Hiroshi Toda used the composition product and Toda brackets to label many of the elements of homotopy groups.
These are problems which can arise in Bayesian inference about any model having a set partition (such as a sample partition) as a parameter, when we try to compute marginal distributions for parameters which depend upon an arbitrary labelling of the elements of the partition.
Neurons in lower areas, like V1, label the individual contour elements of an object for grouping and neurons in higher areas could label the shape.
In contrast to the advice of the Mathematics community, they assume that the indeterminate isotopic labeling state is less than every determinate isotopic labeling state; and hence, the elements of Weichert et al.'s cumomer fraction vectors are out of order, making conversion between isotopomer and cumomer fraction vectors cumbersome in the general case.
Label the different elements of the diorama as if it were part of a natural history museum display.
The site also describes the elements of a "good" label and offers a glossary of terms used on labels.
Each position i in the vector of n integer values represents an individual (i S), and the integer value at position i is an arbitrary label α, indicating the element of the partition (a subset of S) to which that individual is assigned.
Although, both endomannosidase and Gls II could be detected in pre-Golgi intermediates by double immunogold labeling, they labeled different elements of the vesiculotubular clusters (Fig. 4e).
We label the vertices by basis elements, the existence of which is guaranteed by the Fundamental Theorem of Persistent Homology, and we draw an edge between two vertices to represent the maps (f_{i,j}), as explained in the main text.
Ethnographers travelling the African continent in the 18th century labelled all elements of sexual exchange that they encountered as prostitution [ 1, 2, 13] in stark opposition to the informants' own definitions and reasoning about their behaviour [ 1].
