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In some other articles in this blog, I have already written about complex time series, recurrence quantification analysis (RQA) and neural networks. In this series of articles, I will discuss some points to take into account when combining the use of these two tools to identify patterns in complex series, such as detecting anomalies in electrocardiograms or electroencephalograms.

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So far I have shown examples of multitasking that block the application until they finished. This is not very useful in practice. Usually, we want that the user can continue interacting with the application while the tasks are running in the background; we could want also the threads to interact with the user interface.

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After reviewing the classes to implement the basic multitasking, in this article I will review different mechanisms that allow a synchronization between various tasks, all of them defined in the System.Threading namespace, with which you can organize the work when the Interactions between tasks require a particular order.

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The Iterated function systems (IFS) are a simple mathematical tool for constructing fractal sets through a series of contractive affine applications. This method was developed by M.F. Barnsley in 1985. In particular, it is useful to obtain a self-similar fractal based on iteratively applying the system of functions to any set, until arriving at a good approximation of the fractal set that constitutes the attractor of the system.

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WInRQA is an application dedicated to recurrence plots, a tool that is used in the analysis of recurrence of complex time series. In this article I will present the first extension of the application, which mainly consists of a series of tool windows that will help you to make estimates on what may be the most appropriate delay to try to reconstruct the phase space of the system attractor and select the correct embedding dimension.

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To conclude this series on complex time series and their characterization using graphical tools I will show you a tool called recurrence plot, which allows to obtain some measures used in the recurrence quantification analysis, or RQA for its acronym in English. The recurrence is a characteristic property of deterministic dynamical systems, and consists of that two or more states of the system are arbitrarily close after a certain period of time.

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In this new article in the series on time series with complex dynamics, I will show you a procedure to approximately reconstruct the information of a dynamic system with two or more variables from a single series, i.e. a set of data in a single dimension. What we will get from this unique series is a new one for each of the extra dimensions with which we intend to extend the model.

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In this new article in the series on graphic characterization of time series from dynamical systems with chaotic dynamics, I will talk about a way to represent such systems in the domain of space, independently of time, the phase diagram. With this type of diagram, you can see the attractors of the system. An attractor is a point, a curve, in general, a set of points to which converge the system equations, which gives us an idea of the typical behavior of that system.

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