Computational mechanics: from theory to practice

In the last fifty years, computational mechanics has gained the attention of a large number of disciplines, ranging from physics and mathematics to biology, involving all the disciplines that deal with complex systems or processes. With ϵ-machines, computational mechanics provides powerful models that can help characterizing these systems. To date, an increasing number of studies concern the use of such methodologies; nevertheless, an attempt to make this approach more accessible in practice is lacking yet. Starting from this point, this thesis aims at investigating a more practical approach to computational mechanics so as to make it suitable for applications in a wide spectrum of domains. ϵ-machines are analyzed more in the robotics scene, trying to understand if they can be exploited in contexts with typically complex dynamics like swarms. Experiments are conducted with random walk behavior and the aggregation task. Statistical complexity is first studied and tested on the logistical map and then exploited, as a more applicative case, in the analysis of electroencephalograms as a classification parameter, resulting in the discrimination between patients (with different sleep disorders) and healthy subjects. The number of applications that may benefit from the use of such a technique is enormous. Hopefully, this work has broadened the prospect towards a more applicative interest

The flow of information in trading: an entropy approach to market regimes

In this study, we use entropy-based measures to identify different types of trading behaviors.1We detect the return-driven trading using the conditional block entropy that dynamically reflects the “self-causality' of market return flows. Then we use the transfer entropy to identify the news-driven3trading activity that is revealed by the information flows from news sentiment to market returns. We argue that when certain trading behaviour becomes dominant or jointly dominant, the market will form a specific regime, namely return-, news- or mixed regime. Based on 11 years of news and market data, we find that the evolution of financial market regimes in terms of adaptive trading activities over the 2008 liquidity and euro-zone debt crises can be explicitly explained by the information flows. The proposed method can be expanded to make “causal' inferences on other types of economic phenomena

Information Diffusion, Cluster formation and Entropy-based Network Dynamics in Equity and Commodity Markets

This paper investigates the dynamic causal linkages among U.S. equity and commodity futures markets via the utilization of complex network theory. We make use of rolling estimations of extended matrices and time-varying network topologies to reveal the temporal dimension of correlation and entropy relationships. A simulation analysis using randomized time series is also implemented to assess the impact of de-noising on the data dependence structure. We mainly show evidence of emphasized disparity of correlation and entropy-based centrality measurements for all markets between pre- and post-crisis periods. Our results enable the robust mapping of network influences and contagion effects whilst incorporating agent expectations

Information Diffusion, Cluster formation and Entropy-based Network Dynamics in Equity and Commodity Markets

This paper investigates the dynamic causal linkages among U.S. equity and commodity futures markets via the utilization of complex network theory. We make use of rolling estimations of extended matrices and time-varying network topologies to reveal the temporal dimension of correlation and entropy relationships. A simulation analysis using randomized time series is also implemented to assess the impact of de-noising on the data dependence structure. We mainly show evidence of emphasized disparity of correlation and entropy-based centrality measurements for all markets between pre- and post-crisis periods. Our results enable the robust mapping of network influences and contagion effects whilst incorporating agent expectations

Explaining human mobility predictions through a pattern matching algorithm

Understanding what impacts the predictability of human movement is a key element for the further improvement of mobility prediction models. Up to this day, such analyses have been conducted using the upper bound of predictability of human mobility. However, later works indicated discrepancies between the upper bound of predictability and accuracy of actual predictions suggesting that the predictability estimation is not accurate. In this work, we confirm these discrepancies and, instead of predictability measure, we focus on explaining what impacts the actual accuracy of human mobility predictions. We show that the accuracy of predictions is dependent on the similarity of transitions observed in the training and test sets derived from the mobility data. We propose and evaluate five pattern matching based-measures, which allow us to quickly estimate the potential prediction accuracy of human mobility. As a result, we find that our metrics can explain up to 90% of its variability. We also find that measures that were proved to explain the variability of predictability measure, fail to explain the variability of predictions accuracy. This suggests that predictability measure and accuracy of predictions should not be compared. Our metrics can be used to quickly assess how predictable the data will be for prediction algorithms. We share developed metrics as a part of HuMobi, the open-source Python library

An Entropy Measure of Non-Stationary Processes

Shannon’s source entropy formula is not appropriate to measure the uncertainty of non-stationary processes. In this paper, we propose a new entropy measure for non-stationary processes, which is greater than or equal to Shannon’s source entropy. The maximum entropy of the non-stationary process has been considered, and it can be used as a design guideline in cryptography