In this paper we address the problem of learning the structure in nonlinear Markov networks with continuousvariables. Markov networks are well suited to model relationships which do not exhibit a natural causal ordering. We use neural network structures to model the quantitative relationships between variables. Using two data sets we show that interesting structures can be found using our appro...

We consider estimation problems for a continuous-time linear system with a state disturbance and additive errors on the input and the output. The problem formulation and the estimation principle are deterministic. The derived filter is identical to the stochastic Kalman filter. The problem formulation with additive error on both the input and the output, however, is more symmetric then the clas...

The concept of mutually unbiased bases is studied for N pairs of continuous variables. To find mutually unbiased bases reduces, for specific states related to the Heisenberg-Weyl group, to a problem of symplectic geometry. Given a single pair of continuous variables, three mutually unbiased bases are identified while five such bases are exhibited for two pairs of continuous variables. For N = 2...

Many statistical analyses can be undertaken to examine the relationship between two continuous variables within a group of subjects. Two of the main purposes of such analyses are: To assess whether the two variables are associated. There is no distinction between the two variables and no causation is implied, simply association. To enable the value of one variable to be predicted from any known...

We derive several entanglement criteria for bipartite continuous variable quantum systems based on the Shannon entropy. These criteria are more sensitive than those involving only second-order moments, and are equivalent to well-known variance product tests in the case of Gaussian states. Furthermore, they involve only a pair of quadrature measurements, and will thus prove extremely useful in t...