Despite linear programming and duality have correctly been incorporated in algorithms to compute the nucleolus, we have found mistakes in how these have been used in a broad range of applications. Overlooking the fact that a linear program can have multiple optimal solutions and neglecting the relevance of duality appear to be crucial sources of mistakes in computing the nucleolus. We discuss t...

White Blood Cancer is one of the deadliest diseases for human being and its presence can be early diagnosed by detecting the existence of nucleolus in White Blood Cells (WBC) of peripheral blood smear images. In this paper, the author would like to compare the performance of nucleolus candidate zone extraction algorithm by utilizing Wavelet transforms and Curvelet transform. The result confirms...

The life of the nucleolus has proven to be more colorful and multifaceted than had been envisioned a decade ago. A large number of proteins found in this subnuclear compartment have no identifiable tie either to the ribosome biosynthetic pathway or to the other newly established activities occurring within the nucleolus. The questions of how and why these proteins end up in this subnuclear comp...

This paper studies coalition formation, payoff division and expected payoffs in a ”divide the dollar by majority rule” game with random proposers. A power index is called self-confirming if it can be obtained as an equilibrium of the game using the index itself as probability vector. Unlike the Shapley value and other commonly used power indices, the nucleolus has this property. The proof uses ...

In cooperative games, a key question is to find a division of payoffs to coalition members in a fair manner. Nucleolus is one of such solution concepts that provides a stable solution for the grand coalition. We study the computation of the nucleolus of a number of cooperative games, including fractional matching games and fractional edge cover games on general weighted graphs, as well as verte...