We consider approximate counting of colorings of an n-vertex graph using rapidly mixing Markov chains. It has been shown by Jerrum and by Salas and Sokal that a simple random walk on graph colorings would mix rapidly, provided the number of colors k exceeded the maximum degree ∆ of the graph by a factor of at least 2. We prove that this is not a necessary condition for rapid mixing by consideri...

Markov Chain Monte Carlo algorithms are often used to sample combinatorial structures such as matchings and independent sets in graphs. A Markov chain is defined whose state space includes the desired sample space, and which has an appropriate stationary distribution. By simulating the chain for a sufficiently large number of steps, we can sample from a distribution arbitrarily close to the sta...

A study of the equilibrium and disequilibrium thermochemistry of the recently discovered carbon monoxide on Jupiter suggests that the presence of this gas in the visible atmosphere is a direct result of very rapid upward mixing from levels in the deep atmosphere where the temperature is about 1100 degrees K and where carbon monoxide is thermodynamically much more stable. As a consequence the ob...

We study the computational complexity of Markov chain Monte Carlo (MCMC) methods for high-dimensional Bayesian linear regression under sparsity constraints. We first show that a Bayesian approach can achieve variable-selection consistency under relatively mild conditions on the design matrix. We then demonstrate that the statistical criterion of posterior concentration need not imply the comput...

We give a systematic development of the application of matrix norms to rapid mixing in spin systems. We show that rapid mixing of both random update Glauber dynamics and systematic scan Glauber dynamics occurs if any matrix norm of the associated dependency matrix is less than 1. We give improved analysis for the case in which the diagonal of the dependency matrix is 0 (as in heat bath dynamics...

This paper analyzes the effect of mixing on nucleation of protein crystals. The mixing of protein and precipitant was controlled by changing the flow rate in a plug-based microfluidic system. The nucleation rate inversely depended on the flow rate, and flow rate could be used to control nucleation. For example, at higher supersaturations, precipitation happened at low flow rates while large cry...

Evolving ecosystems often are dominated by spatially local dynamics, but many also include long-range transport that mixes spatially separated groups. The existence of such mixing may be of critical importance since research shows spatial separation may be responsible for long-term stability of predator-prey systems. Complete mixing results in rapid global extinction, while spatial systems achi...

Lipid nanoparticles (LNP) are the leading systems for in vivo delivery of small interfering RNA (siRNA) for therapeutic applications. Formulation of LNP siRNA systems requires rapid mixing of solutions containing cationic lipid with solutions containing siRNA. Current formulation procedures employ macroscopic mixing processes to produce systems 70-nm diameter or larger that have variable siRNA ...