We study the fundamental problem of estimating an unknown discrete distribution p over d symbols, given n i.i.d.

This paper studies a variation of the classic network alignment problem, named diffusion-network alignment. The goal is to align the vertices of a rooted diffusion tree to the vertices of a network, where the diffusion tree could be from a communication trace or contact tracing, and the network could be an online or offline social network. Different from the classic network alignment where both networks are fully observed, this model captures the information asymmetry of two networks. To solve this problem, this paper presents an efficient algorithm based on tree correlation tests to extract alignment information from local neighborhoods. We analyze the performance of the algorithm in the sparse graph regime and show that with high probability, all matched pairs are correct. Furthermore, for each vertex on the diffusion tree, this paper establishes an explicit lower bound on the probability that the vertex is correctly matched. These lower bounds are depth-dependent and increase as vertices get closer to the root.

Estimating properties of discrete distributions is a fundamental problem in statistical learning.

We study the problem of generalized uniformity testing of a discrete probability distribution: Given samples from a probability distribution p over an unknown size discrete domain Ω, we want to distinguish, with probability at least 2/ 3, between the case that p is uniform on some subset of Ω versus null -far, in total variation distance, from any such uniform distribution. We establish tight bounds on the sample complexity of generalized uniformity testing. In more detail, we present a computationally efficient tester whose sample complexity is optimal, within constant factors, and a matching worst-case information-theoretic lower bound.

This paper considers the problem of searching for a point of interest (POI) moving along an urban road network with an uncrewed aerial vehicle (UAV). The UAV is modeled as a variable-speed Dubins vehicle with a line-of-sight sensor in an urban environment that may occlude the sensor's view of the POI. A search strategy is proposed that exploits a probabilistic visibility volume (VV) to plan its future motion with iterative deepening $A^\ast$. The probabilistic VV is a time-varying three-dimensional representation of the sensing constraints for a particular distribution of the POI's state. To find the path most likely to view the POI, the planner uses a heuristic to optimistically estimate the probability of viewing the POI over a time horizon. The probabilistic VV is max-pooled to create a variable-timestep planner that reduces the search space and balances long-term and short-term planning. The proposed path planning method is compared to prior work with a Monte-Carlo simulation and is shown to outperform the baseline methods in cluttered environments when the UAV's sensor has a higher false alarm probability.

Traditional vehicle routing systems efficiently optimize singular metrics like time or distance, and when considering multiple metrics, they need more processes to optimize . However, they lack the capability to interpret and integrate the complex, semantic, and dynamic contexts of human drivers, such as multi-step tasks, situational constraints, or urgent needs. This paper introduces and evaluates PAVe (Personalized Agentic Vehicular Routing), a hybrid agentic assistant designed to augment classical pathfinding algorithms with contextual reasoning. Our approach employs a Large Language Model (LLM) agent that operates on a candidate set of routes generated by a multi-objective (time, CO2) Dijkstra algorithm. The agent evaluates these options against user-provided tasks, preferences, and avoidance rules by leveraging a pre-processed geospatial cache of urban Points of Interest (POIs). In a benchmark of realistic urban scenarios, PAVe successfully used complex user intent into appropriate route modifications, achieving over 88% accuracy in its initial route selections with a local model. We conclude that combining classical routing algorithms with an LLM-based semantic reasoning layer is a robust and effective approach for creating personalized, adaptive, and scalable solutions for urban mobility optimization.