State space models, also termed dynamic models, relate observations yt; t = 1; 2; :::, on a response variable Y to unobserved "states" or "parameters" t, t=1,2,..., by an observation model for yt given t. The states are assumed to follow a Markovian transition model. Gaussian linear state space models are de ned by a linear observation model and a linear Markovian transition equation yt = z 0 t...

We construct a strongly minimal set which is not a finite cover of one with DMP. We also prove that for a strongly minimal theory T generic automorphisms exist iff T has DMP, thus proving a conjecture of Kikyo and

Reliability design of fault-tolerant computer-based systems with version-structural redundancy and multiply software updates involves solving number of issues. This paper outlines an availability model of the computer-based systems which shows the algorithm for reliability behavior. For various configurations of the computer-based systems, the use of the proposed model and problem-oriented soft...

Stochastic thermodynamics and the associated fluctuation relations provide the means to extend the fundamental laws of thermodynamics to small scales and systems out of equilibrium. The fluctuating thermodynamic variables are usually treated in the context of either isolated Hamiltonian evolution, or Markovian dynamics in open systems. However, there is no reason a priori why the Markovian appr...

We characterize the dynamical behavior of continuous-time, Markovian quantum systems with respect to a subsystem of interest. Markovian dynamics accurately describes a wide class of open quantum systems of relevance to quantum information processing, subsystem encodings offering a general pathway for faithfully representing quantum information. We provide explicit linear-algebraic characterizat...

Since a real epidemic process is not necessarily Markovian, the epidemic threshold obtained under the Markovian assumption may be not realistic. To understand general non-Markovian epidemic processes on networks, we study the Weibullian SIS process in which the infection process is a renewal process with a Weibull time distribution. We find that, if the infection rate exceeds 1/ ln(λ1 + 1), whe...

Why some strains of a species exhibit a certain phenotype (e.g. drug resistant) but not the other strains of the same species is a critical question to answer. Studying the metabolism of the two groups of strains may discover the corresponding pathways that are conserved in the first group but not in the second group. However, only a few tools provide functions to compare two groups of metaboli...

Since a real epidemic process is not necessarily Markovian, the epidemic threshold obtained under the Markovian assumption may be not realistic. To understand general non-Markovian epidemic processes on networks, we study the Weibullian susceptible-infected-susceptible (SIS) process in which the infection process is a renewal process with a Weibull time distribution. We find that, if the infect...

We introduce Markovian cocycle perturbations of the groups of transformations associated with the classical and quantum stochastic processes with stationary increments, which are characterized by a localization of the perturbation to the algebra of events of the past. It is namely the definition one needs because the Markovian perturbations of the Kolmogorov flows associated with the classical ...

The Mori-Zwanzig formalism for coarse-graining a complex dynamical system typically introduces memory effects. The Markovian assumption of delta-correlated fluctuating forces is often employed to simplify the formulation of coarse-grained (CG) models and numerical implementations. However, when the time scales of a system are not clearly separated, the memory effects become strong and the Marko...