Local Average Research Articles

A Distributed Stochastic Proximal-Gradient Algorithm for Composite Optimization

In this article, we consider distributed composite optimization problems involving a common non-smooth regularization term over an undirected and connected network. Inspired by vast applications of this kind of problem in large-scale machine learning, the local cost function of each node is further set as an average of a certain amount of local cost subfunctions. For this scenario, most existing solutions based on the proximal method tend to ignore the cost of gradient evaluations, which results in degraded performance. We instead develop a distributed stochastic proximal-gradient algorithm to tackle the problems by employing the local unbiased stochastic averaging gradient method. At each iteration, only a single local cost subfunction is demanded by each node to evaluate the gradient, then the average of the latest stochastic gradients serves as the approximation of the true local gradient. An explicit linear convergence rate of the proposed algorithm is established with constant dual step-sizes for strongly convex local cost subfunctions with Lipschitz-continuous gradients. Furthermore, it is shown that, in the smooth cases, our simplified analysis technique can be extended to some notable primal-dual domain algorithms, such as DSA, EXTRA, and DIGing. Numerical experiments are presented to confirm the theoretical findings.

Improvement of spatial resolution by tilt correction in near-field scanning microwave microscopy

The limitation of mechanical manufacturing will result in a small tilt angle of the sample stage in the horizontal direction, which decreases the spatial resolution of imaging in near-field scanning microwave microscopy (NSMM). In this paper, we focus on the tilt correction and improve the spatial resolution of the NSMM image. The results of electromagnetic simulation and line scan measurement demonstrate the critical parameters affecting the sensitivity of NSMM, such as the length of the probe extending out of the cavity, the tip–sample distance, and the tip apex size. The tilt images can rotate successfully to the horizontal plane with the tilt correction methods, and the local average and re-interpolation are applied to denoise the images. Experimental NSMM images of copper thin film grid, coin texture, lithography mask, and leaf vein are obtained. The images before and after correction verify the improvement of the spatial resolution with all the above methods.

Damköhler number scaling of active cascade effects in turbulent premixed combustion

Effects of combustion heat release on turbulent velocity and scalar statistics are investigated as a function of the Damköhler number using three direct numerical simulation databases of spatially developing turbulent premixed jet flames. At low Karlovitz numbers, where heat-release effects dominate turbulent kinetic energy budgets, their relative significance scales with the integral Damköhler number in a priori Reynolds-Averaged Navier–Stokes (RANS) statistics and the filter Damköhler number in Large Eddy Simulation (LES). The Damköhler-number scaling of counter-gradient transport in this regime follows theoretical arguments underpinning linear-algebraic turbulence models, which explains their efficacy at low Karlovitz numbers. Conversely, at moderate Karlovitz numbers, LES subfilter turbulence is more strongly influenced by heat-release effects than the analogous large-scale RANS turbulence. This is consistent with the notion of an “active cascade,” which postulates that heat-release-induced volumetric expansion competes on intermediate scales with classical forward-cascade energy transfer. LES exposes these dynamics as dominant subfilter-scale physics, unlike in RANS, where they are secondary to the effects of mean-shear production at the large scales. The significance of subfilter-scale interactions is promoted by the LES filter itself, which modifies the RANS spectral basis by incorporating local flame-normal averaging. This is highlighted by comparing LES fields obtained using a 3D filter to those using a modified 2D filter, excluding the flame-normal direction, which significantly reduces the apparent influence of heat-release effects but is not representative of LES in practice. The subfilter modeling challenges posed by these distinctions at moderate Karlovitz numbers and order-unity Damköhler numbers remain to be understood.

Novel approaches to investigating spatial variability in channel bank total phosphorus at the catchment scale

Phosphorus (P) is often a limiting nutrient that leads to the eutrophication of aquatic systems. While dissolved P forms are the most bioavailable, the form, mobility, transport and fate of P are directly related to its association with fine-grained riverine sediment. Therefore, to implement successful P catchment management strategies it is important to understand the relative contribution of different sediment sources to P loads across the river continuum. While agricultural topsoil and, to a lesser extent, riverbed sediment are important sources of sediment-associated P, channel banks have been shown to be an important sediment source in some catchments. However, comparatively little is known about the P concentration and corresponding spatial variability in channel bank sediment and the associated implications for catchment management. The present study examines the spatial variability of P associated with channel bank profiles within a series of three nested catchments using both non-spatial and spatial statistical methods, where for the latter, a novel spatial approach was used to estimate the spatial averages and variances of P in channel bank sediment along the stream network. Channel bank P concentrations were compared to factors such as catchment scale, stream order, land use, bank exposure and location along the stream network. Concentrations of TP ranged between 129.6 and 1206.9 mg P kg−1 of which the water extractable P (WEP) content ranged from 0.01 to 0.12%. Stream order was found to influence TP concentrations, while land use and catchment scale provided only a moderate influence. This suggested that focussing channel bank sampling strategies at the largest catchment scale would capture key drivers of TP variability provided stream order is sufficiently represented. Whether the bank was had limited vegetation and was exposed and potentially eroding had a slight influence on TP variability in second-order stream banks in the larger of the two nested catchments. However, the slightly lower TP concentrations measured at these sites indicated that banks that are actually eroding may be contributing less TP than the total channel bank TP values measured across the catchments as a whole. The results of an explicitly spatial analysis demonstrated that local channel bank TP averages and TP variances vary along the stream network. Specifically, the most accurate spatial predictor of TP was local TP means with the use of ‘crow flies’ rather than stream network distances. Local TP variances were used to provide optimal designs for future channel bank TP sampling campaigns, given available resources. Throughout, both standard and outlier-resistant statistical analyses were applied to improve interpretation of the study findings.

An energy-based method for assessing the equivalent static force of a vehicle collision with bridge columns

A new method is proposed to obtain the equivalent static forces of a vehicle collision with bridge columns. The method is based on energy-conservation and, conversely to other existing methods, does not require the use of complex models or experimental data to obtain time histories of impact. A simplified numerical model is also developed to generate data and compare the performance of the energy-conservation method against three other approaches (global average, local average, and equivalent displacement methods) and the AASHTO allowances. The simplified model is efficient and correctly captures the response for different impact velocities and column sizes. The impact velocity was shown to be positively related to the impact force and column displacement, and the size of the column is also positively related to the impact force but negatively with the column displacement. Results of equivalent static forces show that the global average and local average methods may not provide acceptable values for the equivalent impact force from the collision of vehicles with bridge columns, whereas the equivalent displacement and the proposed energy-based method provide adequate values. The latter approach, however, has the advantage of simplicity and convenience since it does not rely on any numerical/experimental model.

Deep learning of the spanwise-averaged Navier–Stokes equations

Simulations of turbulent fluid flow around long cylindrical structures are computationally expensive because of the vast range of length scales, requiring simplifications such as dimensional reduction. Current dimensionality reduction techniques such as strip-theory and depth-averaged methods do not take into account the natural flow dissipation mechanism inherent in the small-scale three-dimensional (3-D) vortical structures. We propose a novel flow decomposition based on a local spanwise average of the flow, yielding the spanwise-averaged Navier–Stokes (SANS) equations. The SANS equations include closure terms accounting for the 3-D effects otherwise not considered in 2-D formulations. A supervised machine-learning (ML) model based on a deep convolutional neural network provides closure to the SANS system. A-priori results show up to 92% correlation between target and predicted closure terms; more than an order of magnitude better than the eddy viscosity model correlation. The trained ML model is also assessed for different Reynolds regimes and body shapes to the training case where, despite some discrepancies in the shear-layer region, high correlation values are still observed. The new SANS equations and ML closure model are also used for a-posteriori prediction. While we find evidence of known stability issues with long time ML predictions for dynamical systems, the closed SANS simulations are still capable of predicting wake metrics and induced forces with errors from 1-10%. This results in approximately an order of magnitude improvement over standard 2-D simulations while reducing the computational cost of 3-D simulations by 99.5%.

A Simultaneous Multiscale Data Assimilation Using Scale-Dependent Localization in GSI-Based Hybrid 4DEnVar for NCEP FV3-Based GFS

AbstractA scale-dependent localization (SDL) method was formulated and implemented in the Gridpoint Statistical Interpolation (GSI)-based four-dimensional ensemble-variational (4DEnVar) system for NCEP FV3-based Global Forecast System (GFS). SDL applies different localization to different scales of ensemble covariances, while performing a single-step simultaneous assimilation of all available observations. Two SDL variants with (SDL-Cross) and without (SDL-NoCross) considering cross-wave-band covariances were examined. The performance of two- and three-wave-band SDL experiments (W2 and W3, respectively) was evaluated through 1-month cycled data assimilation experiments. SDL improves global forecasts to 5 days over scale-invariant localization including the operationally tuned level-dependent scale-invariant localization (W1-Ope). The W3 SDL-Cross experiment shows more accurate tropical storm–track forecasts at shorter lead times than W1-Ope. Compared to the W2 SDL experiments, the W3 SDL counterparts applying tighter horizontal localization at medium-scale wave band generally show improved global forecasts below 100 hPa, but degraded global forecasts above 50 hPa. While the outperformance of the W3 SDL-NoCross experiment versus the W2 SDL-NoCross experiment below 100 hPa lasts for 5 days, that of the W3 SDL-Cross experiment versus the W2 SDL-Cross experiment lasts for 3 days. Due to local spatial averaging of ensemble covariances that may alleviate sampling error, the SDL-NoCross experiments show slightly better forecasts than the SDL-Cross experiments at shorter lead times. However, the SDL-Cross experiments outperform the SDL-NoCross experiments at longer lead times, likely from retention of more heterogeneity of ensemble covariances and resultant analyses with improved balance. Relative performance of tropical storm–track forecasts in the W2 and W3 SDL experiments are generally consistent with that of global forecasts.

Hurst Exponents for Intra- and Intercycle Thermoacoustic Oscillations

The detrended fluctuation analysis, a technique for detecting long-range correlations in fractal time series, is used to characterize thermoacoustic oscillations of impending combustion instabilities. The slope of the linear regime of the structure function with respect to the time scale in a logarithmic plot, referred to as the Hurst exponent, takes a different value across a critical time scale corresponding to one pressure cycle. The slope for pressure oscillations over one pressure cycle, termed as the intercycle Hurst exponent, is a power-law scaling parameter for long-range oscillations; however, the slope for pressure oscillations within one pressure cycle, termed as the “intracycle Hurst exponent,” is no longer a power-law scaling parameter but resultant from the nonstationary, local average of highly nonlinear (as a function of time), seemingly sinusoidal, nearly periodic pressure oscillations. Both parametric studies and analyses of experimental data show that the intracycle Hurst exponent consistently increases with the signal-to-noise ratio and peaks at 1.6, thus having potentials for assessments of the safety margin to the onset of combustion instabilities. Given the same observation window, the measurement error (or uncertainty) of the intracycle Hurst exponent is significantly lower than that of the intercycle Hurst exponent.

CAMEL-Based Performance of a Foreign Bank in Bangladesh: A Study on Commercial Bank of Ceylon

The paper examined the strategic, operational, and financial performance of Commercial Bank of Ceylon Bangladesh Operations using its CAMEL-based performance record. For this study, financial data from the last seven years and organizational historical information, including updates to management structure, were collected. In addition, primary source of practical working experience and observance provided detailed operational information. Analysing the financial data through various key ratios and conducting CAMEL rating analysis has presented a thorough view from different sectors of the bank performance over time, which has ranged from outstanding to satisfactory in all sector parameters except for liability management. Comparison against local industry average has showed that the bank has been in quite a good position in local economy in terms of recent crises such as Non-Performing Loan (NPL) than banking industry. Despite the recommendation for an increase in manpower and promotion that will result in a decrease in liability, the paper also suggests an emphasis on reducing liability.

Calibration-based minimalistic multi-exposure digital sensor camera robust linear high dynamic range enhancement technique demonstration

Demonstrated for a digital image sensor-based camera is a calibration target optimized method for finding the Camera Response Function (CRF). The proposed method uses localized known target zone pixel outputs spatial averaging and histogram analysis for saturated pixel detection. Using the proposed CRF generation method with a 87 dB High Dynamic Range (HDR) silicon CMOS image sensor camera viewing a 90 dB HDR calibration target, experimentally produced is a non-linear CRF with a limited 40 dB linear CRF zone. Next, a 78 dB test target is deployed to test the camera with this measured CRF and its restricted 40 dB zone. By engaging the proposed minimal exposures, weighting free, multi-exposure imaging method with 2 images, demonstrated is a highly robust recovery of the test target. In addition, the 78 dB test target recovery with 16 individual DR value patches stays robust over a factor of 20 change in test target illumination lighting. In comparison, a non-robust test target image recovery is produced by 5 leading prior-art multi-exposure HDR recovery algorithms using 16 images having 16 different exposure times, with each consecutive image having a sensor dwell time increasing by a factor of 2. Further validation of the proposed HDR image recovery method is provided using two additional experiments, the first using a 78 dB calibrated target combined with a natural indoor scene to form a hybrid design target and a second experiment using an uncalibrated indoor natural scene. The proposed technique applies to all digital image sensor-based cameras having exposure time and illumination controls. In addition, the proposed methods apply to various sensor technologies, spectral bands, and imaging applications.

Mapping Gaia Parallax Systematic Errors over the Sky with Faint Milky Way Stars

Abstract Parallaxes measured by the Gaia mission have huge significance for astronomy, but parallaxes in Gaia DR2 are known to have systematic errors that depend on the source position and other quantities. We use the abundant information in faint Milky Way stars, along with the Gaia Object Generator simulation of the Gaia catalog, to probe the spatial dependence of Gaia DR2 parallax systematic errors in an empirical way. The parallax signal, concentrated in thick disk turnoff stars with magnitude G ∼ 17, is sufficient to construct maps of the parallax systematic error over the majority of the sky. These maps show a locally regular “waffle pattern” on ∼1° scales following Gaia scan directions, stronger linear “scar” features, and coherent variations on larger scales. The parallax bias maps also retain traces of astrophysical effects such as dust clouds. The waffle pattern, known from earlier maps of the Magellanic Clouds, extends over the entire sky; its local rms amplitude averages 15 μas and varies by about a factor of two. The strength of this pattern increases by a factor ∼6 from magnitude G = 13 to G = 20. Correlations with parallaxes of quasars and of stars with independent distance estimates support our bias estimates. Using similar methods, we map systematic errors in the proper motion and examine the relationship with the parallax systematics. We provide a code package to access and query our bias maps. Similar tests on the general stellar population should be useful in quantifying systematic errors in future Gaia releases.

The diffusing-velocity random walk: a spatial-Markov formulation of heterogeneous advection and diffusion

Abstract

Denoising for Improved Parametric MRI of the Kidney: Protocol for Nonlocal Means Filtering.

In order to tackle the challenges caused by the variability in estimated MRI parameters (e.g., T2* and T2) due to low SNR a number of strategies can be followed. One approach is postprocessing of the acquired data with a filter. The basic idea is that MR images possess a local spatial structure that is characterized by equal, or at least similar, noise-free signal values in vicinities of a location. Then, local averaging of the signal reduces the noise component of the signal. In contrast, nonlocal means filtering defines the weights for averaging not only within the local vicinity, bur it compares the image intensities between all voxels to define "nonlocal" weights. Furthermore, it generally compares not only single-voxel intensities but small spatial patches of the data to better account for extended similar patterns. Here we describe how to use an open source NLM filter tool to denoise 2D MR image series of the kidney used for parametric mapping of the relaxation times T2* and T2.This chapter is based upon work from the COST Action PARENCHIMA, a community-driven network funded by the European Cooperation in Science and Technology (COST) program of the European Union, which aims to improve the reproducibility and standardization of renal MRI biomarkers.

A novel evolutionary row class entropy based optimal multi-level thresholding technique for brain MR images

The local averaging technique adopted for the construction of 2D histogram in Otsu’s method fails to preserve the edge information. Further, the consideration of the diagonal pixels only results in the loss of information. These make the 2D Otsu method of multi-level thresholding inefficient to retain the spatial correlation information. Although the computation of 2D histogram based on gray gradient information is a better way to threshold an image, it faces a backlash due to the high magnitude peaks. To solve these problems, we suggest a new normalized local variance (NLV) method for constructing 2D histogram using the local variance followed by a novel evolutionary row class entropy (ERCE) method for optimal multi-level image thresholding, which tries to preserve maximum spatial information through normalization of the local variance. A new optimization technique called hybrid Adaptive Cuckoo Search-Squirrel Search Algorithm (ACS-SSA) is also introduced. A new fitness function is suggested. The standard CEC 2005 benchmark test functions are used to validate the performance of our proposed ACS-SSA technique. The optimum threshold values obtained are used to segment 100 slices of T-2 weighted axial brain MR images (taken from the Harvard Medical School database). Several performance evaluation metrics are computed to compare the performance of our method with the state-of-the-art methods. The analysis of the results shows that ERCE method outperforms other methods. This method may set a new direction in the multilevel image thresholding research.

Decentralized stochastic optimization algorithms using uncoordinated step-sizes over unbalanced directed networks

Decentralized stochastic gradient methods play significant roles in large-scale optimization that finds many practical applications in signal processing, machine learning, and coordinated control. In this short communication, we focus on studying large-scale convex optimization problems over multi-agent systems, where the mutual goal of agents in the network is to optimize a global objective function expressed as a sum of local objective functions. Each agent in the system uses only local computation and communication in the overall process without leaking their private information. We first introduce both the local stochastic averaging gradient method and the local stochastic variance-reduced gradient method into decentralized convex optimization (DCO) over unbalanced directed networks. Then, in order to increase the autonomy and flexibility of the agents, uncoordinated step-sizes are considered. Based on the well-known variance-reduced stochastic gradient methods and uncoordinated step-sizes, we propose two fully decentralized algorithms named SAGA-UDN and SVRG-UDN for DCO over unbalanced directed networks, respectively. Finally, both SAGA-UDN and SVRG-UDN are numerically studied under various network parameters and objective functions. Some real-world data sets are used in simulations to demonstrate the improved performance of SAGA-UDN and SVRG-UDN.

Fast inference for semi-varying coefficient models via local averaging

The semi-varying coefficient models are widely used in the application of finance, economics, medical science and many other areas. In general, the functional coefficients are estimated by local smoothing methods, e.g. local linear estimator. So the computation cost is severe because one should point-wisely estimate the value of a coefficient function. In this paper, we give an insight into the trade-off between statistical efficiency and computation simplicity and proposes a fast inference procedure, local average estimator. The proposed method is easy to implement and avoid repeat estimation since it approximates the coefficient functions with piecewise constants. Though the local average estimator is not asymptotically optimal, it is still efficient enough for further inference. Thus, three tests are derived to check whether a coefficient is constant. The experimental evidence shows that when there is limited room for improving the asymptotic efficiency, a proper trade-off between statistical efficiency and computation simplicity may improve the finite-sample performance.

Rainfall shocks, cognitive development and educational attainment among adolescents in a drought-prone region in Kenya

AbstractThere is growing evidence that early life conditions are important for outcomes during adolescence, including cognitive development and education. Economic conditions at the time children enter school are also important. We examine these relationships for young adolescents living in a low-income drought-prone pastoral setting in Kenya using historical rainfall patterns captured by remote sensing as exogenous shocks. Past rainfall shocks measured as deviations from local long-term averages have substantial negative effects on the cognitive development and educational achievement of girls. Results for the effects of rainfall shocks on grades attained, available for both girls and boys, support that finding. Consideration of additional outcomes suggests the effects of rainfall shocks on education are due to multiple underlying mechanisms including persistent effects on the health of children and the wealth of their households, underscoring the potential value of contemporaneous program and policy responses to such shocks.

A Novel Diagonal Class Entropy-Based Multilevel Image Thresholding Using Coral Reef Optimization

In the normal image thresholding methods based on two-dimensional histogram, the edge information of the regions is not maintained because of the local averaging activity used. Moreover, the computation time increases with the increase in the level of thresholds. This paper focusses on retaining more edge information by calculating the image entropy along the diagonal regions of the gray level co-occurrence matrix inspired from the partitioned design structure matrix, which is a novel idea. In addition, the key to our success is the theoretical investigation of a novel diagonal class entropy (DCE) concept that utilizes the minimum area for computation. The benefits of the proposed method are: 1) improved results; 2) efficient to preserve more precise shape of the edges; and 3) the computation time decreases with the increase in the threshold levels. The optimal thresholds are obtained by minimizing the DCE using coral reef optimization (CRO). A first hand fitness function for multilevel image thresholding is derived. The fight for space and the efficient reproduction characteristics of the CRO makes it attractive for this application. Benchmark images from the Berkley segmentation dataset are taken to experiment. Our results are compared with other state-of-the-art thresholding methods. The results obtained are encouraging and may set the path for further investigation in the domain of multilevel thresholding.

Nanoscale structural analysis of Pb(Mg1/3Nb2/3)O3

The determination of local atomic structure at nanoscale for inhomogeneous systems is challenging. The local arrangement of atoms needs to be studied to understand the local or short-range order structures for disordered materials with a lack of long-range order periodicity. Pair distribution function (PDF) analysis is a technique, that is used to study the short-range order structure of materials: this technique is based on the evaluation of local atomic arrangement using synchrotron and neutron sources. An attempt was made to determine the local arrangement at 20 nm-scale for a typical relaxor ferroelectric material, Pb(Mg1/3Nb2/3)O3 (PMN). The PDF technique was employed owing to the limited structural coherence in this disordered material. It was determined that there are three types of structures depending on the distance. A glass-like network structure was observed as a short-range order structure owing to the large off-center shift of lead atoms. With an increase in distance, the structure of PMN changed from rhombohedral to cubic. Using the above-mentioned approach, we elucidated the process of local structure averaging.

Transitional SAX Representation for Knowledge Discovery for Time Series

Numerous dimensionality-reducing representations of time series have been proposed in data mining and have proved to be useful, especially in handling a high volume of time series data. Among them, widely used symbolic representations such as symbolic aggregate approximation and piecewise aggregate approximation focus on information of local averages of time series. To compensate for such methods, several attempts were made to include trend information. However, the included trend information is quite simple, leading to great information loss. Such information is hardly extendable, so adjusting the level of simplicity to a higher complexity is difficult. In this paper, we propose a new symbolic representation method called transitional symbolic aggregate approximation that incorporates transitional information into symbolic aggregate approximations. We show that the proposed method, satisfying a lower bound of the Euclidean distance, is able to preserve meaningful information, including dynamic trend transitions in segmented time series, while still reducing dimensionality. We also show that this method is advantageous from theoretical aspects of interpretability, and practical and superior in terms of time-series classification tasks when compared with existing symbolic representation methods.