We used a database of 4139 Taiwanese HCC patients to take a new approach (Network Phenotyping Strategy) to HCC subset identification. Individual parameters for liver function tests, complete blood count, portal vein thrombosis, AFP levels and clinical demographics of age, gender, hepatitis or alcohol consumption, were considered within the whole context of complete relationships, being networke...

in this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite hamiltonian group. the coverings with three proper subgroups and the principal series of such a group are also counted. finally, we give a complete description of the lattice of characteristic subgroups of a finite h...

Figure 2. Results of Student–Newman–Keuls (SNK) post hoc tests for variables : TOTAL, FUNCTION, EMOTION. Data was grouped into homogeneous subgroups that differ from each other with P< 0.05. Within subgroups no significant differences could be found. CCH, chronic cluster headache; ECHa, episodic cluster headache in the active phase; ECHi, episodic cluster headache outside the active period; MIG...

Let S = Sym(Ω) be the group of all permutations of a countably infinite set Ω, and for subgroups G1, G2 6 S let us write G1 ≈ G2 if there exists a finite set U ⊆ S such that 〈G1 ∪U 〉 = 〈G2 ∪U 〉. It is shown that the subgroups closed in the function topology on S lie in precisely four equivalence classes under this relation. Which of these classes a closed subgroup G belongs to depends on which ...

Let S = Sym(Ω) be the group of all permutations of a countably infinite set Ω, and for subgroups G1, G2 6 S let us write G1 ≈ G2 if there exists a finite set U ⊆ S such that 〈G1 ∪ U 〉 = 〈G2 ∪ U 〉. It is shown that the subgroups closed in the function topology on S lie in precisely four equivalence classes under this relation. Which of these classes a closed subgroup G belongs to depends on whic...

Parabolic subgroups WI of Coxeter systems (W,S), as well as their ordinary and double quotients W/WI and WI\W/WJ , appear in many contexts in combinatorics and Lie theory, including the geometry and topology of generalized flag varieties and the symmetry groups of regular polytopes. The set of ordinary cosets wWI , for I ⊆ S, forms the Coxeter complex of W , and is well-studied. In this article...

In this article, we study symmetric designs D with parameters ( v , k λ ) admitting a flag-transitive and point-primitive automorphism group G whose socle X is finite simple exceptional of Lie type. conclusion, the design q 6 − 1 / 5 4 associated to generalised hexagon H or its dual = 2 point-stabiliser ˆ [ ] : L orthogonal 351 126 45 378 117 36 respectively for ϵ + 3 S . Our analysis depends h...