Related papers: General Board Geometry
We study topological properties of the graph topology.
We consider multi-player games played on graphs, in which the players aim at fulfilling their own (not necessarily antagonistic) objectives. In the spirit of evolutionary game theory, we suppose that the players have the right to repeatedly…
Go gaming is a struggle for territory control between rival, black and white, stones on a board. We model the Go dynamics in a game by means of the Ising model whose interaction coefficients reflect essential rules and tactics employed in…
In cooperative games, the core is the most popular solution concept, and its properties are well known. In the classical setting of cooperative games, it is generally assumed that all coalitions can form, i.e., they are all feasible. In…
Game engines support video game development by providing functionalities such as graphics rendering or input/output device management. However, their architectures are often overlooked, which hinders their integration and extension. In this…
A signed graph has edge signs. A gain graph has oriented edge gains drawn from a group. We define the combination of the two for the abelian case, in which each oriented edge of a signed graph has a gain from an abelian group, concentrating…
Given a graph G with n vertices and k players, each of which is placing a facility on one of the vertices of G, we define the score of the i'th player to be the number of vertices for which, among all players, the facility placed by the…
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…
This is an expository article on the theory of algebraic stacks. After introducing the general theory, we concentrate in the example of the moduli stack of vector budles, giving a detailed comparison with the moduli scheme obtained via…
A bidimensional representation of the space of 2x2 Symmetric Games in the strategic representation is proposed. This representation provides a tool for the classification of 2x2 symmetric games, quantification of the fraction of them having…
We consider Schmidt's game on the space of compact subsets of a given metric space equipped with the Hausdorff metric, and the space of continuous functions equipped with the supremum norm. We are interested in determining the generic…
Video game playing is an extremely structured domain where algorithmic decision-making can be tested without adverse real-world consequences. While prevailing methods rely on image inputs to avoid the problem of hand-crafting state space…
By making use of the greatest common divisor's ($gcd$) properties we can highlight some connections between playing billiard inside a unit square and the Fibonacci sequence as well as the Euclidean algorithm. In particular by defining two…
We discuss here geometric structures of condensed matters by means of a fundamental topological method. Any geometric pattern can be universally represented by a decomposition space of a topological space consisting of the infinite product…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…
This thesis presents some geometric insights into three different types of two player prediction games -- namely general learning task, prediction with expert advice, and online convex optimization. These games differ in the nature of the…
Artificial general intelligence (AGI) refers to research aimed at tackling the full problem of artificial intelligence, that is, create truly intelligent agents. This sets it apart from most AI research which aims at solving relatively…
Graphs provide a powerful framework for modeling complex systems, but their structural variability poses significant challenges for analysis and classification. To address these challenges, we introduce GAUDI (Graph Autoencoder Uncovering…
In the present note we describe geometrically the homology classes in the total space of a surface bundle over a surface in terms of the holonomy map. We treat the cases where the base surface is closed or has one boundary component. We…
We present the Boolean dimension of a graph, we relate it with the notions of inner, geometric and symplectic dimensions, and with the rank and minrank of a graph. We obtain an exact formula for the Boolean dimension of a tree in terms of a…