Related papers: Comparing Poisson and Gaussian channels (extended)
Given a simple transient random walk $(S_n)_{n\geq 0}$ in $\mathbf{Z}$ and a stationary sequence of real random variables $(\xi(s))_{s\in \mathbf{Z}}$, we investigate the extremes of the sequence $(\xi(S_n))_{n\geq 0}$. Under suitable…
We propose to send a Gaussian source over an average-power limited additive white Gaussian noise channel by transmitting a linear combination of the source sequence and the result of its quantization using a high dimensional Gaussian vector…
Asymptotic behavior of the point process of high and medium values of a Gaussian stationary process with discrete time is considered. An approximation by a Poisson cluster point process is given for the point process.
Gaussian Processes (GPs) can be used as flexible, non-parametric function priors. Inspired by the growing body of work on Normalizing Flows, we enlarge this class of priors through a parametric invertible transformation that can be made…
We compare two sets of multimode quantum channels acting on a finite collection of harmonic oscillators: (a) the set of linear bosonic channels, whose action is described as a linear transformation at the phase space level; and (b) Gaussian…
Information transmission over channels with transceiver distortion is investigated via generalized mutual information (GMI) under Gaussian input distribution and nearest-neighbor decoding. A canonical transceiver structure in which the…
This paper quantifies the intuitive observation that adding noise reduces available information by means of non-linear strong data processing inequalities. Consider the random variables $W\to X\to Y$ forming a Markov chain, where $Y=X+Z$…
A generic quantum channel can be represented in terms of a unitary interaction between the information-carrying system and a noisy environment. Here, the minimal number of quantum Gaussian environmental modes required to provide a unitary…
For information transmission a discrete time channel with independent additive Gaussian noise is used. There is also feedback channel with independent additive Gaussian noise, and the transmitter observes without delay all outputs of the…
The Gaussian mixture distribution is important in various statistical problems. In particular it is used in the Gaussian-sum filter and smoother for linear state-space model with non-Gaussian noise inputs. However, for this method to be…
We derive an upper limit for the mixedness of single bosonic mode gaussian states propagating in dissipative channels. It is a function of the initial squeezing and temperature of the channel only. Moreover the time at which von Neumann's…
It is generally known that counting statistics is not correctly described by a Gaussian approximation. Nevertheless, in neutron scattering, it is common practice to apply this approximation to the counting statistics; also at low counting…
A simple lower bound to the capacity of the discrete-time Poisson channel with average energy $\es$ is derived. The rate ${1/2}\log(1+\es)$ is shown to be the generalized mutual information of a modified minimum-distance decoder, when the…
The statistics of a passive tracer immersed in a suspension of active self-propelled particles (swimmers) is derived from first principles by considering a perturbative expansion of the tracer interaction with the microscopic swimmer field.…
Bayesian hierarchical Poisson models are an essential tool for analyzing count data. However, designing efficient algorithms to sample from the posterior distribution of the target parameters remains a challenging task for this class of…
We discuss various models of ion transport through cell membrane channels. Recent experimental data shows that sizes of ion channels are compared to those of ions and that only few ions may be simultaneously in any single channel.…
We show that there exist Gaussian channels which are amendable. A channel is amendable if when applied twice is entanglement breaking while there exists a unitary filter such that, when interposed between the first and second action of the…
In the era of open data, Poisson and other count regression models are increasingly important. Still, conventional Poisson regression has remaining issues in terms of identifiability and computational efficiency. Especially, due to an…
The problem of a diffusing particle moving among diffusing traps is analyzed in general space dimension d. We consider the case where the traps are initially randomly distributed in space, with uniform density rho, and derive upper and…
Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…