A model-independent approach to the theory of experimental designs and a special discussion of bib. i general definition and designs with one or two block factors

Experimental designs are definded by introducing an assignment matrix Z. It is shown by block designs and double block designs that using Z or an operator on Z otherwise defined, well known designs can be got as special cases. Till now we didn' find an experimental design which could not be defined by our matrix Z. The definitions of properties of experimental designs can be given independently of the model of the statistical analysis. This is shown for the property of balance of block designs.     

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.     

New Constructions of BIB Designs

A method of construction of certain balanced incomplete block (BIB) designs is defined from which we get new series of BIB designs.     

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.     

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 Simple Procedure for Constructing Experiment Designs with Incomplete Blocks of Sizes 2 and 3

In order to maximize control of heterogeneity within complete blocks, an experimenter could use incomplete blocks of size k = 2 or 3. In certain situations, incomplete blocks of this nature would eliminate the need for such spatial types of analyses as nearest neighbor. The intrablock efficiency factors for such designs are relatively low. However, with recovery of interblock information, FEDERER and SPEED (1987) have presented measures of design efficiency factors which demonstrate that efficiency factors approach unity for certain ratios of the intrablock and interblock variance components. Hence with recovery of interblock information, even incomplete block designs with k = 2 or 3 have relatively high efficiency factors. The reduction in the intrablock error variance over the complete block error variance in many situations will provide designs with high efficiency. A simple procedure for constructing incomplete blocks of sizes 2 and 3 is presented. It is shown how to obtain additional zero-one association confounding arrangements when v = 4 t, t an integer, and for v = pk, k ≤ p. It is indicated how to do the statistical analysis for these designs.     

Group Divisible Second Order Rotatable Designs

The Group Divisible Rotatable (GDR) designs are the designs in which the factors get divided into groups such that for the factors within group, the designs are rotatable. In the present paper we have obtained a series of Group Divisible Second Order Rotatable designs, by decomposing the v-dimensional space corresponding to v-factors under consideration into three mutually orthogonal spaces. We have given the least squares estimates of the parameters, the analysis and construction of such designs.     

On C-Property in Block Designs

Block designs having a property described in Caliński (1971) and Saha (1976), referred to herein as C-property, are considered. A necessary and sufficient condition for a block design to have C-property is derived, and some methods of construction of such block designs are presented.     

A general target theory of radiobiological action: II

In Part II we prove some of the more complicated theorems stated and used in Part I. In particular, we derive the distribution functionsD ₁,D ₂, andD ₃, and prove some of their properties under various limiting conditions.     

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.     

Examples of non-trivial efficiency-balanced designs with b=v+1

This note provides examples of binary efficiency-balanced block designs with b=v+1, having no complete blocks, which are unequal-replicated and unequal-blocksized from a biometrical and agricultural standpoint.     

Dual Designs and Their Application in Genetical Experiments

The dual of incomplete block designs has been studied with th́eir applications in genetical experiments. Partial diallel crosses (PDC) of type I have been constructed using balanced incomplete block (BIB) designs, partially balanced incomplete block (PBIB) designs and their dual designs. Simplified analysis of PDC has been presented using the dual property of these designs. List of optimal PDC having simple analysis has been given.     

Optimality of Some Class of Incomplete Block Designs

A class of incomplete block designs called C-design, was considered by Caliński (1971), Saha (1976), Ceranka (1983) and Ceranka , Kozłowska (1983, 1984). In this paper we extend the theory of block designs having the C-property. We consider optimality of C-designs with respect to any criterion of a described form. Das and Kageyama (1991) considered a class of E-optimal proper efficiency balanced designs (strictly speaking, Das and Kageyama considered E_R-optimality of some class of block designs). Hence we consider E_R, A_R, D_R optimality of C-designs.     

Application of Partially Balanced Block Designs to Factorial Experiments

In this paper we present partially balanced block designs with F_p and C_p association schemes. These designs play a great role in the experimental theory since they can be applied to factorial experiments. A particular stress is put on the formulation of association schemes _p and C_p, presentation of exemplary constructions of these designs and their analysis of variance. The presented considerations are abundantly illustrated with examples.     

On the Construction of Balanced and Partially Balanced Ternary Design

A method of constructing balanced and partially balanced ternary designs from balanced and partially balanced incomplete block designs, respectively, and two methods of constructing partially balanced ternary designs from association schemes are obtained. Two new and efficient balanced ternary designs having K < V and R ≦ 20 are obtained by the first method.     

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.     

Heterologous expression and purification of neurotoxic Hainantoxin-III in E. coli

In the present study, we used Escherichia coli to produce recombinant Hainantoxin-III (rHNTX-III), a 33-amino acid peptic toxin from the tarantula spider Haplopelma hainanum. The toxin has three pairs of disulfide bonds. A pET-HS-HNTX-III vector was constructed and transformed into the E. coli strain SHuffle^TM. rHNTX-III was expressed using auto-induction medium. After using a Ni–NTA column, the expressed fusion protein was digested using SUMO protease (ULP1) to remove the HIS–SUMO tag, and then RP–HPLC and ultrafiltration were used for further purification. Then the rHNTX-III was identified by MALDI–TOF/TOF mass spectrometry. The purified rHNTX-III was further analyzed using a whole-cell patch-clamp assay. It was shown that the rHNTX-III was able to block currents generated by human Na_v1.7 (hNa_v1.7) at an IC₅₀ of 225?nM and also have high selectivity for different voltage-gated sodium channels. Therefore, it has very similar activity to the natural one.     

Some generalized conjugacy theorems and the concepts of fitness and survival in logistic growth models

Current research into the dynamics of iterative ecological and biological models has lead to a number of theorems concerning the existence of various types of iterative dynamical behavior. In particular, much study has been done on the dynamical behavior of the “simplest dynamical system”f _b(x)=bx(1−x), which is just the canonical discrete form of logistic growth equations found in ecology, sociobiology, and population biology. In this paper, we make use of some of the techniques and concepts of topological dynamics to construct a number of generalized conjugacy theorems. These theorems are then used to demonstrate that the mappingf _b has a number of conjugacy classes in which the dynamics of the iterates is equivalent to within a change of variables. The concepts of fitness and survival in logistic equations are then shown to be independent, if we follow certain intuitive definitions for these concepts. This conclusion follows from a comparison of the conjugacy classes of the functionf _b and the extinction sets off _b.     

The relative power of genome scans to detect local adaptation depends on sampling design and statistical method

Although genome scans have become a popular approach towards understanding the genetic basis of local adaptation, the field still does not have a firm grasp on how sampling design and demographic history affect the performance of genome scans on complex landscapes. To explore these issues, we compared 20 different sampling designs in equilibrium (i.e. island model and isolation by distance) and nonequilibrium (i.e. range expansion from one or two refugia) demographic histories in spatially heterogeneous environments. We simulated spatially complex landscapes, which allowed us to exploit local maxima and minima in the environment in ‘pair’ and ‘transect’ sampling strategies. We compared F_ST outlier and genetic–environment association (GEA) methods for each of two approaches that control for population structure: with a covariance matrix or with latent factors. We show that while the relative power of two methods in the same category (F_ST or GEA) depended largely on the number of individuals sampled, overall GEA tests had higher power in the island model and F_ST had higher power under isolation by distance. In the refugia models, however, these methods varied in their power to detect local adaptation at weakly selected loci. At weakly selected loci, paired sampling designs had equal or higher power than transect or random designs to detect local adaptation. Our results can inform sampling designs for studies of local adaptation and have important implications for the interpretation of genome scans based on landscape data.     

Contrasting Effects of Cd<Superscript>2+</Superscript> and Co<Superscript>2+</Superscript> on the Blocking/Unblocking of Human Ca<Subscript>v</Subscript>3 Channels

Inorganic ions have been used widely to investigate biophysical properties of high voltage-activated calcium channels (HVA: Ca_v1 and Ca_v2 families). In contrast, such information regarding low voltage-activated calcium channels (LVA: Ca_v3 family) is less documented. We have studied the blocking effect of Cd²⁺, Co²⁺ and Ni²⁺ on T-currents expressed by human Ca_v3 channels: Ca_v3.1, Ca_v3.2, and Ca_v3.3. With the use of the whole-cell configuration of the patch-clamp technique, we have recorded Ca²⁺ (2 mM) currents from HEK−293 cells stably expressing recombinant T-type channels. Cd²⁺ and Co²⁺ block was 2- to 3-fold more potent for Ca_v3.2 channels (EC₅₀ = 65 and 122 μM, respectively) than for the other two LVA channel family members. Current-voltage relationships indicate that Co²⁺ and Ni²⁺ shift the voltage dependence of Ca_v3.1 and Ca_v3.3 channels activation to more positive potentials. Interestingly, block of those two Ca_v3 channels by Co²⁺ and Ni²⁺ was drastically increased at extreme negative voltages; in contrast, block due to Cd²⁺ was significantly decreased. This unblocking effect was slightly voltage-dependent. Tail-current analysis reveals a differential effect of Cd²⁺ on Ca_v3.3 channels, which can not close while the pore is occupied with this metal cation. The results suggest that metal cations affect differentially T-type channel activity by a mechanism involving the ionic radii of inorganic ions and structural characteristics of the channels pore.