# MAM Seminars Spring term 2014

Higher seminar in the subject Mathematics/Applied Mathematics, Spring term 2014.

School of Education, Culture and Communication (UKK), Mälardalen University.

**Program for MTM seminar. Spring term 2014**

*Wednesdays afternoon is the normal time for MTM seminars with deviations when necessary. The program is always provisional. The information about each specific talk at MTM seminar becomes final the day before. Suggestions for talks at MTM seminar are very welcome.*

**January 24, 2014, Friday, 13.15-14.30**

**Location:** U2-158, Västerås, Mälardalen University

**Speaker:**

Prof. Dmitrii Silvestrov, Department of Mathematics, Stockholm University,

E-mail: __silvestrov@math.su.se__

__Title__

American-type Options. Stochastic Approximation Methods

__Abstract __

Lecture presents a survey of results from my new book [1], which is devoted to stochastic approximation methods for rewards of American type options for multivariate modulated Markov log-price processes. The classes of discrete and continuous time log-price processes (LPP) under consideration include multivariate modulated Markov chains, modulated random walks, and various autoregressive models, multivariate modulated Markov log-price processes, diffusion and Lévy processes. General convergence results are presented, as well as their applications to space skeleton approximations, tree approximations, and Monte Carlo based approximation algorithms for option rewards. Also, results related to studies of structure for optimal stopping domains are presented as well as results related to option reselling problem. Theoretical results are illustrated by results of experimental studies. The book contains two parts and the lecture will be mainly concentrated on the results related to discrete time processes.

References

[1] Silvestrov D.S. American-type Options. Stochastic Approximation Methods. Volume I. De Gruyter Studies in Mathematics 56, De Gruyter, 2014.

__http://www.degruyter.com/view/product/209685?rskey=ol1K7r&result=2__

__Book flyer Dmitrii Silvestrov (pdf 56 kB)__

**February 19, 2014, Wednesday, 15.15-16.10**

**Location:** U3-104, Turing room, UKK, Västerås, Mälardalen University

**Speakers:**

Karl Lundengård and Jonas Österberg, Division of Applied Mathematics, Mälardalen University,

E-mail: __karl.lundengard@mdh.se__; __jonas.osterberg@mdh.se__

**Title**

Extreme points of the Vandermonde determinant

**Abstract **

In this seminar the determinant of the Vandermonde matrix (and some related matrices) defined by a point on the unit sphere is examined. More specifically the value of the determinant is optimized and the extreme points will be given using roots of certain Hermite polynomials. The results will also be visualized for three to seven dimensions and explicit expressions for the corresponding extreme points will be given.

**February 26, 2014, Wednesday, 16.10-17.00**

**Location: **U3-104, Turing room, UKK, Västerås, Mälardalen University

**Speaker: **

Lars Hellström, Division of Applied Mathematics, Mälardalen University

E-mail: __lars.hellström@mdh.se__

__Title __

Rewriting and the Diamond Lemma

__Abstract __

An important and recurring activity in many branches of mathematics and related sciences is the step-by-step transformation of one symbolic expression to another according to given rules. This is usually taught more as a craft than as a science, making it a matter of individual skill to find a sequence of steps that reach the wanted goal, but there is no fundamental reason why it cannot be studied systematically. Indeed, that idea has been executed many times over the years, often with a particular problem domain in mind, which has resulted in a sometimes confusing proliferation of terminology where fairly simple and general ideas run a significant risk of drowning in technicalities.

This talk aims to give an overview of and introduction to the field, which sits on the boundary between mathematics and computer science. Topics I (time permitting) hope to address are equational reasoning, rewrite systems, confluence and termination, the Diamond Lemma, Gröbner bases, words/terms/graphs/networks, universal algebra, linear structure, normal forms, and the word problem (not necessarily in that order). Familiarity with abstract algebra is not necessary.

**March 5, 2014, Wednesday, 15.30-16.30**

**Location**: U3-083, Hilbert room, Västerås, Mälardalen University

**Speakers: **

Karl Lundengård, Division of Applied Mathematics, UKK, Mälardalen University, MDH, Västerås, Sweden

E-mail: __karl.lundengard@mdh.se__

Milica Rančić, Dept. of Theoretical Electrical Engineering, ELFAK, University of Niš, Serbia, and Division of Applied Mathematics, UKK, Mälardalen University, MDH, Västerås, Sweden

E-mail: __milica.rancic@mdh.se__

__Title__

Marquardt Least-Squares Method: Estimation of Lightning Current Function’s Parameters

__Abstract __

Mathematical modelling of lightning discharge is an important component in the process of risk estimation, lightning protection, and prevention of failures and damage to electrical and electronic systems exposed to lightning electromagnetic field (LEMF). In that sense, a reliable function for representation of different channel-based currents (CBCs) is needed. Significant effort has been put into developing appropriate mathematical functions that would, as accurately as possible, approximate the lightning CBC (measured, or assumed based on typical measurements).

These functions usually have a number of adjustable parameters, whose number should be as little as possible, but still large enough to be able to reproduce the desired lightning current waveshape. A possible procedure that could be used for estimation of lightning current function’s parameters is the Marquardt least-squares method, also known as the *Levenberg-Marquardt algorithm* or *damped least-squares*, an efficient method for least-squares estimation of functions with non-linear parameters developed in the middle of the 20^{th} century.

The talk will give the overview of the method itself, and its application to few specific lightning current functions. Furthermore, the optimized functions will be used for reproduction of various standardized, and recorded lightning current waveshapes.

**March 12, 2014, Wednesday, 15.30-16.30**

**Location: **U2-158, Västerås, Mälardalen University

**Speaker: **Prof. Dr. Tofigh Allahviranloo, Izmir university, Izmir, Turkey

E-mail: __tofigh@allahviranloo.com__

webpage: __www.allahviranloo.com__

__Title __

Fuzzy Differential Equations with Applications

__Abstract __

Fuzzy differential equations (FEDs) play important roles in mathematical and engineering science. The theory of FDE has attracted much attention in recent times because this theory represents a natural way to model dynamical systems under uncertainty.

This presentation is going to cover the following topics:

- The concept, definition, form and different types of fuzzy numbers.
- Different types of derivatives of a fuzzy process and their relations.
- The use of these fuzzy derivatives in accordance with concept of Hukkuhara difference for modelling the FDE.
- The Taylor expansion of a fuzzy function to solve FDE.
- The fuzzy fractional differential equation based on the above mentioned concepts.
- The real applications of FDEs in technology.

**March 19, 2014, Wednesday, 15.15-16.30**

Location: U3-083, Hilbert room, UKK, Västerås, Mälardalen University

**Speaker: **

Johan Richter, Division of Applied Mathematics, Mälardalen University

E-mail: __johan.richter@mdh.se__

__Title __

Centralizers and valuations

__Abstract __

In this talk I will describe a class of rings where one can prove interesting properties of centralizers, the set of elements that commute with a particular element. They are rings that satisfy certain conditions,principally the existence of a valuation. A valuation is a generalization of the degree map for polynomials. My talk is inspired by an article by Hellström and Silvestrov in the Journal of Algebra. I will show how some of their results can be generalized by using valuations. The talk will be comprehensible to a broad mathematical audience.

**April 23, 2014, Wednesday, 15.30-16.45**

**Location: **U3-083, Hilbert room, UKK, Västerås, Mälardalen University

**Speaker: **Vanessa Miemietz, University of East Anglia, UK

** Title:** Introduction to 2-representation theory

__Abstract: __

I will give an introduction to the 2-representation theory of 2-categories, why it is important, and in what ways it is similar to respectively different from classical representation theory.

**April 29, 2014, Tuesday, 15.30-16.30 (OBS! **Not Wednesday because of Valborg holiday)

**Location:** U3-083, Hilbert room, UKK, Västerås, Mälardalen University

**Speaker: **Shailendra Kumar Mishra, Pulchowk Campus, Institute of Engineering, Tribhuvan University, Nepal and Division of Applied Mathematics, The School of Education, Culture and Communication, Mälardalen University, Sweden

__Title__

A Note on exploration of sequence spaces and function spaces on interval [0,1] for DNA sequencing.

__Abstract__

John Maynard Smith in 1970 first proposed a notion of sequence space for protein evolution where all proteins are arranged in a protein spaces in which neighbours can be connected by single mutation. These problems are also relevant to other areas such as DNA sequence, brain imaging, climate data, financial data and others. The process of DNA sequencing (first discovered in 1977 by Fredrick Sanger) is currently evolving towards a heuristic understanding of the sequence function relationship. In the present talk we discuss improved DNA sequencing capacity and improved quality of data analysis from statistical tools and the representation theorems and inclusion relations on sequence spaces and function spaces on [0,1] generated by DNA nucleotides.

**May 7, 2014, Wednesday, 15.30-16.30**

**Location: **R2-202, R-building, Västerås, Mälardalen University

**Speaker: **Erik Darpö, Division of Applied Mathematics, UKK, Mälardalen University, MDH, Västerås, Sweden

E-mail: __erik.darpo@mdh.se__

__Title __

Algebras and representations

__Abstract__

The purpose of this talk is to introduce some basic notions and results in the representation theory of finite-dimensional algebras: modules, extensions, projective modules, semi-simple and hereditary algebras, quivers, the tame/wild dichotomy and the classification of representation-finite hereditary algebras by Gabriel’s theorem.

**May 14, 2014, Wednesday, 15.30-16.30**

**Location: **U2-158, U-building, Västerås, Mälardalen University

**Speaker: **Erik Darpö, Division of Applied Mathematics, UKK, Mälardalen University, MDH, Västerås, Sweden

E-mail: __erik.darpo@mdh.se__

__Title __

Auslander-Reiten theory

__Abstract__

This talk is intended to give an introduction to the Auslander-Reiten theory, which is one of the main tools in modern representation theory. In this theory, the modules of an algebra are studied by considering so-called *irreducible morphisms, *that is, a kind of ”simplest” morphisms from which other morphisms can be constructed. In many cases, the irreducible morphisms give complete information about all modules of an algebra, as well as all morphisms between them.

**June 4, 2014, Wednesday, 15.15-16.30**

**Location: **

R2-202, R-building, Västerås, Mälardalen University

**Speaker: **

**Bojana Petkovic**, Faculty of Computer Science and Automation, Institute of Biomedical Engineering and Informatics, Ilmenau University of Technology, Germany

__Title __

**Title 1: Lorentz Force evaluation: a new approximation method for defect reconstruction (30min)**

We propose a new method for non-contact, non-destructive evaluation of solid conductive materials, termed Lorentz Force Evaluation. Employing a three-dimensional finite volume discretization of the specimen and approximating the crack signal with an electric dipole at each voxel, magnetic fields and Lorentz forces exerting on a permanent magnet, which is moving relative to the specimen, are calculated. Compared with the finite element analysis for small surface and subsurface cracks, the forward method shows an error smaller than 7%. Based on this forward approximation method, a new inverse procedure for defect reconstruction is proposed. A successful reconstruction using data from finite elements method analysis and measurements is obtained.

**Title 2: Optimization of vest sensor array for cardiac source imaging (30min)**

Magnetocardiography non-invasively provides information about the electrical activity of the heart and is used in Magnetocardiographic Field Imaging (MFI) for the early assessment of heart dysfunctions. One of the major limitations of the MFI is that the cryostat restricts the possible location of the superconducting quantum interference devices (SQUIDs) based sensors. New room temperature magnetic sensors allow for placement of sensors around the body in a vest-like setup. Consequently, the question arises of how to place the magnetic field sensors optimally around the torso.

We optimized the positions and orientations of 32 magnetic sensors in a vest-like sensor array, minimizing three different indicators of conditioning of the corresponding linear inverse problem. Best results have been found for non-uniform sensors distribution on the whole torso surface. Additional placement of sensors on the back of the torso improves the condition of the linear inverse problem. In comparison to previous findings can be concluded that quite different sensor sets can perform equally well and therefore an optimal sensor selection is not unique.

**July, 2014, Wednesday, 15.15-16.30**

**Location: Västerås, Mälardalen University**

**Speaker: Alex Tumwesigye Behakanira, Makerere University, Uganda and Division of Applied Mathematics, Mälardalen University**

__Title__

TBA

__Abstract __

TBA