In this paper, we aim at tackling the problem of crowd counting in extremely high-density scenes, which contain hundreds, or even thousands of people. We begin by a comprehensive analysis of the most widely used density mapbased methods, and demonstrate how easily existing methods are affected by the inhomogeneous density distribution problem, e.g., causing them to be sensitive to outliers, or ...

Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct explicit solutions of the models are developed. All statistical characteristics of interest, such as the mean values of the fitness or any trait can be computed e...

Abstract: In a Bayesian interaction game players have diverse preferences and are randomly matched according to an inhomogeneous random graph. A co-evolutionary process of networks and play gives a dynamic formalism for the joint evolution of the random graph and the actions the players use per match. Assuming that the players select actions and links according to log-linear functions taking as...

We introduce a formal testing procedure to assess the goodness-of-fit of a fitted inhomogeneous spatial Poisson process model. Our method is based on a discrepancy measure function Dc(t; θ̂) that is constructed by using residuals obtained from the fitted model. We derive the asymptotic distributional properties of Dc(t; θ̂) and then develop a test statistic based on these properties. Our test sta...

Abstract. The interstellar medium (ISM) reveals strongly inhomogeneous structures at every scale. These structures do not seem completely random since they obey certain power laws. Larson’s law (1981) σ ∝ R and the plausible assumption of virial equilibrium justify to consider fractals as a possible description of the ISM. In the following we investigate how self-gravitation, differential rotat...