Universal transformer Hawkes process with adaptive recursive iteration

Bi-iteration recursive instrumental variable subspace tracking and adaptive filtering

In this paper, we propose a class of fast sequential bi-iteration singular value (Bi-SVD) subspace tracking algorithms for adaptive eigendecomposition of the cross covariance matrix in the recursive instrumental variable (RIV) method of system identification. These algorithms can be used for RIV subspace processing of signals in unknown correlated Gaussian noise. Realizations with O(Nr) and O(N...

Two Recursive Generalizations of Iteration in Process Algebra

Modelling Dyadic Interaction with Hawkes Process

We apply Hawkes process to the analysis of dyadic interaction. Hawkes process is applicable to excitatory interactions, wherein the actions of each individual increase the probability of further actions in the near future. We consider the representation of Hawkes process both as a conditional intensity function and as a cluster Poisson process. The former treats the probability of an action in ...

Markov-modulated Hawkes process with stepwise decay

This paper proposes a new model—the Markov-modulated Hawkes process with stepwise decay (MMHPSD)—to investigate the variation in seismicity rate during a series of earthquake sequences including multiple main shocks. The MMHPSD is a self-exciting process which switches among different states, in each of which the process has distinguishable background seismicity and decay rates. Parameter estim...

Process Algebra with Iteration

We introduce iteration in process algebra by means of (the binary version of) Kleene's star operator: x y is the process that chooses between x and y, and upon termination of x has this choice again. It is proved that adding respectively interleaving, communication and abstraction operators increases expressivity up to the regular processes. However, if the distinction between (successful) term...