Kernelization complexity of possible winner and coalitional manipulation problems in voting

In the POSSIBLE WINNER problem in computational social choice theory, we are given a set of partial preferences and the question is whether a distinguished candidate could be made winner by extending the partial preferences to linear preferences. Previous work has provided, for many common voting rules, fixed parameter tractable algorithms for the POSSIBLE WINNER problem, with number of candidates as the parameter. However, the corresponding kernelization question is still open and in fact, has been mentioned as a key research challenge 10]. In this paper, we settle this open question for many common voting rules. We show that the POSSIBLE WINNER problem for maximin, Copeland, Bucklin, ranked pairs, and a class of scoring rules that includes the Borda voting rule does not admit a polynomial kernel with the number of candidates as the parameter. We show however that the COALITIONAL MANIPULATION problem which is an important special case of the POSSIBLE WINNER problem does admit a polynomial kernel for maximin, Copeland, ranked pairs, and a class of scoring rules that includes the Borda voting rule, when the number of manipulators is polynomial in the number of candidates. A significant conclusion of our work is that the POSSIBLE WINNER problem is harder than the COALITIONAL MANIPULATION problem since the COALITIONAL MANIPULATION problem admits a polynomial kernel whereas the POSSIBLE WINNER problem does not admit a polynomial kernel. (C) 2015 Elsevier B.V. All rights reserved.

Perturbation of nucleo-cytoplasmic transport affects size of nucleus and nucleolus in human cells

Size regulation of human cell nucleus and nucleolus are poorly understood subjects. 3D reconstruction of live image shows that the karyoplasmic ratio (KR) increases by 30-80% in transformed cell lines compared to their immortalized counterpart. The attenuation of nucleo-cytoplasmic transport causes the KR value to increase by 30-50% in immortalized cell lines. Nucleolus volumes are significantly increased in transformed cell lines and the attenuation of nucleo-cytoplasmic transport causes a significant increase in the nucleolus volume of immortalized cell lines. A cytosol and nuclear fraction swapping experiment emphasizes the potential role of unknown cytosolic factors in nuclear and nucleolar size regulation.