DigiPen Institute of Technology

We prove the equivalence between Takagi-Sugeno-Kang (TSK) fuzzy systems and neural networks with ReLU activation function in two or more dimensions. The TSK fuzzy systems considered will have tetrahedral membership functions for their antecedents and singleton outputs. We show an example of a fuzzy system that is locally equivalent to a neural network based on the proposed method, and we discuss the potential to provide a local analysis to explain the decision process of neural networks.

Abstract. The results of prior research investigating whether the violence in violent video games leads to increased subsequent aggression are mixed. Some observers question whether the difficulty and/or the competitive aspects of these games are important, but overlooked, factors that also affect aggression. In the present study, participants ( N = 408) played a violent or nonviolent video game that was either difficult or easy and in which they competed and won, competed and lost, or did not compete against another player. Results revealed that participants became more aggressive only after playing a competitive, as opposed to a noncompetitive, game. Level of violence, winning or losing, and game difficulty did not have any significant effect. These results support the assertion that competition in video games has an independent and significant effect on subsequent aggression beyond violent content and game difficulty.

Most violent video game (VVG) research focuses on aggressive behaviors as the primary outcome variable of interest. Using pro-social behavior as the dependent variable, this study explores factors beyond VVG content as a contributing factor to player outcomes. Participants were randomly assigned to play VVG or non-VVG content with viewing screens obstructed by large pieces of paper to increase difficulty, or unobstructed. Screen condition accounted for 34.5% of the variance in pro-social behavior of helping to retrieve spilled pens. Players in obstructed viewing conditions experienced more in-game losses and engaged in significantly less helping behavior. Fewer pens were retrieved by participants in obstructed viewing conditions while playing either a VVG or non-VVG. The present study cautions against generalized assumptions that VVG content is a primary determinant of behavior and underscores the role of important contextual factors like failure and achievement loss to consider in future studies of this nature.

The question of whether a noncommutative graded quotient singularity $A^G$ is isolated depends on a subtle invariant of the $G$-action on $A$, called the pertinency. We prove a partial dichotomy theorem for isolatedness, which applies to a family of noncommutative quotient singularities arising from a graded cyclic action on the $(-1)$-skew polynomial ring. Our results generalize and extend some results of Bao, He and the third-named author and results of Gaddis, Kirkman, Moore and Won.

In this paper new interpretable neural network architectures are proposed. A Neural Network with sigmoid activation function is converted into a sigmoid-based approximation operator, which, at its turn, can be approximated by a fuzzy system of Takagi-Sugeno type. Altogether this process shows that a neural network with sigmoid activation functions can be approximated by a Takagi-Sugeno fuzzy system. As the TS fuzzy system provides interpretability, while Neural Networks provide approximation capability, we obtain a novel interpretable Neural Network Architecture. Interpretability of the TS fuzzy system can provide insights into data in a new way, enhancing decision making.

Abstract We investigate magnetic effects in correspondence of the Mw6.1 L'Aquila earthquake. Magnetic and seismic records are analyzed. Rapid and distinct changes and an offset can be seen in magnetic field components after the main shock. We show that these effects result from electromagnetic induction due to the movement of the sensors through the Earth's magnetic field and from a permanent displacement of the sensors from their original position caused by the passing seismic waves. A transient signal in total field data from an overhauser magnetometer apparently occurs in correspondence with the earthquake. Our analysis shows that the transient was not observed by other sensors that were operating in close proximity to the overhauser. Thus, the transient signal in the total magnetic field data, and the offset in the magnetic field components, cannot be associated with a hypothetical underground electric current generated by the earthquake, as suggested by Nenovski (2015).

Starting from the classical Weierstrass functions, in this chapter we introduce the so-called Weierstrass functions of max-product type, for which we prove that the set of the points of non-differentiability is uncountable, nowhere dense and of Lebesgue measure 0. Also, the fractal properties of these functions are studied.