Totalistic cellular automata (CA) are an efficient tool for simulating numerous wave phenomena in discrete media. However, their inherent anisotropy often leads to a significant deviation of the model results from experimental data. Here, we propose a computationally efficient isotropic CA with the standard Moore neighborhood. Our model exploits a single postulate: the information transfer in an isotropic medium occurs at constant rate. To fulfill this requirement, we introduce in each cell a local counter keeping track of the distance run by the wave from its source. This allows maintaining the wave velocity constant in all possible directions even in the presence of nonconductive local areas (obstacles) with complex spatial geometry. Then, we illustrate the model on the problem of real-time building of cognitive maps used for navigation of a mobile robot. The isotropic property of the CA helps obtaining “smooth” trajectories and hence natural robot movement. The accuracy and flexibility of the approach are proved experimentally by driving the robot to a target avoiding collisions with obstacles.

In several reinforcement learning (RL) scenarios, mainly in security settings, there may be adversaries trying to interfere with the reward generating process. In this paper, we introduce Threatened Markov Decision Processes (TMDPs), which provide a framework to support a decision maker against a potential adversary in RL. Furthermore, we propose a level-k thinking scheme resulting in a new learning framework to deal with TMDPs. After introducing our framework and deriving theoretical results, relevant empirical evidence is given via extensive experiments, showing the benefits of accounting for adversaries while the agent learns.

The introduction of a new drug to the commercial market follows a complex and long process that typically spans over several years and entails large monetary costs due to a high attrition rate. Because of this, there is an urgent need to improve this process using innovative technologies such as artificial intelligence (AI). Different AI tools are being applied to support all four steps of the drug development process (basic research for drug discovery; pre-clinical phase; clinical phase; and postmarketing). Some of the main tasks where AI has proven useful include identifying molecular targets, searching for hit and lead compounds, synthesising drug-like compounds and predicting ADME-Tox. This review, on the one hand, brings in a mathematical vision of some of the key AI methods used in drug development closer to medicinal chemists and, on the other hand, brings the drug development process and the use of different models closer to mathematicians. Emphasis is placed on two aspects not mentioned in similar surveys, namely, Bayesian approaches and their applications to molecular modelling and the eventual final use of the methods to actually support decisions. Graphic abstract Promoting a perfect synergy

Adversarial risk analysis (ARA) is a relatively new area of research that informs decision-making when facing intelligent opponents and uncertain outcomes. It is a decision-theoretic alternative to game theory. ARA enables an analyst to express her Bayesian beliefs about an opponent's utilities, capabilities, probabilities, and the type of strategic calculations that the opponent is using to make his decision. Within that framework, the analyst then solves the problem from the perspective of the opponent. This calculation produces a distribution over the actions of the opponent that permits the analyst to maximize her expected utility. This review covers conceptual, modeling, computational, and applied issues in ARA as well as interesting open research issues. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and TheoryApplications of Computational Statistics > Defense and National Securityauctions, Bayes Nash equilibrium, decision theory, game theory, level-k thinking | INTRODUCTIONAdversarial risk analysis (ARA) guides decision-making when there are intelligent opponents who reason strategically about each other in the context of uncertain outcomes. It is a decision-theoretic alternative to classical game theory that uses Bayesian subjective distributions to model the goals, resources, beliefs, and reasoning of the opponent. Within this framework, the analyst solves the problem from the perspective of her opponent while placing subjective probability distributions on all unknown quantities. This structure provides a distribution over the actions of the opponent that enables her to maximize her expected utility, accounting for the uncertainty she has about the opponent. ARA applications include convoy routing through an insurgent city with improvised explosive devices (Banks, Petralia, & Wang, 2011), managing Somali piracy (Sevillano, Insua, & Rios, 2012), dealing with crime in a public transportation system (Banks, Aliaga, & Insua, 2015), Emile Borel's game La Relance (Banks et al., 2011), and cybersecurity (Rios Insua et al., 2019). It is relevant whenever one party is trying to model the decision-making process of one or more other parties, in order to achieve an outcome sought by the first party. The mathematics behind ARA can be quite complicated, but the essential idea is very natural. When asking the boss for a raise, one has a mental model for what the boss values (e.g., performance, flattery, punctual paperwork) and his likely response to various pitches. If the model is correct, one has a good chance of obtaining a raise; if not, then success is unlikely.

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