Convergence of alternating Markov chains

Suppose we have two Markov chains defined on the same state space. What happens if we alternate them? If they both converge to the same stationary distribution, will the chain obtained by alternating them also converge? Consideration of these questions is motivated by the possible use of two different updating schemes for MCMC estimation, when much faster convergence can be achieved by alternating both schemes than by using either singly

On Congruence Lattices of Nilsemigroups

We prove that the congruence lattice of a nilsemigroup is modular if and only if the width of the semigroup, as a poset, is at most two, and distributive if and only if its width is one. In the latter case, such semigroups therefore coincide with the nil Δ \u3eΔ Δ -semigroups. It is further shown that if a finitely generated nilsemigroup has modular congruence lattice, then the semigroup is finite

Thermal and Developmental Ecology of Pupfish, Cyprinodon

Pupfish from the genus Cyprinodon are among the most endangered groups of fishes on the planet, with nearly 40% of species being threatened with extinction. These pupfishes are often assumed to be the most temperature tolerant of all fish, coping with temperatures as low as 0 °C and as high as 44 °C. However, conflicting data exist and certain measures of thermal tolerance are not markedly higher in pupfish compared to common game fish. Pupfish egg production and growth has been known to be hampered at temperatures well below what they apparently experience in nature. I addressed why eggs fail to hatch at high temperatures using reciprocal transplant experiments and measurements of oxygen consumption over the course of development. Parental thermal history appears to influence successful hatching more than egg incubation temperature. Eggs which are reared at the ecologically relevant temperature of 33 °C exhibit altered and unusual oxygen consumption patterns compared to eggs incubated at a lower temperature. I employed a capture-mark-recapture study and field experiments in a dynamic and hypervariable creek environment (Salt Creek, CA) to determine whether individual pupfish which experience temperatures as high as 40 °C survive long-term. Pupfish in Salt Creek appear to colonize warm environments during the spring when conditions can be favorable for growth and reproduction; however, these fish risk death by desiccation and heat exposure if they remain in warm environments during the summer months