Related papers: Understanding Mass Transfer Directions via Data-Dr…

We present a model of crowd motion in regions with moving obstacles, which is based on the notion of measure sweeping process. The obstacle is modeled by a set-valued map, whose values are complements to r-prox-regular sets. The crowd…

In this paper, starting from the microscopic dynamics of isolated dislocations, we explain how to derive formally mean field models for the dynamics of dislocation densities. Essentially these models are tranport equations, coupled with the…

We address the description of solutes flow with trapping processes in porous media. Starting from a small-scale model for tracer particles trajectories, we derive the corresponding governing equations for the concentration of the mobile and…

In this paper, we focus on the crowd localization task, a crucial topic of crowd analysis. Most regression-based methods utilize convolution neural networks (CNN) to regress a density map, which can not accurately locate the instance in the…

The pervasive use of new mobile devices has allowed a better characterization in space and time of human concentrations and mobility in general. Besides its theoretical interest, describing mobility is of great importance for a number of…

Understanding human mobility patterns -- how people move in their everyday lives -- is an interdisciplinary research field. It is a question with roots back to the 19th century that has been dramatically revitalized with the recent increase…

Understanding how people move within a geographic area, e.g. a city, a country or the whole world, is fundamental in several applications, from predicting the spatio-temporal evolution of an epidemics to inferring migration patterns. Mobile…

Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…

Large-scale human mobility data is a key resource in data-driven policy making and across many scientific fields. Most recently, mobility data was extensively used during the COVID-19 pandemic to study the effects of governmental policies…

The concept of mobility prediction represents one of the key enablers for an efficient management of future cellular networks, which tend to be progressively more elaborate and dense due to the aggregation of multiple technologies. In this…

Why does a traffic jams form out of nowhere, and why does it stretch for kilometers even after the initial cause is passed? This study examines how congestion moves and spreads across motorways using a surprisingly simple method: response…

Effective medium theory of transport in disordered systems, whose basis is the replacement of spatial disorder by temporal memory, is extended in several practical directions. Restricting attention to a 1-dimensional system with bond…

A classical problem describing the collective motion of cells, is the movement driven by consumption/depletion of a nutrient. Here we analyze one of the simplest such model written as a coupled Partial Differential Equation/Ordinary…

Stochastic models of diffusion are routinely used to study dispersal of populations, including populations of animals, plants, seeds and cells. Advances in imaging and field measurement technologies mean that data are often collected across…

To study the propagation of information from individual to individual, we need mobility datasets. Existing datasets are not satisfactory because they are too small, inaccurate or target a homogeneous subset of population. To draw valid…

Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution.…

Predicting how distributions over discrete variables vary over time is a common task in time series forecasting. But whereas most approaches focus on merely predicting the distribution at subsequent time steps, a crucial piece of…

Understanding human mobility patterns is crucial for urban planning, transportation management, and public health. This study tackles two primary challenges in the field: the reliance on trajectory data, which often fails to capture the…

Many processes in science and engineering can be described by partial differential equations (PDEs). Traditionally, PDEs are derived by considering first principles of physics to derive the relations between the involved physical quantities…

In many developing countries, half the population lives in rural locations, where access to essentials such as school materials, mosquito nets, and medical supplies is restricted. We propose an alternative method of distribution (to…