Eigenvalue Bounds on Restrictions of Reversible Nearly Uncoupled Markov Chains

AbstractIn this paper we analyze decompositions of reversible nearly uncoupled Markov chains into rapidly mixing subchains. We state upper bounds on the 2nd eigenvalue for restriction and stochastic complementation chains of reversible Markov chains, as well as a relation between them. We illustrate the obtained bounds analytically for bunkbed graphs, and furthermore apply them to restricted Markov chains that arise when analyzing conformation dynamics of a small biomolecule

Sequential Change Point Detection in Molecular Dynamics Trajectories

Motivated from a molecular dynamics context we propose a sequential change point detection algorithm for vector-valued autoregressive models based on Bayesian model selection. The algorithm does not rely on any sampling procedure or assumptions underlying the dynamics of the transitions and is designed to cope with high-dimensional data. We show the applicability of the algorithm on a time series obtained from numerical simulation of a penta-peptide molecule

Conformation Dynamics

This article surveys the present state of the transfer operator approach to the effective dynamics of metastable dynamical systems and the variety of algorithms associated with it

Identification of Biomolecular Conformations from Incomplete Torsion Angle Observations by Hidden Markov Models

We present a novel method for the identification of the most important conformations of a biomolecular system from molecular dynamics or Metropolis Monte Carlo time series by means of Hidden Markov Models (HMMs). We show that identification is possible based on the observation sequences of some essential torsion or backbone angles. In particular, the method still provides good results even if the conformations do have a strong overlap in these angles. To apply HMMs to angular data, we use von Mises output distributions. The performance of the resulting method is illustrated by numerical tests and by application to a hybrid Monte Carlo time series of trialanine and to MD simulation results of a DNA-oligomer

Rare events, escape rates and quasistationarity: some exact formulae

We present a common framework to study decay and exchanges rates in a wide class of dynamical systems. Several applications, ranging form the metric theory of continuons fractions and the Shannon capacity of contrained systems to the decay rate of metastable states, are given

Hemophagocytic syndrome caused by primary herpes simplex virus 1 infection: report of a first case

Introduction: Hemophagocytic syndrome represents a severe hyperinflammatory condition by activated macrophages. Leading viral triggering agents are Epstein-Barr virus (EBV), cytomegalovirus (CMV), and adenovirus. Materials and methods: We present a patient with Wegener's granulomatosis on azathioprine and prednisone medication, who developed a life-threatening hemophagocytic syndrome. Positive plasma polymerase chain reaction (PCR) with negative serology revealed a primary, disseminated infection with herpes simplex virus-1 as the triggering pathogen. After treatment with acyclovir, high-dose steroids, immunoglobulins, and etoposide, the patient recovered. Conclusion: Early diagnosis of potentially underlying infections of hemophagocytic syndrome influences the therapeutic approach. It is important to consider a variety of infectious agents, particularly in immunosuppressed individuals. The reported case emphasizes the importance of screening for herpes simplex virus