Best Response Games on Regular Graphs

With the growth of the internet it is becoming increasingly important to understand how the behaviour of players is affected by the topology of the network interconnecting them. Many models which involve networks of interacting players have been proposed and best response games are amongst the simplest. In best response games each vertex simultaneously updates to employ the best response to their current surroundings. We concentrate upon trying to understand the dynamics of best response games on regular graphs with many strategies. When more than two strategies are present highly complex dynamics can ensue. We focus upon trying to understand exactly how best response games on regular graphs sample from the space of possible cellular automata. To understand this issue we investigate convex divisions in high dimensional space and we prove that almost every division of $k-1$ dimensional space into $k$ convex regions includes a single point where all regions meet. We then find connections between the convex geometry of best response games and the theory of alternating circuits on graphs. Exploiting these unexpected connections allows us to gain an interesting answer to our question of when cellular automata are best response games

Complex Networks from Simple Rewrite Systems

Complex networks are all around us, and they can be generated by simple mechanisms. Understanding what kinds of networks can be produced by following simple rules is therefore of great importance. We investigate this issue by studying the dynamics of extremely simple systems where are `writer' moves around a network, and modifies it in a way that depends upon the writer's surroundings. Each vertex in the network has three edges incident upon it, which are colored red, blue and green. This edge coloring is done to provide a way for the writer to orient its movement. We explore the dynamics of a space of 3888 of these `colored trinet automata' systems. We find a large variety of behaviour, ranging from the very simple to the very complex. We also discover simple rules that generate forms which are remarkably similar to a wide range of natural objects. We study our systems using simulations (with appropriate visualization techniques) and analyze selected rules mathematically. We arrive at an empirical classification scheme which reveals a lot about the kinds of dynamics and networks that can be generated by these systems

Evaluating Stationary Distribution of the Binary GA Markov Chain in Special Cases

The evolutionary algorithm stochastic process is well-known to be Markovian. These have been under investigation in much of the theoretical evolutionary computing research. When mutation rate is positive, the Markov chain modeling an evolutionary algorithm is irreducible and, therefore, has a unique stationary distribution, yet, rather little is known about the stationary distribution. On the other hand, knowing the stationary distribution may provide some information about the expected times to hit optimum, assessment of the biases due to recombination and is of importance in population genetics to assess what\u27s called a ``genetic load" (see the introduction for more details). In this talk I will show how the quotient construction method can be exploited to derive rather explicit bounds on the ratios of the stationary distribution values of various subsets of the state space. In fact, some of the bounds obtained in the current work are expressed in terms of the parameters involved in all the three main stages of an evolutionary algorithm: namely selection, recombination and mutation. I will also discuss the newest developments which may allow for further improvements of the bound

A Version of Geiringer-like Theorem for Decision Making in the Environments with Randomness and Incomplete Information

Purpose: In recent years Monte-Carlo sampling methods, such as Monte Carlo tree search, have achieved tremendous success in model free reinforcement learning. A combination of the so called upper confidence bounds policy to preserve the "exploration vs. exploitation" balance to select actions for sample evaluations together with massive computing power to store and to update dynamically a rather large pre-evaluated game tree lead to the development of software that has beaten the top human player in the game of Go on a 9 by 9 board. Much effort in the current research is devoted to widening the range of applicability of the Monte-Carlo sampling methodology to partially observable Markov decision processes with non-immediate payoffs. The main challenge introduced by randomness and incomplete information is to deal with the action evaluation at the chance nodes due to drastic differences in the possible payoffs the same action could lead to. The aim of this article is to establish a version of a theorem that originated from population genetics and has been later adopted in evolutionary computation theory that will lead to novel Monte-Carlo sampling algorithms that provably increase the AI potential. Due to space limitations the actual algorithms themselves will be presented in the sequel papers, however, the current paper provides a solid mathematical foundation for the development of such algorithms and explains why they are so promising.Comment: 53 pages in size. This work has been recently submitted to the IJICC (International Journal on Intelligent Computing and Cybernetics

Majority dynamics with one nonconformist

We consider a system in which a group of agents represented by the vertices of a graph synchronously update their opinion based on that of their neighbours. If each agent adopts a positive opinion if and only if that opinion is sufficiently popular among his neighbours, the system will eventually settle into a fixed state or alternate between two states. If one agent acts in a different way, other periods may arise. We show that only a small number of periods may arise if natural restrictions are placed either on the neighbourhood structure or on the way in which the nonconforming agent may act; without either of these restrictions any period is possible

The practicalities of adapting UK maternity clinical information systems for observational research: Experiences of the POOL study

Background Using routinely collected clinical data for observational research is an increasingly important method for data collection, especially when rare outcomes are being explored. The POOL study was commissioned to evaluate the safety of waterbirth in the UK using routine maternity and neonatal clinical data. This paper describes the design, rationale, set-up and pilot for this data linkage study using bespoke methods. Methods Clinical maternity information systems hold many data items of value for research purposes, but often lack specific data items required for individual studies. This study used the novel method of amending an existing clinical maternity database for the purpose of collecting additional research data fields. In combination with the extraction of existing data fields, this maximised the potential use of existing routinely collected clinical data for research purposes, whilst reducing NHS staff data collection burden. Wellbeing Software® provider of the Euroking® Maternity Information System, added new study specific data fields to their information system, extracted data from participating NHS sites and transferred data for matching with the National Neonatal Research Database to ascertain outcomes for babies admitted to neonatal units. Study set-up processes were put in place for all sites. The data extraction, linkage and cleaning processes were piloted with one pre-selected NHS site. Results Twenty-six NHS sites were set-up over 27 months (January 2019 - April 2021). Twenty-four thousand maternity records were extracted from the one NHS site, pertaining to the period January 2015 to March 2019. Data field completeness for maternal and neonatal primary outcomes were mostly acceptable. Neonatal identifiers flowed to the National Neonatal Research Database for successful matching and linkage between maternity and neonatal unit records. Discussion Piloting the data extraction and linkage highlighted the need for additional governance arrangements, training at NHS sites and new processes for the study team to ensure data quality and confidentiality are upheld during the study. Amending existing NHS electronic information systems and accessing clinical data at scale, is possible, but continues to be a time consuming and a technically challenging exercise

Association of cannabis, cannabidiol and synthetic cannabinoid use with mental health in UK adolescents

No abstract available