Positive dilations of piecewise monotonic Markov maps

We provide an explicit formula which gives natural extensions of piecewise monotonic Markov maps defined on an interval of the real line. These maps are exact endomorphisms and define chaotic discrete dynamical systems.

The Effects of Anti-Hypertensive Drugs Evaluated Using Markov Modelling for Northern Ireland Chronic Kidney Disease Patients

The aim of this paper is to use Markov modelling to<br/>investigate survival for particular types of kidney patients<br/>in relation to their exposure to anti-hypertensive treatment<br/>drugs. In order to monitor kidney function an intuitive three<br/>point assessment is proposed through the collection of blood<br/>samples in relation to Chronic Kidney Disease for Northern<br/>Ireland patients. A five state Markov Model was devised<br/>using specific transition probabilities for males and<br/>females over all age groups. These transition probabilities<br/>were then adjusted appropriately using relative risk scores<br/>for the event death for different subgroups of patients. The<br/>model was built using TreeAge software package in order to<br/>explore the effects of anti-hypertensive drugs on patients.

Nonrigid Structure-From-Motion From 2-D Images Using Markov Chain Monte Carlo

In this paper we present a new method for simultaneously determining three dimensional (3-D) shape and motion of a non-rigid object from uncalibrated two dimensional (2- D) images without assuming the distribution characteristics. A non-rigid motion can be treated as a combination of a rigid rotation and a non-rigid deformation. To seek accurate recovery of deformable structures, we estimate the probability distribution function of the corresponding features through random sampling, incorporating an established probabilistic model. The fitting between the observation and the projection of the estimated 3-D structure will be evaluated using a Markov chain Monte Carlo based expectation maximisation algorithm. Applications of the proposed method to both synthetic and real image sequences are demonstrated with promising results.