# MAM Seminars Autumn term 2014

Higher seminars in the subject Mathematics/Applied Mathematics, Autumn term 2014.

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

**Program for Mathematics and Applied Mathematics seminar. **

**Autumn 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 to Prof. Sergei Silvestrov sergei.silvestrov@mdh.se.*

**September 3, 2014, Wednesday, 15.30-17.00**

Location: U3-083 (Hilbertrummet), Västerås, Mälardalen University

Speaker: Örjan Stenflo, Department of Mathematics, Uppsala University

__Title__

A survey of average contractive iterated function systems

__Abstract __

Iterated function systems (IFSs) are useful for creating fractals, interesting probability distributions and enable a unifying framework for analysing stochastic processes with Markovian properties. In this talk, we present a survey of some basic results within the theory of random iterations of functions from an IFS.

**September 5, 2014, Friday, a one day interdisciplinary workshop ****“Engineering Mathematics for life and health sciences, natural science and technology”**** is being planned.**

Interdisciplinary workshop *“Workshop on Engineering Mathematics for Natural Sciences, Life Sciences and Health and Electromagnetics Technologies”*

**September 10, 2014, Wednesday, 16.30-17.00**

Location: U3-083 (Hilbertrummet), Västerås, Mälardalen University

Speaker: Betuel Canhanga, Division of Applied Mathematics, Mälardalen University

__Title__

Perturbation Methods for Pricing European Options in a Model with Two Stochastic Volatilities

__Abstract __

Financial models have to reflect the characteristics of markets in which they are developed to be able to predict the future behavior of a financial system. The nature of most trading environments is characterized by uncertainty that is expressed in mathematical models in terms of volatilities. In contrast to the classical Black–Scholes model with constant volatility, our model of mean-reversion type includes two stochastic volatilities, a fast-changing and a slow-changing; this can be interpreted as the effects of weekends and the effects of seasons of the year (summer and winter) on the asset price.

We perform explicitly the transition from the historical probability measure to the risk-neutral one by introducing the two market prices of risk and applying Girsanov Theorem. To solve the boundary value problem for the partial differential equation that corresponds to the case of a European option, we perform both regular and singular multi-scale expansion in fractional powers of the speed of mean-reversion factors and construct an approximate solution given by the classical two-dimensional Black–Scholes model plus some terms that expand the results obtained by Black and Scholes. Concrete examples are presented.

This is a joint work with Ying Ni, Anatoliy Malyarenko and Sergei Silvestrov, Mathematics and Applied Mathematics, UKK, Mälardalen University

**September 24, 2014, Wednesday, 15.15-16.00**

Location: U3-083 (Hilbertrummet), Västerås, Mälardalen University

Speaker: Holger Weishaupt, Department of Immunology, Genetics and Pathology, Science for Life Laboratory, Uppsala University, Sweden

(joint work with Cancer, M**,** Bunikis I, Jiang Y, Bolin S, Häggqvist S, Gyllensten U, Uhrbom L, Ameur A and Swartling FJ)

__Title__

A fast forward genetics screen for retrovirus-induced brain tumours

__Abstract __

Malignant brain tumours are one of the most common cancers of childhood with an overall survival of 60-70%. In our group we are focusing on studying medulloblastoma (MB), the most common malignant brain tumour in children. MBs are believed to arise from the small brain, the cerebellum. Current treatment of patients involves surgical removal of the tumour, irradiation and chemotherapy, but due to the aggressive nature of MB and the irradiation of the young developing brain, many patients die or suffer from life-long mental and neurological disorders. Better understanding of the involvement of various developmental pathways and genes that drive MB formation is crucial to improve current treatment strategies. Specifically, we hope that identification of such mechanisms will advance the development of drugs that target the disease more specifically and thus reduce long-term side effects of current standard therapy.

Towards the identification of driver genes and genes contributing to tumour development, we have previously used a retrovirus system (called RCAS) to overexpress the MB driving oncogene MCYN in mice, thus producing brain tumours that closely resemble human medulloblastoma. Retroviruses integrate in an almost random fashion into the host genome and usually produce additional mutations at the genomic location, where the oncogene is integrated. These additional mutations might then alter the expression of proximate genes or activity of enhancers, thereby giving a particular tumour cell a selective malignant advantage over other cells during cancer development.

Here we have used whole genome sequencing (WGS) to identify genes that have acquired additional mutations and might substantially contribute to tumour development. For this purpose we have developed a streamlined analysis pipeline comprising a novel software called Integration Site DetectoR (InSiDeR) for the detection of viral integration, followed by integration site annotation against functional genes and enhancers from reference genome assemblies as well as the detection of common integration sites (CISs).

**October 1, 2014, Wednesday, 15.30-16.30**

Location: U3-083 (Hilbertrummet), Västerås, Mälardalen University

Speaker: Holger Weishaupt, Department of Immunology, Genetics and Pathology, Science for Life Laboratory, Uppsala University, Sweden

(joint work with Christopher Engström, Patrik Johansson, Sergei Silvestrov, Sven Nelander and Swartling FJ)

__Title__

A mathematical graph theory approach to understand gene regulatory networks in cancer

__Abstract __

Mathematics provides us with an abundance of ways to represent and analyze networks and graphs in various scientific fields. In each of these fields, the individual features of the networks will serve as an abstract representation of very particular real world relationships and processes and, accordingly, mathematical operations applied on these networks might bear entirely different meanings depending on situational context. In order to properly utilize mathematical networks in such applied areas it is therefore crucial to understand what exactly is modelled by the network, how the underlying data can be analyzed, and which mathematical method to select when trying to extract certain real world related data from the network.

Here we address these issues in the context of so called gene regulatory networks that have been inferred from gene expression data from the brain of healthy patients and patients suffering from a brain tumour, respectively. The goal of this study is the characterization of network properties inherent to cancer genes, in order to further facilitate the prediction of as of yet unknown cancer genes.

Towards this aim, we will review a number of mathematical methods that include network inference techniques, approaches of clustering networks into meaningful subclusters/modules, measures of similarity for comparing clustering results as well as graph based centrality measures for the identification of central genes.

**October 8, 2014, Wednesday, 15.30-16.30**

Location: U3-083 (Hilbertrummet), Västerås, Mälardalen University

Speaker: Afshan Tabassum, Government College University, Abdus Salam School of Mathematical Sciences, (ASSMS), Lahore, Pakistan

E-mail address: afshintabassum@gmail.com

__Title__

Hyers-Ulam Stability

__Abstract __

**October 15, 2014, Wednesday, 15.30-16.30**

Location: U3-083 (Hilbertrummet), Västerås, Mälardalen University

Speaker: John Musonda, Uppsala University (ISP), Mälardalen University, University of Zambia

__Title __

Three Systems of Orthogonal Polynomials and Associated Operators

__Abstract__

More than a decade ago, Professor Sten Kaijser happened to discover two remarkable systems of orthogonal polynomials. The most interesting of the systems was in fact not a standard system, but it had some other useful properties. These discoveries led to a PhD dissertation by Tsehaye K. Araaya. In January 2012, Professor Lars Holst of KTH in Stockholm presented a new way to calculate the Euler sum. His calculations inspired Professor Kaijser to calculate a third system of polynomials, a system that turned out to fill a gap related to the previous systems, and this led to my own master’s thesis.

In the talk, I will present these three systems of orthogonal polynomials, and discuss some operators related to them.

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

Location: U3-083 (Hilbertrummet), Västerås, Mälardalen University

Speaker: Lars Hellström, Division of Applied Mathematics, Mälardalen University

__Title __

Notations for and notions of tensors

__Abstract __

Tensors tend to be viewed either as plain arrays of numbers carrying lots and lots of indices, which require great care to achieve independence of the coordinate system, or as coordinate-free but painfully abstract algebraic objects. The truth is actually nowhere near that bad, because even the traditional index-based notation can be given a completely coordinate-free interpretation, and there are also diagrammatic notations which can remove much of the clutter that traditional notations suffer from. The proper algebraic framework for discussing this is that of a PROP/symocat, and using that helps to recognise some examples where tensor notations may be applied which are far smaller than the traditional matrices with an exponential number of elements. The seminar does not require previous familiarity with tensors, PROPs, or symocats.

**November 26, 2014, Wednesday, 15.30-16.30**

Location: U3-083 (Hilbertrummet), Västerås, Mälardalen University

Speaker: Milica Rančić, Division of Applied Mathematics, UKK, Mälardalen University, MDH, Västerås, Sweden

E-mail: __milica.rancic@mdh.se__

__Title __

High Frequency Analysis of Horizontal Dipole Antenna Immersed in Lossy Soil Using Point-Matching and Hybrid Circuit Methods

__Abstract __

Modeling of wire conductors buried in finitely conducting soil has been a subject of great amount of research. This problem has been dealt with in different ways, from application of rigorous full-wave approaches to simplified ones more suitable for practical engineering studies. In this paper, the authors compare the range of applicability of two different methodologies.

The first one, the integral equation (IE) approach, considers solution of the Hallén’s IE using the point-matching method and the entire domain polynomial representation of the current distribution along the observed antenna. The second approach presents a modification of the well-known PEEC (Partial Element Equivalent Circuit) method, and is denoted as the Hybrid Circuit Method (HCM).

The analysis is performed in a wide frequency range for different ground conductivities and geometry parameters (antenna length, burial depth). Obtained results indicate a possibility of effective application of applied methodologies to not only antennas immersed in the lossy ground, but also wire grounding systems in such soil, buried telecommunication cables exposed to electromagnetic interferences, submarine dipoles, bare or isolated antennas embedded in dissipative media, etc.

*This is a joint work with **Radoslav Jankoski and Vesna Arnautovski-Toseva from **FEIT, Ss. Cyril and Methodius University, Skopje, Macedonia,** and Sergei Silvestrov from the Division of Applied Mathematics, UKK, **Mälardalen University, Västerås, Sweden.*

**December 10, 2014, Wednesday, 15.30-16.30**

Location: U3-083 (Hilbertrummet), Västerås, Mälardalen University

Speaker: Sara Abbaspour, PhD student at MDH, School of Innovation, Design and Engineering (IDT), Division of Intelligent Future Technologies (IFT), Embedded Sensor Systems for Health (ESS-H)

__Title __

Evaluation of Wavelet Based Methods in Removing Motion Artifact from ECG Signal

__Abstract __

Accurate recording and precise analysis of the electrocardiogram (ECG) signals are crucial in the pathophysiological study and clinical treatment. These recordings are often corrupted by different artifacts. The aim of this study is to propose two different methods, wavelet transform based on nonlinear thresholding and a combination method using wavelet and independent component analysis (ICA), to remove motion artifact from ECG signals. To evaluate the performance of the proposed methods, the developed techniques are applied to the real and simulated ECG data. The results of this evaluation are presented using quantitative and qualitative criteria. The results show that the proposed methods are able to reduce motion artifacts in ECG signals. Signal to noise ratio (SNR) of the wavelet technique is equal to 13.85. The wavelet-ICA method performed better with SNR of 14.23.

**December 17, 2014, Wednesday, 15.30-16.30**

Location: U3-083 (Hilbertrummet), Västerås, Mälardalen University

Speaker:

__Title __

__Abstract__