First-order aggregation models with alignment

We include alignment interactions in a well-studied first-order attractive-repulsive macroscopic model for aggregation. The distinctive feature of the extended model is that the equation that specifies the velocity in terms of the population density, becomes {\em implicit}, and can have non-unique solutions. We investigate the well-posedness of the model and show rigorously how it can be obtained as a macroscopic limit of a second-order kinetic equation. We work within the space of probability measures with compact support and use mass transportation ideas and the characteristic method as essential tools in the analysis. A discretization procedure that parallels the analysis is formulated and implemented numerically in one and two dimensions

BrainPainter: A software for the visualisation of brain structures, biomarkers and associated pathological processes

We present BrainPainter, a software that automatically generates images of highlighted brain structures given a list of numbers corresponding to the output colours of each region. Compared to existing visualisation software (i.e. Freesurfer, SPM, 3D Slicer), BrainPainter has three key advantages: (1) it does not require the input data to be in a specialised format, allowing BrainPainter to be used in combination with any neuroimaging analysis tools, (2) it can visualise both cortical and subcortical structures and (3) it can be used to generate movies showing dynamic processes, e.g. propagation of pathology on the brain. We highlight three use cases where BrainPainter was used in existing neuroimaging studies: (1) visualisation of the degree of atrophy through interpolation along a user-defined gradient of colours, (2) visualisation of the progression of pathology in Alzheimer's disease as well as (3) visualisation of pathology in subcortical regions in Huntington's disease. Moreover, through the design of BrainPainter we demonstrate the possibility of using a powerful 3D computer graphics engine such as Blender to generate brain visualisations for the neuroscience community. Blender's capabilities, e.g. particle simulations, motion graphics, UV unwrapping, raster graphics editing, raytracing and illumination effects, open a wealth of possibilities for brain visualisation not available in current neuroimaging software. BrainPainter is customisable, easy to use, and can run straight from the web browser: https://brainpainter.csail.mit.edu , as well as from source-code packaged in a docker container: https://github.com/mrazvan22/brain-coloring . It can be used to visualise biomarker data from any brain imaging modality, or simply to highlight a particular brain structure for e.g. anatomy courses.Comment: Accepted at the MICCAI Multimodal Brain Imaging Analysis (MBIA) workshop, 201

Aggregation-diffusion energies on Cartan-Hadamard manifolds of unbounded curvature

We consider an aggregation-diffusion energy on Cartan-Hadamard manifolds with sectional curvatures that can grow unbounded at infinity. The energy corresponds to a macroscopic aggregation model that involves nonlocal interactions and linear diffusion. We establish necessary and sufficient conditions on the growth at infinity of the attractive interaction potential for ground states to exist. Specifically, we derive explicit conditions on the attractive potential in terms of the bounds on the sectional curvatures at infinity. To prove our results we establish a new comparison theorem in Riemannian geometry and a logarithmic Hardy-Littlewood inequality on Cartan-Hadamard manifolds.Comment: arXiv admin note: text overlap with arXiv:2306.0485

Efficient Domain Coverage for Vehicles with Second Order Dynamics via Multi-Agent Reinforcement Learning

Collaborative autonomous multi-agent systems covering a specified area have many potential applications, such as UAV search and rescue, forest fire fighting, and real-time high-resolution monitoring. Traditional approaches for such coverage problems involve designing a model-based control policy based on sensor data. However, designing model-based controllers is challenging, and the state-of-the-art classical control policy still exhibits a large degree of suboptimality. In this paper, we present a reinforcement learning (RL) approach for the multi-agent coverage problem involving agents with second-order dynamics. Our approach is based on the Multi-Agent Proximal Policy Optimization Algorithm (MAPPO). To improve the stability of the learning-based policy and efficiency of exploration, we utilize an imitation loss based on the state-of-the-art classical control policy. Our trained policy significantly outperforms the state-of-the-art. Our proposed network architecture includes incorporation of self attention, which allows a single-shot domain transfer of the trained policy to a large variety of domain shapes and number of agents. We demonstrate our proposed method in a variety of simulated experiments.Comment: This paper has been submitted to IEEE Robotics and Automation Letters. Includes 8 pages with 5 figure