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Statistical mechanics is a powerful framework for analyzing optimization yielding analytical results for matching, optimal transport, and other combinatorial problems. However, these methods typically target the zero-temperature limit,…
Exposure to air pollution is associated with increased morbidity and mortality. Recent technological advancements permit the collection of time-resolved personal exposure data. Such data are often incomplete with missing observations and…
Most analyses of randomised trials with incomplete outcomes make untestable assumptions and should therefore be subjected to sensitivity analyses. However, methods for sensitivity analyses are not widely used. We propose a mean score…
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…
The first passage time (FPT) for random walks is a key indicator of how fast information diffuses in a given system. Despite the role of FPT as a fundamental feature in transport phenomena, its behavior, particularly in heterogeneous…
Classical compartmental models in epidemiology often assume a homogeneous population for simplicity, which neglects the inherent heterogeneity among individuals. This assumption frequently leads to inaccurate predictions when applied to…
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…
Analyzing the urban trajectory in cities has become an important topic in data mining. How can we model the human mobility consisting of stay and travel from the raw trajectory data? How can we infer such a mobility model from the single…
Understanding human mobility is of vital importance for urban planning, epidemiology, and many other fields that aim to draw policies from the activities of humans in space. Despite recent availability of large scale data sets related to…
This paper considers the problem of detecting and tracking multiple maneuvering targets, which suffers from the intractable inference of high-dimensional latent variables that include target kinematic state, target visibility state, motion…
Foundation models have driven remarkable progress in text, vision, and video understanding, and are now poised to unlock similar breakthroughs in trajectory modeling. We introduce the GPSMasked Trajectory Transformer (GPS-MTM), a foundation…
The interplay between missing data and model uncertainty -- two classic statistical problems -- leads to primary questions that we formally address from an objective Bayesian perspective. For the general regression problem, we discuss the…
Data-driven research is becoming a new paradigm in transportation, but the natural lack of individual socio-economic attributes in transportation data makes research such as activity purpose inference and mobility pattern identification…
Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…
We introduce a new approach to model and analyze \emph{Mobility}. It is fully based on discrete mathematics and yields a class of mobility models, called the \emph{Markov Trace} Model. This model can be seen as the discrete version of the…
Understanding crowd behaviors in a large social event is crucial for event management. Passive WiFi sensing, by collecting WiFi probe requests sent from mobile devices, provides a better way to monitor crowds compared with people counters…
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…
Understanding human mobility is important for the development of intelligent mobile service robots as it can provide prior knowledge and predictions of human distribution for robot-assisted activities. In this paper, we propose a…
The problem of planning sensing trajectories for a mobile robot to collect observations of a target and predict its future trajectory is known as active target tracking. Enabled by probabilistic motion models, one may solve this problem by…
Despite the extensive collection of individual mobility data over the past decade, fueled by the widespread use of GPS-enabled personal devices, the existing statistical literature on estimating human spatial mobility patterns from…