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By analyzing the gaze trajectories of people viewing screens and advertisements, we can determine what people are interested in. This knowledge can be effective when recommending commercial products and services, and also, when improving…
An innovative method based on the traversal of rays, originating from detected particles, through a three-dimensional grid of voxels is presented. The methodology has as main advantage that the outcome of the method is independent of the…
A simple Monte Carlo (MC) algorithm for the simulation of the passage of low-energy gamma rays and electrons through any material medium is presented. The algorithm includes several approximations that accelerate the simulation while…
We optimize the path of a mobile sensor to minimize the posterior uncertainty of a Bayesian inverse problem. Along its path, the sensor continuously takes measurements of the state, which is a physical quantity modeled as the solution of a…
We propose a new semi-Lagrangian Vlasov-Poisson solver. It employs elements of metric to follow locally the flow and its deformation, allowing one to find quickly and accurately the initial phase-space position $Q(P)$ of any test particle…
Partial differential equations (PDEs) govern nearly every physical process in science and engineering, yet solving them at scale remains prohibitively expensive. Generative AI has transformed language, vision, and protein science, but…
A semi-Lagrangian Characteristic Mapping method for the solution of the tracer transport equations on the sphere is presented. The method solves for the solution operator of the equations by approximating the inverse of the diffeomorphism…
We review matrix methods as applied to tracer transport. Because tracer transport is linear, matrix methods are an ideal fit for the problem. A gridded, Eulerian tracer simulation can be approximated as a system of linear ordinary…
Soft slender structures are ubiquitous in natural and artificial systems and can be observed at scales that range from the nanometric to the kilometric, from polymers to space tethers. We present a practical numerical approach to simulate…
Eye movements hold information about human perception, intention and cognitive state. Various algorithms have been proposed to identify and distinguish eye movements, particularly fixations, saccades, and smooth pursuits. A major drawback…
Identifying local structural motifs and packing patterns of molecular solids is a challenging task for both simulation and experiment. We demonstrate two novel approaches to characterize local environments in different polymorphs of…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
Machine learning methods have been successful in many areas, like image classification and natural language processing. However, it still needs to be determined how to apply ML to areas with mathematical constraints, like solving PDEs.…
The detection and parametrization of molecular clumps is the first step in studying them. We propose a method based on Local Density Clustering algorithm while physical parameters of those clumps are measured using the Multiple Gaussian…
In the field of modern robotics, robots are proving to be useful in tackling high-risk situations, such as navigating hazardous environments like burning buildings, earthquake-stricken areas, or patrolling crime-ridden streets, as well as…
A common approach to compute distances on continuous surfaces is by considering a discretized polygonal mesh approximating the surface and estimating distances on the polygon. We show that exact geodesic distances restricted to the polygon…
Linear scaling methods, or O(N) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N, in contrast to standard approaches which scale with the cube of the number of atoms. These…
The paper proposes a novel machine learning-based approach to the pathfinding problem on extremely large graphs. This method leverages diffusion distance estimation via a neural network and uses beam search for pathfinding. We demonstrate…
Geochemical systems are known to exhibit highly variable spatiotemporal behavior. This may be observed both in non-smooth concentration curves in space for a single sampling time and also in variability between samples taken from the same…
It is of great interest to solve the inverse problem of stationary radiative transport equation (RTE) in optical tomography. The standard way is to formulate the inverse problem into an optimization problem, but the bottleneck is that one…