4,385 research outputs found
PTAS for Minimax Approval Voting
We consider Approval Voting systems where each voter decides on a subset to
candidates he/she approves. We focus on the optimization problem of finding the
committee of fixed size k minimizing the maximal Hamming distance from a vote.
In this paper we give a PTAS for this problem and hence resolve the open
question raised by Carragianis et al. [AAAI'10]. The result is obtained by
adapting the techniques developed by Li et al. [JACM'02] originally used for
the less constrained Closest String problem. The technique relies on extracting
information and structural properties of constant size subsets of votes.Comment: 15 pages, 1 figur
Equivariant Giambelli and determinantal restriction formulas for the Grassmannian
The main result of the paper is a determinantal formula for the restriction
to a torus fixed point of the equivariant class of a Schubert subvariety in the
torus equivariant integral cohomology ring of the Grassmannian. As a corollary,
we obtain an equivariant version of the Giambelli formula.Comment: 16 pages, 3 figures, LaTex, uses epsfig and psfrag; for the revised
version: title changed; Proof of Theorem 3 changed; 3 references added and 1
deleted; other minor change
High precision laser radar tracking device
This thesis explores a relatively new Solid Silver Thin Film Source technology, for the implementation of a novel High Precision Laser Radar Tracking device. The process which consists of a Ag+-Na+ ion exchange, is designed in two steps. It utilizes an initial electric field-aided ion exchange step for a predeposition, and a subsequent second diffusion step to force the profile latitude necessary for optimization of the device. While the entire project of implementing this device, consists of analyzing, processing, polishing and testing, this thesis covers only the process aspect in detail. The success achieved by obtaining the required Power Coupling Ratio curve on a Simple Coupler, demonstrates a novel integrated optic multimode feed for a Monopulse LIDAR application
Quantum versus Semiclassical Description of Selftrapping: Anharmonic Effects
Selftrapping has been traditionally studied on the assumption that
quasiparticles interact with harmonic phonons and that this interaction is
linear in the displacement of the phonon. To complement recent semiclassical
studies of anharmonicity and nonlinearity in this context, we present below a
fully quantum mechanical analysis of a two-site system, where the oscillator is
described by a tunably anharmonic potential, with a square well with infinite
walls and the harmonic potential as its extreme limits, and wherein the
interaction is nonlinear in the oscillator displacement. We find that even
highly anharmonic polarons behave similar to their harmonic counterparts in
that selftrapping is preserved for long times in the limit of strong coupling,
and that the polaronic tunneling time scale depends exponentially on the
polaron binding energy. Further, in agreement, with earlier results related to
harmonic polarons, the semiclassical approximation agrees with the full quantum
result in the massive oscillator limit of small oscillator frequency and strong
quasiparticle-oscillator coupling.Comment: 10 pages, 6 figures, to appear in Phys. Rev.
Parametrized Complexity of Weak Odd Domination Problems
Given a graph , a subset of vertices is a weak odd
dominated (WOD) set if there exists such that
every vertex in has an odd number of neighbours in . denotes
the size of the largest WOD set, and the size of the smallest
non-WOD set. The maximum of and , denoted
, plays a crucial role in quantum cryptography. In particular
deciding, given a graph and , whether is of
practical interest in the design of graph-based quantum secret sharing schemes.
The decision problems associated with the quantities , and
are known to be NP-Complete. In this paper, we consider the
approximation of these quantities and the parameterized complexity of the
corresponding problems. We mainly prove the fixed-parameter intractability
(W-hardness) of these problems. Regarding the approximation, we show that
, and admit a constant factor approximation
algorithm, and that and have no polynomial approximation
scheme unless P=NP.Comment: 16 pages, 5 figure
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