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Events
Interactions between algebra and the sciences

MPI für Mathematik in den Naturwissenschaften Leipzig (Leipzig)

Inselstr. 22
04103 Leipzig
Germany

E1 05 (Leibniz-Saal)

conference

27.05.17

Interactions between algebra and the sciences

This one-day event is a platform for interactions between biology, data science, algebra, and discrete math. It will feature lectures by leading researchers and students, working at the interface between these fields. Our aim is to exchange ideas and give rise to new opportunities for research.

Program

09:30 - 10:30	Ezra Miller (Duke University) Algebra for Topology in Biology and Statistics With "Big Data" comes a surge of geometric data sets and data objects, particularly in biology and medicine, where shapes, images, videos, networks, and small samples in high dimension are common. One way to deal with such data is to summarize topologically. That, in turn, leads to algebraic structures which take their cue from graded polynomial rings and their modules, although the theory is complicated by the passage from integer exponent vectors to real exponent vectors. The path to effective methods requires finitness conditions to replace the usual ones from commutative algebra. Statistical considerations interact with these finiteness conditions in fundamental ways, some of them relying on an understanding of how datasets of this nature relate to moduli of modules. The talk will start with a general discussion of biological and medical investigations that lend themselves to techniques based on geometry, including concrete datasets and underlying statistical questions. The primary focus will be on a fundamental problem in evolutionary biology that drove the genesis of the new algebraic ideas covered here; it concerns evolution of changes to discrete morphological features, for which we are doing statistics on a dataset comprising images of fruit fly wing veins. The main material is joint work in progress with David Houle (Biology, Florida State), Ashleigh Thomas (grad student, Duke Math), Justin Curry (postdoc, Duke Math), and Surabhi Beriwal (undergrad, Duke Math). Slides
10:30 - 10:45	Coffee Break
10:45 - 11:05	Alex Gavryushkin (ETH Zürich) Genetic Interactions and Fitness Landscapes Darwinian fitness of genotypes in a natural population is very hard to measure in practice. To address this challenge, we developed quantitative tools to make inference about epistatic gene interactions when the fitness landscape is only incompletely determined, for example, due to imprecise measurements or partial observations. We demonstrate that higher order genetic interactions can often be inferred for fitness rank orders, where all genotypes are ordered according to fitness, and even for partial fitness orders. In this talk, I will present a complete characterization of rank orders that imply higher order epistasis and an efficient algorithm for detecting such interactions, and show how this can be applied to detect interactions in various biological settings. I will also describe the progress we have made on the way to achieve a similar characterization for fitness graphs and partial fitness orders, and conclude with open problems. Slides
11:15 - 11:35	Kaie Kubjas (Aalto University) Group-based Phylogenetic Models A phylogenetic model describes the evolution of genes. A group-based phylogenetic model assumes extra structure on the parameters of the model that is related to an abelian group. The joint probabilities of a group-based phylogenetic model are functions in the parameters of the model. We study polynomial inequalities that cut out the set of all joint probabilities for a time-reversible group-based model. We apply this knowledge to the study of boundaries and maximum likelihood estimation on group-based models. In particular, we use the degree of an algebraic variety and numerical algebraic geometry to obtain the maximum likelihood estimate exactly for small group-based models. This talk is based on joint work with Dimitra Kosta. Slides
11:45 - 12:05	Daniel Bernstein (North Carolina State University) Tropical Linear Spaces in Phylogenetics One approach to phylogenetic tree reconstruction seeks an ultrametric (i.e. equidistant tree metric) that is l-infinity nearest to a given dissimilarity map. While the l-infinity nearest ultrametric is generally not unique, the set of all l-infinity nearest ultrametrics is a tropical polytope. We give an algorithm to compute a superset of its tropical vertices. Ardila and Klivans showed that the set of all ultrametrics on a finite set of size $n$ is the Bergman fan associated to the matroid underlying the complete graph on $n$ vertices. Therefore, we derive our results in the more general context of Bergman fans of matroids. This generality allows our algorithm to be applied to dissimilarity maps where only a subset of the entries are known. Slides
12:05 - 13:00	Lunch
13:00 - 13:20	Nidhi Kaihnsa (Max Planck Institute for Mathematics in the Sciences) The Attainable Region in Linear Networks Slides
13:25 - 13:45	Robert Flassig (Max Planck Institute for Dynamics of Complex Technical System) Reactor Network Synthesis and Biochemical Process Design Under the hood we are dealing with optimal control problems in form of NLPs as well as dynamic flux balance modeling in form of an ODE system with embedded LP. We focus on the application (hydroformylation, apoptosis in HeLa cells, microalgal-based production) and tailoring of established optimization/solution methods. One of the challenges we address is the consideration of uncertainties (e.g. model parameters, design imperfections) during the phase of model identification but also model-based prediction and optimization. Slides
13:50 - 14:15	Johannes Martini (Universität Göttingen) Binding Polynomials and Cooperativity Slides
14:15 - 14:30	Coffee Break
14:30 - 14:50	Caitlin Lienkaemper (Pennsylvania State University) Using Algebra to Explore Neural Coding Our ability to perceive, process, and interact with our environment depends on a correspondence between patterns of neural activity and stimuli in the environment. This is known as neural coding. A combinatorial neural code describes a pattern of neural activity in terms of which subsets of a population of neurons fire together and which do not. Our canonical example is that of convex neural codes arising from place cells, neurons which fire whenever an animal is within the place cell's place field, a convex region of the environment. Convex neural codes have been studied from a variety of perspectives, including mathematical coding theory, geometry, and topology. Here, we present a summary of algebraic approaches to the study of neural coding, including the neural ideal and the neural toric ideal. Slides
15:00 - 15:20	Carsten Conradi (Hochschule für Technik und Wirtschaft Berlin) Multistationarity in Biochemical Reaction Networks Multistationarity and switching have been recognized as important features of dynamical systems originating in Biology. Often these properties are established numerically. However, parameter uncertainty complicates numerical analysis. Hence techniques allowing the analytic computation of parameters where a given system exhibits either multistationarity or switching are desirable. We present conditions in form of polynomial systems that allow to determine parameter vectors where a mass action system exhibits multistationarity or switching. These polynomial systems arise from the structure of the reaction network and hence are not affected by parameter uncertainty.
15:30 - 17:00	Discussion Session

Participants

Carlos Améndola

TU Berlin

Xenia Auerbach

Leipzig University

Daniel Bernstein

North Carolina State University

Lara Bossinger

University of Cologne

Paul Breiding

TU Berlin

Carsten Conradi

Hochschule für Technik und Wirtschaft Berlin

Alessio D'Alì

MPI Leipzig

Eliana Duarte

MIS MPI Leipzig

Albertas Dvirnas

Lund University

Masud Ehsani

MPI for Mathematics in sciences

Carlotta Ficorella

Leipzig Univerity

Robert Flassig

Max Planck Institute for Dynamics of Complex Technical System

Tobias Fritz

MIS

Alex Gavryushkin

ETH Zürich

Paul Görlach

MPI MIS Leipzig

Corey Harris

MPI MIS Leipzig

Luis Haug

ETH Zürich

Xu He

Jacobs University Bremen

Alexandru Iosif

Otto von Guericke Universität

Nidhi Kaihnsa

Max Planck Institute for Mathematics in the Sciences

Venera Khoromskaia

Max-Planck Institute for Mathematics in the Sciences

Boris Khoromskij

Max-Planck-Institute for Mathematics in the Sciences

Kaie Kubjas

Aalto University

Lisa Lamberti

ETH Zürich

Sara Lamboglia

University of Warwick

Caitlin Lienkaemper

Pennsylvania State University

Johannes Martini

Universität Göttingen

Mateusz Michalek

MPI MiS

Ezra Miller

Duke University

Fatemeh Mohammadi

University of Bristol

Guido Montufar

MPI MIS

Raffaella Mulas

University of Bonn

Simone Naldi

Technische Universität Dortmund

Marta Panizzut

TU Berlin

Daniel Plaumann

Technische Universität Dortmund

Rohini Ramadas

University of Michigan

Yue Ren

MPI MIS Leipzig

Nancy Retzlaff

MPI MIS/ Leipzig University

Mahsa Sayyary Namin

Max Planck Institute for Mathematics in the Sciences

Benjamin Schröter

Technische Universität Berlin

Anna Seigal

University of California

Emre Sertöz

MPI MiS Leipzig

Robert Silversmith

University of Michigan

Liam Solus

Kungliga Tekniska Högskolan

Bernd Sturmfels

MPI Leipzig

Omri Tal

MPI MIS

Jacinta Torres

MPI für Mathematik in den Naturwissenschaften

Martin Ulirsch

University of Michigan

Emanuele Ventura

MPI MIS Leipzig

Stephan Weis

Université libre de Bruxelles

Organizers

Anna Seigal

University of California (Berkeley), USA

Jacinta Torres

Max-Planck-Institut für Mathematik in den Naturwissenschaften (Leipzig), Germany

Administrative Contact

Saskia Gutzschebauch

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail