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.
  • 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.
  • Pose Optimization for feet estimation
  • In order to estimate the shape and measure a pair of feet, it is necessary to have an accurate estimation of the camera pose (including scale). In this project we are going to face challenging scenes with little texture and potentially rapid mo- tion. The goal is to improve the camera pose estimation and the robustness to meet the requirements in industry. This can be done by using more sensor data and/or using information about the scene that is going to be valid for our setting.
  • Single View Foot Estimation
  • This project will focus on estimating the shape of the foot given a single image. From a top view perspective, can we accurately estimate the width and length of the foot? What can be inferred about height etc using machine learning techniques? In this exciting project we are going investigate what can be said about a foot from just a single image. The project will involve both statistics, optimization and computer vision.
  • Multiple View End-To-End Learning Based Shoe Recommendation
  • Can modern machine learning techniques and computer vision be used to infer shoe fit from just a few images? Volumental dispose a large set of 3D scanned feet and customer data of bought shoes. Can we formulate this as a ML-problem and directly use imagery to find a perfect shoe fit? The goal of this project is to develop a neural network that can use multiple images as input and infer the correct shape parameters of a parametric foot model.
  • Bildigenkänning som verktyg för att upptäcka föroreningar
  • Testa om enkla övervakningskameror tillsammans med biligenkänningsteknik kan detektera och varna vid allvarliga föroreningar i dagvattensystemet.
  • Predictions of the next solar cycle maximum
  • TBA
  • Multiscale modeling for materials science
  • TBA
  • Surface growth models
  • TBA
  • Deep learning for the interpretation of 11 453 pages of handwritten tables of Älvsborgs ransom
  • Recent breakthroughs in image analysis and text recognition, fuelled by a rapid progress in machine learning, means that software for the first time can compete with, and sometimes even surpass, humans in tasks such as classifying images and reading handwritten documents. In this project you will develop method for interpreting handwritten documents from the 16th century and evaluate how they work on 11 453 pages from Älvsborgs Ransom. The text is written by several scribes. The consistency of style and layout within the pages of one scribe is high, but there is significant differences between scribes. This is an excellent example of a machine learning problem, where the use of context (the scribe), could be used. This is a research area which is of theoretical interest, with applications in many areas. In the project one could also study how to extract the structure of the documents automatically using convolutional neural networks.
  • AI for Precision farming
  • This master's thesis project concerns the development of methods to model and predict how harvest yield depends on data. In the project we will evaluate potential methods and algorithms to build a predicative model, that can be used for optimization of agriculture inputs and planning. In this project we work with Hushållningssällskapet in Skåne and with T-Kartor. We have harvest data (one point every fifth seconds) that can be used as evaluation data. We have georeferenced spatiotemporal and spectral data that can be used as potential indata both as points and imagery, but also data from soil samples, satellite sensor data, terrain model, rainfall etc. Data will be available from selected fields in Skåne from 2020.

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)

Numerical Analysis