Deterministic Equations for Stochastic Spatial Evolutionary Games

Spatial evolutionary games model individuals who are distributed in a spatial domain and update their strategies upon playing a normal form game with their neighbors. We derive integro-differential equations as deterministic approximations of the microscopic updating stochastic processes. This generalizes the known mean-field ordinary differential equations and provide a powerful tool to investigate the spatial effects in populations evolution. The deterministic equations allow to identify many interesting features of the evolution of strategy profiles in a population, such as standing and traveling waves, and pattern formation, especially in replicator-type evolutions

Automated Knowledge Discovery from Functional Magnetic Resonance Images using Spatial Coherence

Functional Magnetic Resonance Imaging (fMRI) has the potential to unlock many of the mysteries of the brain. Although this imaging modality is popular for brain-mapping activities, clinical applications of this technique are relatively rare. For clinical applications, classification models are more useful than the current practice of reporting loci of neural activation associated with particular disorders. Also, since the methods used to account for anatomical variations between subjects are generally imprecise, the conventional voxel-by-voxel analysis limits the types of discoveries that are possible. This work presents a classification-based framework for knowledge discovery from fMRI data. Instead of voxel-centric knowledge discovery, this framework is segment-centric, where functional segments are clumps of voxels that represent a functional unit in the brain. With simulated activation images, it is shown that this segment-based approach can be more successful for knowledge discovery than conventional voxel-based approaches. The spatial coherence principle refers to the homogeneity of behavior of spatially contiguous voxels. Auto-threshold Contrast Enhancing Iterative Clustering (ACEIC) - a new algorithm based on the spatial coherence principle is presented here for functional segmentation. With benchmark data, it is shown that the ACEIC method can achieve higher segmentation accuracy than Probabilistic Independent Component Analysis - a popular method used for fMRI data analysis. The spatial coherence principle can also be exploited for voxel-centric image-classification problems. Spatially Coherent Voxels (SCV) is a new feature selection method that uses the spatial coherence principle to eliminate features that are unlikely to be useful for classification. For a Substance Use Disorder dataset, it is demonstrated that feature selection with SCV can achieve higher classification accuracies than conventional feature selection methods

Modelling evolution in a spatial continuum

We survey a class of models for spatially structured populations which we have called spatial Λ-Fleming–Viot processes. They arise from a flexible framework for modelling in which the key innovation is that random genetic drift is driven by a Poisson point process of spatial ‘events’. We demonstrate how this overcomes some of the obstructions to modelling populations which evolve in two- (and higher-) dimensional spatial continua, how its predictions match phenomena observed in data and how it fits with classical models. Finally we outline some directions for future research

Pedestrians moving in dark: Balancing measures and playing games on lattices

We present two conceptually new modeling approaches aimed at describing the motion of pedestrians in obscured corridors: * a Becker-D\"{o}ring-type dynamics * a probabilistic cellular automaton model. In both models the group formation is affected by a threshold. The pedestrians are supposed to have very limited knowledge about their current position and their neighborhood; they can form groups up to a certain size and they can leave them. Their main goal is to find the exit of the corridor. Although being of mathematically different character, the discussion of both models shows that it seems to be a disadvantage for the individual to adhere to larger groups. We illustrate this effect numerically by solving both model systems. Finally we list some of our main open questions and conjectures