Abstract:

Connectivity is a concept that might be treacherous for many graduate students. The main idea of connectivity seems to be obvious, and anyone can tell if two elements are connected or not just looking at them. However, it is a broad term whose specific meaning depends on the field. We may consider that two students are connected if there is a physical link between them, for example if they are shaking their hands, but it could be an abstract connection, for example they are also connected if they play chess together every Thursday or if they are relatives. In several scientific fields, including economics, physics and neuroscience, the study of the connectivity shares a common background, which is the analysis of time series. For each element, like the income of a company or the electric field of a neuron, we can acquire a signal that describes its activity along the time, with a different value for each observed time point.

There is an immense number of methods to analyze the connectivity between time series, each one based on a specific feature of the signals and with a different result. For example, we might be interested in the connectivity between the number of pizzas ordered and the profits of the pizza shop. These signals are correlated (they covary), as if people order more pizzas, the company will earn more money. The number of ordered pizzas depends on the day, with more sales during the weekend. That is the frequency of the signal, weekly in this case, and can be estimated with the coherence. Also, the connectivity has a certain delay: the company receives the money when the pizza is delivered, around 30 minutes after it is ordered. Thus, it is mandatory to understand the signal and the methodology before making any interpretation of the result. Using the same example, if we analyze the connectivity between the number of pizzas made (not ordered) and the profits, we may wrongly interpret that making more pizzas causes an increase of the benefits, regardless of whether people are ordering them or not. In this case, one method to differentiate correlations from potential cause-effect relationships is Granger Causality.

The objective of the present work is to develop an interactive application that generates time series based on variable parameters and analyze the connectivity between them with different methods, allowing a direct interpretation of the results in an environment controlled by the student. The software generates three oscillatory signals, where their specific frequency, phase and noise can be tuned through a user-friendly interface, with an immediate representation of the time-series and their frequency information (power spectrum). The connectivity between the signals can be also parameterized, and the student can select the intensity of the link, the directionality (from A to B or from B to A) and the delay. Once the student has determined the desired parameters, several connectivity metrics can be applied on the system, with a visual representation of the results. Importantly, all the parameters can be changed at any moment, with an automatic update of all the figures. Therefore, it permits the comparison of dozens of different networks, i.e., set of elements with a specific configuration of connectivity between them, in a few minutes. Moreover, the software includes a help document, with the theoretical basis of the connectivity and examples of parameters to test certain situations of interest.

Keywords:

Active learning, time-series, connectivity, network, interactive tools.