×

Optimization models for reaction networks: information divergence, quadratic programming and Kirchhoff’s laws. (English) Zbl 1317.90072

Summary: This article presents a simple derivation of optimization models for reaction networks leading to a generalized form of the mass-action law, and compares the formal structure of minimum information divergence, quadratic programming and Kirchhoff type network models. These optimization models are used in related articles to develop and illustrate the operation of ontology alignment algorithms and to discuss closely connected issues concerning the epistemological and statistical significance of sharp or precise hypotheses in empirical science.

MSC:

90B15 Stochastic network models in operations research
90C20 Quadratic programming
94A15 Information theory (general)
62B10 Statistical aspects of information-theoretic topics
62C12 Empirical decision procedures; empirical Bayes procedures
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Quine, On What There Is. Review of Metaphysics In From a Logical Point of View 2 pp 21– (1961)
[2] Pereira, Evidence and credibility: Full bayesian significance test for precise hypotheses, Entropy J. 1 pp 69– (1999) · Zbl 0993.62028
[3] DOI: 10.1080/03610926.2010.508148 · Zbl 1239.62105 · doi:10.1080/03610926.2010.508148
[4] DOI: 10.1080/03610926.2011.563021 · Zbl 1284.62781 · doi:10.1080/03610926.2011.563021
[5] DOI: 10.3390/sym3030611 · Zbl 1360.00084 · doi:10.3390/sym3030611
[6] DOI: 10.1093/jigpal/jzt023 · Zbl 1309.62057 · doi:10.1093/jigpal/jzt023
[7] Stern, Jacob’s ladder and scientific ontologies, Cybernet. Hum. Know. (2013)
[8] DOI: 10.1016/j.jtbi.2011.09.029 · Zbl 1307.92104 · doi:10.1016/j.jtbi.2011.09.029
[9] DOI: 10.1093/jigpal/jzm032 · Zbl 1133.03302 · doi:10.1093/jigpal/jzm032
[10] DOI: 10.1007/BF02595698 · Zbl 1014.62005 · doi:10.1007/BF02595698
[11] DOI: 10.1016/S0378-3758(02)00368-3 · Zbl 1021.62018 · doi:10.1016/S0378-3758(02)00368-3
[12] DOI: 10.1214/08-BA303 · Zbl 1330.62049 · doi:10.1214/08-BA303
[13] Stern, Cognitive constructivism, eigen-solutions, and sharp statistical hypotheses, Cybernet. Hum. Know. 14 pp 9– (2007)
[14] Stern, Language and the self-reference paradox, Cybernet. Hum. Know. 14 pp 71– (2007)
[15] DOI: 10.3390/info2040635 · doi:10.3390/info2040635
[16] Callen, Thermodynamics: An Introduction to the PhysicalTheories of Equilibrium Thermostatics and Irreversible Thermodynamics (1960) · Zbl 0095.23301
[18] DOI: 10.1016/0378-4371(92)90283-V · doi:10.1016/0378-4371(92)90283-V
[19] Prigogine, Introduction to the Thermodynamics of Irreversible Processes (1961)
[20] Ross, Thermodynamics and Fluctuations far from Equilibrium (2008)
[21] Tribus, Thermostatics and Thermodynamics: An Introduction to Energy, Information and States of Matter, with Engineering Applications (1961)
[22] Gardiner, Stochastic Methods: A Handbook for the Natural and Social Sciences (2010)
[23] Van Kanpen, Stochastic Processes in Physics and Chemistry (2007)
[24] Goupil, Du Flou au Clair? Histoire de l’Affinité Chimique de Cardan à Prigogine (in French) (1991)
[25] Muir, A History of Chemical Theories and Laws (1907)
[26] Kapur, Entropy Optimization Principles with Applications (1992)
[27] DOI: 10.1038/scientificamerican0971-179 · doi:10.1038/scientificamerican0971-179
[28] DOI: 10.1146/annurev.pc.31.100180.003051 · doi:10.1146/annurev.pc.31.100180.003051
[29] Jaynes, Probability Theory: The Logic of Science (2003)
[30] Kapur, Maximum Entropy Models in Science and Engineering (1989)
[31] DOI: 10.1103/PhysRevE.80.021113 · doi:10.1103/PhysRevE.80.021113
[32] DOI: 10.1098/rstb.2009.0296 · doi:10.1098/rstb.2009.0296
[33] Niven, Maximum entropy analysis of steady-state flow systems (and extremum entropy production principles), AIP Conf. Proc. 1443 pp 270– (2011)
[34] Luenberger, Linear and Nonlinear Programming (1984)
[35] Minoux, Mathematical Programming (1986)
[36] DOI: 10.1016/0024-3795(80)90171-8 · Zbl 0458.65052 · doi:10.1016/0024-3795(80)90171-8
[37] Fang, Entropy Optimization and Mathematical Programming (1997)
[38] DOI: 10.1137/1023097 · Zbl 0469.65037 · doi:10.1137/1023097
[39] Censor, Parallel Optimization: Theory, Algorithms, and Applications (1997) · Zbl 0945.90064
[40] Censor, On iterative methods for linearly constrained entropy maximization, Num. Anal. Math. Model. Banach Center Publ. Ser. 24 pp 145– (1990) · Zbl 0718.65047
[41] DOI: 10.1016/0041-5553(67)90040-7 · doi:10.1016/0041-5553(67)90040-7
[42] Bertsekas, Parallel and Distributed Computation, Numerical Methods (1989)
[43] Garcia, Generalized line criterion for gauss seidel method, J. Comput. Appl. Math. 22 pp 91– (2002)
[44] Iusem, Métodos de Ponto Proximal em Otimização (in Portuguese) (1995)
[45] Golub, Matrix Computations (1989)
[46] Stern, Esparsidade, Estrutura, Estabilidade e Escalonamento em Álgebra Linear Computacional (in Portuguese) (1994)
[47] Steuer, Computational models of metabolism: Stability and regulation in metabolic networks, Adv. Chem. Phys. 142 pp 105– (2009)
[48] Heinrich, The Regulation of Cellular Systems (1996) · Zbl 0895.92013
[49] Hadley, Nonlinear and Dynamic Programming (1964) · Zbl 0179.24601
[51] Penfield, Tellegen’s Theorem and Electrical Networks (1970)
[52] DOI: 10.3390/e13050966 · Zbl 1303.92152 · doi:10.3390/e13050966
[53] DOI: 10.1007/BF02192638 · Zbl 0866.90059 · doi:10.1007/BF02192638
[54] DOI: 10.1021/jp0374004 · doi:10.1021/jp0374004
[55] DOI: 10.1021/ie050814u · doi:10.1021/ie050814u
[56] DOI: 10.1080/14786445108561361 · doi:10.1080/14786445108561361
[57] Peusner, Studies in Network Thermo-Dynamics (1986)
[58] Wiśniewski, Thermodynamics of Nonequilibrium Processes (1976)
[59] Morveau, Affinity, Supplement to the Encyclopaedia or Dictionary of Arts, Sciences and Miscellaneous Literature pp 391– (1803)
[60] De Morveau, Méthode de Nomenclature Chimique (1787)
[61] Stern, Decoupling, sparsity, randomization, and objective bayesian inference, Cybernet. Hum. Know. 15 pp 49– (2008)
[62] Bryant, Independence Theory in Combinatorics: An Introductiory Account with Applications to Graphs and Transversals (1980) · Zbl 0435.05017
[63] Recski, Matroid Theory and its Applications in Electrical Network Theory and in Statics (1989) · Zbl 0729.05012
[64] Swamy, Graphs, Networks and Algorithms (1981)
[65] Vágó, Graph Theory: Applications to the Calculation of Electrical Networks (1985)
[66] Thoma, Simulation with Entropy in Engineering Thermodynamics. Understanding Matter and Systems with Bondgraphs (2006) · Zbl 1146.80001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.