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Mathematics of Data Analysis - Oberseminar

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  • 18.10.2016: We restart the seminar with a talk of Michael Sandbichler.

Dates

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Winter semester 2016/2017  

Tuesday, 04.04.2017 10:30-11:30
Speaker: Thomas Fink Pfeil (Universität Passau)
Title:
In various fields of image analysis, determining the precise geometry of occurent edges, e.g. the contour of an object, is a crucial task. Especially the curvature of an edge is of great practical relevance. In this talk, we introduce an extension of the continuous shearlet transform which additionally utilizes shears of higher order. This extension, called the Taylorlet transform, allows for a detection of the position and orientation, as well as the curvature and other higher order geometric information of edges. Furthermore, we introduce novel vanishing moment conditions of the form \( \int_{\mathbb{R}} g \left( \pm t^k \right) t^m dt \). We will show that Taylorlets fulfilling such conditions enable a more robust detection of the geometric edge features.
Room: 02.10.011

Tuesday, 28.03.2017 10:30-11:30
Speaker: Dr. Ilaria Lucardesi Pfeil (École des Mines de Nancy)
Title:
The two most studied elliptic PDEs are probably the torsion problem, also known as St-Venant problem, and the Dirichlet eigenvalue problem. For these classical problems, many estimates and qualitative properties have been obtained, see for example works by P\'olya, Szeg\"o, Schiffer, Payne, Hersch, Bandle, and many others. In this seminar I present some recent results about upper and lower bounds of two shape functionals involving the maximum of the torsion function: I consider the ratio $T(Omega)\lambda_1(Omega) Omega$ and the product $M(Omega)\lambda_1(Omega)$, where $Omega$ is bounded open set with finite Lebesgue measure $Omega$, $T(\Omega)$ denotes the torsion, and $\lambda_1(\Omega)$ the first Dirichlet eigenvalue. Particular attention is devoted to the subclass of convex sets.
Room: 02.12.020

Wednesday, 01.03.2017 11:00-12:00
Speaker: Patrick van Meurs Pfeil (Kanazawa University)
Title:
The starting point is a 2D model for the dynamics of n dislocations, which are modelled as point particles with a positive or negative ’charge’. In the celebrated engineering paper by Groma and Balogh in 1999, the limit passage n → ∞ of these dislocation dynamics is performed in a statistical mechanics framework, which relies on a phenomenological closure assumption. In my talk, I present how to pass rigorously to the limit n → ∞ by using the theory of Wasserstein gradient flows and using advanced functional analysis on the weak form of the evolution equation. Interestingly, our conclusion for the limiting dynamics of the dislocation density differs from the conclusion in the paper by Groma and Balogh.
Room: 02.08.011

Tuesday, 07.02.2017 16:00-17:00
Speaker: Kiryung Lee Pfeil (Georgia Tech)
Title:
Multichannel blind deconvolution resolves unknown input signal from multiple channel outputs with unknown impulse responses. It is often easier to estimate only the unknown channel impulse responses when they are modeled with only few parameters. This is the case with channel estimation problems in wireless communications and underwater acoustics. In particular with FIR models, various reconstruction methods based on statistics of the input signal and/or the commutativity of the convolution operator have been proposed with algebraic performance guarantees in 1990s. However, these guarantees are restricted to the case where the observations are noise-free or the input has infinite length. In fact, with finitely many noisy observations, the empirical performance of these classical methods deteriorates dramatically as the length of observation decreases. This weakness restricts their utility in estimating time-varying channels. Motivated from the observation that parametric models with few parameters can be embedded into low-dimensional subspaces, we propose modifications on the classical methods leveraging these subspace models. Our proposed method provides significant improvement over the original method in terms of providing stable estimates from finitely many noisy measurements. Furthermore, using recently developed tools in applied probability, we derive rigorous performance guarantees under certain random subspace models. We verify that the numerical results are aligned with our theory through Monte Carlo simulations. Furthermore, we also verify the empirical success in a realistic setup of channel delay estimation. Finally, we extend the methods and theory to the sparsity case and present corresponding theoretic and numerical results. This is the joint work with Felix Krahmer and Justin Romberg.
Room: 02.12.020

Tuesday, 31.01.2017 16:00-17:00
Speaker: Stefano Almi (TUM)
Title:
The aim of this talk is to present a variational model of the quasi-static evolution of hydraulic crack in the general framework of rate-independent processes.
Room: 02.06.020

Tuesday, 24.01.2017 16:00-17:30
Speaker: Marco Morandotti  Pfeil (TUM)
Title:
In this talk I will present the theory of structured deformations. Starting from the original formulation by Del Piero and Owen, I will move to the variational formulation proposed by Choksi and Fonseca, to conclude with some recent results regarding relaxation of non-convex energies. I will also present some examples and explicit formulas as an application to specific surface energies.
Room: 02.06.020

Tuesday, 17.01.2017 10:30-12:00
Speaker: Giacomo Albi  Pfeil (TUM)
Title:
In this talk I will review some basic results in the modeling and control of multi-agent system. The prototype problem will account a large system of interacting agents, whose dynamics are influenced by a policy maker acting in order to enforce a desired behavior. Different examples will be shown: from opinion-formation processes to crowd-safety management. From the mathematical view-point, this situation can be described by means of a mean-field optimal control problem, governing the dynamics of the probability distribution of the agent population. In order to deal numerically with the high-dimensionality and the non-linearities of this type of problems, I will introduce a novel approximating hierarchy of sub-optimal controls based on a stochastic-Boltzmann approach, whose computation requires a moderate computational effort compared with standard direct approaches. I will compare the behavior of the control hierarchy with respect to the solution of the optimal control problem. Several numerical examples will show the effectiveness of the proposed strategies.
Room: 02.10.011

Tuesday, 10.01.2017 10:30-12:00
Speaker: Prof. Dr. Sergei Pereverzyev Pfeil (RICAM Linz)
Title:
We discuss the parameter choice in learning algorithms generated by general regularization scheme. In contrast to classical deterministic regularization, the performance of regularized learning algorithms is influenced not only by the smoothness of a target function, but also by the capacity of a regularization space. In supervised learning both the smoothness and the capacity are intrinsically unknown. Therefore, we are interested in a posteriori regularization parameter choice rules and propose a new form of the balancing principle. We provide the analysis of the proposed rule and demonstrate its advantages in simulations. Joint research with Peter Mathe (WIAS-Berlin) and Shuai Lu (Fudan University, Shanghai).
Room: 02.10.011

Tuesday, 20.12.2016 11:00-12:00
Speaker: David James  Pfeil (Göttingen)
Title:
In this talk, we investigate subspaces spanned by biased random vectors. The underlying random model is motivated by applications in computational biology, where one aims at computing a low-rank matrix factorization involving a binary factor. In a random model with adjustable expected sparsity of the binary factor, we show for a large class of random binary factors that the corresponding factorization problem is uniquely solvable with high probability. In data analysis, such uniqueness results are of particular interest; ambiguous solutions often lack interpretability and do not give an insight into the structure of the underlying data. For proving uniqueness in this random model, small ball probability estimates are a key ingredient. Since to the best of our knowledge, there are no such estimate suitable for our application, we prove an extension of the famous Lemma of Littlewood and Offord. Hereby, we also discover a connection between the matrix factorization problem at hand and the notion of Sperner families.
Room: 02.10.011

Tuesday, 29.11.2016 16:00-17:00
Speaker: Christian Kümmerle, Juliane Sigl (TUM)
Title:
We propose a new Iteratively Reweighted Least Squares (IRLS) algorithm for the problem of recovering a low-rank matrix from incomplete linear observations. Unlike in previous IRLS approaches for the problem, we exploit the information in the column as well as in the row space of the iterates, using so-called harmonic mean weight matrices. Our non-convex algorithm exhibits local convergence guarantees comparable to previous IRLS algorithms for generic random measurement operators with a number of measurements in the optimal order. Additionally, we prove that the exhibited rate of convergence is superlinear, which is unprecedented even for other iterative approaches for the low-rank recovery problem. Our theoretical findings align very well with our numerical experiments, which also suggest that convergence to non-global minimizers is not an issue and that the proposed algorithm needs fewer measurements for successful recovery than any other algorithm proposed in the literature.
Room: 02.12.020

Tuesday, 22.11.2016 16:00-17:00
Speaker: Young-Pil Choi Pfeil (TUM)
Title:
The jargon "flocking" denotes the phenomenon in which self-propelled individuals using only limited environmental information and simple rules organize into an ordered motion. In this talk, we study the Cucker-Smale flocking model which is a type of Newtonian equations. We first present the large-time behavior of solutions and discuss modified Cucker-Smale models that address several drawbacks of the original model. In the second part, we deal with the rigorous derivation of kinetic Cucker-Smale type equations when sharp sensitivity regions are considered.
Room: 02.12.020

Tuesday, 15.11.2016
Speaker: Kristof Schröder Pfeil (Helmholtz Zentrum München)
Title:
We will look at the possibility of recovering a sum of Dirac measures on the rotation group SO(3) from its low degree moments with respect to Wigner-D functions only. Topics in the talk will cover theoretical results for recovery guarantee and algorithmic aspects of the problem.
Room: 02.10.011

Tuesday, 08.11.2016
Speaker: Jakob Geppert (Göttingen)
Title: Improved convergence guarantees for Sparse Power Factorization
Room: 02.10.011

Tuesday, 25.10.2016
Speaker: Matthias Wissel (TUM)
Title:
We will propose a time-dependent nonhomogeneous Markov model for predicting free parking spaces in urban areas. We therefore will describe the formalized general setting that reflects the real world environment we work in when concerned with parking prediction. Also, issues concerning the matter of availability of the right kind of data will be addressed. Then, the parameter estimation based on a given data set will be of particular interest. To this end, an extended framework of empirical risk minimization for matrix-valued functions and the use of matrix-valued reproducing kernel Hilbert spaces to approximate the time-dependent generator of the Markov process will be introduced. Finally, we want to give an outlook on further research possibilities in this field with a focus on a purely data driven approach.
Room: 02.10.011

Tuesday, 18.10.2016
Speaker: Michael Sandbichler (TUM)
Title:
Efficient data representation is a core aspect of modern signal processing, for example sparsity of data has been very efficiently used in compressed sensing in order to improve the required minimal number of measurements. We will look at a 'dual' version of sparsity, namely Analysis cosparsity and provide new sequential algorithms to find Analysis Operators which sparsify a given class of signals.
Room: 02.10.011

Contact

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  Person E-Mail Office
Organizer   Massimo Fornasier  massimo.fornasierematma.tum.de   MI 02.10.058
Organizer   Felix Krahmer  felix.krahmeremattum.de   MI 02.10.039
Contact Person   Dominik Stöger   dominik.stoegerematma.tum.de MI 02.10.054  

-- DominikStoeger - 15 May 2016