Dynamical structure function identifiability conditions enabling signal structure reconstruction

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 ▲]

Network structure preserving model reduction with weak a priori structural information

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 ▲]

A Comparison of Network Reconstruction Methods for Chemical Reaction Networks

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 ▲]