Binary vector

The final methodological chapter (Chapter 6) is devoted to cluster analysis. Besides a general treatment of different clustering approaches, also more specific problems in chemometrics are included, like clustering binary vectors indicating presence or absence of certain substructures. 

Chemical structures are often characterized by binary vectors in which each vector component (with value 0 or 1) indicates absence or presence of a certain substructure (binary substructure descriptors). An appropriate and widely used similarity measure for such binary vectors is the Tanimoto index (Willett 1987), also called Jaccard similarity coefficient (Vandeginste et al. 1998). Let xA and xB be binary vectors with m components for two chemical structures A and B, respectively. The Tanimoto index fAB is given by... 

Vectors whose components are based upon categorical or integer variables are described in Subheading 2.2.3. As was the case for binary vectors, these vectors are also classical sets, and, as was the case in the previous subsection, the associated similarity measures are set-based rather than vector-based. Here it will also be seen that the form of the set measures are, in some cases, modified from those associated with traditional classical sets. 

Distances in these spaces should be based upon an Zj or city-block metric (see Eq. 2.18) and not the Z2 or Euclidean metric typically used in many applications. The reasons for this are the same as those discussed in Subheading 2.2.1. for binary vectors. Set-based similarity measures can be adapted from those based on bit vectors using an ansatz borrowed from fuzzy set theory (41,42). For example, the Tanimoto similarity coefficient becomes... 

Fig. 5. In the scheme shown above, a 20-bit integer-valued vector (maximum integer value for each bit is 4) is converted into a 80-bit binary vector by converting each integer bit into a binary bit of four-bit length 0=0000 1 = 1000 2=1100 3=1110 4=1111. ...

The most commonly used 3D descriptors are pharmacophore keys, which are usually represented as binary vectors (17). The starting point when generating a... 

The development of T-DNA binary vectors revolutionalized the use of Agrobacteria to introduce genes into plants. A large number of binary vectors have been designed for highly specialized purposes and are commonly used in plant biotechnology today. 

Stiekema, W. I, Heidekamp, F., Louwerse, J. D., Verhoeven, H. A., Dijkhuis, P. (1988). Introduction of foreign genes into potato cultivars Bintje and Desiree using Agrobacterium tumefaciens binary vector. Plant Cell Rep., 7, 47-50. 

The most advanced method utilizes a binary vector system. One of the binary vectors is shown in Figure 7.11. This system depends on a small vector which contains the minimum elements required in cis. Other functions necessary for the gene transfer mechanism are donated from a separate helper, Ti plasmid. These features permit an easy introduction and maintenance of an exogenous DNA containing a manipulated gene. 

Plant cells can be transformed with a foreign gene by the cocultivation method. In the method, A. tumefaciens cells containing the binary vector and a helper Ti plasmid are mixed with actively growing cultured cells or freshly cut plant slices. After incubation of the cell mixture for two days, the transformed plant cells are selected on an antibiotic agar medium. Transformants can be normally visualized within two to three weeks after cocultivation. Several plants have been transformed with this technique. 

McBride, K. Summerfelt, K. (1990). Improved binary vectors for Agrobacterium-mediated plant transformation. Plant Molecular Biology 14, 269-76. 

A population is made of a series of chromosomes. Each chromosome is a binary vector, where each position (a gene) corresponds to a variable (i.e. a chromosome represents a model made up of a subset of... 

The block cipher can be considered as key-dependent permutation on a set of binary vectors corresponding to separate blocks. For the purpose of weakness elimination of permutation ciphers, for block ciphers several modes of operation were designed. They are intended for processing a large amount of information. These modes actually define the schemes of stream ciphering on basis of a block cipher. 

Alfalfa leaf explants from a highly regenerable clone of Regen-SY (19) were cocultured with A. tumefaciens containing each binary vector, and... 

Scheme 1. Design elements of a typical plant cell expression vector, including promoter sequence (35S), terminator sequence (T7), resistance gene (npt), right and left borders (Br and Bl), and insertion point for genes of interest. This binary vector is suitable for plant and Agrobacterium host cells...

For Agrobacterium transformation, the gene of interest must be carried in a binary vector with appropriate bacterial T-DNA elements. For other transformation methods the requirements maybe less stringent. However, even in these cases, the DNA of interest is typically amplified in bacteria. The choice of a promoter is of particular importance, as this element will dictate both the expression level and the time course of protein expression. The inclusion of additional elements, such as enhancers, 5 and 3 untranslated regions, and fusion elements (e.g. fluorescent or 6-histidine tags), should also be considered for improved expression, detection, and downstream processing. 

A prior distribution must also be assigned to the subset indicator vector 6. Because 6 is a binary vector with It elements, there are 2h possible subsets of active effects. The prior distribution on 6 must assign probability to each subset. An initially appealing choice is to make each of the 2h subsets equally likely. This is equivalent to prior independence of all elements of 6, and p(8j = 0) = p(8j = 1) = 0.5. In a screening context, this is implausible under the following widely accepted principles ... 

The coding sequence for the D. lanata CGH 1 was inserted downstream of the 35S promoter in the binary vector pBI121 resulting in plant expression vector pB1121cgh (Shi and Lindemann, 2006). Explants excised from seedlings of... 

The methods for variable subset selection can be divided into two main categories methods which work on the original p variables xi, X2,. .., Xp, direct variable subset selection, where the best binary vector I is evaluated by considering the relationships among the x, variables and a response variable y, i.e. 

Using the information contained in the binary vector I collecting the selected variables, it is possible to calculate the regression coefficients by ordinary least squares regression,... 

Soltzberg Wilkins introduced a number of simplifications in order to obtain a binary code. Only the zero crossing of the I s) curve, i.e. the values at which I(s) = 0 in the range 1 - 31 A-i are considered. The s range is then divided into 100 equal intervals, each described by a binary variable equal to 1 if the interval contains a zero crossing, 0 otherwise. Thus, a 3D-MoRSE code consisting of a 100-dimensional binary vector is obtained. 

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