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ORAM 8 List of Abstracts

The boundary rigidity problem consist of recovering a Riemannian metric in a domain, up to an isometry, from the distance between boundary points. We show that in dimensions three and higher, knowing the distance near a fixed strictly convex boundary point allows us to reconstruct the metric inside the domain near that point, and that this reconstruction is stable. We also prove semi-global and...

the 8 the najaf division in valfajr 8 operation, adrance in depth

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Lecture 8 : More Results on List Decoding

Proof. Let C be a binary code with minimum relative distance δ. Suppose x ∈ {0, 1} is arbitrary and c1, c2, . . . , cL ∈ C are codewords such that for all i, ∆ (x, ci) < ρn. Since each ci is a codeword, we have that ∆ (ci, cj) ≥ δn for all i 6= j. Let Φ : {0, 1} → Rn be the map sending 0 to 1 and 1 to −1. Define u = Φ (x), and, for all i, define vi = Φ (ci). Let ū = 1 √ n u denote the normaliza...