It is widely believed that to efficiently represent an otherwise smooth object with discontinuities along edges, one must use an adaptive representation that in some sense ‘tracks ’ the shape of the discontinuity set. This folk-belief — some would say folk-theorem — is incorrect. At the very

— Compressed sensing, tight frames, Grass-mannian frames

In order to build autonomous robots that can carry out useful work in unstructured environments new approaches have been developed to building intelligent systems. The relationship to traditional academic robotics and traditional artificial intelligence is examined. In the new approaches a tight

We introduce a new variant of tight closure associated to any fixed ideal a, which we call a-tight closure, and study various properties thereof. In our theory, the annihilator ideal τ(a) of all a-tight closure relations, which is a generalization of the test ideal in the usual tight closure

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this relationship, frame-theoretical analogues of various quantum-mechanical concepts and results are developed. The analogue of a least-squares quantum measurement is a tight frame that is closest in a least-squares sense to a given set of vectors. The least-squares tight frame is found for both the case in which

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are closest to being tight (in the sense of minimizing potential enerty) for any sequence {an} ∞ n=1. 1.

is the number of nodes in the network, and α is the edge expansion of the network. The time bound is tight in the sense that for any graph with edge expansion α, and for any value ∆, there exists an initial distribution of tokens with imbalance ∆ for which the time to reduce the imbalance to even ∆/2

extraneous activation and deactivation clusters visible in the GLM analysis to reveal brain regions that constitute independent and tightly coupled networks. Fig. 3. Granger causality analysis (GCA) of the six key nodes of the Salience (blue nodes), Central-Executive (green nodes) and Default-Mode (yellow