Convergence Rates for a Hierarchical Gibbs Sampler

Analysis and Stochastic

Metastability on the hierarchical lattice

Analysis and Stochastic

Metastability for Glauber dynamics on random graphs

Analysis and Stochastic

Reduced Spontaneous Eye Blink Rates in Recreational Cocaine Users: Evidence for Dopaminergic Hypoactivity

Chronic use of cocaine is associated with a reduced density of dopaminergic D2 receptors in the striatum, with negative consequences for cognitive control processes. Increasing evidence suggests that cognitive control is also affected in recreational cocaine consumers. This study aimed at linking these observations to dopaminergic malfunction by studying the spontaneous eyeblink rate (EBR), a marker of striatal dopaminergic functioning, in adult recreational users and a cocaine-free sample that was matched on age, race, gender, and personality traits. Correlation analyses show that EBR is significantly reduced in recreational users compared to cocaine-free controls, suggesting that cocaine use induces hypoactivity in the subcortical dopamine system

Metastability on the Hierarchical Lattice

Analysis and Stochastic

Metastability for Glauber dynamics on random graphs

In this paper, we study metastable behaviour at low temperature of Glauber spin-flip dynamics on random graphs. We fix a large number of vertices and randomly allocate edges according to the configuration model with a prescribed degree distribution. Each vertex carries a spin that can point either up or down. Each spin interacts with a positive magnetic field, while spins at vertices that are connected by edges also interact with each other via a ferromagnetic pair potential. We start from the configuration where all spins point down, and allow spins to flip up or down according to a Metropolis dynamics at positive temperature. We are interested in the time it takes the system to reach the configuration where all spins point up. In order to achieve this transition, the system needs to create a sufficiently large droplet of up-spins, called critical droplet, which triggers the crossover. In the limit as the temperature tends to zero, and subject to a certain key hypothesis implying metastable behaviour, the average crossover time follows the classical Arrhenius law, with an exponent and a prefactor that are controlled by the energy and the entropy of the critical droplet. The crossover time divided by its average is exponentially distributed. We study the scaling behaviour of the exponent as the number of vertices tends to infinity, deriving upper and lower bounds. We also identify a regime for the magnetic field and the pair potential in which the key hypothesis is satisfied. The critical droplets, representing the saddle points for the crossover, have a size that is of the order of the number of vertices. This is because the random graphs generated by the configuration model are expander graphs

Metastability for Glauber dynamics on random graphs

\u3cp\u3eIn this paper, we study metastable behaviour at low temperature of Glauber spin-flip dynamics on random graphs. We fix a large number of vertices and randomly allocate edges according to the configuration model with a prescribed degree distribution. Each vertex carries a spin that can point either up or down. Each spin interacts with a positive magnetic field, while spins at vertices that are connected by edges also interact with each other via a ferromagnetic pair potential. We start from the configuration where all spins point down, and allow spins to flip up or down according to a Metropolis dynamics at positive temperature. We are interested in the time it takes the system to reach the configuration where all spins point up. In order to achieve this transition, the system needs to create a sufficiently large droplet of up-spins, called critical droplet, which triggers the crossover. In the limit as the temperature tends to zero, and subject to a certain key hypothesis implying metastable behaviour, the average crossover time follows the classical Arrhenius law, with an exponent and a prefactor that are controlled by the energy and the entropy of the critical droplet. The crossover time divided by its average is exponentially distributed. We study the scaling behaviour of the exponent as the number of vertices tends to infinity, deriving upper and lower bounds. We also identify a regime for the magnetic field and the pair potential in which the key hypothesis is satisfied. The critical droplets, representing the saddle points for the crossover, have a size that is of the order of the number of vertices. This is because the random graphs generated by the configuration model are expander graphs.\u3c/p\u3