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Our ability to know when to trust the decisions made by machine learning systems has not kept up with the staggering improvements in their performance, limiting their applicability in high-stakes domains. We introduce Prover-Verifier Games…
The game industry is moving into an era where old-style game engines are being replaced by re-engineered systems with embedded machine learning technologies for the operation, analysis and understanding of game play. In this paper, we…
Systems of cooperation and interaction are usually studied in the context of real or complex vector spaces. Additional insight, however, is gained when such systems are represented in vector spaces with multiplicative structures, i.e., in…
Scientific research involves mathematical modelling in the context of an interactive balance between theory, experiment and computation. However, computational methods and tools are still far from being appropriately integrated in the high…
This document focuses on modeling a complex situations to achieve an advantage within a competitive context. Our goal is to devise the characteristics of games to teach and exercise non-easily quantifiable tasks crucial to the math-modeling…
The need for data preservation and reproducible research is widely recognized in the scientific community. Yet, researchers often struggle to find the motivation to contribute to data repositories and to use tools that foster…
As intelligent systems gain autonomy and capability, it becomes vital to ensure that their objectives match those of their human users; this is known as the value-alignment problem. In robotics, value alignment is key to the design of…
Interacting with human agents in complex scenarios presents a significant challenge for robotic navigation, particularly in environments that necessitate both collision avoidance and collaborative interaction, such as indoor spaces. Unlike…
In active visual tracking, it is notoriously difficult when distracting objects appear, as distractors often mislead the tracker by occluding the target or bringing a confusing appearance. To address this issue, we propose a mixed…
This article introduces a pedagogical method for {\it solving combinatorial problems} that frequently involve structures that are unfamiliar or less familiar. Indeed, an indirect method has been proposed in order to evade any possible…
Physics instructors often rely on demonstrations when teaching, using real-time examples to appeal to student intuition or tinkering with a physical system to develop a deeper and more natural understanding of a topic. However, some…
This paper introduces a card game called "Quark Matter Card Games," inspired by the creativity of a high school student, Csaba T\"or\"ok, and developed in collaboration with physicist Tam\'as Cs\"org\H{o}. The game utilizes a deck of 66…
As artificial intelligence systems become increasingly prevalent in education, a fundamental challenge emerges: how can we verify if an AI truly understands how students think and reason? Traditional evaluation methods like measuring…
In this paper, we introduce a framework of new mathematical representation of Game Theory, including static classical game and static quantum game. The idea is to find a set of base vectors in every single-player strategy space and to…
Strong foundations in basic AI techniques are key to understanding more advanced concepts. We believe that introducing AI techniques, such as search methods, early in higher education helps create a deeper understanding of the concepts seen…
Successfully navigating a complex environment to obtain a desired outcome is a difficult task, that up to recently was believed to be capable only by humans. This perception has been broken down over time, especially with the introduction…
This paper introduces an educational card game designed to elucidate fundamental particle physics concepts, specifically emphasizing the classification of hadrons through the "Eightfold Path." Derived from the Quark Matter Card Games…
We explore how to build a vector field from the various functions involved in a given mathematical program, and show that locally-stable equilibria of the underlying dynamical system are precisely the local solutions of the optimization…
We describe a variant of the popular game "Pictionary" based on terms used in elementary and high school physics. We believe that drawing of physical terms helps students develop a deeper understanding of physical concepts behind them, as…
Children learn though play. We introduce the analogous idea of learning programs through play. In this approach, a program induction system (the learner) is given a set of tasks and initial background knowledge. Before solving the tasks,…