Mode Poset Probability Polytopes

A mode of a probability distribution is an elementary event that has more probability mass than each of its direct neighbors, with respect to some vicinity structure on the set of elementary events. The mode inequalities cut out a polytope from the simplex of probability distributions. Related to this is the concept of strong modes. A strong mode of a probability distribution is an elementary event that has more probability mass than all its direct neighbors together. The set of probability distributions with a given set of strong modes is again a polytope. We study the vertices, the facets, and the volume of such polytopes depending on the sets of (strong) modes and the vicinity structures.

Reliability Analysis of Ventilation System Based on Fuzzy Fault Tree

The fuzzy Fault Tree Analysis (FTA) of mine ventilation system is set up based on thorough composition of the system, with triangular fuzzy number being used as probability of elementary event and “mine ventilation system fault” being deemed as top event. In this paper, the reliability of FTA has been analyzed and applied to a mine in Gansu Province. The result shows that the minimum cut set of fault tree is 549 and the main reason why it has a huge number of minimum cut set is Level 1，Event 7，“Monitoring feedback system failure”. The reliability of top event and Level 1 event is low, and fuzzy failure probability of top event is (0.009, 0.014, 0.009), the maximum of which is 2.3% of it. The degree of fuzzy importance of elementary event is the highest in Level 1，Event 7. The maximum of fuzzy importance is 0.0843 by the normalization and the rest vary from 0.0050 to 0.0100 mostly.

Topological Solitons in Non-Degenerate One-Component Chains: Part I — Analytical Study

For the first time, the possibility of existence of topological solitons in one-component chain with a non-degenerate potential of gradient type is proven. The existence and stability of the solitons is ensured by competing piecewise-parabolic nearest-neighbor and parabolic second-nearest-neighbor interactions. The solitons are shown to move at a unique velocity. Soliton propagation may constitute an elementary event of structural transformations in the chain.

The Fine Temporal Structure of The EV Lacertae Flare on February 6, 1986 at the C IV (λl550 Å) Resonance Line II. Interpretation

Flare optical continuum with duration above one minute is emitted by a gas condensation with T ≈ 104 K, which may form in a gas-dynamic process. The light carve slope implies that this flare consists of several elementary events. The features of the initial C IV line burst during one elementary event are determined by numerical simulation. The comparison of theoretical intensity and duration of the C IV burst with the observations of the EV Lac flare on February 6, 1986 shows that the observed elementary event in the C IV line is consistent with the formation of a radiative shock wave with an explosive evaporation of the chromosphere. The possibility of the appearance of C IV doublet emission, accompanying the entire process, is also discussed.