Algebraic structure for the crossing of balanced and stair nested designs

Stair nesting allows us to work with fewer observations than the most usual form of nesting, the balanced nesting. In the case of stair nesting the amount of information for the different factors is more evenly distributed. This new design leads to greater economy, because we can work with fewer observations. In this work we present the algebraic structure of the cross of balanced nested and stair nested designs, using binary operations on commutative Jordan algebras. This new cross requires fewer observations than the usual cross balanced nested designs and it is easy to carry out inference.

Crossing balanced and stair nested desings

Balanced nesting is the most usual form of nesting and originates, when used singly or with crossing of such sub-models, orthogonal models. In balanced nesting we are forced to divide repeatedly the plots and we have few degrees of freedom for the first levels. If we apply stair nesting we will have plots all of the same size rendering the designs easier to apply. The stair nested designs are a valid alternative for the balanced nested designs because we can work with fewer observations, the amount of information for the different factors is more evenly distributed and we obtain good results. The inference for models with balanced nesting is already well studied. For models with stair nesting it is easy to carry out inference because it is very similar to that for balanced nesting. Furthermore stair nested designs being unbalanced have an orthogonal structure. Other alternative to the balanced nesting is the staggered nesting that is the most popular unbalanced nested design which also has the advantage of requiring fewer observations. However staggered nested designs are not orthogonal, unlike the stair nested designs. In this work we start with the algebraic structure of the balanced, the stair and the staggered nested designs and we finish with the structure of the cross between balanced and stair nested designs.

Joining models with stair nesting

In the stair nested designs with u factors we have u steps and a(1), ... , a(u) "active" levels. We would have a(1) observations with different levels for the first factor each of them nesting a single level of each of the remaining factors; next a(2) observations with level a(1) + 1 for the first factor and distinct levels for the second factor each nesting a fixed level of each of the remaining factors, and so on. So the number of level combinations is Sigma(u)(i=1) a(i). In meta-analysis joint treatment of different experiments is considered. Joining the corresponding models may be useful to carry out that analysis. In this work we want joining L models with stair nesting.

Cobs and stair nesting – segregation and crossing

Stair nesting leads to very light models since the number of their treatments is additive on the numbers of observations in which only the level of one factor various. These groups of observations will be the steps of the design. In stair nested designs we work with fewer observations when compared with balanced nested designs and the amount of information for the different factors is more evenly distributed. We now integrate these models into a special class of models with orthogonal block structure for which there are interesting properties.

Whither PQL?

Generalized linear mixed models (GLMM) are generalized linear models with normally distributed random effects in the linear predictor. Penalized quasi-likelihood (PQL), an approximate method of inference in GLMMs, involves repeated fitting of linear mixed models with “working” dependent variables and iterative weights that depend on parameter estimates from the previous cycle of iteration. The generality of PQL, and its implementation in commercially available software, has encouraged the application of GLMMs in many scientific fields. Caution is needed, however, since PQL may sometimes yield badly biased estimates of variance components, especially with binary outcomes. Recent developments in numerical integration, including adaptive Gaussian quadrature, higher order Laplace expansions, stochastic integration and Markov chain Monte Carlo (MCMC) algorithms, provide attractive alternatives to PQL for approximate likelihood inference in GLMMs. Analyses of some well known datasets, and simulations based on these analyses, suggest that PQL still performs remarkably well in comparison with more elaborate procedures in many practical situations. Adaptive Gaussian quadrature is a viable alternative for nested designs where the numerical integration is limited to a small number of dimensions. Higher order Laplace approximations hold the promise of accurate inference more generally. MCMC is likely the method of choice for the most complex problems that involve high dimensional integrals.

Estimating the spatial scales of regionalized variables by nested sampling, hierarchical analysis of variance and residual maximum likelihood

The variogram is essential for local estimation and mapping of any variable by kriging. The variogram itself must usually be estimated from sample data. The sampling density is a compromise between precision and cost, but it must be sufficiently dense to encompass the principal spatial sources of variance. A nested, multi-stage, sampling with separating distances increasing in geometric progression from stage to stage will do that. The data may then be analyzed by a hierarchical analysis of variance to estimate the components of variance for every stage, and hence lag. By accumulating the components starting from the shortest lag one obtains a rough variogram for modest effort. For balanced designs the analysis of variance is optimal; for unbalanced ones, however, these estimators are not necessarily the best, and the analysis by residual maximum likelihood (REML) will usually be preferable. The paper summarizes the underlying theory and illustrates its application with data from three surveys, one in which the design had four stages and was balanced and two implemented with unbalanced designs to economize when there were more stages. A Fortran program is available for the analysis of variance, and code for the REML analysis is listed in the paper. (c) 2005 Elsevier Ltd. All rights reserved.

Estimating the spatial scales of regionalized variables by nested sampling, hierarchical analysis of variance and residual maximum likelihood

The variogram is essential for local estimation and mapping of any variable by kriging. The variogram itself must usually be estimated from sample data. The sampling density is a compromise between precision and cost, but it must be sufficiently dense to encompass the principal spatial sources of variance. A nested, multi-stage, sampling with separating distances increasing in geometric progression from stage to stage will do that. The data may then be analyzed by a hierarchical analysis of variance to estimate the components of variance for every stage, and hence lag. By accumulating the components starting from the shortest lag one obtains a rough variogram for modest effort. For balanced designs the analysis of variance is optimal; for unbalanced ones, however, these estimators are not necessarily the best, and the analysis by residual maximum likelihood (REML) will usually be preferable. The paper summarizes the underlying theory and illustrates its application with data from three surveys, one in which the design had four stages and was balanced and two implemented with unbalanced designs to economize when there were more stages. A Fortran program is available for the analysis of variance, and code for the REML analysis is listed in the paper. (c) 2005 Elsevier Ltd. All rights reserved.

Uniformization tool for systolic array designs

The paper is concerned with the uniformization of a system of affine recurrence equations. This transformation is used in the design (or compilation) of highly parallel embedded systems (VLSI systolic arrays, signal processing filters, etc.). We present and implement an automatic system to achieve uniformization of systems of affine recurrence equations. We unify the results from many earlier papers, develop some theoretical extensions, and then propose effective uniformization algorithms. Our results can be used in any high level synthesis tool based on polyhedral representation of nested loop computations.

Recursive Methods for Construction of Balanced N-ary Block Designs

2000 Mathematics Subject Classification: Primary 05B05; secondary 62K10.

Assessment Of Robustness On Analysis Using Headspace Solid-phase Microextraction And Comprehensive Two-dimensional Gas Chromatography Through Experimental Designs.

Plackett-Burman experimental design was applied for the robustness assessment of GC×GC-qMS (Comprehensive Two-Dimensional Gas Chromatography with Fast Quadrupolar Mass Spectrometric Detection) in quantitative and qualitative analysis of volatiles compounds from chocolate samples isolated by headspace solid-phase microextraction (HS-SPME). The influence of small changes around the nominal level of six factors deemed as important on peak areas (carrier gas flow rate, modulation period, temperature of ionic source, MS photomultiplier power, injector temperature and interface temperature) and of four factors considered as potentially influential on spectral quality (minimum and maximum limits of the scanned mass ranges, ions source temperature and photomultiplier power). The analytes selected for the study were 2,3,5-trimethylpyrazine, 2-octanone, octanal, 2-pentyl-furan, 2,3,5,6-tetramethylpyrazine, and 2-nonanone e nonanal. The factors pointed out as important on the robustness of the system were photomultiplier power for quantitative analysis and lower limit of mass scanning range for qualitative analysis.

Human Herpesvirus Infections Of The Central Nervous System: Laboratory Diagnosis Based On Dna Detection By Nested Pcr In Plasma And Cerebrospinal Fluid Samples.

Infections of the central nervous systems (CNS) present a diagnostic problem for which an accurate laboratory diagnosis is essential. Invasive practices, such as cerebral biopsy, have been replaced by obtaining a polymerase chain reaction (PCR) diagnosis using cerebral spinal fluid (CSF) as a reference method. Tests on DNA extracted from plasma are noninvasive, thus avoiding all of the collateral effects and patient risks associated with CSF collection. This study aimed to determine whether plasma can replace CSF in nested PCR analysis for the detection of CNS human herpesvirus (HHV) diseases by analysing the proportion of patients whose CSF nested PCR results were positive for CNS HHV who also had the same organism identified by plasma nested PCR. In this study, CSF DNA was used as the gold standard, and nested PCR was performed on both types of samples. Fifty-two patients with symptoms of nervous system infection were submitted to CSF and blood collection. For the eight HHV, one positive DNA result-in plasma and/or CSF nested PCR-was considered an active HHV infection, whereas the occurrence of two or more HHVs in the same sample was considered a coinfection. HHV infections were positively detected in 27/52 (51.9%) of the CSF and in 32/52 (61.5%) of the plasma, difference not significant, thus nested PCR can be performed on plasma instead of CSF. In conclusion, this findings suggest that plasma as a useful material for the diagnosis of cases where there is any difficulty to perform a CSF puncture.

Effect of different ferrule designs on the fracture resistance and failure pattern of endodontically treated teeth restored with fiber posts and all-ceramic crowns

OBJECTIVE: This study investigated the effect of different ferrule heights on endodontically treated premolars. MATERIAL AND METHODS: Fifty sound mandibular first premolars were endodontically treated and then restored with 7-mm fiber post (FRC Postec Plus #1 Ivoclar-Vivadent) luted with self-polymerized resin cement (Multilink, Ivoclar Vivadent) while the coronal section was restored with hybrid composite core build-up material (Tetric Ceram, Ivoclar-Vivadent), which received all-ceramic crown. Different ferrule heights were investigated: 1-mm circumferential ferrule without post and core (group 1 used as control), a circumferential 1-mm ferrule (group 2), non-uniform ferrule 2-mm buccally and 1-mm lingually (group 3), non-uniform ferrule 3-mm buccally and 2-mm lingually (group 4), and finally no ferrule preparation (group 5). The fracture load and failure pattern of the tested groups were investigated by applying axial load to the ceramic crowns (n=10). Data were analyzed statistically by one-way ANOVA and Tukey's post-hoc test was used for pair-wise comparisons (α=0.05). RESULTS: There were no significant differences among the failure load of all tested groups (P<0.780). The control group had the lowest fracture resistance (891.43±202.22 N) and the highest catastrophic failure rate (P<0.05). Compared to the control group, the use of fiber post reduced the percentage of catastrophic failure while increasing the ferrule height did not influence the fracture resistance of the restored specimens. CONCLUSIONS: Within the limitations of this study, increasing the ferrule length did not influence the fracture resistance of endodontically treated teeth restored with glass ceramic crowns. Insertion of a fiber post could reduce the percentage of catastrophic failure of these restorations under function.

Influence of separate and mixed experimental designs on reaction times to two simple visual stimuli

Testing contexts have been shown to critically influence experimental results in psychophysical studies. One of these contexts that show important modulation of the behavioral effects of different stimulatory conditions is the separate (blocked) or mixed presentation of these stimulatory conditions. The study presents evidence that the apparent discriminabilities of two target stimuli can change according to which of these two testing contexts is used. A cross inside a ring and a vertical line inside a ring were presented as go stimuli in a go/no-go reaction time task. In one experiment, each of these stimuli was presented to a different group of volunteers and in another experiment they were presented to the same group of volunteers, randomly mixed in the blocks of trials. Similar reaction times were obtained for the two stimuli in the first experiment, and different reaction times (faster for the cross) in the second experiment. The latter result indicates that the two stimuli have different discriminabilities from the no-go stimulus; the cross having greater discriminability. This difference is however masked, presumably by the adoption of specific compensatory attentional sets, in a separate testing context.

Rapid detection of bovine coronavirus by a semi-nested RT-PCR

Bovine coronavirus (BCoV) is a member of the group 2 of the Coronavirus (Nidovirales: Coronaviridae) and the causative agent of enteritis in both calves and adult bovine, as well as respiratory disease in calves. The present study aimed to develop a semi-nested RT-PCR for the detection of BCoV based on representative up-to-date sequences of the nucleocapsid gene, a conserved region of coronavirus genome. Three primers were designed, the first round with a 463bp and the second (semi-nested) with a 306bp predicted fragment. The analytical sensitivity was determined by 10-fold serial dilutions of the BCoV Kakegawa strain (HA titre: 256) in DEPC treated ultra-pure water, in fetal bovine serum (FBS) and in a BCoV-free fecal suspension, when positive results were found up to the 10-2, 10-3 and 10-7 dilutions, respectively, which suggests that the total amount of RNA in the sample influence the precipitation of pellets by the method of extraction used. When fecal samples was used, a large quantity of total RNA serves as carrier of BCoV RNA, demonstrating a high analytical sensitivity and lack of possible substances inhibiting the PCR. The final semi-nested RT-PCR protocol was applied to 25 fecal samples from adult cows, previously tested by a nested RT-PCR RdRp used as a reference test, resulting in 20 and 17 positives for the first and second tests, respectively, and a substantial agreement was found by kappa statistics (0.694). The high sensitivity and specificity of the new proposed method and the fact that primers were designed based on current BCoV sequences give basis to a more accurate diagnosis of BCoV-caused diseases, as well as to further insights on protocols for the detection of other Coronavirus representatives of both Animal and Public Health importance.

Experimental investigation on adaptive robust controller designs applied to a free-floating space manipulator

This paper aims to formulate and investigate the application of various nonlinear H(infinity) control methods to a fiee-floating space manipulator subject to parametric uncertainties and external disturbances. From a tutorial perspective, a model-based approach and adaptive procedures based on linear parametrization, neural networks and fuzzy systems are covered by this work. A comparative study is conducted based on experimental implementations performed with an actual underactuated fixed-base planar manipulator which is, following the DEM concept, dynamically equivalent to a free-floating space manipulator. (C) 2011 Elsevier Ltd. All rights reserved.