# ITN Seminar Series in Mathematics

This seminar series is intended for researchers and teachers with interest in various aspects of mathematics in their research and education. The seminars are held Wednesdays, every even week, 13:30-14:30. Location: SP5226. Contact Berkant Savas if you would like to visit our group and give presentation.

## Spring 2018 Seminars

### Wednesday 13:30-14:30, May 2, 2018

Matematik – kunskapsbygge med hjälp av ämnesdidaktik
Constanta Olteanu, Institutionen för matematik, Linnéuniversitetet
Abstract: Ämnesdidaktik är ett kunskapsområde där utbildningsvetenskap möter ämnesinnehåll och skolpraktik. Innebörden av ämnesdidaktiken kan dock se olika ut inom olika ämnesinriktningar. Matematikdidaktik, en av dessa inriktningar, omfattar alla objekt och fenomen som har med matematikundervisning och lärande i matematik att göra. Genom att ta avstamp dels i ett postkvalitativt perspektiv, med särskild inspiration i Gilles Deleuzes och Félix Guattaris filosofi, kommer min presentation att fokusera på viktigheten av att låta elevernas tänkande utgöra undervisningsinnehåll i matematik.

This seminar will be in Swedish.

Location: SP5226

### Wednesday 13:30-14:30, May 23, 2018

Title: tba
Guest, Affiliation
Abstract:

Location: SP5226

## Previous seminars

### Wednesday 14:30-15:30, December 13, 2017

On the sharpness of the Stolz approach
Fausto Di Biase, Università degli Studi G. d'Annunzio Chieti e Pescara
Abstract: We study the sharpness of the Stolz approach for the a.e. convergence of functions in the Hardy spaces in the unit disc, first settled in the rotation invariant case by J. E. Littlewood in 1927 and later examined, under less stringent, quantitative hypothesis, by H. Aikawa in 1991. We introduce a new regularity condition, of a qualitative type, under which we prove a version of Littlewood's theorem for tangential approach whose shape may vary from point to point. Our regularity condition can be extended in those contexts where no group is involved, such as NTA domains in $$R^n$$. We show exactly in what sense our regularity condition is sharp.

Location: SP5226

### Wednesday 13:30-14:30, November 15, 2017

Strategier att motverka studentfrånvaro
Abstract: Studenternas närvaro vid undervisningen är ett ämne som på förekommen anledning just nu diskuteras aktivt. Som lärare försöker vi alltid se till att de lektioner och föreläsningar vi har är av god kvalité så att studenterna ges möjlighet att lära sig det som krävs, men dessvärre räcker inte allt det. Här kommer jag att presentera ett upplägg med frivilliga men bonusgrundande redovisningsuppgifter vid tavlan på lektioner inom ramen för kandidatkursen i statistik våren 2017. Tanken var att såväl förmå studenterna till ett kontinuerligt lärande under kursens gång som att öka närvaron vid undervisningen. Resultaten efter en kursomgång är mestadels positiva, men det finns delar som behöver utvecklas.

Location: SP5226

### Wednesday 13:30-14:30, September 20, 2017

Wireless Network Problems
Abstract: The talk will present some research problems I have been work on during the last 11 years. Among these problems is on modeling and improving performance of wireless networking using Markovian theory, Quality of Experience, applied optimization and queueing theory.

Location: SP5226

### Wednesday 13:30-14:30, May 17, 2017

40 års undervisning i matematik inom svenskt utbildningsväsende: En grundskola, ett gymnasium och ett universitet
Sixten Nilsson, ITN, LiU
Abstract: Undervisning på en grundskola, ett gymnasium och ett universitet. Finns gemensamma villkor och beröringspunkter? Vad skiljer? Hur kan erfarenheter från ett stadium befrämja kvalitéten i undervisningen på ett annat? På seminariet diskuteras olika skeenden som påverkat undervisningen på de skolor jag själv verkat, och hur min egen roll som lärare förändrats genom åren. Seminariet tar således specifik utgångspunkt i min egen praktik som lärare under ca 40 år, och kan därmed ses som ett bidrag till analysen av skolutvecklingen i Sverige. Som bakgrund kommer jag att använda, och berätta om, mina år som lärare på grundskolans högstadium (12 år), gymnasieskolan (10 år) och LiU (19 år).

Location: tba

### Wednesday 13:30-14:30, May 3, 2017

Fundamental Mathematical Knowledge (FMK) – en kunskapsklassificering, ett diagnosverktyg och ett internationellt samarbete
Jonas Bergman Ärlebäck, MAI, LiU
Abstract: På LiU bedrivs lärarutbildning mot samtliga årskurser inom det svenska skolväsendet. För lärarstudenter som i sina framtida värv kommer att undervisa i matematik innebär detta att de som del av sin utbildning läser såväl rena ämneskurser i matematik som kurser i matematikdidaktik. En aspekt som har fått relativt lite belysning i forskningen är vilka kunskaper i matematik begynnande lärarstudenter bör ha som bas för att kunna tillgodose sig lärarutbildningens kurser i matematik och matematikdidaktik. På det här seminariet diskuteras och redovisas preliminära resultat från ett nystartat internationellt samarbete som bland annat har som syfte att formulera och undersöka lärarstudenters Fundamental Mathematical Knowledge (FMK) – det minimum av kunskaper i matematik som utbildningen till matematiklärare bygger vidare på och utvecklar i matematik- och matematikdidaktikkurser. Förutom att presentera det internationella samarbetsprojektet och FMK-ramverket, presenteras och diskuteras även resultat från en diagnos av FMK genomförd av 172 lärarstudenter på LiU VT2017 i relation till motsvarande studentgrupper i Finland, Spanien och Storbritannien.

Location: SP5226

### Wednesday 13:30-14:30, March 22, 2017

Machine learning in medical imaging - what, why and how
Daniel Forsberg, Research scientist at Sectra
Abstract: Machine learning has in recent years gained significant interest from media, which is especially due to the surge surrounding deep learning. Something which has placed machine learning at the top of the Gartner's hype curve. In this seminar, we will discuss the general aspects of machine learning and show how it relates to the fundamentals of mathematics taught at an undergraduate level. In addition, deep learning will be presented and its use in medical imaging exemplified.

Location: SP5226

### Wednesday 13:30-14:30, Feb 8, 2017

Computational Mathematics at Örebro University
Mårten Gulliksson and Ye Zhang, Institutionen för naturvetenskap och teknik, Örebro Universitet
Abstract: We will give some examples of problems in computational mathematics that we have worked with during the last 3 years. Among these problems are inverse problems in PDE, homogenization, Chromatography, biosensors, robot assisted gas detection, sparse solutions in nonlinear equations, and neuro field modelling. We will also describe a method using damped second order dynamical systems to solve equations.

Location: SP5226

### Wednesday 13:30-14:30, Nov 30, 2016

An approximate Nash equilibrium for pure Jump Markov games of mean-field type on continuous state space
Rani Basna, PhD in Applied Mathematics, Linnaeus University
Abstract: We investigate mean-field games from the point of view of a large number of indistinguishable players which eventually converges to infinity. The players are weakly coupled via their empirical measure. The dynamics of the states of the individual players is governed by a non-autonomous pure jump type semigroup in a Euclidean space, which is not necessarily smoothing. Investigations are conducted in the framework of non-linear Markov processes. We show that the individual optimal strategy results from a consistent coupling of an optimal control problem with a forward non-autonomous dynamics. In the limit as the number $$N$$ of players goes to infinity this leads to a jump-type analog of the well-known non-linear McKean-Vlasov dynamics. The case where one player has an individual preference different from the ones of the remaining players is also covered. The two results combined reveal an epsilon-Nash Equilibrium for the $$N$$-player games.

Location: SP5226

### Wednesday 13:30-14:30, Nov 16, 2016

Optimization of HDR Brachytherapy - Mathematical Derivation of the Linear Penalty Model from a Dose-Volume Constrained Model
Björn Morén, Division of Optimization at the Department of Mathematics, LiU
Abstract: High dose rate brachytherapy is a method for cancer treatment where the radiation source is placed inside the body, in or close to a tumour. Optimization is being used in practice to create dose plans and the most common approach is using an ad hoc linear penalty model, which penalises deviations from given dose limits for the radiation target and for organs at risk. This model is easy to solve but a weakness is the low correlation with dose-volume measures that are used clinically to evaluate dose plans. Further, the model contains parameters that have no clear interpretations in clinical measures. An alternative approach to dose planning is the use of mixed-integer models with explicit dose-volume constraints which include parameters that directly correspond to dose-volume measures, and are therefore easy to understand and interpret. In this presentation we will show a mathematical derivation of the linear penalty model from a dose-volume constrained model.

Location: SP5226

### Wednesday 13:30-14:30, Oct 5, 2016

Är det lämpligt att matematisk modellering ingår i universitetens grundläggande matematikkurser?
Peter Frejd, Department of Mathematics, Linköpings universitet
Abstract: Inom matematikdidaktisk forskning beskrivs matematisk modellering som en central del av ämnet matematik, som knyter ihop matematiken med verkligheten. Avsikten med seminariet är att väcka debatt kring begreppet matematisk modellering; särskilt att undersöka den matematiska modellerings möjligheter och begränsningar i universitetsundervisningen. Utgående från matematikdidaktisk forskningslitteratur behandlar seminariet bland annat följande frågor:

• Hur arbetar professionella modellerare?
• Kan och bör matematisk modellering ingå i universitetets grundkurser i matematik? Syfte? Organisation?

Exempel på mer och mindre realistisk modellering i universitetens nuvarande grundläggande kurser presenteras och seminariet avslutas med en allmän diskussion.

Location: SP5226

### Wednesday 13:30-14:30, Sep 21, 2016

Multilinear least-squares problem in design of filter networks: global optimization and sparse optimization techniques
Spartak Zikrin, PhD in optimization, Linköpings university
Abstract: The talk concerns the multilinear least-squares (MLLS) problem, which is an extension of the linear least-squares problem by using a multilinear operator in place of a matrix-vector product. The MLLS is typically a large-scale problem characterized by a large number of local minimizers, each of which is singular and non-isolated. I will present our computationally effective approaches for solving the MLLS and the cardinality-constrained MLLS. They are based on global optimization and sparse optimization techniques, respectively. The efficiency of our approaches is illustrated by results of numerical experiments performed for some problems related to the design of filter networks in medical imaging.

Location: SP5226

### Wednesday 13:30-14:30, Sep 7, 2016

Weather Derivatives and Stochastic Modelling of Temperature
Fredrik Berntsson, Department of mathematics, Linköping University
Abstract: Weather derivatives are financial instruments based on a weather related index variable, e.g. mean daily temperature or daily rainfall. These derivatives are used by companies to guard against bad weather or by investors reduce risk in a portfolio. In this seminar we cover the basic idea of weather derivatives, a bit of the history, give a back ground on financial derivatives, and point out the differences between weather derivatives and traditional ones. In our research project we use a statistical model of the temperature at a specific location to place a value on a weather derivative contract.

Location: SP5226

### Wednesday, May 18, 13:30-14:30, 2016

Dispersionless (3+1)-dimensional integrable hierarchies
Abstract: In the lecture I present a multi-dimensional realization of the R-matrix approach for the construction of integrable hierarchies. Using that formalism for particular Jacobi algebra, I construct integrable hierarchies of (3+1)-dimensional dispersionless systems.
Location: SP5226

### Monday, May 16, 13:30-15:00, 2016

Solitons II
Abstract: Part two in two part lecture. I explain in elementary way, how particular partial differential equations (PDEs) model various kinds of wave phenomena in the real world. What kind of terms from considered PDEs are responsible for dispersion processes, dissipation processes and nonlinear effects, respectively. In particular I will concentrate on distinguish class of nonlinear PDEs, which despite of their nonlinearity are integrable and have very interesting, from the physical point of view, class of solutions, so called soliton solutions. Such class of solutions is represented by arbitrary number of localized solitary waves, stable with respect to mutual interactions.

Last 30 minutes are planed for discussion.

Location: SP5226

### Wednesday, May 11, 13:30-14:30, 2016

Solitons I
Abstract: Part one in two part lecture. I explain in elementary way, how particular partial differential equations (PDEs) model various kinds of wave phenomena in the real world. What kind of terms from considered PDEs are responsible for dispersion processes, dissipation processes and nonlinear effects, respectively. In particular I will concentrate on distinguish class of nonlinear PDEs, which despite of their nonlinearity are integrable and have very interesting, from the physical point of view, class of solutions, so called soliton solutions. Such class of solutions is represented by arbitrary number of localized solitary waves, stable with respect to mutual interactions.

Location: SP5226

### Wednesday, May 4, 13:30-14:30, 2016

A Functional Hodrick Prescott Filter
Hiba Nassar, Department of Mathematics, Linnaeus University
Abstract: We propose a functional version of the Hodrick-Prescott filter for functional data which take values in an infinite dimensional separable Hilbert space. We further characterize the associated optimal smoothing parameter when the associated linear operator is compact and the underlying distribution of the data is Gaussian. Moreover, we study a version of the functional Hodrick-Prescott filter where the associated operator is not necessarily compact, but merely closed and densely defined with closed range. We show that the associated optimal smoothing operator preserves the structure obtained in the compact case, when the underlying distribution of the data is Gaussian.
Location: SP5226

### Wednesday, April 20, 13:30-14:30, 2016

Designing Mathematics Lessons Using Japanese Problem Solving Oriented Lesson Structure. A Swedish case study
Yukiko Asami-Johansson, Department of Electronics, Mathematics and Natural Sciences, University of Gävle
Abstract: My seminar is concerned with applying the Japanese problem solving oriented (PSO) teaching approach to Swedish mathematics classrooms. The overall aim of my research project is to describe and investigate the viability of PSO as design tool for teaching mathematics. The PSO approach is a variation of a more general Japanese teaching paradigm referred to as “structured problem solving”. These teaching methods aim to stimulate the process of students’ mathematical thinking and have their focus on enhancing the students’ attitudes towards engaging in mathematical activities. Chevallard’s anthropological framework is used to analyse which mathematical knowledge is exposed in the original Japanese lesson plans and in the lessons observed in the classrooms.

Location: SP5226

The seminar will be in Swedish.

### Wednesday, April 6 , 13:30-14:30, 2016

Historical epistemology, symbolic tools and threshold concepts
Jonte Bernhard, Department of Science and Technology, Linköpings universitet
Abstract: The notion of threshold concepts developed by Meyer and Land is related to a “new and previously inaccessible way of thinking about something” that opens up ways of “seeing things in a new way”.
In my talk I will present some cultural and historical views on the notion of “troublesome knowledge” and “threshold concepts” in relation to the development of mathematical tools mathematical tools used are seen as “counter-intuitive” or even “absurd” and therefore are what is called “troublesome knowledge”. What many learners see as troublesome corresponds often very well to “thresholds” that have been problematic for mankind to overcome in their development of new tools in mathematics and science. I will give some historical examples of how development of new tools has enabled us to “see things in new and more powerful ways”. I will also argue that some of the historically developed terminologies are misleading, for example “natural” and “real” numbers are less suited to describe phenomena in nature than “complex” (imaginary) numbers are. Finally I will relate this historical epistemological approach to my present research into students’ understanding of phase represented by phasors and complex numbers as tools in electric circuit theory.
Location: SP5226

### Wednesday, March 9, 13:30-14:30, 2016

Source Localization of Brain Tumors via Reaction Diffusion Models
Rym Jaroudi, Tunis el Manar University, Tunisia
Abstract: In this work, we propose a mathematical method for locating the brain tumor source starting from the following reaction diffusion model: $\left\{\begin{array}{rcll} \partial_{t}u - div (D(x) \nabla u) - f(u) &=& 0& \mbox{in }\Omega\times(0,T)\\ u(0) & = &\varphi&\mbox{in }\Omega\\ D\nabla u\cdot n &=&0& \mbox{on }\partial\Omega\times(0,T) \end{array}\right. \nonumber$ This equation describes the change over time of the normalised tumour cell density $$u$$ as a consequence of two biological phenomena: proliferation and invasion. Our approach consists in recovering the initial spatial distribution of the tumor cells $$\varphi=u(0)$$ starting from a later state $$\psi=u(T)$$ which can be given by a medical image. For that, we use a regularization method posing the inverse problem as a sequence of well-posed forward problems. Simulation with synthetic images show the accuracy of our approach for locating brain tumor sources.
This work is a joint collaboration with George Baravdish (Linköping University) and Freddie Åström (Heidelberg University).
Location: SP5226

### Wednesday, February 24, 13:30-14:30, 2016

Real-time Fluid Simulation using Position-Based Dynamics
Niklas Andersson, Gabriel Baravdish, Joakim Deborg , Department of Science and Technology, Linköpings universitet
Abstract: Being able to simulate fluids in real time is important in many applications including games and interactive visualizations. This presentation will focus on and describe a modern approach to modeling fluid simulation in real-time, even on mediocre hardware. This method is called Position-Based Dynamics and works by enforcing certain constraints on a set of particles. We also present a method for implementing Position- Based Dynamics on graphics hardware (GPU) in order to take advantage of the massively parallel architecture available and achieve the desired performance. Finally we address some ways in which Position-Based Dynamics can be used to simulate phenomena other than fluids.

This work was achieved in the course TN1008 "Advanced Simulation and Visualization of Fluids in Computer Graphics”.
Location: SP5226

### Wednesday, February 10, 13:30-14:30, 2016

Tröskelbegrepp – en portal till ny förståelse
Abstract: Tröskelbegrepp är begrepp som till en början är svåra att lära men som också har potential att öppna upp för en ny förståelse av ett helt område. Forskning visar att fokus på tröskelbegrepp gynnar studenters lärande. I min forskning har jag studerat hur studenter utvecklar sina uppfattningar om matematiska tröskelbegrepp. Resultat från en studie av studenters uppfattningar om begreppet funktion presenteras i föredraget.

Location: TP53

The seminar will be in Swedish.

### Wednesday, December 9, 13:30-14:30, 2015

Tackling molecular evolution with bioinformatics; what's in a sequence?
Robert Pilstål, Linköpings universitet, IFM, Bioinformatics
Abstract: Proteins make up the basic building blocks of life, all composed by chains of amino acids connected by peptide bonds and in varying lengths. They fold up into, more or less, distinct three dimensional structures performing a plethora of specific functions essential for all cellular lifeforms. The connection between protein chain amino acid sequence, structure and function is well accepted but poorly understood. We explain here how molecular evolution is related to protein function and how it can be studied by methods employing sequence mutation covariance; extracting graph models utilizing the graphical lasso inverse of a covariance matrix or optimizing a pseudolikelihood.
Location: SP5226

### Wednesday, November 25, 13:30-14:30, 2015

Learning Spatially Regularized Correlation Filters for Visual Tracking
Martin Danelljan, Computer Vision Laboratory, ISY, Linköpings universitet,
Abstract: Robust and accurate visual tracking is one of the most challenging computer vision problems. Due to the inherent lack of training data, a robust approach for constructing a target appearance model is crucial. Recently, discriminatively learned correlation filters (DCF) have been successfully applied to address this problem for tracking. These methods utilize a periodic assumption of the training samples to efficiently learn a classifier on all patches in the target neighborhood. However, the periodic assumption also introduces unwanted boundary effects, which severely degrade the quality of the tracking model.

We propose Spatially Regularized Discriminative Correlation Filters (SRDCF) for tracking. A spatial regularization component is introduced in the learning to penalize correlation filter coefficients depending on their spatial location. Our SRDCF formulation allows the correlation filters to be learned on a significantly larger set of negative training samples, without corrupting the positive samples. We further propose an optimization strategy, based on the iterative Gauss-Seidel method, for efficient online learning of our SRDCF.
Location: SP5226

### Wednesday, November 11, 13:30-14:30, 2015

Nonelectrostatic Interactions in Electrical Double Layer Theory
Abstract: Electrical double layers arise at the interface of objects in contact with fluids, their description thus of great interest where interfacial phenomena are important; colloid science, physological and nanotechnological applications, crude oil recovery, to mention a few. Most vapour-liquid, liquid-solid or gas-solid interfaces acquire electric charge by adsorption of charged entities, whereby ionic species in the immediate surrounds become attracted to, or repelled from, the interface. This formation of a compact chemically bound surface charge and its surrounding diffuse charge cloud constitutes the electric double layer. A simple way to model it is with the Poisson-Boltzmann equation, a nonlinear differential equation. Traditional models of ion-surface interaction only included electrostatic potentials with the unsatisfactory consequence of ignoring ion specific effects, ubiquitous in nature and frequently exploited in industrial processes. These effects originate from the unique features of ions, such as their radius or polarizability, rather than their valency charge.

The mathematical treatment of the free energy of two interacting electrical double layers is the theme of this talk. In previous studies employing extended models, the inclusion of nonelectrostatic potentials was consistently handled only under certain boundary conditions imposed on the Poisson-Boltzmann equation. A correction to inconsistent practices is presented, indicating that ionic nonelectrostatic potentials play a more prominent role than has previously been suggested.
Location: SP5226

### Wednesday, October 14, 13:30-14:30, 2015

Classical and quantum ODE's in Hamiltonian mechanics
Maciej Blaszak, Adam Mickiewicz University, Poland
Abstract: We define a class of ODE's which describe classical and quantum Hamiltonian evolutin. Then, we describe the properties of their solutions, i.e. related classical and quantum flows. Finally we show how to derive the time evolution of measurable quantities of the model, so called expectation values of observables.
Location: SP5226

### Wednesday, September 30, 13:30-14:30, 2015

Riesz Potentials: Estimates, Asymptotics, Inversion and Applications
Johan Thim, Department of Mathematics, Linköpings universitet,
Abstract: In this seminar, we will study both global and local properties of Riesz potentials. Introduced by Marcel Riesz in the 1930s, these objects are central in both potential and PDE theory and are also closely related to fractional derivatives and the fractional Laplacian. Results concerning boundedness and asymptotics will be presented and inversion of Riesz potential equations (to find a "density function") is considered. Specifically, we will employ a radial/spherical decomposition for functions to obtain sharper estimates and asymptotic results. It turns out that the radial part of a function determines the dominating behaviour of Riesz potentials.
Location: SP5226

### Wednesday, September 16, 13:30-14:30, 2015

Introduction to Compressed Sensing: Theory and Applications
Ehsan Miandji, Visual Computing Laboratory, ITN, Linköpings universitet,
Abstract: The presentation starts with a gentle introduction to the field of compressed sensing, which introduces key definitions such as dictionary, sparsity, Restricted Isometry Property (RIP) and more. Afterwards, some of the fundamental and theoretical results in compressed sensing for reconstructing sparse signals from random measurements will be presented. I will consider two very distinct applications. First, I will discuss a new compressed sensing framework for reconstruction of incomplete and possibly noisy images and their higher dimensional variants, e.g. animations and light-fields. The algorithm relies on a learning-based two-dimensional basis representation and represents the input signal in a reduced union of subspaces model, while allowing sparsity in each subspace. I will also discuss a theoretical analysis, deriving conditions for obtaining a unique solution of the reconstruction algorithm. The second application is related to the array of antennas and the problem of finding the Direction Of Arrival (DOA). We show that using Orthogonal Matching Pursuit (OMP), one can estimate the DOA with high probability considering the dynamic rage, signal to noise ratio, and mutual coherence of antenna elements. The main theoretical results will be presented, showing tighter bounds on probability of detection compared to previous work.
Location: SP5226

### Wednesday, May 27, 13:30-14:30, 2015

Optimal decomposition in real interpolation and total variation regularization on the graph
Abstract: In 1992 Rudin, Osher, and Fatemi proposed to approximate the denoised image $$f_{\ast}$$ by the solution of a minimization problem $f_{\ast} \approx g_{t} = \underset{{g\in BV(\Omega)}}{\mathop{\rm arg min}}\left( \frac{1}{2}\left\| f_{ob}-g \right\|^{2}_{L^{2}(\Omega)} + t\left\|g\right\|_{BV(\Omega)} \right), \qquad \qquad \qquad (1)$ where $$f_{ob}$$ is the observed image or data, and is related to the real image $$f_{\ast}$$ according to $$f_{ob} = f_{\ast} + \eta$$ where $$\eta$$ is an additive noise (often considered as Gaussian) and where $$t$$ is a positive parameter. This problem is referred to as the Rudin-Osher-Fatemi or ROF problem. Let $$g_{t}$$ be the excat minimizer of (1). Then we can talk of optimal decomposition $$f_{ob}=\left(f_{ob}-g_{t}\right) + g_{t}$$ of $$f_{ob}$$ for the functional $$L_{2,1}\left(t,f_{ob};L^{2}(\Omega),BV(\Omega)\right)=\underset{{g\in BV(\Omega)}}\inf \left( \frac{1}{2}\left\| f_{ob}-g \right\|^{2}_{L^{2}(\Omega)} + t\left\|g\right\|_{BV(\Omega)} \right)$$. The problem of characterizing this optimal decomposition was considered by Yves Meyer in 2001. In this talk we plan to present the characterization of optimal decomposition for more general functionals arising in real interpolation such as $L_{p_0,p_1}\left(t,x;X_0,X_1\right) = \inf_{x=x_0+x_1}\left( \frac{1}{p_0}\left\|x_0\right\|^{p_0}_{X_0}+\frac{t}{p_1}\left\|x_1\right\|^{p_1}_{X_1} \right),$ where $$\left(X_0,X_1\right)$$ is a compatible Banach couple, $$x\in X_{0}+X_{1}$$, $$1\leq p_0, p_1< \infty$$ and $$t>0$$. The characterization presented uses duality in convex analysis. Based on this, we also present a new algorithm for constructing the exact minimizer $$g_{t}$$ of (1) considered on a (finite) directed and connected graph.
Location: SP5226

### Wednesday, May 13, 13:30-14:30, 2015

Analysis of a Growth Curve model in high dimension
Abstract: In this talk we will consider the problem of estimating and testing the mean and covariance matrix in high dimension for a general multivariate linear model, the so called Growth Curve model, i.e., the $$n \times P$$ observation matrix is normally distributed with unknown bilinear mean and unknown covariance matrix. The maximum likelihood estimator (MLE) for the mean is a weighted estimator with the inverse of the sample covariance matrix which is unstable for large $$p$$ close to $$N$$ and singular for $$p$$ larger than $$N$$. We modify the MLE to an unweighted estimator and propose new tests, for the mean and covariance matrix, which we compare with the previous likelihood ratio tests (LRTs) based on the weighted estimator. To compare the performance of the tests we compute the attained significance level and the empirical power.
Location: SP5226

### Wednesday, April 29, 13:30-14:30, 2015

Introduction to Wireless Sensor Networks
Abstract: Wireless Sensor Networks (WSN) were first developed for military applications such as battlefield surveillance. They are now widely used for various applications, for example, detecting ambient conditions such as temperature, movement, sound, light, or the presence of certain objects, inventory control, disaster management, structure health monitoring and home automation. The first half of the seminar will give a general introduction to the design and development of wireless sensor networks. The second half is an introduction to ZigBee wireless sensor network and its applications.
Location: SP5226

### Wednesday, April 15, 13:30-14:30, 2015

A gentle introduction to peakons
Abstract: The Camassa-Holm equation is a nonlinear PDE which was derived in 1993 as a model for waves in shallow water. It has many remarkable mathematical features, one of which is that it admits a particular type of solution where several peak-shaped waves interact. Such waves are known as "peakons" (an abbreviation for "peaked solitons"), and they are described by completely explicit solution formulas in terms of elementary functions. The derivation of these formulas involves surprising connections to topics such as vibrating strings, orthogonal polynomials and continued fractions. The aim of this talk is to give a short introduction to the fascinating world of peakons.
Location: SP5226

### Wednesday, March 18, 13:30-14:30, 2015

Gram-Schmidt orthogonalization: 100 years and more.
Abstract: Orthogonalization algorithms have been around for more than 200 years. However, it was a paper from 1907 by Erhard Schmidt that led to the popularization of orthonormalization techniques. His orthogonalization algorithm has since become known as the Gram-Schmidt process, because it is essentially the same as an earlier one published by J. P. Gram in 1883. The Gram-Schmidt process is now used in a variety of numerical algorithms such as least squares solvers and Krylov subspace methods. The year 2007 marked the 100th anniversary of Schmidt's paper. This talk surveys the evolution of the understanding of the Gram-Schmidt process from a numerical point of view.
Location: SP5226

### Wednesday, March 4, 13:30, 2015, in K2 (Kåkenhus)

Licentiatseminarium: Elevers möjligheter till lärande av matematiska resonemang
Jonas Jäder, ISV, Linköpings universitet, och Bromangymnasiet, Hudiksvall.
Abstract: En av de viktiga anledningarna till varför många elever har svårigheter med matematik i skolan är att utantill-inlärning utgör grunden för utbildningen för många av dem. Procedurella och konceptuella kunskaper behövs för att skapa en bred matematisk kompetens. Eleverna lär sig bara det som de får en möjlighet att lära sig, vilket innebär att vi måste beakta vilka möjligheter till lärande som erbjudas eleverna i skolan. Ett väletablerat ramverk som gör det möjligt att analysera det resonemang som krävs för att lösa läroboksuppgifter samt det resonemang som används av eleverna vid uppgiftslösning har använts för att undersöka möjligheterna att lära sig resonera matematiskt. Ramverket gör en mer förfinad diskussion av vilken typ av kunskap som används av eleverna möjlig. Ramverket skiljer på kreativa matematiska resonemang, där en lösning måste skapas av eleven, och imitativa resonemang som bygger på utantill-inlärning eller imitering av en lösningsalgoritm. Möjligheterna att lära sig beror på klassrummets normer som har förhandlats fram mellan elever och lärare. Dessa normer påverkas i sin tur av flera faktorer. I denna avhandling diskuteras läroboken, både som en objektiv bild av undervisningen och utifrån hur det används i klassrummet, samt elevernas uppfattningar om matematik. Den första studien är en analys av läromedel som används i gymnasieskolor över hela världen. Den andra studien anser hur elever faktiskt resonerar i klassrumssituationer och i den tredje studien relateras elevers resonemang med de uppfattningar de visar upp.

Resultaten visar att läroböckerna från tolv olika länder har en liknande andelen uppgifter som kräver att eleverna använda kreativa matematiska resonemang. Detta antyder att läroboken inte är den enda faktorn som påverkar elevernas möjligheter till lärande. I genomsnitt krävde ungefär var tionde uppgift ett mer genomgripande kreativt matematiskt resonemang, vilket verkar vara en låg andel, speciellt då man beaktar att denna typ av uppgifter ofta återfinns mindre frekvent i den grupp av uppgifter eleverna först stöter på inom varje nytt avsnitt. Resultaten visar även att elever i den svenska gymnasieskolan främst löser de första, lättare uppgifterna och även i stor utsträckning använder imitativa resonemang. Då elever guidar varandra genom uppgiftslösning verkar det som att fokus främst ligger på att komma fram till ett svar som överensstämmer med facit. Inte heller då elever får hjälp av en lärare verkar möjligheter till annat än imitativa resonemang skapas. Eleverna indikerar dessutom uppfattningar om att matematiska uppgifter i de allra flesta fall ska kunna lösas genom ett imitativt resonemang och att utantill-inlärning därför bör vara en central del av undervisningen. Lärarens roll i klassrummet är viktig, då han är en av aktörerna då gemensamma normer skapas. Läraren bör bland annat lägga stor vikt vid vilka uppgifter och vilka läromedel som används i undervisningen. Även elevernas sätt att arbeta i klassrummet måste beaktas i relation till möjligheterna till lärande, och den matematiska förståelsen bör spela en större roll.

Location: Kåkenhus, K2

This seminar is a licentiate presentation with the opponent Mogens Niss. The seminar will be in Swedish.

### Wednesday, Februari 18, 13:30-14:30, 2015

Konst och Matematik: Möbiusbandet.
Abstract: Ett Möbiusband får man genom att ta en pappersremsa och klistra ihop ändarna efter att ha vridit ena änden upp och ner. Det är ett matematiskt begrepp som har Möbius' namn. Möbiusbandet har inspirerad många konstnärer under 1900-talet. I föredraget använder vi Möbusbandet för att illustrera hur matematiska begrepp hjälper oss att "se" på konst och hur konst hjälper oss att illustrera matematiska begrepp.
Location: SP5226

### Wednesday, Februari 4, 13:30-14:30, 2014

Spectral Graph Partitioning and a Generalization to Tensors
Abstract: Spectral graph partitioning is a method for clustering data organized as undirected graphs. The method is based on the computation of eigenvectors of the graph Laplacian. We give a brief account of spectral graph partitioning and a couple of applications in information sciences. In many areas one wants to cluster data from a sequence of graphs. Such data can be organized as a large sparse tensor. We present a spectral method for tensor partitioning based on the computation of the best multilinear rank approximation of the tensor. A few applications are briefly discussed.
Location: SP5226

### Wednesday, January 21, 13:30-14:30, 2015

Flat coordinates for flat Stäckel systems, Part 2
Abstract: A Stäckel system in on a $$2n$$-dimensional Poisson manifold is a family of n quadratic in momenta and commuting in the sense of Poisson bracket Hamiltonian systems separable (in the sense of Hamilton--Jacobi theory) in orthogonal coordinates. These systems are most conveniently obtained from appropriate so called separation relations, a concept intorduced by Sklyanin. In this talk I use this fact to show how to explicitly construct flat coordinates -- for those Stäckel systems of the so called Benenti type that are flat -- from a single generating function. Our construction encompasses the already known cases of flat coordinates for Benenti systems, namely Jacobi elliptic coordinates, Jacobi parabolic coordinates and (in certain cases) coordinates recently discovered by A. Sergyeyev and M. Błaszak. Moreover, I will demonstrate the explicit form (in flat coordinates) of some important geometric objects related with these systems, namely Killing tensors and families of separable potentials.
Location: SP5226

### Wednesday, December 10, 13:30-14:30, 2014

Models for Nonlinear Scalar Conservation Laws in Traffic Flow and Godunov's scheme
Abstract: This talk concerns the solution of the scalar hyperbolic conservation law: $u_t(x,t) + f(u(x,t))_x = 0.$ This equation appears in traffic modeling where $$u$$ is the traffic density and $$f$$ is the traffic flux. It is assumed here that the total mass of the system is conserved. Many practical problems in science and engineering involve conserved quantities which lead to PDE of the type above. There are special difficulties associated with solving the PDE (e.g. shock formation) that are not seen elsewhere and must be dealt with carefully in developing numerical methods. Methods based on naive finite difference approximations may work well for smooth solutions but can give disastrous results when discontinuities are present. In this talk I will give a short introduction to the Godunov's scheme for approximating the solution of this equation which overcomes difficulties with discontinuities.
Location: SP5226

### Wednesday, November 26, 13:30-14:30, 2014

Flat coordinates for flat Stäckel systems, Part 1
Abstract: A Stäckel system in on a 2n-dimensional Poisson manifold is a family of n quadratic in momenta and commuting in the sense of Poisson bracket Hamiltonian systems separable (in the sense of Hamilton--Jacobi theory) in orthogonal coordinates. These systems are most conveniently obtained from appropriate so called separation relations, a concept intorduced by Sklyanin. In this talk I use this fact to show how to explicitly construct flat coordinates -- for those Stäckel systems of the so called Benenti type that are flat -- from a single generating function. Our construction encompasses the already known cases of flat coordinates for Benenti systems, namely Jacobi elliptic coordinates, Jacobi parabolic coordinates and (in certain cases) coordinates recently discovered by A. Sergyeyev and M. Błaszak. Moreover, I will demonstrate the explicit form (in flat coordinates) of some important geometric objects related with these systems, namely Killing tensors and families of separable potentials.
Location: SP5226

### Wednesday, November 12, 13:30-14:30, 2014

Hamiltonian systems: from classical to quantum models
Maciej Blaszak, Adam Mickiewicz University, Poland
Abstract: The mathematical structure of classical and quantum Hamiltonian dynamics is discussed. The smooth passage between both models is presented using a deformation procedure.
Location: SP5226

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