A Recipe for the Estimation of Information Flow in a Dynamical System

Information-theoretic quantities, such as entropy and mutual information (MI), can be used to quantify the amount of information needed to describe a dataset or the information shared between two datasets. In the case of a dynamical system, the behavior of the relevant variables can be tightly coupled, such that information about one variable at a given instance in time may provide information about other variables at later instances in time. This is often viewed as a flow of information, and tracking such a flow can reveal relationships among the system variables. Since the MI is a symmetric quantity; an asymmetric quantity, called Transfer Entropy (TE), has been proposed to estimate the directionality of the coupling. However, accurate estimation of entropy-based measures is notoriously difficult. Every method has its own free tuning parameter(s) and there is no consensus on an optimal way of estimating the TE from a dataset. We propose a new methodology to estimate TE and apply a set of methods together as an accuracy cross-check to provide a reliable mathematical tool for any given data set. We demonstrate both the variability in TE estimation across techniques as well as the benefits of the proposed methodology to reliably estimate the directionality of coupling among variables

A Recipe for the Estimation of Information Flow in a Dynamical System

Information-theoretic quantities, such as entropy and mutual information (MI), can be used to quantify the amount of information needed to describe a dataset or the information shared between two datasets. In the case of a dynamical system, the behavior of the relevant variables can be tightly coupled, such that information about one variable at a given instance in time may provide information about other variables at later instances in time. This is often viewed as a flow of information, and tracking such a flow can reveal relationships among the system variables. Since the MI is a symmetric quantity; an asymmetric quantity, called Transfer Entropy (TE), has been proposed to estimate the directionality of the coupling. However, accurate estimation of entropy-based measures is notoriously difficult. Every method has its own free tuning parameter(s) and there is no consensus on an optimal way of estimating the TE from a dataset. We propose a new methodology to estimate TE and apply a set of methods together as an accuracy cross-check to provide a reliable mathematical tool for any given data set. We demonstrate both the variability in TE estimation across techniques as well as the benefits of the proposed methodology to reliably estimate the directionality of coupling among variables

Processing of eutectic Zn-5% Al alloy by equal-channel angular pressing

Multi-pass equal-channel angular pressing (ECAP) was applied to the eutectic Zn-5% Al alloy as a first step in the examination of the binary Zn-Al alloy system by using two different processing routes: route A, where the sample is pressed repetitively through the die without rotation, and route C, where the sample is rotated by 180° after each pass. A three-block die for ECAP was designed and manufactured. Evolution of hardness was investigated and microstructural changes were noted during ECAP. Variations in the applied load during ECAP of the alloy were analyzed, and the relationship between maximum load and hardness was discussed. It was observed that the equiaxed grain structure of the as-received alloy completely disappeared and instead a banded structure was formed during the ECAP process. Hardness of the alloy decreased with increasing number of passes for both processing routes. The applied load during ECAP increased up to a maximum value, and this was followed by a decrease until the end of pressing in all processing conditions. The maximum load required for the ECAP of the alloy decreased for both routes with increasing number of passes. It was observed that the hardness and the maximum load showed similar trends with number of passes for both processing routes. © 2004 Elsevier B.V. All rights reserved