In a two node communication environment, the number of key bits (IK) per observation of the reciprocal channel can be computed using the mutual information between the forward and reverse estimated channels. The mutual information can not be computed in closed form, if the probability density function (pdf) of the channel is unknown. This work studies the computation of IK for an arbitrary chan...

We address the issue of knots selection for Gaussian predictive process methodology. Predictive process approximation provides an effective solution to the cubic order computational complexity of Gaussian process models. This approximation crucially depends on a set of points, called knots, at which the original process is retained, while the rest is approximated via a deterministic extrapolati...

A new technique for generating an approximate replica of Gaussian pulses with good accuracy is proposed and investigated. The Gaussian function is approximated with a waveform that results from the convolution of two triangles. The proposed pulse performs better than other previously reported pulse. The results show good agreement not only for the Gaussian pulse but also for its first and secon...

We study posterior rates of contraction in Gaussian process regression with potentially unbounded covariate domain. Our argument relies on developing a Gaussian approximation to the posterior of the leading coefficients of a Karhunen–Loève expansion of the Gaussian process. The salient feature of our result is deriving such an approximation in the L2 Wasserstein distance and relating the speed ...

We demonstrate that the coherence of a noisy or chaotic self-sustained oscillator can be efficiently controlled by the delayed feedback. We develop a theory of this effect, considering noisy systems in the Gaussian approximation. We obtain a closed equation system for the phase diffusion constant and the mean frequency of oscillation. For weak feedback and strong noise, the theory is in good ag...

With the Gaussian Process model, the predictive distribution of the output corresponding to a new given input is Gaussian. But if this input is uncertain or noisy, the predictive distribution becomes non-Gaussian. We present an analytical approach that consists of computing only the mean and variance of this new distribution (Gaussian approximation). We show how, depending on the form of the co...

We consider a bidimensional system of few identical bosons trapped in a harmonic well that interact through a two-body gaussian potential. We discuss the ground state energy using a mean-field approximation and introducing pair correlations. To solve the many-body problem we used Monte Carlo techniques: Variational and Diffusion Monte Carlo. We find that two-body correlations lower significantl...

Receiver algorithms which combine belief propagation (BP) with the mean field (MF) approximation are well-suited for inference of both continuous and discrete random variables. In wireless scenarios involving detection of multiple signals, the standard construction of the combined BP-MF framework includes the equalization or multi-user detection functions within the MF subgraph. In this paper, ...

System identiication for stationary Gaussian processes includes an approximation problem. Currently the subspace algorithm for this problem enjoys much attention. This algorithm is based on a transformation of a nite time series to canonical variable form followed by a truncation. There is no proof that this algorithm is the optimal solution to an approximation problem with a speciic criterion....