The large-inputs asymptotic capacity of a peak and average power limited discrete-time Poisson channel is derived using a new firm (non-asymptotic) lower bound and an asymptotic upper bound. The upper bound is based on the dual expression for channel capacity and the recently introduced notion of capacityachieving input distributions that escape to infinity. The lower bound is based on a lemma ...

We are concerned with the study of the diffusion and homogenization approximation of the Boltzmann-Poisson system in presence of a spatially oscillating electrostatic potential. By analyzing the relative entropy, we prove uniform energy estimate for well prepared boundary data. An averaging lemma and two scale convergence techniques are used to prove rigorously the convergence of the scaled Bol...

We revisit Tsallis Maximum Entropy Solutions to the Vlasov-Poisson Equation describing gravitational N -body systems. We review their main characteristics and discuss their relationship with other applications of Tsallis statistics to systems with long range interactions. In the following considerations we shall be dealing with a D-dimensional space so as to be in a position to investigate poss...

A perturbed multi-agent system is a scheme self-possessed of multiple networking agents within a location. This scheme can be used to discuss problems that are impossible or difficult for a specific agent to solve. Intelligence cloud entropy management systems involve functions, methods, procedural approaches, and algorithms. In this study, we introduce a new perturbed algorithm based on the fr...

We prove that the Poisson distribution maximises entropy in the class of ultralog-concave distributions, extending a result of Harremoës. The proof uses ideas concerning log-concavity, and a semigroup action involving adding Poisson variables and thinning. We go on to show that the entropy is a concave function along this semigroup. 1 Maximum entropy distributions It is well-known that the dist...

We develop a general method for computing logarithmic and log-gamma expectations of distributions. As a result, we derive series expansions and integral representations of the entropy for several fundamental distributions, including the Poisson, binomial, beta-binomial, and negative binomial distributions. Our results also establish connections between the entropy functions and to the Riemann z...

In this paper, we prove the existence and uniqueness of weak entropy solutions to the Burgers-Poisson equation for initial data in L(R). Additional an Oleinik type estimate is established and some criteria on local smoothness and wave breaking for weak entropy solutions are provided.