On classical state space realizability of bilinear inout-output differential equations

This paper studies the realizability property of continuous-time bilinear i/o equations in the classical state space form. Constraints on the parameters of the bilinear i/o model are suggested that lead to realizable models. The paper proves that the 2nd order bilinear i/o differential equation, unlike the discrete-time case, is always realizable in the classical state space form. The complete list of 3rd and 4th order realizable i/o bilinear models is given and two subclasses of realizable i/o bilinear systems are suggested. Our conditions rely basically upon the property that certain combinations of coefficients of the i/o equations are zero or not zero. We provide explicit state equations for all realizable 2nd and 3rd order bilinear i/o equations, and for one realizable subclass of bilinear i/o equations of arbitrary orde

Measuring the gravitational field in General Relativity: From deviation equations and the gravitational compass to relativistic clock gradiometry

How does one measure the gravitational field? We give explicit answers to this fundamental question and show how all components of the curvature tensor, which represents the gravitational field in Einstein's theory of General Relativity, can be obtained by means of two different methods. The first method relies on the measuring the accelerations of a suitably prepared set of test bodies relative to the observer. The second methods utilizes a set of suitably prepared clocks. The methods discussed here form the basis of relativistic (clock) gradiometry and are of direct operational relevance for applications in geodesy.Comment: To appear in "Relativistic Geodesy: Foundations and Application", D. Puetzfeld et. al. (eds.), Fundamental Theories of Physics, Springer 2018, 52 pages, in print. arXiv admin note: text overlap with arXiv:1804.11106, arXiv:1511.08465, arXiv:1805.1067

State space realization of bilinear continuous-time input0output equations

This paper studies the realizability property of continuous-time bilinear input-output (i/o) equations in the classical state space form. Constraints on the parameters of the bilinear i/o model are suggested that lead to realizable models. The paper proves that the 2nd order bilinear i/o differential equation, unlike the discrete-time case, is always realizable in the classical state space form. The complete list of 3rd and 4th order realizable i/o bilinear models is given and two subclasses of realizable i/o bilinear systems are suggested. Our conditions rely basically upon the property that certain combinations of coefficients of the i/o equations are zero or not zero. We provide explicit state equations for all realizable 2nd and 3rd order bilinear i/o equations, and for one realizable subclass of bilinear i/o equations of arbitrary order

Realization of nonlinear composite systems

The paper studies the realization problem for series and parallel connections of nonlinear single-input single-output systems, described by higher order differential equations. Necessary and sufficient conditions are given for the existence of the classical state space realization in both cases. It is proved that post- and parallel compensators are of no help in overcoming non-realizability. Results are illustrated by an example

Weak reachability and controllability of discrete-time nonlinear systems: generic approach and singular points

International audienceThe paper finds the singular points from which (to which) the generically accessible system is not weakly reachable (controllable) in k steps. These points are found with the help of the space of vector fields, being the discrete-time analogue of the strong accessibility distribution. Unlike in the continuous-time case, a separate object is needed to find the singular points related to weak reachability

Weak reachability and controllability of discrete-time nonlinear systems: generic approach and singular points

International audienceThe paper finds the singular points from which (to which) the generically accessible system is not weakly reachable (controllable) in k steps. These points are found with the help of the space of vector fields, being the discrete-time analogue of the strong accessibility distribution. Unlike in the continuous-time case, a separate object is needed to find the singular points related to weak reachability

Characterising the RNA-binding protein atlas of the mammalian brain uncovers RBM5 misregulation in mouse models of Huntington’s disease

Abstract RNA-binding proteins (RBPs) are key players regulating RNA processing and are associated with disorders ranging from cancer to neurodegeneration. Here, we present a proteomics workflow for large-scale identification of RBPs and their RNA-binding regions in the mammalian brain identifying 526 RBPs. Analysing brain tissue from males of the Huntington’s disease (HD) R6/2 mouse model uncovered differential RNA-binding of the alternative splicing regulator RBM5. Combining several omics workflows, we show that RBM5 binds differentially to transcripts enriched in pathways of neurodegeneration in R6/2 brain tissue. We further find these transcripts to undergo changes in splicing and demonstrate that RBM5 directly regulates these changes in human neurons derived from embryonic stem cells. Finally, we reveal that RBM5 interacts differently with several known huntingtin interactors and components of huntingtin aggregates. Collectively, we demonstrate the applicability of our method for capturing RNA interactor dynamics in the contexts of tissue and disease