Parallelization of the discrete gradient method of non-smooth optimization and its applications

We investigate parallelization and performance of the discrete gradient method of nonsmooth optimization. This derivative free method is shown to be an effective optimization tool, able to skip many shallow local minima of nonconvex nondifferentiable objective functions. Although this is a sequential iterative method, we were able to parallelize critical steps of the algorithm, and this lead to a significant improvement in performance on multiprocessor computer clusters. We applied this method to a difficult polyatomic clusters problem in computational chemistry, and found this method to outperform other algorithms.

A generalized data windowing scheme for adaptive conjugate gradient algorithms

The performance of the modified adaptive conjugate gradient (CG) algorithms based on the iterative CG method for adaptive filtering is highly related to the ways of estimating the correlation matrix and the cross-correlation vector. The existing approaches of implementing the CG algorithms using the data windows of exponential form or sliding form result in either loss of convergence or increase in misadjustment. This paper presents and analyzes a new approach to the implementation of the CG algorithms for adaptive filtering by using a generalized data windowing scheme. For the new modified CG algorithms, we show that the convergence speed is accelerated, the misadjustment and tracking capability comparable to those of the recursive least squares (RLS) algorithm are achieved. Computer simulations demonstrated in the framework of linear system modeling problem show the improvements of the new modifications.

Least squares splines with free knots: global optimization approach

Splines with free knots have been extensively studied in regard to calculating the optimal knot positions. The dependence of the accuracy of approximation on the knot distribution is highly nonlinear, and optimisation techniques face a difficult problem of multiple local minima. The domain of the problem is a simplex, which adds to the complexity. We have applied a recently developed cutting angle method of deterministic global optimisation, which allows one to solve a wide class of optimisation problems on a simplex. The results of the cutting angle method are subsequently improved by local discrete gradient method. The resulting algorithm is sufficiently fast and guarantees that the global minimum has been reached. The results of numerical experiments are presented.

Mathematical modelling of the refractive index reconstruction through global optimization

We examine a mathematical model of non-destructive testing of planar waveguides, based on numerical solution of a nonlinear integral equation. Such problem is ill-posed, and the method of Tikhonov regularization is applied. To minimize Tikhonov functional, and find the parameters of the waveguide, we use two new optimization methods: the cutting angle method of global optimization, and the discrete gradient method of nonsmooth local optimization. We examine how the noise in the experimental data influences the solution, and how the regularization parameter has to be chosen. We show that even with significant noise in the data, the numerical solution is of high accuracy, and the method can be used to process real experimental da.ta..

Density based fuzzy c-means clustering of non-convex patterns

We propose a new technique to perform unsupervised data classification (clustering) based on density induced metric and non-smooth optimization. Our goal is to automatically recognize multidimensional clusters of non-convex shape. We present a modification of the fuzzy c-means algorithm, which uses the data induced metric, defined with the help of Delaunay triangulation. We detail computation of the distances in such a metric using graph algorithms. To find optimal positions of cluster prototypes we employ the discrete gradient method of non-smooth optimization. The new clustering method is capable to identify non-convex overlapped d-dimensional clusters.

A QoE centric distributed caching approach for vehicular video streaming in cellular networks

Distributed caching-empowered wireless networks can greatly improve the efficiency of data storage and transmission and thereby the users' quality of experience (QoE). However, how this technology can alleviate the network access pressure while ensuring the consistency of content delivery is still an open question, especially in the case where the users are in fast motion. Therefore, in this paper, we investigate the caching issue emerging from a forthcoming scenario where vehicular video streaming is performed under cellular networks. Specifically, a QoE centric distributed caching approach is proposed to fulfill as many users' requests as possible, considering the limited caching space of base stations and basic user experience guarantee. Firstly, a QoE evaluation model is established using verified empirical data. Also, the mathematic relationship between the streaming bit rate and actual storage space is developed. Then, the distributed caching management for vehicular video streaming is formulated as a constrained optimization problem and solved with the generalized-reduced gradient method. Simulation results indicate that our approach can improve the users' satisfaction ratio by up to 40%.

Application of the gradient boosted method in randomised clinical trials: participant variables that contribute to depression treatment efficacy of duloxetine, SSRIs or placebo

Randomised, placebo-controlled trials of treatments for depression typically collect outcomes data but traditionally only analyse data to demonstrate efficacy and safety. Additional post-hoc statistical techniques may reveal important insights about treatment variables useful when considering inter-individual differences amongst depressed patients. This paper aims to examine the Gradient Boosted Model (GBM), a statistical technique that uses regression tree analyses and can be applied to clinical trial data to identify and measure variables that may influence treatment outcomes.

Method for determining reaction rate of mild steel containers during melting of magnesium-aluminium alloys and effect of aluminium content on directionally solidified microstructures

A magnesium alloy of eutectic composition (33 wt-'%Al) was directionally solidified in mild steel tubes at two growth rates, 32 and 580 mum s(-1,) in a temperature gradient between 10 and 20 K mm(-1). After directional solidification, the composition of each specimen varied dramatically, from 32'%Al in the region that had remained solid to 18%Al (32 mum s(-1) specimen) and 13%Al (580 mum s(-1) specimen) at the plane that had been quenched from the eutectic temperature. As the aluminium content decreased, the microstructure contained an increasing volume fraction of primary magnesium dendrites and the eutectic morphology gradually changed from lamellar to partially divorced. The reduction in aluminium content was caused by the growth of an Al-Fe phase ahead of the Mg-Al growth front. Most of the growth of the Al-Fe phase occurred during the remelting period before directional solidification. The thickness of the Al-Fe phase increased with increased temperature and time of contact with the molten Mg-Al alloy. (C) 2003 Maney Publishing.

Transport properties in ionic liquids and ionic liquid mixtures : the challenges of NMR pulsed field gradient diffusion measurements

Pulsed field gradient NMR is a powerful method for the measurement of diffusion coefficients in liquids and solids and has begun to attract much attention in the ionic liquids field. However, aspects of the methodology as traditionally applied to solutions may not be uniformly applicable in these more viscous and chemically complex systems. In this paper we present data which shows that the Pulsed Gradient Spin Echo (PGSE) method in particular suffers from intrinsic internal gradients and can produce apparent diffusion coefficients which vary by as much as 20% for different ¹H nuclei within a given moleculean obvious anomaly. In contrast, we show that the Pulsed Gradient Stimulated Echo method does not suffer from this problem to the same extent and produces self-consistent data to a high degree of accuracy (better than 1%). This level of significance has allowed the detection, in this work, of subtle mixing effects in [C₃mpyr][NTf₂] and [C₄mpyr][NTf₂] mixtures.

Wettability gradient-driven directional water transport across thin fibrous materials

Recently, novel properties have been observed when superhydrophobic and superhydrophilic surfaces are combined. For example, the Stenocara beetle, an insect in the Namib Desert, has an incredible ability to capture fresh water from air for its survival in the dry desert environment [1]. Such a feature derives from its special wing that has a hydrophilic-patterned superhydrophobic surface. Materials having a similar surface feature also exhibited a similar water-harvesting function [2]. A spider silk has been reported to show a periodic alternation of hydrophobic and hydrophilic surfaces along the fiberlength direction [3], which can quickly collect water from air. It was also observed that water droplets moved in one direction along a superhydrophobic-to-superhydrophilic gradient surface [4]. However, all these works are based on two dimension surfaces. The work on water transfer through porous media induced by a gradient wettability change has received little attention until very recently [5]. In this study, we have developed a simple, but very effective and versatile, method to produce wettability gradient across the thickness of fabrics, and demonstrated that the fabrics have the ability to spontaneously transfer water unidirectionally through the fibrous architecture. A plain weave polyester fabric was mainly used as a sample material.

Very high pressure liquid chromatography using fully porous particles: Quantitative analysis of fast gradient separations without post-run times

Using a column packed with fully porous particles, four methods for controlling the flow rates at which gradient elution runs are conducted in very high pressure liquid chromatography (VHPLC) were tested to determine whether reproducible thermal conditions could be achieved, such that subsequent analyses would proceed at nearly the same initial temperature. In VHPLC high flow rates are achieved, producing fast analyses but requiring high inlet pressures. The combination of high flow rates and high inlet pressures generates local heat, leading to temperature changes in the column. Usually in this case a post-run time is input into the analytical method to allow the return of the column temperature to its initial state. An alternative strategy involves operating the column without a post-run equilibration period and maintaining constant temperature variations for subsequent analysis after conducting one or a few separations to bring the column to a reproducible starting temperature. A liquid chromatography instrument equipped with a pressure controller was used to perform constant pressure and constant flow rate VHPLC separations. Six replicate gradient separations of a nine component mixture consisting of acetophenone, propiophenone, butyrophenone, valerophenone, hexanophenone, heptanophenone, octanophenone, benzophenone, and acetanilide dissolved in water/acetonitrile (65:35, v/v) were performed under various experimental conditions: constant flow rate, two sets of constant pressure, and constant pressure operation with a programmed flow rate. The relative standard deviations of the response factors for all the analytes are lower than 5% across the methods. Programming the flow rate to maintain a fairly constant pressure instead of using instrument controlled constant pressure improves the reproducibility of the retention times by a factor of 5, when plotting the chromatograms in time.

Frequency-domain beamformers using conjugate gradient techniques for speech enhancement

A multiple-iteration constrained conjugate gradient (MICCG) algorithm and a single-iteration constrained conjugate gradient (SICCG) algorithm are proposed to realize the widely used frequency-domain minimum-variance-distortionless-response (MVDR) beamformers and the resulting algorithms are applied to speech enhancement. The algorithms are derived based on the Lagrange method and the conjugate gradient techniques. The implementations of the algorithms avoid any form of explicit or implicit autocorrelation matrix inversion. Theoretical analysis establishes formal convergence of the algorithms. Specifically, the MICCG algorithm is developed based on a block adaptation approach and it generates a finite sequence of estimates that converge to the MVDR solution. For limited data records, the estimates of the MICCG algorithm are better than the conventional estimators and equivalent to the auxiliary vector algorithms. The SICCG algorithm is developed based on a continuous adaptation approach with a sample-by-sample updating procedure and the estimates asymptotically converge to the MVDR solution. An illustrative example using synthetic data from a uniform linear array is studied and an evaluation on real data recorded by an acoustic vector sensor array is demonstrated. Performance of the MICCG algorithm and the SICCG algorithm are compared with the state-of-the-art approaches.

A comprehensive method to identify the kinetics of static recrystallization using the hot torsion test results with an inverse solution

Many difficulties exist in directly following the static recrystallization of metals, particularly during hotworking. Indirect measurement of static recrystallization has been extensively performed in the literature where, for example, the recrystallization behavior of austenite in steels has commonly been measured indirectly using the fractional softening method. This method relies on the yield stress changes during recrystallization which are physically simulated by hot torsion or compression tests. However, the inherent heterogeneity of deformation during a mechanical test leads to a non-uniform static recrystallization distribution in the test sample. This, in turn, poses a serious question concerning the reliability of the measurement since the stress calculation techniques during recrystallization are not adequately developed in the existing literature. This paper develops a computer-based method to account for heterogeneous deformation during fractional softening measurements based on the hot torsion test data. The importance of the fractional softening gradient in determining the kinetics is emphasized and deficiencies in our understanding of the basic mechanisms are highlighted. A computer-based method is introduced to generate the experimental and computational components in a cost function. The cost function is then utilized by an inverse solution to calibrate the design parameters in a static recrystallization model.

Parent-related mechanisms underlying the social gradient of childhood overweight and obesity: a systematic review

BACKGROUND: Low socio-economic status (SES) is a significant risk factor for childhood overweight and obesity (COWOB) in high-income countries. Parents to young children buffer and accentuate social and cultural influences, and are central to the development of this disease. An understanding of the parent-related mechanisms that underlie the SES-COWOB relationship is needed to improve the efficacy of prevention and intervention efforts. OBJECTIVE: A systematic review of relevant literature was conducted to investigate the mechanisms by which levels of SES (low, middle and high) are associated to COWOB, by exploring mediation and interaction effects. METHOD: Six electronic databases were searched yielding 5155 initial records, once duplicates were removed. Studies were included if they investigated COWOB, SES, parent-related factors and the multivariate relationship between these factors. Thirty studies were included. Factors found to be mediating the SES-COWOB relationship or interacting with SES to influence COWOB were categorized according to an ecological systems framework, at child, parent, household and social system level factors. RESULTS: High parent body mass index, ethnicity, child-care attendance, high TV time (mother and child), breastfeeding (early weaning), food intake behaviours and birthweight potentially mediate the relationship between SES and COWOB. Different risk factors for COWOB in different SES groups were found. For low SES families, parental obesity and maternal depressive symptoms were strong risk factors for COWOB, whereas long maternal working hours and a permissive parenting style were risk factors for higher SES families. None of the studies investigated parental psychological attributes such as attitudes, beliefs, self-esteem and so on as potential mechanisms/risk factors. CONCLUSIONS: Families from different SES groups have different risk and protective factors for COWOB. Prevention and intervention efforts may have improved efficacy if they are tailored to address specific risk factors within SES.