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Methods for the visualization of circadian rhythms: From molecules to organisms
Published in Raquel Seruca, Jasjit S. Suri, João M. Sanches, Fluorescence Imaging and Biological Quantification, 2017
Rukeia El-Athman, Jeannine Mazuch, Luise Fuhr, Mónica Abreu, Nikolai Genov, Angela Relógio
This technology is a very powerful tool for the large-scale analysis of gene expression. The most commonly used type of arrays are provided by the company Affymetrix [25] and allow for genome-wide screening in a single sample. Microarrays are glass-coated chips with a matrix type distribution of oligonucleotides of known sequences, named probes. The hybridization of the target sample (fragmented and labeled) to its complementary probe allows for a relative quantification of gene expression via measurement of optical intensity of the hybridized sample fragments. A pipeline of open-source tools provides the means for the data analysis, mainly based on R [26]. Graphical user interface (GUI) tools such as the RStudio IDE allow for better development of individual scripts [27]. The Bioconductor/Biobase [28] software repository provides an increasing number of packages that automate many steps related to computational biology and bioinformatics. For exon arrays, the R package oligo provides all necessary tools for reading and normalizing the raw data [29]. The most common normalization technique is the robust multiarray average (RMA) [30] that is also part of the oligo package. The quality control of the arrays can be performed with the R package arrayQualityMetrics [31]. Subsequent analysis can be done with the R package limma [32] as it provides the tools for the creation of linear models that are fitted to the data of the arrays given an appropriate design matrix. The design matrix represents a numerical vector or a matrix which delivers information on the experimental design. The genes that show the biggest difference between the elements specified in the matrix can be determined and further investigated.
Computations and Sustainability in Material Forming
Published in R. Ganesh Narayanan, Jay S. Gunasekera, Sustainable Material Forming and Joining, 2019
Zhengjie Jia, R. Ganesh Narayanan
The QFD has been widely successfully employed by various manufactures in Japan since 1975 and in United States since 1984 (King, 1989, Phadke, 1989, Dehnad, 1989, American Supplier Institute, 1987, Hauser et al., 1988, Jia, 1995b). The QFD is an algorithmic design approach and a cross-functional tool. The QFD approach is a system for defining the design problem based on customer demands in terms of a conceptual map, which supports inter-functional planning and communications. The design problem is subsequently solved by a comprehensive prioritization scheme. In the QFD approach, the QFD matrix is a disciplined way of comparing two series of items and provides a logical, in-depth look at many of the critical aspects of any product/process. It virtually eliminates the need for redesign, especially on critical items (King, 1989). Matrix Approach stemming from the QFD is adopted in attempts to understand the relationships between functional requirements and design (process) parameters of material-forming processes, to identify main process design parameters and to define the design space. In Matrix Approach, there are two matrix charts (Jia, 1998): Design Matrix and Process Matrix. Each of them takes two groups of ideas and compares them against each other to decide if there are any correlations. The Design Matrix maps out in matrix form what the functions of the product require and how the material-forming process will meet that need. The design matrix chart compares functional requirements with design parameters and identifies strong, moderate, and possible correlations. The purpose of a Design Matrix is to develop the initial plan of how the functional requirements will be met based on the current process design and to find out which design parameters interact with others. The inputs include functional requirements and design parameters. The outputs include 3–6 key design parameters. A Process Matrix examines the correlations between the design parameters and the process factors with the most critical design parameters on the left side and the process factors on the top. The purpose is to identify which process factors are most related to the 3–6 critical design parameters.
Effect of Operational Uncertainties on the Stochastic Dynamics of Composite Laminates
Published in Sudip Dey, Tanmoy Mukhopadhyay, Sondipon Adhikari, Uncertainty Quantification in Laminated Composites, 2018
Sudip Dey, Tanmoy Mukhopadhyay, Sondipon Adhikari
where ‘Y’ is a vector of observations of sample size, ‘ε’ is the vector of errors having normal distribution with zero mean, ‘X’ is the design matrix and ‘β’ is a vector of unknown model coefficients (βo and βi). The design matrix is a set of combinations of the values of the coded variables, which specifies the settings of the design parameters to be performed during data observation. The representative two factor central composite design is furnished in Fig. 6.2. In CCD, second order design is used consisting of the following three portions for obtaining design points: a complete (or a fraction of) 2k factorial design coded as ±1 (corresponding to the lower and upper value bound of the design space) consisting of 2k design points, 2k axial points coded as ± α (α ≥ 1) and n0 centre points as shown in Fig. 6.2. Here ‘k’ is the number of input variables. Thus the total number of design points in CCD model, n = 2k + 2k + n0 where n0 = 1 for present numerical study. CCD possesses the following properties according to the chosen values of a and n0: Rotatable (used for up to 5 factors to creates a design with standard error of predictions equal at points equidistant from the centre of the design).Face-centred (the axial points into the faces of the cube at ± 1 levels to produce a design with each factor having 3 levels).Spherical (all factorial and axial points on the surface of a sphere of radius equals to square root of the number of factors).Orthogonal quadratic (α values allowing the quadratic terms to be independently estimated from the other terms).Practical (used for 6 or more factors wherein a value is the fourth root of the number of factors).
Gaussian Process Modeling Using the Principle of Superposition
Published in Technometrics, 2019
We can estimate y0(v, x0), , by using the simulator output data at specially chosen design points in the design region . By definition (see (15)), y0(v, x0) is the response at the point (x, z) = (x0, 0) in the experiment region, which we take as , that is, . In addition, (20) implies that is approximately equal (exactly equal if ϵ = 0) to the response at the point given by x = x0, , and all other ’s and ’s equal to 0, that is, . Thus, our estimate of is obtained by subtracting the output at (x, z) = (x0, 0) from the output at . We estimate in a similar fashion. Thus, estimation of the mean function (21) requires 1 + k + m1 + ⋅⋅⋅ + mq runs of the simulator. The design runs for this purpose are given by the rows of the design matrix where dz = k + m1 + ⋅⋅⋅ + mq, is a (1 + dz) × 1 vector of 1’s, is a dz × 1 vector of 0’s, and is a dz × dz identity matrix. Note that is a one-factor-at-a-time design for z given fixed x = x0. We append to a maximin Latin hypercube design (LHD) , which is a commonly used design for constructing GP emulators. Typically, the size (number of rows) of far exceeds the size of . In the examples in Section 5, we choose the size of so that the size of the combined design is 7d, where d is dz plus the dimension of x. Note that is of size 1 + dz ⩽ d, if we assume x has at least one component.