All Years Seminars
[INMA] 2015-03-17 (14.00) : Discretization of manifold-valued partial differential equations
At Euler building (A002)
Speaker :
Olivier Sander (University of Aachen)
Abstract : There is a number of partial differential equations whose solutions are not scalar functions, but take their values in a nonlinear manifold. Examples of such functions are configurations of liquid crystals and ferromagnets, elastic materials with orientation degrees of freedom, and fields of symmetric positive definite matrices. The spaces of such functions are themselves nonlinear, which makes the discretization and numerical treatment of such partial differential equations notoriously difficult. We present generalizations of standard finite element methods to function spaces with a nonlinear target. These generalized FE spaces are H^1 conforming, and we show optimal a priori discretization error bounds. The resulting algebraic problems are minimization problems on large products of low-dimensional manifolds, which can be solved efficiently by combining a monotone multigrid method with a Riemannian trust-region solver. We use the presented machinery to simulate solitons in ferromagnetic materials, and wrinkling patterns in thin elastic sheets, where we obtain good quantitative agreement with experimental results from the literature.
[INMA] 2015-03-10 (14.00) : Modelling stochastic gene expression using the Master Equation
At Euler building (A002)
Speaker :
Martin Hemberg (Wellcome Trust Sanger Institute, Cambridge, UK)
Abstract : One of the central processes in the cell is transcription, ie when the information stored in the DNA is read out in the form of messenger RNAs. Transcription typically involves a very small number of
molecules, and thus the law of mass action is no longer applicable. In the low molecule regime, fluctuations are no longer negligible, and a stochastic model is required.
The most rigorous approach is to use the Master Equation (ME), which is a difference-differential equation describing the probability of finding n molecules as a function of time. We present a closed form fully analytical solution of the ME for the most widely used model of gene expression. Analysis of the parameter space reveals a novel solution which has not been previously characterized. Using published data, we show that this regime is biologically relevant.
In the second part of the talk, I will discuss functional implications of gene expression noise. In particular, I will show that the mutual information between the promoter (input) and the mRNA level (output)
is proportional to the noise level. This proportionality implies that it is impossible to maximize the mutual information and to minimize the noise at the same time. Using genome-wide expression data, we demonstrate that the noise (and mutual information) in annotatedpathways are higher than expected by chance, suggesting that noise levels have been selected to allow for efficient signal propagation in the cell.
[INMA] 2015-03-03 (14.00) : Alan Turing and the origins of modern Gaussian elimination
At Euler building (A002)
Speaker :
Froilán M. Dopico (University Carlos III of Madrid)
Abstract : The solution of a system of linear equations is by far the most important problem in Applied Mathematics. It is important in itself and because it is an intermediate step in many other relevant problems. Gaussian elimination is nowadays the standard method for solving this problem numerically on a computer and it was the first numerical algorithm to be subjected to rounding error analysis. In 1948, Alan Turing published a remarkable paper on this topic: ``Rounding-off errors in matrix processes (Quart. J. Mech. Appl. Math. 1, 287-308). In this paper, Turing formulated Gaussian elimination as the matrix LU factorization and introduced the condition number of a matrix, both of them fundamental notions of modern Numerical Analysis. In addition, Turing presented an error analysis of Gaussian elimination that improved previous analyses and deeply influenced the definitive analysis developed by James Wilkinson in 1961. Alan Turings work on Gaussian elimination appears in a fascinating period for modern Numerical Analysis. Other giants of Mathematics, as John Von Neumann, Herman Goldstine, and Harold Hotelling were also working in the mid-1940s on Gaussian elimination. The goal of these researchers was to find an efficient and reliable method to solve systems of linear equations in the recently invented automatic computers. At that time, it was not clear at all whether Gaussian elimination was a right choice or not. The purpose of this talk is to revise, at an introductory level, Alan Turings contribution to the analysis of Gaussian elimination, its historical context, and its influence on modern Numerical Analysis.
[INMA] 2015-02-24 (14.00) : Leakage Certification and the Perceived Information
At Euler building (A002)
Speaker :
Standaert, François-Xavier
Abstract : Evaluating side-channel attacks and countermeasures requires determining the amount of information leaked by a target device. For this purpose, information extraction procedures published so far essentially combine a "leakage model" with a "distinguisher". Fair evaluations ideally require exploiting a perfect leakage model (i.e. exactly corresponding to the true leakage distribution) with a Bayesian distinguisher. But since such perfect models are generally unknown, density estimation techniques have to be used to approximate the leakage distribution. This raises the fundamental problem that all security evaluations are potentially biased by both estimation and assumption errors. Hence, the best that we can hope is to be aware of these errors. In this talk, I will describe methodological tools to solve this issue. Namely, I will show how sound statistical techniques allow both quantifying the leakage of a chip, and certifying that the amount of information extracted is close to the maximum value that would be obtained with a perfect model. This amounts to showing that the "Perceived Information" that can be extracted by concrete adversaries is close enough to the (standard) Mutual Information metric. While introduced in the context of cryptographic circuits, I will then argue that the Perceived Information (and leakage certification tests) have potential application in other areas (such as in statistical databases).
[INMA] 2015-02-17 (14.00) : Event-triggered Control: Performance, Robustness and Zeno-freeness
At Euler building (A002)
Speaker :
Maurice Heemels (Eindhoven University of Technology)
Abstract : Recent developments in computer and communication technologies are leading to an increasingly networked and wireless world. In the context of networked control systems this raises new challenging questions, especially when the computation, communication and energy resources of the system are limited. To efficiently use the available resources it is desirable to limit the control actions to instances when the system really needs attention. Unfortunately, the classical time-triggered control paradigm is based on performing sensing and actuation actions periodically in time (irrespective of the state of the system) rather than when the system needs attention. Therefore, it is of interest to consider event-triggered control as an alternative paradigm, as it seems much more natural to trigger control actions by well-designed events involving the systems state, output or other available information, i.e. bringing feedback in the sensing and actuation processes.
In this talk, we discuss the basics of event-triggered control with a focus on Lp-gain performance, robustness and Zeno-freeness in the resulting closed-loop systems. Stability, performance and robustness are important control-related properties, while Zeno-freeness is essential from an implementation point of view and the side of utilization of the computation, communication and energy resources. In particular, the existence of a positive lower bound on the inter-event times implies so-called Zeno-freeness (a term stemming from hybrid systems in which Zenoness refers to the occurrence of an infinite number of events in a finite-length time interval). The challenges and recent advances regarding the design of event-triggered controllers that combine the features of robustness, performance and Zeno-freeness will be discussed. Real measurements obtained from an experimental inverted pendulum setup and from a platoon of vehicles complement the theoretical results.
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