ECMI Modelling Week 2023

The topic is related to off-axis vortex beam propagation through the classical optical system. In the microscope, the Gaussian beam with embedded optical vortex is focused into the sample plane. Additionally, the optical vortex can be moved inside the beam, which allows fine scanning of the sample. The task is to calculate Fresnel integrals and present an analytical model of the optical vortex scanning microscope.

The main goal is analytical solutions using special functions.

The precise prediction of water levels of rivers is crucial for societies, as it supports the mitigation of flood hazards, the planning and management of water withdrawal, and drought prevention. In Central Europe, Hungary, the water level of rivers has been recorded since the early 19th century, and various water level and flood prediction methods were developed during the centuries. Since data recording was significantly improved in the last 30 years, there are large and just partially used datasets in the water management domain. The project involves understanding the time series data collected at various gauging stations and applying data-driven methods either to extract patterns from the data or to predict water level for multiple days ahead from a multivariate time series data.

The main goal is to set up a minimal framework including processing pipelines and providing insights about potential usage of data in the water level forecasting.

We will utilize a fairly comprehensive data set for pandemic outcomes in Canada, including confirmed cases, hospitalization, intensive case unit (ICU) admission, and death, stratified by age, gender, and time of event to understand the temporal variation in the outcomes. Statistical and regression analysis will be conducted to determine the differences in risk of outcomes in different age groups, and in pandemic waves. This will be a descriptive analysis that can shed lights on the burden of pandemic and the effect of interventions.

The main goal is to provide an understanding of variations in the burden of COVID-19 pandemic over time.

Influenza A(H5N1) epidemics are common in certain animals and the virus occasionally infects humans. If the virus could easily spread from human to human due to changes in its genetic makeup, it would have pandemic potential. A simple deterministic mathematical model could provide a new basis for pandemic planning and preparedness.

The main goal is to use a mathematical model for scenario analysis and provide evidence-based answers to crucial questions for decision-makers (e.g. on vaccination targeting, and non-pharmacological measures).

The main goal is to develop permutation entropy based feature extraction technique for vibrational data to predict remaining useful life of a ball bearing.

The main goal is to develop and test a simulation code based on a novel numerical approach.

The main goal is to create a framework to handle and correct real-time projection of BGR and depth camera data. Optionally the framework can be expanded the built in IMU data.

In actuarial mathematics, one of the main goals is to provide appropriate models for fair premiums to be calculated by means of various statistical methods. Non-life insurance lines such as car insurance, or proprietary insurance are more challenging due to the underlying uncertainty types. Claim sizes and number of claims are separately modeled by statistical distributions and data-fitting methods. Aggregate claim sizes for a portfolio of insurance policies can be obtained by probabilistic methods for summing i.i.d. random variables. These methods provide the so-called manual premium for a larger population. More advanced models require an in-depth analysis of risk parameters based on risk classes stratified by gender, geographic region or other possible predictors, as well as Bayesian credibility factors assigned to the empirical claim size data.

The main goal is to calculate the fair premium for a portfolio of insurance policies based on data of previous claim sizes and previous number of claims for a certain non-life insurance line of business.

The main goal is to compute the optical system that converts a given light source into a desired target distribution. This is done by solving differential equations numerically.

With the rise of personalized therapeutic approaches, computational drug testing, and artificial tissue engineering, modeling cell cultures has become a prominent field in mathematical and in silico biology. To be successful in these areas, it is crucial to understand the complex collective behavior that emerges from simple phenomena such as migration, proliferation, and intercellular communication.

Cells are mesoscopic discrete entities within a multicellular organism, existing on a scale much larger than the molecules they are composed of, yet much smaller than the organism itself. When it comes to mathematical models describing cells, our typical expectations are that they should be capable of describing a large range of cell numbers, including extremely low counts, account for spatial distribution, and enable the investigation of various phenotypes.

In this project, students will utilize agent-based stochastic simulations (ABM) to study the response of cell cultures to drug treatments. Unlike continuum models, ABMs treat each particle as an individual that follows a prescribed set of rules. By analyzing the collective behavior of these agents using statistical methods, information about the system can be obtained. This technique provides a comprehensive description of individual behavior and considers stochastic effects arising from the finite number of agents and their interactions.

The main goal is to develop a stochastic simulation framework that can depict the time evolution of cell cultures, run simulations, and investigate the effects of drug dosage.