4,733 research outputs found
Clustering Financial Time Series: How Long is Enough?
Researchers have used from 30 days to several years of daily returns as
source data for clustering financial time series based on their correlations.
This paper sets up a statistical framework to study the validity of such
practices. We first show that clustering correlated random variables from their
observed values is statistically consistent. Then, we also give a first
empirical answer to the much debated question: How long should the time series
be? If too short, the clusters found can be spurious; if too long, dynamics can
be smoothed out.Comment: Accepted at IJCAI 201
A Sublinear Tester for Outerplanarity (and Other Forbidden Minors) With One-Sided Error
We consider one-sided error property testing of -minor freeness
in bounded-degree graphs for any finite family of graphs that
contains a minor of , the -circus graph, or the -grid
for any . This includes, for instance, testing whether a graph
is outerplanar or a cactus graph. The query complexity of our algorithm in
terms of the number of vertices in the graph, , is . Czumaj et~al.\ showed that cycle-freeness and -minor
freeness can be tested with query complexity by using
random walks, and that testing -minor freeness for any that contains a
cycles requires queries. In contrast to these results, we
analyze the structure of the graph and show that either we can find a subgraph
of sublinear size that includes the forbidden minor , or we can find a pair
of disjoint subsets of vertices whose edge-cut is large, which induces an
-minor.Comment: extended to testing outerplanarity, full version of ICALP pape
Structural Quantification of Entanglement
We introduce an approach which allows a detailed structural and quantitative
analysis of multipartite entanglement. The sets of states with different
structures are convex and nested. Hence, they can be distinguished from each
other using appropriate measurable witnesses. We derive equations for the
construction of optimal witnesses and discuss general properties arising from
our approach. As an example, we formulate witnesses for a 4-cluster state and
perform a full quantitative analysis of the entanglement structure in the
presence of noise and losses. The strength of the method in multimode
continuous variable systems is also demonstrated by considering a dephased
GHZ-type state.Comment: 12 pages, 1 table and 3 figure
Estimation of household demand systems with theoretically compatible Engel curves and unit value specifications
We develop a method for estimation of price reactions using unit value
data which exploits the implicit links between quantity and unit value
choices. This allows us to combine appealing Engel curve specifications
with a model of unit value determination in a way which is consistent
with demand theory, unlike methods hitherto prominent in the literature.
The method is applied to Czech data
Entanglement properties of multipartite entangled states under the influence of decoherence
We investigate entanglement properties of multipartite states under the
influence of decoherence. We show that the lifetime of (distillable)
entanglement for GHZ-type superposition states decreases with the size of the
system, while for a class of other states -namely all graph states with
constant degree- the lifetime is independent of the system size. We show that
these results are largely independent of the specific decoherence model and are
in particular valid for all models which deal with individual couplings of
particles to independent environments, described by some quantum optical master
equation of Lindblad form. For GHZ states, we derive analytic expressions for
the lifetime of distillable entanglement and determine when the state becomes
fully separable. For all graph states, we derive lower and upper bounds on the
lifetime of entanglement. To this aim, we establish a method to calculate the
spectrum of the partial transposition for all mixed states which are diagonal
in a graph state basis. We also consider entanglement between different groups
of particles and determine the corresponding lifetimes as well as the change of
the kind of entanglement with time. This enables us to investigate the behavior
of entanglement under re-scaling and in the limit of large (infinite) number of
particles. Finally we investigate the lifetime of encoded quantum superposition
states and show that one can define an effective time in the encoded system
which can be orders of magnitude smaller than the physical time. This provides
an alternative view on quantum error correction and examples of states whose
lifetime of entanglement (between groups of particles) in fact increases with
the size of the system.Comment: 27 pages, 11 figure
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