Project Examples
Explore a range of project scenarios and delve into our university projects portfolio
 

Project Scenarios

Example Scenario for Deterministic Modeling

Power Grid of Luxembourg City

Imagine your goal is to forecast the impact of electric vehicle (EV) adoption on Luxembourg City’s power grid by the year 2040. A potential solution is a model that computes the increased electricity demand in year t + 1 based on the demand in year t, using available data from years 2019 to 2023 to initiate and calibrate the model. Ideally, the model includes parameters to assess how infrastructure improvements, such as the addition of charging stations and policy decisions, like incentives for EV purchases, influence the predicted load on the power grid by 2040. This analysis can assist in ensuring the reliability of the power supply in light of the growing popularity of electric vehicles, and predicting the effects of policy decisions.

Example Scenario for Stochastic Modeling

Supply Chain Vulnerabilities

Facing the challenge of optimizing stock levels amidst unpredictable supply chain disruptions, a manufacturing firm seeks to delve into historical incidents of production halts – ranging from local natural disasters like flooding to global health crises like pandemics. The firm is set to examine past disruption patterns to estimate the timing and duration of future interruptions with a 95% confidence level. This effort includes a thorough assessment of all costs associated with such disruptions. By comparing these costs against the expenses of maintaining increased inventory, the firm aims to pinpoint the most economically viable stock levels. The objective of this strategy is to strike a balance between minimizing risk and managing costs to create a resilient supply chain.

Example Questions in General Mathematics

1. Signal Processing

In the context of my experience as an electrical engineer working in signal processing over the past seven years, I am faced with the challenge of solving a system of linear trigonometric equations. I am seeking assistance to not only find solutions to these equations but also to understand the methodology behind their resolution.

2. Topological Data Analysis

Could you provide a short introduction to Homology Theory and Topological Data Analysis, explaining in particular how Persistent Homology aids in identifying hidden structures within complex datasets? We seek to understand the main ideas behind these techniques and their application in revealing patterns and connections that are not immediately apparent through traditional data analysis methods.

3. Epidemic Dynamics Modeling

We seek elucidation on the primary insights presented in the paper titled ‘The Field Theoretical ABC of Epidemic Dynamics’, accessible in the ArXiv open-access repository. Our focus is on understanding the application of field theory principles from physics in modeling the transmission of infectious diseases.

Example Scenario for Data Science

Urban Air Quality

In an urban setting, a municipal agency has deployed a network of 100 air quality monitoring stations to track concentrations of five key air pollutants: carbon monoxide (CO), nitrogen dioxide (NO2), sulfur dioxide (SO2), ozone (O3), and particulate matter (PM10). The mission is to identify, for each pollutant, the six most significant contributors from urban pollution sources, which include vehicular emissions, industrial emissions known for their pollutant output, residential heating systems, and localized sources such as construction dust and traffic congestion areas. The analysis will scrutinize 20 parameters, focusing on measures of factors directly impacting urban air quality like vehicular traffic density, emissions from specific types of industrial activities, meteorological conditions affecting pollutant dispersion, and the role of urban green spaces in air quality improvement. The goal is to methodically rank these variables for each pollutant according to their significance, providing a clear priority list for targeted pollution reduction strategies.

Example Scenario for Probabilistic Quality Management

Optimal Drug Formulation

In the critical phase of developing a new drug, a company must optimally allocate resources between two promising drug formulations. The goal is to optimize efficacy and minimize side effects. This decision’s complexity is heightened by regulatory requirements, financial stakes, and the urgency to market a safe and effective drug swiftly. By employing probabilistic quality management to assess the ‘success probability’ of each drug formulation, the company can make informed decisions, strategically guiding their resource allocation.

Example Corporate Training Programs

Our training approach usually begins with an industry-relevant problem, providing intuitive insight into the required mathematical concepts. Next, we guide participants through the generation and explanation of code to solve the problem, employing the discussed technique. Finally, we interpret the solution, ensuring comprehensive understanding and practical application.

Here are two examples of training options, each offering three different focuses.

Example Data Science and Machine Learning

• For IT / OT Generalists in Manufacturing: Data Science, AI, and ML Fundamentals for IT / OT Generalists in the Manufacturing Industry – A fast paced, 10-hour journey designed for the manufacturing sector, focusing on topics like: Time-Series Data Modeling & Analysis, Data Wrangling with Pandas & NumPy, Industrial Data ETL Processes, Data Normalization Techniques, Deep Learning Foundations (CNNs), DNN Architectures, Introduction to TensorFlow or PyTorch, Anomaly Detection in Manufacturing, Process Optimization with Machine Learning...
  
• For Industry Professionals: Hands-On Data Science and ML for Industry Professionals – A comprehensive 10-hour program across various industries, created to equip participants with practical skills for real world applications. Topics include: Supervised & Unsupervised Learning (scikit learn), Reinforcement Learning, Deep Learning (CNNs; TensorFlow / PyTorch), Data Modeling (Normalization, Warehousing; Pandas), ETL Processes, Regression Analysis (e.g., Sales Prediction), Classification (e.g., Customer Churn), Clustering (e.g., Market Segmentation) with k-means, Dimensionality Reduction (PCA), Model Selection & Cross-Validation, DNN Development (TensorFlow / PyTorch)...
  
• For Python Beginners: Python for Data Science: A Guide for IT / OT Generalists in Manufacturing – A specialized 10-hour course emphasizing Python programming skills crucial for data science applications in the manufacturing industry. Possible topics encompass: Python Coding Essentials, Data Structuring and NumPy Computing, Pandas for Production Data (e.g., production logs, sensor readings), Precision Data Preprocessing Techniques, Visual Insights with Matplotlib & Seaborn, Predictive Analytics with scikit-learn (e.g., equipment failure, optimized production processes, improved quality control), Deep Learning Applications with PyTorch.
  

• High-Performance Computing for IT Professionals: Mathematical Foundations of High-Performance Computing: A Hands-On Approach for IT Professionals – An intensive 10 hour course, designed for IT professionals, focusing on the art of mathematical fine-tuning for high-performance computing (HPC), enriched with AI tools and practical exercises to boost algorithm design and optimization skills.
• Cross-Industry HPC Focus: High-Performance Computing: Essential Mathematics and Applications – An accessible yet thorough training program on HPC, merging essential mathematical concepts and case studies in a 10-hour course that prepares professionals to tackle complex HPC problems across various industries.
• Foundational Mathematics in Computer Science: Comprehensive Mathematics for Algorithms and Machine Learning with Practical Applications – A 15-hour course that navigates through the mathematical underpinnings of algorithms and ML with real industry case studies across various sectors.

 
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