This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables. As an example, it is shown how a universal quantum computer for the amplitudes of the electromagnetic field might be constructed using simple linear devices such as beam-splitters and phase shifters, together with squeezers and nonlinear devices such as Kerr-effect fi...

Bayesian Constraint-based Causal Discovery (BCCD) is a state-of-the-art method for robust causal discovery in the presence of latent variables. It combines probabilistic estimation of Bayesian networks over subsets of variables with a causal logic to infer causal statements. Currently BCCD is limited to discrete or Gaussian variables. Most of the real-world data, however, contain a mixture of d...

We study the class of functions called monodiffric of the second kind by Rufus Philip Isaacs. They are discrete analogues of holomorphic functions of one or two complex variables. Discrete analogues of the Cauchy–Riemann operator, of domains of holomorphy in one discrete variable, and of the Hartogs phenomenon in two discrete variables are investigated. Two fundamental solutions to the discrete...

Discrete-time synergetic optimal control strategies are proposed for a class of nonlinear discrete-time dynamic systems, in which a special performance index is used that results in closed-form solutions of the optimal problems. Reduced-dimension aggregated variables representing a combination of the actual controlled plant variables are used to define the performance index. The control law opt...

This chapter introduces the underlying theory of Fuzzy Probability and Statistics related to the differences and similarities between discrete probability and possibility spaces. Fuzzy Probability Theory for Discrete Case starts with the fundamental tools to implement an immigration of crisp probability theory into fuzzy probability theory. Fuzzy random variables are the initial steps to develo...