We saw in the last lecture how Markov chains can be useful algorithmically. If we have a probability distribution we’d like to generate random samples from, we design an ergodic Markov chain whose unique stationary distribution is the desired distribution. We then run the chain (i.e., start at an arbitrary state and evolve according to the transition matrix), until the process is at (or close t...

In this paper, we investigate a sequential test for binary hypothesis testing for stationary, first-order Markov dependent observations in steady state. Wald’s first and second lemmas are generalized. For a Markov chain with symmetric transition probability matrix the average sample number required by the test to decide a hypothesis is derived. Numerical analysis shows that accounting for a pos...

Type II topoisomerases are enzymes that change the topology of DNA by performing strand-passage. In particular, they unknot knotted DNA very efficiently. Motivated by this experimental observation, we investigate transition probabilities between knots. We use the BFACF algorithm to generate ensembles of polygons in Z(3) of fixed knot type. We introduce a novel strand-passage algorithm which gen...

Probabilistic Boolean Networks (PBNs) are useful models for modeling genetic regulatory networks. In this paper, we propose efficient algorithms for constructing a sparse probabilistic Boolean network when its transition probability matrix and a set of possible Boolean networks are given. This is an interesting inverse problem in network inference and it is important in the sense that most micr...

In this issue of NDT, Flessner in a commentary [1] argues that the three-pore model (TPM) of peritoneal transport, although mathematically a powerful predictor of solute transport and ultrafiltration (UF) in peritoneal dialysis (PD), may be too simple as a tool for understanding the physiology of transperitoneal exchange. Flessner then disregards the fact that the TPM can be modified in a very ...

The emerging feature of network slicing in future Fifth Generation (5G) mobile communication networks calls for efficient inter-slice resource management technologies. Multiple recent studies have been focusing on the mechanism of requestbased slice admission control, which functions in a state-machinealike approach. This paper proposes a general state model for synchronous request-based inter-...

Let (St)t be a k-state Markov chain with ergodic transition probability matrix (t.p.m.) Γ = (γi,j)i,j=1,...,k having the stationary distribution π = (π1, . . . , πk). In the following we always assume πj > 0 for j = 1, . . . , k. For a (disjoint) partition G = {G1, . . . , Gr} of the state space (into non-empty sets), we let G(j) be the function which maps a state j ∈ {1, . . . , k} onto its gr...

This paper contains an analytical method for the failure analysis of a matrix configuration of switches in series and parallel. The concept is to use lower voltage and current rating switches in series and parallel to attain the higher ratings needed in power engineering applications. The analysis is based on probability state transition. A discussion of voltage and current snubbing is given. R...

We discuss five attack strategies against BitLocker, which target the way BitLocker is using the TPM sealing mechanism. BitLocker is a disk encryption feature included in some versions of Microsoft Windows. It represents a state-of-the-art design, enhanced with TPM support for improved security. We show that, under certain assumptions, a dedicated attacker can circumvent the protection and brea...

Consider a Markov chain X0, X1, X2 . . . , with transition probability matrix P and set of states S. A state j is said to be accessible from i if for some n ≥ 0 the probability of going from i to j in n steps is positive, that is, p ij ≥ 0. We write i → j to represent this. If i → j and j → i, we say that i and j communicate and denote it by i↔ j. The definition of communicating states introduc...