In the quest to understand the nature of π (pi), visualizations can offer intuitive insights into its irrationality. A captivating way to explore π is through animated visualizations that bring out the essence of its continuous and non-repeating nature. In this post, we delve into a beautiful geometric animation crafted in Python, which provides a visual representation of π’s irrationality. Let’s start by understanding the core function that drives our visualization: z = np.exp(1j*theta) + np.exp(1j*np.pi*theta) Here, z is a complex number that changes with theta, a variable that ranges from 0 to 2π, making a full circle in the complex plane.

In a delightful dive into the visual world of matrices and eigenvalues, I stumbled upon a Twitter post showcasing a fascinating visualization of eigenvalue distributions evolving over a parameter space. Intrigued by the aesthetics and the mathematical underpinnings, I decided to recreate and explore this visual journey using Python. Unveiling the Mathematics The process of visualizing the eigenvalue distributions involves three primary steps: Matrix Generation: We start by defining a matrix whose elements are governed by mathematical functions and parameters. The original post used a specific 6x6 matrix, but the beauty of this exploration lies in its versatility. We can craft different matrix generation functions to unveil unique visual patterns.

Question An ant leaves its anthill in order to forage for food. It moves with the speed of 1 unit per time step, but it doesn’t know where to go, therefore every time step it moves randomly 1 unit directly north, south, east or west with equal probability. If the food is located on east-west lines 2 units to the north and 2 units to the south, as well as on north-south lines 2 units to the east and 2 units to the west from the anthill, how long will it take the ant to reach it on average? What is the average time the ant will reach food if it is located only on a diagonal line passing through (1, 0) and (0, 1) points?

Summary We show how to use Evolution Strategies (ES) to train neural networks for managing inventory in lost sales problem. ES can learn significantly smaller neural network architechtures in comparison to RL methods without much need for hyper-parameter optimization. Introduction Deep Reinforcement Learning (DRL) agents have recently demonstrated their potential for solving sequential decision-making problems in various domains, such as playing Atari and Alpha Go games. This suggests that DRL agents could also be used to solve sequential decision-making problems in inventory management. While exact algorithms solve small instances of these problems efficiently, they fail in solving bigger instances in a reasonable amount of time due to the curse of dimensionality.

My primary and future research interests focus on the methodological areas of reinforcement learning and stochastic optimization with applications in inventory management, production planning, resource allocation, robotics, and healthcare operations. With the advances in data collection methods, decision-makers gather a massive amount of data describing the environment of the operations. The objective of data collection is to transform it into useful information for improved decision-making. However, translation of the swell of data into actionable information is challenging in operational problems. The recent advances in Machine Learning (ML) introduce the possibility for improving the decision-making in these problems. However, current ML algorithms are not directly applicable to these problems.

Addressing the problems posed to modern operations research requires adapting our teaching style into the realities of the digital era. It is only through adapting our teaching methods that a new generation of students will recognize the existing challenges and learn how to apply the knowledge acquired in their university courses to real world problems, and discover new and innovative solutions of their own. Through teaching, I hope to inspire the new generation to observe, ask why, and sketch solutions. My teaching philosophy has been shaped by my experiences as both a student and an instructor, as well as the realities of our rapidly evolving fields.

Title: Modelling and Control of Production Systems based on Observed Inter-event Times: An Analytical and Empirical Investigation Technological advances allow manufacturers to collect and access data from a production system more easily and effectively. The objective of data collection is deploying the collected data in developing decision support systems for performance evaluation, problem identification, and production control. As a result, data-driven modeling and control methods are now considered as enabling technologies to address the technology challenges for implementing factory of the future. Over the years, manufacturers have become more successful in efficient control of their supply chain and deploying new methodologies that match supply with demand by adopting data-driven methodologies.