Disentangling direct from indirect relationships in association networks

Networks are vital tools for understanding and modeling interactions in complex systems in science and engineering, and direct and indirect interactions are pervasive in all types of networks. However, quantitatively disentangling direct and indirect relationships in networks remains a formidable task. Here, we present a framework, called iDIRECT (Inference of Direct and Indirect Relationships with Effective Copula-based Transitivity), for quantitatively inferring direct dependencies in association networks. Using copula-based transitivity, iDIRECT eliminates/ameliorates several challenging mathematical problems, including ill-conditioning, self-looping, and interaction strength overflow. With simulation data as benchmark examples, iDIRECT showed high prediction accuracies. Application of iDIRECT to reconstruct gene regulatory networks in Escherichia coli also revealed considerably higher prediction power than the best-performing approaches in the DREAM5 (Dialogue on Reverse Engineering Assessment and Methods project, #5) Network Inference Challenge. In addition, applying iDIRECT to highly diverse grassland soil microbial communities in response to climate warming showed that the iDIRECT-processed networks were significantly different from the original networks, with considerably fewer nodes, links, and connectivity, but higher relative modularity. Further analysis revealed that the iDIRECT-processed network was more complex under warming than the control and more robust to both random and target species removal (P < 0.001). As a general approach, iDIRECT has great advantages for network inference, and it should be widely applicable to infer direct relationships in association networks across diverse disciplines in science and engineering.

Implicit Co-Simulation and Solver-Coupling: Efficient Calculation of Interface-Jacobian and Coupling Sensitivities/Gradients

We consider implicit co-simulation and solver-coupling methods, where different subsystems are coupled in time domain in a weak sense. Within such weak coupling approaches, a macro-time grid is introduced. Between the macro-time points, the subsystems are integrated independently. The subsystems only exchange information at the macro-time points. To describe the connection between the subsystems, coupling variables have to be defined. For many implicit co-simulation and solver-coupling approaches an Interface-Jacobian is required. The Interface-Jacobian describes, how certain subsystem state variables at the interface depend on the coupling variables. Concretely, the Interface-Jacobian contains partial derivatives of the state variables of the coupling bodies with respect to the coupling variables. Usually, these partial derivatives are calculated numerically by means of a finite difference approach. A calculation of the coupling gradients based on finite differences may entail problems with respect to the proper choice of the perturbation parameters and may therefore cause problems due to ill-conditioning. A second drawback is that additional subsystem integrations with perturbed coupling variables have to be carried out. In this manuscript, analytical approximation formulas for the Interface-Jacobian are derived, which may be used alternatively to numerically calculated gradients based on finite differences. Applying these approximation formulas, numerical problems with ill-conditioning can be circumvented. Moreover, efficiency of the implementation may be increased, since parallel simulations with perturbed coupling variables can be omitted. The derived approximation formulas converge to the exact gradients for small macro-step sizes.

Robot calibration based on nonlinear formulation for modular reconfigurable robots (MRRs).

Developed in this thesis is a full pose kinematic calibration method for modular reconfigurable robots (MRRs). This method is based on a nonlinear formulation as opposed to the conventional linear method that has a number of critical limitations. By avoiding linearization of the nonlinear robot forward kinematic equations, these nonlinear equations are directly used to identify the robot calibration parameters. A hybrid search method is developed to solve the nonlinear error equations by combining genetic algorithms with Monte Carlo simulations to ensure a global search over the robot workspace with good accuracy. A number of comparisons are made between the proposed method and the conventional linear method, indicating the advantages of the former over the latter by eliminating two critical limitations. The first one is the orthogonality sacrifice that leads to ill-conditioning of the Jacobian used in the linear method. The second one is quadrant sensitivity during the determination of the (Tait) Bryan angles from inverting the rotation matrix.

Robot calibration based on nonlinear formulation for modular reconfigurable robots (MRRs).

Developed in this thesis is a full pose kinematic calibration method for modular reconfigurable robots (MRRs). This method is based on a nonlinear formulation as opposed to the conventional linear method that has a number of critical limitations. By avoiding linearization of the nonlinear robot forward kinematic equations, these nonlinear equations are directly used to identify the robot calibration parameters. A hybrid search method is developed to solve the nonlinear error equations by combining genetic algorithms with Monte Carlo simulations to ensure a global search over the robot workspace with good accuracy. A number of comparisons are made between the proposed method and the conventional linear method, indicating the advantages of the former over the latter by eliminating two critical limitations. The first one is the orthogonality sacrifice that leads to ill-conditioning of the Jacobian used in the linear method. The second one is quadrant sensitivity during the determination of the (Tait) Bryan angles from inverting the rotation matrix.

Adaptive Shell Spherical Reflector Actuated with PVDF-TrFE Thin Film Strain Actuators

This paper discusses the design and manufacturing of a thin polymer spherical adaptive reflector of diameter D=200 mm, controlled by an array of 25 independent electrodes arranged in a keystone configuration actuating a thin film of PVDF-TrFE in d31-mode. The 5 μm layer of electrostrictive material is spray-coated. The results of the present study confirm that the active material can be modelled by a unidirectional quadratic model and that excellent properties can be achieved if the material is properly annealed. The experimental influence functions of the control electrodes are determined by a quasi-static harmonic technique; they are in good agreement with the numerical simulations and their better circular symmetry indicates a clear improvement in the manufacturing process, as compared to a previous study. The low order optical modes can be reconstructed by combining the 25 influence functions; a regularization technique is used to alleviate the ill-conditioning of the Jacobian and allow to approximate the optical modes with reasonable voltages.

A robust LU polynomial matrix decomposition for spatial multiplexing

This paper considers time-domain spatial multiplexing in MIMO wideband system, using an LU-based polynomial matrix decomposition. Because the corresponding pre- and post-filters are not paraunitary, the noise output power is amplified and the performance of the system is degraded, compared to QR-based spatial multiplexing approach. Degradations are important as the post-filter polynomial matrix is ill-conditioned. In this paper, we introduce simple transformations on the decomposition that solve the ill-conditioning problem. We show that this results in a MIMO spatial multiplexing scheme that is robust to noise and channel estimation errors. In the latter context, the proposed LU-based beamforming compares favorably to the QR-based counterpart in terms of complexity and bit error rate.

Identifying the Cause of and Fixing Ill-Conditioned Matrices in Nuclear Analysis Codes

Many of the analytical codes used in the nuclear industry, such as TRACE, RELAP5, and PARCS, approximate the equations that model the physics via a linearized system of equations. One common difficulty when solving linearized systems is that an accurately formulated system of equations may be ill-conditioned. Ill-conditioned matrices can result in significant amplification of error leading to poor, or even invalid, results. Ill-conditioned matrices lead to some challenging issues for the analytical code developers: • An ill-conditioned matrix is often solvable, and there may be no obvious indication numerically that something has gone wrong even though numerical error is large. Thus, how can ill-conditioning be effectively detected for a matrix? • When ill-conditioning is detected, how can the source of the ill-conditioning be determined so that it can be analyzed and corrected? Ill-conditioning is fundamentally a geometric problem that can be understood with geometric concepts associated with matrices and vectors. Geometric concepts and tools, useful for understanding the cause of ill-conditioning of a matrix, are presented. A geometric understanding of ill-conditioning can point to the rows or columns of the matrix that most contribute to ill-conditioning so that the source of ill-conditioning can be analyzed and understood, and leads to techniques for building matrix preconditioners to improve the solvability of the matrix.

A robust LU polynomial matrix decomposition for spatial multiplexing

This paper considers time-domain spatial multiplexing in MIMO wideband system, using an LU-based polynomial matrix decomposition. Because the corresponding pre- and post-filters are not paraunitary, the noise output power is amplified and the performance of the system is degraded, compared to QR-based spatial multiplexing approach. Degradations are important as the post-filter polynomial matrix is ill-conditioned. In this paper, we introduce simple transformations on the decomposition that solve the ill-conditioning problem. We show that this results in a MIMO spatial multiplexing scheme that is robust to noise and channel estimation errors. In the latter context, the proposed LU-based beamforming compares favorably to the QR-based counterpart in terms of complexity and bit error rate.