Flag complex

Perhaps the simplest situation of an abstract simplicial complex derived from combinatorial data is that of a flag complex. For a graph G and a subset S CV (G) of its vertices, we let G[corresponding induced graph. 

The abstract simplicial complex Cl (G) has various names it is called a flag complex in algebraic topology, while it is called a clique complex in combinatorics, prompted by the fact that clique is another term used in graph theory for complete subgraphs. 

Order complexes of posets are special cases of flag complexes, which appear in many contexts. Let us mention two of these here. 

For example, the minimal nonsimplices in flag complexes are all of cardinality 2 these are the pairs of vertices that are not connected by an edge. As a consequence, for the order complexes of posets, the minimal nonsimplices are pairs of noncomparable elements. 

Definition 9.16. Let G he an arbitrary graph. We define the prodsimplicial complex PF[G) as follows the graph G is taken to be the 1-dimensional skeleton of PF[G), and the higher-dimensional cells are taken to be all those products of simplices whose 1-dimensional skeleton is contained in the graph G. The complex PF G) is called prodsimplicial flag complex ofG. 

The prodsimplicial flag construction allows one to specify a prodsimplicial complex by a relatively compact set of data. The reader should note that while a simplicial complex is always also a prodsimplicial complex, a simplicial flag complex is usually not a prodsimplicial flag complex. An example of that is provided by a hollow square. 

Clearly, these complexes are prodsimplicial. It will be shown in Section 18.1.1 that complexes of morphisms Horn, —) are in fact prodsimplicial flag complexes. 

Proposition 18.1 comes in handy when we need to show that certain prod-simplicial complexes caimot be represented as Horn complexes, since it imposes the rather rigid restriction of being a prodsimplicial flag complex. 

Purification of FLAG-Tagged Eukaryotic Initiation Factor 2B Complexes, Subcomplexes, and Fragments from Saccharomyces cerevisiae... 

To reduce the complexity of the master planning model, not all products are considered in the SNP optimization run. The selection is made by flagging specific products as not relevant for SNP planning. SNP planning takes into account ... 

The only potential trouble is A = , which gives the return value of the status flag ER = 1. The return value of MR is the number of real roots. If NR = 3, the real roots will occupy the variables XI, X2 and X3. If MR = 1 then the only real root will occupy X, whereas you will find the real and imaginary parts of the conjugate complex pair in the variables XR and XI, respectively. 

The module assumes that the sample points are complex. The real components are placed in vector A, i.e., Re y0 is stored in A(l) an input. For a real valued sample (like a titration curve) vector should contain zeros. On output the transform is stored in the same vectors, i.e., Re aQ can be found in A(l) and Im a0 in B(l). The module computes the inverse transform (4.38) if the inverse transformation flag IN has a nonzero value. 

In the following sections, it is not the intention of the author to repeat the analysis of Kapral [285] in its detail or clear exposition, but rather to emphasise the simplicity and elegance of the description of a very complex situation, A few flags are raised to show the general trend of the analysis. It is hoped these will help the reader to dip into these articles. 

Modular construction of the ternary complex begins with the epitope tag immobilization of Gfly subunits on beads. Scheme A represents the display of > d 1, 4) subunits tethered to the bead, by an epitope tag (hexahistidine or FLAG), with soluble oq subunit completing the hetero-trimer assembly (G-beads). The typical G-bead sample preparation involves the initial capture and immobilization of the fly subunits, on beads bearing chelated nickel or biotinylated M2 anti-FLAG antibodies. The bead samples are then washed and resuspended in buffer. For the anti-FLAG... 

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