Fractional Plans to Estimate Main Effects and Two Factor Interactions Inclusive of a Specific Factor

Balanced incomplete block designs are used to construct non‐geometric 2ⁿ fractional factorial plans to estimate all n main effects and n – 1, 2 factor interactions with a specific factor included in each interaction. When the balanced incomplete block design is of Family (A), the resulting fractional factorial plan has the same number of runs as a fold‐over Hadamard matrix giving same variances for the estimates; however, some new designs are shown to be non‐isomorphic to the fold‐over Hadamard matrix plans.     

A necessary condition for balance of a block design

It is shown that, barring orthogonal designs, a necessary condition for a block design, BD(v, b, N), to be J-balanced is that the rows of its incidence matrix, N, are linearly independent. This strengthens the condition b v known in the literature as FISHER'S inequality. V-balanced block designs are also discussed.     

Group screening for rare events based on incomplete block designs

Fields such as, diagnostic testing, biotherapeutics, drug development, and toxicology among others, center on the premise of searching through many specimens for a rare event. Scientists in the business of “searching for a needle in a haystack” may greatly benefit from the use of group screening design strategies. Group screening, where specimens are composited into pools with each pool being tested for the presence of the event, can be much more cost-efficient than testing each individual specimen. A number of group screening designs have been proposed in the literature. Incomplete block screening designs are described here and compared with other group screening designs. It is shown under certain conditions, that incomplete block screening designs can provide nearly a 90% cost saving compared to other group screening designs such as when prevalence is 0.001 and screening 3876 specimens with an ICB-sequential design vs. a Dorfman design. In other cases, previous group screening designs are shown to be most efficient. Overall, when prevalence is small (≤0.05) group screening designs are shown to be quite cost effective at screening a large number of specimens and in general there is no one design that is best in all situations. © 2018 American Institute of Chemical Engineers Biotechnol Progress, 35: e2770, 2019.     

Equi-replicated balanced block designs generated by a balanced matrix

In this paper it is shown that if N= \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{i = 1}^{S_h} $\end{document} c_ihN_ih, where c_ih are some non-negative integer numbers and N_ih are such incidence matrices that A_h = \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{i = 1}^{S_h} $\end{document} i N_ih is a balanced matrix defined by SHAH (1959), for h = 1, 2,…, p, then a block design with an incidence matrix Ñ = [N, N,…,N] is an equi-replicated balanced block design. Here the balance of a block design is defined in terms of the matrix M₀ introduced by CALI?SKI (1971).     

Sequentially Generated Designs

Procedures for sequential generation of nearly D-optimal designs are described. Two kinds of designs can be obtained: symmetrical block designs and nonsymmetrical ones. It is shown that in a special case when the number of the support points of a continuous D-optimal design equals to the number of regression coefficients the sequential designs can be constructed very easy without use of a computer. A Catalogue containing 135 designs has been developed by use of these procedures. 34 of them can be used for experiments in cuboidal factor space and the remaining for experiments with mixture and process variables. Comparison with other designs is done.     

Use of uniform designs in combination with neural networks for viral infection process development

This work aimed to compare the predictive capacity of empirical models, based on the uniform design utilization combined to artificial neural networks with respect to classical factorial designs in bioprocess, using as example the rabies virus replication in BHK‐21 cells. The viral infection process parameters under study were temperature (34°C, 37°C), multiplicity of infection (0.04, 0.07, 0.1), times of infection, and harvest (24, 48, 72 hours) and the monitored output parameter was viral production. A multilevel factorial experimental design was performed for the study of this system. Fractions of this experimental approach (18, 24, 30, 36 and 42 runs), defined according uniform designs, were used as alternative for modelling through artificial neural network and thereafter an output variable optimization was carried out by means of genetic algorithm methodology. Model prediction capacities for all uniform design approaches under study were better than that found for classical factorial design approach. It was demonstrated that uniform design in combination with artificial neural network could be an efficient experimental approach for modelling complex bioprocess like viral production. For the present study case, 67% of experimental resources were saved when compared to a classical factorial design approach. In the near future, this strategy could replace the established factorial designs used in the bioprocess development activities performed within biopharmaceutical organizations because of the improvements gained in the economics of experimentation that do not sacrifice the quality of decisions. © 2015 American Institute of Chemical Engineers Biotechnol. Prog., 31:532–540, 2015     

A comparison of four experimental designs for the estimation of heritability

Summary The partial diallel cross, the complete diallel cross, and the designs known as North Carolina Experiments 1 and 2 are compared for their usefulness in estimating heritability. It is first shown that reliable values for the sampling mean and variance of heritability estimates are obtained from approximate expressions based on the moments of the chi-square distribution. These expressions are then applied to determine the optimum experimental designs for a range of situations.The main basis for discrimination is the amount of information per unit, defined as i = 1/(N var( ²)), where ² is the estimate of the heritability h ² and N is the number of units in the experiment, either individuals or families.The two parameters considered were the heritability of individuals and the heritability of full-sib families, and for each of these the partial diallel cross was the most preferred, followed in decreasing order of preference by design NC2, the complete diallel, and design NC1.It is first shown that there is no optimum number of parents for a partial diallel cross or male parents for designs NC1 and NC2. The number of crosses per parent for a partial diallel or dams per sire for designs NC2 and NC2 should generally be six or less. Any expansion should be in the direction of using more parents in the case of the partial diallel, or more male parents in the case of designs NC1 and NC2. For the two heritability parameters considered in this study it is inefficient to increase the number of replicates beyond two.     

A Generalization of the GMANOVA-Model

It is shown that in some experimental designs the MANOVA- and the GMANOVA-model are too restrictive either to yield all hypothesis tests of interest or to reflect all known features of the design. An extension of these models is derived by relating the response vectors with the unknown model parameters by linear equations which may be completely different for each of the p components of the response vector and for each of the n independent vectors. For situations, in which a Wishart-distributed estimator for the underlying common covariance matrix is attainable, a test for any s-dimensional linear hypothesis on the model parameters is derived.     

Some algebraic relations between involutions,convolutions, and correlations,with applications to holographic memories

Convolutions * and correlations # in spacesH of doubly infinite sequences are related bya#b=S(a * Sb), whereS is an involution which reflects the order in the integral domainZ on which the sequences are defined. This relation can be used to represent a non-associative correlation algebra 〈H, #〉 by an associative convolution algebra equipped with the involutionS which, as is shown, greatly simplifies derivations. Related matrix representations of #, *,S are given for sequences with finite support in Re ⁿ . Some implications for holographic memory models are discussed. An erratum to this article is available at .     

Application of the Biased Spring Balance Weighing Design Theory to Estimation of Differences of Line Effects for Legume Content

The incidence matrix of a BIB design for v treatments has been used to construct a biased spring balance weighing design. Conditions under which an optimum biased spring balance weighing design exists are given. It is also shown how this theory may be utilized to obtain treatment and experiment designs to estimate differences in legume content between pair of lines in an experiment overseeded with grass species.     

Predicting mean and variance of all possible lines and hybrids from designs with partially inbred progenies

Two-factor mating designs at consecutive S_n and S_(n+1) levels (S₀ and S₁ S₁ and S₂, or F₂ and F₃) allow estimation of all components of the variation among homozygous lines and F₁ hybrids that can be derived from a given population. They also allow for the prediction of the mean of these lines and single-cross hybrids. Some tests for the presence of epistasis are possible at the levels of means and of variances. Such mating designs can be very useful for predicting the value of the best possible lines or the best possible F₁ hybrids when it is difficult to produce, at an experimental level for exploratory purposes, either lines or hybrids.     

Applications of a Vectorized MANOVA-Model

If the observation matrix of n independent p-dimensional normal vectors with common covariance matrix is transformed into an np-vector, linear models and hypotheses on the expectations can be formulated, that are not attainable in standard MANOVA or GMANOVA models. The distribution of an earlier proposed test procedure for this vectorized model is derived for p = 2, and its application is demonstrated for crossover and repeated measurement designs. Numerical results are compared in situations, in which both the standard and the vectorized model are applicable.     

Responses of male winter moths (Operophtera brumata) to their sex attactant (3Z,6Z,9Z)-1,3,6,9 nonadecatetraene and to some structural analogues

Conclusion (3Z,6Z,9Z)-1,3,6,9-nonadecatetraene, the synthetic sex pheromone of the female of O. brumata is highly active in attracting males of this species in the field (Germany and Switzerland). No analogous compounds possessing attractivity to O. brumata males have been found up to now, nor did they show any inhibitory effects to the same species.Therefore (3Z,6Z,9Z)-1,3,6,9-nonadecatetraene (I) can be recommended as a good attractant in the prognosis or monitoring of this lepidopteran pest.     

Designs Suited for Varietal Trials with Multiple Basals

DAS (1960) gave a method of construction of confounded balanced asymmetrical factorial designs of the type v × 2² by using BIB designs. In the present paper a method has been given for construction of balanced asymmetrical factorial designs of the type (v–t) × 2² by using truncated balanced incomplete block designs obtainable by omitting t treatments. Likewise, partially balanced asymmetrical factorial designs can also be obtained by omitting any particular treatment alongwith its first or second associate treatments from the v treatments of a PBIB design. We can get a large number of new designs not available in literature through this technique. These designs are well suited for varietal trials with multiple basals.     

On the E-Optimality of Block Designs with Unequal Block Sizes

In this paper an inequality for the smallest positive eigenvalues of the C-matrix of a block design are derived. This inequality is a generalization of a result by Constantine (1982) to the case of unequal block sizes. On the basis of the above result a certain E-optimality criterium of block designs is given. Furthermore coefficient e_d has been introduced which permits to assess how close the block design is from the optimal one.     

A Simple Construction Procedure for Eesolvable Incomplete Block Designs for any Number of Treatments

A simple, straightforward procedure, which requires no special tables or generators, is presented for constructing resolvable incomplete block designs for v=pk, v=p²k, …, treatments, for k≥p, in incomplete blocks of size k. Also, it is shown, how to obtain incomplete block designs for any v in blocks of size k and k+1. The procedure allows construction of balanced incomplete block designs for p = k a prime number. For p = n not a prime number, incomplete block designs can be obtained by the procedure, but are not balanced. However, for p_s being the smallest prime factor of n, p_s + 1 for v = n², p_s²+ p_s + 1 for v = n³, …, arrangements can be obtained for which the occurrence of any treatment pair in the blocks is either zero or one. This is called a zero-one concurrence design. Procedures are described for obtaining additional zero-one concurrence arrangements. It is shown that the efficiency of these designs is maximum. Both intra-block and inter-block analyses are described.     

A comparison of responses from olfactory receptor neurons of<Emphasis Type="Italic"> Heliothis subflexa</Emphasis> and<Emphasis Type="Italic"> Heliothis virescens</Emphasis> to components of their sex pheromone

Single-cell electrophysiological recordings were obtained from olfactory receptor neurons in sensilla trichodea on male antennae of the heliothine species Heliothis subflexa and the closely related congener H. virescens. A large percentage of sensilla (72% and 81%, respectively, of all sensilla sampled) contained a single odor-responsive receptor neuron tuned to the major pheromone component of both species, Z-11-hexadecenal. A second population of sensilla on H. subflexa antennae (18%) housed receptor neurons that were tuned to Z-9-hexadecenal but also responded with less sensitivity to Z-9-tetradecenal. A similar population of sensilla (4%) on H. virescens male antennae housed receptor neurons that were shown to be tuned specifically only to Z-9-tetradecenal, with no response to even high dosages of Z-9-hexadecenal. A third population of sensilla (comprising 8% and 16% of the sensilla sampled in H. subflexa and H. virescens, respectively) housed two olfactory receptor neurons, one of which was tuned to Z-11-hexadecenyl acetate and the other tuned to Z-11-hexadecenol. In H. subflexa the Z-11-hexadecenyl acetate-tuned neuron also responded to Z-9-tetradecenal with nearly equivalent sensitivity. The behavioral requirements of males of these two species for distinct pheromonal blends was, therefore, reflected by the subtle differences in the tuning properties of antennal olfactory receptor neurons.Abbreviations MGC macroglomerular complex - ORN olfactory receptor neuron - Z9–14:Ald (Z)-9-tetradecenal - Z9–16:Ald (Z)-9-hexadecenal - Z11–16:Ac (Z)-11-hexadecenyl acetate - Z11–16:Ald (Z)-11-hexadecenal - Z11–16:OH (Z)-11-hexadecenol     

Identification of two components of the female sex pheromone of the sugarcane‐borer Diatraea flavipennella (Lepidoptera: Crambidae)

Analysis by gas chromatography with electroantennographic detection of extracts of pheromone glands derived from calling females of the sugarcane‐borer Diatraea flavipennella revealed two antennally active compounds. These components were identified as (Z)‐9‐hexadecenal (Z9–16:Ald) and (Z)‐11‐hexadecenal (Z11–16:Ald) by comparison of the retention times of the natural compounds and the synthetic compounds supported by two‐dimensional gas chromatography – time‐of‐flight mass spectrometric analysis and the positions of the double bounds in the chains were confirmed from the mass spectral fragmentation patterns of their dimethyldisulphide adducts. The analysis indicated that Z9–16:Ald and Z11–16:Ald were present in the sex pheromone in the proportions 25 : 75. Trace amounts of tetradecanal, hexadecanal, (Z)‐7‐hexadecenal (Z7–16:Ald), (Z)‐9‐hexadecen‐1‐ol and (Z)‐11‐hexadecen‐1‐ol were also found in the extract, but of these only Z9–16:Ald and Z11–16:Ald appeared to be antennally active. Behavioural bioassays demonstrated that a binary blend composed of Z9–16:Ald and Z11–16:Ald in the ratio of 25 : 75 induced a response in D. flavipennella virgin males similar to that elicited by live virgin females or by an hexane extract of the pheromone glands of calling females. Z9–16:Ald and Z11–16:Ald are, therefore, considered to be the major constituents of the female sex pheromone of D. flavipennella.     

A model-independent approach to the theory of experimental designs and a special discussion of bib. II. properties and construction of bib

In addition to the first part we prove independently of the model some theorems on properties of balanced block designs. Then we propose nine methods of construction of BIB and prove theorems in connection with these methods. In a table we give a survey on block designs with v$25 and possibilities of their construction with these methods. Further follow theorems with the number of nonisomorphic BIB for some fixed v and k.