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Reliable Computation In The Presence Of Noise, Nicholas Pippenger
Reliable Computation In The Presence Of Noise, Nicholas Pippenger
All HMC Faculty Publications and Research
This talk concerns computation by systems whose components exhibit noise (that is, errors committed at random according to certain probabilistic laws). If we aspire to construct a theory of computation in the presence of noise, we must possess at the outset a satisfactory theory of computation in the absence of noise.
A theory that has received considerable attention in this context is that of the computation of Boolean functions by networks (with perhaps the strongest competition coming from the theory of cellular automata; see [G] and [GR]). The theory of computation by networks associates with any two sets Q and …
A Prime Strongly Positive Amphicheiral Knot Which Is Not Slice, Erica Flapan
A Prime Strongly Positive Amphicheiral Knot Which Is Not Slice, Erica Flapan
Pomona Faculty Publications and Research
We begin by giving several definitions. A knot K in S3 is said to be amphicheiral if there is an orientation-reversing diffeomorphism h of S3 which leaves K setwise invariant. Suppose, in addition, that K is given an orientation. ThenK is said to be positive amphicheiral if h preserves the orientation of K. If, in addition, the diffeomorphism h is an involution then K is strongly positive amphicheiral. Finally, we say a knot is slice if it bounds a smooth disc in B4. In this note we shall give a smooth example of …