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tion of pq. This procedure repeats until the Su is strongly connected. Then u keeps a directed edge uv if and only if uv is also an edge in Su. The de nition of DRNG is illustrated in Figure 10.19. The following lemmas and theorems show that both DLSS and DRNG can preserve the strong connectivity of the original graph. Lemma 1. For any edge uv in the original graph E(G), u is still connected to v in DLSS [37]. Proof. Sort all edges uv [ E(G) in ascending order of weight, that is, w(u1v1) , w(u2v2) , . . . , w(ulvl), where l is the total number of edges. We now prove by induction. Basis: The rst edge u1v1 satis es w(u1v1) minfw(uv)j uv [ E(G)g. According to the algorithm for constructing Su , u1v1 [ E(DLSS), that is, u1 is connected to v1 in DLSS. Induction: Assuming the hypothesis holds for all edges uivi, i , k, we prove uk is connected to vk in DLSS. Since this is obviously true if ukvk [ E(DLSS), we only need to consider the case where ukvk E(DLSS). Before edge ukvk was considered in the local topology construction of vk, there must already exist a path p (w0 uk, w1, w2, . . . , wm21, wm vk) from uk to vk, where wiwi 1 [ E(Suk), wi 1 [ E(Suk), i 0, 1, . . . , m 2 1. Since edges are inserted in ascending order of weight, we have w(wiwi 1) , w(ukvk). Applying the induction hypothesis, wi is connected to wi 1 for i 0, 1, . . . , m 2 1. Therefore, uk is connected to vk. A

Swann and Predmore (1985) gave people feedback that was discrepant from their self-views and watched how they and their romantic partners responded When the subject and his or her partner agreed that the feedback was wrong, the pair then joined forces to reject it: They discussed its aws and decided how best to refute or dismiss it In contrast, when the partner s view of the subject differed from the subject s self-view, the discrepant feedback led to further disagreements between the subject and partner It may be that one vital function of close relationship partners is to help maintain and defend one s self-concept against the attacks of the outer world (see also De La Ronde & Swann, 1998) Sedikides, Campbell, Reeder, and Elliott (1998) explored another important link between self-deception and the interpersonal self.

The projected cluster centers ti and the induced matrixes Mi proj de ne the input ~ clusters Ci , i 1 . . . ; c. The parameter mproj > 1 determines the fuzziness of an individual cluster.

1551 Utility-Based Data Transport General approaches along this line of research are to (1) formulate the problem as a nonconvex programming problem and solve it in a centralized manner (so as to provide performance bounds); or (2) formulate the problem (with some approximations) as a convex programming problem that can be solved in a decentralized manner, and devise the corresponding distributed algorithm Some of the datagathering and -fusion approaches discussed in Sections 153 and 154 can be cast in this optimization framework by properly assigning the utility of each packet (eg, packets that carry updated digests are assigned higher utilities) In this subsection we rst introduce a nonconvex programming problem formulation [51] that is general enough to encompass a wide variety of applications in sensor networks, each with a different objective function and subject to different constraints.

Then we discuss various simpli ed convex or linear programming problems Note that utility-based approaches have been exploited in conventional wired networks by Kelly et al [52] and Low and Lapsley [53] Kelly et al [52] propose a pricing scheme to achieve weight-proportional fair-rate allocation for users in a wireline network The same problem considered in ref [52] is solved by Low and Lapsley [53] differently with the use of the dual optimization problem A major advantage of Low and Lapsley s solution approach is that the dual optimization problem can be solved in a distributed manner via a pricing mechanism.

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They examined the self-serving bias, a classic pattern of self-deception that occurs when people take credit for success but deny blame for failure When people work in groups, the self-serving bias produces the tendency to claim all the credit for success at joint tasks but to dump the blame for failure on the other group members However, the authors found that self-serving bias is mitigated when the group members feel a close interpersonal bond with each other..

In the context of wireless sensor networks, there are three types of objective functions in the optimization problem: (1) maximizing the overall utility of the sensor data collected at sinks throughout the system lifetime [51,54,55], (2) maximizing the amount of data extracted from sensors [56,57], and (3) maximizing the system lifetime (or equivalently minimizing the energy expenditure) [57,58] We formulate the rst optimization problem, subject to the ow constraint, the energy constraint, and the channel capacity constraint As will become clearer, the second and the third problems are special cases of the rst one For notational convenience, we de ne the following notion: Us the utility function that speci es the commodity generated from a sensor s and sent to a sink (perhaps through multiple routes); Sn and Si the set of sensors and sinks in the sensing eld; Nk the set of one-hop neighbors of node k;.