BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Reinhard Laubenbacher DTSTART:20200605T162000Z DTEND:20200605T165000Z DTSTAMP:20260422T185428Z UID:BIRS_20w5204/1 DESCRIPTION:Title: Ask not what algebra can do for biology - ask what biology can do for algebra\nby Reinhard Laubenbacher as part of Model Theory of Differen tial Equations\, Algebraic Geometry\, and their Applications to Modeling\n \n\nAbstract\nDiscrete models\, such as Boolean networks\, are an increasi ngly popular modeling framework in systems biology\, with many hundreds of published models. The advantages are\, among others\, that they are intui tive and don't require detailed quantitative knowledge such as kinetic par ameters. One disadvantage is that there are relatively few mathematical an d computational tools available for this model type. As a basic example\, given a model\, how can we compute all its steady states? The basic mathem atical framework they can be cast in is polynomial dynamical systems over finite fields. There is a rich convergence of dynamic\, algebraic\, combin atorial\, and graph-theoretic features that come together within this type of mathematical object. Yet very little of this convergence has been used to study a mathematically rich class of objects\, with important applicat ions to problems in the life sciences and elsewhere. This talk will discus s several mathematical and computational problems\, inspired but not direc tly connected to applications in biology\, that can stimulate interesting research in algebra\, broadly defined.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5204/1/ END:VEVENT BEGIN:VEVENT SUMMARY:David Marker DTSTART:20200601T150000Z DTEND:20200601T155000Z DTSTAMP:20260422T185428Z UID:BIRS_20w5204/2 DESCRIPTION:Title: Tutorial: Model Theory\, Quantifier Elimination and Differential Alge bra - 1\nby David Marker as part of Model Theory of Differential Equat ions\, Algebraic Geometry\, and their Applications to Modeling\n\n\nAbstra ct\nI will introduce the basic notions on model theory focusing on effecti ve methods such as quantifier elimination and discuss applications to alge braic theory of differential equations.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5204/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Elisenda Feliu DTSTART:20200601T160000Z DTEND:20200601T165000Z DTSTAMP:20260422T185428Z UID:BIRS_20w5204/3 DESCRIPTION:Title: Tutorial: Challenges in the study of Algebraic Models of Biochemical Reaction Networks\nby Elisenda Feliu as part of Model Theory of Differ ential Equations\, Algebraic Geometry\, and their Applications to Modeling \n\n\nAbstract\nIn the context of (bio)chemical reaction networks\, the dy namics of the concentrations of the chemical species over time are often m odelled by a system of parameter-dependent ordinary differential equations \, which are typically polynomial or described by rational functions. The polynomial structure of the system allows the use of techniques from algeb ra (e.g.\, real algebraic geometry) to study properties of the system arou nd steady states\, for all parameter values. In this talk I will start by presenting the formalism of the theory of reaction networks. Afterwards I will outline the qualitative questions one would like to address\, which i nclude deciding upon the existence of multiple equilibrium points or perio dic orbits\, and their stability. If time permits\, I will discuss selecte d methods with emphasis on their limitations.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5204/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Patrick Speissegger DTSTART:20200602T150000Z DTEND:20200602T153000Z DTSTAMP:20260422T185428Z UID:BIRS_20w5204/4 DESCRIPTION:Title: Limit cycles of Planar Vector Fields\, Hilbert's 16th Problem and o-m inimality\nby Patrick Speissegger as part of Model Theory of Different ial Equations\, Algebraic Geometry\, and their Applications to Modeling\n\ n\nAbstract\nRecent work links certain aspects of the second part of Hilbe rt’s 16th problem (H16) to the theory of o-minimality. One of these aspe cts is the generation and destruction of limit cycles in families of plana r vector fields\, commonly referred to as ”bifurcations”. I will outli ne the significance of bifurcations for H16 and explain how logic–in par ticular\, o-minimality–can be used to understand them well enough to be able to count limit cycles.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5204/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Polly Yu DTSTART:20200602T154000Z DTEND:20200602T161000Z DTSTAMP:20260422T185428Z UID:BIRS_20w5204/5 DESCRIPTION:Title: Mass-action systems: From linear to non-linear inequalities\nby P olly Yu as part of Model Theory of Differential Equations\, Algebraic Geom etry\, and their Applications to Modeling\n\n\nAbstract\nFor mass-action k inetics\, a common model for biochemistry\, much work has gone into relati ng network structure to the possible dynamics of the resulting systems of polynomial ODEs. A family of mass-action systems\, complex-balancing\, is defined by having a positive equilibrium that balances monomials across ve rtices. Surprisingly\, every positive equilibrium of such a system similar ly balance monomials across vertices. These systems enjoy a variety of alg ebraic and stability properties: toricity in the steady state variety and in parameter space\; Lyapunov and conjectured global stability. Unfortunat ely\, most systems are vertex-balanced if and only if the parameters come from a toric ideal. By searching for different graphs representing the sam e ODEs\, we can expand the parameter region for which the system is dynami cally equivalent to a complex-balanced system. The expanded region is defi ned in the space of states and parameters\, and the challenge is to elimin ate the state variables to obtain explicit conditions on parameters (that is\, to perform quantifier elimination over the reals). In this talk\, I w ill introduce and set up the problem via examples.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5204/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Nidhi Kaihnsa DTSTART:20200602T162000Z DTEND:20200602T165000Z DTSTAMP:20260422T185428Z UID:BIRS_20w5204/6 DESCRIPTION:Title: Convex Hulls of Trajectories\nby Nidhi Kaihnsa as part of Model T heory of Differential Equations\, Algebraic Geometry\, and their Applicati ons to Modeling\n\n\nAbstract\nI will talk about the convex hulls of traje ctories of polynomial dynamical systems. Such trajectories also include re al algebraic curves. The main problem is to describe the boundary of the r esulting convex hulls. The motivation to describe these convex hulls comes from attainable region theory in chemistry\, where taking convex combinat ions of points corresponds to mixing results of reactions. We stratify the boundary into families of faces comprised of patches. We define patches u sing the notion of normal cycles from integral geometry. I will discuss th e numerical algorithms we developed for identifying these patches. This is a joint work with Daniel Ciripoi\, Andreas Loehne\, and Bernd Sturmfels.\ n LOCATION:https://researchseminars.org/talk/BIRS_20w5204/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolette Meshkat DTSTART:20200603T150000Z DTEND:20200603T155000Z DTSTAMP:20260422T185428Z UID:BIRS_20w5204/7 DESCRIPTION:Title: Tutorial: Structural Identifiability of Biological Models\nby Nic olette Meshkat as part of Model Theory of Differential Equations\, Algebra ic Geometry\, and their Applications to Modeling\n\n\nAbstract\nA common p roblem in mathematical modeling of biological phenomena is to have unknown parameters in an ODE model. We would like to know if those unknown parame ters can be determined from given data\, often in the form of inputs and o utputs. This problem is called the parameter identifiability problem. If t he data is assumed to be perfect\, this problem of determining whether or not the parameters of a model can be determined from input-output data is called structural identifiability (as opposed to the numerical identifiabi lity problem\, which deals with real and often "noisy" data.) We examine t his problem of structural identifiability for the case where our ODE model is in terms of polynomial or rational functions. For this special case\, we can use differential algebra to attack the problem. We demonstrate the differential algebra approach and also discuss some important questions th at arise\, such as what to do with an "unidentifiable" model. We also exam ine the special case of linear models and use some tools from graph theory to answer other related questions\, e.g. is a submodel of an identifiable model also identifiable or when can we combine two identifiable models to obtain an identifiable model?\n LOCATION:https://researchseminars.org/talk/BIRS_20w5204/7/ END:VEVENT BEGIN:VEVENT SUMMARY:David Marker DTSTART:20200603T160000Z DTEND:20200603T165000Z DTSTAMP:20260422T185428Z UID:BIRS_20w5204/8 DESCRIPTION:Title: Tutorial: Model Theory\, Quantifier Elimination and Differential Alge bra - 2\nby David Marker as part of Model Theory of Differential Equat ions\, Algebraic Geometry\, and their Applications to Modeling\n\n\nAbstra ct\nI will introduce the basic notions on model theory focusing on effecti ve methods such as quantifier elimination and discuss applications to alge braic theory of differential equations.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5204/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Alejandro F. Villaverde DTSTART:20200604T150000Z DTEND:20200604T153000Z DTSTAMP:20260422T185428Z UID:BIRS_20w5204/9 DESCRIPTION:Title: Finding and breaking Lie symmetries: implications for structural iden tifiability and observability of dynamic models\nby Alejandro F. Villa verde as part of Model Theory of Differential Equations\, Algebraic Geomet ry\, and their Applications to Modeling\n\n\nAbstract\nA dynamic model is structurally identifiable (respectively\, observable) if it is theoretical ly possible to infer its unknown parameters (respectively\, states) by obs erving its output over time. The two properties\, structural identifiabili ty and observability\, are completely determined by the model equations. T heir analysis is of interest for modellers because it informs about the po ssibility of gaining insight about the unmeasured variables of a model. He re we cast the problem of analysing structural identifiability and observa bility as that of finding Lie symmetries. We build on previous results tha t showed that structural unidentifiability amounts to the existence of Lie symmetries. We consider nonlinear models described by ordinary differenti al equations and restrict ourselves to rational functions. We revisit a me thod for finding symmetries by transforming rational expressions into line ar systems\, and extend it by enabling it to provide symmetry-breaking tra nsformations. This extension allows for a semi-automatic model reformulati on that renders a non-observable model observable. We have implemented the methodology in MATLAB\, as part of the STRIKE-GOLDD toolbox for observabi lity and identifiability analysis. We illustrate its use in the context of biological modelling by applying it to a set of problems taken from the l iterature\, which also allow us to discuss the implications of (non)observ ability.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5204/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Remi Jaoui DTSTART:20200604T154000Z DTEND:20200604T161000Z DTSTAMP:20260422T185428Z UID:BIRS_20w5204/10 DESCRIPTION:Title: A model-theoretic analysis of geodesic equations in negative curvatu re\nby Remi Jaoui as part of Model Theory of Differential Equations\, Algebraic Geometry\, and their Applications to Modeling\n\n\nAbstract\nTo any algebraic differential equation\, one can associate a first-order stru cture which encodes some of the properties of algebraic integrability and of algebraic independence of its solutions. To describe the structure asso ciated to a given algebraic (non linear) differential equation (E)\, typic al questions are:\n\nIs it possible to express the general solutions of (E ) from successive resolutions of linear differential equations?\n\nIs it p ossible to express the general solutions of (E) from successive resolution s of algebraic differential equations of lower order than (E)?\n\nGiven di stinct initial conditions for (E)\, under which conditions are the solutio ns associated to these initial conditions algebraically independent?\n\nIn my talk\, I will discuss in this setting one of the simplest examples of non completely integrable Hamiltonian systems: the geodesic motion on an a lgebraically presented compact Riemannian surface with negative curvature. I will explain a qualitative model-theoretic description of the associate d structure (and its content in the differential algebraic language used a bove) based on the global hyperbolic dynamical properties identified by An osov in the 70’s (today called Anosov flows) for the geodesic motion in negative curvature.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5204/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Yue Ren DTSTART:20200604T162000Z DTEND:20200604T165000Z DTSTAMP:20260422T185428Z UID:BIRS_20w5204/11 DESCRIPTION:Title: Introduction to tropical algebraic geometry\nby Yue Ren as part of Model Theory of Differential Equations\, Algebraic Geometry\, and their Applications to Modeling\n\n\nAbstract\nThis talk offers a brief and intr oductory overview of tropical algebraic geometry with a heavy emphasis on computations. We introduce the notions of tropical semirings and tropical varieties\, and discuss some of the algorithms surrounding them. Finally\, we will highlight recent and ongoing works on the frontiers of tropical d ifferential algebra.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5204/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Joel Nagloo DTSTART:20200605T150000Z DTEND:20200605T153000Z DTSTAMP:20260422T185428Z UID:BIRS_20w5204/12 DESCRIPTION:Title: Irreducibility and generic ODEs\nby Joel Nagloo as part of Model Theory of Differential Equations\, Algebraic Geometry\, and their Applica tions to Modeling\n\n\nAbstract\nThe irreducibility of an ODE is a notion that was introduce by P. Painlevé at the turn of the 20th century and lat er refined by H. Umemura. Roughly\, an ODE is irreducible if all of its so lutions are ‘new’ functions. This notion is also almost equivalent to strong minimality\, a central notion in model theory. In this talk we will go over the definitions of these concepts and discuss new methods to prov e that ODEs with generic constant parameters are irreducible. We use the P ainlevé equations as examples.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5204/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Miruna-Stefana Sorea DTSTART:20200605T154000Z DTEND:20200605T161000Z DTSTAMP:20260422T185428Z UID:BIRS_20w5204/13 DESCRIPTION:Title: Disguised toric dynamical systems\nby Miruna-Stefana Sorea as pa rt of Model Theory of Differential Equations\, Algebraic Geometry\, and th eir Applications to Modeling\n\n\nAbstract\nDynamical systems arising from chemical reactions can be generated by finite directed graphs embedded in the Euclidean space\, called Euclidean embedded graphs (E-graphs). These dynamical systems have polynomial right-hand-side\, which creates a strong connection between real algebraic geometry and reaction network theory. I n this talk\, we will focus on complex-balanced systems\, which have been also called “toric dynamical systems" by Craciun\, Dickenstein\, Shiu an d Sturmfels. Toric dynamical systems are known or conjectured to enjoy exc eptionally strong dynamical properties\, such as existence and uniqueness of positive equilibria\, as well as local and global stability. We will di scuss the use of E-graphs and algebraic geometry in understanding how the same is true for a larger class of systems. Inspired by work done in [Crac iun\, Jin\, Yu\, "An efficient characterization of complex-balanced\, deta iled-balanced\, and weakly reversible systems”]\, we further analyse fro m an algebraic perspective the property of being dynamically equivalent to a complex balanced system\, which we call "disguised toric dynamical syst ems". This is based on joint work with George Craciun and Laura Brustenga. \n LOCATION:https://researchseminars.org/talk/BIRS_20w5204/13/ END:VEVENT END:VCALENDAR