Model-independent rate control for intra-coding based on piecewise linear approximations

This paper proposes a rate control (RC) algorithm for intra-coded sequences (I-frames) within the context of block-based predictive transform coding that departs from using trained models to approximate the rate-distortion (R-D) characteristics of the video sequence. Our algorithm employs piecewise linear approximations of the rate-distortion (R-D) curve of a frame at the block-level. Specifically, it employs information about the rate and distortion of already compressed blocks within the current frame to linearly approximate the slope of the R-D curve of each block. The proposed algorithm is implemented in the High-Efficiency Video Coding (H.265/HEVC) standard and compared with its current RC algorithm, which is based on a trained model. Evaluations on a variety of intra-coded sequences show that the proposed RC algorithm not only attains the overall target bit rate more accurately than the RC algorithm used by H.265/HEVC algorithm but is also capable of encoding each I-frame at a more constant bit rate according to the overall bit budget

A Semigroup associated to a linear control system on a Lie group

Let us consider a linear control system \Sigma on a connected Lie group G. It is known that the accessibility set A from the identity e is in general not a semigroup. In this article we associate a new algebraic object S to \Sigma which turns out to be a semigroup, allowing the use of the semigroup machinery to approach \Sigma. In particular, we obtain some controllability results

Temporal evolution of the "thermal" and "superthermal" income classes in the USA during 1983-2001

Personal income distribution in the USA has a well-defined two-class structure. The majority of population (97-99%) belongs to the lower class characterized by the exponential Boltzmann-Gibbs ("thermal") distribution, whereas the upper class (1-3% of population) has a Pareto power-law ("superthermal") distribution. By analyzing income data for 1983-2001, we show that the "thermal" part is stationary in time, save for a gradual increase of the effective temperature, whereas the "superthermal" tail swells and shrinks following the stock market. We discuss the concept of equilibrium inequality in a society, based on the principle of maximal entropy, and quantitatively show that it applies to the majority of population.Comment: v.3: 7 pages, 5 figures, EPL style, more references adde