Past events 2010

References for the data examples are:

Hay, J.L. and Pettitt, A.N. (2001): Bayesian analysis of a time series of counts with covariates: an application to the control of an infectious disease. Biostatistics, 2, 433-444.

A seminar in our special series of seminars, "Matematiske Perler" (= Mathematical Pearls") - seminars that will be of general interest for mathematicians within all mathematical disciplines and other scientists with mathematical interest.

In verification of concurrent and reactive systems, one generally seeks to assert properties of systems expressed in terms of sets of traces (or languages) or in terms of computation trees. The language point of view leads to what is generally called linear semantics, whereas the tree point of view leads to branching semantics.  When working with applications in complex reactive systems or in embedded systems, classical notions of linear and branching equivalence (or inclusion) of processes often need to be extended to accommodate quantitative information. In such settings, equivalences and inclusions are replaced by symmetric or asymmetric distances between systems.

This thesis focuses on models and methodology for spatial data of two distinct types: spatial point pattern data composed of the random locations of an event of interest are analyzed using point process models, and lattice data composed of the values of a random quantity at fixed locations are analysed using random field models.

In classical statistics the score test is commonly used for model selection and for model validation. In spatial statistics, the score test is used mainly to support formal inference about covariate effects for Poisson point process models. In the thesis it is described how the score test can be applied in the case of much more general point processes with interactions between points. The thesis also provides theoretical support for the established practice of using functional summary statistics to study clustering and inhibition between points. It is shown that the customary goodness-of-fit procedure of comparing a functional summary statistic of the data with its expectation under the model can be interpreted as a score test for point process models. Furthermore, new graphical diagnostics for assessing the goodness-of-fit of a point process model are developed based on the score test and on score test approximations.

In the thesis alpha-permanental random fields are studied in detail. They constitute a flexible model class for non-negative integer valued lattice data with positive associations between locations, meaning that values at two locations close to each other tend to be alike. Such data e.g. appear when counting the cases of a particular disease within a number of administrative regions. In this example it is of interest to estimate the model parameters and the disease incidence ratio in each region. While the likelihood of an alpha-permanental random field model can be expressed on closed form, it is usually very computer intensive to evaluate. To accommodate this problem it is shown how inference can be based either on approximate evaluation of the likelihood or on less computer intensive quantities such as the quasi-likelihood or composite likelihood. Furthermore, a computationally tractable empirical Bayes estimate is given for the incidence ratios in the example above.

Video i stedet for eller som supplement til traditionel undervisning giver både muligheder og begrænsninger. Hvis ens hold så små, at den traditionelle undervisning er for dyr, eller man bare gerne vil prøve noget pædagogisk nyt for at få de studerende til at forstå stoffet, kan asynkron videoundervisning måske være en mulighed. Jeg vil fortælle om nogle forskellige løsninger (dyre såvel som billige) og mine erfaringer med disse, bl.a. til fjernundervisning. 

Since for a Neyman-Scott process the Papangelou conditional intensity does not have a closed analytical form, one cannot use the martingale residuals to assess the goodness-of-fit of the fitted Neyman-Scott model. On the other hand, the Laplace functional of Neyman-Scott processes can be expressed in a closed analytical form. In this talk, I will discuss about the Laplace functional residuals and how they can be useful in  model checking for cluster point process models.

Video i stedet for eller som supplement til traditionel undervisning giver både muligheder og begrænsninger. Hvis ens hold så små, at den traditionelle undervisning er for dyr, eller man bare gerne vil prøve noget pædagogisk nyt for at få de studerende til at forstå stoffet, kan asynkron videoundervisning måske være en mulighed. Jeg vil fortælle om nogle forskellige løsninger (dyre såvel som billige) og mine erfaringer med disse, bl.a. til fjernundervisning. 

Sparse approximation techniques have been at the core of a rapidly evolving and very active area of research since the 1990s. Their most visible technological success has certainly been in the compression of high-dimensional data using wavelets. However, approximating a signal or an image with a sparse linear expansion from a possibly overcomplete dictionary of basis functions (called atoms) has turned out to be an extremely useful tool to solve many other signal processing problems. In this talk, I will discuss some of the mathematical and computational aspects of sparse representations using redundant dictionaries.

Everybody is welcome!

After the lecture the Department will host a small reception.

Since the days of Georg Cantor mathematicians have availed themselves of transfinite methods. The most common of these methods is probably the use of Zorn’s Lemma or the axiom of choice. These methods have been so successful that David Hilbert in the famous paper On the Infinite claimed: “No one shall drive us out of the paradise which Cantor has created for us”. However, it was not possible for Hilbert and other mathematicians interested in the foundations of mathematics to find a consistent and epistemological solid justification of these important transfinite methods.

Today we know that the axiom of choice and other strong axioms are independent of ordinary set theory (ZF), but we have no guarantee of the consistency of either ZF or our transfinite methods. Although mathematical results seem to hold with unerring certainty we have no proof of this because our mathematical proof procedures involve or presuppose transfinite methods that cannot be reduced to more elementary and acceptable methods.

The lecture has two purposes:

1) To recall and elaborate some results from the extension theory for elliptic operators. It dates back many years, but has been revived in recent years by increased interest. One of the purposes is to establish Krein resolvent formulas, which link the resolvents of general realizations with the resolvent of a fixed well-known “reference operator”, and involve certain Weyl-Titchmarsh operator-valued holomorphic functions.

2) To indicate how the results can be extended to nonsmooth situations (nonsmooth domain and coefficients); this demands modern techniques.

The main interest of our research is investigations of the dynamics and trafficking of receptors (trans-membrane proteins) in the cell membrane, using advanced fluorescence microscopy. The proteins of interest play major roles in neuronal processes relating to the development of neurodegenerative and mood disorders. A detailed understanding of these processes at the molecular level is a pre-request for understanding these complex diseases and for qualified development of new drugs with high specificity and sensitivity and fewest possible side effects. In fluorescence microscopy small fluorescent probes are attached specifically to the protein, allowing the localization or trafficking of the proteins within the cells to be visualized. We can apply state of the art fluorescence microscopy techniques for advanced imaging of living and fixed cells in culture and tissue. Given our interdisciplinary background, ranging from biology and medicine to statistics and mathematics, we are in a strong position to extract quantitative information about intracellular protein diffusion and interaction behaviour under physiological conditions. The techniques that we intend to apply are FRET (Fluorescence Resonance Energy Transfer) microscopy, FLIM (Fluorescence Lifetime Imaging Microscopy), FCS (Fluorescence Correlation Spectroscopy) and FRAP (Fluorescence Recovery After Photobleaching) microscopy. All of these techniques are relatively well-established at the basic level but we would like to take them one step further by developing statistical and mathematical models that will allow us to understand in greater depth the molecular processes giving rise to the measured observables.

Joint work with Merete Raarup and Eva Bjørn Vedel Jensen

Host: Jesper Møller