Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many of these problems, players are organized according to either a hierarchical structure or a levels structure that restrict the players’ possibilities to cooperate. In this paper, we propose three new solutions for games with hierarchical structure and characterize them by properties ...

An ideal semantic representation of text corpus should exhibit a hierarchical topic tree structure, and topics residing at different node levels of the tree should exhibit different levels of semantic abstraction( i.e., the deeper level a topic resides, the more specific it would be). Instead of learning every node directly which is a quite time consuming task, our approach bases on a nonparame...

Many natural and engineered complex networks have intricate mesoscopic organization, e.g., the clustering of the constituent nodes into several communities or modules. Often, such modularity is manifested at several different hierarchical levels, where the clusters defined at one level appear as elementary entities at the next higher level. Using a simple model of a hierarchical modular network...

Multitype spatial point patterns with hierarchical interactions are considered. Here hierarchical interaction means directionality: points on a higher level of hierarchy affect the locations of points on the lower levels, but not vice versa. Such relations are common, for example, in ecological communities. Interacting point patterns are often modeled by Gibbs processes with pairwise interactio...

Novel idea of hierarchical visual cryptography is stated in this paper. The key concept of hierarchical visual cryptography is based upon visual cryptography. Visual cryptography encrypts secret information into two pieces called as shares. These two shares are stacked together by logical XOR operation to reveal the original secret. Hierarchical visual cryptography encrypts the secret in variou...

We examine hierarchical modularity modularity on multiple levels, in which the modules at a lower level of abstraction can serve as nodes in a network at a higher level of abstraction that also has positive modularity as well as degree of modularity on a single level of abstraction, in evolved neural networks in single-task, parallel-subtask environments, and sequential-subtask environments, us...

As the number of modules grows, performance scalability of planar topology networks-on-chip (NoCs) becomes limited due to the increasing hop-distances. The growing hopdistance affects both end-to-end network latency and overall network saturation. Hierarchical topologies provide better traffic hop distance and therefore are more adequate for large systems. However, the introduction of hierarchi...

We would like to thank the discussants for the valuable insights and for commenting on important aspects of model checking that we did not touch in our paper. Our goal was modest (but crucial): to select an appropriate distribution with which to judge the compatibility of the data with a hypothesized (hierarchical) model, when the test statistic is not ancillary and an improper prior is used fo...

Bayarri and Castellanos (BC) have written an interesting paper discussing two forms of posterior model check, one based on cross-validation and one based on replication of new groups in a hierarchical model. We think both these checks are good ideas and can become even more effective when understood in the context of posterior predictive checking. For the purpose of discussion, however, it is m...