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.
  • Reconstruction of 3D structure and situational awareness by fusing image sequences with lidar data
  • ABB Crane systems today apply a great number of cameras that capture projections of the three dimensional surrounding to the container cranes under operation. LIDAR data is also being collected in several cases. Fusing these two measurement modalities would possibly yield an aggregate data that would benefit from both the strong point of the information rich camera image and the robust depth estimate of the LIDAR. One way of fusing such data would be to formulate a model representation that could be updated with the measurement of the image and lidar frame as they become available. The suggested theme for this master thesis work is to investigate the details of such reconstruction.
  • 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.

Mathematical Statistics

  • Unbiased pitch detection in entomological lidar
  • The world leading group in laser remote sensing located at Lund University collects hundreds of thousands insect observation per day from airborne insects using entomological lidar measurements. The measurements, where the signals are of time-varying character and suffer from the influence of varying noise and other disturbances, are used for classification of species, sex and age groups. Exploitation relies on robust estimation of the parameters of the time-varying signals and especially the fundamental tone. In this master thesis we suggest an investigation of a novel technique, matched reassignment, which is a mathematical method that relies on the phase of the Fourier transform to reassign the power of the spectrogram. The method has been shown to outperform other time-frequency techniques and it gives accurate estimates of the time- as well as the frequency locations. Supervisors: Maria Sandsten,; Mikkel Brydegaard and Samuel Jansson, Dept. Physics. Prerequisites: FMSF10/MASC04, FMSN35/MASM26
  • Resistivity and time domain induced polarization (DCIP) measurements is a great tool for mapping properties of the subsurface. This master thesis project invloves analysis of existiving DCIP data to find suitable machine learning or signal processing apporaches to deal with non-stationary disturbances from trams and metro. Prerequisites: FMSF10/MASC04, (FMS051/MASM17), (FMSN35/MASM26)

Numerical Analysis