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A minimal realization technique for the dynamical structure function of a class of LTI systems Goncalves, Jorge ; ; et al in IEEE Transactions on Control of Network Systems (in press) Detailed reference viewed: 152 (10 UL)Network Identifiability from Intrinsic Noise Goncalves, Jorge ; ; in IEEE Transactions on Automatic Control (in press) Detailed reference viewed: 291 (23 UL)Dynamical differential expression (DyDE) reveals the period control mechanisms of the Arabidopsis circadian oscillator Mombaerts, Laurent ; ; et al in PLoS Computational Biology (2019) The circadian oscillator, an internal time-keeping device found in most organisms, enables timely regulation of daily biological activities by maintaining synchrony with the external environment. The ... [more ▼] The circadian oscillator, an internal time-keeping device found in most organisms, enables timely regulation of daily biological activities by maintaining synchrony with the external environment. The mechanistic basis underlying the adjustment of circadian rhythms to changing external conditions, however, has yet to be clearly elucidated. We explored the mechanism of action of nicotinamide in Arabidopsis thaliana, a metabolite that lengthens the period of circadian rhythms, to understand the regulation of circadian period. To identify the key mechanisms involved in the circadian response to nicotinamide, we developed a systematic and practical modeling framework based on the identification and comparison of gene regulatory dynamics. Our mathematical predictions, confirmed by experimentation, identified key transcriptional regulatory mechanisms of circadian period and uncovered the role of blue light in the response of the circadian oscillator to nicotinamide. We suggest that our methodology could be adapted to predict mechanisms of drug action in complex biological systems. [less ▲] Detailed reference viewed: 45 (2 UL)Linear system identification from ensemble snapshot observations Aalto, Atte ; Goncalves, Jorge E-print/Working paper (2019) Developments in transcriptomics techniques have caused a large demand in tailored computational methods for modelling gene expression dynamics from experimental data. Recently, so-called single-cell ... [more ▼] Developments in transcriptomics techniques have caused a large demand in tailored computational methods for modelling gene expression dynamics from experimental data. Recently, so-called single-cell experiments have revolutionised genetic studies. These experiments yield gene expression data in single cell resolution for a large number of cells at a time. However, the cells are destroyed in the measurement process, and so the data consist of snapshots of an ensemble evolving over time, instead of time series. The problem studied in this article is how such data can be used in modelling gene regulatory dynamics. Two different paradigms are studied for linear system identification. The first is based on tracking the evolution of the distribution of cells over time. The second is based on the so-called pseudotime concept, identifying a common trajectory through the state space, along which cells propagate with different rates. Therefore, at any given time, the population contains cells in different stages of the trajectory. Resulting methods are compared in numerical experiments. [less ▲] Detailed reference viewed: 43 (4 UL)Dynamic controllers for column synchronization of rotation matrices: a QR-factorization approach Thunberg, Johan ; Markdahl, Johan ; Goncalves, Jorge in Automatica (2018), 93 In the multi-agent systems setting, this paper addresses continuous-time distributed synchronization of columns of rotation matrices. More precisely, k specific columns shall be synchronized and only the ... [more ▼] In the multi-agent systems setting, this paper addresses continuous-time distributed synchronization of columns of rotation matrices. More precisely, k specific columns shall be synchronized and only the corresponding k columns of the relative rotations between the agents are assumed to be available for the control design. When one specific column is considered, the problem is equivalent to synchronization on the (d-1)-dimensional unit sphere and when all the columns are considered, the problem is equivalent to synchronization on SO(d). We design dynamic control laws for these synchronization problems. The control laws are based on the introduction of auxiliary variables in combination with a QR-factorization approach. The benefit of this QR-factorization approach is that we can decouple the dynamics for the $k$ columns from the remaining d-k ones. Under the control scheme, the closed loop system achieves almost global convergence to synchronization for quasi-strong interaction graph topologies. [less ▲] Detailed reference viewed: 70 (1 UL)Almost Global Consensus on the n-Sphere Markdahl, Johan ; Thunberg, Johan ; Goncalves, Jorge in IEEE Transactions on Automatic Control (2018), 63(6), 1664-1675 This paper establishes novel results regarding the global convergence properties of a large class of consensus protocols for multi-agent systems that evolve in continuous time on the n-dimensional unit ... [more ▼] This paper establishes novel results regarding the global convergence properties of a large class of consensus protocols for multi-agent systems that evolve in continuous time on the n-dimensional unit sphere or n-sphere. For any connected, undirected graph and all n 2 N\{1}, each protocol in said class is shown to yield almost global consensus. The feedback laws are negative gradients of Lyapunov functions and one instance generates the canonical intrinsic gradient descent protocol. This convergence result sheds new light on the general problem of consensus on Riemannian manifolds; the n-sphere for n 2 N\{1} differs from the circle and SO(3) where the corresponding protocols fail to generate almost global consensus. Moreover, we derive a novel consensus protocol on SO(3) by combining two almost globally convergent protocols on the n-sphere for n in {1, 2}. Theoretical and simulation results suggest that the combined protocol yields almost global consensus on SO(3). [less ▲] Detailed reference viewed: 58 (4 UL)Bayesian variable selection in linear dynamical systems Aalto, Atte ; Goncalves, Jorge E-print/Working paper (2018) We develop a method for reconstructing regulatory interconnection networks between variables evolving according to a linear dynamical system. The work is motivated by the problem of gene regulatory ... [more ▼] We develop a method for reconstructing regulatory interconnection networks between variables evolving according to a linear dynamical system. The work is motivated by the problem of gene regulatory network inference, that is, finding causal effects between genes from gene expression time series data. In biological applications, the typical problem is that the sampling frequency is low, and consequentially the system identification problem is ill-posed. The low sampling frequency also makes it impossible to estimate derivatives directly from the data. We take a Bayesian approach to the problem, as it offers a natural way to incorporate prior information to deal with the ill-posedness, through the introduction of sparsity promoting prior for the underlying dynamics matrix. It also provides a framework for modelling both the process and measurement noises. We develop Markov Chain Monte Carlo samplers for the discrete-valued zero-structure of the dynamics matrix, and for the continuous-time trajectory of the system. [less ▲] Detailed reference viewed: 88 (10 UL)A lifting method for analyzing distributed synchronization on the unit sphere Thunberg, Johan ; Markdahl, Johan ; et al in Automatica (2018) This paper introduces a new lifting method for analyzing convergence of continuous-time distributed synchronization/consensus systems on the unit sphere. Points on the d-dimensional unit sphere are lifted ... [more ▼] This paper introduces a new lifting method for analyzing convergence of continuous-time distributed synchronization/consensus systems on the unit sphere. Points on the d-dimensional unit sphere are lifted to the (d+1)-dimensional Euclidean space. The consensus protocol on the unit sphere is the classical one, where agents move toward weighted averages of their neighbors in their respective tangent planes. Only local and relative state information is used. The directed interaction graph topologies are allowed to switch as a function of time. The dynamics of the lifted variables are governed by a nonlinear consensus protocol for which the weights contain ratios of the norms of state variables. We generalize previous convergence results for hemispheres. For a large class of consensus protocols defined for switching uniformly quasi-strongly connected time-varying graphs, we show that the consensus manifold is uniformly asymptotically stable relative to closed balls contained in a hemisphere. Compared to earlier projection based approaches used in this context such as the gnomonic projection, which is defined for hemispheres only, the lifting method applies globally. With that, the hope is that this method can be useful for future investigations on global convergence. [less ▲] Detailed reference viewed: 34 (0 UL)Post-operative deep brain stimulation assessment: Automatic data integration and report generation Husch, Andreas ; ; et al in Brain Stimulation (2018) Background The gold standard for post-operative deep brain stimulation (DBS) parameter tuning is a monopolar review of all stimulation contacts, a strategy being challenged by recent developments of more ... [more ▼] Background The gold standard for post-operative deep brain stimulation (DBS) parameter tuning is a monopolar review of all stimulation contacts, a strategy being challenged by recent developments of more complex electrode leads. Objective Providing a method to guide clinicians on DBS assessment and parameter tuning by automatically integrating patient individual data. Methods We present a fully automatic method for visualization of individual deep brain structures in relation to a DBS lead by combining precise electrode recovery from post-operative imaging with individual estimates of deep brain morphology utilizing a 7T-MRI deep brain atlas. Results The method was evaluated on 20 STN DBS cases. It demonstrated robust automatic creation of 3D-enabled PDF reports visualizing electrode to brain structure relations and proved valuable in detecting miss placed electrodes. Discussion Automatic DBS assessment is feasible and can conveniently provide clinicians with relevant information on DBS contact positions in relation to important anatomical structures. [less ▲] Detailed reference viewed: 82 (6 UL)PaCER - A fully automated method for electrode trajectory and contact reconstruction in deep brain stimulation Husch, Andreas ; ; et al in NeuroImage: Clinical (2018), 17 Abstract Deep brain stimulation (DBS) is a neurosurgical intervention where electrodes are permanently implanted into the brain in order to modulate pathologic neural activity. The post-operative ... [more ▼] Abstract Deep brain stimulation (DBS) is a neurosurgical intervention where electrodes are permanently implanted into the brain in order to modulate pathologic neural activity. The post-operative reconstruction of the DBS electrodes is important for an efficient stimulation parameter tuning. A major limitation of existing approaches for electrode reconstruction from post-operative imaging that prevents the clinical routine use is that they are manual or semi-automatic, and thus both time-consuming and subjective. Moreover, the existing methods rely on a simplified model of a straight line electrode trajectory, rather than the more realistic curved trajectory. The main contribution of this paper is that for the first time we present a highly accurate and fully automated method for electrode reconstruction that considers curved trajectories. The robustness of our proposed method is demonstrated using a multi-center clinical dataset consisting of N=44 electrodes. In all cases the electrode trajectories were successfully identified and reconstructed. In addition, the accuracy is demonstrated quantitatively using a high-accuracy phantom with known ground truth. In the phantom experiment, the method could detect individual electrode contacts with high accuracy and the trajectory reconstruction reached an error level below 100 μm (0.046 ± 0.025 mm). An implementation of the method is made publicly available such that it can directly be used by researchers or clinicians. This constitutes an important step towards future integration of lead reconstruction into standard clinical care. [less ▲] Detailed reference viewed: 138 (28 UL)Continuous time Gaussian process dynamical models in gene regulatory network inference Aalto, Atte ; ; et al E-print/Working paper (2018) One of the focus areas of modern scientific research is to reveal mysteries related to genes and their interactions. The dynamic interactions between genes can be encoded into a gene regulatory network ... [more ▼] One of the focus areas of modern scientific research is to reveal mysteries related to genes and their interactions. The dynamic interactions between genes can be encoded into a gene regulatory network (GRN), which can be used to gain understanding on the genetic mechanisms behind observable phenotypes. GRN inference from time series data has recently been a focus area of systems biology. Due to low sampling frequency of the data, this is a notoriously difficult problem. We tackle the challenge by introducing the so-called continuous-time Gaussian process dynamical model (GPDM), based on Gaussian process framework that has gained popularity in nonlinear regression problems arising in machine learning. The model dynamics are governed by a stochastic differential equation, where the dynamics function is modelled as a Gaussian process. We prove the existence and uniqueness of solutions of the stochastic differential equation. We derive the probability distribution for the Euler discretised trajectories and establish the convergence of the discretisation. We develop a GRN inference method based on the developed framework. The method is based on MCMC sampling of trajectories of the GPDM and estimating the hyperparameters of the covariance function of the Gaussian process. Using benchmark data examples, we show that our method is computationally feasible and superior in dealing with poor time resolution. [less ▲] Detailed reference viewed: 27 (4 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: 91 (5 UL)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: 68 (10 UL)Distributed synchronization of euclidean transformations with guaranteed convergence Thunberg, Johan ; Goncalves, Jorge ; in 56th IEEE Conference on Decision and Control (2017, December) This paper addresses synchronization of Euclidean transformations over graphs. Synchronization in this context, unlike rendezvous or consensus, means that composite transformations over loops in the graph ... [more ▼] This paper addresses synchronization of Euclidean transformations over graphs. Synchronization in this context, unlike rendezvous or consensus, means that composite transformations over loops in the graph are equal to the identity. Given a set of non-synchronized transformations, the problem at hand is to find a set of synchronized transformations approximating well the non-synchronized transformations. This is formulated as a nonlinear least-squares optimization problem. We present a distributed synchronization algorithm that converges to the optimal solution to an approximation of the optimization problem. This approximation stems from a spectral relaxation of the rotational part on the one hand and from a separation between the rotations and the translations on the other. The method can be used to distributively improve the measurements obtained in sensor networks such as networks of cameras where pairwise relative transformations are measured. The convergence of the method is verified in numerical simulations. [less ▲] Detailed reference viewed: 39 (1 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: 69 (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: 113 (20 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: 118 (4 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: 121 (12 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: 95 (8 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: 106 (12 UL) |
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