## Mathematics LTH

- Dynamical Borel–Cantelli lemmata The purpose with this project is to study dynamical Borel–Cantelli lemmata and their applications.
- Linear programming methods for decoding The goal of the project is to compare different methods of decoding binary linear codes and find out how well they work on certain classes of codes.
- Primality tests The object is to explore different methods for testing if a number is prime, among them the famous so called AKS primality test. This algorithm runs in time that is a polynomial in the length of the number being tested.
- Calibration of a new PDE-based simulation model of reactive settling in wastewater treatment plants The project means working with the latest developments of the modelling and numerical simulation of biological reactions and sedimentation processes that occur in a wastewater treatment plant. The work consists of implementation of a new numerical method and calibration of the model to real data from a pilot plant. Prerequisites: Good grades in courses in mathematics (e.g., LTH courses including “Kontinuerliga system”) and numerical analysis.
- Modelling sedimentation of particles in a fluid with a PDE as an alternative to a particle-based model The main part of the project is to calibrate a model of sedimentation written as a nonlinear partial differential equation (PDE) on conservation law form.

## Mathematical Statistics

- Cross Spectral analysis of Heart Rate Variability connected to work related stress A number of recent studies report that decreased heart rate variability (HRV) power is related to cardivascular disease, depression, various anxiety disorders, and long-term work related stress or burnout. This project aims for classification of groups of patients with stress related diagnosis using a novel methodology for time-frequency analysis of locally stationary processes. The work includes analysis and evaluation on a novel set of HRV measurement data controlled by metronome guided respitation. Prerequisites: FMSF10/MASC04, FMSN35/MASM26
- Phase and cross-spectral analysis for understanding the relations between sound and the ‘listening’ brain We are remarkably good at focusing on only one talker in a scene consisting of multiple, spatially separated talkers, also known as the cocktail-party scenario. However, our knowledge of the brain’s ability in these situations is very limited. Phase and cross-spectral analysis of the sound and the brain responses should be investigated using different techniques, to find such relations. The project is performed in close collaboration with Eriksholm Research Centre, Oticon A/S, Denmark. Prerequisites: FMSF10/MASC04, (FMS051/MASM17), FMSN35/MASM26
- Songbird dialects Quantification of similarity between complex songs recorded in noisy environments in the wild is a substantial challenge. Therefore, the goal of this project is to improve existing quantitative methods for assessing similarity between the songs of Spiza americana. The project is a collaboration with Timothy Parker, Dept of Biology, Whitham College, Walla Walla, USA Prerequisites: FMSF10/MASC04, (FMSN35/MASM26)
- Respiratory and pulse monitoring The goal of this project is to achieve respiratory and/or pulse monitoring using novel radar technology. The project will be done at Acconeer using their 60 GHz pulsed coherent radar which originates from research at LTH. Prerequisites: FMSF10/MASC04, (FMSN45/MASM17, FMSN35/MASM26)
- Multiple-channel dolphin sonar beam characterization The sonar beam of toothed whales contains several signal components and to accurately detect and localize the components in the time-frequency domain is essential to understand to what extent the signal can be controlled by the animal and what functions it serves. This project aims to studying and characterizing multiple-channel sonar beam measurements and also possibly develop and tailor the method using information from the multiple-channel structure. Prerequisites: FMSF10/MASC04, (FMSN35/MASM26)