Related papers: CM Sequence based Trajectory Modeling with Destina…
A Markov tree is a random vector indexed by the nodes of a tree whose distribution is determined by the distributions of pairs of neighbouring variables and a list of conditional independence relations. Upon an assumption on the tails of…
Trajectory prediction facilitates effective planning and decision-making, while constrained trajectory prediction integrates regulation into prediction. Recent advances in constrained trajectory prediction focus on structured constraints by…
Full integration of robots into real-life applications necessitates their ability to interpret and execute natural language directives from untrained users. Given the inherent variability in human language, equivalent directives may be…
Accurate human mobility prediction underpins many important applications across a variety of domains, including epidemic modelling, transport planning, and emergency responses. Due to the sparsity of mobility data and the stochastic nature…
Structural Causal Models (SCMs) provide a popular causal modeling framework. In this work, we show that SCMs are not flexible enough to give a complete causal representation of dynamical systems at equilibrium. Instead, we propose a…
Understanding how latent representations evolve during generation is a central open problem in large language model interpretability. We introduce \textbf{Dynamical Manifold Evolution Theory} (DMET), a phenomenological framework that models…
Mathematical models are vital interpretive and predictive tools used to assist in the understanding of cell migration. There are typically two approaches to modelling cell migration: either micro-scale, discrete or macro-scale, continuum.…
For both driving safety and efficiency, automated vehicles should be able to predict the behavior of surrounding traffic participants in a complex dynamic environment. To accomplish such a task, trajectory prediction is the key. Although…
Models for predicting aircraft motion are an important component of modern aeronautical systems. These models help aircraft plan collision avoidance maneuvers and help conduct offline performance and safety analyses. In this article, we…
Trajectory prediction for traffic agents is critical for safe autonomous driving. However, achieving effective zero-shot generalization in previously unseen domains remains a significant challenge. Motivated by the consistent nature of…
We consider learning-based adaptive dynamic routing for a single-origin-single-destination queuing network with stability guarantees. Specifically, we study a class of generalized shortest path policies that can be parameterized by only two…
In this paper, we revisit the computation of controlled invariant sets for linear discrete-time systems through a trajectory-based viewpoint. We begin by introducing the notion of convex feasible points, which provides a new…
Sequential and terminal constraint feasibility of the model predictive control (MPC) play important roles in ensuring MPC control continuity. This study thus investigates these two properties theoretically using an MPC model for vehicle…
The Ensemble of trajectories $x(0 \leq t \leq T)$ produced by the Markov generator $M$ can be considered as 'Canonical' for the following reasons : (C1) the probability of the trajectory $x(0 \leq t \leq T)$ can be rewritten as the…
Diffusion-Limited Aggregation (DLA) is a cluster-growth model that consists in a set of particles that are sequentially aggregated over a two-dimensional grid. In this paper, we introduce a biased version of the DLA model, in which…
Understanding the dynamics of an environment, such as the movement of humans and vehicles, is crucial for agents to achieve long-term autonomy in urban environments. This requires the development of methods to capture the multi-modal and…
This paper studies sequence prediction based on the monotone Kolmogorov complexity Km=-log m, i.e. based on universal deterministic/one-part MDL. m is extremely close to Solomonoff's universal prior M, the latter being an excellent…
Diffusion Models (DM) and Consistency Models (CM) are two types of popular generative models with good generation quality on various tasks. When training DM and CM, intermediate weight checkpoints are not fully utilized and only the last…
We derive a conservation law on a network made of two incoming branches and a single outgoing one from a discrete traffic flow model. The continuous model is obtained from the discrete one by letting the number of vehicles tend to infinity…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…