Formal reaction kinetics and related questions

2024/2025, 1st semester

Our online seminar on Formal Reaction Kinetics and Related Questions will continue using Zoom. You can access the seminar through the following invite link.

KEY DETAILS

Starting Time: The seminar will commence at 17:15 CET. (Daylight Saving Time!)

Duration: Each talk is allocated 50-60 minutes, allowing time for questions from the audience.

Testing the System: If you are scheduled to speak and would like to test the system beforehand, please feel free to contact János: jtoth at math dot bme dot hu. If you haven't already done so, please send us the title and abstract of your talk.

Recording: In all the cases when the speaker is not against it we shall record the talk and put it onto youtube.

Our seminar aims not only to disseminate new research findings but also to foster a collaborative learning environment, which includes engaging with students and occasional participants with varying levels of preliminary knowledge. We would like to encourage you to propose/offer topics, and speakers, including yourselves.

The organizers: Gábor (Szederkényi), János (Tóth), Balázs (Boros)

The list of more or less confirmed speakers for the next semester is as follows, with the schedule being continuously updated:

Plans for 2024/25, 1rst semester

Date	Speaker	Title	Manuscript/paper	Slides/abstract
17th September	J. García Galofre^{1}, M. Pérez MILLÁN^{2,3}, A. Galarza Rial^{4}, R. Laubenbachers^{5}, A. Dickenstein^{2,3} ( 1 Dept.Math. and Sciences, U. San Andres, Victoria, Argentina, 2 "Luis A. Santaló" Inst. of Math. Investigations, Buenos Aires, 3 Dept. Math., U. Buenos Aires, 4 Dept. of Exact Sciences, U. Buenos Aires, 5 Lab. for Systems Medicine, Dept. of Medicine, U. Florida, Gainesville, FL, USA.)	Beyond Boolean networks, a multi-valued approach	Manuscript	Slides
24th September	Elisenda Feliu, Oskar HENRIKSSON, Beatriz Pascual-Escudero (Copenhagen)	Dimension and degeneracy of zeros of parametric polynomial systems with applications to reaction networks	Manuscript
1st October			Manuscript
8th October	Gheorghe CRACIUN (Univ. Wisconsin), Radek Erban (Univ. Oxford)	Planar chemical reaction systems with algebraic and non-algebraic limit cycles	Manuscript
15th October	Shesha Gopal Marehalli Srinivas, Francesco Avanzini, and Massimiliano Esposito (University of Luxembourg and University of Padova, Italy)	Characterizing the conditions for indefinite growth in open chemical reaction networks	Phys. Rev. E 109, 064153
22nd October	Tomislav PLESA (Cambridge)	Mapping dynamical systems into chemical reactions	Manuscript
29th October	A Duvall, MA Al-Radhawi, DD Jatkar, E Sontag:	Interplay between Contractivity and Monotonicity for Reaction Networks	Manuscript
5th November	M. A. Vághy, G. SZEDERKÉNYI (PPKE)	Asymptotic stability of delayed complex balanced reaction networks	Manuscript
12th November	Murad BANAJIi (Oxford), Balázs Boros (Vienna U.), Josef Hofbauer (Vienna U.)	Bifurcations in planar, quadratic mass-action networks with few reactions and low molecularity	Manuscript
19th November	Marc R. ROUSSEL, T Soares (University of Lethbridge, Department of Chemistry and Biochemistry):	Graph-based, dynamics-preserving reduction of (bio) chemical systems	Paper
26th November	Vit Piskovsky, Philip Maini (Oxford Univ.):	Turing patterns for multiple interacting species	Three species, first.
3rd December	Lőrinc Márton, Gábor Szederkényi, Katalin M. Hangos (and PPKE)	Modelling and control of interconnected CRNs	Paper01	Paper02
10th December			Manuscript

Previous talks in 2024

Date	Speaker	Title	Abstract and slides	Further reading
7th May	Badal JOSHI (Calif. State Univ., San Marcos)	Computation with reaction networks	Manuscript	Slides
30th April	Nicola VASSENA (FU Berlin)	Mass action systems: two criteria for Hopf bifurcation without Hurwitz	Slides	Manuscript
23rd April	Hamid RAHKOOY (MI of Univ. Oxford), H. Byrne, H. Harrington, A. Ovchinnikov, G. Pogudin and P. Soto	Algebraic identifiability of partial differential equation models	Slides	Manuscript
16th April	Kelvin KIPRONO, János Tóth (BME)	Symbolic solution of some kinetic differential equations	Slides	Manuscript
9th April	Francois FAGES, Mathieu Hemery (Inria and Ecole Polytechnique)	Chemical reaction networks as a programming language: Turing-completeness, compiler of real functions into finite CRNs, and absolute functional robustness.	Paper and slides	Preview
2nd April	Dimitri LOUTCHKO (Univ. of Tokyo)	Cramer-Rao bound and absolute sensitivity in chemical reaction networks	Abstract and slides	Manuscript
26nd March	Murad BANAJI (MI of Univ. Oxford), Balázs Boros (Univ. Vienna), Josef Hofbauer (Univ. Vienna)	The inheritance of local bifurcations in mass action networks	Slides	Manuscript
19th March	Jiaxin JIN (OSU), Gheorghe Craciun (WISC), Abhishek Deshpande (IIIT Hyderabad)	The Dimension of the R-Disguised Toric Locus of a Reaction Network	Slides	Paper
5th March	Bo HUANG, Dongming Wang (Beihang Univ.)	Using Symbolic Computation to Analyze Zero-Hopf Bifurcations of Polynomial Differential Systems	Abstract and Slides	Manuscript
27th Feb.	SZEDERKÉNYI Gábor (PPKE)	Modeling traffic flows with reaction networks	Slides	Paper
20th Feb.	O. O. Aybar, M. SENTURK (Piri Reis Univ.)	Implementation of a triangular probabilistic distribution for optimal parametrization of the SEIR model recovery rates with delay	Programs	Chaos 33, 093137 (2023)
13rd Feb.	Nicolette MESHKAT (SCU)	Identifiability and Indistinguishability of Linear Compartmental Models		Slides
6th Feb.	Josef HOFBAUER (Univ. Vienna) and Balázs Boros (Univ. Vienna)	Mass action systems with many limit cycles

Previous talks in 2023

Date	Speaker	Title	Abstract and slides	Further reading
12th Dec.	Hirokazu Komatsu (National Institute of Technology, Toyota College) and Hiroyuki Nakajima (Kindai University)	Stability analysis for single linkage class chemical reaction networks with distributed time delays
5th Dec.	Carsten Wiuf (Copenhagen)	Stationary distributions and reaction networks
28th Nov.	Orhan Ozgur AYBAR, Ph.D. (Piri Reis University)	Biochemical models of SIR and SIRS: Effects of bilinear incidence rate on infection-free and endemic states		Paper
21st Nov.	Diego Rojas La Luz, Polly Yu, Gheorghe Craciun	Unveiling Surprising Connections Between the Classical Theory of Reaction Networks and Generalized Lotka-Volterra Systems
14th Nov.	Polly Yu (Harvard)	A Spatiotemporal Model of GPCR-G protein Interactions
7th Nov.	Murad Banaji (Oxford Univ.), Balázs Boros (Univ. of Vienna), Josef Hofbauer (Univ. of Vienna)	Oscillations in three-reaction quadratic mass-action systems
31st Oct.	Enrico Bibbona, Daniele Cappelletti, Paola Siri, Elena Sabbioni, Rebeka SZABÓ, Gábor Lente	Final nanoparticle size distribution under unusual parameter regimes
24th Oct.	Hideyuki MIYAHARA (Hokkaido University, Sapporo)	Information geometric bound on general chemical reaction networks
17th Oct.	Carsten Conradi and Maya Mincheva	In distributive phosphorylation catalytic constants enable non-trivial dynamics
10th Oct.	Tomislav Plesa (Department of Applied Mathematics and Theoretical Physics, University of Cambridge)	Integral feedback in synthetic biology: Negative-equilibrium catastrophe
3rd Oct.	Vághy Mihály, Szederkényi Gábor (PPKE)	Exogenous population-level control of gene regulatory networks
26th Sept.	Mirco Tribastone and Max Tschaikowski, Luca Cardelli	Formal Lumping of Polynomial Differential Equations through Approximate Equivalences
9th May	Bryan S. Hernandez	Deriving analytic positive steady states of biochemical reaction networks with non-trivial independent decompositions
2nd May	Mustafa Khammash	Theory and Design of Biomolecular Integral Feedback Controllers
25th April	Polly Yu	Global stability of perturbed complex-balanced systems
18th April	M. Vághy, I. Otero-Muras, M. Pájaro, G. Szederkényi	Kinetic discretization of the multidimensional PIDE model of gene regulatory networks
11th April	Giulia Giordano (Trento)	: Structural stability of biochemical reaction networks
4th April	Maya MINCHEVA (Northern Illinois University, Dekalb IL), George Craciun, Casian Pantea, and Polly Yu	Reaction networks with time delays
21st March	B. Joshi, N Kaihnsa, TD Nguyen, A. Shiu: (California State University, San Marcos, University of Copenhagen, Texas A&M University, Texas A&M University)	Prevalence of multistationarity and absolute concentration robustness in reaction networks
14th March	Chuang Xu (Hawaii)	Structural classification of continuous-time Markov chains with applications
7th March	C. Wiuf (Univ. of Copenhagen)	Molecular Machines and the EM algorithm
28th Feb.	Carsten Conradi (Hochschule für Technik und Wirtschaft Berlin)	Multistationarity in the Space of Total Concentrations
21st Feb.	J. Hofbauer (Vienna Univ.)	The smallest bimolecular mass-action system with a vertical Andronov-Hopf bifurcation
14th Feb.	Radek Erban (Univ. of Oxford)	Chemical reaction networks: systematic design, noise control, and limit cycles

Previous talks in 2022

13th Dec.	M. VÁGHY, G. Szederkényi (PPKE)	Lyapunov stability of generalized ribosome flow models
6th Dec.	D. Lichtblau (Wolfram Research)	Computing Periodicities in Genomic Sequences
29th Nov.	Polly Yu (NSF-Simons Center for Mathematical and Statistical Analysis of Biology, Harvard University)	Weakly reversible and deficiency zero realizations: Structural characterization and uniqueness
22nd Nov.	Abhishek Deshpande (IIIT-Hyderabad)	Source-only realizations, weakly reversible deficiency one networks, and dynamical equivalence.
15th Nov.	Telek Máté László (Copenhagen Univ.)	(Dis)connectivity of the parameter region of multistationarity in reaction networks
8th Nov.	Casian Pantea (West Virginia University)	Multistationarity of mass action networks with one-dimensional stoichiometric subspace
1st Nov.	M. A. Al-Radhawi (Northeastern University, Boston), D. Angeli (Imperial College London and University of Florence), and E. D. Sontag (Northeastern University and Harvard Medical School, Boston)	A computational framework for a Lyapunov-enabled analysis of biochemical reaction networks.
25th Oct.	V. Gáspár (ELTE), J. Tóth (BUTE)	Reaction extent
18th Oct.	Boldog Péter (Szeged, Bolyai Inst.)	Exact lattice-based stochastic cell culture simulation algorithms
4th Oct.	Péter Polcz, Balázs Csutak, Gábor Szederkényi (PPKE)	Reconstruction of epidemiological data using nonlinear control
27th Sept.	Balázs Boros (Vienna Univ.)	(Part II): The smallest bimolecular mass-action reaction networks admitting Andronov-Hopf bifurcation	Slides
20th Sept.	Murad Banaji (Middlesex Univ., London)	(Part I): The smallest bimolecular mass-action reaction networks admitting Andronov-Hopf bifurcation
13th Sept.	Xiaoxian Tang (Beihang Univ., Beijing), K. Wang	Hopf Bifurcations of Reaction Networks with Zero-One Stoichiometric Coefficients	Slides

The publications in Hungarian (including my Hungarian books) can be found on the Hungarian part.

My publications in English can be found in Google Scholar Citations List

Papers found by MathSciNet

Next, my English books follow.

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Tóth, J., Nagy A. L., Papp, D.: Reaction Kinetics: Exercises, Programs and Theorems. Mathematica for Deterministic and Stochastic Kinetics, Springer Nature, New York, 2018. 1. Introduction. 2. Preparations. 3. Graphs of reactions. 4. Mass conservation. 5. Decomposition of Reactions. 6. The induced kinetic differential equation. 7. Stationary points. 8. Time-dependent behavior of the concentrations. 9. Approximation of the models 10. Stochastic models 11. Inverse problems 12. Past, presentand future programs for reaction kinetics 13. Mathematical background 14. Solutions Glossary Index

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Érdi, P., Tóth, J.: Mathematical Models of Chemical Reactions. Theory and Applications of Deterministic and Stochastic Models, Manchester University Press, Manchester and Princeton University Press, Princeton, 1989. 1. Chemical kinetics: a prototype of nonlinear science. 2. The structure of kinetic models 3. Stoichiometry: the algebraic structure of complex chemical reactions. 4. Mass action kinetics deterministic models 5. Continuous time discrete state stochastic models 6. Chemical reactions accompanied by diffusion. 7. Applications References (32 pages). Index.

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The title of my books in Hungarian.

Tóth, J.; Simon, P.: Differential equations. Introduction into the theory and its applications (Differenciálegyenletek. Bevezetés az eléletbe és az alkalmazásokba), TYPOTEX, Budapest, 2005. 2009: Second edition, 2018: Third edition.

Tóth, J., Simon, L. P., Csikja R.: Problem book on differential equations (Differenciálegyenletek. Példatár), Budapest, 2013.

Csermely, P., Gergely, P., Koltay, T., Tóth, J.: Kutatás és közlés a természettudományokban(Research and Publication in Science), Osiris, Budapest, 1999.

Szili, L., Tóth, J.: Mathematics and Mathematica (Matematika és Mathematica), ELTE Eötvös Kiadó, Budapest, 1996.

 

Tóth, János CV PhD (candidate of the mathematical science) Department of Analysis and Operations Research Institute of Mathematics Faculty of Sciences Budapest University of Technology and Economics Budapest, Műegyetem rkp. 3-9. P. O. Box 91, H-1521 HUNGARY Tel.: (36-1)463-2314 or (36-1)463-2475 Home: (36-1)242-06-40 Fax: (36-1)463-3172 E-mail: jtoth at math dot bme dot hu

Scientific activity

• The mathematical theory of formal reaction kinetics involves nonlinear differential equations and Markovian jump processes. The theory went through a kind of explosion recently. A program package has been written in Mathematica, which treats the reactions also from a structural point of view. Beyond the chemical applicability of our codes and theoretical results, they can be used in other fields such as in Systems Biology, Atmospheric Chemistry, Combustion etc. Some details.
• Symbolic, qualitative and numerical analysis of models of formal reaction kinetics
• Relations between qualitative properties of deterministic and stochastic models of reaction kinetics and the algebraic and graph theoretic properties of the underlying mechanism
• Reduction of the number of variables (lumping, dimension reduction) in continuous time deterministic and stochastic models with special reference to the models of chemical reaction kinetics
• Algebraic and graph theoretic questions of stoichiometry
• Applications of Mathematica (Wolfram language) in teaching and research
• Emergence of stationary spatial patterns via Turing instability

Topics for BSc/MSc/PhD theses

Qualitative and quantitative investigations of polynomial differential equations with special reference to applications in reaction kinetics, etc.

Applications of Mathematica in one of the areas of applied calculus

Important or favorite scientific publications by others

Burger, M., Field, R.: Oscillations and travelling waves in chemical systems, Wiley, New York, 1985.

Császár, A., Jicsinszky, L., Turányi, T.: Generation of model reactions leading to limit cycle behaviour, Reaction Kinetics and Catalysis Letters 18 (1/2), 65-71 (1981).

Farkas, Gy.: Local controllability of reactions, Journal of Mathematical Chemistry 24 (1) (1998), 1-14.

Farkas, Gy.: On local observability of reactions, Journal of Mathematical Chemistry 24 (1) (1998), 15-22.

Farkas, Gy.: Kinetic lumping schemes, Chemical Engineering Science 54 (1999), 3909-3915.

Horváth, Zsófia: Effect of lumping on controllability and observability, Journal of Mathematical Chemistry Paper Poster

Hoyle, M. H.: Transformations - An introduction and a bibliography, Int. Stat. Rev. 41 (2), (1973), 203-223.

Inselberg, A.: Don't panic ... just do it parallel! Computational Statistics 14 (1999), 53-77.

Kirschner, I.; Bálint, Á.; Csikja, R.; Gyarmati, B.; Balogh, A.; Mészáros, Cs.: An approximate symbolic solution for convective instability flows in vertical cylindrical tubes, Journal of Physics A, Mathematical and Theoretical 40 (2007) 9361-9369.

Kovács, B.: Rate based call gapping with priorities and fairness between traffic classes, IEEE Trans. Comm. Paper

Kovács, B.; Szalay, M.; Imre, S.: Modelling and quantitative analysis of LTRACK - A novel mobility management algorithm, Mobile Information Systems 2 (1) (2006) 21-50.

Kozma, R., Th.: Horosphere Packings of the (3, 3, 6) Coxeter Honeycomb in Three-Dimensional Hyperbolic Space, from The Wolfram Demonstrations Project.

Ladics, T.: The analysis of the splitting error for advection-reaction problems in air pollution models, Időjárás ADATOK Manuscript and figures.

Ladics, T.: Application of Operator Splitting to Solve Reaction Diffusion Equations, arXiv:1011.4810 Manuscript and figures.

Orlov, N. N., Rozonoer, L. I.: The macrodynamics of open systems and the variational principle of the local potential, J. Franklin Inst. 318(1984) 283-314 and 315-347.

Papp, D., Vizvári, B.: Effective solution of linear Diophantine equation systems with an application in chemistry RUTCOR Research Reports 28-2004.

Recski, A.: Calculus exercises with and without Mathematica, New Haven, 1995.

Rényi, A.: Foundations of probability, Holden-Day Inc., San Francisco, Calif., 1970. ZBL 0203.49801, MR 41:9314.

Scott, S. K.: Chemical Chaos, Oxford Univ. Press, 1991.

Molnár, Z.; Nagy, I.; Szilágyi, T.: A change of variables theorem for the multidimensional Riemann integral, Ann. Univ. Sci. Eötvös, Sectio Math. ADATOK

Tóth, Ágnes: Fast edge colouring of graphs, 2007 Wolfram Technology Conference.

Turányi, T.: Sensitivity analysis of complex kinetic systems: Tools and applications, J. Math. Chem. 5 (1990) 203-248.

Volpert, A. I., Hudjaev, S. I.: Analysis in classes of discontinuous functions and the equations of mathematical physics, Martinus Nijhoff Publ., Dordrecht, Boston, Lancaster, 1985.

Wehrl, A.: General properties of entropy, Rev. Mod. Phys. 50 (2) (1978) 221-260.

Zachár, A.: Comparison of transformations from nonkinetic to kinetic models, Acta Chimica Hungarica - Models in Chemistry 135 (3) (1998), 425-434.

Zhang, S. Y.: Bibliography on Chaos, World Scientific, Singapore, New Jersey, London, Hong Kong, 1991.

Important or favorite publications by others

Clifford Ambrose Truesdell IIIMathematical Reviews 12 p. 561: This paper gives wrong solutions to trivial problems. The basic error, however, is not new.

E. Hemingway: He always thought of the sea as la mar which is what people call her in Spanish when they love her. Sometimes those who love her say bad things of her but they are always said as though she were a woman. Some of the younger fishermen those who used buoys as floats for their lines and had motor-boats, bought when the shark-lovers had brought much money, spoke of her as el mar which is masculine. They spoke of her as a contestant or a place or even an enemy. But the old man always thought of her as feminine and as something that gave or withheld great favours, and if she did wild and wicked things it was because she could not help them. The moon affects her it does a woman, he thought.