Moment Closure - A Brief Review

Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation describes the evolution of one "moment", a suitable coarse-grained quantity computable from the full state space. If the system is too large for analytical and/or numerical methods, then one aims to reduce it by finding a moment closure relation expressing "higher-order moments" in terms of "lower-order moments". In this brief review, we focus on highlighting how moment closure methods occur in different contexts. We also conjecture via a geometric explanation why it has been difficult to rigorously justify many moment closure approximations although they work very well in practice.Comment: short survey paper (max 20 pages) for a broad audience in mathematics, physics, chemistry and quantitative biolog

Virtual player design using self-learning via competitive coevolutionary algorithms

The Google Artificial Intelligence (AI) Challenge is an international contest the objective of which is to program the AI in a two-player real time strategy (RTS) game. This AI is an autonomous computer program that governs the actions that one of the two players executes during the game according to the state of play. The entries are evaluated via a competition mechanism consisting of two-player rounds where each entry is tested against others. This paper describes the use of competitive coevolutionary (CC) algorithms for the automatic generation of winning game strategies in Planet Wars, the RTS game associated with the 2010 contest. Three different versions of a prime algorithm have been tested. Their common nexus is not only the use of a Hall-of-Fame (HoF) to keep note of the winners of past coevolutions but also the employment of an archive of experienced players, termed the hall-of-celebrities (HoC), that puts pressure on the optimization process and guides the search to increase the strength of the solutions; their differences come from the periodical updating of the HoF on the basis of quality and diversity metrics. The goal is to optimize the AI by means of a self-learning process guided by coevolutionary search and competitive evaluation. An empirical study on the performance of a number of variants of the proposed algorithms is described and a statistical analysis of the results is conducted. In addition to the attainment of competitive bots we also conclude that the incorporation of the HoC inside the primary algorithm helps to reduce the effects of cycling caused by the use of HoF in CC algorithms.This work is partially supported by Spanish MICINN under Project ANYSELF (TIN2011-28627-C04-01),3 by Junta de Andalucía under Project P10-TIC-6083 (DNEMESIS) and by Universidad de Málaga, Campus de Excelencia Internacional Andalucía Tech

Procedural Content Generation for Real-Time Strategy Games

Videogames are one of the most important and profitable sectors in the industry of entertainment. Nowadays, the creation of a videogame is often a large-scale endeavor and bears many similarities with, e.g., movie production. On the central tasks in the development of a videogame is content generation, namely the definition of maps, terrains, non-player characters (NPCs) and other graphical, musical and AI-related components of the game. Such generation is costly due to its complexity, the great amount of work required and the need of specialized manpower. Hence the relevance of optimizing the process and alleviating costs. In this sense, procedural content generation (PCG) comes in handy as a means of reducing costs by using algorithmic techniques to automatically generate some game contents. PCG also provides advantages in terms of player experience since the contents generated are typically not fixed but can vary in different playing sessions, and can even adapt to the player herself. For this purpose, the underlying algorithmic technique used for PCG must be also flexible and adaptable. This is the case of computational intelligence in general and evolutionary algorithms in particular. In this work we shall provide an overview of the use of evolutionary intelligence for PCG, with special emphasis on its use within the context of real-time strategy games. We shall show how these techniques can address both playability and aesthetics, as well as improving the game AI

Affect and believability in game characters:a review of the use of affective computing in games

Virtual agents are important in many digital environments. Designing a character that highly engages users in terms of interaction is an intricate task constrained by many requirements. One aspect that has gained more attention recently is the effective dimension of the agent. Several studies have addressed the possibility of developing an affect-aware system for a better user experience. Particularly in games, including emotional and social features in NPCs adds depth to the characters, enriches interaction possibilities, and combined with the basic level of competence, creates a more appealing game. Design requirements for emotionally intelligent NPCs differ from general autonomous agents with the main goal being a stronger player-agent relationship as opposed to problem solving and goal assessment. Nevertheless, deploying an affective module into NPCs adds to the complexity of the architecture and constraints. In addition, using such composite NPC in games seems beyond current technology, despite some brave attempts. However, a MARPO-type modular architecture would seem a useful starting point for adding emotions

Dynamical Networks of Social Influence: Modern Trends and Perspectives

Dynamics and control of processes over social networks, such as the evolution of opinions, social influence and interpersonal appraisals, diffusion of information and misinformation, emergence and dissociation of communities, are now attracting significant attention from the broad research community that works on systems, control, identification and learning. To provide an introduction to this rapidly developing area, a Tutorial Session was included into the program of IFAC World Congress 2020. This paper provides a brief summary of the three tutorial lectures, covering the most “mature” directions in analysis of social networks and dynamics over them: 1) formation of opinions under social influence; 2) identification and learning for analysis of a network’s structure; 3) dynamics of interpersonal appraisals

Evolution of social power over influence networks containing antagonistic interactions

Individual social power in the opinion formation process over social influence networks has been under intense scientific investigation. Most related works assume explicitly or implicitly that the interpersonal influence weights are always non-negative. In sharp comparison, we argue that such influence weights can be both positive and negative since there exist various contrasting relationships in real-world social networks. Hence, this article studies the evolution of opinion dynamics and social power on cooperative-competitive networks whose influence structure changes via a reflected appraisal mechanism along a sequence of issue discussions. Of particular focus is on identifying the pathways and effects of social power on shaping public opinions from a graph-theoretic perspective. Then, we propose a dynamic model for the reflected self-appraisal process, which enables us to discuss how the individual social power evolves over sequential issue discussions. By accommodating differential Lyapunov theory, we show the global exponential convergence of the self-appraisal model for almost all network topologies. Finally, we conclude that the self-appraisals and social powers are eventually dependent only on an interpersonal appraisal profile