an achievement associated with Klein's Erlangen Programme).
Yet, when we come to the most challenging and foundational problem of building autonomous agents capable of performing scene understanding in unrestricted videos, there is still a lot to be done.
These are fail-safe points in discussions of artistic freedom, and they sidestep a foundational problem: the decision to make art without regard for the lives involved, and no matter the consequences.
Hill (2004, p. 627, 628) argues that the concept of superaddition "is quite out of place" in connection with cohesion, because Locke regards cohesion as a foundational problem, which thwarts our efforts to conceive of body.
The fourth foundational problem, the decision problem for predicate logic, was shown to have a negative solution in a short paper by Church in 1936 as a corollary to Gödel's incompleteness theorem.
The foundational problem pushes the question about cohesion into the corpuscles themselves.
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