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This paper analyzes the use of variable speed limits to optimize travel time reliability for commuters. The investigation focuses on a traffic corridor with a bottleneck subject to the capacity drop phenomenon. The optimization criterion is…
We present a tractable framework for detecting changes in performance metrics and apply these methods to Major League Baseball (MLB) batting and pitching data from the 2023 and 2024 seasons. We propose a changepoint detection algorithm that…
In baseball, every play on the field is quantitatively evaluated and has an effect on individual and team strategies. The weighted on base average (wOBA) is well known as a measure of an batter's hitting contribution. However, this measure…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
The methods are proposed for evaluation of complex dynamical systems, choice of their optimal operating modes, determination of optimal operating system from given class of equivalent systems, system's timeline behaviour analysis on the…
Scenario pathways (e.g. for the energy transition) often use a single trajectory or a band. That is not sufficient when one needs to understand why outcomes differ and under what stress or uncertainty they arise. Doing so requires tracking…
We develop a Markov model of curling matches, parametrised by the probability of winning an end and the probability distribution of scoring ends. In practical applications, these end-winning probabilities can be estimated econometrically,…
Predicting pedestrian behavior is one of the main challenges for intelligent driving systems. In this paper, we present a new paradigm for evaluating egocentric pedestrian trajectory prediction algorithms. Based on various contextual…
We analyse under a simple approach the problem one must decide the best strategy to minimize the contact with rain when moving between two points through the rain. The available strategies: walk (low speed boost $<<$ $c$) or run…
This paper is interested in the problem of optimal stopping in a mean field game context. The notion of mixed solution is introduced to solve the system of partial differential equations which models this kind of problem. This notion…
In this paper, we present a new model for ranking sports teams. Our model uses all scoring data from all games to produce a functional rating by the method of least squares. The functional rating can be interpreted as a teams average point…
Iterative trajectory optimization techniques for non-linear dynamical systems are among the most powerful and sample-efficient methods of model-based reinforcement learning and approximate optimal control. By leveraging time-variant local…
We investigate statistical properties of the optimal value of the Sample Average Approximation of stochastic programs, continuing the study in Kr\"atschmer (2023). Central Limit Theorem type results are derived for the optimal value. As a…
Large-scale competitive platforms are interacting multi-agent systems in which latent skills drift over time and pairwise interactions are shaped by matchmaking. We study a controlled rating dynamics in the mean-field limit and derive a…
The expected goal provides a more representative measure of the team and player performance which also suit the low-scoring nature of football instead of score in modern football. The score of a match involves randomness and often may not…
We address the reachability problem for continuous-time stochastic dynamic systems. Our objective is to present a unified framework that characterizes the reachable set of a dynamic system in the presence of both stochastic disturbances and…
This paper presents an extension of Keller's classical model to address the dynamics of long-distance trail running, a sport characterized by varying terrains, changing elevations, and the critical influence of in-race nutrition uptake. The…
In this work we develop a new algorithm for rating of teams (or players) in one-on-one games by exploiting the observed difference of the game-points (such as goals), also known as a margin of victory (MOV). Our objective is to obtain the…
Brownian particles interacting sequentially with distinct temperatures and driving forces at each stroke have been tackled as a reliable alternative for the construction of engine setups. However they can behave very inefficiently depending…
In-game win probability models, which provide a sports team's likelihood of winning at each point in a game based on historical observations, are becoming increasingly popular. In baseball, basketball and American football, they have become…