We derive a new master equation with and without Markovian approximation for the reduced density operator of a quantum system. We study a multiphoton Jaynes-Cummings model (JCM) with the dissipation at a finite temperature by making use of the new master equation under Markovian approximation. We present an exact solution of a non-resonant multiphoton JCM with the dissipstion by the use of the ...

Networks have become an important tool for infectious disease epidemiology. Most previous theoretical studies of transmission network models have either considered simple Markovian dynamics at the individual level, or have focused on the invasion threshold and final outcome of the epidemic. Here, we provide a general theory for early real-time behaviour of epidemics on large configuration model...

In this paper we consider existing and new representation transformation methods for non-Markovian generalizations of Markov chain driven stochastic models which intend transforming non-Markovian representations into Markovian ones and evaluate their efficiency through numerical experiments. One of the new features of the considered methods is the ability to obtain a Markovian representation of...

This paper examines the problem of designing a robust H∞ state-feedback controller for a class of nonlinear two-time scale systems with Markovian Jumps described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear two-time scale systems to have an H∞ performance are derived. The propo...

Recently, there has been an outburst of interest in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. The representational capabilities and internal representations of the models are not well understood. We concentrate on a generalization of the Self-Organizing Map (SOM) for processing sequential data – the Recursive SOM (RecSOM [1]). We a...

We propose a calculus MPA for reasoning about random behaviour through time. In contrast to classical calculi each atomic action is supposed to happen after a delay that is characterized by a certain exponentially distributed random variable. The operational semantics of the calculus deenes markovian labelled transition systems as a combination of classical action-oriented transition systems an...

Continuous quantum measurement is the backbone of various methods in quantum control, quantum metrology, and quantum information. Here, we present a generalized formulation of dispersive measurement of a complex quantum systems. We describe the complex system as an open quantum system that is strongly coupled to a non-Markovian environment, enabling the treatment of a broad variety of natural o...

This paper examines the problem of designing a robust H∞ state-feedback controller for a class of nonlinear two-time scale systems with Markovian Jumps described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear two-time scale systems to have an H∞ performance are derived. The propo...

This paper examines the problem of designing a robust H∞ state-feedback controller for a class of nonlinear two-time scale systems with Markovian Jumps described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear two-time scale systems to have an H∞ performance are derived. The propo...