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5 Jun 2020: where the infimum is taken over all jointly distributed random variables (X,Y ) such that X hasdistribution P and Eρ(X,Y ) D. ... H(W‖P1Q) λ1EW(ρ) λ2EQ[log M(Y )] ΛP1,Q(λ). Taking the supremum over all λ R2 and recalling (23) this becomes.

22 Oct 2020: The model category we work inwill be the category of simplicial algebras over a ring. ... Furthermore, given a sequence:. Fi> E. p> B. where E is a Serre fibration and i is the inclusion of the fibre F over the base pointB, then there is a

5 Jun 2020: codebook; equivalently, thiscan be thought of as the rate loss of the straightforward schemewhich uses a mismatched codebook without entropy coding.b) The rate loss due to quantizer mismatch, over the ... bits/symbol (5). where the expectation is taken

5 Jun 2020: Part (ii) follows from (i) on multiplying each side of (19) by αeαT , andintegrating over T R. ... Dκv = κ[κRκv v] δκ. δ κv. κ. δ κb0v. This gives (31) on choosing the worst-case over κ 1:.

5 Jun 2020: b) The rate loss due to quantizer mis-match, over the optimal rate-distortion function: We will derive a universal upper bound for this rate. ... where the expectation is taken over both the message Xn1 and the random codebook Cn.

6 May 2020: ii) For all (a,b) , (a′,b′) R, we have |dA (a,a′) dB (b,b′)| ε. ... We define. Dh(A,B) = infA,BX. DH(A,B),. where the infimum is taken over all compact metric spaces X containing isometric copiesof A and B, and DH is the

5 Jun 2020: and the infimum is taken over all joint distributions onsuch that the -marginal of is and. ... where the infimum is over all stationary probabilitymeasures on such that the -marginal of isand.

5 Jun 2020: Theorem 8: Averaging uniformly over all binning com-pressors f: X {1, 2,. ... 1d ). (141). α(d) = sup{|P(B A) P(B)P( A)|} (142)where the sup is over A F0 and B Fd.

3 Jun 2020: The problem is to minimize the sparsity over all cuts. This is NP-hard. ... over all cuts with nonzero demand, where dS is the cut semimetric (c.f.

5 Jun 2020: support; or (b) Qhas tails heavy enough so that, for some ρ,β > 0 and N0 1, we have, Q(x) ρx. ... As can be seen there, conditions (a) and (b) areintroduced purely for technical reasons, and can probably be significantly relaxed; see Section 7 for