In this paper, we describe a copy-and-paste method for constructing a class of infinite self-similar trees. A copy-paste tree is constructed by repeatedly attaching copies of a finite tree (called a generator) to certain designated attachment vertices. We show that each generator has an associated nonnegative matrix which can be used to determine a formula for the growth function of the copy-pa...

Stochastic Automata Networks (SANs) are widely used in modeling communication systems , manufacturing systems and computer systems. The solution of the steady state distribution cannot be obtained eeciently by direct methods such as LU decomposition due to the huge size of the generator matrix. EEcient numerical algorithm should make use of the tensor structure of SANs' generator matrix. The ge...

We present update formulas that allow us to express the stationary distribution of a continuous-time Markov process with denumerable state space having generator matrix Q∗ through a continuous-time Markov process with generator matrix Q. Under suitable stability conditions, numerical approximations can be derived from the update formulas, and we show that the algorithms converge at a geometric ...

The evolution of a continuous time Markov process with a finite number of states is usually calculated by the Master equation a linear differential equations with a singular generator matrix. We derive a general method for reducing the dimensionality of the Master equation by one by using the probability normalization constraint, thus obtaining a affine differential equation with a (non-singula...

We evaluate typical performance of irregular low-density generator-matrix (LDGM) codes, which is defined by sparse matrices with arbitrary irregular bit degree distribution and arbitrary check degree distribution, for lossy compression. We apply the replica method under one-step replica symmetry breaking (1RSB) ansatz to this problem. Typical performance of irregular LDGM codes for lossy compre...

˗ Polar codes are provably capacity achieving linear block codes. The generator matrix of these codes is specified by knowing the parameters of transmission channel, length and dimension of the used code. On the other hand, for the cryptosystems based on general decoding problem (i.e. code based cryptosystems), the generator matrix of the applied code should be properly hidden from the attacker...

We describe a fraction free version of the Matrix Berlekamp/Massey algorithm. The algorithm computes a minimal matrix generator of linearly generated square matrix sequences over an integral domain. The algorithm performs all operations in the integral domain, so all divisions performed are exact. For scalar sequences, the matrix algorithm specializes to a more efficient algorithm than the algo...