Sentence examples for for which graphs from inspiring English sources

With both Leavitt's Theorem (part 2 of Theorem 1) and The Simplicity Theorem for graph C ∗ -algebras (Theorem 4) in mind, the author and Aranda Pino focused their initial investigation on an internal, multiplicative question about the algebras L K ( E ) : for which graphs E and fields K is L K ( E ) simple?

You can't throw a copy of Mathematica these days (and I plan to) without hitting somebody working on a topic for which graph theory plays a central role.

These models need not be conditioned on a fixed number of vertices, as is often the case in the literature, and can be used for problems in which graphs have attributes associated with their vertices and edges.

We believe that its applicability range covers different fields of computational biology and will grow in the future, as increasingly more data for which bipartite graphs provide a natural representation become available.

A graphical model is a probabilistic model for which a graph denotes the conditional independence structure between random variables.

For example, 'allothreonine' [rel-(2xtitR,3R -2-amino-3-hydroxybutanoic 2xtitR,3R -2-amino-3-hydroxybutanoic 2xtitR,3R -2-amino-3-hydroxybutanoic 2xtitR,3R -2-amino-3-hydroxybutanoic 2xtitR,3R -2-amino-3-hydroxybutanoicch acidaph cannot currently be drawn.

Xuan and Murphy [ 12] introduced an iterative procedure based on a similar modelling ansatz, which switches between a convex optimization approach for determining a suitable candidate graph structure and a dynamic programming algorithm for calculating the segmentation of the time into distinct phases, i.e. the sets of successive time-points for which the graph structure remains unchanged.

Remarkably, E⊆ E V| W) holds for every subset E of E V) for which the graph (V, E) is connected and minimizes the sum | E | : = ∑ e ∈ E | e |, that is, for the edge set of any minimum spanning tree T= X, E) for W.

In other words, if x01 and x02 are two values for which the graph crosses the vertical axis at point 0, two average-risk categories will be considered, as long as x 0 1 inf, x 0 1 sup and x 0 2 inf, x 0 2 sup do not overlap.

Then the task of identifying coherent gene subsets is reduced to the task of finding highly connected subgraphs from the graph, for which different existing graph-cut algorithms can be employed.

We take two problem domains for which the search graphs are directed acyclic graphs of similar structure, and determine the average case performance of the best-first search algorithm A∗ on these graphs.