Conjecture. Based on our empirical results presented in Figures 6 and 7, we are able to conjecture a more precise behavior of the free energy for the two optimization problems discussed in this paper. We shall introduce a correction coefficient α whose value is determines experimentally in the sequel.
Conjecture. Does critical edges have the same rate of increase? We conjecture that ρ = + S |P∗(ZV )|−1 |S|−1 for all S ∈ S crit V (Z ). APPENDIX C UNIQUENESS OF THE OPTIMAL PARTITION To check whether there is a unique optimal partition in strongly polynomial time, we can make use of the zero- xxxxxxxxx-submodular function g defined in (B.3) based on the fundamental partition P ∗(ZV ) and the MMI. In essense of (B.7), we only need to check whether the zero sets | | Z(g) in (B.5) consists only of the singletons. This can computed in O(|V |2) submodular function minimizations, namely minB⊇{i,j} g(B) for all pair (i, j) of distinct elements. P ∗(ZV ) and I(ZV ) can also be computed in O( V 2) submod- ular function minimizations [23].
Conjecture. (P.Shumyatskii, [KN, 17.125]). In any finite group G, there is a pair a, b of conjugate elements such that π(G) = π(⟨a, b⟩). In 2013 X. Xxxxxxx, X. Xxxxxx and X.Xxxxxxxxxxx proved, in any finite group G, there is a pair a, b (not necessarily conjugate) elements such that π(G) = π(⟨a, b⟩). The Shumyatskii conjecture is equivalent to the following Conjecture. Every prime spectrum minimal group is generated by a pair of conjugate elements. Moreover, a minimal counterexample to one of these conjectures will also be a minimal counterexample to the other one. Conjecture. (P.Shumyatskii, [KN, 17.125]). In any finite group G, there is a pair a, b of conjugate elements such that π(G) = π(⟨a, b⟩). In 2013 X. Xxxxxxx, X. Xxxxxx and X.Xxxxxxxxxxx proved, in any finite group G, there is a pair a, b (not necessarily conjugate) elements such that π(G) = π(⟨a, b⟩). The Shumyatskii conjecture is equivalent to the following Conjecture. Every prime spectrum minimal group is generated by a pair of conjugate elements. Moreover, a minimal counterexample to one of these conjectures will also be a minimal counterexample to the other one.
Conjecture. Implementation of the SDDS’s provisions may further reduce a nation’s susceptibility to contagion relative to the effect of subscription. This statement is merely a conjecture since past research and theory does not provide enough evidence to suggest that SDDS subscription and implementation have independent effects. However, nations must implement significant reforms to improve their data dissemination practices in order to meet SDDS specifications. While SDDS subscription inevitably leads to implementation, the pace of a newly subscribed nation towards adopting the Standard is unclear. However, once implementation has occurred, remaining investor uncertainty about data quality should be reduced. Full compliance to the SDDS also increases the comparability of national data. Accordingly, investors can investigate the relationship between two nations more easily once nations have implemented the common data structure established by the SDDS. $+ The marginal benefit of implementation that is suggested by this conjecture also has an important policy implication. While SDDS subscription incurs minimal costs, implementation requires expenditure on institutional improvements. The null hypothesis is that implementation has no marginal benefit over subscription. If the null is confirmed, then policymakers’ cost-benefit analysis of implementation vis-à-vis contagion would be affected.
