Inset plots can be used to “zoom in” on densely populated areas of a graph or to add extra relevant data in the form of, for example, distribution plots. However, the standard Stata command for combining plots, graph combine, does not permit this type of seamless integration. Each plot within a graph combine object is allocated a grid cell that cannot be placed within another grid cell— at least not without certain (invariably unwanted) graphical complications. We present a fairly simple work-around to this issue using reproducible examples. The main idea is to plot insets along a second axis and then artificially modify the range of this axis to constrain the inset plot within a specified area of the main graph. Additional tips are included for producing more intricate, multilayered inset graphs.
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Recently, we have introduced and modified two graph-decomposition theorems based on a new graph product, motivated by applications in the context of synchronising periodic real-time processes. This vertex-removing synchronised product (VRSP), is based on modifications of the well-known Cartesian product and is closely related to the synchronised product due to Wohrle and Thomas. Here, we recall the definition of the VRSP and the two modified graph-decompositions and introduce three new graph-decomposition theorems. The first new theorem decomposes a graph with respect to the semicomplete bipartite subgraphs of the graph. For the second new theorem, we introduce a matrix graph, which is used to decompose a graph in a manner similar to the decomposition of graphs using the Cartesian product. In the third new theorem, we combine these two types of decomposition. Ultimately, the goal of these graph-decomposition theorems is to come to a prime-graph decomposition.
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Recently, we have introduced two graph-decomposition theorems based on a new graph product, motivated by applications in the context of synchronising periodic real-time processes. This vertex-removing synchronised product (VRSP) is based on modifications of the well-known Cartesian product and is closely related to the synchronised product due to Wöhrle and Thomas. Here, we recall the definition of the VRSP and the two graph-decomposition theorems, we relax the requirements of these two graph-decomposition theorems and prove these two (relaxed) graph-decomposition theorems.
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In this paper, the performance gain obtained by combining parallel peri- odic real-time processes is elaborated. In certain single-core mono-processor configurations, for example, embedded control systems in robotics comprising many short processes, process context switches may consume a considerable amount of the available processing power. For this reason, it can be advantageous to combine processes, to reduce the number of context switches and thereby increase the performance of the application. As we consider robotic applications only, often consisting of processes with identical periods, release times and deadlines, we restrict these configurations to periodic real-time processes executing on a single-core mono-processor. By graph-theoretical concepts and means, we provide necessary and sufficient conditions so that the number of context switches can be reduced by combining synchronising processes.
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In bepaalde single-core configuraties met één processor, b.v. embedded control systems zoals robotic applications die uit vele korte processen bestaan, kunnen de context switches van een proces een aanzienlijke hoeveelheid van de beschikbare processing power verbruiken. Het verminderen van het aantal context switches vermindert de executietijd en verhoogt daardoor de prestaties van de toepassing. Bovendien is de end-to-end executietijd van de processen langer dan strict noodzakelijk, b.v. omdat de processen moeten wachten op controllers die een taak uitvoeren. Door de regels voor synchrone communicatie via kanalen in de procesalgebraïsche specificatietaal Communicating Sequential Processes te versoepelen, kunnen we de end-to-end executietijd verkorten. In ons onderzoek definiëren we verschillende graafproducten, bewijzen we dat deze producten een prestatiewinst opleveren (onder bepaalde voorwaarden) en we werken de numerieke en combinatorische aspecten van deze graafproducten uit.
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Author supplied: Abstract—The growing importance and impact of new technologies are changing many industries. This effect is especially noticeable in the manufacturing industry. This paper explores a practical implementation of a hybrid architecture for the newest generation of manufacturing systems. The papers starts with a proposition that envisions reconfigurable systems that work together autonomously to create Manufacturing as a Service (MaaS). It introduces a number of problems in this area and shows the requirements for an architecture that can be the main research platform to solve a number of these problems, including the need for safe and flexible system behaviour and the ability to reconfigure with limited interference to other systems within the manufacturing environment. The paper highlights the infrastructure and architecture itself that can support the requirements to solve the mentioned problems in the future. A concept system named Grid Manufacturing is then introduced that shows both the hardware and software systems to handle the challenges. The paper then moves towards the design of the architecture and introduces all systems involved, including the specific hardware platforms that will be controlled by the software platform called REXOS (Reconfigurable EQuipletS Operating System). The design choices are provided that show why it has become a hybrid platform that uses Java Agent Development Framework (JADE) and Robot Operating System (ROS). Finally, to validate REXOS, the performance is measured and discussed, which shows that REXOS can be used as a practical basis for more specific research for robust autonomous reconfigurable systems and application in industry 4.0. This paper shows practical examples of how to successfully combine several technologies that are meant to lead to a faster adoption and a better business case for autonomous and reconfigurable systems in industry.
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Graphs are ubiquitous. Many graphs, including histograms, bar charts, and stacked dotplots, have proven tricky to interpret. Students’ gaze data can indicate students’ interpretation strategies on these graphs. We therefore explore the question: In what way can machine learning quantify differences in students’ gaze data when interpreting two near-identical histograms with graph tasks in between? Our work provides evidence that using machine learning in conjunction with gaze data can provide insight into how students analyze and interpret graphs. This approach also sheds light on the ways in which students may better understand a graph after first being presented with other graph types, including dotplots. We conclude with a model that can accurately differentiate between the first and second time a student solved near-identical histogram tasks.
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Key to reinforcement learning in multi-agent systems is the ability to exploit the fact that agents only directly influence only a small subset of the other agents. Such loose couplings are often modelled using a graphical model: a coordination graph. Finding an (approximately) optimal joint action for a given coordination graph is therefore a central subroutine in cooperative multi-agent reinforcement learning (MARL). Much research in MARL focuses on how to gradually update the parameters of the coordination graph, whilst leaving the solving of the coordination graph up to a known typically exact and generic subroutine. However, exact methods { e.g., Variable Elimination { do not scale well, and generic methods do not exploit the MARL setting of gradually updating a coordination graph and recomputing the joint action to select. In this paper, we examine what happens if we use a heuristic method, i.e., local search, to select joint actions in MARL, and whether we can use outcome of this local search from a previous time-step to speed up and improve local search. We show empirically that by using local search, we can scale up to many agents and complex coordination graphs, and that by reusing joint actions from the previous time-step to initialise local search, we can both improve the quality of the joint actions found and the speed with which these joint actions are found.
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In mathematics, sciences and economics, understanding and working with graphs are important skills. However, developing these skills has been shown to be a challenge in secondary and higher education as it involves high order thinking processes such as analysis, reflection and creativity. In this study, we present Interactive Virtual Math, a tool that supports the learning of a specific kind of graphs: dynamic graphs which represent the relation between at least two quantities that covary. The tool supports learners in visualizing abstract relations through enabling them to draw, move and modify graphs, and by combining graphs with other representations, especially interactive animations and textual explanations. This paper reports a design experiment about students’ learning graphs with this tool. Results show that students with difficulty in generating acceptable graphs improve their ability while working with the tool.
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We present a novel architecture for an AI system that allows a priori knowledge to combine with deep learning. In traditional neural networks, all available data is pooled at the input layer. Our alternative neural network is constructed so that partial representations (invariants) are learned in the intermediate layers, which can then be combined with a priori knowledge or with other predictive analyses of the same data. This leads to smaller training datasets due to more efficient learning. In addition, because this architecture allows inclusion of a priori knowledge and interpretable predictive models, the interpretability of the entire system increases while the data can still be used in a black box neural network. Our system makes use of networks of neurons rather than single neurons to enable the representation of approximations (invariants) of the output.
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