A. Agung Julius

Zidi Tao, A. Agung Julius, John T Wen

Sleep is vital for maintaining cognitive function, facilitating metabolic waste removal, and supporting memory consolidation. However, modern societal demands, particularly shift work, often disrupt natural sleep patterns. This can induce excessive sleepiness among shift workers in critical sectors such as healthcare and transportation and increase the risk of accidents. The primary contributors to this issue are misalignments of circadian rhythms and enforced sleep-wake schedules. Regulating circadian rhythms that are tied to alertness can be regarded as a control problem with control inputs in the form of light and sleep schedules. In this paper, we address the problem of optimizing alertness by optimizing light and sleep schedules to improve the cognitive performance of shift workers. A key tool in our approach is a mathematical model that relates the control input variables (sleep and lighting schedules) to the dynamics of the circadian clock and sleep. In the sleep and circadian modeling literature, the newer physiology-based model shows better accuracy in predicting the alertness of shift workers than the phenomenology-based model, but the dynamics of physiological-based model have differential equations with different time scales, which pose challenges in optimization. To overcome the challenge, we propose a hybrid version of the PR model by applying singular perturbation techniques to reduce the system to a non-stiff, differentiable hybrid system. This reformulation facilitates the application of the calculus of variation and the gradient descent method to find the optimal light and sleep schedules that maximize the subjective alertness of shift worker. Our approach is validated through numerical simulations, and the simulation results demonstrate improved alertness compared to other existing schedules.

Sayan Saha, A. Agung Julius

The fundamental idea of this work is to synthesize reactive controllers such that closed-loop execution trajectories of the system satisfy desired specifications that ensure correct system behaviors, while optimizing a desired performance criteria. In our approach, the correctness of a system's behavior can be defined according to the system's relation to the environment, for example, the output trajectories of the system terminate in a goal set without entering an unsafe set. Using Metric Temporal Logic (MTL) specifications we can further capture complex system behaviors and timing requirements, such as the output trajectories must pass through a number of way-points within a certain time frame before terminating in the goal set. Given a Mixed Logical Dynamical (MLD) system and system specifications in terms of MTL formula or simpler reach-avoid specifications, our goal is to find a closed-loop trajectory that satisfies the specifications, in non-deterministic environments. Using an MILP framework we search over the space of input signals to obtain such valid trajectories of the system, by adding constraints to satisfy the MTL formula only when necessary, to avoid the exponential complexity of solving MILP problems. We also present experimental results for planning a path for a mobile robot through a dynamically changing environment with a desired task specification.

Quan Wang, Yan Ou, A. Agung Julius et al.

Matching cells over time has long been the most difficult step in cell tracking. In this paper, we approach this problem by recasting it as a classification problem. We construct a feature set for each cell, and compute a feature difference vector between a cell in the current frame and a cell in a previous frame. Then we determine whether the two cells represent the same cell over time by training decision trees as our binary classifiers. With the output of decision trees, we are able to formulate an assignment problem for our cell association task and solve it using a modified version of the Hungarian algorithm.