相关论文: The Struggles of Chessland
Wonderland, a compact, integrated economic, demographic and environmental model is investigated using methods developed for studying critical phenomena. Simulation results show the parameter space separates into two phases, one of which…
The ability of machines to grasp spatial understanding within narrative contexts is an intriguing aspect of reading comprehension that continues to be studied. Motivated by the goal to test the AI's competence in understanding the…
In this paper we review some of the main results obtained in the field of truels. A "truel" is a generalization of a duel involving three players. Depending on the rules used for chosing the players, we may distinguish between the random,…
Since the mathematicians of ancient Greece until Fermat, since Gauss until today; the way how the primes along the numerical straight line are distributed has become perhaps the most difficult math problem; many people believe that their…
Magic: the Gathering is a popular and famously complicated card game about magical combat. Recently, several authors including Chatterjee and Ibsen-Jensen (2016) and Churchill, Biderman, and Herrick (2019) have investigated the…
It is a story about the problem whether folding a square on the plane can increase its perimeter. The paper is written primary for school students.
The dynamics in three-dimensional billiards leads, using a Poincar\'e section, to a four-dimensional map which is challenging to visualize. By means of the recently introduced 3D phase-space slices an intuitive representation of the…
A metric space $\mathcal{T}$ is a \emph{real tree} if for any pair of points $x, y \in \mathcal{T}$ all topological embeddings $\sigma$ of the segment $[0,1]$ into $\mathcal{T}$, such that $\sigma (0)=x$ and $\sigma (1)=y$, have the same…
Jigsaw percolation is a model for the process of solving puzzles within a social network, which was recently proposed by Brummitt, Chatterjee, Dey and Sivakoff. In the model there are two graphs on a single vertex set (the `people' graph…
Reasoning is an essential skill to enable Large Language Models (LLMs) to interact with the world. As tasks become more complex, they demand increasingly sophisticated and diverse reasoning capabilities for sequential decision-making,…
Finding, counting and/or listing triangles (three vertices with three edges) in large graphs are natural fundamental problems, which received recently much attention because of their importance in complex network analysis. We provide here a…
Successful and accurate modelling of level difficulty is a fundamental component of the operationalisation of player experience as difficulty is one of the most important and commonly used signals for content design and adaptation. In games…
Cryptography has a pivotal role in securing our digital world. Nonetheless, it is a challenging topic to learn. In this paper, we show that despite its complex nature, dyslexia$-$a learning disorder that influences reading and writing…
We introduce a novel metric to quantify the fragility of chess positions using the interaction graph of pieces. This fragility score $F$ captures the tension within a position and serves as a strong indicator of tipping points in a game. In…
In many schools throughout the United States, it is customary to hold a yearly "Secret Santa" event. With the approach of Christmas, all the students place their names in a hat; each student, in turn, draws a name out of the hat, thus…
We propose a neural network-based approach to calculate the value of a chess square-piece combination. Our model takes a triplet (Color, Piece, Square) as an input and calculates a value that measures the advantage/disadvantage of having…
The network coloring game has been proposed in the literature of social sciences as a model for conflict-resolution circumstances. The players of the game are the vertices of a graph with $n$ vertices and maximum degree $\Delta$. The game…
All human societies present unique narratives that shape their customs and beliefs. Despite cultural differences, some symbolic elements (e.g., heroes and tricksters) are common across many cultures. Here, we reconcile these seemingly…
Warnsdorffs rule for a knights tour is a heuristic, i.e., it is a rule that does not produce the desired result all the time. It is a classic example of a greedy method in that it is based on a series of locally optimal choices. This note…
AI research in chess has been primarily focused on producing stronger agents that can maximize the probability of winning. However, there is another aspect to chess that has largely gone unexamined: its aesthetic appeal. Specifically, there…