Grid structure impact in sparse point representation of derivatives

In the Sparse Point Representation (SPR) method the principle is to retain the function data indicated by significant interpolatory wavelet coefficients, which are defined as interpolation errors by means of an interpolating subdivision scheme. Typically, a SPR grid is coarse in smooth regions, and refined close to irregularities. Furthermore, the computation of partial derivatives of a function from the information of its SPR content is performed in two steps. The first one is a refinement procedure to extend the SPR by the inclusion of new interpolated point values in a security zone. Then, for points in the refined grid, such derivatives are approximated by uniform finite differences, using a step size proportional to each point local scale. If required neighboring stencils are not present in the grid, the corresponding missing point values are approximated from coarser scales using the interpolating subdivision scheme. Using the cubic interpolation subdivision scheme, we demonstrate that such adaptive finite differences can be formulated in terms of a collocation scheme based on the wavelet expansion associated to the SPR. For this purpose, we prove some results concerning the local behavior of such wavelet reconstruction operators, which stand for SPR grids having appropriate structures. This statement implies that the adaptive finite difference scheme and the one using the step size of the finest level produce the same result at SPR grid points. Consequently, in addition to the refinement strategy, our analysis indicates that some care must be taken concerning the grid structure, in order to keep the truncation error under a certain accuracy limit. Illustrating results are presented for 2D Maxwell's equation numerical solutions.

A fully adaptive multiresolution scheme for shock computations

The scheme is based on Ami Harten's ideas (Harten, 1994), the main tools coming from wavelet theory, in the framework of multiresolution analysis for cell averages. But instead of evolving cell averages on the finest uniform level, we propose to evolve just the cell averages on the grid determined by the significant wavelet coefficients. Typically, there are few cells in each time step, big cells on smooth regions, and smaller ones close to irregularities of the solution. For the numerical flux, we use a simple uniform central finite difference scheme, adapted to the size of each cell. If any of the required neighboring cell averages is not present, it is interpolated from coarser scales. But we switch to ENO scheme in the finest part of the grids. To show the feasibility and efficiency of the method, it is applied to a system arising in polymer-flooding of an oil reservoir. In terms of CPU time and memory requirements, it outperforms Harten's multiresolution algorithm.The proposed method applies to systems of conservation laws in 1Dpartial derivative(t)u(x, t) + partial derivative(x)f(u(x, t)) = 0, u(x, t) is an element of R-m. (1)In the spirit of finite volume methods, we shall consider the explicit schemeupsilon(mu)(n+1) = upsilon(mu)(n) - Deltat/hmu ((f) over bar (mu) - (f) over bar (mu)-) = [Dupsilon(n)](mu), (2)where mu is a point of an irregular grid Gamma, mu(-) is the left neighbor of A in Gamma, upsilon(mu)(n) approximate to 1/mu-mu(-) integral(mu-)(mu) u(x, t(n))dx are approximated cell averages of the solution, (f) over bar (mu) = (f) over bar (mu)(upsilon(n)) are the numerical fluxes, and D is the numerical evolution operator of the scheme.According to the definition of (f) over bar (mu), several schemes of this type have been proposed and successfully applied (LeVeque, 1990). Godunov, Lax-Wendroff, and ENO are some of the popular names. Godunov scheme resolves well the shocks, but accuracy (of first order) is poor in smooth regions. Lax-Wendroff is of second order, but produces dangerous oscillations close to shocks. ENO schemes are good alternatives, with high order and without serious oscillations. But the price is high computational cost.Ami Harten proposed in (Harten, 1994) a simple strategy to save expensive ENO flux calculations. The basic tools come from multiresolution analysis for cell averages on uniform grids, and the principle is that wavelet coefficients can be used for the characterization of local smoothness.. Typically, only few wavelet coefficients are significant. At the finest level, they indicate discontinuity points, where ENO numerical fluxes are computed exactly. Elsewhere, cheaper fluxes can be safely used, or just interpolated from coarser scales. Different applications of this principle have been explored by several authors, see for example (G-Muller and Muller, 1998).Our scheme also uses Ami Harten's ideas. But instead of evolving the cell averages on the finest uniform level, we propose to evolve the cell averages on sparse grids associated with the significant wavelet coefficients. This means that the total number of cells is small, with big cells in smooth regions and smaller ones close to irregularities. This task requires improved new tools, which are described next.

A template model predicts detection of sparse stimul

Contemporary models of contrast integration across space assume that pooling operates uniformly over the target region. For sparse stimuli, where high contrast regions are separated by areas containing no signal, this strategy may be sub-optimal because it pools more noise than signal as area increases. Little is known about the behaviour of human observers for detecting such stimuli. We performed an experiment in which three observers detected regular textures of various areas, and six levels of sparseness. Stimuli were regular grids of horizontal grating micropatches, each 1 cycle wide. We varied the ratio of signals (marks) to gaps (spaces), with mark:space ratios ranging from 1 : 0 (a dense texture with no spaces) to 1 : 24. To compensate for the decline in sensitivity with increasing distance from fixation, we adjusted the stimulus contrast as a function of eccentricity based on previous measurements [Baldwin, Meese & Baker, 2012, J Vis, 12(11):23]. We used the resulting area summation functions and psychometric slopes to test several filter-based models of signal combination. A MAX model failed to predict the thresholds, but did a good job on the slopes. Blanket summation of stimulus energy improved the threshold fit, but did not predict an observed slope increase with mark:space ratio. Our best model used a template matched to the sparseness of the stimulus, and pooled the squared contrast signal over space. Templates for regular patterns have also recently been proposed to explain the regular appearance of slightly irregular textures (Morgan et al, 2012, Proc R Soc B, 279, 2754–2760)

Grid-texture mechanisms in human vision:contrast detection of regular sparse micro-patterns requires specialist templates

Previous work has shown that human vision performs spatial integration of luminance contrast energy, where signals are squared and summed (with internal noise) over area at detection threshold. We tested that model here in an experiment using arrays of micro-pattern textures that varied in overall stimulus area and sparseness of their target elements, where the contrast of each element was normalised for sensitivity across the visual field. We found a power-law improvement in performance with stimulus area, and a decrease in sensitivity with sparseness. While the contrast integrator model performed well when target elements constituted 50–100% of the target area (replicating previous results), observers outperformed the model when texture elements were sparser than this. This result required the inclusion of further templates in our model, selective for grids of various regular texture densities. By assuming a MAX operation across these noisy mechanisms the model also accounted for the increase in the slope of the psychometric function that occurred as texture density decreased. Thus, for the first time, mechanisms that are selective for texture density have been revealed at contrast detection threshold. We suggest that these mechanisms have a role to play in the perception of visual textures.

Wavelets And Adaptive Grids For The Discontinuous Galerkin Method

In this paper, space adaptivity is introduced to control the error in the numerical solution of hyperbolic systems of conservation laws. The reference numerical scheme is a new version of the discontinuous Galerkin method, which uses an implicit diffusive term in the direction of the streamlines, for stability purposes. The decision whether to refine or to unrefine the grid in a certain location is taken according to the magnitude of wavelet coefficients, which are indicators of local smoothness of the numerical solution. Numerical solutions of the nonlinear Euler equations illustrate the efficiency of the method. © Springer 2005.

Resource use pattern analysis for predicting resource availability in opportunistic grids

This work presents a method for predicting resource availability in opportunistic grids by means of use pattern analysis (UPA), a technique based on non-supervised learning methods. This prediction method is based on the assumption of the existence of several classes of computational resource use patterns, which can be used to predict the resource availability. Trace-driven simulations validate this basic assumptions, which also provide the parameter settings for the accurate learning of resource use patterns. Experiments made with an implementation of the UPA method show the feasibility of its use in the scheduling of grid tasks with very little overhead. The experiments also demonstrate the method`s superiority over other predictive and non-predictive methods. An adaptative prediction method is suggested to deal with the lack of training data at initialization. Further adaptative behaviour is motivated by experiments which show that, in some special environments, reliable resource use patterns may not always be detected. Copyright (C) 2009 John Wiley & Sons, Ltd.

A numerical study of large sparse matrix exponentials arising in Markov chains

Krylov subspace techniques have been shown to yield robust methods for the numerical computation of large sparse matrix exponentials and especially the transient solutions of Markov Chains. The attractiveness of these methods results from the fact that they allow us to compute the action of a matrix exponential operator on an operand vector without having to compute, explicitly, the matrix exponential in isolation. In this paper we compare a Krylov-based method with some of the current approaches used for computing transient solutions of Markov chains. After a brief synthesis of the features of the methods used, wide-ranging numerical comparisons are performed on a power challenge array supercomputer on three different models. (C) 1999 Elsevier Science B.V. All rights reserved.AMS Classification: 65F99; 65L05; 65U05.

Population pharmacokinetics of perhexiline from very sparse, routine monitoring data

Using NONMEM, the population pharmacokinetics of perhexiline were studied in 88 patients (34 F, 54 M) who were being treated for refractory angina. Their mean +/- SD (range) age was 75 +/- 9.9 years (46-92), and the length of perhexiline treatment was 56 +/- 77 weeks (0.3-416). The sampling time after a dose was 14.1 +/- 21.4 hours (0.5-200), and the perhexiline plasma concentrations were 0.39 +/- 0.32 mg/L (0.03-1.56). A one-compartment model with first-order absorption was fitted to the data using the first-order (FO) approximation. The best model contained 2 subpopulations (obtained via the $MIXTURE subroutine) of 77 subjects (subgroup A) and 11 subjects (subgroup B) that had typical values for clearance (CL/F) of 21.8 L/h and 2.06 L/h, respectively. The volumes of distribution (V/F) were 1470 L and 260 L, respectively, which suggested a reduction in presystemic metabolism in subgroup B. The interindividual variability (CV%) was modeled logarithmically and for CL/F ranged from 69.1% (subgroup A) to 86.3% (subgroup B). The interindividual variability in V/F was 111%. The residual variability unexplained by the population model was 28.2%. These results confirm and extend the existing pharmacokinetic data on perhexiline, especially the bimodal distribution of CL/F manifested via an inherited deficiency in hepatic and extrahepatic CYP2D6 activity.

An augmented Lanczos algorithm for the efficient computation of a dot-product of a function of a large sparse symmetric matrix

The Lanczos algorithm is appreciated in many situations due to its speed. and economy of storage. However, the advantage that the Lanczos basis vectors need not be kept is lost when the algorithm is used to compute the action of a matrix function on a vector. Either the basis vectors need to be kept, or the Lanczos process needs to be applied twice. In this study we describe an augmented Lanczos algorithm to compute a dot product relative to a function of a large sparse symmetric matrix, without keeping the basis vectors.

Eigenvalue computations in the context of data-sparse approximations of integral operators

In this work, we consider the numerical solution of a large eigenvalue problem resulting from a finite rank discretization of an integral operator. We are interested in computing a few eigenpairs, with an iterative method, so a matrix representation that allows for fast matrix-vector products is required. Hierarchical matrices are appropriate for this setting, and also provide cheap LU decompositions required in the spectral transformation technique. We illustrate the use of freely available software tools to address the problem, in particular SLEPc for the eigensolvers and HLib for the construction of H-matrices. The numerical tests are performed using an astrophysics application. Results show the benefits of the data-sparse representation compared to standard storage schemes, in terms of computational cost as well as memory requirements.

A regulatory framework for short-term stochastic maintenance outage scheduling in smart grids

The current regulatory framework for maintenance outage scheduling in distribution systems needs revision to face the challenges of future smart grids. In the smart grid context, generation units and the system operator perform new roles with different objectives, and an efficient coordination between them becomes necessary. In this paper, the distribution system operator (DSO) of a microgrid receives the proposals for shortterm (ST) planned outages from the generation and transmission side, and has to decide the final outage plans, which is mandatory for the members to follow. The framework is based on a coordination procedure between the DSO and other market players. This paper undertakes the challenge of optimization problem in a smart grid where the operator faces with uncertainty. The results show the effectiveness and applicability of the proposed regulatory framework in the modified IEEE 34- bus test system.

Advances in smart grids - benefits on sharing background experiences from Portugal, Central Europe and Brazil

This paper presents ELECON - Electricity Consumption Analysis to Promote Energy Efficiency Considering Demand Response and Non-technical Losses, an international research project that involves European and Brazilian partners. ELECON focuses on energy efficiency increasing through consumer´s active participation which is a key area for Europe and Brazil cooperation. The project aims at significantly contributing towards the successful implementation of smart grids, focussing on the use of new methods that allow the efficient use of distributed energy resources, namely distributed generation, storage and demand response. ELECON puts together researchers from seven European and Brazilian partners, with consolidated research background and evidencing complementary competences. ELECON involves institutions of 3 European countries (Portugal, Germany, and France) and 4 Brazilian institutions. The complementary background and experience of the European and Brazilian partners is of main relevance to ensure the capacities required to achieve the proposed goals. In fact, the European Union (EU) and Brazil have very different resources and approaches in what concerns this area. Having huge hydro and fossil resources, Brazil has not been putting emphasis on distributed renewable based electricity generation. On the contrary, EU has been doing huge investments in this area, taking into account environmental concerns and also the economic EU external dependence dictated by huge requirements of energy related products imports. Sharing these different backgrounds allows the project team to propose new methodologies able to efficiently address the new challenges of smart grids.

Day-ahead resource scheduling in smart grids considering Vehicle-to-Grid and network constraints

Energy resource scheduling becomes increasingly important, as the use of distributed resources is intensified and massive gridable vehicle use is envisaged. The present paper proposes a methodology for dayahead energy resource scheduling for smart grids considering the intensive use of distributed generation and of gridable vehicles, usually referred as Vehicle- o-Grid (V2G). This method considers that the energy resources are managed by a Virtual Power Player (VPP) which established contracts with V2G owners. It takes into account these contracts, the user´s requirements subjected to the VPP, and several discharge price steps. Full AC power flow calculation included in the model allows taking into account network constraints. The influence of the successive day requirements on the day-ahead optimal solution is discussed and considered in the proposed model. A case study with a 33 bus distribution network and V2G is used to illustrate the good performance of the proposed method.

An integrated approach for distributed energy resource short term scheduling in smart grids considering realistic power system simulation

The large increase of distributed energy resources, including distributed generation, storage systems and demand response, especially in distribution networks, makes the management of the available resources a more complex and crucial process. With wind based generation gaining relevance, in terms of the generation mix, the fact that wind forecasting accuracy rapidly drops with the increase of the forecast anticipation time requires to undertake short-term and very short-term re-scheduling so the final implemented solution enables the lowest possible operation costs. This paper proposes a methodology for energy resource scheduling in smart grids, considering day ahead, hour ahead and five minutes ahead scheduling. The short-term scheduling, undertaken five minutes ahead, takes advantage of the high accuracy of the very-short term wind forecasting providing the user with more efficient scheduling solutions. The proposed method uses a Genetic Algorithm based approach for optimization that is able to cope with the hard execution time constraint of short-term scheduling. Realistic power system simulation, based on PSCAD , is used to validate the obtained solutions. The paper includes a case study with a 33 bus distribution network with high penetration of distributed energy resources implemented in PSCAD .