27,425 research outputs found
Universal Voting Protocol Tweaks to Make Manipulation Hard
Voting is a general method for preference aggregation in multiagent settings,
but seminal results have shown that all (nondictatorial) voting protocols are
manipulable. One could try to avoid manipulation by using voting protocols
where determining a beneficial manipulation is hard computationally. A number
of recent papers study the complexity of manipulating existing protocols. This
paper is the first work to take the next step of designing new protocols that
are especially hard to manipulate. Rather than designing these new protocols
from scratch, we instead show how to tweak existing protocols to make
manipulation hard, while leaving much of the original nature of the protocol
intact. The tweak studied consists of adding one elimination preround to the
election. Surprisingly, this extremely simple and universal tweak makes typical
protocols hard to manipulate! The protocols become NP-hard, #P-hard, or
PSPACE-hard to manipulate, depending on whether the schedule of the preround is
determined before the votes are collected, after the votes are collected, or
the scheduling and the vote collecting are interleaved, respectively. We prove
general sufficient conditions on the protocols for this tweak to introduce the
hardness, and show that the most common voting protocols satisfy those
conditions. These are the first results in voting settings where manipulation
is in a higher complexity class than NP (presuming PSPACE NP)
Numerical Solution of Quantum-Mechanical Pair Equations
We discuss and illustrate the numerical solution of the differential equation satisfied by the firstāorder pair functions of SinanoÄlu. An expansion of the pair function in spherical harmonics and the use of finite difference methods convert the differential equation into a set of simultaneous equations. Large systems of such equations can be solved economically. The method is simple and straightforward, and we have applied it to the firstāorder pair function for helium with 1ā/ār_(12) as the perturbation. The results are accurate and encouraging, and since the method is numerical they are indicative of its potential for obtaining atomicāpair functions in general
Effective theory of excitations in a Feshbach resonant superfluid
A strongly interacting Fermi gas, such as that of cold atoms operative near a
Feshbach resonance, is difficult to study by perturbative many-body theory to
go beyond mean field approximation. Here I develop an effective field theory
for the resonant superfluid based on broken symmetry. The theory retains both
fermionic quasiparticles and superfluid phonons, the interaction between them
being derived non-perturbatively. The theory converges and can be improved
order by order, in a manner governed by a low energy expansion rather than by
coupling constant. I apply the effective theory to calculate the specific heat
and propose a mechanism of understanding the empirical power law of energy
versus temperature recently measured in a heat capacity experiment.Comment: 4+ pages, 1 figure; Added references, corrected and clarified minor
statements (v.2
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