Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

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The technological mediation of mathematics and its learning

This paper examines the extent to which mathematical knowledge, and its related pedagogy, is inextricably linked to the tools – physical, virtual, cultural – in which it is expressed. Our goal is to focus on a few exemplars of computational tools, and to describe with some illustrative examples, how mathematical meanings are shaped by their use. We begin with an appraisal of the role of digital technologies, and our rationale for focusing on them. We present four categories of digital tool-use that distinguish their differing potential to shape mathematical cognition. The four categories are: i. dynamic and graphical tools, ii. tools that outsource processing power, iii. new representational infrastructures, and iv. the implications of highbandwidth connectivity on the nature of mathematics activity. In conclusion, we draw out the implications of this analysis for mathematical epistemology and the mathematical meanings students develop. We also underline the central importance of design, both of the tools themselves and the activities in which they are embedded

On inferring intentions in shared tasks for industrial collaborative robots

Inferring human operators' actions in shared collaborative tasks, plays a crucial role in enhancing the cognitive capabilities of industrial robots. In all these incipient collaborative robotic applications, humans and robots not only should share space but also forces and the execution of a task. In this article, we present a robotic system which is able to identify different human's intentions and to adapt its behavior consequently, only by means of force data. In order to accomplish this aim, three major contributions are presented: (a) force-based operator's intent recognition, (b) force-based dataset of physical human-robot interaction and (c) validation of the whole system in a scenario inspired by a realistic industrial application. This work is an important step towards a more natural and user-friendly manner of physical human-robot interaction in scenarios where humans and robots collaborate in the accomplishment of a task.Peer ReviewedPostprint (published version

When is a Network a Network? Multi-Order Graphical Model Selection in Pathways and Temporal Networks

We introduce a framework for the modeling of sequential data capturing pathways of varying lengths observed in a network. Such data are important, e.g., when studying click streams in information networks, travel patterns in transportation systems, information cascades in social networks, biological pathways or time-stamped social interactions. While it is common to apply graph analytics and network analysis to such data, recent works have shown that temporal correlations can invalidate the results of such methods. This raises a fundamental question: when is a network abstraction of sequential data justified? Addressing this open question, we propose a framework which combines Markov chains of multiple, higher orders into a multi-layer graphical model that captures temporal correlations in pathways at multiple length scales simultaneously. We develop a model selection technique to infer the optimal number of layers of such a model and show that it outperforms previously used Markov order detection techniques. An application to eight real-world data sets on pathways and temporal networks shows that it allows to infer graphical models which capture both topological and temporal characteristics of such data. Our work highlights fallacies of network abstractions and provides a principled answer to the open question when they are justified. Generalizing network representations to multi-order graphical models, it opens perspectives for new data mining and knowledge discovery algorithms.Comment: 10 pages, 4 figures, 1 table, companion python package pathpy available on gitHu

Integration of decision support systems to improve decision support performance

Decision support system (DSS) is a well-established research and development area. Traditional isolated, stand-alone DSS has been recently facing new challenges. In order to improve the performance of DSS to meet the challenges, research has been actively carried out to develop integrated decision support systems (IDSS). This paper reviews the current research efforts with regard to the development of IDSS. The focus of the paper is on the integration aspect for IDSS through multiple perspectives, and the technologies that support this integration. More than 100 papers and software systems are discussed. Current research efforts and the development status of IDSS are explained, compared and classified. In addition, future trends and challenges in integration are outlined. The paper concludes that by addressing integration, better support will be provided to decision makers, with the expectation of both better decisions and improved decision making processes

Causal Discovery from Temporal Data: An Overview and New Perspectives

Temporal data, representing chronological observations of complex systems, has always been a typical data structure that can be widely generated by many domains, such as industry, medicine and finance. Analyzing this type of data is extremely valuable for various applications. Thus, different temporal data analysis tasks, eg, classification, clustering and prediction, have been proposed in the past decades. Among them, causal discovery, learning the causal relations from temporal data, is considered an interesting yet critical task and has attracted much research attention. Existing casual discovery works can be divided into two highly correlated categories according to whether the temporal data is calibrated, ie, multivariate time series casual discovery, and event sequence casual discovery. However, most previous surveys are only focused on the time series casual discovery and ignore the second category. In this paper, we specify the correlation between the two categories and provide a systematical overview of existing solutions. Furthermore, we provide public datasets, evaluation metrics and new perspectives for temporal data casual discovery.Comment: 52 pages, 6 figure

Open semantic service networks

Online service marketplaces will soon be part of the economy to scale the provision of specialized multi-party services through automation and standardization. Current research, such as the *-USDL service description language family, is already defining the basic building blocks to model the next generation of business services. Nonetheless, the developments being made do not target to interconnect services via service relationships. Without the concept of relationship, marketplaces will be seen as mere functional silos containing service descriptions. Yet, in real economies, all services are related and connected. Therefore, to address this gap we introduce the concept of open semantic service network (OSSN), concerned with the establishment of rich relationships between services. These networks will provide valuable knowledge on the global service economy, which can be exploited for many socio-economic and scientific purposes such as service network analysis, management, and control

Data Driven Techniques for Modeling Coupled Dynamics in Transient Processes

We study the problem of modeling coupled dynamics in transient processes that happen in a network. The problem is considered at two levels. At the node level, the coupling between underlying sub-processes of a node in a network is considered. At the network level, the direct influence among the nodes is considered. After the model is constructed, we develop a network-based approach for change detection in high dimension transient processes. The overall contribution of our work is a more accurate model to describe the underlying transient dynamics either for each individual node or for the whole network and a new statistic for change detection in multi-dimensional time series. Specifically, at the node level, we developed a model to represent the coupled dynamics between the two processes. We provide closed form formulas on the conditions for the existence of periodic trajectory and the stability of solutions. Numerical studies suggest that our model can capture the nonlinear characteristics of empirical data while reducing computation time by about 25% on average, compared to a benchmark modeling approach. In the last two problems, we provide a closed form formula for the bound in the sparse regression formulation, which helps to reduce the effort of trial and error to find an appropriate bound. Compared to other benchmark methods in inferring network structure from time series, our method reduces inference error by up to 5 orders of magnitudes and maintain better sparsity. We also develop a new method to infer dynamic network structure from a single time series. This method is the basis for introducing a new spectral graph statistic for change detection. This statistic can detect changes in simulation scenario with modified area under curve (mAUC) of 0.96. When applying to the problem of detecting seizure from EEG signal, our statistic can capture the physiology of the process while maintaining a detection rate of 40% by itself. Therefore, it can serve as an effective feature to detect change and can be added to the current set of features for detecting seizures from EEG signal