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However, time-varying graph assumption does not affect the existence of steady state.
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This has already been investigated intensively by [ 31] who showed that in certain situations (sparse graphs, faithfulness assumption etc).
Many of these works investigate the b-chromatic number of graphs under assumptions that involve the existence of large cycles.
The final hypothesis is extracted from this graph under the assumption that the wiring was carried out minimizing material costs.
Note that the exponent q > 1 in part C is governed by the fourth moment of the eigenvector components of the graph Laplacian (see assumption A4a).
In return, the acyclicity of the causal graph is an assumption which might not hold true for biological networks.
Not only does the choice of scale-free background graphs more closely match the topology of real biological graphs; it also poses an additional challenge for the new algorithm, since such graphs break with the assumption of a random graph prior distribution for G.
We also show that though our multi-regularized sparse reconstruction technique improves over conventional sparse recovery, it still suffers from the graph-signal smoothness assumption it implicitly considers.
In several instances we impose on our random graph ensemble, as assumptions, properties that are known to hold for broad classes of random matrices, such as the Wigner ensemble [19, 20].
However, the existence of "cycle" in Tanner Graph invalidates this independence assumption, thus degrades the BER performance of BP algorithm.
Based on this assumption, a graph representation is constructed in order to reflect the metabolic variability with respect to by-production within a pool of genetically different cells [ 32].
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