20,670 research outputs found
A distributionally robust perspective on uncertainty quantification and chance constrained programming
The objective of uncertainty quantification is to certify that a given physical, engineering or economic system satisfies multiple safety conditions with high probability. A more ambitious goal is to actively influence the system so as to guarantee and maintain its safety, a scenario which can be modeled through a chance constrained program. In this paper we assume that the parameters of the system are governed by an ambiguous distribution that is only known to belong to an ambiguity set characterized through generalized moment bounds and structural properties such as symmetry, unimodality or independence patterns. We delineate the watershed between tractability and intractability in ambiguity-averse uncertainty quantification and chance constrained programming. Using tools from distributionally robust optimization, we derive explicit conic reformulations for tractable problem classes and suggest efficiently computable conservative approximations for intractable ones
Quantum Sampling Problems, BosonSampling and Quantum Supremacy
There is a large body of evidence for the potential of greater computational
power using information carriers that are quantum mechanical over those
governed by the laws of classical mechanics. But the question of the exact
nature of the power contributed by quantum mechanics remains only partially
answered. Furthermore, there exists doubt over the practicality of achieving a
large enough quantum computation that definitively demonstrates quantum
supremacy. Recently the study of computational problems that produce samples
from probability distributions has added to both our understanding of the power
of quantum algorithms and lowered the requirements for demonstration of fast
quantum algorithms. The proposed quantum sampling problems do not require a
quantum computer capable of universal operations and also permit physically
realistic errors in their operation. This is an encouraging step towards an
experimental demonstration of quantum algorithmic supremacy. In this paper, we
will review sampling problems and the arguments that have been used to deduce
when sampling problems are hard for classical computers to simulate. Two
classes of quantum sampling problems that demonstrate the supremacy of quantum
algorithms are BosonSampling and IQP Sampling. We will present the details of
these classes and recent experimental progress towards demonstrating quantum
supremacy in BosonSampling.Comment: Survey paper first submitted for publication in October 2016. 10
pages, 4 figures, 1 tabl
Theory and Applications of Robust Optimization
In this paper we survey the primary research, both theoretical and applied,
in the area of Robust Optimization (RO). Our focus is on the computational
attractiveness of RO approaches, as well as the modeling power and broad
applicability of the methodology. In addition to surveying prominent
theoretical results of RO, we also present some recent results linking RO to
adaptable models for multi-stage decision-making problems. Finally, we
highlight applications of RO across a wide spectrum of domains, including
finance, statistics, learning, and various areas of engineering.Comment: 50 page
Solving the stationary Liouville equation via a boundary element method
Intensity distributions of linear wave fields are, in the high frequency
limit, often approximated in terms of flow or transport equations in phase
space. Common techniques for solving the flow equations for both time dependent
and stationary problems are ray tracing or level set methods. In the context of
predicting the vibro-acoustic response of complex engineering structures,
reduced ray tracing methods such as Statistical Energy Analysis or variants
thereof have found widespread applications. Starting directly from the
stationary Liouville equation, we develop a boundary element method for solving
the transport equations for complex multi-component structures. The method,
which is an improved version of the Dynamical Energy Analysis technique
introduced recently by the authors, interpolates between standard statistical
energy analysis and full ray tracing, containing both of these methods as
limiting cases. We demonstrate that the method can be used to efficiently deal
with complex large scale problems giving good approximations of the energy
distribution when compared to exact solutions of the underlying wave equation
An adaptive hierarchical domain decomposition method for parallel contact dynamics simulations of granular materials
A fully parallel version of the contact dynamics (CD) method is presented in
this paper. For large enough systems, 100% efficiency has been demonstrated for
up to 256 processors using a hierarchical domain decomposition with dynamic
load balancing. The iterative scheme to calculate the contact forces is left
domain-wise sequential, with data exchange after each iteration step, which
ensures its stability. The number of additional iterations required for
convergence by the partially parallel updates at the domain boundaries becomes
negligible with increasing number of particles, which allows for an effective
parallelization. Compared to the sequential implementation, we found no
influence of the parallelization on simulation results.Comment: 19 pages, 15 figures, published in Journal of Computational Physics
(2011
A Distributed Approach for the Optimal Power Flow Problem Based on ADMM and Sequential Convex Approximations
The optimal power flow (OPF) problem, which plays a central role in operating
electrical networks is considered. The problem is nonconvex and is in fact NP
hard. Therefore, designing efficient algorithms of practical relevance is
crucial, though their global optimality is not guaranteed. Existing
semi-definite programming relaxation based approaches are restricted to OPF
problems where zero duality holds. In this paper, an efficient novel method to
address the general nonconvex OPF problem is investigated. The proposed method
is based on alternating direction method of multipliers combined with
sequential convex approximations. The global OPF problem is decomposed into
smaller problems associated to each bus of the network, the solutions of which
are coordinated via a light communication protocol. Therefore, the proposed
method is highly scalable. The convergence properties of the proposed algorithm
are mathematically substantiated. Finally, the proposed algorithm is evaluated
on a number of test examples, where the convergence properties of the proposed
algorithm are numerically substantiated and the performance is compared with a
global optimal method.Comment: 14 page
CT Image Reconstruction by Spatial-Radon Domain Data-Driven Tight Frame Regularization
This paper proposes a spatial-Radon domain CT image reconstruction model
based on data-driven tight frames (SRD-DDTF). The proposed SRD-DDTF model
combines the idea of joint image and Radon domain inpainting model of
\cite{Dong2013X} and that of the data-driven tight frames for image denoising
\cite{cai2014data}. It is different from existing models in that both CT image
and its corresponding high quality projection image are reconstructed
simultaneously using sparsity priors by tight frames that are adaptively
learned from the data to provide optimal sparse approximations. An alternative
minimization algorithm is designed to solve the proposed model which is
nonsmooth and nonconvex. Convergence analysis of the algorithm is provided.
Numerical experiments showed that the SRD-DDTF model is superior to the model
by \cite{Dong2013X} especially in recovering some subtle structures in the
images
Automatic acquisition of LFG resources for German - as good as it gets
We present data-driven methods for the acquisition of LFG resources from two German treebanks. We discuss problems specific to semi-free word order languages as well as problems arising fromthe data structures determined
by the design of the different treebanks. We compare two ways of encoding semi-free word order, as done in the two German treebanks, and argue that the design of the TiGer treebank is more adequate for the acquisition of LFG
resources. Furthermore, we describe an architecture for LFG grammar acquisition for German, based on the two German treebanks, and compare our results with a hand-crafted German LFG grammar
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