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:20260404T041806Z 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 D ifferential Equations\, Algebraic Geometry\, and their Applications to Mod eling\n\n\nAbstract\nDiscrete models\, such as Boolean networks\, are an i ncreasingly popular modeling framework in systems biology\, with many hund reds of published models. The advantages are\, among others\, that they ar e intuitive and don't require detailed quantitative knowledge such as kine tic parameters. One disadvantage is that there are relatively few mathemat ical and computational tools available for this model type. As a basic exa mple\, given a model\, how can we compute all its steady states? The basic mathematical framework they can be cast in is polynomial dynamical system s over finite fields. There is a rich convergence of dynamic\, algebraic\, combinatorial\, and graph-theoretic features that come together within th is type of mathematical object. Yet very little of this convergence has be en used to study a mathematically rich class of objects\, with important a pplications to problems in the life sciences and elsewhere. This talk will discuss several mathematical and computational problems\, inspired but no t directly connected to applications in biology\, that can stimulate inter esting research in algebra\, broadly defined.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5204/1/ END:VEVENT BEGIN:VEVENT SUMMARY:David Marker DTSTART:20200601T150000Z DTEND:20200601T155000Z DTSTAMP:20260404T041806Z UID:BIRS_20w5204/2 DESCRIPTION:Title: Tutorial: Model Theory\, Quantifier Elimination and Differenti al Algebra - 1\nby David Marker as part of Model Theory of Differentia l Equations\, Algebraic Geometry\, and their Applications to Modeling\n\n\ nAbstract\nI will introduce the basic notions on model theory focusing on effective methods such as quantifier elimination and discuss applications to algebraic theory of differential equations.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5204/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Elisenda Feliu DTSTART:20200601T160000Z DTEND:20200601T165000Z DTSTAMP:20260404T041806Z UID:BIRS_20w5204/3 DESCRIPTION:Title: Tutorial: Challenges in the study of Algebraic Models of Bioch emical Reaction Networks\nby Elisenda Feliu as part of Model Theory of Differential Equations\, Algebraic Geometry\, and their Applications to M odeling\n\n\nAbstract\nIn the context of (bio)chemical reaction networks\, the dynamics of the concentrations of the chemical species over time are often modelled by a system of parameter-dependent ordinary differential eq uations\, which are typically polynomial or described by rational function s. The polynomial structure of the system allows the use of techniques fro m algebra (e.g.\, real algebraic geometry) to study properties of the syst em around steady states\, for all parameter values. In this talk I will st art by presenting the formalism of the theory of reaction networks. Afterw ards I will outline the qualitative questions one would like to address\, which include deciding upon the existence of multiple equilibrium points o r periodic orbits\, and their stability. If time permits\, I will discuss selected methods with emphasis on their limitations.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5204/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Patrick Speissegger DTSTART:20200602T150000Z DTEND:20200602T153000Z DTSTAMP:20260404T041806Z UID:BIRS_20w5204/4 DESCRIPTION:Title: Limit cycles of Planar Vector Fields\, Hilbert's 16th Problem and o-minimality\nby Patrick Speissegger as part of Model Theory of Di fferential Equations\, Algebraic Geometry\, and their Applications to Mode ling\n\n\nAbstract\nRecent work links certain aspects of the second part o f Hilbert’s 16th problem (H16) to the theory of o-minimality. One of the se aspects is the generation and destruction of limit cycles in families o f planar vector fields\, commonly referred to as ”bifurcations”. I wil l outline the significance of bifurcations for H16 and explain how logic –in particular\, o-minimality–can be used to understand them well enou gh to be able to count limit cycles.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5204/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Polly Yu DTSTART:20200602T154000Z DTEND:20200602T161000Z DTSTAMP:20260404T041806Z UID:BIRS_20w5204/5 DESCRIPTION:Title: Mass-action systems: From linear to non-linear inequalities\nby Polly Yu as part of Model Theory of Differential Equations\, Algebra ic Geometry\, and their Applications to Modeling\n\n\nAbstract\nFor mass-a ction kinetics\, a common model for biochemistry\, much work has gone into relating network structure to the possible dynamics of the resulting syst ems of polynomial ODEs. A family of mass-action systems\, complex-balancin g\, is defined by having a positive equilibrium that balances monomials ac ross vertices. Surprisingly\, every positive equilibrium of such a system similarly balance monomials across vertices. These systems enjoy a variety of algebraic and stability properties: toricity in the steady state varie ty and in parameter space\; Lyapunov and conjectured global stability. Unf ortunately\, most systems are vertex-balanced if and only if the parameter s come from a toric ideal. By searching for different graphs representing the same ODEs\, we can expand the parameter region for which the system is dynamically equivalent to a complex-balanced system. The expanded region is defined in the space of states and parameters\, and the challenge is to eliminate the state variables to obtain explicit conditions on parameters (that is\, to perform quantifier elimination over the reals). In this tal k\, I will introduce and set up the problem via examples.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5204/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Nidhi Kaihnsa DTSTART:20200602T162000Z DTEND:20200602T165000Z DTSTAMP:20260404T041806Z UID:BIRS_20w5204/6 DESCRIPTION:Title: Convex Hulls of Trajectories\nby Nidhi Kaihnsa as part of Model Theory of Differential Equations\, Algebraic Geometry\, and their Ap plications to Modeling\n\n\nAbstract\nI will talk about the convex hulls o f trajectories of polynomial dynamical systems. Such trajectories also inc lude real algebraic curves. The main problem is to describe the boundary o f the resulting convex hulls. The motivation to describe these convex hull s comes from attainable region theory in chemistry\, where taking convex c ombinations of points corresponds to mixing results of reactions. We strat ify the boundary into families of faces comprised of patches. We define pa tches using the notion of normal cycles from integral geometry. I will dis cuss the numerical algorithms we developed for identifying these patches. This is a joint work with Daniel Ciripoi\, Andreas Loehne\, and Bernd Stur mfels.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5204/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolette Meshkat DTSTART:20200603T150000Z DTEND:20200603T155000Z DTSTAMP:20260404T041806Z UID:BIRS_20w5204/7 DESCRIPTION:Title: Tutorial: Structural Identifiability of Biological Models\ nby Nicolette Meshkat as part of Model Theory of Differential Equations\, Algebraic Geometry\, and their Applications to Modeling\n\n\nAbstract\nA c ommon problem in mathematical modeling of biological phenomena is to have unknown parameters in an ODE model. We would like to know if those unknown parameters can be determined from given data\, often in the form of input s and outputs. This problem is called the parameter identifiability proble m. If the data is assumed to be perfect\, this problem of determining whet her or not the parameters of a model can be determined from input-output d ata is called structural identifiability (as opposed to the numerical iden tifiability problem\, which deals with real and often "noisy" data.) We ex amine this problem of structural identifiability for the case where our OD E model is in terms of polynomial or rational functions. For this special case\, we can use differential algebra to attack the problem. We demonstra te the differential algebra approach and also discuss some important quest ions that arise\, such as what to do with an "unidentifiable" model. We al so examine 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 ident ifiable model also identifiable or when can we combine two identifiable mo dels to obtain an identifiable model?\n LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5204/7/ END:VEVENT BEGIN:VEVENT SUMMARY:David Marker DTSTART:20200603T160000Z DTEND:20200603T165000Z DTSTAMP:20260404T041806Z UID:BIRS_20w5204/8 DESCRIPTION:Title: Tutorial: Model Theory\, Quantifier Elimination and Differenti al Algebra - 2\nby David Marker as part of Model Theory of Differentia l Equations\, Algebraic Geometry\, and their Applications to Modeling\n\n\ nAbstract\nI will introduce the basic notions on model theory focusing on effective methods such as quantifier elimination and discuss applications to algebraic theory of differential equations.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5204/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Alejandro F. Villaverde DTSTART:20200604T150000Z DTEND:20200604T153000Z DTSTAMP:20260404T041806Z UID:BIRS_20w5204/9 DESCRIPTION:Title: Finding and breaking Lie symmetries: implications for structur al identifiability and observability of dynamic models\nby Alejandro F . Villaverde as part of Model Theory of Differential Equations\, Algebraic Geometry\, and their Applications to Modeling\n\n\nAbstract\nA dynamic mo del is structurally identifiable (respectively\, observable) if it is theo retically possible to infer its unknown parameters (respectively\, states) by observing its output over time. The two properties\, structural identi fiability and observability\, are completely determined by the model equat ions. Their analysis is of interest for modellers because it informs about the possibility of gaining insight about the unmeasured variables of a mo del. Here we cast the problem of analysing structural identifiability and observability as that of finding Lie symmetries. We build on previous resu lts that showed that structural unidentifiability amounts to the existence of Lie symmetries. We consider nonlinear models described by ordinary dif ferential equations and restrict ourselves to rational functions. We revis it a method for finding symmetries by transforming rational expressions in to linear systems\, and extend it by enabling it to provide symmetry-break ing transformations. This extension allows for a semi-automatic model refo rmulation that renders a non-observable model observable. We have implemen ted the methodology in MATLAB\, as part of the STRIKE-GOLDD toolbox for ob servability and identifiability analysis. We illustrate its use in the con text of biological modelling by applying it to a set of problems taken fro m the literature\, which also allow us to discuss the implications of (non )observability.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5204/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Remi Jaoui DTSTART:20200604T154000Z DTEND:20200604T161000Z DTSTAMP:20260404T041806Z UID:BIRS_20w5204/10 DESCRIPTION:Title: A model-theoretic analysis of geodesic equations in negative curvature\nby Remi Jaoui as part of Model Theory of Differential Equat ions\, Algebraic Geometry\, and their Applications to Modeling\n\n\nAbstra ct\nTo any algebraic differential equation\, one can associate a first-ord er structure which encodes some of the properties of algebraic integrabili ty and of algebraic independence of its solutions. To describe the structu re associated to a given algebraic (non linear) differential equation (E)\ , typical questions are:\n\nIs it possible to express the general solution s of (E) from successive resolutions of linear differential equations?\n\n Is it possible to express the general solutions of (E) from successive res olutions of algebraic differential equations of lower order than (E)?\n\nG iven distinct initial conditions for (E)\, under which conditions are the solutions associated to these initial conditions algebraically independent ?\n\nIn my talk\, I will discuss in this setting one of the simplest examp les of non completely integrable Hamiltonian systems: the geodesic motion on an algebraically presented compact Riemannian surface with negative cur vature. I will explain a qualitative model-theoretic description of the as sociated structure (and its content in the differential algebraic language used above) based on the global hyperbolic dynamical properties identifie d by Anosov in the 70’s (today called Anosov flows) for the geodesic mot ion in negative curvature.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5204/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Yue Ren DTSTART:20200604T162000Z DTEND:20200604T165000Z DTSTAMP:20260404T041806Z UID:BIRS_20w5204/11 DESCRIPTION:Title: Introduction to tropical algebraic geometry\nby Yue Ren a s part of Model Theory of Differential Equations\, Algebraic Geometry\, an d their Applications to Modeling\n\n\nAbstract\nThis talk offers a brief a nd introductory overview of tropical algebraic geometry with a heavy empha sis on computations. We introduce the notions of tropical semirings and tr opical varieties\, and discuss some of the algorithms surrounding them. Fi nally\, we will highlight recent and ongoing works on the frontiers of tro pical differential algebra.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5204/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Joel Nagloo DTSTART:20200605T150000Z DTEND:20200605T153000Z DTSTAMP:20260404T041806Z UID:BIRS_20w5204/12 DESCRIPTION:Title: Irreducibility and generic ODEs\nby Joel Nagloo as part o f Model Theory of Differential Equations\, Algebraic Geometry\, and their Applications 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 later refined by H. Umemura. Roughly\, an ODE is irreducible if all of its solutions are ‘new’ functions. This notion is also almost equival ent 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 prove that ODEs with generic constant parameters are irreducible. We us e the Painlevé equations as examples.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5204/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Miruna-Stefana Sorea DTSTART:20200605T154000Z DTEND:20200605T161000Z DTSTAMP:20260404T041806Z UID:BIRS_20w5204/13 DESCRIPTION:Title: Disguised toric dynamical systems\nby Miruna-Stefana Sore a as part of Model Theory of Differential Equations\, Algebraic Geometry\, and their Applications to Modeling\n\n\nAbstract\nDynamical systems arisi ng from chemical reactions can be generated by finite directed graphs embe dded 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 th eory. In this talk\, we will focus on complex-balanced systems\, which hav e been also called “toric dynamical systems" by Craciun\, Dickenstein\, Shiu and Sturmfels. Toric dynamical systems are known or conjectured to en joy exceptionally strong dynamical properties\, such as existence and uniq ueness of positive equilibria\, as well as local and global stability. We will discuss the use of E-graphs and algebraic geometry in understanding h ow the same is true for a larger class of systems. Inspired by work done i n [Craciun\, Jin\, Yu\, "An efficient characterization of complex-balanced \, detailed-balanced\, and weakly reversible systems”]\, we further anal yse from an algebraic perspective the property of being dynamically equiva lent to a complex balanced system\, which we call "disguised toric dynamic al systems". This is based on joint work with George Craciun and Laura Bru stenga.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5204/13/ END:VEVENT END:VCALENDAR