3,173 research outputs found
Optimal discrimination of single-qubit mixed states
We consider the problem of minimum-error quantum state discrimination for
single-qubit mixed states. We present a method which uses the Helstrom
conditions constructively and analytically; this algebraic approach is
complementary to existing geometric methods, and solves the problem for any
number of arbitrary signal states with arbitrary prior probabilities.Comment: 8 pages, 1 figur
The extensional realizability model of continuous functionals and three weakly non-constructive classical theorems
We investigate wether three statements in analysis, that can be proved
classically, are realizable in the realizability model of extensional
continuous functionals induced by Kleene's second model . We prove that a
formulation of the Riemann Permutation Theorem as well as the statement that
all partially Cauchy sequences are Cauchy cannot be realized in this model,
while the statement that the product of two anti-Specker spaces is anti-Specker
can be realized
The Combinatorial World (of Auctions) According to GARP
Revealed preference techniques are used to test whether a data set is
compatible with rational behaviour. They are also incorporated as constraints
in mechanism design to encourage truthful behaviour in applications such as
combinatorial auctions. In the auction setting, we present an efficient
combinatorial algorithm to find a virtual valuation function with the optimal
(additive) rationality guarantee. Moreover, we show that there exists such a
valuation function that both is individually rational and is minimum (that is,
it is component-wise dominated by any other individually rational, virtual
valuation function that approximately fits the data). Similarly, given upper
bound constraints on the valuation function, we show how to fit the maximum
virtual valuation function with the optimal additive rationality guarantee. In
practice, revealed preference bidding constraints are very demanding. We
explain how approximate rationality can be used to create relaxed revealed
preference constraints in an auction. We then show how combinatorial methods
can be used to implement these relaxed constraints. Worst/best-case welfare
guarantees that result from the use of such mechanisms can be quantified via
the minimum/maximum virtual valuation function
A polyhedral model of partitions with bounded differences and a bijective proof of a theorem of Andrews, Beck, and Robbins
The main result of this paper is a bijective proof showing that the
generating function for partitions with bounded differences between largest and
smallest part is a rational function. This result is similar to the closely
related case of partitions with fixed differences between largest and smallest
parts which has recently been studied through analytic methods by Andrews,
Beck, and Robbins. Our approach is geometric: We model partitions with bounded
differences as lattice points in an infinite union of polyhedral cones.
Surprisingly, this infinite union tiles a single simplicial cone. This
construction then leads to a bijection that can be interpreted on a purely
combinatorial level.Comment: 12 pages, 5 figure
Constructive aspects of Riemann's permutation theorem for series
The notions of permutable and weak-permutable convergence of a series
of real numbers are introduced. Classically, these
two notions are equivalent, and, by Riemann's two main theorems on the
convergence of series, a convergent series is permutably convergent if and only
if it is absolutely convergent. Working within Bishop-style constructive
mathematics, we prove that Ishihara's principle \BDN implies that every
permutably convergent series is absolutely convergent. Since there are models
of constructive mathematics in which the Riemann permutation theorem for series
holds but \BDN does not, the best we can hope for as a partial converse to our
first theorem is that the absolute convergence of series with a permutability
property classically equivalent to that of Riemann implies \BDN. We show that
this is the case when the property is weak-permutable convergence
Influence of Materials and Design Parameters on Zinc Oxide Surface Acoustic Devices
This thesis presents research into Zinc Oxide (ZnO) based resonators to include Width Extensional Mode (WEM), Length Extensional Mode (LEM), and Surface Acoustic Wave (SAW) devices. The design and operation of ZnO based SAW devices are investigated further to characterize design parameters and operating modes. Their design, fabrication, and results are discussed in detail. SAW device testing in conjunction with X-Ray Diffractometry (XRD) and Atomic Force Microscopy (AFM) are utilized to characterize ZnO and its deposition parameters on a variety of different substrates and interlayers, with different deposition temperatures and annealing parameters. These substrates include silicon, silicon oxide-on-silicon, and sapphire wafers with interlayers including titanium, tungsten, and silicon oxide. Fabrication methods are discussed to explain all processing steps associated with SAW and released contour mode resonators. The SAW devices in this research test different design parameters to establish better reflector design spacing for higher frequency Sezawa wave modes. The characterization and design of ZnO based SAW devices establishes the potential for prototyping high frequency SAW designs using standard lithography techniques. These devices are desired for space-based operations for use in GPS filters, signal processing, and sensing in satellites and space vehicles
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