Department of Mathematics

CoSy Seminars Autumn 2016

29 November
SpeakerMariarosa Mazza, Max-Planck-Institut fur Plasmaphysik, Garching bei Munchen, Germany
Title: The GLT theory and some applications to fractional diffusion equations 
Place: A11167
Time: 12:00 -- 13:00

22 November
SpeakerGinevra Castellano, Division of Visual Information and Interaction, Department of Information Technology, Uppsala University
Title: Robots for learning
Place: A11167
Time: 12:00 -- 13:00

15 November
Speaker: Prof. Zoltan Kato, University of Szeged, Institute of Informatics
Title: Relative Pose Estimation of Omnidirectional, Perspective and Lidar Camera Systems
Place: A11167
Time: 12:00 -- 13:00

8 November
Speaker: Ruth Baker, Mathematical Biology, Oxford Centre for Collaborative Applied Mathematics
Title:  Cell biology processes: model validation using quantitative data
Place: A11167
Time: 12:00 -- 13:00

25 October
Speaker: Prof. Dr. Antoine VACAVANT ISIT (Image Science for Interventional Techniques), Université d'Auvergne Clermont1 - CNRS, France
Title: Computer aided diagnosis and treatment of liver pathologies
Place: A11167
Time: 12:00 -- 13:00

11 October
Speaker: Prof. Dr. Caroline Lasser, Zentrum Mathematik - M3, Technische Universität München
TitleSemiclassical methods for computing molecular quantum dynamics
Place: A4007
Time: 12:00 -- 13:00

11 October
Speaker:  Massimo Buscema,Semeion Research Center, Rome, Italy & Dept of Mathematical and Statistical Sciences, University of Colorado, Denver, USA
TitleHidden Information Invariants in Nature and in Cultures
Place: A4007
Time: 13:00 -- 14:30

23 August
Speaker:  Prof.dr.ir. C.W. Oosterlee , CWI - Center for Mathematics and Computer Science Amsterdam, the Netherlands
TitleFourier, Wavelet and Monte Carlo Methods in Computational Finance
Place: Polacksbacken 4308
Time: 12:00 -- 13:00
Local contact person: Lina von Sydow, Elisabeth Larsson

29 November
SpeakerMariarosa Mazza, Max-Planck-Institut fur Plasmaphysik, Garching bei Munchen, Germany
Title: The GLT theory and some applications to fractional diffusion equations 
Place: A11167
Time: 12:00 -- 13:00
Abstract:
When discretizing a linear PDE by a linear numerical method, the computation of the numerical solution reduces to solving a linear system. The size of this system grows when the discretization parameter n increases, i.e., when we refine the discretization mesh. We are then in the presence of a sequence of linear systems  with increasing size. It is usually observed in practice that the corresponding sequence of discretization matrices {An} inherits a structure from the continuous problem and enjoys an asymptotic spectral distribution, which is compactly described by a function, the so-called symbol. The knowledge of the symbol and of its properties has a very crucial role, since it can be used to perform a convergence analysis and predict the behavior of preconditioned Krylov and multigrid methods applied to An, or to design effective preconditioners and multigrid solvers for the associated linear systems.
The main tool for computing spectral symbols of PDE discretization matrices is the theory of Generalized Locally Toeplitz (GLT) sequences [4]. In this talk, we discuss such a theory and we outline its application to the Fractional Diffusion Equations (FDEs), a generalization of classical PDEs used to model anomalous diffusion phenomena. More precisely, using the GLT machinery, we provide a spectral analysis of the FDE discretization matrices both in the case of constant and nonconstant diffusion coefficients.
The obtained spectral information allow us to easily derive results on the optimality of some multigrid methods and circulant preconditioners recently appeared in the literature [3, 2]. Moreover, such spectral analysis guides the design of new preconditioning and multigrid strategies. In detail, we propose structure preserving preconditioners with minimal bandwidth (and so with efficient computational cost) and geometric multigrid methods for 1D and 2D problems, respectively (see [1] for the proposals in the 1D case). Some numerical results confirm the theoretical analysis and the quality of the proposed algorithms.
References
[1] M.Donatelli,M.Mazza,S.Serra-Capizzano,Spectralanalysisandstructurepreservingpreconditionersforfractional diffusion equations, J. Comput. Phys., 307 (2016) 262–279.
[2]  S. L. Lei, H. W. Sun, A circulant preconditioner for fractional diffusion equations, J. Comput. Phys., 242 (2013) 715–725.
[3]  H. Pang, H. W. Sun, Multigrid iterative methods for fractional diffusion equations, J. Comput. Phys., 231 (2012) 693–703.
[4]  S. Serra-Capizzano, The GLT class as a generalized Fourier Analysis and applications, Linear Algebra Appl., 419 (2006) 180–233. 

22 November
Speaker: Ginevra Castellano, Division of Visual Information and Interaction, Department of Information Technology, Uppsala University
Title: Robots for learning
Place: A11167
Time: 12:00 -- 13:00
Abstract:
Robotics is now one of a few technologies that have the potential to have an impact over the next few decades similar to the one that the Internet has today. One of the main reasons is that new robotics applications are extending the role of robots beyond those dangerous and difficult jobs that humans do not want or cannot do to socially assistive scenarios that aim to help people in more personal ways and provide not only physical, but also social support. Robots are now developed to act as assistants and companions for the elderly at home, as educational tutors, as therapeutic tools for children with autism, as instructors in industrial settings, as systems that can effectively signal their internal states and intentions to humans through progressively more social and human-like appearance and behaviour.
This talk will give an overview of my work on robots used as educational agents to support children's learning in different instructional scenarios. The focus of the talk will be on computational models for robot's learning to adapt to individual users. Examples of work from the EU-funded LIREC (Living with robots and interactive companions) and EMOTE (Embodied-perceptive tutors for empathy-based learning) projects, as well as from ongoing projects, will be presented.

15 November
Speaker: Prof. Zoltan Kato, University of Szeged, Institute of Informatics
Title: Relative Pose Estimation of Omnidirectional, Perspective and Lidar Camera Systems
Place: A11167
Time: 12:00 -- 13:00
Abstract: A novel method is presented for the relative pose estimation of a camera - 3D lidar pair without the use of any special calibration pattern or point correspondences. The proposed method has no specific assumption about the data source: plain depth information is expected from the lidar scan and a central projection camera (both traditional perspective or omnidirectional) is used for the 2D images. The calibration is solved as a 2D-3D registration problem using a minimum of one (for extrinsic) or two (for intrinsic-extrinsic) planar regions visible in both cameras. The registration is then traced back to the solution of a non-linear system of equations which directly provides the calibration parameters between the bases of the two sensors. The method has been tested on a large set of synthetic lidar - camera image pairs as well as on real data acquired in outdoor environment.

8 November
Speaker: Ruth Baker, Mathematical Biology, Oxford Centre for Collaborative Applied Mathematics
Title:  Cell biology processes: model validation using quantitative data
Place: A11167
Time: 12:00 -- 13:00
Abstract:
Cell biology processes such as motility, adhesion, proliferation and death are essential to a host of phenomena such as development, wound healing and tumour invasion, and a huge number of different modelling approaches have been applied to study them. In this talk I will focus on an on-lattice exclusion process model, where each cell occupies at most one lattice site, and simple rules are used to encode cell behaviours. I will discuss the extent to which parameters of this model can be inferred data from simple cell biology assays, demonstrating that different summary statistics of the data are useful in different contexts, and how experiments can be designed to maximize the utility of the data with respect to the model under consideration.

11 October
Speaker: Prof. Dr. Caroline Lasser, Zentrum Mathematik - M3, Technische Universität München
Title: Semiclassical methods for computing molecular quantum dynamics
Place: A4007
Time: 12:00 -- 13:00
Abstract: The time-dependent semiclassical Schroedinger equation is the key equation of molecular quantum dynamics. In this talk we review several numerical methods in the field, as the Herman-Kluk propagator, the linearised semiclassical initial value representation or Landau-Zener type surface hopping. Our results are joint work with Clotilde Fermanian-Kammerer, Johannes Keller, and David Sattlegger.

11 October
Speaker:  Massimo Buscema, Semeion Research Center, Rome, Italy & Dept of Mathematical and Statistical Sciences, University of Colorado, Denver, USA
Title: Hidden Information Invariants in Nature and in Cultures
Place: A4007
Time: 13:00 -- 14:30
Abstract: A System is a compact region into the space-time. A System Dynamics is generated by the local and parallel interaction of its atomic components trough the time. The apparent rules governing this dynamics are simply one of the effects of the dynamics itself trough the time. A system is complex when its global dynamics is unpredictable by a local point of view and when this dynamics is not equal to the summation of the dynamics of its components (Multiphase system).  A complex system is by the way an adaptive system.

23 August
Speaker:  Prof.dr.ir. C.W. Oosterlee , CWI - Center for Mathematics and Computer Science Amsterdam, the Netherlands
TitleFourier, Wavelet and Monte Carlo Methods in Computational Finance
PlacePolacksbacken 4308
Time: 12:00 -- 13:00
Local contact person: Lina von Sydow, Elisabeth Larsson
Abstract:
In this presentation we will explain how we can solve linear, semi-linear as well as nonlinear partial differential equations by the concept of conditional expectations  and (backward) stochastic differential equations, Fourier cosine expansions, wavelets and Monte Carlo simulation. We connect this to typical research questions in finance from a mathematical perspective.  We will discuss in some detail the highly efficient pricing of financial options in the Fourier context. The use of the Stochastic Grid Bundling Method (SGBM) which is a Monte Carlo technique in the financial context of high-dimension option pricing and risk management is also explained.

25 October
Speaker: Prof. Dr. Antoine VACAVANT ISIT (Image Science for Interventional Techniques), Université d'Auvergne Clermont1 - CNRS, France
Title: Computer aided diagnosis and treatment of liver pathologies
Place: A11167
Time: 12:00 -- 13:00
Abstract:
Liver cancer is the third leading cancer in the World and reveals numerous researches in both clinical studies about the evolution of the lesions for health-care issues and methodologies from fields related to computer science and mathematics as image processing, visualization, pattern recognition or simulation. In particular, the HepatoCellular Carcinoma (HCC) is one of the most critical primal cancers, leading to 500,000 new cases per year in the World. In this talk, I will present the recent research activities of the ’Embolization in parenchymal disease’ group within the ISIT lab (Image Science for Interventional Techniques). Our multi-disciplinary group aims at making the connection between (1) clinical research about intermediate and advanced HCC diagnosis and treatment (by TransArterial Chemo- Embolization or TACE) and (2) fundamental research at the intersection between digital geometry and topology, image processing, computer vision and even machine learning. In addition, I will expose our current projects and collaborations, devoted to two main targets : (1) the automatic detection of liver diseases within medical images, by the means of home- made algorithms ; (2) the numerical simulation of drug delivery within the liver components and its possible lesions.