4 research outputs found
Structure Identifiability of an NDS with LFT Parametrized Subsystems
Requirements on subsystems have been made clear in this paper for a linear
time invariant (LTI) networked dynamic system (NDS), under which subsystem
interconnections can be estimated from external output measurements. In this
NDS, subsystems may have distinctive dynamics, and subsystem interconnections
are arbitrary. It is assumed that system matrices of each subsystem depend on
its (pseudo) first principle parameters (FPPs) through a linear fractional
transformation (LFT). It has been proven that if in each subsystem, the
transfer function matrix (TFM) from its internal inputs to its external outputs
is of full normal column rank (FNCR), while the TFM from its external inputs to
its internal outputs is of full normal row rank (FNRR), then the NDS is
structurally identifiable. Moreover, under some particular situations like
there are no direct information transmission from an internal input to an
internal output in each subsystem, a necessary and sufficient condition is
established for NDS structure identifiability. A matrix valued polynomial (MVP)
rank based equivalent condition is further derived, which depends affinely on
subsystem (pseudo) FPPs and can be independently verified for each subsystem.
From this condition, some necessary conditions are obtained for both subsystem
dynamics and its (pseudo) FPPs, using the Kronecker canonical form (KCF) of a
matrix pencil.Comment: 16 page
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Novel methods for biological network inference: an application to circadian Ca2+ signaling network
Biological processes involve complex biochemical interactions among a large number of species like cells, RNA, proteins and metabolites. Learning these interactions is essential to interfering artificially with biological processes in order to, for example, improve crop yield, develop new therapies, and predict new cell or organism behaviors to genetic or environmental perturbations. For a biological process, two pieces of information are of most interest. For a particular species, the first step is to learn which other species are regulating it. This reveals topology and causality. The second step involves learning the precise mechanisms of how this regulation occurs. This step reveals the dynamics of the system. Applying this process to all species leads to the complete dynamical network. Systems biology is making considerable efforts to learn biological networks at low experimental costs. The main goal of this thesis is to develop advanced methods to build models for biological networks, taking the circadian system of Arabidopsis thaliana as a case study. A variety of network inference approaches have been proposed in the literature to study dynamic biological networks. However, many successful methods either require prior knowledge of the system or focus more on topology. This thesis presents novel methods that identify both network topology and dynamics, and do not depend on prior knowledge. Hence, the proposed methods are applicable to general biological networks. These methods are initially developed for linear systems, and, at the cost of higher computational complexity, can also be applied to nonlinear systems. Overall, we propose four methods with increasing computational complexity: one-to-one, combined group and element sparse Bayesian learning (GESBL), the kernel method and reversible jump Markov chain Monte Carlo method (RJMCMC). All methods are tested with challenging dynamical network simulations (including feedback, random networks, different levels of noise and number of samples), and realistic models of circadian system of Arabidopsis thaliana. These simulations show that, while the one-to-one method scales to the whole genome, the kernel method and RJMCMC method are superior for smaller networks. They are robust to tuning variables and able to provide stable performance. The simulations also imply the advantage of GESBL and RJMCMC over the state-of-the-art method. We envision that the estimated models can benefit a wide range of research. For example, they can locate biological compounds responsible for human disease through mathematical analysis and help predict the effectiveness of new treatments