STOCHASTIC DYNAMICS OF CELL LINEAGE IN TISSUE HOMEOSTASIS.

During epithelium tissue maintenance, lineages of cells differentiate and proliferate in a coordinated way to provide the desirable size and spatial organization of different types of cells. While mathematical models through deterministic description have been used to dissect role of feedback regulations on tissue layer size and stratification, how the stochastic effects influence tissue maintenance remains largely unknown. Here we present a stochastic continuum model for cell lineages to investigate how both layer thickness and layer stratification are affected by noise. We find that the cell-intrinsic noise often causes reduction and oscillation of layer size whereas the cell-extrinsic noise increases the thickness, and sometimes, leads to uncontrollable growth of the tissue layer. The layer stratification usually deteriorates as the noise level increases in the cell lineage systems. Interestingly, the morphogen noise, which mixes both cell-intrinsic noise and cell-extrinsic noise, can lead to larger size of layer with little impact on the layer stratification. By investigating different combinations of the three types of noise, we find the layer thickness variability is reduced when cell-extrinsic noise level is high or morphogen noise level is low. Interestingly, there exists a tradeoff between low thickness variability and strong layer stratification due to competition among the three types of noise, suggesting robust layer homeostasis requires balanced levels of different types of noise in the cell lineage systems

A HYBRID METHOD FOR STIFF REACTION-DIFFUSION EQUATIONS.

The second-order implicit integration factor method (IIF2) is effective at solving stiff reaction-diffusion equations owing to its nice stability condition. IIF has previously been applied primarily to systems in which the reaction contained no explicitly time-dependent terms and the boundary conditions were homogeneous. If applied to a system with explicitly time-dependent reaction terms, we find that IIF2 requires prohibitively small time-steps, that are relative to the square of spatial grid sizes, to attain its theoretical second-order temporal accuracy. Although the second-order implicit exponential time differencing (iETD2) method can accurately handle explicitly time-dependent reactions, it is more computationally expensive than IIF2. In this paper, we develop a hybrid approach that combines the advantages of both methods, applying IIF2 to reaction terms that are not explicitly time-dependent and applying iETD2 to those which are. The second-order hybrid IIF-ETD method (hIFE2) inherits the lower complexity of IIF2 and the ability to remain second-order accurate in time for large time-steps from iETD2. Also, it inherits the unconditional stability from IIF2 and iETD2 methods for dealing with the stiffness in reaction-diffusion systems. Through a transformation, hIFE2 can handle nonhomogeneous boundary conditions accurately and efficiently. In addition, this approach can be naturally combined with the compact and array representations of IIF and ETD for systems in higher spatial dimensions. Various numerical simulations containing linear and nonlinear reactions are presented to demonstrate the superior stability, accuracy, and efficiency of the new hIFE method

Co-Simulation in Virtual Verification of Vehicles with Mechatronic Systems

In virtual verification of vehicle and mechatronic systems, a mixture of subsystems are integrated numerically in an offline simulation or integrated physically in a hardware-in-loop (HIL) simulation. This heterogeneous engineering approach is crucial for system-level development and widely spreads with\ua0the industrial standard, e.g. Functional Mock-Up Interface (FMI) standard.For the engineers, not only the local subsystem and solver should be known,\ua0but also the global coupled dynamic system and its coupling effect need to be\ua0understood. Both the local and global factors influence the stability, accuracy, numerical efficiency and further on the real-time simulation capability.In this thesis, the explicit parallel co-simulation, which is the most common and closest to the integration with a physical system, is investigated.In the vehicle development, the vehicle and the mechatronic system, e.g. an\ua0Electrcial Power Assisted Steering (EPAS) system can be simulated moreefficiently by a tailored solver and communicative step. The accuracy and\ua0numerical stability problem, which highly depends on the interface dynamics, can be investigated similarly in the linear robust control framework. The\ua0vehicle-mechatronic system should be coupled to give a smaller loop gain for robustness and stability. Physically, it indicates that the splitting part\ua0should be less stiff and the force or torque variable should be applied towardsthe part with a higher impedance in the force-displacement coupling. Furthermore, to compensate the troublesome low-passed and delay effect fromthe coupling, a new coupling method based on H∞ synthesis is developed,\ua0which can improve the accuracy of co-simulation. The method shows robustness to the system dynamics, which makes it more applicable for a complex\ua0vehicle-mechatronic system

Virtual prototyping of vehicular electric steering assistance system using co-simulations

Virtual prototyping is a practical necessity in vehicle system development. From desktop simulation to track testing, several simulation approaches, such as co-simulation and hardware-in-loop (HIL) simulation, are used. However, due to interfacing problems, the consistency of testing results may not be ensured. Correspondingly, inherent inaccuracies result from numerical coupling error and non-transparent HIL interface, which involves control tracking error, delay error, and attached hardware and noise effects. This work aims to resolve these problems and provide seamless virtual prototypes for vehicle and electric power-assisted steering (EPAS) system development.The accuracy and stability of explicit parallel co-simulation and HIL simulation are investigated. The imperfect factors propagate in the simulation tools like perturbations, yield inaccuracy, and even instability according to system dynamics. Hence, reducing perturbations (coupling problem) and improving system robustness (architecture problem) are considered.In the coupling problem, a delay compensation method relying on adaptive filters is developed for real-time simulation. A novel co-simulation coupling method on H-infinity synthesis is developed to improve accuracy for a wide frequency range and achieve low computational cost. In the architecture problem, a force(torque)-velocity coupling approach is employed. The application of a force (torque) variable to a component with considerable impedance, e.g., the steering rack (EPAS motor), yields a small loop gain as well as robust co-simulation and HIL simulation. On a given EPAS HIL system, an interface algorithm is developed for virtually shifting the impedance, thus enhancing system robustness.The theoretical findings and formulated methods are tested on generic benchmarks and implemented on a vehicle-EPAS engineering case. In addition to the acceleration of simulation speed, accuracy and robustness are also improved. Consequently, consistent testing results and extended validated ranges of virtual prototypes are obtained

Magnitude estimation for early warning applications using the initial part of P waves: A case study on the 2008 Wenchuan sequence

A period parameter τ_c and an amplitude parameter Pd determined from the very beginning of P wave are important for earthquake early warning (EEW), yet their dependence on source mechanism, focal depth and epicentral distance has not been fully studied. After the devastating Mw7.9 Wenchuan earthquake, hundreds of M4-6 earthquakes occurred with diverse focal mechanisms and depth range of 2–20 km. We calculate τ_c and Pd of these aftershocks and examine their dependence on magnitude, τ_c, distance, and depth. We find that τ_c correlates well with magnitude, but joint regression including distance and depth does not significantly improve the correlation. The effect of focal mechanism on the τ_c-magnitude correlation is not obvious. When P wave is nodal, τ_c measurement becomes inaccurate. Also, τ_c is systematically greater for slow earthquakes, leading to a possible false alarm. Thus, more studies are required to discriminate slow earthquakes for robust early warning

Service Selection of Ensuring Transactional Reliability and QoS for Web Service Composition

Service-Oriented Architecture (SOA) provides a flexible framework of service composition. Using standard-based protocols, composite service can be constructed by integrating component services independently. As component services are developed by different organization and offer diverse transactional properties and QoS characteristics, it is a challenging problem how to select suitable component services which ensure reliable execution of composite Web service and construct the optimal composite Web service. In this paper, we propose a selection approach that combines transactional properties of ensuring reliability and QoS characteristics. In the selection approach, we build automaton model to implement transactional-aware service selection and use the model to guarantee reliable execution of composite Web service. We also define aggregation functions, and use a Multiple-Attribute Decision-Making approach for the utility function to achieve Qos-based optimal service selection. Finally, two scenarios of experiments are presented to demonstrate the validity of the selection approach