2018

Abstracts, see below.

18/1 - Bernhard Mehlig (GU): DNA extension in nano-channels
15/2 - Giovanni Volpe (GU): Active Matter in Complex and Crowded Environments
27/2 (Tuesday) - Ruth Baker (University of Oxford): In vitro and in vivo studies of tissue growth: model building and validation using quantitative data
15/3 -  Niek Welkenhuysen & Johannes Borgqvist (Chalmers/GU): A systems biology approach to identify the source of cell-to-cell variability
12/4 -  Johannes Borgqvist (Chalmers/GU): The triangle of ageing: dynamic damage retention and repair are essential
19/4 - Raj Bhansali (Imperial College): Rational Spectral Density Models For Lattice Data
17/5 - Adam Malik (Chalmers/GU):  Modelling cell migration as a jump process with spatially dependent rates
24/5 - Erwan Koch (EPFL): Spatial risk measures induced by powers of max-stable random fields. Abstract
31/5 - Henrike Häbel (Natural Resources Institute Finland): Remote sensing based estimation of forest biodiversity
7/6 - Thordis Thorarinsdottir (Norwegian Computing Center): Paths and pitfalls in model evaluation: The importance of being proper
13/6 (Wednesday at 10:00 in MVL15): Roeland Mercks (Universiteit Leiden): Mathematical biology of mechanical cell-extracellular matrix interactions during angiogenesis
6/9 - Lukas Käll (KTH Genteknologi, SciLifeLab): Distillation of label-free quantitative mass spectrometry data by clustering and Bayesian modeling
14/9 - Alex Fletcher (University of Sheffield): Mathematical modelling and analysis of epithelial morphogenesis
17/9 - Julia Gog (Cambridge University): Some topics in infectious disease modelling
26/9 - Andreas Deutsch (Technical University of Dresden): Biological lattice-gas cellular automaton models for the analysis of collective behaviour in interacting cell populations
27/9 - Jukka Corander (Department of Biostatistics, University of Oslo): Resolving the mysteries of bacterial evolution by ultra-fast ABC inference
28/9 - Kenneth C. Millett (Department of Mathematics, University of California Santa Barbara): Knots and Links in Proteins
4/10 - Marco Longfils: Single diffusing particles observed through a confocal microscope: an application of the doubly stochastic Poisson point process
5/10 - Charlotte Hemelrijk (University of Groningen): Collective motion of flocks in relation to a predator
9/10 - Gunnar Carlsson (Stanford): Topological Data Analysis and Deep Learning. This seminar is joint with Computational and Applied Mathematics.
11/10 - Maria Bruna (Oxford University): Diffusion of particles with short-range interactions
19/10 - Maria-Rita D’Orsogna (California State University Northridge): Mathematical Models of Criminal Behaviour
25/10 - Harri Lähdesmäki (Department of Computer Science at Aalto University School of Science): Non-parametric methods for learning continuous-time dynamical systems
1/11 - Petter Mostad (Chalmers): Error rates for unvalidated medical age assessment procedures
7/11 - Thomas Schön (Dept. of Information Technology, Uppsala University): Assembling stochastic quasi-Newton algorithms using Gaussian processes
21/11 - Josef Wilzén: Physiological Gaussian Process Priors for the Hemodynamics in fMRI Analysis


24/5 - Erwan Koch (EPFL): Spatial risk measures induced by powers of max-stable random fields
A meticulous assessment of the risk of extreme environmental events is of great necessity for populations, civil authorities as well as the insurance/reinsurance industry. Koch (2017, 2018) introduced a concept of spatial risk measure and a related set of axioms which are well-suited to analyse and quantify the risk due to events having a spatial extent, precisely such as natural disasters. In this paper, we first carry out a detailed study of the correlation (and covariance) structure of powers of the Smith and Brown-Resnick max-stable random fields. Then, using the latter results, we thoroughly investigate spatial risk measures associated with variance and induced by powers of max-stable random fields. In addition, we show that spatial risk measures associated with several classical risk measures and induced by such cost fields satisfy (at least) part of the previously mentioned axioms under appropriate conditions on the max-stable fields. Considering such cost fields is particularly relevant when studying the impact of extreme wind speeds on buildings and infrastructure.

Key words: Powers of max-stable random fields; Spatial dependence; Spatial diversification; Spatial risk measures and corresponding axioms; Wind damage.

The corresponding paper is available at
https://arxiv.org/pdf/1804.05694.pdf

References in the abstract:
- Koch, E. (2017). Spatial risk measures and applications to max-stable processes. Extremes, 20(3):635-670.
- Koch, E. (2018). Spatial risk measures and rate of spatial diversification. Available at https://arxiv.org/abs/1803.07041

6/9 - Lukas Käll (KTH Genteknologi, SciLifeLab): Distillation of label-free quantitative mass spectrometry data by clustering and Bayesian modeling
Abstract: Protein quantification by label-free shotgun proteomics experiments is complicated by a multitude of error sources. Typical pipelines for identifying differentially expressed proteins use intermediate filters in an attempt to control the error rate. However, they often ignore certain error sources and, moreover, regard filtered lists as completely correct in subsequent steps. These two indiscretions can easily lead to a loss of control of the false discovery rate (FDR). We propose a probabilistic graphical model, Triqler, that propagates error information through all steps, employing distributions in favour of point estimates, most notably for missing value imputation. The model outputs posterior probabilities for fold changes between treatment groups, highlighting uncertainty rather than hiding it. We will also discuss a method, MaRaQuant, in which we reverse the typical processing workflow into a quantification-first approach. Specifically, we apply unsupervised clustering on both MS1 and MS2 level to summarize all analytes of interest without assigning identities. This ensures that no valuable information is discarded due to analytes missing identification thresholds and as well allows us to spend more effort on the identification process due to the data reduction achieved by clustering.

Proteomics; Graphical Models; Clustering; Mass spectrometry; Data Analysis

14/9 - Alex Fletcher (University of Sheffield): Mathematical modelling and analysis of epithelial morphogenesis
Abstract: The study of morphogenesis - the generation of biological shape and form - promises to shed light on a wide range of developmental defects and inform strategies for the artificial growth of organs. Recently, the experimental study of morphogenesis has thrived due to a rise in quantitative methods. The resulting avalanche of data motivates us to design quantitative hypotheses through mathematical models, make quantitative experimental predictions, devise methods for quantitative data analysis, and design methods for quantitative inference using models and data. In this talk, I describe our recent work on the integrative analysis of morphogenesis in epithelia, one of the major tissue types in animals. Focusing on a widely used cell-based model of epithelia, the vertex model, I discuss to what extent quantitative model predictions may be influenced by parameter values and implementation details. Next, I illustrate how such models can be used to help gain mechanistic insights into, and generate quantitative predictions on, morphogenetic processes such as tissue size control and axis extension. I then outline a method for estimating mechanical parameters of vertex models from imaging data and quantifying the uncertainty associated with such estimates. Together, these contributions help enable the quantitative study of epithelia for a wide range of applications.

27/9 - Jukka Corander (Department of Biostatistics, University of Oslo): Resolving the mysteries of bacterial evolution by ultra-fast ABC inference.
Abstract: DNA in bacteria is known to be a subject to multiple evolutionary forces, including mutations, homologous recombination and horizontal transfer of genes. Such changes may be beneficial, deleterious or selectively neutral. Several models have been proposed to explain the variation we see in the genomes of bacteria across natural populations, including ecotype and neutral models. In particular simple neutral models have been shown to have a surprisingly good fit to population surveys. However, in the light of most recent functional data we present conclusive evidence that both neutral and ecotype models provide poor explanations for the strong correlations discovered between accessory genome loci across multiple populations of Streptococcus pneumoniae, a major human pathogen. We introduce a mechanistic model of frequency-dependent selection operating via accessory genes which is able to accurately predict the changes to the composition of the populations following introduction of a vaccination campaign. Unrelated recent large-scale genome data from an E. coli population suggests that the frequency-dependent selection may be a common mechanism regulating the evolution of bacterial populations of many species. These modeling advances have been in practice enable by ultra-fast ABC inference based on Bayesian optimization, which can be up to 4 orders of magnitude faster than sequential population Monte Carlo. The general potential of this inference method is now harnessed by the new open-source software initiative ELFI, which offers automated parallelization and a flexible platform for algorithm developers.

https://www.nature.com/articles/s41559-017-0337-x
https://www.biorxiv.org/content/early/2018/08/28/400374
http://jmlr.csail.mit.edu/papers/v17/15-017.html
http://jmlr.csail.mit.edu/papers/v19/17-374.html  

28/9 - Kenneth C. Millett (Department of Mathematics, University of California Santa Barbara): Knots and Links in Proteins
Abstract: Some proteins contain important topological structures: knots, slipknots, and links as well as spatial graphs if one includes cysteine bonds.  As a consequence, the geometrical and topological character of these spatial structures is of interest to mathematicians as well as molecular biologists, biochemists and biophysicists.  We will describe characterizations of these spatial geometric and topological structures within proteins.

4/10 - Marco Longfils: Single diffusing particles observed through a confocal microscope: an application of the doubly stochastic Poisson point process
Abstract: Diffusing particles observed with a confocal laser scanning microscope give rise to a doubly stochastic Poisson point process. In particular, the photon detected by the microscope in one pixel follows a Poisson distribution with parameter that depends on the particle positions in space, which is modelled as a Poisson point process. Many techniques such as Fluorescence correlation spectroscopy, Raster image correlation spectroscopy and photon counting histograms have been developed to study molecular transport in cells and solution. All these techniques are based on the statistics of the photon detection process.
We show that the moments of the photon detection process can be computed in terms of physically relevant parameters such as the diffusion coefficient of the particles, their brightness and others. As a direct consequence, the statistical accuracy of the above mentioned techniques can be evaluated. Thus, we can relate the different experimental parameters that affects the photon detection process to the accuracy of each techniques, allowing us to optimally design an experiment.

5/10 - Charlotte Hemelrijk (University of Groningen): Collective motion of flocks in relation to a predator
Abstract: Many species of animals live in groups. This is supposed to protect them against predation. Yet when animals aggregate, they are easier to detect from a distance due to the larger mass of the group. Two evolutionary computational models of collective motion (including ours)  show that grouping is advantageous for survival of prey only when the predator can be confused as to whom to attack. This confusion effect we  also studied in an experimental design with human ‘predators’ when attacking starlings that flock in a computer simulation called StarDisplay. Humans appeared to become more confused whom to attack, the larger and denser flocks are. 
Grouping animals also seem to protect themselves actively against attacks by displaying many patterns of collective escape in relation to the presence of predators, such as herd, ball, flash expansion, agitation wave. Using two computational models, we explain how some of them may arise.  Asking when patterns of collective escape appear and whether they offer extra protection to groups of prey, we recorded them for flocks of starlings in Rome. It became clear that some are a direct reaction to an attack of the raptor, others already to its mere presence. Remarkably, in our empirical data the display of patterns of collective escape does not reduce the raptor’s catch success, leaving interesting questions concerning their emergence and asking for new methods of studying them.

25/10 - Harri Lähdesmäki (Department of Computer Science at Aalto University School of Science): Non-parametric methods for learning continuous-time dynamical systems
Abstract: Conventional differential equation models are parametric. However, for many complex/real-world systems it is practically impossible to determine parametric equations or interactions governing the underlying dynamics, rendering conventional models unpractical in many applications. To overcome this issue, we propose to use nonparametric models for differential equations by defining Gaussian process priors for the vector-field/drift and diffusion functions. We have developed statistical machine learning methods that can learn the underlying (arbitrary) ODE and SDE systems without prior knowledge. We formulate sensitivity equations for learning or use automatic differentiation with explicitly defined forward simulator for efficient model inference. Using simulated and real data, we demonstrate that our non-parametric methods can efficiently learn the underlying differential equation system, show the models' capabilities to infer unknown dynamics from sparse data, and to simulate the system forward into future. I will also highlight how our non-parametric models can learn stochastic differential equation transformations of inputs prior to a standard classification or regression function to implement state-of-the-art methods for continuous-time (infinitely) deep learning.
https://arxiv.org/abs/1803.04303
https://arxiv.org/abs/1807.05748
https://arxiv.org/abs/1810.04066

1/11 - Petter Mostad (Chalmers): Error rates for unvalidated medical age assessment procedures
Abstract: During 2014–2015, Sweden received asylum applications from more than 240,000 people of which more than 40,000 were termed unaccompanied minors. In a large number of cases, claims by asylum seekers of being below 18 years were not trusted by Swedish authorities. To handle the situation, the Swedish national board of forensic medicine (Rättsmedicinalverket, RMV) was assigned by the government to create a centralized system for medical age assessments.
RMV introduced a procedure including two biological age indicators; x-ray of the third molars and magnetic resonance imaging of the distal femoral epiphysis. In 2017, a total of 9617 males and 337 females were subjected to this procedure. No validation study for the procedure was however published, and the observed number of cases with different maturity combinations in teeth and femur were unexpected given the claims originally made by RMV. We present a general stochastic model enabling us to study which combinations of age indicator model parameters and age population profiles are consistent with the observed 2017 data for males. We find that, contrary to some RMV claims, maturity of the femur, as observed by RMV, appears on average well before maturity of teeth. According to our estimates, approximately 15% of the tested males were children. These children had an approximate 33% risk of being classified as adults. The corresponding risk for an adult to be misclassified as a child was approximately 7%.
We determine uncertainties and ranges of estimates under reasonable perturbations of the prior. https://rdcu.be/6PNI

7/11 - Thomas Schön (Dept. of Information Technology, Uppsala University): Assembling stochastic quasi-Newton algorithms using Gaussian processes
Abstract: In this talk I will focus on one of our recent developments where we show how the Gaussian process (GP) can be used to solve stochastic optimization problems. Our main motivation for studying these problems is that they arise when we are estimating unknown parameters in nonlinear state space models using sequential Monte Carlo (SMC). The very nature of this problem is such that we can only access the cost function (in this case the likelihood function) and its derivative via noisy observations, since there are no closed-form expressions available. Via SMC methods we can obtain unbiased estimates of the likelihood function. However, our development is fully general and hence applicable to any stochastic optimization problem. We start from the fact that many of the existing quasi-Newton algorithms can be formulated as learning algorithms, capable of learning local models of the cost functions. Inspired by this we can start assembling new stochastic quasi-Newton-type algorithms, applicable in situations where we only have access to noisy observations of the cost function and its derivatives. We will show how we can make use of the GP model to learn the Hessian allowing for efficient solution of these stochastic optimization problems. Additional motivation for studying the stochastic optimization problem stems from the fact that it arise in almost all large-scale supervised machine learning problems, not least in deep learning. I will very briefly mention some ongoing work where we have removed the GP representation and scale our ideas to much higher dimensions (both in terms of the size of the dataset and the number of unknown parameters).

21/11 - Josef Wilzén: Physiological Gaussian Process Priors for the Hemodynamics in fMRI Analysis
Abstract: Inference from fMRI data faces the challenge that the hemodynamic system, that relates the underlying neural activity to the observed BOLD fMRI signal, is not known. We propose a new Bayesian model for task fMRI data with the following features: (i) joint estimation of brain activity and the underlying hemodynamics, (ii) the hemodynamics is modelled nonparametrically with a Gaussian process (GP) prior guided by physiological information and (iii) the predicted BOLD is not necessarily generated by a linear time-invariant (LTI) system. We place a GP prior directly on the predicted BOLD time series, rather than on the hemodynamic response function as in previous literature. This allows us to incorporate physiological information via the GP prior mean in a flexible way. The prior mean function may be generated from a standard LTI system, based on a canonical hemodynamic response function, or a more elaborate physiological model such as the Balloon model. This gives us the nonparametric flexibility of the GP, but allows the posterior to fall back on the physiologically based prior when the data are weak. Results on simulated data show that even with an erroneous prior for the GP, the proposed model is still able to discriminate between active and non-active voxels in a satisfactory way. The proposed model is also applied to real fMRI data, where our Gaussian process model in several cases finds brain activity where a baseline model with fixed hemodynamics does not.

Published: Fri 15 Feb 2019.