Empirical evaluation of accuracy of mathematical software used for availability assessment of fault-tolerant computer systems

Dependability assessment is typically based on complex probabilistic models. Markov and semi-Markov models are widely used to model dependability of complex hardware/software architectures. Solving such models, especially when they are stiff, is not trivial and is usually done using sophisticated mathematical software packages. We report a practical experience of comparing the accuracy of solutions stiff Markov models obtained using well known commercial and research software packages. The study is conducted on a contrived but realistic cases study of computer system with hardware redundancy and diverse software under the assumptions that the rate of failure of software may vary over time, a realistic assumption. We observe that the disagreement between the solutions obtained with the different packages may be very significant. We discuss these findings and directions for future research

Do not be afraid of local minima: affine shaker and particle swarm

Stochastic local search techniques are powerful and flexible methods to optimize difficult functions. While each method is characterized by search trajectories produced through a randomized selection of the next step, a notable difference is caused by the interaction of different searchers, as exemplified by the Particle Swarm methods. In this paper we evaluate two extreme approaches, Particle Swarm Optimization, with interaction between the individual "cognitive" component and the "social" knowledge, and Repeated Affine Shaker, without any interaction between searchers but with an aggressive capability of scouting out local minima. The results, unexpected to the authors, show that Affine Shaker provides remarkably efficient and effective results when compared with PSO, while the advantage of Particle Swarm is visible only for functions with a very regular structure of the local minima leading to the global optimum and only for specific experimental conditions

Real-time simulation of three-dimensional shoulder girdle and arm dynamics

Electrical stimulation is a promising technology for the restoration of arm function in paralyzed individuals. Control of the paralyzed arm under electrical stimulation, however, is a challenging problem that requires advanced controllers and command interfaces for the user. A real-time model describing the complex dynamics of the arm would allow user-in-the-loop type experiments where the command interface and controller could be assessed. Real-time models of the arm previously described have not included the ability to model the independently controlled scapula and clavicle, limiting their utility for clinical applications of this nature. The goal of this study therefore was to evaluate the performance and mechanical behavior of a real-time, dynamic model of the arm and shoulder girdle. The model comprises seven segments linked by eleven degrees of freedom and actuated by 138 muscle elements. Polynomials were generated to describe the muscle lines of action to reduce computation time, and an implicit, first-order Rosenbrock formulation of the equations of motion was used to increase simulation step-size. The model simulated flexion of the arm faster than real time, simulation time being 92% of actual movement time on standard desktop hardware. Modeled maximum isometric torque values agreed well with values from the literature, showing that the model simulates the moment-generating behavior of a real human arm. The speed of the model enables experiments where the user controls the virtual arm and receives visual feedback in real time. The ability to optimize potential solutions in simulation greatly reduces the burden on the user during development

Development of the adjoint of GEOS-Chem

We present the adjoint of the global chemical transport model GEOS-Chem, focusing on the chemical and thermodynamic relationships between sulfate – ammonium – nitrate aerosols and their gas-phase precursors. The adjoint model is constructed from a combination of manually and automatically derived discrete adjoint algorithms and numerical solutions to continuous adjoint equations. Explicit inclusion of the processes that govern secondary formation of inorganic aerosol is shown to afford efficient calculation of model sensitivities such as the dependence of sulfate and nitrate aerosol concentrations on emissions of SOx, NOx, and NH3. The adjoint model is extensively validated by comparing adjoint to finite difference sensitivities, which are shown to agree within acceptable tolerances; most sets of comparisons have a nearly 1:1 correlation and R2>0.9. We explore the robustness of these results, noting how insufficient observations or nonlinearities in the advection routine can degrade the adjoint model performance. The potential for inverse modeling using the adjoint of GEOS-Chem is assessed in a data assimilation framework through a series of tests using simulated observations, demonstrating the feasibility of exploiting gas- and aerosol-phase measurements for optimizing emission inventories of aerosol precursors

Numerical study of cancer cell invasion dynamics using adaptive mesh refinement: the urokinase model

In the present work we investigate the chemotactically and proteolytically driven tissue invasion by cancer cells. The model employed is a system of advection-reaction-diffusion equations that features the role of the serine protease urokinase-type plasminogen activator. The analytical and numerical study of this system constitutes a challenge due to the merging, emerging, and travelling concentrations that the solutions exhibit. Classical numerical methods applied to this system necessitate very fine discretization grids to resolve these dynamics in an accurate way. To reduce the computational cost without sacrificing the accuracy of the solution, we apply adaptive mesh refinement techniques, in particular h-refinement. Extended numerical experiments exhibit that this approach provides with a higher order, stable, and robust numerical method for this system. We elaborate on several mesh refinement criteria and compare the results with the ones in the literature. We prove, for a simpler version of this model, $L^\infty$ bounds for the solutions, we study the stability of its conditional steady states, and conclude that it can serve as a test case for further development of mesh refinement techniques for cancer invasion simulations