If moreover P(Xn+1 = j|Xn = i) = pij is independent of n, then X is said to be a timehomogeneous Markov chain. We will focus on such chains during the course. Terminology. * The possible values taken by the random variables Xn are called the states of the chain. S is called the state space. * The chain is said to be finite-state if the set S is finite (S = {0, . . . , N}, typically). * P = (pij...

Using state space technique and GF(2) theory, a simulation model for external exclusive NOR type LFSR structures is developed. Through this tool a systematic procedure is devised for computing pseudo-random binary sequences from such structures. Keywords—LFSR, external exclusive NOR type, recursive binary sequence, initial state next state, state transition matrix.

Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the discrete state space is large or uncountable. Classical methods such as matrix exponentiation are infeasible for large or countably infinite state spaces, an...

Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the discrete state space is large or uncountable. Classical methods such as matrix exponentiation are infeasible for large or countably infinite state spaces, an...

MOTIVATION Probabilistic Boolean networks (PBNs) have been proposed to model genetic regulatory interactions. The steady-state probability distribution of a PBN gives important information about the captured genetic network. The computation of the steady-state probability distribution usually includes construction of the transition probability matrix and computation of the steady-state probabil...

Final state-selected spectra in unimolecular decomposition are obtained by a random matrix version of Feshbach’s optical model. The number of final states which are independently coupled to the molecular quasibound states is identified with the number of states at the dividing surface of transition state theory ~TST!. The coupling of the transition state to the molecular complex is modeled via ...

All traditional data compression techniques, such as Huffman coding, the Lempel-Ziv algorithm, run-length limited coding, Tunstall coding and arithmetic coding are highly susceptible to residual channel errors and noise. We have recently proposed the use of parallel concatenated codes and iterative decoding for fixed-length to fixed-length source coding, i.e., turbo coding for data compression ...