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Dynamical structure function identifiability conditions enabling signal structure reconstruction ; ; et al in The proceedings of the 51st IEEE Conference on Decision and Control (CDC) (2012, December) Networks of controlled dynamical systems exhibit a variety of interconnection patterns that could be interpreted as the structure of the system. One such interpretation of system structure is a system's ... [more ▼] Networks of controlled dynamical systems exhibit a variety of interconnection patterns that could be interpreted as the structure of the system. One such interpretation of system structure is a system's signal structure, characterized as the open-loop causal dependencies among manifest variables and represented by its dynamical structure function. Although this notion of structure is among the weakest available, previous work has shown that if no a priori structural information is known about the system, not even the Boolean structure of the dynamical structure function is identifiable. Consequently, one method previously suggested for obtaining the necessary a priori structural information is to leverage knowledge about target specificity of the controlled inputs. This work extends these results to demonstrate precisely the a priori structural information that is both necessary and sufficient to reconstruct the network from input-output data. This extension is important because it significantly broadens the applicability of the identifiability conditions, enabling the design of network reconstruction experiments that were previously impossible due to practical constraints on the types of actuation mechanisms available to the engineer or scientist. The work is motivated by the proteomics problem of reconstructing the Per-Arnt-Sim Kinase pathway used in the metabolism of sugars. [less ▲] Detailed reference viewed: 84 (0 UL)In-silico Robust Reconstruction of the Per-Arnt-Sim Kinase Pathway using Dynamical Structure Functions ; ; et al Scientific Conference (2012, October) Detailed reference viewed: 54 (1 UL)Mathematical relationships between representations of structure in linear interconnected dynamical systems ; Goncalves, Jorge ; et al in The proceedings of the 2011 American Control Conference (ACC) (2011) A dynamical system can exhibit structure on multiple levels. Different system representations can capture different elements of a dynamical system's structure. We consider LTI input-output dynamical ... [more ▼] A dynamical system can exhibit structure on multiple levels. Different system representations can capture different elements of a dynamical system's structure. We consider LTI input-output dynamical systems and present four representations of structure: complete computational structure, subsystem structure, signal structure, and input output sparsity structure. We then explore some of the mathematical relation ships that relate these different representations of structure. In particular, we show that signal and subsystem structure are fundamentally different ways of representing system structure. A signal structure does not always specify a unique subsystem structure nor does subsystem structure always specify a unique signal structure. We illustrate these concepts with a numerical example. [less ▲] Detailed reference viewed: 91 (2 UL)Representing Structure in Linear Interconnected Dynamical Systems ; Goncalves, Jorge ; et al in The proceedings of the 49th IEEE Conference on Decision and Control (CDC) (2010) Interconnected dynamical systems are a pervasive component in our modern world's infrastructure. One of the fundamental steps to understanding the complex behavior and dynamics of these systems is ... [more ▼] Interconnected dynamical systems are a pervasive component in our modern world's infrastructure. One of the fundamental steps to understanding the complex behavior and dynamics of these systems is determining how to appropriately represent their structure. In this work, we discuss different ways of representing a system's structure. We define and present, in particular, four representations of system structure-complete computational, subsystem, signal, and zero pattern structure-and discuss some of their fundamental properties. We illustrate their application with a numerical example and show how radically different representations of structure can be consistent with a single LTI input-output system. [less ▲] Detailed reference viewed: 71 (0 UL)Robust dynamical network structure reconstruction ; ; et al Scientific Conference (2010) Motivated by biological applications, this paper addresses the problem of network reconstruction from data. Previous work has shown necessary and sufficient conditions for network reconstruction of noise ... [more ▼] Motivated by biological applications, this paper addresses the problem of network reconstruction from data. Previous work has shown necessary and sufficient conditions for network reconstruction of noise-free LTI systems. This paper assumes that the conditions for network reconstruction have been met but here we additionally take into account noise and unmodelled dynamics (including nonlinearities). Algorithms are therefore proposed to reconstruct dynamical (Boolean) network structure from time-series (steady-state) data respectively in presence of noise and nonlinearities. In order to identify the network structure that generated the data, we compute the smallest distances between the measured data and the data that would have been generated by particular Boolean structures. Information criteria and optimisation technique balancing such distance and model complexity are introduced to search for the true structure. We conclude with biologically-inspired network reconstruction examples which include noise and nonlinearities. [less ▲] Detailed reference viewed: 72 (0 UL)Robust dynamical network reconstruction ; ; et al in The proceedings of the 49th IEEE Conference on Decision and Control (CDC) (2010) Motivated by biological applications, this paper addresses the problem of network reconstruction from data. Previous work has shown necessary and sufficient conditions for network reconstruction of noise ... [more ▼] Motivated by biological applications, this paper addresses the problem of network reconstruction from data. Previous work has shown necessary and sufficient conditions for network reconstruction of noise-free LTI systems. This paper assumes that the conditions for network reconstruction have been met but here we additionally take into account noise and unmodelled dynamics (including nonlinearities). Algorithms are therefore proposed to reconstruct dynamical (Boolean) network structure from time-series (steady-state) data respectively in presence of noise and nonlinearities. In order to identify the network structure that generated the data, we compute the smallest distances between the measured data and the data that would have been generated by particular Boolean structures. Information criteria and optimisation technique balancing such distance and model complexity are introduced to search for the true structure. We conclude with biologically-inspired network reconstruction examples which include noise and nonlinearities. [less ▲] Detailed reference viewed: 74 (0 UL)Network structure preserving model reduction with weak a priori structural information ; Goncalves, Jorge ; et al in The proceedings of the Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (2009) This paper extends a state projection method for structure preserving model reduction to situations where only a weaker notion of system structure is available. This weaker notion of structure ... [more ▼] This paper extends a state projection method for structure preserving model reduction to situations where only a weaker notion of system structure is available. This weaker notion of structure, identifying the causal relationship between manifest variables of the system, is especially relevant is settings such as systems biology, where a clear partition of state variables into distinct subsystems may be unknown, or not even exist. The resulting technique, like similar approaches, does not provide theoretical performance guarantees, so an extensive computational study is conducted, and it is observed to work fairly well in practice. Moreover, conditions characterizing structurally minimal realizations and sufficient conditions characterizing edge loss resulting from the reduction process, are presented. [less ▲] Detailed reference viewed: 70 (0 UL)Minimal dynamical structure realisations with application to network reconstruction from data ; ; et al in The proceedings of the Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (2009) Network reconstruction, i.e., obtaining network structure from data, is a central theme in systems biology, economics, and engineering. Previous work introduced dynamical structure functions as a tool for ... [more ▼] Network reconstruction, i.e., obtaining network structure from data, is a central theme in systems biology, economics, and engineering. Previous work introduced dynamical structure functions as a tool for posing and solving the problem of network reconstruction between measured states. While recovering the network structure between hidden states is not possible since they are not measured, in many situations it is important to estimate the number of hidden states in order to understand the complexity of the network under investigation and help identify potential targets for measurements. Estimating the number of hidden states is also crucial to obtain the simplest state-space model that captures the network structure and is coherent with the measured data. This paper characterises minimal order state-space realisations that are consistent with a given dynamical structure function by exploring properties of dynamical structure functions and developing algorithms to explicitly obtain a minimal reconstruction. [less ▲] Detailed reference viewed: 67 (0 UL)Network Structure Preserving Model Reduction: Results of a Simulation Study ; Goncalves, Jorge ; et al in The proceedings of the Third International Conference on Foundations of Systems Biology in Engineering (FOSBE 2009) (2009) Reconstructed models of biochemical networks often reflect the high level of complexity inherent in the biological system being modeled. The difficulties of predicting gene expression and analyzing the ... [more ▼] Reconstructed models of biochemical networks often reflect the high level of complexity inherent in the biological system being modeled. The difficulties of predicting gene expression and analyzing the effects of individual perturbations at a system-wide resolution are exacerbated by model complexity. This paper extends a state projection method for structure preserving model reduction to a particular model class of reconstructed networks known as dynamical structure functions. In contrast to traditional approaches where a priori knowledge of partitions on unmeasured species is required, dynamical structure functions require a weaker notion of system structure, specifying only the causal relationship between measured chemical species of the system. The resulting technique, like similar approaches, does not provide theoretical performance guarantees, so an extensive computational study is conducted, and it is observed to work fairly well in practice. Moreover, sufficient conditions, characterizing edge loss resulting from the reduction process, are presented. [less ▲] Detailed reference viewed: 44 (2 UL)A Comparison of Network Reconstruction Methods for Chemical Reaction Networks ; ; et al in The proceedings of the Third International Conference on Foundations of Systems Biology in Engineering (FOSBE 2009) (2009) Chemical reaction networks model biological interactions that regulate the functional properties of a cell; these networks characterize the chemical pathways that result in a particular phenotype. One ... [more ▼] Chemical reaction networks model biological interactions that regulate the functional properties of a cell; these networks characterize the chemical pathways that result in a particular phenotype. One goal of systems biology is to understand the structure of these networks given concentration measurements of various species in the system. Previous work has shown that this network reconstruction problem is fundamentally impossible, even for simplified linear models, unless a particular experiment design is followed. Nevertheless, reconstruction algorithms have been developed that attempt to approximate a solution using sparsity or similar heuristics. This work compares, in silico, the results of three of these methods in situations where the necessary experiment design has been followed, and it illustrates the degradation of each method as increasing noise levels are added to the data. [less ▲] Detailed reference viewed: 51 (1 UL)Control Theory and Systems Biology Goncalves, Jorge ; in Iglesias, P. A.; Ingalls, B. P. (Eds.) Dynamical structure Functions in Network Reconstruction (2009) Presenting a control-theoretic treatment of stoichiometric systems, ... local parametric sensitivity analysis, the two approaches yield identical results. ... Detailed reference viewed: 136 (4 UL)Necessary and sufficient conditions for dynamical structure reconstruction of LTI networks Goncalves, Jorge ; in IEEE Transactions on Automatic Control (2008), 53(7), 1670-1674 This paper formulates and solves the network reconstruction problem for linear time-invariant systems. The problem is motivated from a variety of disciplines, but it has recently received considerable ... [more ▼] This paper formulates and solves the network reconstruction problem for linear time-invariant systems. The problem is motivated from a variety of disciplines, but it has recently received considerable attention from the systems biology community in the study of chemical reaction networks. Here, we demonstrate that even when a transfer function can be identified perfectly from input–output data, not even Boolean reconstruction is possible, in general, without more information about the system.We then completely characterize this additional information that is essential for dynamical reconstruction without appeal to ad-hoc assumptions about the network, such as sparsity or minimality. [less ▲] Detailed reference viewed: 80 (1 UL)Dynamical structure analysis of sparsity and minimality heuristics for reconstruction of biochemical networks ; ; Goncalves, Jorge et al in The proceedings of the 47th IEEE Conference on Decision and Control (2008) Network reconstruction, i.e. obtaining network structure from input-output information, is a central theme in systems biology. A variety of approaches aim to obtaining structural information from ... [more ▼] Network reconstruction, i.e. obtaining network structure from input-output information, is a central theme in systems biology. A variety of approaches aim to obtaining structural information from available data. Previous work has introduced dynamical structure functions as a tool for posing and solving the network reconstruction problem. Even for linear time invariant systems, reconstruction requires specific additional information not generated in the typical system identification process. This paper demonstrates that such extra information can be obtained through a limited sequence of system identification experiments on structurally modified systems, analogous to gene silencing and overexpression experiments. In the absence of such extra information, we discuss whether combined assumptions of network sparsity and minimality contribute to the recovery of the network dynamical structure. We provide sufficient conditions for a transfer function to have a completely decoupled minimal realization, and demonstrate that every transfer function is arbitrarily close to one that admits a perfectly decoupled minimal realization. This indicates that the assumptions of sparsity and minimality alone do not lend insight into the network structure. [less ▲] Detailed reference viewed: 70 (1 UL)Dynamical structure functions for the reverse engineering of LTI networks Goncalves, Jorge ; ; in Proceedings of the 46th IEEE Conference on Decision and Control (2007) This research explores the role and representation of network structure for LTI systems with partial state observations. We demonstrate that input-output representations, i.e. transfer functions, contain ... [more ▼] This research explores the role and representation of network structure for LTI systems with partial state observations. We demonstrate that input-output representations, i.e. transfer functions, contain no internal structural information of the system. We further show that neither the additional knowledge of system order nor minimality of the true realization is generally sufficient to characterize network structure. We then introduce dynamical structure functions as an alternative, graphical-model based representation of LTI systems that contain both dynamical and structural information of the system. The main result uses dynamical structure to precisely characterize the additional information required to obtain network structure from the transfer function of the system. [less ▲] Detailed reference viewed: 73 (0 UL) |
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