Arpan Bhowmik

Identification of Differentially Expressed Genes in RNA-seq Data of Arabidopsis thaliana: A Compound Distribution Approach

Abstract Gene expression is the process by which information from a gene is used in the synthesis of a functional gene product, which may be proteins. A gene is declared differentially expressed if an observed difference or change in read counts or expression levels between two experimental conditions is statistically significant. To identify differentially expressed genes between two conditions, it is important to find statistical distributional property of the data to approximate the nature of differential genes. In the present study, the focus is mainly to investigate the differential gene expression analysis for sequence data based on compound distribution model. This approach was applied in RNA-seq count data of Arabidopsis thaliana and it has been found that compound Poisson distribution is more appropriate to capture the variability as compared with Poisson distribution. Thus, fitting of appropriate distribution to gene expression data provides statistically sound cutoff values for identifying differentially expressed genes.

Universally optimal second order neighbour designs

This paper deals with optimality aspects of complete block designs with interference effects arising from the neighbouring units up to distance 2 (first and second order) from one side. Conditions have been obtained for the block design to be universally optimal for estimating direct and interference effects. Some classes of balanced and strongly balanced complete block designs have been identified to be universally optimal for the estimation of direct effects, first order neighbour effects and second order neighbour effects.

On the generation of cost effective response surface designs

SAS Macros for the generation of Cost Effective Response Surface Designs.Generation of Plackett-Burman Designs, CCD and BBD with minimum level changes.Output can be saved in MS-Word Format.Macro developed is freely available for the researchers working in this area. Run order consideration for mixed factorial, fractional factorial and confounded factorial have been studied by several authors in depth, but is lacking for Response Surface Designs (RSDs) except the results obtained by Quinlan and Lin (2015) for Plackett-Burman Design, a commonly used first order response surface design for screening purpose. Second Order Response Surface Designs (SORDs) are used to explore relationship between the response variable and the input variables and to find out the optimum input combinations to achieve a desired response. In this paper, we aim to find out optimal run orders with respect to minimizing level changes using a computer programme. Minimizing the level changes implies the minimization of experimental cost. Generation of four classes of designs viz., Plackett-Burman Design, Cost-effective Central Composite Design (CCD) with full factorial as well as fractional factorial points and Cost-effective Box Behnken Design (BBD) have been described through Macros developed using SAS IML.

Optimal block designs with non additive mixed effects interference

ABSTRACT This paper deals with optimality aspects of block designs balanced for interference effects from neighboring units on both sides under a general non additive model along with random block effects. Here, a class of complete, circular block designs strongly balanced for interference effects has been shown to be universally optimal for the estimation of direct effects and interference effects (left and right) of treatments under a non additive mixed effects model.

Minimally Changed Run Sequences in Factorial Experiments

ABSTRACT Randomization of run sequences in factorial experiments may result in large number of changes in factor levels which will make the experimentation expensive, time-consuming and difficult. Experiments in which it is difficult to change the levels of factor(s) use of minimally changed run sequences may often be preferable to a random run sequence. In the present paper, we have developed method for obtaining minimally changed run sequences for factorial experiments. The general expression of factor-wise number of level changes for the developed minimally changed run sequences has also been obtained. A relationship has been established between the time count effect of a lower order factorial with minimally changed run sequences and that of a higher order factorial with minimally changed run sequences obtained through the lower order minimally changed run sequences. For providing a readymade solution to the end users, a SAS macro has also been developed for generating these minimally changed run sequences along with its parameters.

A note on circular neighbor balanced designs

ABSTRACT This paper describes some methods of constructing circular neighbor balanced and circular partially neighbor balanced block designs for estimation of direct and neighbor effects of the treatments. A class of circular neighbor balanced block designs with unequal block sizes is also proposed.

Optimal Block Designs With Interference Effects From Neighboring Units Under a Non Additive Model

Here, the optimality of block design with interference effect from neighboring unit under a general non additive model is investigated, which allows for the presence of interactions among the treatments applied in the adjacent plots. A non additive model with interference × direct effects of treatments is considered as these effects contribute significantly to the response. A class of complete block designs balanced for interference effects from left neighboring unit is shown to be universally optimal for the estimation of direct and interference effects of treatments and two such series of designs have been constructed. Furthermore, considering direct treatment × block non additivity with interference effects, the optimality is studied and the optimal designs are obtained.

An algorithmic approach to construct D-optimal saturated designs for logistic model

ABSTRACT In this paper, locally D-optimal saturated designs for a logistic model with one and two continuous input variables have been constructed by modifying the famous Fedorov exchange algorithm. A saturated design not only ensures the minimum number of runs in the design but also simplifies the row exchange computation. The basic idea is to exchange a design point with a point from the design space. The algorithm performs the best row exchange between design points and points form a candidate set representing the design space. Naturally, the resultant designs depend on the candidate set. For gain in precision, intuitively a candidate set with a larger number of points and the low discrepancy is desirable, but it increases the computational cost. Apart from the modification in row exchange computation, we propose implementing the algorithm in two stages. Initially, construct a design with a candidate set of affordable size and then later generate a new candidate set around the points of design searched in the former stage. In order to validate the optimality of constructed designs, we have used the general equivalence theorem. Algorithms for the construction of optimal designs have been implemented by developing suitable codes in R.

Experimental designs for open pollination in polycross trials

A polycross is the pollination by natural hybridization of a group of genotypes, generally selected, grown in isolation from other compatible genotypes in such a way to promote random open pollination. A particular practical application of the polycross method occurs in the production of a synthetic variety resulting from cross-pollinated plants. Laying out these experiments in appropriate designs, known as polycross designs, would not only save experimental resources but also gather more information from the experiment. Different situations may arise in polycross nurseries where accordingly different polycross designs may be used. For situations in which some genotypes interfere in the growth or production of other genotypes, but have to be grown together, neighbour-restricted design is a better option. Furthermore, when the topography of the nursery is such that a known wind system in a certain direction may prevail, then designs balanced for neighbour effects of genotypes only in the direction of wind are appropriate which may help in saving experimental resources to a great extent. Also, when genotypes are planted in a small area without leaving much space between rows, designs balanced for neighbour effects from all possible eight directions are useful to have equal chance of pollinating and being pollinated by every other genotype. Here, polycross designs have been obtained to match above-mentioned three situations. SAS Macros have also been developed to generate these proposed designs.