Related papers: Explaining the Entombed Algorithm
Several modifications of the famous mathematical Game of Life are introduced by making Game of Life rules stochastic and mutual influence of cells in their 8-neighborhood on a rectangular lattice spatially non-uniform. Results are reported…
In this paper we present efficient algorithmic solutions for several constrained resource allocation, management and discovery problems. We consider new types of resource allocation models and constraints, and we present new geometric…
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…
Recent work has proven the existence of extreme inbreeding in a European ancestry sample taken from the contemporary UK population \cite{nature_01}. This result brings our attention again to a math problem related to inbreeding family trees…
This paper studies a large class of two-player perfect-information turn-based parity games on infinite graphs, namely those generated by collapsible pushdown automata. The main motivation for studying these games comes from the connections…
In [2] it was proven that the Cass algorithm is a polynomial-time algorithm for constructing level<=2 networks from clusters. Here we demonstrate, for each k>=0, a polynomial-time algorithm for constructing level-k phylogenetic networks…
Two-dimensional constrained coding is a problem that is much more difficult than its one-dimensional counterpart. Indeed, in two dimensions, obtaining the answers to very natural questions becomes uncomputable. In particular, it is…
Tandem duplication is an evolutionary process whereby a segment of DNA is replicated and proximally inserted. The different configurations that can arise from this process give rise to some interesting combinatorial questions. Firstly, we…
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…
This book summarizes ongoing research introducing probability space isomorphic mappings into the strategy spaces of game theory. This approach is motivated by discrepancies between probability theory and game theory when applied to the same…
Schemata theory, Markov chains, and statistical mechanics have been used to explain how evolutionary algorithms (EAs) work. Incremental success has been achieved with all of these methods, but each has been stymied by limitations related to…
The practice of evolutionary algorithms involves the tuning of many parameters. How big should the population be? How many generations should the algorithm run? What is the (tournament selection) tournament size? What probabilities should…
Many popular video games use pseudorandom number generators to create randomly distributed locations for game objects as highly unpredictable as possible. Some scenarios like game competition also need reproducible randomness, namely the…
Asking questions is a pervasive human activity, but little is understood about what makes them difficult to answer. An analysis of a pair of large databases, of New York Times crosswords and questions from the quiz-show Jeopardy,…
Embedding tables are used by machine learning systems to work with categorical features. In modern Recommendation Systems, these tables can be very large, necessitating the development of new methods for fitting them in memory, even during…
Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutorial provides a…
Tree ensembles (TEs) find a multitude of practical applications. They represent one of the most general and accurate classes of machine learning methods. While they are typically quite concise in representation, their operation remains…
Results of experimental investigation are presented of evolutionary dynamics of several stochastic pattern formation and growth models designed by modifications of the famous mathematical Game of Life. The modifications are two-fold: Game…
An unconstrained crossword puzzle is a generalization of the constrained crossword problem. In this problem, only the word vocabulary, and optionally the grid dimensions are known. Hence, it not only requires the algorithm to determine the…
It is well known, and appreciated, that quantum computers have the potential to be the most powerful computational devices ever created. This newfound power comes from a quantum parallelism effect that allows the computer to be in multiple…