On 1-factorizations of Bipartite Kneser Graphs

It is a challenging open problem to construct an explicit 1-factorization of the bipartite Kneser graph $H(v,t)$, which contains as vertices all $t$-element and $(v-t)$-element subsets of $[v]:=\{1,\ldots,v\}$ and an edge between any two vertices when one is a subset of the other. In this paper, we propose a new framework for designing such 1-factorizations, by which we solve a nontrivial case where $t=2$ and $v$ is an odd prime power. We also revisit two classic constructions for the case $v=2t+1$ --- the \emph{lexical factorization} and \emph{modular factorization}. We provide their simplified definitions and study their inner structures. As a result, an optimal algorithm is designed for computing the lexical factorizations. (An analogous algorithm for the modular factorization is trivial.)Comment: We design the first explicit 1-factorization of H(2,q), where q is a odd prime powe

Bears with Hats and Independence Polynomials

Consider the following hat guessing game. A bear sits on each vertex of a graph $G$, and a demon puts on each bear a hat colored by one of $h$ colors. Each bear sees only the hat colors of his neighbors. Based on this information only, each bear has to guess $g$ colors and he guesses correctly if his hat color is included in his guesses. The bears win if at least one bear guesses correctly for any hat arrangement. We introduce a new parameter - fractional hat chromatic number $\hat{\mu}$, arising from the hat guessing game. The parameter $\hat{\mu}$ is related to the hat chromatic number which has been studied before. We present a surprising connection between the hat guessing game and the independence polynomial of graphs. This connection allows us to compute the fractional hat chromatic number of chordal graphs in polynomial time, to bound fractional hat chromatic number by a function of maximum degree of $G$, and to compute the exact value of $\hat{\mu}$ of cliques, paths, and cycles

Generating and Adapting to Diverse Ad-Hoc Cooperation Agents in Hanabi

Hanabi is a cooperative game that brings the problem of modeling other players to the forefront. In this game, coordinated groups of players can leverage pre-established conventions to great effect, but playing in an ad-hoc setting requires agents to adapt to its partner's strategies with no previous coordination. Evaluating an agent in this setting requires a diverse population of potential partners, but so far, the behavioral diversity of agents has not been considered in a systematic way. This paper proposes Quality Diversity algorithms as a promising class of algorithms to generate diverse populations for this purpose, and generates a population of diverse Hanabi agents using MAP-Elites. We also postulate that agents can benefit from a diverse population during training and implement a simple "meta-strategy" for adapting to an agent's perceived behavioral niche. We show this meta-strategy can work better than generalist strategies even outside the population it was trained with if its partner's behavioral niche can be correctly inferred, but in practice a partner's behavior depends and interferes with the meta-agent's own behavior, suggesting an avenue for future research in characterizing another agent's behavior during gameplay.Comment: arXiv admin note: text overlap with arXiv:1907.0384

On the beliefs off the path: equilibrium refinement due to quantal response and level-k

This paper studies the relevance of equilibrium and nonequilibrium explanations of behavior, with respects to equilibrium refinement, as players gain experience. We investigate this experimentally using an incomplete information sequential move game with heterogeneous preferences and multiple perfect equilibria. Only the limit point of quantal response (the limiting logit equilibrium), and alternatively that of level-k reasoning (extensive form rationalizability), restricts beliefs off the equilibrium path. Both concepts converge to the same unique equilibrium, but the predictions differ prior to convergence. We show that with experience of repeated play in relatively constant environments, subjects approach equilibrium via the quantal response learning path. With experience spanning also across relatively novel environments, though, level-k reasoning tends to dominate

A Computational Model of Creative Design as a Sociocultural Process Involving the Evolution of Language

The aim of this research is to investigate the mechanisms of creative design within the context of an evolving language through computational modelling. Computational Creativity is a subfield of Artificial Intelligence that focuses on modelling creative behaviours. Typically, research in Computational Creativity has treated language as a medium, e.g., poetry, rather than an active component of the creative process. Previous research studying the role of language in creative design has relied on interviewing human participants, limiting opportunities for computational modelling. This thesis explores the potential for language to play an active role in computational creativity by connecting computational models of the evolution of artificial languages and creative design processes. Multi-agent simulations based on the Domain-Individual-Field-Interaction framework are employed to evolve artificial languages with features that may support creative designing including ambiguity, incongruity, exaggeration and elaboration. The simulation process consists of three steps: (1) constructing representations associating topics, meanings and utterances; (2) structured communication of utterances and meanings through the playing of “language games”; and (3) evaluation of design briefs and works. The use of individual agents with different evaluation criteria, preferences and roles enriches the scope and diversity of the simulations. The results of the experiments conducted with artificial creative language systems demonstrate the expansion of design spaces by generating compositional utterances representing novel concepts among design agents using language features and weighted context free grammars. They can be used to computationally explore the roles of language in creative design, and possibly point to computational applications. Understanding the evolution of artificial languages may provide insights into human languages, especially those features that support creativity

Instruction effects on randomness in sequence generation

Randomness is a fundamental property of human behavior. It occurs both in the form of intrinsic random variability, say when repetitions of a task yield slightly different behavioral outcomes, or in the form of explicit randomness, say when a person tries to avoid being predicted in a game of rock, paper and scissors. Randomness has frequently been studied using random sequence generation tasks (RSG). A key finding has been that humans are poor at deliberately producing random behavior. At the same time, it has been shown that people might be better randomizers if randomness is only an implicit (rather than an explicit) requirement of the task. We therefore hypothesized that randomization performance might vary with the exact instructions with which randomness is elicited. To test this, we acquired data from a large online sample (n = 388), where every participant made 1,000 binary choices based on one of the following instructions: choose either randomly, freely, irregularly, according to an imaginary coin toss or perform a perceptual guessing task. Our results show significant differences in randomness between the conditions as quantified by conditional entropy and estimated Markov order. The randomization scores were highest in the conditions where people were asked to be irregular or mentally simulate a random event (coin toss) thus yielding recommendations for future studies on randomization behavior

Cooperation in social groups: reactions to (moral) deviants

The present dissertation examines the influence of self-involvement with perpetrators and victims on third-party reactions to deviants. Dealing with others’ social behaviors regulates social life and successful cooperation between interaction partners. Third-party reactions to deviants are sensitive to group context, and thereby more likely to protect ingroup interests. Such biased reactions raise the question of how much they are triggered by involvement (i.e., shared group membership, empathy) with perpetrators or victims of deviance. Three reported lines of research extend the current knowledge on cognitive (memory), emotional (anger), and behavioral (punishment) reactions to deviance within and between social groups. Research Line I examined whether accurate memory for persons’ social behavior is group-specific. The reported studies show that deviant ingroup members are remembered better than other ingroup and outgroup members (uncooperative or cheating). Guessing behavior indicates that participants assumed more cooperative ingroup members than outgroup members. Research Line II investigated whether involvement with victims is crucial for anger about deviance. Results show that the wrongfulness (i.e., perpetrator’s intentions) elicits more anger than the harmfulness (i.e., consequences for a cared-for-other) of deviance. Research Line III examined how involvement with perpetrators or victims influences anger and punishment of deviance. Anger and (altruistic) punishment emerge consistently as responses to unfairness, even in outgroup interactions. Negative reactions to ingroup perpetrators and victims varies with the contextual settings of the studies. Taken together, memory, anger, and punishment are sensitive to perpetrators’ and victims’ group memberships, and also emerge irrespective of self-involvement. The discussion addresses how such reactions facilitate social life and cooperation in groups

The Missouri Miner, October 07, 1970

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