Smooth Weight Research Articles

Control of Canadian once-through direct cycle supercritical water-cooled reactors

Canadian supercritical water-cooled reactor (SCWR) can be modelled as a Multiple-input Multiple-output (MIMO) system. It has a high power-to-flow ratio, strong cross-coupling and high degree of nonlinearity in its dynamic characteristics. Among the outputs, the steam temperature is strongly affected by the reactor power and the most challenging to control. It is difficult to adopt a traditional control system design methodology to obtain a control system with satisfactory performance. In this paper, feedforward control is applied to reduce the effect on steam temperature from the reactor power. Single-input Single-output (SISO) feedback controllers are synthesized in the frequency domain. Using the feedforward controller, the steam temperature variation due to disturbances at the reactor power has been significantly suppressed. The control system can effectively maintain the overall system stability and regulate the plant around a specified operating condition. To deal with the nonlinearities, gain scheduling control strategy is adopted. Different sets of controllers combined by smooth weight functions are used for the plant at different load conditions. The proposed control strategies have been evaluated under various operating scenarios. Simulation results show that satisfactory performance can successfully achieved by the designed control system.

Integral Operators, Embedding Theorems and a Littlewood–Paley Formula on Weighted Fock Spaces

We obtain a complete characterization of the entire functions $$g$$ such that the integral operator $$(T_ g f)(z)=\int _{0}^{z}f(\zeta )\,g'(\zeta )\,d\zeta $$ is bounded or compact, on a large class of Fock spaces $${\mathcal {F}}^\phi _p$$ , induced by smooth radial weights that decay faster than the classical Gaussian one. In some respects, these spaces turn out to be significantly different from the classical Fock spaces. Descriptions of Schatten class integral operators are also provided. En route, we prove a Littlewood–Paley formula for $$||\cdot ||_{{\mathcal {F}}^\phi _p}$$ and we characterize the positive Borel measures for which $${\mathcal {F}}^\phi _p\subset L^q(\mu )$$ , $$0<p,q<\infty $$ . In addition, we also address the question of describing the subspaces of $${\mathcal {F}}^\phi _p$$ that are invariant under the classical Volterra integral operator.

Optimal one-parameter observables for the Abelian Z′ in e+e-→μ+μ-process

To detect off-shell Abelian Z′ boson in e+e-→μ+μ-, we propose one-parameter observables with the best value-to-uncertainty ratio. The observables are constructed by angular integration of the differential cross-section with smooth weight functions. The value-to-uncertainty ratio is used as a criterion to select the unique weight function leading to the observable with the best statistical power for data analysis. The observables allow to select either vector or axial-vector Z′ couplings to leptons. The obtained observable can be useful in future experiments at lepton colliders such as the ILC.

Geodesic Binding for Degenerate Character Geometry Using Sparse Voxelization.

We propose a fully automatic method for specifying influence weights for closed-form skinning methods, such as linear blend or dual quaternion skinning. Our method is designed to work with production meshes that may contain non-manifold geometry, be non-watertight, have intersecting triangles, or be comprised of multiple connected components. Starting from a character rest pose mesh and skeleton hierarchy, we first voxelize the input geometry. The resulting sparse voxelization is then used to calculate binding weights, based on the geodesic distance between each voxel lying on a skeleton "bone" and all non-exterior voxels. This yields smooth weights at interactive rates, without time-constants, iteration parameters, or costly optimization at bind or pose time. By decoupling weight assignment from distance computation we make it possible to modify weights interactively, at pose time, without additional pre-processing or computation. This allows artists to assess impact of weight selection in the context in which they are used.

Effects of the smoothness of partitions of unity on the quality of representation of singular enrichments for GFEM/XFEM stress approximations around brittle cracks

The convergence rates of the conventional generalized/extended finite element method (GFEM/XFEM) in crack modeling are similar to the convergence rates of the finite element method (FEM) (Laborde et al., 2005 and Béchet et al., 2005) unless the crack tip enrichment functions are applied in a subdomain with fixed dimension, independently of the mesh parameter h and also demanding some special care for blending along the transition zone (Chahine et al., 2006 and Taracón et al., 2009). Thus, to improve convergence rates, more degrees of freedom (DOF) are generated due to the larger quantity of enriched nodes. This work seeks to identify and understand the advantages of better capturing the information provided by singular enrichments over mesh-based smooth partitions of unity (PoU). Such PoU with higher regularity can be built through the so-called Ck-GFEM framework, following Duarte et al. (2006), based on a moving least square of degree zero and considering mesh-based smooth weighting functions associated with arbitrary polygonal clouds. The purpose herein is to investigate some possible advantages of mesh-based smooth PoU for modeling discontinuities and singularities, in two-dimensional problems of linear elastic fracture mechanics, in such a fashion that the discretization error associated to stress discontinuities inherent in standard C0-continuous GFEM/XFEM approximations is eliminated. The procedure shares features similar to the standard FEM regarding domain partition and numerical integration but, as neither the PoU nor the enrichment functions are defined in natural domains, the integrations are performed using only global coordinates. The approximation capabilities of Ck-GFEM discretizations with different patterns of singular enrichment distribution are investigated by analyzing the convergence rates of the h and p versions, considering global measures in terms of strain energy and L2-norm of displacements. The effects on stability are also verified by analyzing the evolution of the condition number. The effect of smoothness on conditioning is investigated and the eigenvalues distributions are used to identify the several aspects involved: the smoothness of the PoU, the different types of enrichment functions and the pattern of enrichment. The performance of the smooth approximations is compared to the C0 counterparts built using conventional C0 FEM-based PoU. It is shown that smoothness in the presence of extrinsically applied singular enrichments is important, as the information provided by such enrichment is better captured. In addition, there are no stress jumps around singularities, reducing error propagation beyond the neighborhood of the singularity.

Near-realtime source analysis of the 20 March 2012 Ometepec-Pinotepa Nacional, Mexico earthquake

We apply a single-step, finite-fault analysis procedure to derive a coseismic slip model for the large MW 7.4 Ometepec-Pinotepa Nacional, Mexico earthquake of 20 March 2012, using teleseismic P waveforms recorded by the Global Seismographic Network. The inversion is conducted in near-realtime using source parameters available from the USGS/NEIC and the Global Centroid Moment Tensor (gCMT) project. The fault orientation and slip angle are obtained from the gCMT mechanism assuming that the fault coincides with the shallow-dipping nodal plane. The fault dimensions and maximum rise time are based on the magnitude reported for the event. Teleseismic data from the USGS/NEIC Continuous Waveform Buffer database are used in the inversion with record start times set to the P-wave arrivals used to compute the earthquake hypocenter. The inversion is stabilized by requiring a smooth transition of slip across the fault while minimizing the seismic moment. These constraints are applied using a smoothing weight that is estimated from the inverse problem, allowing the recovery of the least-complicated rupture history in a single step. Inversion of the deconvolved, ground-displacement waveforms reveals a simple, circular rupture similar in extent to the source identified by the USGS/NEIC using body-and surface-wave data, indicating that the teleseismic P waves can provide a first-order source model for the event in near-realtime. Additional inversions conducted using velocity records identify a more-detailed rupture model characterized by an elliptical 2500km2 source region extending updip and downdip from the hypocenter. This elliptical source preserves the orientation and overall dimensions of a dual-source slip model obtained recently by other investigators using local strong motions and global seismic waveforms. The results indicate that velocity waveforms could provide additional details of the earthquake rupture in near-realtime, finite-fault inversions using teleseismic P waves.

Low-Lying Zeros of Maass Form L-Functions

The Katz-Sarnak density conjecture states that the scaling limits of the distributions of zeros of families of automorphic $L$-functions agree with the scaling limits of eigenvalue distributions of classical subgroups of the unitary groups $U(N)$. This conjecture is often tested by way of computing particular statistics, such as the one-level density, which evaluates a test function with compactly supported Fourier transform at normalized zeros near the central point. Iwaniec, Luo, and Sarnak studied the one-level densities of cuspidal newforms of weight $k$ and level $N$. They showed in the limit as $kN \to\infty$ that these families have one-level densities agreeing with orthogonal type for test functions with Fourier transform supported in $(-2,2)$. Exceeding $(-1,1)$ is important as the three orthogonal groups are indistinguishable for support up to $(-1,1)$ but are distinguishable for any larger support. We study the other family of ${\rm GL}_2$ automorphic forms over $\mathbb{Q}$: Maass forms. To facilitate the analysis, we use smooth weight functions in the Kuznetsov formula which, among other restrictions, vanish to order $M$ at the origin. For test functions with Fourier transform supported inside $\left(-2 + \frac{2}{2M+1}, 2 - \frac{2}{2M+1}\right)$, we unconditionally prove the one-level density of the low-lying zeros of level 1 Maass forms, as the eigenvalues tend to infinity, agrees only with that of the scaling limit of orthogonal matrices.

Small Deviations of Series of Independent Nonnegative Random Variables with Smooth Weights

We study the logarithmic small deviations of $\sum_{j\ge 1} \lambda_j X_j$, where $\{X_j\}$ are independent identically distributed nonnegative random variables and $\{\lambda_j\}$ is a sequence of positive and nonincreasing numbers satisfying certain conditions of regularity.

Multi-structural fast nonlinear model-based predictive control of a hydronic heating system

Buildings consume a significant amount of energy to maintain the indoor thermal comfort. One way to reduce the energy consumption in buildings is to improve the overall energy efficiency through integrated advanced controls. It is undoubted that incorporating a model and utilizing future information in real-time building operation offers great energy saving potentials. However, there are many barriers preventing this from happening. Building systems are nonlinear and multiple-input-multiple-output (MIMO) in nature. Conventional approach with a global search solver and a detailed model simulator or direct nonlinear model predictive control (MPC) incurs prohibitive computational cost. This paper proposes a multi-structural fast nonlinear model predictive control (MPC) for handling nonlinear building systems and applied it on a hydronic heating system. The methodology remains the advantages of linear classical MPC and solves the nonlinearity issues involved in thermal comfort and energy conservation oriented control. The simulation shows that the controllers can achieve the optimal solutions in less than five minutes for five days simulation in a full look-ahead scenario with a Duo T6400 2.0 GHz computer. The fastest scenario takes only thirty more seconds to accomplish, which makes the approach feasible for online implementation. The techniques of using MPC for achieving smooth day-night switch, band control, dynamic constraints, and dynamic weighting are discussed. The energy saving potential of applying the proposed MPCs is found to be between six to forty two percent. In addition, the techniques decouple the building system from the mechanical system and are applicable to other space conditioning systems as well.

On sums of $\mathit{SL}(3,\mathbb{Z})$ Kloosterman sums

We show that sums of the \(\mathit{SL}(3,\mathbb{Z})\) long element Kloosterman sum against a smooth weight function have cancelation due to the variation in argument of the Kloosterman sums, when each modulus is at least the square root of the other. Our main tool is Li’s generalization of the Kuznetsov formula on \(\mathit{SL}(3,\mathbb{R})\), which has to date been prohibitively difficult to apply. We first obtain analytic expressions for the weight functions on the Kloosterman sum side by converting them to Mellin–Barnes integral form. This allows us to relax the conditions on the test function and to produce a partial inversion formula suitable for studying sums of the long-element \(\mathit{SL}(3,\mathbb{Z})\) Kloosterman sums.

Optimal forecasts in the presence of structural breaks

This paper considers the problem of forecasting under continuous and discrete structural breaks and proposes weighting observations to obtain optimal forecasts in the MSFE sense. We derive optimal weights for one step ahead forecasts. Under continuous breaks, our approach largely recovers exponential smoothing weights. Under discrete breaks, we provide analytical expressions for optimal weights in models with a single regressor, and asymptotically valid weights for models with more than one regressor. It is shown that in these cases the optimal weight is the same across observations within a given regime and differs only across regimes. In practice, where information on structural breaks is uncertain, a forecasting procedure based on robust optimal weights is proposed. The relative performance of our proposed approach is investigated using Monte Carlo experiments and an empirical application to forecasting real GDP using the yield curve across nine industrial economies.

Anisotropic nonlocal means denoising

It has recently been proved that the popular nonlocal means (NLM) denoising algorithm does not optimally denoise images with sharp edges. Its weakness lies in the isotropic nature of the neighborhoods it uses to set its smoothing weights. In response, in this paper we introduce several theoretical and practical anisotropic nonlocal means (ANLM) algorithms and prove that they are near minimax optimal for edge-dominated images from the Horizon class. On real-world test images, an ANLM algorithm that adapts to the underlying image gradients outperforms NLM by a significant margin.

Full Field Image Reconstruction Is Suitable for High-Pitch Dual-Source Computed Tomography

The field of view (FOV) in high-pitch dual-source computed tomography (DSCT) is limited by the size of the second detector. The goal of this study was to develop and evaluate a full FOV image reconstruction technique for high-pitch DSCT. For reconstruction beyond the FOV of the second detector, raw data of the second system were extended to the full dimensions of the first system, using the partly existing data of the first system in combination with a very smooth transition weight function. During the weighted filtered backprojection, the data of the second system were applied with an additional weighting factor. This method was tested for different pitch values from 1.5 to 3.5 on a simulated phantom and on 25 high-pitch DSCT data sets acquired at pitch values of 1.6, 2.0, 2.5, 2.8, and 3.0. Images were reconstructed with FOV sizes of 260 × 260 and 500 × 500 mm. Image quality was assessed by 2 radiologists using a 5-point Likert scale and analyzed with repeated-measure analysis of variance. In phantom and patient data, full FOV image quality depended on pitch. Where complete projection data from both tube-detector systems were available, image quality was unaffected by pitch changes. Full FOV image quality was not compromised at pitch values of 1.6 and remained fully diagnostic up to a pitch of 2.0. At higher pitch values, there was an increasing difference in image quality between limited and full FOV images (P = 0.0097). With this new image reconstruction technique, full FOV image reconstruction can be used up to a pitch of 2.0.

Noise-resistant structure-preserving multiscale image decomposition

A challenge for current edge-preserving image decompositions is to deal with noisy images. Gradient- or magnitude difference-based techniques regard the noise boundary as edges, while the local extrema-based method suffers from averaging noisy envelops. We introduce local anisotropy derived from nonlinear local structure tensor to differentiate edges from fine-scale details and noises. Providing low smoothness weights to the places with large local anisotropy rather than a large gradient under the improved weighted least squares optimization framework, we present a noise-resistant, structure-preserving smoothing operator. By either progressively or recursively applying this operator we construct our structure-preserving multiscale image decomposition. Based on the key property of our algorithm, noise resistance, we compare our results with existing edge-preserving image decomposition methods and demonstrate the effectiveness and robustness of our structure-preserving decompositions in the context of image restoration, noisy image abstraction, and noisy image dehazing.

Evaluating a Case of Trochanteric Fracture and Left-sided Kyphosis Inhibiting Smooth Weight Shift

Evaluating a Case of Trochanteric Fracture and Left-sided Kyphosis Inhibiting Smooth Weight Shift

Optimal Forecasts in the Presence of Structural Breaks

This paper considers the problem of forecasting under continuous and discrete structural breaks and proposes weighting observations to obtain optimal forecasts in the MSFE sense. We derive optimal weights for continuous and discrete break processes. Under continuous breaks, our approach recovers exponential smoothing weights. Under discrete breaks, we provide analytical expressions for the weights in models with a single regressor and asymptotically for larger models. It is shown that in these cases the value of the optimal weight is the same across observations within a given regime and differs only across regimes. In practice, where information on structural breaks is uncertain a forecasting procedure based on robust weights is proposed. Monte Carlo experiments and an empirical application to the predictive power of the yield curve analyze the performance of our approach relative to other forecasting methods.

Fast low-memory seamless photo blending on massive point clouds using a streaming framework

We present an efficient scalable streaming technique for mapping highly detailed color information on extremely dense point clouds. Our method does not require meshing or extensive processing of the input model, works on a coarsely spatially reordered point stream, and can adaptively refine point cloud geometry on the basis of image content. Seamless multiband image blending is obtained by using GPU-accelerated screen-space operators, which solve point set visibility, compute a per-pixel view-dependent weight, and ensure a smooth weighting function over each input image. The proposed approach works independently on each image in a memory-coherent manner, and can be easily extended to include further image-quality estimators. The effectiveness of the method is demonstrated on a series of massive real-world point datasets.

MODELING DEFOLIATION CONDITIONS IN MODERATE CANOPY DENSITY AND CLOSED CONIFEROUS FOREST USING LANDSAT TM DATA

It is an important subject to monitor and assess forest resource quality.This not only relates to forest industry, but also affects regional environment and continuable development.This paper quantatively probes into the feasibility of mapping and assessing forest defoliation by remote sensing data, and indicates there is some correlative relation between the TM5/TM4 ratio and needle loss percentage. The nonlinear relation between the defoliation and TM5/TM4 ratio is established by using nonparametric smoothing weight method and it is compared with linear relation. Powerful numericai results are provided to search for the best remote sensing parameter discriminating needle loss percentage. It is concluded that Logist curve is suitable for describing forest strecture change caused by defoliation.

Blended intrinsic maps

This paper describes a fully automatic pipeline for finding an intrinsic map between two non-isometric, genus zero surfaces. Our approach is based on the observation that efficient methods exist to search for nearly isometric maps (e.g., Möbius Voting or Heat Kernel Maps), but no single solution found with these methods provides low-distortion everywhere for pairs of surfaces differing by large deformations. To address this problem, we suggest using a weighted combination of these maps to produce a "blended map." This approach enables algorithms that leverage efficient search procedures, yet can provide the flexibility to handle large deformations. The main challenges of this approach lie in finding a set of candidate maps { m i } and their associated blending weights { b i ( p )} for every point p on the surface. We address these challenges specifically for conformal maps by making the following contributions. First, we provide a way to blend maps, defining the image of p as the weighted geodesic centroid of m i ( p ). Second, we provide a definition for smooth blending weights at every point p that are proportional to the area preservation of m i at p . Third, we solve a global optimization problem that selects candidate maps based both on their area preservation and consistency with other selected maps. During experiments with these methods, we find that our algorithm produces blended maps that align semantic features better than alternative approaches over a variety of data sets.

Optic Flow in Harmony

Most variational optic flow approaches just consist of three constituents: a data term, a smoothness term and a smoothness weight. In this paper, we present an approach that harmonises these three components. We start by developing an advanced data term that is robust under outliers and varying illumination conditions. This is achieved by using constraint normalisation, and an HSV colour representation with higher order constancy assumptions and a separate robust penalisation. Our novel anisotropic smoothness is designed to work complementary to the data term. To this end, it incorporates directional information from the data constraints to enable a filling-in of information solely in the direction where the data term gives no information, yielding an optimal complementary smoothing behaviour. This strategy is applied in the spatial as well as in the spatio-temporal domain. Finally, we propose a simple method for automatically determining the optimal smoothness weight. This method bases on a novel concept that we call "optimal prediction principle" (OPP). It states that the flow field obtained with the optimal smoothness weight allows for the best prediction of the next frames in the image sequence. The benefits of our "optic flow in harmony" (OFH) approach are demonstrated by an extensive experimental validation and by a competitive performance at the widely used Middlebury optic flow benchmark.