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- Category: Mathematical Modeling and Numerical Analysis
- Created: 17 April 2014
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Mathematical Modeling and Numerical Analysis Seminar

On **12.11.2017** at **11:00** in room 478 of IMI-BAS

Theme of the lecture:

*"**A black-box algorithm for fast matrix assembly in isogeometric analysis"*

**Dr. Clemens Hofreither** , Institute of Computational Mathematics, Johannes Kepler University, Linz, Austria

Mathematical Modeling and Numerical Analysis Seminar

On **15.06.2017** at **14:00** in room 403 of IMI-BAS

Theme of the lecture:

*"*** On best uniform approximation by low-rank matrices**"

**Clemens Hofreither** , Institute of Computational Mathematics, Johannes Kepler University, Linz, Austria

**Abstract. **We study the problem of best approximation, in the elementwise maximum norm,of a given matrix by another matrix of lower rank.

We generalize a recent result by Pinkus that describes the bestapproximation error in a class of low-rank approximation problems and givean elementary proof for it.Based on this result, we describe the best approximation error and theerror matrix in the case of approximation by a matrix of rank one lessthan the original one.

For the case of approximation by matrices with arbitrary rank, we givelower and upper bounds for the best approximation error in terms ofcertain submatrices of maximal volume.

We illustrate our results using 2x2 matrices as examples,for which we also give a simple closed form of the bestapproximation error.

Mathematical Modeling and Numerical Analysis Seminar

On **7.12.2016** at **11:00** in room 403 of IMI-BAS

Theme of the lecture:

*"**Processing of high-resolution CT data: denoising, edge detection, and segmentation**"*

Chief Assist. Prof., Ph.D. *Stanislav Harizanov*, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

Mathematical Modeling and Numerical Analysis Seminar

On ** 03.10.2016** at

Theme of the lecture:**"Parallel algorithms for some actual problems***"*

Dr. Alexander Ayriyan, Joint Institute for Nuclear research, Dubna

Mathematical Modeling and Numerical Analysis Seminar

On **27.07.2016** at **1****0****:****0****0** in room 403 of IMI-BAS

Theme of the lecture:**"Mathematical model for the dynamics of the autoimmune disease alopecia areata in cycling hair follicles****"**

*Dr.**Atanaska Dobreva, **Department of Mathematics, Florida State University*

* Abstract*. Alopecia areata is an autoimmune condition which causes distinct patterns of hair loss. The disease development mechanisms are still not completely understood, and treatment is often difficult. Hair follicles are organs that constantly cycle through phases of growth, regression, and rest. A main feature of alopecia areata is that it interrupts and makes the growth stage very short. We first construct a model of ordinary differential equations to describe how the condition develops over time in a small cluster of homogeneous growing follicles. The model incorporates interactions between hair follicles and the immune system in accordance with the immune privilege collapse hypothesis for disease pathogenesis. As a next step, we elaborate the dynamical system by including the underlying hair cycle and provide simulations for states of health, disease, and treatment. In addition, we apply parameter sensitivity analysis to determine how the processes reflected in the model influence the growth phase length.

Mathematical Modeling and Numerical Analysis Seminar

On **27.07.2016** at **1****0****:****0****0** in room 403 of IMI-BAS

Theme of the lecture:

* "Low-Rank Approximation and Its Applications*"

*Prof. Ivan Markovsky,* *Vrije Universiteit, Brussel*

**Abstract**. Mathematical engineering continuously addresses new applications and solves new problems. The expansion of existing methods and applications makes it difficult to maintain a common theoretical framework. This talk shows the potential of the structured low-rank approximation setting to unify problems of data modeling from diverse application areas. An example treated in more details in the presentation is identification of a linear time-invariant system from observed trajectories of the system. We present an optimization method based on the variable projection principle. The method can deal with data with exact as well as missing (unknown) values.

Mathematical Modeling and Numerical Analysis Seminar

On **26.05.2016** at **1****4****:****0****0** in room 403 of IMI-BAS

Theme of the lecture:**"On best uniform approximation with low-rank matrices"**

Clemens Hofreither, Institute of Computational Mathematics, Johannes Kepler University, Linz, Austria.

**Abstract. **Given a matrix, we study the best-approximation error by a matrix of lower rank. Here we are interested in a class of elementwise norms, of which the Frobenius and the Chebyshev (entrywise maximum) norms are special cases. Based on a result by A. Pinkus (2012), we derive both lower and upper bounds for the best-approximation error by a rank k matrix in the maximum norm. The quantities used in the estimates are absolute determinants of certain maximal submatrices, and we establish some connections to the theory of pseudoskeleton approximation, where this "maximal volume concept" has been applied previously. We illustrate the results by the simple example of some 2x2 matrices.

Mathematical Modeling and Numerical Analysis Seminar

On** 07.03.2016** at **1****3****:****0****0** in room 403 of IMI-BAS

Theme of the lecture:**"Steady states of polynomial ODEs****"**

*Prof. Carsten Conradi, ** HTW, Berlin*

**Abstract**. Polynomial Ordinary Differential Equations are an important tool in many areas of quantitative biology. Due to large measurement errors few experimental repetitions and a limited number of measurable components, confidence intervals of estimated parameter values are often several orders of magnitude. One therefore has to study families of parametrized polynomial ODEs. In this talk a class of ODEs is discussed that admits a monomial parameterization of the steady state variety. To this class belong, for example, multisite phosphorylation systems. For a special instance of this subclass, one can formulate parameter conditions that guarantee the existence of three steady states.

Mathematical Modeling and Numerical Analysis Seminar

On** 02.11.2015** at

Theme of the lecture:

**"Modelling of intrinsic Josephson junctions in high temperature superconductors"**prof. Yury Madzhnunovich Shukrinov, Joint Institute for Nuclear research, Dubna

Mathematical Modeling and Numerical Analysis Seminar

On** 02.11.2015** at

Theme of the lecture:

**"Cavity and background oscillations inintrinsic Josephson junctions"**

Dr. Ivan Hristov, FMI, Sofia University

Mathematical Modeling and Numerical Analysis Seminar

On** 29 .05.2015** at

Theme of the lecture:**"All-at-once multigrid methods for optimal control problems with inequality constraints"**

Dr. DI. Stefan Takacs от Technische Universität Chemnitz

**Abstract.** In this talk we will discuss the solution of all-at-once multigrid methods for optimal control problems of tracking type with box constraints for the control variable.

One possibility to solve such problems using multigrid methods is to use a (semi-smooth) Newton solver.

Here, a standard multigrid method would be used as an solver for linear sub-problems that occur within this iteration.

Recently, it was possible to construct and analyze multigrid solvers that can be directly applied to elliptic problems with box constraints (like obstacle problems).

Those methods have shown good convergence behavior in practice. In the present talk we will discuss how the ideas of such methods can be extended to control problems.