Variance Balance Research Articles

Employing factor analytic tools for selecting high‐performance and stable tropical maize hybrids

AbstractGenotype‐by‐environment interaction (GEI) is a major concern in tropical maize breeding. Here, we used factor analytic mixed models (FAMM) to study GEI in a tropical maize dataset. Our goal was to select high‐performance and stable hybrids using factor analytic selection tools (FAST) derived from FAMM outputs. Because the dataset comprised two different planting seasons, we also investigated differences in the genetic gains between seasonal and general selection (i.e., for both seasons simultaneously). The trials were installed in a lattice design with 36 hybrids containing two replicates and blocks with six plants each. We evaluated 53 hybrids and seven checks in 48 environments, represented by a combination of locations, years and seasons. We fitted the FAMMs with distinct sets of factors. The best‐fitted FAMM was selected considering a parsimony‐explained variance balance. Using the best FAMM for both seasonal and general analyses, we estimated the following selection tools: overall performance (); root mean square deviation (), which represents general stability; and responsiveness , which represents specific stability. We selected hybrids based on an index built with and . Five and three hybrids were selected considering both general and seasonal analyses for the first and second season, respectively. Two hybrids were amongst the top eight for both seasonal analyses (i.e., only first season and only second season simultaenously). Higher genetic gains may be obtained by employing FAMM and using FAST in each season rather than analysing both seasons in a joint fashion.

Quantification of numerical mixing in coastal ocean models through an offline method

It is well known that discrete advection schemes can induce spurious numerical mixing in numerical models. In the present study, an offline method is applied to several idealized lock-exchange simulations and a realistic model simulation of BYECS (Bohai Sea, Yellow Sea, and East China Sea) to estimate the magnitude of numerical mixing. Numerical mixing is defined as the tracer variance dissipation rate induced by the discretization of advection schemes, and the offline method is achieved through diagnosing the residual of the tracer variance balance equation in terms of model output data. The offline method is demonstrated to be appropriate to estimate the volume (or depth) and temporally averaged numerical mixing when the model output data capture typical flow timescales. In both of the lock-exchange and BYECS simulations, the spatial distributions of numerical and explicit physical mixing of salinity correspond to the distributions of horizontal and vertical salinity gradients, respectively. In the lock-exchange simulations, explicit physical mixing depresses the magnitude of numerical mixing through reducing the horizontal salinity gradients at the heading fronts. In the BYECS simulations, numerical mixing of salinity inside the Changjiang River plume region is stronger during spring tides than neap tides.

Fatigue tests simulation of materials with a random endurance limit

Fatigue tests of materials are characterized by long duration and high cost. In this regard, it is relevant to develop methods for modeling test results in the widest possible range of loads. Fatigue curve mathematical model includes the equation of the relationship between the amplitude of the stress and the durability of the samples, considering the random nature of the values of durability and the limit of unbounded endurance. At the first stage, the values of the model parameters are determined using the maximum likelihood function using real test data in a limited range of stress amplitudes. At the second stage, the problem solution is found considering the random value of the limit of unbounded endurance. Moreover, the mean estimate is obtained from the solution of the first part of the problem. The estimate of the unbounded endurance limit variance is obtained by calculation from the variance balance conditions. The results of modeling fatigue tests for aluminum alloy samples in a wide range of stress amplitude values are presented. Simulation results for determining the values of the fatigue curve left tolerance are considered.

The Balance of Salinity Variance in a Partially Stratified Estuary: Implications for Exchange Flow, Mixing, and Stratification

AbstractSalinity variance dissipation is related to exchange flow through the salinity variance balance equation, and meanwhile its magnitude is also proportional to the turbulence production and stratification inside the estuary. As river flow increases, estuarine volume-integrated salinity variance dissipation increases owing to more variance input from the open boundaries driven by exchange flow and river flow. This corresponds to the increased efficient conversion of turbulence production to salinity variance dissipation due to the intensified stratification with higher river flow. Through the spring–neap cycle, the temporal variation of salinity variance dissipation is more dependent on stratification than turbulence production, so it reaches its maximum during the transition from neap to spring tides. During most of the transition time from spring to neap tides, the advective input of salinity variance from the open boundaries is larger than dissipation, resulting in the net increase of variance, which is mainly expressed as vertical variance, that is, stratification. The intensified stratification in turn increases salinity variance dissipation. During neap tides, a large amount of enhanced salinity variance dissipation is induced by the internal shear stress near the halocline. During most of the transition time from neap to spring tides, dissipation becomes larger than the advective input, so salinity variance decreases and the stratification is destroyed.

The Transformation of Salinity Variance: A New Approach to Quantifying the Influence of Straining and Mixing on Estuarine Stratification

AbstractThe roles of straining and dissipation in controlling stratification are derived analytically using a vertical salinity variance method. Stratification is produced by converting horizontal variance to vertical variance via straining, that is, differential advection of horizontal salinity gradients, and stratification is destroyed by the dissipation of vertical variance through turbulent mixing. A numerical model is applied to the Changjiang estuary in order to demonstrate the salinity variance balance and how it reveals the factors controlling stratification. The variance analysis reveals that dissipation reaches its maximum during spring tide in the Changjiang estuary, leading to the lowest stratification. Stratification increases from spring tide to neap tide because of the increasing excess of straining over dissipation. Throughout the spring–neap tidal cycle, straining is almost always larger than dissipation, indicating a net excess of production of vertical variance relative to dissipation. This excess is balanced on average by advection, which exports vertical variance out of the estuarine region into the plume. During neap tide, tidal straining shows a general tendency of destratification during the flood tide and restratification during ebb, consistent with the one-dimensional theory of tidal straining. During spring tide, however, positive straining occurs during flood because of the strong baroclinicity induced by the intensified horizontal salinity gradient. These results indicate that the salinity variance method provides a valuable approach for examining the spatial and temporal variability of stratification in estuaries and coastal environments.

Measuring the Spatial Distribution of Cities in West Azarbaijan Province

The aim of this paper is to analyze the hierarchical network of urban areas of West Azarbaijan for examining the rate of balance in variance and spatial distribution of population of urban areas in the province of West Azarbaijan. The methodology in use is a pragmatic-developing one. The quantitative models, such as bulk modulus, urban centralization index, anthropy model and gini coefficient index, are used in order to analyze the urban hierarchy of West Azarbaijan. Findings of this study shows that Urban centralization index in all the studied periods was higher that one. Population bulk modulus of all cities of the province in the years of 1956, 1966 and 1976 had augmented but in the years of 1986, 1996 and 2006 has reduced. Anthropy index in all the studied periods was less than one, which shows the unbalance in population in urban areas of the province. Calculation of spatial coefficient LQ shows that small cities of the province are exporter of services and their basic economy is based of services sector. The communicative network of the province, specially the roads, is in a condition that economically targets the capital of the province and like a radius ends to Urumieh. The final conclusion of this research is that the unbalance in variance and the spatial distribution of population in urban areas of the province is the characteristic of network of urban hierarchy of the province of West Azarbaijan; in a manner that transactions between the cities of the province are also affected by the political-administrative structure of the country as well.

An improved two‐stage variance balance approach for constructing partial profile designs for discrete choice experiments

In many discrete choice experiments set up for product innovation, the number of attributes is large, which results in a substantial cognitive burden for the respondents. To reduce the cognitive burden in such cases, Green suggested in the early '70s the use of partial profiles that vary only the levels of a subset of the attributes. In this paper, we present two new methods for constructing Bayesian ‐optimal partial profile designs for estimating main‐effects models. They involve alternative generalizations of Green's approach that makes use of balanced incomplete block designs and take into account the fact that attributes may have differing numbers of levels. We refer to our methods as variance balance I and II because they vary an attribute with a larger number of levels more often than an attribute with fewer levels to stabilize the variances of the individual part‐worth estimates. The two variance balance methods differ in the way attributes with differing numbers of levels are weighted. Both methods provide statistically more efficient partial profile designs for differing numbers of attribute levels than another generalization of Green's approach that does not weight the attributes. This method is called attribute balance. We show results from an actual experiment in software development demonstrating the usefulness of our methods. Copyright © 2014 John Wiley & Sons, Ltd.

Partial logistic relevance vector machines in survival analysis

The use of relevance vector machines to flexibly model hazard rate functions is explored. This technique is adapted to survival analysis problems through the partial logistic approach. The method exploits the Bayesian automatic relevance determination procedure to obtain sparse solutions and it incorporates the flexibility of kernel-based models. Example results are presented on literature data from a head-and-neck cancer survival study using Gaussian and spline kernels. Sensitivity analysis is conducted to assess the influence of hyperprior distribution parameters. The proposed method is then contrasted with other flexible hazard regression methods, in particular the HARE model proposed by Kooperberg et al. [16]. A simulation study is conducted to carry out the comparison. The model developed in this paper exhibited good performance in the prediction of hazard rate. The application of this sparse Bayesian technique to a real cancer data set demonstrated that the proposed method can potentially reveal characteristics of the hazards, associated with the dynamics of the studied diseases, which may be missed by existing modeling approaches based on different perspectives on the bias vs. variance balance.

Baroclinic Frontal Arrest: A Sequel to Unstable Frontogenesis

Abstract In a large-scale deformation flow, lateral and vertical buoyancy gradients sharpen through baroclinic frontogenesis near the surface boundary. A “thermally direct” ageostrophic secondary circulation cell arises during frontogenesis to maintain geostrophic, hydrostatic (thermal wind) momentum balance for the alongfront flow. Unstable three-dimensional fluctuations can grow during frontogenesis by baroclinic instability of the alongfront shear flow that converts frontal potential energy to fluctuation energy. At finite amplitude, the fluctuations provide alongfront-averaged eddy momentum and buoyancy fluxes that arrest the frontal sharpening even while the deformation flow persists. The frontal ageostrophic secondary circulation reverses to become a “thermally indirect” cell in the center of the front. This allows an approximate opposition between ageostrophic advection and eddy-flux divergence in the frontal buoyancy gradient variance (i.e., frontal strength) balance equation, implying frontal equilibration. During the approximately equilibrated phase, the energy exchange rates among the deformation flow, front, and fluctuations are all reduced in comparison with a solution without eddy-flux feedback on the frontal evolution. The mean stratification is enhanced by both frontogenesis and eddy vertical buoyancy flux. The thermally indirect secondary circulation arises from eddy fluxes acting to force a departure in thermal-wind balance for the alongfront flow, overwhelming the single-cell thermally direct circulation induced by the deformation flow. The equilibrated thermal-wind imbalance in the frontal flow is appreciable, and its magnitude is set by the cross-front eddy flux of alongfront vorticity. This demonstrates an essentially inviscid, baroclinic, dynamical process for frontogenetic arrest through frontal instability.

Energy balance invariance for interacting particle systems

This paper studies the principle of invariance of balance of energy and its consequences for a system of interacting particles under groups of transformations. Balance of energy and its invariance is first examined in Euclidean space. Unlike the case of continuous media, it is shown that conservation and balance laws do not follow from the assumption of invariance of balance of energy under time-dependent isometries of the ambient space. However, the postulate of invariance of balance of energy under arbitrary diffeomorphisms of the ambient (Euclidean) space, does yield the correct conservation and balance laws.

Wavelet domain de-noising of time-courses in MR image sequences

Magnetic resonance images acquired with high temporal resolution often exhibit large noise artifacts, which arise from physiological sources as well as from the acquisition hardware. These artifacts can be detrimental to the quality and interpretation of the time-course data in functional MRI studies. A class of wavelet-domain de-noising algorithms estimates the underlying, noise-free signal by thresholding (or ‘shrinking’) the wavelet coefficients, assuming the underlying temporal noise of each pixel is uncorrelated and Gaussian. A Wiener-type shrinkage algorithm is developed in this paper, for de-noising either complex- or magnitude-valued image data sequences. Using the de-correlation properties of the wavelet transform, as elucidated by Johnstone and Silverman, the assumption of i.i.d. Gaussian noise can be abandoned, opening up the possibility of removing colored noise. Both wavelet- and wavelet-packet based algorithms are developed, and the Wiener method is compared to the traditional Hard and Soft wavelet thresholding methods of Donoho and Johnstone. The methods are applied to two types of data sets. In the first, an artificial set of complex-valued images was constructed, in which each pixel has a simulated bimodal time-course. Gaussian noise was added to each of the real and imaginary channels, and the noise removed from the complex image sequence as well as the magnitude image sequence (where the noise is Rician). The bias and variance between the original and restored paradigms was estimated for each method. It was found that the Wiener method gives better balance in bias and variance than either Hard or Soft methods. Furthermore, de-noising magnitude data provides comparable accuracy of the restored images to that obtained from de-noising complex data. In the second data set, an actual in vivo complex image sequence containing unknown physiological and instrumental noise was used. The same bimodal paradigm as in the first data set was added to pixels in a small localized region of interest. For the paradigm investigated here, the smooth Daubechies wavelets provide better de-noising characteristics than the discontinuous Haar wavelets. Also, it was found that wavelet packet de-noising offers no significant improvement over the computationally more efficient wavelet de-noising methods. For the in vivo data, it is desirable that the groups of “activated” time-courses are homogeneous. It was found that the internal homogeneity of the group of time-courses increases when de-noising is applied. This suggests using de-noising as a pre-processing tool for both exploratory and inferential data analysis methods in fMRI.

Construction of Non-Proper Balanced Bipartite Block Designs

The purpose of this paper is to give some methods of construction of balanced bipartite block designs. These designs are useful for comparing a set of test treatments to a set of control treatments. The methods of construction of non-proper balanced bipartite block designs are based on the UBe of incidence matrices of block designs with known patterns, such as balanced incomplete block (BiB) designs, group divisible (GD) designs and variance balanced (VB) designs. Using resolvable BIB designs and certain GD designs, two methods of construction of proper balanced bipartite block designs have also been given.

On the Construction of VB Designs

This paper gives complete analytical study of suitability and non-availability of I-associate and II-associate designs of a given 2-class partially balanced incomplete block (2-PBIB) design in the construction of a variance balance (VB) design using the given 2-PBIB design.

Experiments on density-gradient anisotropies and scalar dissipation of turbulence in a stably stratified fluid

The anisotropic behaviour of density-gradient fluctuations in stably stratified grid turbulence and the consequences for simplified (isotropic) estimates of scalar dissipation rates χ were experimentally studied in a thermally stratified wind tunnel at moderate Reynolds numbers (Reλ ≃ 20). Strong stable stratifications were attained, with Brunt-Väisälä frequency N as high as 4 rad s−1. The correlation method was used to estimate the mean-square cross-stream and streamwise density gradients. Cross-stream gradients were measured using two cold wires. The mean-square vertical gradients were found to become larger than the streamwise gradients by as much as a factor of 2.2 for the largest dimensionless buoyancy times (Nt = 7). This corresponds to a 40% error in the scalar dissipation estimates based on ∂θ/∂x alone, and assuming the validity of the isotropic relations. Gradient spectral relations show that this buoyancy-induced anisotropy persists at all length scales. Better closure of the scalar variance balance was attained than in previously reported measurements by other researchers. This is attributed to our use of cold-wire temperature sensors having larger length-to-diameter ratio than used in the previous measurements.

Construction of Variance Balanced Designs through Triangular PBIB Designs

Several authors have obtained variance balanced (VB) and ternary variance balanced ( V B) designs using balanced incomplete block (BIB) designs and group divisible (GD) designs. In the present investigation, another systematic methods have been developed for the construction of VB designs using A Triangular PBIB design and an incomplete block design where the blocks of the incomplete block design are formed by taking the second associate treatments of the given triangular PBIB design. Two Triangular PBIB designs. The methods of construction of VB designs are further illustrated by examples.

Cross-Over Experiments: Design, Analysis, and Application.

Introduction to the analysis of cross-over designs - basic principles and some useful tools Latin square designs the 2-treatment, 2-period, 2-sequence design modifications of the 2-treatment, 2-period, 2-sequence design cross-over designs with variance balance cross-over designs lacking variance balance the analysis of categorical data from cross-over designs ordinary least squares estimation versus other criteria of estimation - justification for using the methodology presented in this book other topics in cross-over designs.

Cross-Over Experiments: Design, Analysis and Application.

Introduction to the analysis of cross-over designs - basic principles and some useful tools Latin square designs the 2-treatment, 2-period, 2-sequence design modifications of the 2-treatment, 2-period, 2-sequence design cross-over designs with variance balance cross-over designs lacking variance balance the analysis of categorical data from cross-over designs ordinary least squares estimation versus other criteria of estimation - justification for using the methodology presented in this book other topics in cross-over designs.

Balance, efficiency and orthogonality concepts in block designs

Some of the most basic terms and concepts used in connection with the balancing of treatments in block experiments are reexamined. In particular, two rival concepts of balance are considered. The first is based on the equality of weighted concurrences, and is commonly called variance balance. The other is based on the proportionality of weighted concurrences to the products of the relevant treatment replications, and is usually called efficiency balance. Their implications for estimating contrasts of treatment parameters are derived and discussed. As a consequence, the terminology used for these two concepts is questioned and some advantage of the second concept in relation to the randomization model is indicated. A reference to the notion of general balance is also made.

A Second-Order Bulk Boundary-Layer Model

Bulk mass-flux models represent the large eddies that are primarily responsible for the turbulent fluxes in the planetary boundary layer as convective circulations, with an associated convective mass flux. In order for such models to be useful, it is necessary to determine the fractional area covered by rising motion in the convective circulations. This fraction can be used as an estimate of the cloud amount, under certain conditions. “Matching” conditions have been developed that relate the convective mass flux to the ventilation and entrainment mass fluxes. These are based on conservation equations for the scalar means and variances in the entrainment and ventilation layers. Methods are presented to determine both the fractional area covered by rising motion and the convective mass flux. The requirement of variance balance is used to relax the “well-mixed” assumption. The vertical structures of the mean state and the turbulent fluxes are determined analytically. Several aspects of this simple model's formulation are evaluated using results from large-eddy simulations.

Minimum number of experimental units in connected block designs with certain additional properties

It is known (cf. Dodge (1985) and Kageyama (1985)) that the minimum number of experimental units for a block design with v treatments and b blocks to be connected is v+ b−1. This minimum number may not be attainable, however, when it is required that the design in question should satisfy certain additional conditions on treatment replications and/or block sizes or have certain additional properties, such as variance balance, efficiency balance and/or pairwise balance. In this paper, the problem of determining the minimum number of experimental units in connected block designs satisfying such additional requirements is considered. Some of the results derived are extensions of those given by Kageyama (1985), some other results are new.