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See detailExperimental design trade-offs for gene regulatory network inference: an in silico study of the yeast Saccharomyces cerevisiae cell cycle
Markdahl, Johan UL; Colombo, Nicolo UL; Thunberg, Johan UL et al

in Proceedings of the 56th IEEE Conference on Decision and Control (in press)

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 ▲]

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See detailGlobal converegence properties of a consensus protocol on the n-sphere
Markdahl, Johan UL; Goncalves, Jorge UL

Scientific Conference (2016, December 13)

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 ▲]

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See detailGlobal and Invariant Aspects of Consensus on the n-Sphere
Markdahl, Johan UL; Song, Wenjun; Hu, Xiaoming 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 ▲]

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See detailExact solutions to a class of feedback systems on SO(n)
Markdahl, Johan UL; Hu, Xiaoming

in Automatica (2016), 63

This paper provides a novel approach to the problem of attitude tracking for a class of almost globally asymptotically stable feedback laws on View the MathML source. The closed-loop systems are solved ... [more ▼]

This paper provides a novel approach to the problem of attitude tracking for a class of almost globally asymptotically stable feedback laws on View the MathML source. The closed-loop systems are solved exactly for the rotation matrices as explicit functions of time, the initial conditions, and the gain parameters of the control laws. The exact solutions provide insight into the transient dynamics of the system and can be used to prove almost global attractiveness of the identity matrix. Applications of these results are found in model predictive control problems where detailed insight into the transient attitude dynamics is utilized to approximately complete a task of secondary importance. Knowledge of the future trajectory of the states can also be used as an alternative to the zero-order hold in systems where the attitude is sampled at discrete time instances. [less ▲]

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