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Experimental design trade-offs for gene regulatory network inference: an in silico study of the yeast Saccharomyces cerevisiae cell cycle Markdahl, Johan ; Colombo, Nicolo ; Thunberg, Johan et al in Proceedings of the 56th IEEE Conference on Decision and Control (2017, December) Time-series of high throughput gene sequencing data intended for gene regulatory network (GRN) inference are often short due to the high costs of sampling cell systems. Moreover, experimentalists lack a ... [more ▼] Time-series of high throughput gene sequencing data intended for gene regulatory network (GRN) inference are often short due to the high costs of sampling cell systems. Moreover, experimentalists lack a set of quantitative guidelines that prescribe the minimal number of samples required to infer a reliable GRN model. We study the temporal resolution of data vs.quality of GRN inference in order to ultimately overcome this deficit. The evolution of a Markovian jump process model for the Ras/cAMP/PKA pathway of proteins and metabolites in the G1 phase of the Saccharomyces cerevisiae cell cycle is sampled at a number of different rates. For each time-series we infer a linear regression model of the GRN using the LASSO method. The inferred network topology is evaluated in terms of the area under the precision-recall curve (AUPR). By plotting the AUPR against the number of samples, we show that the trade-off has a, roughly speaking, sigmoid shape. An optimal number of samples corresponds to values on the ridge of the sigmoid. [less ▲] Detailed reference viewed: 117 (10 UL)On definition and inference of nonlinear Boolean dynamic networks Yue, Zuogong ; Thunberg, Johan ; et al in On definition and inference of nonlinear Boolean dynamic networks (2017, December) Network reconstruction has become particularly important in systems biology, and is now expected to deliver information on causality. Systems in nature are inherently nonlinear. However, for nonlinear ... [more ▼] Network reconstruction has become particularly important in systems biology, and is now expected to deliver information on causality. Systems in nature are inherently nonlinear. However, for nonlinear dynamical systems with hidden states, how to give a useful definition of dynamic networks is still an open question. This paper presents a useful definition of Boolean dynamic networks for a large class of nonlinear systems. Moreover, a robust inference method is provided. The well-known Millar-10 model in systems biology is used as a numerical example, which provides the ground truth of causal networks for key mRNAs involved in eukaryotic circadian clocks. In addition, as second contribution of this paper, we suggest definitions of linear network identifiability, which helps to unify the available work on network identifiability. [less ▲] Detailed reference viewed: 149 (5 UL)Distributed methods for synchronization of orthogonal matrices over graphs Thunberg, Johan ; Bernard, Florian ; Goncalves, Jorge in Automatica (2017), 80 This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We ... [more ▼] This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as a least-squares optimization problem with nonlinear constraints. The synchronization problem appears as one of the key components in applications ranging from 3D-localization to image registration. The main contributions of this work can be summarized as the introduction of two novel algorithms; one for symmetric graphs and one for graphs that are possibly asymmetric. Under general conditions, the former has guaranteed convergence to the solution of a spectral relaxation to the synchronization problem. The latter is stable for small step sizes when the graph is quasi-strongly connected. The proposed methods are verified in numerical simulations. [less ▲] Detailed reference viewed: 103 (3 UL)Shape-aware surface reconstruction from sparse 3D point-clouds Bernard, Florian ; Salamanca Mino, Luis ; Thunberg, Johan et al in Medical Image Analysis (2017), 38 The reconstruction of an object’s shape or surface from a set of 3D points plays an important role in medical image analysis, e.g. in anatomy reconstruction from tomographic measurements or in the process ... [more ▼] The reconstruction of an object’s shape or surface from a set of 3D points plays an important role in medical image analysis, e.g. in anatomy reconstruction from tomographic measurements or in the process of aligning intra-operative navigation and preoperative planning data. In such scenarios, one usually has to deal with sparse data, which significantly aggravates the problem of reconstruction. However, medical applications often provide contextual information about the 3D point data that allow to incorporate prior knowledge about the shape that is to be reconstructed. To this end, we propose the use of a statistical shape model (SSM) as a prior for surface reconstruction. The SSM is represented by a point distribution model (PDM), which is associated with a surface mesh. Using the shape distribution that is modelled by the PDM, we formulate the problem of surface reconstruction from a probabilistic perspective based on a Gaussian Mixture Model (GMM). In order to do so, the given points are interpreted as samples of the GMM. By using mixture components with anisotropic covariances that are “oriented” according to the surface normals at the PDM points, a surface-based fitting is accomplished. Estimating the parameters of the GMM in a maximum a posteriori manner yields the reconstruction of the surface from the given data points. We compare our method to the extensively used Iterative Closest Points method on several different anatomical datasets/SSMs (brain, femur, tibia, hip, liver) and demonstrate superior accuracy and robustness on sparse data. [less ▲] Detailed reference viewed: 162 (21 UL)Local Lyapunov Functions for Consensus in Switching Nonlinear Systems Thunberg, Johan ; Goncalves, Jorge ; in IEEE Transactions on Automatic Control (2017) This note presents two theorems on asymptotic state consensus of continuous time nonlinear multi-agent systems. The agents reside in Rm and have switching interconnection topologies. Both the first ... [more ▼] This note presents two theorems on asymptotic state consensus of continuous time nonlinear multi-agent systems. The agents reside in Rm and have switching interconnection topologies. Both the first theorem, formulated in terms of the states of individual agents, and the second theorem, formulated in terms of the pairwise states for pairs of agents, can be interpreted as variants of Lyapunov’s second method. The two theorems complement each other; the second provides stronger convergence results under weaker graph topology assumptions, whereas the first often can be applied in a wider context in terms of the structure of the right-hand sides of the systems. The second theorem also sheds some new light on well-known results for consensus of nonlinear systems where the right-hand sides of the agents’ dynamics are convex combinations of directions to neighboring agents. For such systems, instead of proving consensus by using the theory of contracting convex sets, a local quadratic Lyapunov function can be used. [less ▲] Detailed reference viewed: 158 (4 UL)Linear identification of nonlinear systems: A lifting technique based on the Koopman operator Mauroy, Alexandre ; Goncalves, Jorge in Proceedings of the 55th IEEE Conference on Decision and Control (2016, December) We exploit the key idea that nonlinear system identification is equivalent to linear identification of the socalled Koopman operator. Instead of considering nonlinear system identification in the state ... [more ▼] We exploit the key idea that nonlinear system identification is equivalent to linear identification of the socalled Koopman operator. Instead of considering nonlinear system identification in the state space, we obtain a novel linear identification technique by recasting the problem in the infinite-dimensional space of observables. This technique can be described in two main steps. In the first step, similar to a component of the Extended Dynamic Mode Decomposition algorithm, the data are lifted to the infinite-dimensional space and used for linear identification of the Koopman operator. In the second step, the obtained Koopman operator is “projected back” to the finite-dimensional state space, and identified to the nonlinear vector field through a linear least squares problem. The proposed technique is efficient to recover (polynomial) vector fields of different classes of systems, including unstable, chaotic, and open systems. In addition, it is robust to noise, well-suited to model low sampling rate datasets, and able to infer network topology and dynamics. [less ▲] Detailed reference viewed: 133 (8 UL)Global converegence properties of a consensus protocol on the n-sphere Markdahl, Johan ; Goncalves, Jorge in Proceedings of the 55th IEEE Conference on Decision and Control (2016, December) This paper provides a novel analysis of the global convergence properties of a well-known consensus protocol for multi-agent systems that evolve in continuous time on the n-sphere. The feedback is ... [more ▼] This paper provides a novel analysis of the global convergence properties of a well-known consensus protocol for multi-agent systems that evolve in continuous time on the n-sphere. The feedback is intrinsic to the n-sphere, i.e., it does not rely on the use of local coordinates obtained through a parametrization. It is shown that, for any connected undirected graph topology and all n>1, the consensus protocol yields convergence that is akin to almost global consensus in a weak sense. Simulation results suggest that actual almost global consensus holds. This result is of interest in the context of consensus on Riemannian manifolds since it differs from what is known with regard to the 1-sphere and SO(3) where more advanced intrinsic consensus protocols are required in order to generate equivalent results. [less ▲] Detailed reference viewed: 163 (12 UL)Optimising time-series experimental design for modelling of circadian rhythms: the value of transient data Mombaerts, Laurent ; Mauroy, Alexandre ; Goncalves, Jorge in IFAC-PapersOnLine (2016, October) Circadian clocks consist of complex networks that coordinate the daily cycle of most organisms. In light/dark cycles, the clock is synchronized (or entrained) by the environment, which corresponds to a ... [more ▼] Circadian clocks consist of complex networks that coordinate the daily cycle of most organisms. In light/dark cycles, the clock is synchronized (or entrained) by the environment, which corresponds to a constant rephasing of the oscillations and leads to a steady state regime. Some circadian clocks are endogenous oscillators with rhythms of about 24-hours that persist in constant light or constant darkness. This operating mechanism with and without entrainment provides flexibility and robustness to the clock against perturbations. Most of the clock-oriented experiments are performed under constant photoperiodic regime, overlooking the transitory regime that takes place between light/dark cycles and constant light or darkness. This paper provides a comparative analysis of the informative potential of the transient time-series data with the other regimes for clock modelling. Realistic data were simulated from 2 experimentally validated plant circadian clock models and sliced into several time windows. These windows represent the different regimes that take place before, meanwhile and after the switch to constant light. Then, a network inference tool was used over each window and its capability of retrieving the ground-truth of the network was compared for each window. The results suggest that including the transient data to the network inference technique significally improves its performance. [less ▲] Detailed reference viewed: 157 (15 UL)Shaping Pulses to Control Bistable Monotone Systems Using Koopman Operator ; Mauroy, Alexandre ; Goncalves, Jorge in 10th IFAC Symposium on Nonlinear Control Systems (2016, August) In this paper, we further develop a recently proposed control method to switch a bistable system between its steady states using temporal pulses. The motivation for using pulses comes from biomedical and ... [more ▼] In this paper, we further develop a recently proposed control method to switch a bistable system between its steady states using temporal pulses. The motivation for using pulses comes from biomedical and biological applications (e.g. synthetic biology), where it is generally di cult to build feedback control systems due to technical limitations in sensing and actuation. The original framework was derived for monotone systems and all the extensions relied on monotone systems theory. In contrast, we introduce the concept of switching function which is related to eigenfunctions of the so-called Koopman operator subject to a xed control pulse. Using the level sets of the switching function we can (i) compute the set of all pulses that drive the system toward the steady state in a synchronous way and (ii) estimate the time needed by the ow to reach an epsilon neighborhood of the target steady state. Additionally, we show that for monotone systems the switching function is also monotone in some sense, a property that can yield e cient algorithms to compute it. This observation recovers and further extends the results of the original framework, which we illustrate on numerical examples inspired by biological applications. [less ▲] Detailed reference viewed: 101 (1 UL)Global and invariant aspects of consensus on the n-sphere Markdahl, Johan ; ; et al in Proceedings of the 22nd International Symposium on Mathematical Theory of Networks and Systems (2016, July) This paper concerns two aspects of the multi- agent consensus problem on the n-sphere. Firstly, it proves that a standard consensus protocol, in a certain sense, yields asymptotical stability on a global ... [more ▼] This paper concerns two aspects of the multi- agent consensus problem on the n-sphere. Firstly, it proves that a standard consensus protocol, in a certain sense, yields asymptotical stability on a global level for a nontrivial class of graph topologies. Secondly, it provides a novel consensus protocol that leaves the centroid of agent states in Rn+1 projected back to the sphere invariant. It hence becomes possible to determine the consensus point as a function of the initial states. Much of the stability analysis has an intuitive geometric appeal since it is based on the symmetries of the n-sphere rather than generic Lyapunov theory. [less ▲] Detailed reference viewed: 95 (7 UL)Sparse Network Identifiability via Compressed Sensing Goncalves, Jorge ; ; et al in Automatica (2016), 68 Detailed reference viewed: 274 (18 UL)Fast Correspondences for Statistical Shape Models of Brain Structures Bernard, Florian ; Vlassis, Nikos ; et al in SPIE Medical Imaging (2016, March) Detailed reference viewed: 202 (17 UL)Robust stability analysis of active voltage control for high-power IGBT switching by Kharitonov's theorem Goncalves, Jorge ; ; et al in IEEE Transactions on Power Electronics (2016), 31(3), 2584-2595 Detailed reference viewed: 92 (8 UL)A Sparse Bayesian Approach to the Identification of Nonlinear State-Space Systems Pan, Wei ; ; Goncalves, Jorge et al in IEEE Transaction on Automatic Control (2016), 61(1), 182-187 This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated ... [more ▼] This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear functional forms and their associated parameters from a limited number of time-series data points. For this, we cast this identification problem as a sparse linear regression problem and take a Bayesian viewpoint to solve it. As such, this approach typically leads to nonconvex optimisations. We propose a convexification procedure relying on an efficient iterative re-weighted ℓ1-minimisation algorithm that uses general sparsity inducing priors on the parameters of the system and marginal likelihood maximisation. Using this approach, we also show how convex constraints on the parameters can be easily added to our proposed iterative re-weighted ℓ1-minimisation algorithm. In the supplementary material \cite{appendix}, we illustrate the effectiveness of the proposed identification method on two classical systems in biology and physics, namely, a genetic repressilator network and a large scale network of interconnected Kuramoto oscillators. [less ▲] Detailed reference viewed: 257 (18 UL)An Iterative Projection method for Synchronization of Invertible Matrices Over Graphs Thunberg, Johan ; Colombo, Nicolo ; Yue, Zuogong et al in 22nd International Symposium on Mathematical Theory of Networks and Systems (2016) This paper addresses synchronization of invertible matrices over graphs. The matrices represent pairwise transformations between n euclidean coordinate systems. Synchronization means that composite ... [more ▼] This paper addresses synchronization of invertible matrices over graphs. The matrices represent pairwise transformations between n euclidean coordinate systems. Synchronization means that composite transformations over loops are equal to the identity. Given a set of measured matrices that are not synchronized, the synchronization problem amounts to fining new synchronized matrices close to the former. Under the assumption that the measurement noise is zero mean Gaussian with known covariance, we introduce an iterative method based on linear subspace projection. The method is free of step size determination and tuning and numerical simulations show significant improvement of the solution compared to a recently proposed direct method as well as the Gauss-Newton method. [less ▲] Detailed reference viewed: 129 (10 UL)Expression of the Parkinson’s Disease-Associated Gene Alpha-Synuclein is Regulated by the Neuronal Cell Fate Determinant TRIM32 Pavlou, Maria Angeliki ; Colombo, Nicolo ; et al in Molecular Neurobiology (2016) Detailed reference viewed: 224 (13 UL)Consensus and Formation Control on SE(3) for Switching Topologies Thunberg, Johan ; Goncalves, Jorge ; in Automatica (2016), 66 This paper addresses the consensus problem and the formation problem on SE(3) in multi-agent systems with directed and switching interconnection topologies. Several control laws are introduced for the ... [more ▼] This paper addresses the consensus problem and the formation problem on SE(3) in multi-agent systems with directed and switching interconnection topologies. Several control laws are introduced for the consensus problem. By a simple transformation, it is shown that the proposed control laws can be used for the formation problem. The design is first conducted on the kinematic level, where the velocities are the control laws. Then, for rigid bodies in space, the design is conducted on the dynamic level, where the torques and the forces are the control laws. On the kinematic level, first two control laws are introduced that explicitly use Euclidean transformations, then separate control laws are defined for the rotations and the translations. In the special case of purely rotational motion, the consensus problem is referred to as consensus on SO(3) or attitude synchronization. In this problem, for a broad class of local representations or parameterizations of SO(3), including the Axis–Angle Representation, the Rodrigues Parameters and the Modified Rodrigues Parameters, two types of control laws are presented that look structurally the same for any choice of local representation. For these two control laws we provide conditions on the initial rotations and the connectivity of the graph such that the system reaches consensus on SO(3). Among the contributions of this paper, there are conditions for when exponential rate of convergence occurs. A theorem is provided showing that for any choice of local representation for the rotations, there is a change of coordinates such that the transformed system has a well known structure. [less ▲] Detailed reference viewed: 103 (12 UL)Global Optimality Bounds for ICA Algorithms Colombo, Nicolo ; Thunberg, Johan ; Goncalves, Jorge in 22nd International Symposium on Mathematical Theory of Networks and Systems (2016) Independent Component Analysis is a popular statistical method for separating a multivariate signal into additive components. It has been shown that the signal separation problem can be reduced to the ... [more ▼] Independent Component Analysis is a popular statistical method for separating a multivariate signal into additive components. It has been shown that the signal separation problem can be reduced to the joint diagonalization of the matrix slices of some higher-order cumulants of the signal. In this approach, the unknown mixing matrix can be computed directly from the obtained joint diagonalizer. Various iterative algorithms for solving the non-convex joint diagonalization problem exist, but they usually lack global optimality guarantees. In this paper, we introduce a procedure for computing an optimality gap for local optimal solutions. The optimality gap is then used to obtain an empirical error bound for the estimated mixing matrix. Finally, a class of simultaneous matrix decomposition problems that admit such relaxation procedure is identified. [less ▲] Detailed reference viewed: 167 (9 UL)Inverse Problems for Matrix Exponential in System Identification: System Aliasing Yue, Zuogong ; Thunberg, Johan ; Goncalves, Jorge in 22nd International Symposium on Mathematical Theory of Networks and Systems (2016) This note addresses identification of the A-matrix in continuous time linear dynamical systems on state-space form. If this matrix is partially known or known to have a sparse structure, such knowledge ... [more ▼] This note addresses identification of the A-matrix in continuous time linear dynamical systems on state-space form. If this matrix is partially known or known to have a sparse structure, such knowledge can be used to simplify the identification. We begin by introducing some general conditions for solvability of the inverse problems for matrix exponential. Next, we introduce “system aliasing” as an issue in the identification of slow sampled systems. Such aliasing give rise to nonunique matrix logarithms. As we show, by imposing additional conditions on and prior knowledge about the A-matrix, the issue of system aliasing can, at least partially, be overcome. Under conditions on the sparsity and the norm of the A-matrix, it is identifiable up to a finite equivalence class. [less ▲] Detailed reference viewed: 130 (15 UL)Linear Shape Deformation Models with Local Support using Graph-based Structured Matrix Factorisation Bernard, Florian ; ; Hertel, Frank et al in Linear Shape Deformation Models with Local Support using Graph-based Structured Matrix Factorisation (2016) Representing 3D shape deformations by linear models in high-dimensional space has many applications in computer vision and medical imaging, such as shape-based interpolation or segmentation. Commonly ... [more ▼] Representing 3D shape deformations by linear models in high-dimensional space has many applications in computer vision and medical imaging, such as shape-based interpolation or segmentation. Commonly, using Principal Components Analysis a low-dimensional (affine) subspace of the high-dimensional shape space is determined. However, the resulting factors (the most dominant eigenvectors of the covariance matrix) have global support, i.e. changing the coefficient of a single factor deforms the entire shape. In this paper, a method to obtain deformation factors with local support is presented. The benefits of such models include better flexibility and interpretability as well as the possibility of interactively deforming shapes locally. For that, based on a well-grounded theoretical motivation, we formulate a matrix factorisation problem employing sparsity and graph-based regularisation terms. We demonstrate that for brain shapes our method outperforms the state of the art in local support models with respect to generalisation ability and sparse shape reconstruction, whereas for human body shapes our method gives more realistic deformations. [less ▲] Detailed reference viewed: 129 (14 UL) |
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