A note on anti-coordination and social interactions

This note confirms a conjecture of [Bramoull\'{e}, Anti-coordination and social interactions, Games and Economic Behavior, 58, 2007: 30-49]. The problem, which we name the maximum independent cut problem, is a restricted version of the MAX-CUT problem, requiring one side of the cut to be an independent set. We show that the maximum independent cut problem does not admit any polynomial time algorithm with approximation ratio better than $n^{1-\epsilon}$, where $n$ is the number of nodes, and $\epsilon$ arbitrarily small, unless P=NP. For the rather special case where each node has a degree of at most four, the problem is still MAXSNP-hard.Comment: 7 page

Preliminary Report on the Feasibility of Using the IUCF Cooler Ring Synchrotron as an Electron Storage Ring

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Independent Set Reconfiguration in Cographs

We study the following independent set reconfiguration problem, called TAR-Reachability: given two independent sets $I$ and $J$ of a graph $G$, both of size at least $k$, is it possible to transform $I$ into $J$ by adding and removing vertices one-by-one, while maintaining an independent set of size at least $k$ throughout? This problem is known to be PSPACE-hard in general. For the case that $G$ is a cograph (i.e. $P_4$-free graph) on $n$ vertices, we show that it can be solved in time $O(n^2)$, and that the length of a shortest reconfiguration sequence from $I$ to $J$ is bounded by $4n-2k$, if such a sequence exists. More generally, we show that if $X$ is a graph class for which (i) TAR-Reachability can be solved efficiently, (ii) maximum independent sets can be computed efficiently, and which satisfies a certain additional property, then the problem can be solved efficiently for any graph that can be obtained from a collection of graphs in $X$ using disjoint union and complete join operations. Chordal graphs are given as an example of such a class $X$

Pionic Atoms as Compound States in Nucleon-Nucleus Collisons: Status Report on the Cooler Experiment CE02

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Cooler Intensity Limitations

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Measurement of the Total Cross Section for the Reaction p + p → p + p + pio

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Effect of Parametric Resonances on the Bunched-beam Dilution Mechanism

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Study of the Feasibility of Decreasing the Emittance of the SSC Beam Through the Use of Electron Cooling in the SSC Medium Energy Booster

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Study of a Depolarizing Resonance at the IUCF Cooler Ring

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Siberian Snake and Depolarizing Resonance Studies at the Cooler Ring

This research was sponsored by the National Science Foundation Grant NSF PHY-931478