Examensarbete, förslag

På institutionen för cell- och organismbiologi studeras hur nervcellsutskott väljer väg på konstgjorda underlag. Tanken är att kunna styra nervcellernas utskott (axoner) till specifika ställen på till exempel elektroniska chip. Examensarbetet går ut på att analysera bilder och ta fram metoder för att kunna avgöra hur väl nervutskotten följer olika typer av underlag, som kan vara preparerade med t.ex. spår i försök att styra tillväxten.

Bildanalys av odlade nervutskott på ytor

Piecewise expanding interval maps are simple but important dynamical systems. This project is about the statistical properties of such dynamical systems.

Statistical properties of piecewise expanding interval maps

Speech and music signals are often modeled frame-by-frame as a sum of harmonically related sinusoids. However, short-term Fourier transforms of such signals often reveal that the peaks of the harmonics are not at exact integer multiples of the fundamental frequency, a phenomenon called inharmonicity. An important problem in audio signal processing is to find accurate estimates of the signal parameters despite such modeling mismatches. In this regard, we will be looking into the possibility of using quasi-harmonic models to develop general iterative and adaptive estimates of sinusoidal signal parameters that can also be used for audio signal processing.

"Who Said That?" - Accurate Estimation of Audio Signal Parameters

In the metal cutting industry there is a need to know how worn out a tool is. In the industry a wide variety of cutting tools are used. To narrow down this project we will focus on inserts. Inserts are 'tips' that do the actual cutting and they are replaceable which is good for the produces since it improves the machining process considerably, especially when looking at time for replacing/changing tools and the overall performance. This is a research proposal suitable for a master thesis of one or possibly two persons depending on the extent of the project. Applicants should have a good understanding of image analysis, optimization, machine learning and some programming skills. The project is done in collaboration with Sandviken AB.

Flank wear classification using image analysis

Random graphs became perhaps the most studied objects in probability theory over the last decade. Many "real-world networks" such as electrical power networks, social networks, railways, WWW, or even neuronal networks can be modelled with a help of random graphs. The most intriguing feature of random graphs is the phase transition, which is an abrupt change of global properties of a system due to a continuous change of parameters. Study of the phase transitions is central in the theory of random graphs, and information on the critical parameters is crucial for understanding of real world systems. Here are some possible areas for a Master Thesis project: -- Phase transition in dynamical random graphs. -- Modelling and analysis of evolution of a neural network. -- Spread of epidemics in biological systems.

Random networks and their applications

In many cases we see that real assets cannot be modeled with reasonable accuracy by Geometric Brownian motions. So we need more complex models to get a good fit to real data. This project will deal with techniques to valuate derivatives using such models.

Pricing of exotic derivatives in the presence of jumps and stochastic volatility

In practice we seldom know if we have used the correct model specification. Moreover even when we have the correct model structure we are not sure of the correct model parameters. Your task is to investigate the impact of mis-specification and parameter uncertainty for different applications such as valuation, hedging, risk evaluation and risk management.

Model risk in mathematical finance

De flesta avloppsvattenreningsverk i världen har minst en sedimenteringstank, i vilken separation av biologiskt slam och vatten sker under kontinuerliga flöden. Denna process kan modelleras med en olinjär partiell differentialekvation (PDE). I denna ekvation förekommer konstitutiva relationer om partiklarnas sjunkegenskaper och deras förmåga att komprimeras i botten av sedimenteringstanken. Att fastställa hur dessa konstitutiva samband ser ut utifrån verkliga satsvisa sedimenteringsförsök i en kolonn är ett inverst problem vars lösning utgör en viktig länk för att kunna få fram pålitliga modeller. Vi har tillgång till de troligtvis bästa publicerade data över sådana experiment från en forskargrupp i Belgien. Projektet innebär implementering av dels en numerisk lösare för PDEn, dels det inversa problemet, vilket kan angripas med ickelinjär optimering av parametrar i de konstitutiva antagandena.

Sedimentering av biologiskt slam – parameterkalibrering av PDE

Examensarbete i samarbete med Biologiska institutionen. Detta projekt handlar om nerver i urinblåsan. Den är i det närmaste sfärisk så för att få platta preparat klipper vi upp blåsan och plattar ut den. Huvuduppgiften är att skriva ett användarvänligt program som från denna typ av bild rekonstruerar den ursprungliga urinblåsan i tre dimensioner.

Tredimensionell rekonstruktion av tvådimensionell uppklippt sfärisk yta

This is a joint thesis proposal together with Axis Communications AB. In the project we will use both multiple axis cameras and microphones in order to detect, track and classify traffic-users (cars, bicycles, pedestrians) based on both multiple images and multiple audio. Such tracks can be used to assess trafic safety parameters and reduce risks for accidents in traffic. In the project there are several potential areas to focus on, e g camera and/or microphone node calibration, audio feature detection and tracking, audio and video feature extraction, machine learning and classification of traffic-user type.

Object classification using both video and audio

This research project concerns a comparison between different approaches to modelling dependent stochastic variables which are common in financial and actuarial applications. The main work involves investigating the difference between modelling insurance claims using multivariate credibility and copulas both from practical and theoretical point of view. Direct applications include insurance pricing where claims information related to multiple insurance coverages of a specific customer (e.g. car, boat, house, etc.) can be allowed to influence on each other. In such situations the claims dependence between coverage is crucial and an efficient method for modelling this dependence is of great interest for an insurance company. A similar problem also arises in banking where customers can have different loss inducing behaviour in correlated products such as mortgage loans, credit cards and other (potentially loss making) credit instruments. To carry out the project the student(s) should have knowledge equivalent to the course on "Statistical modelling of Multivariate Extremes"; see the home page of the course for more information: http://www.maths.lth.se/matstat/kurser/fmsn15masm23/.

On dependence modelling of insurance claims

The goal is to identify robust features of a birds song that could be used to classify different common bird species that can be seen in the suroundings. Data can be found from existing data bases but can also be recorded as a part of the master thesis. The time-varying structure of the song makes time-frequency analysis a promising tool in the classification of structures and identification of unique elements of the song. The variation of quality of the recordings is a big challenge and call for robust methods in the analysis and extraction of features. Relevant background knowledge for the project are courses in stationary stochastic processes, time series analysis and signal processing. The project is a co-operation with Molecular Ecology and Evolution Lab, department of Biology at Lund University.

Which bird is singing?

This project is part of our ongoing research regarding estimation of high frequency heart rate variability (HF-HRV) or respiratory sinus arrhythma (RSA). RSA refer to variations in heart rate that follow the respiratory cycle: when we inhale the heart beats faster and when we exhile heart beats slower. In this project we will use a classic "tilt" manouver to affect RSA. The tilt includes two conditions: supine position (laying down) and upright position. Genarally parasympathetic cardiac regulation, HF-HRV, is higher in supine position that in upright position. The aim is to study if modern robust spectral analysis methods (such as multitapers), better differentiates between the two conditions compared to traditional spectral analysis. The project is a collaboration between Mathematical statistics and Occupational- and environmental medicine at Lund University. Relevant courses are stationary stochastic processes, time series analysis and signal processing.

Spectrum analysis of Heart Rate Variability (HRV)

The project goal is to very precisely determine the timing of the onsets of different frequency components in the echolocation signal of the SONAR beam of the dolphin. In connection to ongoing research at LTH is has been recently found that dolphins can shape their SONAR beam into two separate peaks, only partially overlapping in space and frequency content instead of the more commonly seen type of beam with just one uniform peak. However, it is not yet understood how the animal generates these two peaks within the beam. One way of finding out more about this is to investigate the spatial origin of different parts of the acoustic beam. The time-frequency reassignment technique is a novel way to localize time-frequency signals. To develop such a method for localization and precise onsets and offsets would be very valuable and directly applicable to a currently very “hot” topic in marine bioacoustics as well as in signal processing. Relevant courses are stationary stochastic processes, time series analysis and signal processing. The project is done in cooperation with department of Measurement Technology and Industrial Electrical Engineering, Lund University.

Time-frequency analysis of the dolphin SONAR beam

Using time-frequency representations of EEG-signals, will give us insight into local processing properties by looking at the energy of the brain oscillations and we can shed light on the synchronization of distant brain areas by means of phase-coupling and coherence estimates. In this project, socalled stroop test data will be used, which in its classical form presents a color (e.g., "blue," "green," or "red") in a color not denoted by the name (e.g., the word "red" printed in blue ink instead of red ink). The Stroop-test measures fundamental cognitive functions, such as selective attention and cognitive control, and has shown to have substantial predictive value also in clinical psychology. At department of psychology in Lund, a form with no demand of verbal response has been developed (Digit-stroop). This can be used for different brain imaging methods such as EEG/ERP and fMRI. The goal is to comprise the analysis of EEG data by means of locally stationary process optimal multitapers, which are low-rank approximations of time-frequency kernels, for robust classification and estimation of non-stationary spectra. The project is done in cooperation with dept of Psychology, Lund University. Relevant background knowledge for the project are courses in stationary stochastic processes, time series analysis and signal processing.

Time-frequency modeling of EEG-signals

In this project probabilistic algorithms (e.g. MCMC) will be applied together with a relatively recent Bayesian methodology, named ABC (approximate Bayesian computation). ABC comes as a poweful tool allowing for Bayesian inference in situations where the likelihood function is unavailable or is expensive to evaluate. An application scenario and the specific choice for the data to consider can be negotiated with the supervisor.

Inference via Likelihood-free approximate Bayesian computation

This project focuses on registered electrophysiological reaction signals, auditory brain response (ABR) data, that originate in the brainstem when click stimuli are presented. The company SensoDetect AB has developed the globally patented SD-BERA (SensoDetect-Brainstem Evoked Response Audiometry) technology based on over thirty years research experiences in Lund University. The SD-BERA technology registers electrophysiological reaction patterns that emanate in the brain when specific sound stimuli are presented. Today the brainstem activity is usually illustrated as microvolt activity vs time in milliseconds. The goal is to visulize the brainstem responses using time-frequency analysis and possibly to amplify certain features and to reduce noise. The data will be healthy control recordings and possibly also recordings from different patient groups, e.g., to compare intrasubject changes due to placebo and neuroactive substances. Relevant courses are stationary stochastic processes, time series analysis and signal processing.

Time-frequency analysis of auditory brainstem data

På institutionen för cell- och organismbiologi studeras hur nervcellsutskott väljer väg på konstgjorda underlag. Tanken är att kunna styra nervcellernas utskott (axoner) till specifika ställen på till exempel elektroniska chip. Examensarbetet går ut på att modellera och simulera hur enstaka nervutskott växer till sig på olika underlag, som kan vara preparerade med t.ex. spår i försök att styra tillväxten.

Modellering och simulering av tillväxt av nervutskott på ytor

Koncentrationen av fordon längs en väg kan modelleras med en olinjär PDE, som innehåller konstitutiva antaganden vilka behöver kalibreras för att modellen ska kunna användas. Kalibrering görs genom att jämföra modell-lösning med filmer av trafikflöden. Projektet omfattar matematisk teori, numerik, programmering, optimering, och viss bildanalys. Därför lämpar det sig för 2 personer.

Kalibrering och simulering av trafikflöde som modelleras med olinjär PDE