On the Efficiency of An Election Game of Two or More Parties: How Bad Can It Be?

We extend our previous work on two-party election competition [Lin, Lu & Chen 2021] to the setting of three or more parties. An election campaign among two or more parties is viewed as a game of two or more players. Each of them has its own candidates as the pure strategies to play. People, as voters, comprise supporters for each party, and a candidate brings utility for the the supporters of each party. Each player nominates exactly one of its candidates to compete against the other party's. A candidate is assumed to win the election with higher odds if it brings more utility for all the people. The payoff of each player is the expected utility its supporters get. The game is egoistic if every candidate benefits her party's supporters more than any candidate from the competing party does. In this work, we first argue that the election game always has a pure Nash equilibrium when the winner is chosen by the hardmax function, while there exist game instances in the three-party election game such that no pure Nash equilibrium exists even the game is egoistic. Next, we propose two sufficient conditions for the egoistic election game to have a pure Nash equilibrium. Based on these conditions, we propose a fixed-parameter tractable algorithm to compute a pure Nash equilibrium of the egoistic election game. Finally, perhaps surprisingly, we show that the price of anarchy of the egoistic election game is upper bounded by the number of parties. Our findings suggest that the election becomes unpredictable when more than two parties are involved and, moreover, the social welfare deteriorates with the number of participating parties in terms of possibly increasing price of anarchy. This work alternatively explains why the two-party system is prevalent in democratic countries

Lutein Protects against Methotrexate-Induced and Reactive Oxygen Species-Mediated Apoptotic Cell Injury of IEC-6 Cells

Purpose High-dose chemotherapy using methotrexate (MTX) frequently induces side effects such as mucositis that leads to intestinal damage and diarrhea. Several natural compounds have been demonstrated of their effectiveness in protecting intestinal epithelial cells from these adverse effects. In this paper, we investigated the protection mechanism of lutein against MTX-induced damage in IEC-6 cells originating from the rat jejunum crypt. Methods: The cell viability, induced-apoptosis, reactive oxygen species (ROS) generation, and mitochondrial membrane potential in IEC-6 cells under MTX treatment were examined in the presence or absence of lutein. Expression level of Bcl2, Bad and ROS scavenging enzymes (including SOD, catalase and Prdx1) were detected by quantitative RT-PCR. Results: The cell viability of IEC-6 cells exposed to MTX was decreased in a dose- and time-dependent manner. MTX induces mitochondrial membrane potential loss, ROS generation and caspase 3 activation in IEC-6 cells. The cytotoxicity of MTX was reduced in IEC-6 cells by the 24 h pre-treatment of lutein. We found that pre-treatment of lutein significantly reduces MTX-induced ROS and apoptosis. The expression of SOD was up-regulated by the pre-treatment of lutein in the MTX-treated IEC-6 cells. These results indicated that lutein can protect IEC-6 cells from the chemo-drugs induced damage through increasing ROS scavenging ability. Conclusion: The MTX-induced apoptosis of IEC-6 cells was shown to be repressed by the pre-treatment of lutein, which may represent a promising adjunct to conventional chemotherapy for preventing intestinal damages

Tight Approximation for Partial Vertex Cover with Hard Capacities

We consider the partial vertex cover problem with hard capacity constraints (Partial VC-HC) on hypergraphs. In this problem we are given a hypergraph G=(V,E) with a maximum edge size f and a covering requirement R. Each edge is associated with a demand, and each vertex is associated with a capacity and an (integral) available multiplicity. The objective is to compute a minimum vertex multiset such that at least R units of demand from the edges are covered by the capacities of the vertices in the multiset and the multiplicity of each vertex does not exceed its available multiplicity. In this paper we present an f-approximation for this problem, improving over a previous result of (2f+2)(1+epsilon) by Cheung et al to the tight extent possible. Our new ingredient of this work is a generalized analysis on the extreme points of the natural LP, developed from previous works, and a strengthened LP lower-bound obtained for the optimal solutions

The role of Causality in Tunable Fermi Gas Condensates

We develop a new formalism for the description of the condensates of cold Fermi atoms whose speed of sound can be tuned with the aid of a narrow Feshbach resonance. We use this to look for spontaneous phonon creation that mimics spontaneous particle creation in curved space-time in Friedmann-Robertson-Walker and other model universes.Comment: 9 pages, 2 figures. In v.3 the formalism is different from the existing arXiv versions, but the final results are unchanged. Title changed, one author added. The article will be published in the special edition of Journal of Physics: Condensed Matter on "Condensed matter analogues of cosmology