The four data matrices were compared for congruence by using the partition-homogeneity test, with 100 replicates and significance threshold value P < 0.05 as implemented in PAUP [ 66].
For example, by using the network partition, Zhao et al. (2006) investigated the functional and evolutionary modularity of human metabolic networks from a topological perspective [ 3].
Then a factored HMM in which the hidden variable has values drawn from the Cartesian product = [ C1] × ··· × [ C m ], where [ C l ] is the set of equivalence classes of cluster C l generated by using the counting partition, satisfies Condition II.
Then a factorial HMM in which the hidden variable has values drawn from the Cartesian product = [ C1]× ··· ×[ C m ] × F, where F is some fixed state space, [ C l ] is the set of equivalence classes of cluster C l generated by using the counting partition, satisfies Condition II.
By using the space-partition technique, the prediction model in the study area can be extended into the surrounding areas with similar geology, geomorphology and land use conditions.
By using the nonuniform partitioning method iteratively, we can form several multiresolution histograms and the inequality chain in (3) can be rewritten as (5).
By using the delay partitioning technology, new criteria are derived which guarantee the filtering error system to be regular, causal, stochastically stable with a certain H∞ performance index.
By using the delay partitioning technique, a delay-dependent condition is established to guarantee the filtering error systems to be stochastically admissible and achieve a prescribed l2 l∞ performance index.
Therefore, the upper bounds of the time-varying delays τ 1 ( t ) and τ 2 ( t ) are τ 1 M and τ 2 M. From the analysis in Remark 2, we know that τ 1 M and τ 2 M can be divided into r and n 1 slices by using the delay-partition approach in Theorem 1.
By using the K-partition { Ω k }, we are able to explore potential KJ-strongly relevant feature-pairs whose R2-Correlation values are beyond a threshold ε, which is estimated by the following method (see Definition 6).
