In this paper we derive entropy bounds for hierarchical networks. More precisely, starting from a recently introduced measure to determine the topological entropy of non-hierarchical networks, we provide bounds for estimating the entropy of hierarchical graphs. Apart from bounds to estimate the entropy of a single hierarchical graph, we see that the derived bounds can also be used for character...

The concepts of entropy and dimension as applied to dynamical systems are reviewed from a physical point of view. The information dimension, which measures the rate at which the information contained in a probability density scales with resolution, fills a logical gap in the classification of attractors in terms of metric entropy, fractal dimension, and topological entropy. Several examples are...

This paper considers the problem of estimating the power consumption at logic and register transfer levels of design from an information theoretical point of view. In particular, it is demonstrated that the average switching activity in the circuit can be calculated using either entropy or informational energy averages. For control circuits and random logic, the output entropy (informational en...

The contribution of this work is a control formulation for a mobile sensor to track a target using an information-theoretic cost function based on a particle filter estimate of the target state. The particle filter representation fully models the non-linearity and limited field of view of the sensor and is able to search for a lost target by updating the estimate to eliminate areas which have b...

We consider the problem of approximating the entropy of a discrete distribution P on a domain of size q, given access to n independent samples from the distribution. It is known that n ≥ q is necessary, in general for a good additive estimate of the entropy. A problem of multiplicative entropy estimate was recently addressed by Batu, Dasgupta, Kumar, and Rubinfeld. They show that n = q suffices...

The energy dissipated during the atomic force microscopy-based mechanical unfolding and extension of proteins is typically an order of magnitude greater than their folding free energy. The vast majority of the "excess" energy dissipated is thought to arise due to backbone conformational entropy losses as the solvated, random-coil unfolded state is stretched into an extended, low-entropy conform...

in this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. it is shown that it generates the kolmogorov entropy as a special case. if $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.

We develop a generalized method of moments (GMM) estimator for the distribution of a variable where summary statistics are available only for intervals of the random variable. Without individual data, one cannot calculate the weighting matrix for the GMM estimator. Instead, we propose a simulated weighting matrix based on a first-step consistent estimate. When the functional form of the underly...

K e y w o r d s C o n v e x hull, Entropy, Hankel matrix, Moment problem. 1. I N T R O D U C T I O N Every probability distribution has some uncertainty associated with it, and its entropy provides a quantitat ive measure of this uncertainty. Partial information given, for instance, in terms of averages about a random variate decreases its entropy. It thus appears interesting to provide an entr...