Related papers: Explaining the Entombed Algorithm
We investigate combinatorial issues relating to the use of random orbit approximations to the attractor of an iterated function system with the aim of clarifying the role of the stochastic process during generation the orbit. A Baire…
Network embedding which encodes all vertices in a network as a set of numerical vectors in accordance with it's local and global structures, has drawn widespread attention. Network embedding not only learns significant features of a…
Genetic programming is the practice of evolving formulas using crossover and mutation of genes representing functional operations. Motivated by genetic evolution we develop and solve two combinatorial games, and we demonstrate some…
We propose a randomized algorithm for enumerating the vertices of a zonotope, which is a low-dimensional linear projection of a hypercube. The algorithm produces a pair of the zonotope's vertices by sampling a random linear combination of…
Since the advent of computers, many tasks which required humans to spend a lot of time and energy have been trivialized by the computers' ability to perform repetitive tasks extremely quickly. Playing chess is one such task. It was one of…
In this paper, we study the generation of entanglement in a double-$\Lambda $ system. Employing standard method of laser theory, we deduce the dynamic evolution equation of the two-mode field. We analyze the available entanglement criterion…
Conditional neural text generation models generate high-quality outputs, but often concentrate around a mode when what we really want is a diverse set of options. We present a search algorithm to construct lattices encoding a massive number…
Topological Ramsey theory studies a class of combinatorial topological spaces, known as topological Ramsey spaces, unifying the essential features of those combinatorial frames where the Ramsey property is equivalent to the Baire property.…
The infinite time-evolving block decimation (iTEBD) algorithm [Phys. Rev. Lett. 98, 070201 (2007)] allows to simulate unitary evolution and to compute the ground state of one-dimensional quantum lattice systems in the thermodynamic limit.…
We tackle the task of Term Set Expansion (TSE): given a small seed set of example terms from a semantic class, finding more members of that class. The task is of great practical utility, and also of theoretical utility as it requires…
We propose a new task in the area of computational creativity: acrostic poem generation in English. Acrostic poems are poems that contain a hidden message; typically, the first letter of each line spells out a word or short phrase. We…
Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium…
I consider motivation and value-alignment in AI systems from the perspective of (constrained) entropy maximization. Though the structures encoding knowledge in any physical system can be understood as energetic constraints, only living…
Black box systems for automated decision making, often based on machine learning over (big) data, map a user's features into a class or a score without exposing the reasons why. This is problematic not only for lack of transparency, but…
Random magnetic field configurations are ubiquitous in nature. Such fields lead to a variety of dynamical phenomena, including localization and glassy physics in some condensed matter systems and novel transport processes in astrophysical…
In this paper the results of a simulation of a prisoner's dilemma robin-round tournament are presented. In the tournament each participating strategy plays an iterated prisoner's dilemma against each other strategy (round-robin) and as a…
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
Cryptic crossword clues are challenging language tasks for which new test sets are released daily by major newspapers on a global basis. Each cryptic clue contains both the definition of the answer to be placed in the crossword grid (in…
Recent studies have suggested that Large Language Models (LLMs) could provide interesting ideas contributing to mathematical discovery. This claim was motivated by reports that LLM-based genetic algorithms produced heuristics offering new…
The Axelrod library is an open source Python package that allows for reproducible game theoretic research into the Iterated Prisoner's Dilemma. This area of research began in the 1980s but suffers from a lack of documentation and test code.…