14,226 research outputs found
The Complexity of Manipulating -Approval Elections
An important problem in computational social choice theory is the complexity
of undesirable behavior among agents, such as control, manipulation, and
bribery in election systems. These kinds of voting strategies are often
tempting at the individual level but disastrous for the agents as a whole.
Creating election systems where the determination of such strategies is
difficult is thus an important goal.
An interesting set of elections is that of scoring protocols. Previous work
in this area has demonstrated the complexity of misuse in cases involving a
fixed number of candidates, and of specific election systems on unbounded
number of candidates such as Borda. In contrast, we take the first step in
generalizing the results of computational complexity of election misuse to
cases of infinitely many scoring protocols on an unbounded number of
candidates. Interesting families of systems include -approval and -veto
elections, in which voters distinguish candidates from the candidate set.
Our main result is to partition the problems of these families based on their
complexity. We do so by showing they are polynomial-time computable, NP-hard,
or polynomial-time equivalent to another problem of interest. We also
demonstrate a surprising connection between manipulation in election systems
and some graph theory problems
Excitable Delaunay triangulations
In an excitable Delaunay triangulation every node takes three states
(resting, excited and refractory) and updates its state in discrete time
depending on a ratio of excited neighbours. All nodes update their states in
parallel. By varying excitability of nodes we produce a range of phenomena,
including reflection of excitation wave from edge of triangulation, backfire of
excitation, branching clusters of excitation and localized excitation domains.
Our findings contribute to studies of propagating perturbations and waves in
non-crystalline substrates
The metal insulator transition in cluster dynamical mean field theory: intersite correlation, cluster size, interaction strength, and the location of the transition line
To gain insight into the physics of the metal insulator transition and the
effectiveness of cluster dynamical mean field theory (DMFT) we have used one,
two and four site dynamical mean field theory to solve a polaron model of
electrons coupled to a classical phonon field. The cluster size dependence of
the metal to polaronic insulator phase boundary is determined along with
electron spectral functions and cluster correlation functions. Pronounced
cluster size effects start to occur in the intermediate coupling region in
which the cluster calculation leads to a gap and the single-site approximation
does not. Differences (in particular a sharper band edge) persist in the strong
coupling regime. A partial density of states is defined encoding a generalized
nesting property of the band structure; variations in this density of states
account for differences between the dynamical cluster approximation and the
cellular-DMFT implementations of cluster DMFT, and for differences in behavior
between the single band models appropriate for cuprates and the multiband
models appropriate for manganites. A pole or strong resonance in the self
energy is associated with insulating states; the momentum dependence of the
pole is found to distinguish between Slater-like and Mott-like mechanisms for
metal insulator transition. Implications for the theoretical treatment of doped
manganites are discussed.Comment: 28 pages (single column, double space) 15 figure
Implications of the Low-Temperature Instability of Dynamical Mean Theory for Double Exchange Systems
The single-site dynamical mean field theory approximation to the double
exchange model is found to exhibit a previously unnoticed instability, in which
a well-defined ground state which is stable against small perturbations is
found to be unstable to large-amplitude but purely local fluctuations. The
instability is shown to arise either from phase separation or, in a narrow
parameter regime, from the presence of a competing phase. The instability is
therefore suggested as a computationally inexpensive means of locating regimes
of parameter space in which phase separation occurs.Comment: 5 pages 5 figure
Symmetrized importance samplers for stochastic differential equations
We study a class of importance sampling methods for stochastic differential
equations (SDEs). A small-noise analysis is performed, and the results suggest
that a simple symmetrization procedure can significantly improve the
performance of our importance sampling schemes when the noise is not too large.
We demonstrate that this is indeed the case for a number of linear and
nonlinear examples. Potential applications, e.g., data assimilation, are
discussed.Comment: Added brief discussion of Hamilton-Jacobi equation. Also made various
minor corrections. To appear in Communciations in Applied Mathematics and
Computational Scienc
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