In the present paper we propose to describe gene networks in biological systems using probabilistic algorithms. We describe gene duplication in the process of biological evolution using introduction of the replica procedure for probabilistic algorithms. We construct the examples of such a replica procedure for hidden Markov models. We introduce the family of hidden Markov models where the set o...

We revisit some results obtained recently in min-plus algebra following the ideas of statistical mechanics. Computation of geodesics in a graph can be done by min-plus matrix products. A min-plus matrix is seen as a kind of finite states mechanical system. The energy of this system is the eigenvalue of its min-plus matrix. The graph interpretation of the eigenvalue may be seen as a kind of Mari...

In this paper, a novel Markov system dynamics (MSD) simulation frame work for the availability modeling of a repairable system is developed. The proposed method combines the Markov approach with system dynamics simulation approach for availability modeling. This approach will have the advantages of both Markov as well as System dynamics methodologies. Initially, the proposed framework is illust...

It is easily verified that the quantum Markov property is equivalent to the strong additivity of von Neumann entropy for graded quantum systems. However, the structure of Markov states for graded systems is different from that for tensor-product systems which have trivial grading. For three-composed graded systems we have U(1)-gauge invariant Markov states whose restriction to the marginal pair...

Mostmodels of agents andmulti-agent systems include information about possible states of the system (that defines relations between states and and their external characteristics), and information about relationships between states. Qualitativemodels of this kind assign no numerical measures to these relationships. At the same time, quantitative models assume that the relationships are measurabl...

The application of parametric reliability analysis methods for repairable units, such as Power law process, is quite clear and straightforward for a single repairable unit. However, in practice, the analyst needs to know the reliability characteristics of units at a fleet level. The application of parametric reliability analysis methods at the fleet level, even if it is limited in scope, is qui...

Optimal operation and maintenance of engineering systems heavily rely on the accurate prediction of their failures. Most engineering systems, especially mechanical systems, are susceptible to failure interactions. These failure interactions can be estimated for repairable engineering systems when determining optimal maintenance strategies for these systems. An extended Split System Approach is ...