High-Dimensional Kuramoto Models on Stiefel Manifolds Synchronize Complex Networks Almost Globally

in Automatica (2020)

A multifactorial evaluation framework for gene regulatory network reconstruction

in Foundations of Systems Biology in Engineering (2019)

In the past years, many computational methods have been developed to infer the structure of gene regulatory networks from time series data. However, the applicability and accuracy presumptions of such ... [more ▼]

In the past years, many computational methods have been developed to infer the structure of gene regulatory networks from time series data. However, the applicability and accuracy presumptions of such algorithms remain unclear due to experimental heterogeneity. This paper assesses the performance of recent and successful network inference strategies under a novel, multifactorial evaluation framework in order to highlight pragmatic tradeoffs in experimental design. The effects of data quantity and systems perturbations are addressed, thereby formulating guidelines for efficient resource management. Realistic data were generated from six widely used benchmark models of rhythmic and nonrhythmic gene regulatory systems with random perturbations mimicking the effect of gene knock-out or chemical treatments. Then, time series data of increasing lengths were provided to five state-of-the-art network inference algorithms representing distinctive mathematical paradigms. The performances of such network reconstruction methodologies are uncovered under various experimental conditions. We report that the algorithms do not benefit equally from data increments. Furthermore, at least for the studied rhythmic system, it is more profitable for network inference strategies to be run on long time series rather than short time series with multiple perturbations. By contrast, for the non-rhythmic systems, increasing the number of perturbation experiments yielded better results than increasing the sampling frequency. We expect that future benchmark and algorithm design would integrate such multifactorial considerations to promote their widespread and conscientious usage. [less ▲]

Dynamic controllers for column synchronization of rotation matrices: a QR-factorization approach

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 ▲]

A lifting method for analyzing distributed synchronization on the unit sphere

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 ▲]

Experimental design trade-offs for gene regulatory network inference: an in silico study of the yeast Saccharomyces cerevisiae cell cycle

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 ▲]

A geodesic feedback law to decouple the full and reduced attitude

in Systems and Control Letters (2017), 102

This paper presents a novel approach to the problem of almost global attitude stabilization. The reduced attitude is steered along a geodesic path on the n−1-sphere. Meanwhile, the full attitude is ... [more ▼]

This paper presents a novel approach to the problem of almost global attitude stabilization. The reduced attitude is steered along a geodesic path on the n−1-sphere. Meanwhile, the full attitude is stabilized on SO(n). This action, essentially two maneuvers in sequel, is fused into one smooth motion. Our algorithm is useful in applications where stabilization of the reduced attitude takes precedence over stabilization of the full attitude. A two parameter feedback gain affords further trade-offs between the full and reduced attitude convergence speed. The closed loop kinematics on SO(3) are solved for the states as functions of time and the initial conditions, providing precise knowledge of the transient dynamics. The exact solutions also help us to characterize the asymptotic behavior of the system such as establishing the region of attraction by straightforward evaluation of limits. The geometric flavor of these ideas is illustrated by a numerical example. [less ▲]

Global and invariant aspects of consensus on the n-sphere

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 ▲]