Aggregation of Variables in Dynamic Systems

Simon, Herbert A.; Ando, Albert

doi:10.2307/1909285

Cited by 503 publications

(88 citation statements)

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“…Simon and Ando (1961) describe how to utilize the neardecomposability of hierarchical systems into schemes of aggregation. This effectively allows one to analyze, measure, and quantify important facets of complex systems, particularly emergent properties.…”

Section: Hierarchy Theorymentioning

confidence: 99%

“…So what? Recall that by taking advantage of the feature of near-decomposability found in these hierarchical systems, one can aggregate components at different levels of a system and then quantify salient emergent properties of that system (Simon and Ando 1961;Simon 1962;Jørgensen 1995Jørgensen , 1997Nielsen and Müller 2000;Wu 2013). This ability, due to near-decomposability coupled with the similarity of rates at a given hierarchical level (identified by Allen 2009), has quite literally been capitalized on, formally, for over 70 years in financial systems (Markowitz 1952).…”

Section: The Portfolio Effectmentioning

confidence: 99%

“…This is done cognizant of the level of risk facing the portfolio; in a fisheries context that would be primarily to not have any stock overfished. The dynamics of this aggregate level are almost always much less variable than that of the individual components (Simon and Ando 1961;Booth and Fama 1992;Brown et al 2016). It is well known in financial contexts that more diversified portfolios are less volatile (e.g., Markowitz 1952; Brigham and Gapenski 1988;Gruber 1977, 1995;Choueifaty and Coignard 2008;Fabozzi and Markowitz 2011;Marston 2011).…”

Section: The Portfolio Effectmentioning

confidence: 99%

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System-level optimal yield: increased value, less risk, improved stability, and better fisheries

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2018

Can. J. Fish. Aquat. Sci.

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Abstract:The discipline and practice of fisheries science and management have had an useful, successful, and interesting history. The discipline has developed over the past century and a half into a very reductionist, highly quantitative, socially impactful endeavor. Yet given our collective successes in this field, some notable challenges remain. To address these challenges, many have proposed ecosystem-based fisheries management that takes a more systematic approach to the management of these living marine resources. Here I describe systems theory and associated constructs underlying system dynamics, elucidate how aggregate properties of systems can and have been used, contextualize these aggregate features relative to optimal yield, and note how this approach can produce useful estimates and outcomes for fisheries management. I explore two contrasting examples where this approach has and has not been considered, highlighting the benefits of applying such an approach. I conclude by discussing ways in which we might move forward with a portfolio approach for both the discipline and practice of fisheries science and management.Résumé : La discipline et la pratique des sciences halieutiques et de la gestion des pêches ont une histoire utile, intéressante et couronnée de succès. La discipline est devenue, au cours du dernier siècle et demi, une entreprise très réductionniste, hautement quantitative et à forte incidence sociale. Malgré nos réussites collectives dans ce domaine, des défis notables demeurent. Pour relever ces défis, de nombreuses personnes ont proposé une gestion écosystémique des pêches qui adopte une approche plus systématique de gestion de ces ressources marines vivantes. Je décris la théorie des systèmes et les constructions associées qui sous-tendent la dynamique des systèmes, j'explique comment les propriétés groupées de systèmes peuvent être utilisées et l'ont été, je mets ces éléments groupés dans un contexte de rendement optimal et je souligne comment cette approche peut produire des estimations et des résultats utiles pour la gestion des pêches. J'explore deux exemples dans lesquels cette approche a, d'une part, été prise en considération et, d'autre part, ne l'a pas été, afin de souligner les avantages de son application. Je conclus en discutant d'avenues possibles pour l'avenir qui reposent sur une approche de portefeuille tant pour la discipline que pour la pratique des sciences halieutiques et de la gestion des pêches. [Traduit par la Rédaction]

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Section: Hierarchy Theorymentioning

confidence: 99%

Section: The Portfolio Effectmentioning

confidence: 99%

Section: The Portfolio Effectmentioning

confidence: 99%

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System-level optimal yield: increased value, less risk, improved stability, and better fisheries

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2018

Can. J. Fish. Aquat. Sci.

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“…Model reduction approaches based on singular perturbation theory have been used in various areas of engineering and science 5,6,7,8 , but the overwhelming complexity of some biological models has severely limited applicability of these approaches in some areas in biosciences. The Finite State Projection retains an important subset of the state space and projects the remaining part (which can be infinite) onto a single state, while keeping the approximation error strictly within prespecified accuracy.…”

Section: Introductionmentioning

confidence: 99%

Model Reduction Using Multiple Time Scales in Stochastic Gene Regulatory Networks

Peleš¹,

Munsky²,

Khammash³

2006

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Gene network dynamics often involves processes that take place on widely differing time scalesfrom the order of nanoseconds to the order of several days. Multiple time scales in mathematical models often lead to serious computational difficulties, such as numerical stiffness in the case of differential equations or excessively redundant Monte Carlo simulations in the case of stochastic processes. We present a method that takes advantage of multiple time scales and dramatically reduces the computational time for a broad class of problems arising in stochastic gene regulatory networks. We illustrate the efficiency of our method in two gene network examples, which describe two substantially different biological processes -cellular heat shock response and expression of the pap gene in Escherichia coli bacteria.

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“…In fact, not only is it an impossible task to obtain analytic solutions, but also the direct numerical approximation can be overwhelming and the straightforward use of numerical methods may not be adequate. Naturally, one seeks to break the large job into small pieces with the hope that certain decompositions and aggregations will lead to a simplification of the intractable systems; see Simon and Ando [13]. A viable alternative calls for taking advantage of the high contrast rates (some states vary an order of magnitude faster than the rest) of changes in the physical systems and using a singular perturbation approach as a tool to reduce the complexity of the underlying systems.…”

Section: Introductionmentioning

confidence: 99%

Singularly Perturbed Markov Chains with Two Small Parameters: A Matched Asymptotic Expansion

Liu

Yin

Zhang

2002

Journal of Mathematical Analysis and Applications

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This work is concerned with asymptotic properties of solutions to forward equations for singularly perturbed Markov chains with two small parameters. It is motivated by the model of a cost-minimizing firm involving production planning and capacity expansion and a two-level hierarchical decomposition. Our effort focuses on obtaining asymptotic expansions of the solutions to the forward equation. Different from previous work on singularly perturbed Markov chains, the inner expansion terms are constructed by solving certain partial differential equations. The methods of undetermined coefficients are used. The error bound is obtained.  2002 Elsevier Science (USA)

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Aggregation of Variables in Dynamic Systems

Cited by 503 publications

References 0 publications

System-level optimal yield: increased value, less risk, improved stability, and better fisheries

System-level optimal yield: increased value, less risk, improved stability, and better fisheries

Model Reduction Using Multiple Time Scales in Stochastic Gene Regulatory Networks

Singularly Perturbed Markov Chains with Two Small Parameters: A Matched Asymptotic Expansion

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