In the last few decades, Artificial Neural Networks have become more and more important, evolving into a powerful tool to implement learning algorithms. Spiking neural networks represent the third generation of Artificial Neural Networks; they have earned growing significance due to their remarkable achievements in pattern recognition, finding extensive utility across diverse domains such as e.g. diagnostic medicine. Usually, Spiking Neural Networks are slightly less accurate than other Artificial Neural Networks, but they require a reduced amount of energy to perform calculations; this amount of energy further reduces in a very significant manner if they are implemented on hardware specifically designed for them, like neuromorphic hardware. In this work, we focus on exploring the versatility of Spiking Neural Networks and their potential applications across a range of scenarios by exploiting their adaptability and dynamic processing capabilities, which make them suitable for various tasks. A first rough network is designed based on the dataset's general attributes; the network is then refined through an extensive grid search algorithm to identify the optimal values for hyperparameters. This dual-step process ensures that the Spiking Neural Network can be tailored to diverse and potentially very different situations in a direct and intuitive manner. We test this by considering three different scenarios: epileptic seizure detection, both considering binary and multi-classification tasks, as well as wine classification. The proposed methodology turned out to be highly effective in binary class scenarios: the Spiking Neural Networks models achieved significantly lower energy consumption compared to Artificial Neural Networks while approaching nearly 100% accuracy. In the case of multi-class classification, the model achieved an accuracy of approximately 90%, thus indicating that it can still be further improved.

We determine the exact value of the Wiener index, the edge-Wiener index, and the vertex-edge-Wiener index of the Basilica graphs, i.e., the sequence of finite Schreier graphs associated with the action of the Basilica group on the rooted binary tree. Moreover, we give a formula for the total distance of every vertex in the Basilica graphs, and we are able to make it explicit for some special vertices. We finally introduce the notions of asymptotic Wiener index and asymptotic total distance, which are compatible with that of convergence of the sequence of finite Basilica graphs to an infinite orbital limit graph in the Gromov–Hausdorff topology: the asymptotic values are explicitly computed.