We introduce the concept of stochastic measure-valued solutions to complete Euler system describing motion a compressible inviscid fluid subject forcing, where nonlinear terms are described by defect measures. These weak in probabilistic sense (probability space is not given ‘priori’, but part solution) and analytical (derivatives only exist distributions). In particular, we show that existence...

The framework is presented of Bayesian image restoration for multi-valued images by means of the multi-state classical spin systems. Hyperparameters in the probabilistic models are determined so as to maximize the marginal likelihood. A practical algorithm is described for multi-valued image restoration based on loopy belief propagations in probabilistic inference. Loopy belief propagations are...

The paper reports a method for compressed representation of matrix data on the principles quantum theory. is formalized as complex-valued factorization based standard singular value decomposition. developed approach establishes bridge between methods semantic analysis and models cognition decision. According to theory, real-valued observable quantities are generated by wavefunctions being vecto...

We study languages that specify Markov Decision Processes with Imprecise Probabilities (MDPIPs) by mixing probabilities and logic programming. We propose a novel language that can capture MDPIPs and Markov Decision Processes with Set-valued Transitions (MDPSTs); we then obtain the complexity of one-step inference for the resulting MDPIPs and MDPSTs. We also present results of independent intere...

Kinetic equations describe the limiting deterministic evolution of properly scaled systems interacting particles. A rather universal extension classical evolutions, that aims to take into account effects memory, suggests generalization these evolutions obtained by changing standard time derivative with a fractional one. In present paper, extending some previous notes authors related models fini...

In order to improve the effectiveness of shape based classification there is an ongoing interest in creating new shape descriptors or creating new measures for descriptors that are already defined and used in shape classification tasks. Convexity is one of the most widely used shape descriptors and also one of the most studied in the literature. There are already several defined convexity measu...

Model checking in probabilistic real-time temporal logic of knowledge PTACTLK confronts the same challenge as in traditional model checking, that is the state space explosion problem. Abstraction is one of the most effective methods to alleviate the state space explosion problem, under the traditional framework of two-valued abstraction, the abstract model obtained using abstraction techniques ...

In this paper, we provide an algebraic approach to Markov Decision Processes (MDPs), which allows a unified treatment of MDPs and includes many existing models (quantitative or qualitative) as particular cases. In algebraic MDPs, rewards are expressed in a semiring structure, uncertainty is represented by a decomposable plausibility measure valued on a second semiring structure, and preferences...