Effective Human-Machine Interaction (HMI) depends on accurately capturing and interpreting information from the human user. For systems relying on hand-based operation, understanding the limits of human cognitive-motor abilities is crucial to designing intuitive and efficient interfaces. This study presents an experimental setup involving four analog buttons with a minimally complex control, where human hand performance is assessed through simultaneous multi-finger Fitts' Law tasks. Initially, task difficulty was assumed to be computed by summing the individual indices of difficulty for each button, which resulted in peak throughput performance with two fingers. However, this approach did not align with Fitts' Law. By applying a weighted summation, with weights based on the variation of distances within a task, the difficulty measure better conformed to Fitts' Law, and the highest throughput was achieved with a single finger. These findings highlight the interdependence in multi-finger movement complexity and emphasize the importance of considering cognitive-motor limitations when designing HMI interfaces to optimize user performance.

In this thesis we have looked into the complexity of neural networks. Especially convolutional neural networks (CNNs), which are useful for image recognition, are looked into. In order to better understand the process in the neural networks, in the first half of this report a mathematical foundation for neural networks and CNNs is constructed. After this, during different experiments on a simple CNN, a better understanding of the variables that can be chosen for the network is gained. In the first experiment the network was trained on two translated images of a cat in order to test the common believe that CNNs are translation invariant. The result of this experiment refuted this believe and led to the understanding of translation equivariance, with which translation invariance often is confused. After this, the network was trained to learn the difference between a cat and a dog. From this, it appeared that the network can become translation invariant if the right training data is chosen. Also, a look was taken at the kernels of the convolution layer and the feature maps they produce. Finally, there was looked into an other transformation of the images, namely rotation. This led to the idea that the resolution of the images has influence on classifying the rotated cats and dogs.