Mathematical Sciences

Lund University

Mathematics LTH

  • Dynamical Borel–Cantelli lemmata
  • The purpose with this project is to study dynamical Borel–Cantelli lemmata and their applications.
  • Image processing to interpret protein crystal structures
  • Our understanding of the function of proteins, DNA, RNA and other biological macromolecules, as well as the design of new drug molecules, rely strongly on the possibility to obtain atomic-resolution structures by X-ray and neutron crystallography. Currently, almost 150 000 such structures are freely available in the protein databank. In Lund, data collection for such structures can be performed at the Max IV laboratory and when ESS is running, it will be possible to collect data for neutron structures at an unprecedented speed. To start with, we will restrict the project to identify water molecules in X-ray crystallographic maps. To train the model, we will employ a set of (~1000) curated maps where standard methods clearly identify the presence or absence of a water molecule. Additional data can easily be generated, both from existing crystal structures or from simulated molecular data.
  • 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.

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. Cross spectral analysis between the HRV and the breathing signals can be used as a refined technique for analyzing the HRV power. The project aim is to compare and develop such methods for the analysis of HRV data collected from individuals at different stages of work related 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
  • Songbird dialects
  • Many songbird species have geographically structured vocal culture in which individuals at a location produce songs similar to each other that clearly differ from songs produced at other locations by members of the same species.  Scientific study of such vocal culture is facilitated by reliable quantification of the similarity between pairs of songs. However, quantification of similarity between complex songs recorded in noisy environments in the wild is a substantial challenge. For instance, in the North American bird Spiza americana, human observers can still readily outperform existing quantitative methods in assessing the similarity between songs. 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. Challenges lie both in extracting the displacement of the chest and abdomen from the raw radar signal, and then also in extracting respiratory/pulse information from that data. General knowledge of methods for analysis of stochastic processes as well as understanding of filtering techniques are essential. 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
  • Transient signals are by nature difficult to characterize. 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. The scaled reassigned spectrogram estimates the time- and frequency centers of individual signals and is therefore well suited for detection and localization of transient signal components, also when they are closely located in the time-frequeny domain. 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)

Numerical Analysis