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Robust synchronization in networks of cyclic feedback systems ; Goncalves, Jorge ; in The proceedings of the 47th IEEE Conference on Decision and Control (2008) This paper presents a result on the robust synchronization of outputs of statically interconnected non-identical cyclic feedback systems that are used to model, among other processes, gene expression. The ... [more ▼] This paper presents a result on the robust synchronization of outputs of statically interconnected non-identical cyclic feedback systems that are used to model, among other processes, gene expression. The result uses incremental versions of the small gain theorem and dissipativity theory to arrive at an upper bound on the norm of the synchronization error between corresponding states, giving a measure of the degree of convergence of the solutions. This error bound is shown to be a function of the difference between the parameters of the interconnected systems, and disappears in the case where the systems are identical, thus retrieving an earlier synchronization result. [less ▲] Detailed reference viewed: 79 (2 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: 81 (1 UL)Batch control of the master equation: a linear programming approach Goncalves, Jorge ; Scientific Conference (2008) Detailed reference viewed: 50 (0 UL)Heterogeneous agent models in economics: a study of heterogeneous productivity of sectors ; Goncalves, Jorge ; in Proceedings of the 2008 American Control Conference (2008) Macroeconomic modeling is undergoing a change from the ground up. Previously models based on fully rational representative agents were constructed to give macroeconomics soli microeconomic foundations ... [more ▼] Macroeconomic modeling is undergoing a change from the ground up. Previously models based on fully rational representative agents were constructed to give macroeconomics soli microeconomic foundations. However the representative agent models have been shown to be inconsistent with empirical evidence and a new method of approach has emerged, one based on heterogeneity of agents. Recently heterogenous models have been used to simulate expected outcomes but due to their complexity little analytic work has been done. In this paper a basic model of the macro economy, with heterogeneous sectors differentiated by productivity, and driven by a jump Markov process, is investigated and steady state solutions for a sector’s output variance are discovered. We adjust the model to include a gain term, to represent a sector’s reaction to its error signal, excess demand, and then linearize the transition rates and apply the fluctuation dissipation theorem to solve the model. [less ▲] Detailed reference viewed: 50 (0 UL)The Arabidopsis circadian clock incorporates a cADPR-based feedback loop ; ; et al in SCIENCE (2007), 318(5857), 1789-1792 Transcriptional feedback loops are a feature of circadian clocks in both animals and plants. We show that the plant circadian clock also incorporates the cytosolic signaling molecule cyclic adenosine ... [more ▼] Transcriptional feedback loops are a feature of circadian clocks in both animals and plants. We show that the plant circadian clock also incorporates the cytosolic signaling molecule cyclic adenosine diphosphate ribose (cADPR). cADPR modulates the circadian oscillator’s transcriptional feedback loops and drives circadian oscillations of Ca2+ release. The effects of antagonists of cADPR signaling, manipulation of cADPR synthesis, and mathematical simulation of the interaction of cADPR with the circadian clock indicate that cADPR forms a feedback loop within the plant circadian clock. [less ▲] Detailed reference viewed: 131 (14 UL)Existence and stability of limit cycles in a macroscopic neuronal population model Rodrigues, Sandra ; Goncalves, Jorge ; in Physica D: Nonlinear Phenomena (2007), 233(1), 39-65 We present rigorous results concerning the existence and stability of limit cycles in a macroscopic model of neuronal activity. The specific model we consider is developed from the Ki set methodology ... [more ▼] We present rigorous results concerning the existence and stability of limit cycles in a macroscopic model of neuronal activity. The specific model we consider is developed from the Ki set methodology, popularized by Walter Freeman. In particular we focus on a specific reduction of the KII sets, denoted RKII sets. We analyse the unfolding of supercritical Hopf bifurcations via consideration of the normal forms and centre manifold reductions. Subsequently we analyse the global stability of limit cycles on a region of parameter space and this is achieved by applying a new methodology termed Global Analysis of Piecewise Linear Systems. The analysis presented may also be used to consider coupled systems of this type. A number of macroscopic mean-field approaches to modelling human EEG may be considered as coupled RKII networks. Hence developing a theoretical understanding of the onset of oscillations in models of this type has important implications in clinical neuroscience, as limit cycle oscillations have been demonstrated to be critical in the onset of certain types of epilepsy. [less ▲] Detailed reference viewed: 98 (0 UL)Output synchronisation in networks of cyclic biochemical oscillators ; ; et al in Proceedings of the 2007 American Control Conference (ACC 2007) (2007) This paper is concerned with the global analysis of asymptotic synchronization of outputs in networks of identical oscillators. The oscillator models are assumed to possess a cyclic feedback structure ... [more ▼] This paper is concerned with the global analysis of asymptotic synchronization of outputs in networks of identical oscillators. The oscillator models are assumed to possess a cyclic feedback structure. Such networks of oscillators abound in biochemistry, and are exemplified by circadian rhythm and cardiac cell networks. The main result exploits an incremental output feedback passivity property of cyclic feedback systems to prove global asymptotic output synchronization in a network composed of identical cyclic feedback systems. This result is illustrated on a network of Goodwin oscillators. [less ▲] Detailed reference viewed: 48 (0 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: 81 (0 UL)Reconstruction of biological networks through gene silencing and overexpression ; Goncalves, Jorge ; et al in Proceedings of the eighth International Conference on Systems Biology (2007) Many methods that exist for reconstructing biological networks take into account assumptions of sparsity or already known relationships among states of the network. We show that we can completely ... [more ▼] Many methods that exist for reconstructing biological networks take into account assumptions of sparsity or already known relationships among states of the network. We show that we can completely characterize the relationships among observed states and inputs in a linearized network through a series of easily performed biological experiments--inducible overexpression and gene silencing. We briefly review dynamical structure and give conditions for a set of experiments that will give all necessary information to obtain the structure. [less ▲] Detailed reference viewed: 49 (0 UL)New tools for self-organised pattern formation ; ; et al in IET Synthetic Biology (2007), 1(1.2), 29-31 Position-dependent gene expression is a critical aspect of the development and behaviour of multicellular organisms. It requires a complex series of interactions to occur between different cell types in ... [more ▼] Position-dependent gene expression is a critical aspect of the development and behaviour of multicellular organisms. It requires a complex series of interactions to occur between different cell types in addition to intracellular signalling cascades. We used Escherichia coli to study the properties of an artificial signalling system at the interface between two expanding cell populations. We genetically engineered one population to produce a diffusible acyl-homoserine lactone (AHL) signal, and another population to respond to it. Our experiments demonstrate how such a signal can be used to reproducibly generate simple visible patterns with high accuracy in swimming agar. The producing and responding cassettes of two such signalling systems can be linked to produce a symmetric interface for bidirectional communication that can be used to visualise molecular logic. Intracellular feedback between these two cassetteswould then create a framework for self-organised patterning of higher complexity. Adapting the experiments of Basu et al. (Basu et al., 2005) using cell motility, rather than a differential response to AHL concentrations as a way to define zones of response, we noted how the interaction of sender and receiver cell populations on a swimming plate could lead to complex pattern formation. Equipping highly motile strains such as E. coli MC1000 with AHL-mediated autoinducing systems based on Vibrio fischeri luxI/luxR and Pseudomonas aeruginosa lasI/lasR cassettes would allow the amplification of a response to an AHL signal and its propagation. We designed and synthesised codon-optimised auto-inducing luxI/R and lasI/R cassettes as optimal gene expression is crucial for the generation of robust patterns. We still have to complete and test the entire genetic circuitry, although by modelling the system we were able to demonstrate its feasibility. [less ▲] Detailed reference viewed: 100 (0 UL)Mathematical models of circadian Ca2+ oscillations ; Goncalves, Jorge ; in Proceedings of the eighth International Conference on Systems Biology (2007) In the model plant Arabidopsis thaliana, the concentration of cytosolic-free Ca2+ ([Ca2+]cyt) oscillates with a circadian rhythm. We are investigating the regulation and role of these oscillations both ... [more ▼] In the model plant Arabidopsis thaliana, the concentration of cytosolic-free Ca2+ ([Ca2+]cyt) oscillates with a circadian rhythm. We are investigating the regulation and role of these oscillations both experimentally and mathematically. Through systems identification, we have developed simple mathematical models from a single experiment measuring [Ca2+]cyt and the promoter activity of CIRCADIAN CLOCK ASSOCIATED 1 (CCA1). Through validation with 4 contrasting datasets, including a clock-arrhythmic transgenic line (CCA1 overexpressor), we demonstrate the necessity for a light input pathway to regulate basal [Ca2+]cyt levels. [less ▲] Detailed reference viewed: 33 (2 UL)Clinical data based optimal STI strategies for HIV: a reinforcement learning approach ; ; Goncalves, Jorge et al in Proceedings of the IEEE Conference on Decision and Control (2006) This paper addresses the problem of computing optimal structured treatment interruption strategies for HIV infected patients. We show that reinforcement learning may be useful to extract such strategies ... [more ▼] This paper addresses the problem of computing optimal structured treatment interruption strategies for HIV infected patients. We show that reinforcement learning may be useful to extract such strategies directly from clinical data, without the need of an accurate mathematical model of HIV infection dynamics. To support our claims, we report simulation results obtained by running a recently proposed batch-mode reinforcement learning algorithm, known as fitted Q iteration, on numerically generated data. [less ▲] Detailed reference viewed: 105 (0 UL)On L2 error bounds between systems ; ; Goncalves, Jorge Scientific Conference (2006) Detailed reference viewed: 31 (1 UL)Rhythmic regulation of Ca2+ signalling networks ; ; et al Scientific Conference (2006) The circadian clock is the internal timekeeper of plants. This clock regulates most aspects of plant physiology providing considerable competitive advantage. We are investigating the role for oscillations ... [more ▼] The circadian clock is the internal timekeeper of plants. This clock regulates most aspects of plant physiology providing considerable competitive advantage. We are investigating the role for oscillations in the cytosolic free Ca2+ concentration ([Ca2+]cyt) in the circadian control of cellular physiology. We have previously demonstrated that circadian oscillations of [Ca2+]cyt encode photoperiodic information but the precise role of circadian [Ca2+]cyt oscillations remain obscure. We have been taking a systems wide approach to determine the origin and function of circadian oscillations of [Ca2+]cyt. Using pharmacology, bioinformatics and biochemical tools we have new evidence that oscillations of [Ca2+]cyt are generated by the small signalling intermediate, cADPR. Positioning the oscillations of [Ca2+]cyt with respect to the molecular oscillator using reverse genetics indicates that [Ca2+]cyt is an output of the clock. Using a whole genome transcriptional profile we have identified over 1800 circadian-regulated transcripts, many of which encode for Ca2+ signalling elements. The function of circadian-regulated transcripts encoding signalling components is being investigated by reverse genetic screens with automated imaging. Using our extensive data sets describing the circadian regulation of [Ca2+]cyt in different backgrounds and conditions we have constructed a mathematical model. This is being validated using mutant analysis and refined by introducing complexity to the model. Our data and models suggest that [Ca2+]cyt acts an output of the clock that regulates diverse aspects of physiology and has the potential to form a feedback loop with the molecular components of the oscillator. [less ▲] Detailed reference viewed: 53 (0 UL)Regions of stability for limit cycle oscillations in piecewise linear systems Goncalves, Jorge in IEEE Transactions on Automatic Control (2005), 50(11), 1877-1882 Oscillations appear in numerous applications from biology to technology.However, besides local results, rigorous stability and robustness analysis of oscillations are rarely done due to their intrinsic ... [more ▼] Oscillations appear in numerous applications from biology to technology.However, besides local results, rigorous stability and robustness analysis of oscillations are rarely done due to their intrinsic nonlinear behavior. Poincarémaps associated with the system cannot typically be found explicitly and stability is estimated using extensive simulations and experiments. This paper gives conditions in the form of linear matrix inequalities (LMIs) that guarantee asymptotic stability in a reasonably large region around a limit cycle for a class of systems known as piecewise linear systems (PLS). Such conditions, based on recent results on impact maps and surface Lyapunov functions (SuLF), allow a systematic and efficient analysis of oscillations of PLS or arbitrarily close approximations of nonlinear systems by PLS. The methodology applies to any locally stable limit cycle of a PLS, regardless of the dimension and the number of switching surfaces of the system, and is illustrated with a biological application: a fourth-order neural oscillator, also used in many robotics applications such as juggling and locomotion. [less ▲] Detailed reference viewed: 125 (0 UL)Application of robust model validation using SOSTOOLS to the study of G-Protein signalling in yeast ; ; et al Scientific Conference (2005) Two major methodological challenges in modeling biological systems are model (in)validation and parameter estimation. The traditional approach is to fit the model parameters to data. An alternative ... [more ▼] Two major methodological challenges in modeling biological systems are model (in)validation and parameter estimation. The traditional approach is to fit the model parameters to data. An alternative approach pioneered by Packard, Frenklach, Seiler and colleagues (Frenklach et al., 2002) defines the range of parameter values that is consistent with the data while taking into account parametric and data uncertainty. If an invalidation certificate is found, the feasible parameter space is proved empty; otherwise, attempts to describe the feasible parameter space are carried out. We refer to this methodology as Robust Model Validation (RMV). Here we perform RMV using sum of squares (SOS) programs implemented by the MATLAB toolbox SOSTOOLS (Prajna et al., 2002). The principal advantage of SOS over conventional semidefinite programming (SDP) techniques such as the Sprocedure is the possibility of using higher-order multipliers to obtain tighter parameter bounds. We applied SOSTOOLS to a simple model of the yeast heterotrimeric G-protein cycle. We were able to invalidate the model based on real experimental data. Furthermore, using synthetic data that did not invalidate the model, we explored different techniques for representing the feasible parameter space. [less ▲] Detailed reference viewed: 71 (1 UL)Reachability analysis of continuous time piecewise linear systems ; Goncalves, Jorge in Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference (2005) This paper presents a new approach to the reachability problem for a class of hybrid systems called Piecewise Linear Systems (PLS). The principal tool used is the impact map between switching surfaces ... [more ▼] This paper presents a new approach to the reachability problem for a class of hybrid systems called Piecewise Linear Systems (PLS). The principal tool used is the impact map between switching surfaces. The method consists of specifying a ellipsoidal set on the initial switching surface and finding upper- and lower-bound estimates of the possible reach sets using tools such as the S-procedure to set up linear matrix inequalities, of which numerical solutions are then computed. [less ▲] Detailed reference viewed: 78 (0 UL)Tradeoffs in networks with positive and negative feedback Goncalves, Jorge ; ; Scientific Conference (2005) Detailed reference viewed: 58 (0 UL)Drosophila circadian rhythms: stability robustness analysis and model reduction Goncalves, Jorge ; in Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (2004) Detailed reference viewed: 115 (9 UL)Finding surface Lyapunov functions through sum-of-squares Programming ; Goncalves, Jorge in Proceedings of the American Control Conference 2004 (2004) This work presents a sum-of-squares method to construct polynomial surface Lyapunov functions (SuLF) of arbitrary order for the impact maps of limit cycles in piecewise linear systems (PLS). This work ... [more ▼] This work presents a sum-of-squares method to construct polynomial surface Lyapunov functions (SuLF) of arbitrary order for the impact maps of limit cycles in piecewise linear systems (PLS). This work extends previous results on stability analysis of such limit cycles, which utilized quadratic SuLFs. This paper also discusses an initial study of hierarchical jump linear systems where the switching is driven by feedback of low-level dynamical system states and a Markovian process. [less ▲] Detailed reference viewed: 81 (0 UL) |
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