449 research outputs found
Uniqueness of Kusuoka Representations
This paper addresses law invariant coherent risk measures and their Kusuoka
representations. By elaborating the existence of a minimal representation we
show that every Kusuoka representation can be reduced to its minimal
representation. Uniqueness -- in a sense specified in the paper -- of the risk
measure's Kusuoka representation is derived from this initial result.
Further, stochastic order relations are employed to identify the minimal
Kusuoka representation. It is shown that measures in the minimal representation
are extremal with respect to the order relations. The tools are finally
employed to provide the minimal representation for important practical
examples. Although the Kusuoka representation is usually given only for
nonatomic probability spaces, this presentation closes the gap to spaces with
atoms
Integration of Skyline Queries into Spark SQL
Skyline queries are frequently used in data analytics and multi-criteria
decision support applications to filter relevant information from big amounts
of data. Apache Spark is a popular framework for processing big, distributed
data. The framework even provides a convenient SQL-like interface via the Spark
SQL module. However, skyline queries are not natively supported and require
tedious rewriting to fit the SQL standard or Spark's SQL-like language. The
goal of our work is to fill this gap. We thus provide a full-fledged
integration of the skyline operator into Spark SQL. This allows for a simple
and easy to use syntax to input skyline queries. Moreover, our empirical
results show that this integrated solution of skyline queries by far
outperforms a solution based on rewriting into standard SQL
Probing many-body dynamics on a 51-atom quantum simulator
Controllable, coherent many-body systems can provide insights into the
fundamental properties of quantum matter, enable the realization of new quantum
phases and could ultimately lead to computational systems that outperform
existing computers based on classical approaches. Here we demonstrate a method
for creating controlled many-body quantum matter that combines
deterministically prepared, reconfigurable arrays of individually trapped cold
atoms with strong, coherent interactions enabled by excitation to Rydberg
states. We realize a programmable Ising-type quantum spin model with tunable
interactions and system sizes of up to 51 qubits. Within this model, we observe
phase transitions into spatially ordered states that break various discrete
symmetries, verify the high-fidelity preparation of these states and
investigate the dynamics across the phase transition in large arrays of atoms.
In particular, we observe robust manybody dynamics corresponding to persistent
oscillations of the order after a rapid quantum quench that results from a
sudden transition across the phase boundary. Our method provides a way of
exploring many-body phenomena on a programmable quantum simulator and could
enable realizations of new quantum algorithms.Comment: 17 pages, 13 figure
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