# CoSy Lunch Seminars 2017 Spring

**24 January**

**Speaker**: Örjan Stenflo, Department of Mathematics, Uppsala University

**Title**: V-VARIABLE IMAGE COMPRESSION

**Place**: Å11167

**Time**: 12:00 -- 13:00

**7 February**

**Speaker**: Lothar Reichel, Professor in Kent State University, Department of Mathematical Sciences

**Title**: Matrix functions, quadrature, and network analysis

**Place**: Å4003

**Time**: 12:00 -- 13:00

**14 February**

**Speaker**: Raazesh Sainudiin, Department of Mathematics, Uppsala University

**Title**: The transmission process: A combinatorial stochastic process for the evolution of transmission trees over networks

**Place**: Å11167

**Time**: 12:00 -- 13:00

**28 February**

**Speaker**: Peter Broqvist, Department of Chemistry - Ångström, Uppsala University

**Title**: Multi-scale modeling of complex oxides: an ongoing struggle

**Place**: Å11167

**Time**: 12:00 -- 13:00

**21 March**

**Speaker**: Kristi Kuljus, Senior Research Fellow in Mathematical Statistics, Institute of Mathematics and Statistics, University of Tartu

**Title**: Comparison of hidden Markov chain models and hidden Markov random field models in estimation of computed tomography images

**Place**: Å11167

**Time**: 12:00 -- 13:00

**28 March**

**Speaker**: Francisco Gancedo, Department of Mathematical Analysis, Faculty of Mathematics, University of Seville

**Title**: Regularity vs singularities for incompressible fluids interfaces

**Place**: Å11167

**Time**: 12:00 -- 13:00

**4 April**

**Speaker**: Wim Hordijk, SmartAnalytiX.com

**Title**: Autocatalytic Sets: The Origin and Organization of Life

**Place**: Å11167

**Time**: 12:00 -- 13:00

**18 April**

**Speaker**: Prof. Alfred M. Bruckstein, Technion Ollendorff Chair in Science, Israel Institute of Technology

**Title**: The Joys of the Elementary: Three Easy Pieces

**Place**: Å11167

**Time**: 12:00 -- 13:00

Local contact person: Christer Kiselman

**9 May**

**Speaker**: Dr. Milias Argeitis, Faculty of Mathematics and Natural Sciences, University of Groningen

**Title**: Dynamic disorder in simple enzymatic reactions induces stochastic amplification of substrate

**Place**: Å11167

**Time**: 12:05 -- 13:00

**23 May**

**Speaker**: Dr Antoni Guillamon Grabolosa, Department of Mathematics, Universitat Politècnica de Catalunya

**Title**: The role of nonlinear dynamics in some neuroscience problems

**Place**: Å11167

**Time**: 12:05 -- 13:00

**24 May**

**Speaker**: Dr Natasha Flyer, Institute for Mathematics Applied to Geosciences, National Center for Atmospheric Research. Prof. Bengt Fornberg Department of Applied Mathematics, University of Colorado.

**Title**: Radial Basis Function-generated Finite Differences(RBF-FD): Freedom from meshes in scientific computing

**Place**: Å11167

**Time**: 12:15 -- 13:00

**30 May**

**Speaker**: Prof. Lambert Schomaker, Scientific Director, Artificial Intelligence and Cognitive Engineering (ALICE), Kunstmatige Intelligentie

**Title**: Continuous learning in massive and diverse collections of historical handwriting

**Place**: Å11167

**Time**: 12:15 -- 13:00

**30 May**

**Speaker**: Prof. Lambert Schomaker, Scientific Director, Artificial Intelligence and Cognitive Engineering (ALICE), Kunstmatige Intelligentie

**Title**: Continuous learning in massive and diverse collections of historical handwriting

**Place**: Å11167

**Time**: 12:15 -- 13:00

**Abstract:**

We are currently experiencing the third wave of neural-network

research. The presence of big data, sufficient computing resources and

improved learning rules have resulted in exciting progress. However, not

everything is rosy. Without sufficient numbers of labels, deep learning will

not work. Even with optimal settings, training a model with more than

a million parameters is a daunting task. In many applications however, there

are no labels from the start: For a freshly digitized historical handwritten

collection, there are usually no shape or language models. Therefore, there is

still a need for convenient label harvesting methods as are used in the

'Monk' trainable search engine for historical collections. With proper feature

schemes and distance functions, even nearest-neighbour and nearest-mean

classifiers have an attractive performance level in big data, with just a few

labels. The recognized results can then be used to train ever more complex models

as the harvest grows, in progressive 'ball parks'. Recent results will be presented.

**24 May**

**Speaker**: Dr Natasha Flyer, Institute for Mathematics Applied to Geosciences, National Center for Atmospheric Research. Prof. Bengt Fornberg Department of Applied Mathematics, University of Colorado.

**Title**: Radial Basis Function-generated Finite Differences(RBF-FD): Freedom from meshes in scientific computing

**Place**: Å11167

**Time**: 12:15 -- 13:00

**Abstract: **Finite difference (FD) methods were first used for solving PDEs over a century ago. Ever since then, FD stencils have typically been based on Cartesian grids, requiring the results to be exact for polynomials of as high degree as permitted by the stencil size. When the polynomials are either supplemented with or altogether replaced by radial basis functions (RBFs), grids become unnecessary and the node points can be scattered as needed. Such RBF-FD approximations combine high levels of accuracy with much improved geometric flexibility, essential both for local refinement and to accurately handle irregular boundaries and material interfaces. Additional benefits include high computational efficiency, short and simple codes, and excellent opportunities for scalability on high performance computing architectures. We will in this presentation highlight some recent RBF-FD calculations, mostly from the geosciences.

**23 May**

**Speaker**: Dr Antoni Guillamon Grabolosa, Department of Mathematics, Universitat Politècnica de Catalunya

**Title**: The role of nonlinear dynamics in some neuroscience problems

**Place**: Å11167

**Time**: 12:05 -- 13:00

**Abstract:**

The talk will turn around several vehicular examples from our recent work that illustrate important current challenges in neuroscience. The examples chosen have a common factor of showing the importance of applying recent methods in nonlinear dynamics that help getting a better understanding of the underlying neuroscience problems. A first example will be the problem of estimating synaptic conductances as a sample problem within those related to brain connectivity. Next, phase response curves associated to biological oscillators will be used to introduce synchronization questions. Finally, models on bistable perception will serve as an approximation to cognitive issues. We thus aim at showing different neuroscience challenges, together with different ways of modelling and different mathematical techniques used to solve theoretical questions, although we will not deepen in technical details, but rather try to bring up inspiring problems and show modi operandi as mathematicians.

**9 May**

**Speaker**: Dr. Milias Argeitis, Faculty of Mathematics and Natural Sciences, University of Groningen

**Title**: Dynamic disorder in simple enzymatic reactions induces stochastic amplification of substrate

**Place**: Å11167

**Time**: 12:05 -- 13:00

**Abstact:**

It is known that many enzymes exhibit fluctuations in their catalytic activity, which are associated with conformational changes on a broad range of timescales. The experimental study of this phenomenon, termed dynamic disorder, has become possible thanks to advances in single-molecule measurement techniques. However, the biological role and importance of these fluctuations in a system with a small number of enzymes such as a living cell, have only started to be explored very recently.

In this talk, we will examine a simple stochastic reaction system consisting of an inflowing substrate and an enzyme with a randomly fluctuating catalytic reaction rate that converts the substrate into an outflowing product. To describe analytically the effect of rate fluctuations on the average substrate abundance at steady-state, we derive an explicit formula that connects the relative speed of enzymatic fluctuations with the mean substrate level. Under fairly general modeling assumptions, we demonstrate that the relative speed of rate fluctuations can have a dramatic effect on the mean substrate, and lead to large positive deviations from predictions based on the assumption of deterministic enzyme activity. As the techniques of single-molecule enzymology continuously evolve, it may soon be possible to study the stochastic phenomena due to enzymatic activity fluctuations within living cells. Our work can be used to formulate testable experimental hypotheses regarding the nature and magnitude of these fluctuations, as well as their phenotypic consequences.

**18 April**

**Speaker**: Prof. Alfred M. Bruckstein, Technion Ollendorff Chair in Science, Israel Institute of Technology

**Title**: The Joys of the Elementary: Three Easy Pieces

**Place**: Å11167

**Time**: 12:00 -- 13:00

**Abstract:**

The talk will discuss three problems in planar geometry. The first problem involves finding a center of point sets defined via disc-covers, and connects to some old results of Steiner. The second problem addresses cutting planar shapes with shortest cutting curves, and yields some interesting isoperimetric inequalities. The third problem is a crazy-cut puzzle that was implemented as game for smart-phones. The results presented are based on three papers co-authored with Yael Yankelevsky, Yaniv Altshuler, Doron Shaked and Yotam Elor.

Local contact person: Christer Kiselman

**4 April**

**Speaker**: Wim Hordijk, SmartAnalytiX.com

**Title**: Autocatalytic Sets: The Origin and Organization of Life

**Place**: Å11167

**Time**: 12:00 -- 13:00

Abstract:

*Life is a chemical reaction network. *More specifically, living systems produce their own components (from a basic “food set”), which in turn maintain and regulate the chemical reaction network that produces these same components. In other words, life is a functionally closed and self-sustaining system.

During the 1970s, several researchers independently developed formal models of a minimal living system based on this view of life. However, most of these models do not explain how these systems could have emerged spontaneously from basic (prebiotic) chemistry. They provide insights into the *organization *of life, but not necessarily its *origin*.

A new mathematical framework, based on the original notion of autocatalytic sets, is able to shed more light on both of these aspects. *Autocatalytic sets *capture the functionally closed and self-sustaining properties of life in a formal way, and detailed studies have shown how such sets emerge spontaneously, and can then evolve further, in simple models of chemical reaction networks. Furthermore, this theory has been applied directly and successfully to study real chemical and biological networks. The autocatalytic sets framework thus provides a useful and formal tool for studying and understanding both the origin and organization of life.

In this talk, I will give a non-technical overview of the background, concepts, and main results of the formal framework, and how it can perhaps be generalized beyond chemistry and the origin of life to entire living systems, ecological networks, and possibly even social systems like the economy.

**28 March**

**Speaker**: Francisco Gancedo, Department of Mathematical Analysis, Faculty of Mathematics, University of Seville

**Title**: Regularity vs singularities for incompressible fluids interfaces.

**Place**: Å11167

**Time**: 12:00 -- 13:00

**Abstract:**

In this talk we consider several scenarios involving the interaction among incompressible fluids of different nature. The main concern is the dynamics of the free boundary separating the fluids, which evolves with the flow velocity. The important question to address is whether the regularity is preserved in time or on the other hand the system develops singularities. We focus on several important physical models: Euler or water-waves, Muskat or porous media interfaces, front dynamics by Surface Quasi-Geostrophic, Navier-Stokes equations, Boussinesq, etc. At first we show results on finite time blow-up. Later we discuss new recent results on global existence for 1996 P.L. Lions' conjecture for density patches evolving by inhomogeneous Navier-Stokes equations.

**21 March**

**Speaker**: Kristi Kuljus, Senior Research Fellow in Mathematical Statistics, Institute of Mathematics and Statistics, University of Tartu

**Title**: Comparison of hidden Markov chain models and hidden Markov random field models in estimation of computed tomography images

**Place**: Å11167

**Time**: 12:00 -- 13:00

**Abstract:**

There is an interest to replace computed tomography (CT) images with magnetic resonance (MR) images for a number of diagnostic and therapeutic workflows. We explore the problem of predicting CT images from a number of magnetic resonance imaging (MRI) sequences using regression approach. Two principal areas of application for estimated CT images are dose calculations in MRI based radiotherapy treatment planning and attenuation correction for positron emission tomography (PET)/MRI. The main purpose of this work is to compare the performance of hidden Markov (chain) models (HMMs) and hidden Markov random field (HMRF) models for predicting CT images of head. Our study shows that HMMs have clear advantages over HMRF models in this particular application. Obtained results suggest that HMMs deserve a further study for investigating their potential in obtaining good estimates of CT images.

**28 February**

**Speaker**: Peter Broqvist, Department of Chemistry - Ångström, Uppsala University

**Title**: Multi-scale modeling of complex oxides: an ongoing struggle

**Place**: Å11167

**Time**: 12:00 -- 13:00

**Abstract:**

A hierarchical multi-scale modeling scheme developed for chemically reactive metal oxides will be presented. The multi-scale approach is based on three levels; (i) the density functional theory (DFT), (ii) the self-consistent density functional based tight binding method (SCC-DFTB), and (iii) a reactive force-field (ReaxFF). The chosen combination of methods allow for a scale-up in both size and time by several orders of magnitude, but still with the accuracy of a DFT calculation, and enables us to take a large step towards experimentally relevant size and time-scales in our simulations. Within this context, I will present recent results obtained for ZnO and CeO_{2}.

**14 February**

**Speaker**: Raazesh Sainudiin, Department of Mathematics, Uppsala University

**Title**: The transmission process: A combinatorial stochastic process for the evolution of transmission trees over networks

**Place**: Å11167

**Time**: 12:00 -- 13:00

Abstract:

We derive a combinatorial stochastic process for the evolution of the transmission tree over the infected vertices of a host contact network in a susceptible-infected (SI) model of an epidemic. Models of transmission trees are crucial to understanding the evolution of pathogen populations. We provide an explicit description of the transmission process on the product state space of (rooted planar ranked labelled) binary transmission trees and labelled host contact networks with SI-tags as a discrete-state continuous-time Markov chain. We give the exact probability of any transmission tree when the host contact network is a complete, star or path network – three illustrative examples. We then develop a biparametric Beta-splitting model that directly generates transmission trees with exact probabilities as a function of the model parameters, but without explicitly modelling the underlying contact network, and show that for specific values of the parameters we can recover the exact probabilities for our three example networks through the Markov chain construction that explicitly models the underlying contact network. We use the maximum likelihood estimator (MLE) to consistently infer the two parameters driving the transmission process based on observations of the transmission trees and use the exact MLE to characterize equivalence classes over the space of contact networks with a single initial infection. An exploratory simulation study of the MLEs from transmission trees sampled from three other deterministic and four random families of classical contact networks is conducted to shed light on the relation between the MLEs of these families with some implications for statistical inference along with pointers to further extensions of our models. The insights developed here are also applicable to the simplest models of “meme” evolution in online social media networks through transmission events that can be distilled from observable actions such as “likes”, “mentions”, “retweets” and “+1s” along with any concomitant comments.

Links:

The Transmission Process: A Combinatorial Stochastic Process for the Evolution of Transmission Trees over Networks, Raazesh Sainudiin and David Welch, Journal of Theoretical Biology, Volume 410, Pages 137–170, 10.1016/j.jtbi.2016.07.038, 2016

http://dx.doi.org/10.1016/j.jtbi.2016.07.038

http://lamastex.org/lmse/mep/

**7 February**

**Speaker**: Lothar Reichel, Professor in Kent State University, Department of Mathematical Sciences

**Title**: Matrix functions, quadrature, and network analysis

**Place**: Å4003

**Time**: 12:00 -- 13:00

Abstract:

Networks arise in many applications. It is often of interest to be able to identify the most important nodes of a network or to determine the ease of traveling between them. We are interested in carrying out these tasks for large undirected and directed networks. Many quantities of interest can be determined by computing certain matrix functionals. We discuss how for directed and undirected graphs a few steps of the Lanczos method in combination with Gauss-type quadrature rules can be applied to determine upper and lower bounds for quantities of interest.

**24 January**

**Speaker**: Örjan Stenflo, Department of Mathematics Uppsala University

**Title**: V-VARIABLE IMAGE COMPRESSION

**Place**: Å11167

**Time**: 12:00 -- 13:00

Abstract: Consider a rectangular image (or picture), and divide, for each fixed positive integer n, the image into 4^n non-overlapping “image pieces” of side lengths (1/2)^n times the side-lengths of the image.

Let V be a fixed positive integer. We say that the image is V-variable if the image contains at most V distinct image pieces for any n.

We describe a simple algorithm for lossy image compression where a given target image is approximated by a V-variable image. Joint work with Franklin Mendivil, Acadia University, Canada.