Theorem 3 definition

Theorem 3. AdvPA' (t, qex, qs) ≤ (qs + 2qex) ∗ SuccDDH 2k q +qexqs (t′)+ |P| ∗ SuccΣ(t′)+ s

Theorem 3. The new upper bound represents a strict improvement over the previously best known upper bound for the case of u = m = 2: there exists an example for which the new upper bound is strictly smaller than supp(x1) infZ→Z→X1X2 I(X1; X2|Z) which in turn is always less than or equal to infZ→Z→X1X2 supp(x1) I(X1; X2|Z).

Theorem 3. For MSP k, the optimal BS switching on/off strategies are as follows: turn off if V (a)(on, on) < V (a)(off, on) + Ek and its QoS commitment is honored (case Ak); turn on otherwise (i.e., either turning off leading to QoS commitment violation (case Bk) or V (a)(on, on) > V (a)(off, on) + Ek (case Ck)). The proof is straightforward by recalling the utility defini- tion above. The NEs for the BS switching on/off game are then stated 1, and reward rate of MSP 2 vs. β1 and β2, respectively (lower bounds in S2).

Examples of Theorem 3 in a sentence

• Assumption 2(b) implies that zt satisfies a functional central limit theorem (Brown, 1971, Theorem 3), since the higher moment assumption implies a conditional Lindeberg condition.

• Note that Theorem 3 implies the Liveness property of our Lattice Agreement specification.

• Notice, however, that for this this result to hold Assumption 1 must be satisfied, since this is needed to ensure that the restricted PML estimate,˜θ, from (1) is consistent, as demonstrated in Theorem 3.

• It deals mostly with the protocol aspects; indeed, our cryptographic proof for Theorem 3, conducted with EasyCrypt, concerns less than 200 lines of F#.

• Given that, Theorem 5 is a straightforward consequence of the soundness of the model (Theorem 3).

• Theorem 3 shows that, at equilibrium each supplier charges their execution costs only, and adds a premium to their reservation costs.

• We now show that it is sufficient to check that a modification is a subflow-preserving extension to guarantee composition back to an effectively-acyclic composite graph: Theorem 3.

• Detailed proofs will come in the sections that follow.► Theorem 3.

• Nevertheless, we believe that, when the assumptions are adjusted to reflect this change, the results of the paper will go through with the “max” mechanism (the mediator announcing whether the maximum of the cost reports exceeds a certain threshold) replacing the “min” mechanism in Theorem 3.

• Most importantly, Theorem 3 implies that the existence of equilibrium is guaranteed in our model, while there may be no equilibrium in their model.In sharp contrast, Martinez-de-Albeniz and Simchi-Levi (2009) show that, in a continuous version of such a problem without capacity constraints, suppliers offer bids that cluster together in groups of two to three, a phenomenon termed as “cluster competition”.

More Definitions of Theorem 3

Theorem 3. For given rk, qk, and ζk, the MMSE estimator for ge is given by normalized received signal vector at Bob in (6), we can derive 1 + w2ck ckM the MLE, wˆk, as gˆe = wkck √ζk − gˆ , (20) wˆk = arg max f (rk qk, ζk; wk), (15) wh where qk is given by the information reconciliation using a rateless Xxxxxxx-Xxxx code. The pdf f (rk|qk, ζk; wk) in (15) can be factorized as where gˆk is the MMSE estimate of gk in (18). Proof: From (19), we can find gˆe by conducting a serious of decomposition as follows: gef (ge|rk, qk, ζk; wk)dge ∫ gˆe = f (rk|qk, ζk; wk) = ∫ ge ∫ f (ge, g |r , q , x ; w )dg dge ∫ = ∫ f (rk|qk, ζk, gk; wk)f (gk|qk, ζk; wk)dgk