Multiplicative random walk Metropolis-Hastings on the real line

In this article we propose multiplication based random walk Metropolis Hastings (MH) algorithm on the real line. We call it the random dive MH (RDMH) algorithm. This algorithm, even if simple to apply, was not studied earlier in Markov chain Monte Carlo literature. The associated kernel is shown to have standard properties like irreducibility, aperiodicity and Harris recurrence under some mild assumptions. These ensure basic convergence (ergodicity) of the kernel. Further the kernel is shown to be geometric ergodic for a large class of target densities on $\mathbb{R}$. This class even contains realistic target densities for which random walk or Langevin MH are not geometrically ergodic. Three simulation studies are given to demonstrate the mixing property and superiority of RDMH to standard MH algorithms on real line. A share-price return data is also analyzed and the results are compared with those available in the literature

Quantum energy teleportation in a quantum Hall system

We propose an experimental method for a quantum protocol termed quantum energy teleportation (QET), which allows energy transportation to a remote location without physical carriers. Using a quantum Hall system as a realistic model, we discuss the physical significance of QET and estimate the order of energy gain using reasonable experimental parameters

Disrupted functional brain network organization in patients with obstructive sleep apnea.

IntroductionObstructive sleep apnea (OSA) subjects show impaired autonomic, affective, executive, sensorimotor, and cognitive functions. Brain injury in OSA subjects appears in multiple sites regulating these functions, but the integrity of functional networks within the regulatory sites remains unclear. Our aim was to examine the functional interactions and the complex network organization of these interactions across the whole brain in OSA, using regional functional connectivity (FC) and brain network topological properties.MethodsWe collected resting-state functional magnetic resonance imaging (MRI) data, using a 3.0-Tesla MRI scanner, from 69 newly diagnosed, treatment-naïve, moderate-to-severe OSA (age, 48.3 ± 9.2 years; body mass index, 31 ± 6.2 kg/m(2); apnea-hypopnea index (AHI), 35.6 ± 23.3 events/h) and 82 control subjects (47.6 ± 9.1 years; body mass index, 25.1 ± 3.5 kg/m(2)). Data were analyzed to examine FC in OSA over controls as interregional correlations and brain network topological properties.ResultsObstructive sleep apnea subjects showed significantly altered FC in the cerebellar, frontal, parietal, temporal, occipital, limbic, and basal ganglia regions (FDR, P < 0.05). Entire functional brain networks in OSA subjects showed significantly less efficient integration, and their regional topological properties of functional integration and specialization characteristics also showed declined trends in areas showing altered FC, an outcome which would interfere with brain network organization (P < 0.05; 10,000 permutations). Brain sites with abnormal topological properties in OSA showed significant relationships with AHI scores.ConclusionsOur findings suggest that the dysfunction extends to resting conditions, and the altered FC and impaired network organization may underlie the impaired responses in autonomic, cognitive, and sensorimotor functions. The outcomes likely result from the prominent structural changes in both axons and nuclear structures, which occur in the condition

Ab initio theory of helix-coil phase transition

In this paper we suggest a theoretical method based on the statistical mechanics for treating the alpha-helix-random coil transition in alanine polypeptides. We consider this process as a first-order phase transition and develop a theory which is free of model parameters and is based solely on fundamental physical principles. It describes essential thermodynamical properties of the system such as heat capacity, the phase transition temperature and others from the analysis of the polypeptide potential energy surface calculated as a function of two dihedral angles, responsible for the polypeptide twisting. The suggested theory is general and with some modification can be applied for the description of phase transitions in other complex molecular systems (e.g. proteins, DNA, nanotubes, atomic clusters, fullerenes).Comment: 24 pages, 3 figure

Noisy Monte Carlo: Convergence of Markov chains with approximate transition kernels

Monte Carlo algorithms often aim to draw from a distribution $\pi$ by simulating a Markov chain with transition kernel $P$ such that $\pi$ is invariant under $P$. However, there are many situations for which it is impractical or impossible to draw from the transition kernel $P$. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace $P$ by an approximation $\hat{P}$. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how 'close' the chain given by the transition kernel $\hat{P}$ is to the chain given by $P$. We apply these results to several examples from spatial statistics and network analysis.Comment: This version: results extended to non-uniformly ergodic Markov chain