We consider three central problems in optimization: the restricted assignment load-balancing problem, the Steiner tree network design problem, and facility location clustering. We consider the online setting, where the input arrives over time, and irrevocable decisions must be made without knowledge of the future. For all these problems, any online algorithm must incur a cost that is approximately log | I | times the optimal cost in the worst-case, where | I | is the length of the input. But can we go beyond the worst-case? In this work we give algorithms that perform substantially better when a p -fraction of the input is given as a sample: the algorithm use this sample to learn a good strategy to use for the rest of the input.

In this paper we present novel methodology for automatic anomaly and switch event filtering to improve load estimation in power grid systems. By leveraging unsupervised methods with supervised optimization, our approach prioritizes interpretability while ensuring robust and generalizable performance on unseen data. Through experimentation, a combination of binary segmentation for change point detection and statistical process control for anomaly detection emerges as the most effective strategy, specifically when ensembled in a novel sequential manner. Results indicate the clear wasted potential when filtering is not applied. The automatic load estimation is also fairly accurate, with approximately 90% of estimates falling within a 10% error margin, with only a single significant failure in both the minimum and maximum load estimates across 60 measurements in the test set. Our methodology's interpretability makes it particularly suitable for critical infrastructure planning, thereby enhancing decision-making processes.

Clustering is a fundamental task in theoretical computer science and machine learning aimed at dividing a set of data items into several groups or clusters, such that each group contains similar data items. Typically, the similarity between data items is measured using a metric distance function. Clustering is often modeled as an optimization problem where the objective is to minimize a global cost function that reflects the quality of the clusters; this function varies depending on the application. Among the many cost functions studied for clustering, the most popular are k-median, k-means, and k-center. These objectives generally aim to minimize the variance within the clusters, serving as a proxy for grouping similar data items In this work, we study clustering problems with fairness constraints, commonly known as fair clustering problems. Fair clustering emerged as one of the most active research areas in algorithms motivated by the recent trend of research on fairness in artificial intelligence. In a seminal work, Chierichetti et al. [18] introduced a fair clustering problem, where given a set R of red points, a set B of blue points, and an integer balance parameter t 1, a clustering is said to be balanced if, in every cluster, the number of red points is at least 1/t times the number of blue points and at most t times the number of blue points.

The widespread adoption of large language models (LLMs), such as OpenAI's ChatGPT, could revolutionize various industries, including geotechnical engineering. However, GPT models can sometimes generate plausible-sounding but false outputs, leading to hallucinations. In this article, we discuss the importance of prompt engineering in mitigating these risks and harnessing the full potential of GPT for geotechnical applications. We explore the challenges and pitfalls associated with LLMs and highlight the role of context in ensuring accurate and valuable responses. Furthermore, we examine the development of context-specific search engines and the potential of LLMs to become a natural interface for complex tasks, such as data analysis and design. We also develop a unified interface using natural language to handle complex geotechnical engineering tasks and data analysis. By integrating GPT into geotechnical engineering workflows, professionals can streamline their work and develop sustainable and resilient infrastructure systems for the future.

We study a multi-leader single-follower congestion game where multiple users (leaders) choose one resource out of a set of resources and, after observing the realized loads, an adversary (single-follower) attacks the resources with maximum loads, causing additional costs for the leaders. For the resulting strategic game among the leaders, we show that pure Nash equilibria may fail to exist and therefore, we consider approximate equilibria instead. As our first main result, we show that the existence of a $K$-approximate equilibrium can always be guaranteed, where $K \approx 1.1974$ is the unique solution of a cubic polynomial equation. To this end, we give a polynomial time combinatorial algorithm which computes a $K$-approximate equilibrium. The factor $K$ is tight, meaning that there is an instance that does not admit an $\alpha$-approximate equilibrium for any $\alpha

A robot has completed the prestigious task of ringing the famed New York Stock Exchange bell to signal the end of trading. Traders witnessed the modern twist to the historical tradition as Universal Robots' UR5e successfully completed the task. The collaborative robot - or cobot - rang the day's closing bell with the help of a two-finger gripper from Robotiq. The UR5e robot has a range of uses and a maximum load of five kilograms (11 pounds). It can operate successfully within a radius of up to 33.5 inches (85 cm) and they are used extensively throughout industries that require low-weight processes, such as picking, placing, and testing.