Narrow Results

The assessment of node centrality in complex networks has been a central issue of great interest. With the continuous evolution of modern science, the single-layer network model is no longer sufficient to meet the current needs of complex networks. It is necessary to accurately identify important nodes in multilayer networks. In this paper, we propose a novel node centrality method called LCTR for multilayer networks. LCTR evaluates node importance by tournament ranking, which combines the node ranking information in both aggregated and expanded formations of a multilayer network. The concept of “tournament ranking” is borrowed from graph theory. Multiple experiments on different datasets reveal that the LCTR method significantly outperforms existing centrality methods.

The problem of merging two intransitive sorted sequences (that is, to generate a sorted total order without the transitive property) is considered. A cost-optimal parallel merging algorithm is proposed under the EREW PRAM model. This algorithm has a run time of O(log² n) using O(n/log² n) processors. The cost-optimal merge in the strong sense is still an open problem.

A directed graph $G$ is intrinsically linked if every embedding of that graph contains a nonsplit link $L$, where each component of $L$ is a consistently oriented cycle in $G$. A tournament is a directed graph where each pair of vertices is connected by exactly one directed edge.

We consider intrinsic linking and knotting in tournaments, and study the minimum number of vertices required for a tournament to have various intrinsic linking or knotting properties. We produce the following bounds: intrinsically linked ($n=8$), intrinsically knotted ($9\le n\le 12$), intrinsically 3-linked ($10\le n\le 23$), intrinsically 4-linked ($12\le n\le 66$), intrinsically 5-linked ($15\le n\le 154$), intrinsically $m$-linked ($3m\le n\le 8{(2m-3)}^2$), intrinsically linked with knotted components ($9\le n\le 107$), and the disjoint linking property ($12\le n\le 14$).

We also introduce the consistency gap, which measures the difference in the order of a graph required for intrinsic $n$-linking in tournaments versus undirected graphs. We conjecture the consistency gap to be nondecreasing in $n$, and provide an upper bound at each $n$.

A two-stage, two-person tournament is discussed, in which each player can influence the other one at the first stage by choosing help, sabotage or no action. At the second stage, the players choose effort to win the tournament. Helping and sabotaging have two effects — they influence the likelihood of winning (likelihood effect) and they determine the equilibrium efforts and, therefore, effort costs (cost effect). Depending on the interplay of the two effects, diverse types of equilibria are possible. In particular, if the cost effect dominates the likelihood effect (i.e., both players concentrate on minimizing effort costs), two asymmetric equilibria will coexist in which one player helps his opponent, whereas the other one chooses sabotage and vice versa.

A real $n\times n$ matrix is a $Q$-matrix if for $k=1,\dots ,n$ the sum of all $k\times k$ principal minors is positive. A digraph $D$ is said to have positive $Q$-completion if every partial positive $Q$-matrix specifying $D$ can be completed to a positive $Q$-matrix. In this paper, necessary conditions for a digraph to have positive $Q$-completion are obtained and sufficient conditions for a digraph to have positive $Q$-completion are provided. The digraphs of order at most 4 that include all loops and have positive $Q$-completion are characterized. Tournaments whose complements have positive $Q$-completion are singled out. Further, some comparisons between the $Q$-matrix and positive $Q$-matrix completion problems have been made.

This study investigates theoretically and empirically mutual fund managers’ risk-taking behavior due to ranking objectives. We argue that managers can not only choose the riskiness of their portfolio but can also determine how hard to work (their effort). The combination of risk and effort depends on the interim performance gap and the effort cost level. Both interim winner and loser gamble by taking high risk and spending low effort when the interim performance gap is below a certain threshold. Only the interim loser gambles when the interim performance gap is small and the effort cost is sufficiently high. Otherwise, managers adopt the same choice of risk-effort. In many cases, high (low) risk-taking induces higher (lower) effort. Empirically, we find that managerial effort is strongly and positively linked to their risk-shifting level. The worst-performers behave differently from the others but are not necessarily riskier and lazier.