Accelerating BST Methods for Model Reduction with Graphics Processors

Model order reduction of dynamical linear time-invariant system appears in many scientific and engineering applications. Numerically reliable SVD-based methods for this task require O(n3) floating-point arithmetic operations, with n being in the range 103 − 105 for many practical applications. In this paper we investigate the use of graphics processors (GPUs) to accelerate model reduction of large-scale linear systems via Balanced Stochastic Truncation, by off-loading the computationally intensive tasks to this device. Experiments on a hybrid platform consisting of state-of-the-art general-purpose multi-core processors and a GPU illustrate the potential of this approach

Order reduction approaches for the algebraic Riccati equation and the LQR problem

We explore order reduction techniques for solving the algebraic Riccati equation (ARE), and investigating the numerical solution of the linear-quadratic regulator problem (LQR). A classical approach is to build a surrogate low dimensional model of the dynamical system, for instance by means of balanced truncation, and then solve the corresponding ARE. Alternatively, iterative methods can be used to directly solve the ARE and use its approximate solution to estimate quantities associated with the LQR. We propose a class of Petrov-Galerkin strategies that simultaneously reduce the dynamical system while approximately solving the ARE by projection. This methodology significantly generalizes a recently developed Galerkin method by using a pair of projection spaces, as it is often done in model order reduction of dynamical systems. Numerical experiments illustrate the advantages of the new class of methods over classical approaches when dealing with large matrices

The pursuit of isotopic and molecular fire tracers in the polar atmosphere and cryosphere

We present an overview of recent multidisciplinary, multi-institutional efforts to identify and date major sources of combustion aerosol in the current and paleoatmospheres. The work was stimulated, in part, by an atmospheric particle \u27sample of opportunity\u27 collected at Summit, Greenland in August 1994, that bore the 14C imprint of biomass burning. During the summer field seasons of 1995 and 1996, we collected air filter, surface snow and snowpit samples to investigate chemical and isotopic evidence of combustion particles that had been transported from distant fires. Among the chemical tracers employed for source identification are organic acids, potassium and ammonium ions, and elemental and organic components of carbonaceous particles. Ion chromatography, performed by members of the Climate Change Research Center (University of New Hampshire), has been especially valuable in indicating periods at Summit that were likely to have been affected by the long range transport of biomass burning aerosol. Univariate and multivariate patterns of the ion concentrations in the snow and ice pinpointed surface and snowpit samples for the direct analysis of particulate (soot) carbon and carbon isotopes. The research at NIST is focusing on graphitic and polycyclic aromatic carbon, which serve as almost certain indicators of fire, and measurements of carbon isotopes, especially 14C, to distinguish fossil and biomass combustion sources. Complementing the chemical and isotopic record, are direct \u27visual\u27 (satellite imagery) records and less direct backtrajectory records, to indicate geographic source regions and transport paths. In this paper we illustrate the unique way in which the synthesis of the chemical, isotopic, satellite and trajectory data enhances our ability to develop the recent history of the formation and transport of soot deposited in the polar snow and ice

Generation of spin-wave dark solitons with phase engineering

We generate experimentally spin-wave envelope dark solitons from rectangular high-frequency dark input pulses with externally introduced phase shifts in yttrium-iron garnet magnetic fims. We observe the generation of both odd and even numbers of magnetic dark solitons when the external phase shift varies. The experimental results are in a good qualitative agreement with the theory of the dark-soliton generation in magnetic films developed earlier [Phys. Rev. Lett. 82, 2583 (1999)].Comment: 6 pages, including 7 figures, submitted to Phys. Rev.

Coupling Biophysical Processes and Water Rights To Simulate Spatially Distributed Water Use in an Intensively Managed Hydrologic System

Humans have significantly altered the redistribution of water in intensively managed hydrologic systems, shifting the spatiotemporal patterns of surface water. Evaluating water availability requires integration of hydrologic processes and associated human influences. In this study, we summarize the development and evaluation of an extensible hydrologic model that explicitly integrates water rights to spatially distribute irrigation waters in a semi-arid agricultural region in the western US, using the Envision integrated modeling platform. The model captures both human and biophysical systems, particularly the diversion of water from the Boise River, which is the main water source that supports irrigated agriculture in this region. In agricultural areas, water demand is estimated as a function of crop type and local environmental conditions. Surface water to meet crop demand is diverted from the stream reaches, constrained by the amount of water available in the stream, the waterrights- appropriated amount, and the priority dates associated with particular places of use. Results, measured by flow rates at gaged stream and canal locations within the study area, suggest that the impacts of irrigation activities on the magnitude and timing of flows through this intensively managed system are well captured. The multi-year averaged diverted water from the Boise River matches observations well, reflecting the appropriation of water according to the water rights database. Because of the spatially explicit implementation of surface water diversion, the model can help diagnose places and times where water resources are likely insufficient to meet agricultural water demands, and inform future water management decisions

Stability and Manipulation in Representative Democracies

This paper is devoted to the analysis of all constitutions equipped with electoral systems involving two step procedures. First, one candidate is elected in every jurisdiction by the electors in that jurisdiction, according to some aggregation procedure. Second, another aggregation procedure collects the names of the jurisdictional winners in order to designate the final winner. It appears that whenever individuals are allowed to change jurisdiction when casting their ballot, they are able to manipulate the result of the election except in very few cases. When imposing a paretian condition on every jurisdiction?s voting rule, it is shown that, in the case of any finite number of candidates, any two steps voting rule that is not manipulable by movement of the electors necessarily gives to every voter the power of overruling the unanimity on its own. A characterization of the set of these rules is next provided in the case of two candidates

7th Workshop on Matrix Equations and Tensor Techniques

No abstract availabl