Báo cáo tin học: "Graph-based upper bounds for the probability of the union of events" ppt

... vertex x of degree 6. Thus V is a disjoint union of the closed neighborhood N[x]ofxand a set A of cardinality 6. Consider the 6 × 12 matrix M whose rows are indexed by the elements of A and the columns ... the subgraph of G induced by A. Table 1 contains the value of γ(n, δ) for n ≤ 16, 0 ≤ δ ≤ n − 1 if the value is known, otherwise upper and lower bounds fo...

Ngày tải lên: 07/08/2014, 06:20

... approximations of the roots for specific values of d are found easily, and so are the inverses of the roots of smallest modulus giving us the entries of first line of table 2. the electronic journal of combinatorics ... denotes the identity matrix and A is the state transfer matrix of the automaton. Consequently, the root of smallest modulus of the deno...

Ngày tải lên: 07/08/2014, 06:20

... definition of δ k (n). The theorem therefore follows. In the next section we show that if k = 3 then the above theorem holds for n ≥ 6. Note that the results in this section are stated for fixed ... asterisks. The values given for these cases are the best known upper bounds. the electronic journal of combinatorics 7 (2000), #R58 14 Lemma 4 If there esists an (n, k, 1)...

Ngày tải lên: 07/08/2014, 06:22

... spoke. As the set of spokes form an edge-cut of the graph W (n, 2k +3), such a cycle must in fact use an even number of spokes. If the number of spokes used is four or more then the number of vertices ... preceding it in the clockwise orientation and q the distance along the rim from n p,κ . We place the following restriction on the spokes of the wheel, indicat...

Ngày tải lên: 07/08/2014, 13:21

... 1) for 1  k  ⌊ n−1 2 ⌋ (v) µ(n, 4, 3)  n(n − 1) 3 for n  4 The following theorem provides upper bounds for µ(n, d, w) even if w > d. Theorem 9. For all n  3, the electronic journal of ... [15], many of the upper bounds obtained by linear pro- gramming coincide with the bound µ(n, d)  n! (d−1)! of theorem 1. For 14  n  16, computations of the LP b...

Ngày tải lên: 08/08/2014, 12:22

... (14) is the best in all known upper bounds for G 2 , and bound (18) is the best in all known upper bounds for G 3 . Finally, bound (22) is the best upper bound for G 1 and bound (1 8) is the second-best ... new and sharp upper bounds for λ(G), which are better than all of the above mentioned upper bounds in some sense, and determine the extremal g r aph...

Ngày tải lên: 08/08/2014, 12:23

... T κ . 2.22 The proof of Corollary 2.6 is complete. Remark 2.7. The result of Theorem 2.5 holds for an arbitrary time scale. Therefore, using Theorem 2.5, we can obtain many results for some peculiar ... follows, R denotes the set of real numbers, R  0, ∞, Z denotes the set of integers, N 0  {0, 1, 2, } denotes the set of nonnegative integers, CM, S denotes th...

Ngày tải lên: 21/06/2014, 20:20

... when the number of relays is relatively large, the gain of ergodic capacity is co nstant, approximately. Take the symmetric channels as example, at SNR = 10 dB, the gain of the upper bound of ergodic ... exploited. For the investigation of TWOR-NC-Dir systems, the canonical argument line [18] is that we must first obtain the statistical description of the ins...

Ngày tải lên: 20/06/2014, 21:20

... best; next is the upper WS bound followed by the upper C bound. For λ 2 (Q), the SS bounds are the same as the C bounds. For λ 3 (Q), the upper SS bound is the best; next is the upper WS bound ... bounds of the eigenvalues of Q are functions of ρ in the interval [0, 1]. Therefore, we are able to find optimal bounds of the eigenvalues of Q by c...

Ngày tải lên: 21/06/2014, 20:20

... condition I  . Therefore, by Theorem 2.4,from3.7, we easily obtain the estimate 3.3 of solutions of 3.1. The proof of Theorem 3.2 is complete. Using Theorem 2.5, we easily obtain the following ... T 0 . 2.25 Therefore, the desired inequality 2.6 follows from 2.10, 2.22,and2.25. This completes the proof. Theorem 2.5. Suppose that all assumptions of Theorem...

Ngày tải lên: 22/06/2014, 03:20