Local Average Research Articles

Stochastic subgrid‐scale parametrization for one‐dimensional shallow‐water dynamics using stochastic mode reduction

We address the question of parametrizing the subgrid scales in simulations of geophysical flows by applying stochastic mode reduction to the one‐dimensional stochastically forced shallow‐water equations. The problem is formulated in physical space by defining resolved variables as local spatial averages over finite‐volume cells and unresolved variables as corresponding residuals. Based on the assumption of a time‐scale separation between the slow spatial averages and the fast residuals, the stochastic mode reduction procedure is used to obtain a low‐resolution model for the spatial averages alone with local stochastic subgrid‐scale parametrization coupling each resolved variable only to a few neighbouring cells. The closure improves the results of the low‐resolution model and outperforms two purely empirical stochastic parametrizations. It is shown that the largest benefit is in the representation of the energy spectrum. By adjusting only a single coefficient (the strength of the noise) we observe that there is a potential for improving the performance of the parametrization, if additional tuning of the coefficients is performed. In addition, the scale‐awareness of the parametrizations is studied.

Improved MUP Template Estimation Using Local Time Warping and Kernel Weighted Averaging.

A motor unit potential (MUP) template, which represents the shapes of the MUPs within a MUP train, provides information related to the morphology and physiology of the sampled motor unit. This work presents an improved MUP template estimation technique that uses local time warping and kernel weighted ensemble averaging. An analysis of the algorithm, and a description of the improvements compared with spike triggered averaging is given. MUP template estimates were evaluated using simulated EMG signals with a known gold standard template for each motor unit potential train. Statistically significant reduction in template estimation error is shown, both within the baseline and duration portions of a MUP.

A case study of multi-structure turbulence: Uniformly sheared flow distorted by a grid

The fine and large–scale structures of spatially developing uniformly sheared flow (USF) and USF distorted by a square–mesh grid were examined experimentally using one– and two–point, two–component hot–wire anemometry. In agreement with previous findings, it was confirmed that USF has a far downstream region, where the dissipation parameter Cε is approximately constant, and an intermediate region, where it scales with the local turbulent Reynolds number as Cɛ∝Reλ−0.6. The insertion of a grid across the USF resulted in the creation of multi-structure turbulence (a flow in which at least two kinds of dominant eddies exist and contribute significantly to the local averages at the energy-containing level) and a permanent reduction of the kinetic energy and the integral length scales of the turbulence. Near the grid the dissipation parameter scaled as Cɛ∝Reλ−1, as in decaying grid turbulence, despite the opposite evolution rates of Reλ in the two flows. The turbulence fine structure within this multi–structure region was unaffected significantly by the grid, whereas the large–scale anisotropy was markedly changed. Second–order structure functions, normalised by Kolmogorov scales, collapsed in the viscous sub–range , whereas within the inertial sub–range the effects of grid insertion were measurable.

Approximating Forest Resource Dynamics in Peninsular Malaysia Using Parametric and Nonparametric Models, and Its Implications for Establishing Forest Reference (Emission) Levels under REDD+

Forest reference (emission) levels (FREL/FRLs) are baselines for REDD+, and 34 countries have submitted their FREL/FRLs to UNFCCC by January 2018. Most of them used simple historical average without considering the stages of forest transition. This research suggested that the period of calculating FREL/FRLs of simple historical average should be properly chosen if these countries are occupying multiple stages or sub-stages of forest transition. Moreover, as a case study, this research applied both parametric and nonparametric models to approximate forest area dynamics with regard to per capita GDP in Peninsular Malaysia from 1971 to 2016. This research found that, in the case of Peninsular Malaysia, among the parametric models, the biexponential model outperformed the other growth models, while two of the nonparametric models i.e. Friedman local averaging and Nadaraya–Watson kernel smoothing models are the best among all the models on the basis of their RSS, RMSE, and MAE indices. Based on the results of our leave-last-five-out CV, however, the research found that the biexponential and Nadaraya–Watson kernel smoothing models performed best, although the performance of the other two nonparametric models remains unknown. Nonparametric model results indicated that Peninsular Malaysia experienced four sub-stages since 1971 and each sub-stage had different linear trends, yet it still did not reach the turning point of forest transition. This research also found that a linear projection using historical deforestation data when the per capita GDP level reached US$8000 was appropriate for setting FREL/FRLs.

Theoretical Prediction of Thermal Polarization.

We present a mean-field theory to explain the thermo-orientation effect in an off-center Stockmayer fluid. This effect is the underlying cause of thermally induced polarization and thermally induced monopoles, which have recently been predicted theoretically. Unlike previous theories that are based either on phenomenological equations or on scaling arguments, our approach does not require any fitting parameters. Given an equation of state and assuming local equilibrium, we construct an effective Hamiltonian for the computation of local Boltzmann averages. This simple theoretical treatment predicts molecular orientations that are in very good agreement with simulation results for the range of dipole strengths investigated. By decomposing the overall alignment into contributions from the temperature and density gradients, we shed further light on how the nonequilibrium result arises from the competition between the two gradients.

Efficient estimation for time-varying coefficient longitudinal models

ABSTRACTFor estimation of time-varying coefficient longitudinal models, the widely used local least-squares (LS) or covariance-weighted local LS smoothing uses information from the local sample average. Motivated by the fact that a combination of multiple quantiles provides a more complete picture of the distribution, we investigate quantile regression-based methods to improve efficiency by optimally combining information across quantiles. Under the working independence scenario, the asymptotic variance of the proposed estimator approaches the Cramér–Rao lower bound. In the presence of dependence among within-subject measurements, we adopt a prewhitening technique to transform regression errors into independent innovations and show that the prewhitened optimally weighted quantile average estimator asymptotically achieves the Cramér–Rao bound for the independent innovations. Fully data-driven bandwidth selection and optimal weights estimation are implemented through a two-step procedure. Monte Carlo studies show that the proposed method delivers more robust and superior overall performance than that of the existing methods.

The Value and Feasibility of Farming Differently Than the Local Average

The purpose of this research is to quantify the value of being different than the local average and feasibility of distinguishing particular parts of an operation from the local average. Kansas crop farms are broken down by their farm characteristics, production practices, and management performances. An ordinary least squares regression model is used to quantify the value of having different than average characteristics, practices, and management performances. The degree farms have distinguished particular parts of their operations from the average, and how consistently they distinguish their cost, yields, and prices from the average are also analyzed. Farms’ relative size, workers per acre, planting intensity, machine costs, yields, and prices are all significantly related to farm relative performance. Farms’ characteristics are generally more different from one another than their production practices and management performances, while over time farms’ relative cost management performances are more consistent than their relative yield and price management performances.

Rotation-invariant features based on directional coding for texture classification

A directional coding (DC) method is proposed to extract rotation-invariant features for texture classification. DC uses four orientations in $$3\times 3$$ neighborhood pixel. For each orientation, the rank order of the central gray-level pixel is calculated. The four ranks are used to get 15 codes. The codes are combined with the information of the central pixel to extract 30 rotation-invariant features. For a multi-resolution study, DC is calculated by altering the window size around a central pixel. The number of samples is restricted to eight neighbors by local averaging. Therefore, in each single-scale DC histogram, the number of bins is kept small and constant. Outex, CUReT and KTH_TIPS2 databases are used to evaluate and compare the proposed method against some state-of-the-art local binary techniques and other texture analysis methods. The results obtained suggest that the proposed DC method outperforms other methods making it attractive for use in computer vision problems.

Classification with incomplete functional covariates

We consider the problem of functional classification when the covariate may be unavailable (unobservable) on some subsets of its domain. Given the observed fragments of the functional covariates, we propose a strongly consistent nonparametric classifier based on local averaging.

2SLS versus 2SRI: Appropriate methods for rare outcomes and/or rare exposures.

This study used Monte Carlo simulations to examine the ability of the two-stage least squares (2SLS) estimator and two-stage residual inclusion (2SRI) estimators with varying forms of residuals to estimate the local average and population average treatment effect parameters in models with binary outcome, endogenous binary treatment, and single binary instrument. The rarity of the outcome and the treatment was varied across simulation scenarios. Results showed that 2SLS generated consistent estimates of the local average treatment effects (LATE) and biased estimates of the average treatment effects (ATE) across all scenarios. 2SRI approaches, in general, produced biased estimates of both LATE and ATE under all scenarios. 2SRI using generalized residuals minimized the bias in ATE estimates. Use of 2SLS and 2SRI is illustrated in an empirical application estimating the effects of long-term care insurance on a variety of binary health care utilization outcomes among the near-elderly using the Health and Retirement Study.

Investigation on vertical plug formation of coarse particles in a non-mechanical feeder by CFD-DEM coupling method

Plug flow attracts continuous interest due to its advantages of low particle attrition, low pipeline wear and low energy consumption. A novel non-mechanical draft tube type feeder (DTF) has been proposed in our previous work for vertical plug conveying of coarse particles. Detailed particle motion behaviors and plug formation mechanisms in the draft tube type feeder are investigated by the combined approach of Computational Fluid Dynamics and Discrete Element Method (CFD-DEM) in the present study. The CFD-DEM method based on local averaging of granular matter is used to deal with fluid cell sizes smaller than particle sizes under the specific conditions. The applicability of the model is verified by comparing the calculated results with the experimental results of vertical plug formation of 6mm glass beads in a draft tube type feeder, in terms of plug flow pattern, pressure drop and solid mass flow rate. Detailed analysis of the particle entrainment in feeder container, flow properties at riser inlet and natural plug formation in riser are then carried out. It is found that both gas and particle flows result in entrainment effect on particles, respectively, through fluid-particle and particle-particle interactions. The linear increase of solid mass flow rate with superficial gas velocity is closely related to the linear increase of particle vertical velocity at riser inlet. Plug formation is achieved in a natural way, which shows the features of self-organization phenomenon. Particle concentration is a key parameter in this self-organization process. This study provides some insights into the natural plug formation of coarse particles in a non-mechanical feeder. The model should be useful to study the gas-solid flow of coarse particles in a confined domain with complex geometry, where the fluid cell size may be smaller than the particle size.

Equine Caregiver Information-Seeking Preferences: Surveys in the Midwest

Two surveys of equine owners/managers and professionals using convenience sampling via multimodal distribution were conducted on perceptions of equid health and well-being (n = 142) and equine nutrition and feeding practices (n = 151). Surveys were distributed in 2014–2015 (health and well-being) and 2016 (nutrition and feeding) to similar email lists and social media sites; both included questions regarding information-seeking preferences. Respondents were mostly female (62% health and well-being, 84% nutrition and feeding) and had over 20 years of equine ownership/management experience (47% and 61%, respectively). Participants in the Nutrition and Feeding survey reported seeking information from veterinarians (77%), books/magazines (42%), horse enthusiasts (38%), friends/family (35%), Internet/social media (28%), feed company representative (28%), farrier (25%), scientific publications (25%), trainer/instructor (21%), equine nutritionist (19%), equine dentist (7%), extension specialist (7%), and radio (1%). The Health and Well-Being survey requested information regarding participants' likeliness (5-point Likert scale) of trusting various sources for animal well-being information. Respondents from the Health and Well-Being survey indicated veterinarians/nutritionists (average = 4.5) and extension specialists/university personnel (average = 4.0) as their top two trusted sources of information, and local (average = 2.9) and national humane societies/rescues (average = 2.8) their least-trusted sources of information. These results elucidated the information-seeking preferences of horse owners from the Upper Midwest regarding two equine topics. Veterinarians are sought as a source of equine information in the Upper Midwest.

Mixed method evaluation of the Virtual Traveller physically active lesson intervention: An analysis using the RE-AIM framework

BackgroundPhysically active lessons integrating movement into academic content are a way to increase children’s physical activity levels. Virtual Traveller was a physically active lesson intervention set in Year 4 (aged 8–9) primary school classes in Greater London, UK. Implemented by classroom teachers, it was a six-week intervention providing 10-min physically active Virtual Field Trips three times a week. The aim of this paper is to report the process evaluation of the Virtual Traveller randomized controlled trial according to RE-AIM framework criteria (Reach, Effectiveness, Adoption, Implementation and Maintenance). MethodsA mixed methods approach to evaluation was conducted with five intervention group classes. Six sources of data were collected via informed consent logs, teacher session logs, teacher and pupil questionnaires, teacher interviews and pupil focus groups. ResultsHigh participation and low attrition rates were identified (Reach) alongside positive evaluations of Virtual Traveller sessions from pupil and teachers (Effectiveness). Participants were from more deprived and ethnic backgrounds than local and national averages, with Virtual Traveller having the potential to be a free intervention (Adoption). 70% of sessions were delivered overall (Implementation) but no maintenance of the programme was evident at three month follow-up (Maintenance). ConclusionsMixed method evaluation of Virtual Traveller showed potential for it to be implemented as a low-cost physically active lesson intervention in UK primary schools.

Category structure determines the relative attractiveness of global versus local averages.

Stimuli that capture the central tendency of presented exemplars are often preferred-a phenomenon also known as the classic beauty-in-averageness effect. However, recent studies have shown that this effect can reverse under certain conditions. We propose that a key variable for such ugliness-in-averageness effects is the category structure of the presented exemplars. When exemplars cluster into multiple subcategories, the global average should no longer reflect the underlying stimulus distributions, and will thereby become unattractive. In contrast, the subcategory averages (i.e., local averages) should better reflect the stimulus distributions, and become more attractive. In 3 studies, we presented participants with dot patterns belonging to 2 different subcategories. Importantly, across studies, we also manipulated the distinctiveness of the subcategories. We found that participants preferred the local averages over the global average when they first learned to classify the patterns into 2 different subcategories in a contrastive categorization paradigm (Experiment 1). Moreover, participants still preferred local averages when first classifying patterns into a single category (Experiment 2) or when not classifying patterns at all during incidental learning (Experiment 3), as long as the subcategories were sufficiently distinct. Finally, as a proof-of-concept, we mapped our empirical results onto predictions generated by a well-known computational model of category learning (the Generalized Context Model [GCM]). Overall, our findings emphasize the key role of categorization for understanding the nature of preferences, including any effects that emerge from stimulus averaging. (PsycINFO Database Record

NetSmooth: Network-smoothing based imputation for single cell RNA-seq

Single cell RNA-seq (scRNA-seq) experiments suffer from a range of characteristic technical biases, such as dropouts (zero or near zero counts) and high variance. Current analysis methods rely on imputing missing values by various means of local averaging or regression, often amplifying biases inherent in the data. We present netSmooth, a network-diffusion based method that uses priors for the covariance structure of gene expression profiles on scRNA-seq experiments in order to smooth expression values. We demonstrate that netSmooth improves clustering results of scRNA-seq experiments from distinct cell populations, time-course experiments, and cancer genomics. We provide an R package for our method, available at: https://github.com/BIMSBbioinfo/netSmooth.

NetSmooth: Network-smoothing based imputation for single cell RNA-seq.

Single cell RNA-seq (scRNA-seq) experiments suffer from a range of characteristic technical biases, such as dropouts (zero or near zero counts) and high variance. Current analysis methods rely on imputing missing values by various means of local averaging or regression, often amplifying biases inherent in the data. We present netSmooth, a network-diffusion based method that uses priors for the covariance structure of gene expression profiles on scRNA-seq experiments in order to smooth expression values. We demonstrate that netSmooth improves clustering results of scRNA-seq experiments from distinct cell populations, time-course experiments, and cancer genomics. We provide an R package for our method, available at: https://github.com/BIMSBbioinfo/netSmooth.

Greedy Algorithms for Optimal Measurements Selection in State Estimation Using Reduced Models

We consider the problem of optimal recovery of an unknown function u in a Hilbert space V from measurements of the form j (u), j = 1,. .. , m, where the j are known linear functionals on V. We are motivated by the setting where u is a solution to a PDE with some unknown parameters , therefore lying on a certain manifold contained in V. Following the approach adopted in [9, 3], the prior on the unknown function can be described in terms of its approximability by finite-dimensional reduced model spaces (V n) n≥1 where dim(V n) = n. Examples of such spaces include classical approximation spaces, e.g. finite elements or trigonometric polynomials, as well as reduced basis spaces which are designed to match the solution manifold more closely. The error bounds for optimal recovery under such priors are of the form µ(V n , W m)e n , where e n is the accuracy of the reduced model V n and µ(V n , W m) is the inverse of an inf-sup constant that describe the angle between V n and the space W m spanned by the Riesz representers of (1 ,. .. , m). This paper addresses the problem of properly selecting the measurement func-tionals, in order to control at best the stability constant µ(V n , W m), for a given reduced model space V n. Assuming that the j can be picked from a given dictionary D we introduce and analyze greedy algorithms that perform a sub-optimal selection in reasonable computational time. We study the particular case of dictionaries that consist either of point value evaluations or local averages, as idealized models for sensors in physical systems. Our theoretical analysis and greedy algorithms may therefore be used in order to optimize the position of such sensors.

NONLINEAR NONLOCAL MULTICONTINUA UPSCALING FRAMEWORK AND ITS APPLICATIONS

In this paper, we discuss multiscale methods for nonlinear problems. The main idea of these approaches is to use local constraints and solve problems in oversampled regions for constructing macroscopic equations. These techniques are intended for problems without scale separation and high contrast, which often occur in applications. For linear problems, the local solutions with constraints are used as basis functions. This technique is called Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM). GMsFEM identifies macroscopic quantities based on rigorous analysis. In corresponding upscaling methods, the multiscale basis functions are selected such that the degrees of freedom have physical meanings, such as averages of the solution on each continuum. This paper extends the linear concepts to nonlinear problems, where the local problems are nonlinear. The main concept consists of: (1) identifying macroscopic quantities; (2) constructing appropriate oversampled local problems with coarse-grid constraints; (3) formulating macroscopic equations. We consider two types of approaches. In the first approach, the solutions of local problems are used as basis functions (in a linear fashion) to solve nonlinear problems. This approach is simple to implement; however, it lacks the nonlinear interpolation, which we present in our second approach. In this approach, the local solutions are used as a nonlinear forward map from local averages (constraints) of the solution in oversampling region. This local fine-grid solution is further used to formulate the coarse-grid problem. Both approaches are discussed on several examples and applied to single-phase and two-phase flow problems, which are challenging because of convection-dominated nature of the concentration equation.

Uniform-in-Time Error Estimates for the Postprocessing Galerkin Method Applied to a Data Assimilation Algorithm

We apply the postprocessing Galerkin method to a recently introduced continuous data assimilation (downscaling) algorithm for obtaining a numerical approximation of the solution of the two-dimensional Navier--Stokes equations corresponding to given measurements from a coarse spatial mesh. Under suitable conditions on the relaxation (nudging) parameter, the resolution of the coarse spatial mesh, and the resolution of the numerical scheme, we obtain uniform-in-time estimates for the error between the numerical approximation given by the postprocessing Galerkin method and the reference solution corresponding to the measurements. Our results are valid for a large class of interpolant operators, including low Fourier modes and local averages over finite volume elements. Notably, we use here the two-dimensional Navier--Stokes equations as a paradigm, but our results apply equally to other evolution equations, such as the Boussinesq system of Benard convection and other oceanic and atmospheric circulation models.

Estimating the Spot Covariation of Asset Prices—Statistical Theory and Empirical Evidence

ABSTRACTWe propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semimartingale log asset price process, which is subject to noise and nonsynchronous observations. The estimator is constructed based on a local average of block-wise parametric spectral covariance estimates. The latter originate from a local method of moments (LMM), which recently has been introduced by Bibinger et al.. We prove consistency and a point-wise stable central limit theorem for the proposed spot covariance estimator in a very general setup with stochastic volatility, leverage effects, and general noise distributions. Moreover, we extend the LMM estimator to be robust against autocorrelated noise and propose a method to adaptively infer the autocorrelations from the data. Based on simulations we provide empirical guidance on the effective implementation of the estimator and apply it to high-frequency data of a cross-section of Nasdaq blue chip stocks. Employing the estimator to estimate spot covariances, correlations, and volatilities in normal but also unusual periods yields novel insights into intraday covariance and correlation dynamics. We show that intraday (co-)variations (i) follow underlying periodicity patterns, (ii) reveal substantial intraday variability associated with (co-)variation risk, and (iii) can increase strongly and nearly instantaneously if new information arrives. Supplementary materials for this article are available online.