Embedding fault-free cycles in crossed cubes with conditional link faults

The crossed cube, which is a variation of the hypercube, possesses some properties that are superior to those of the hypercube. In this paper, we show that with the assumption of each node incident with at least two fault-free links, an n-dimensional crossed cube with up to 2n−5 link faults can embed, with dilation one, fault-free cycles of lengths ranging from 4 to 2 ⁿ . The assumption is meaningful, for its occurrence probability is very close to 1, and the result is optimal with respect to the number of link faults tolerated. Consequently, it is very probable that algorithms executable on rings of lengths ranging from 4 to 2 ⁿ can be applied to an n-dimensional crossed cube with up to 2n−5 link faults.

Stochastic allocation and scheduling for conditional task graphs in multi-processor systems-on-chip

Embedded systems designers are turning to multicore architectures to satisfy the ever-growing computational needs of applications within a reasonable power envelope. One of the most daunting challenges for MultiProcessor System-on-Chip (MPSoC) platforms is the development of tools for efficient mapping multi-task applications onto hardware platforms. Software mapping can be formulated as an optimal allocation and scheduling problem, where the application is modeled as a task graph, the target hardware is modeled as a set of heterogeneous resources, and the objective function represents a design goal α (e.g. minimum execution time, minimum usage of communication resources, etc.). Conditional task graphs, where inter-task edges represent data as well as control dependencies, are a well-known computational model to describe complex real-life applications where alternative execution paths, guarded by conditionals, can be specified. Each condition has a probability associated with each possible outcome.     

Analytical modeling and comparison of fault-tolerant message flow control mechanisms in torus-connected networks

In many environments, rather than minimizing message latency or maximizing network performance, the ability to survive beyond the failure of individual network components is the main issue of interests. The nature of Wormhole Switching (WS) leads to high network throughput and low message latencies. However, in the vicinity of faulty regions, these behaviors cause rapid congestion, provoking the network becomes deadlocked. While techniques such as adaptive routing can alleviate the problem, they cannot completely solve the problem. Thus, there have been extreme studies on other types of switching mechanisms in networking and multicomputers communities. In this paper, we present a general mathematical model to assess the relative performance merits of three well-known fault-tolerant switching methods in tori, namely Scouting Switching (SS), Pipelined Circuit Switching (PCS), and Circuit Switching (CS). We have carried out extensive simulation experiments, the results of which are used to validate the proposed analytical models. We have also conducted an extensive comparative performance analysis, by means of analytical modeling, of SS, PCS, and CS under various working conditions. The analytical results reveal that SS shows substantial performance improvements for low to moderate failure rates over PCS and CS, which achieves close to WS performance. PCS can provide superior performance over CS and behaves the same or in some occasions worse than SS, under light and moderate traffic, especially with the same hardware requirements.     

Optimal Control of Systems with Random Gain of Plant †

A theoretical study is made of optimizing an nth order system which has a random variation of gain of the plant of (a) Gaussian white noise, or (b) generalized Poisson process. The problem is formulated by dynamic programming.     

Security control of positive semi‑Markovian jump systems with actuator faults

Actuator faults usually cause security problem in practice. This paper is concerned with the security control of positive semi-Markovian jump systems with actuator faults. The considered systems are with mode transition-dependent sojourntime distributions, which may also lead to actuator faults. First, the time-varying and bounded transition rate that satisfies the mode transition-dependent sojourn-time distribution is considered. Then, a stochastic co-positive Lyapunov function is constructed. Using matrix decomposition technique, a set of state-feedback controllers for positive semi-Markovian jump systems with actuator faults are designed in terms of linear programming. Under the designed controllers, stochastic stabilization of the systems with actuator faults are achieved and the security of the systems can be guaranteed. Furthermore, the proposed results are extended to positive semi-Markovian jump systems with interval and polytopic uncertainties. By virtue of a segmentation technique of the transition rates, a less conservative security control design is also proposed. Finally, numerical examples are provided to demonstrate the validity of the presented results.     

Improvement of Convergence to Steady State Solutions of Euler Equations with the WENO Schemes

The convergence to steady state solutions of the Euler equations for high order weighted essentially non-oscillatory (WENO) finite difference schemes with the Lax-Friedrichs flux splitting (Jiang and Shu, in J. Comput. Phys. 126:202–228, 1996) is investigated. Numerical evidence in Zhang and Shu (J. Sci. Comput. 31:273–305, 2007) indicates that there exist slight post-shock oscillations when we use high order WENO schemes to solve problems containing shock waves. Even though these oscillations are small in their magnitude and do not affect the “essentially non-oscillatory” property of the WENO schemes, they are indeed responsible for the numerical residue to hang at the truncation error level of the scheme instead of settling down to machine zero. Differently from the strategy adopted in Zhang and Shu (J. Sci. Comput. 31:273–305, 2007), in which a new smoothness indicator was introduced to facilitate convergence to steady states, in this paper we study the effect of the local characteristic decomposition on steady state convergence. Numerical tests indicate that the slight post-shock oscillation has a close relationship with the local characteristic decomposition process. When this process is based on an average Jacobian at the cell interface using the Roe average, as is the standard procedure for WENO schemes, such post-shock oscillation appears. If we instead use upwind-biased interpolation to approximate the physical variables including the velocity and enthalpy on the cell interface to compute the left and right eigenvectors of the Jacobian for the local characteristic decomposition, the slight post-shock oscillation can be removed or reduced significantly and the numerical residue settles down to lower values than other WENO schemes and can reach machine zero for many test cases. This new procedure is also effective for higher order WENO schemes and for WENO schemes with different smoothness indicators.     

Regularized Reconstruction of Shapes with Statistical a priori Knowledge

The reconstruction of geometry or, in particular, the shape of objects is a common issue in image analysis. Starting from a variational formulation of such a problem on a shape manifold we introduce a regularization technique incorporating statistical shape knowledge. The key idea is to consider a Riemannian metric on the shape manifold which reflects the statistics of a given training set. We investigate the properties of the regularization functional and illustrate our technique by applying it to region-based and edge-based segmentation of image data. In contrast to previous works our framework can be considered on arbitrary (finite-dimensional) shape manifolds and allows the use of Riemannian metrics for regularization of a wide class of variational problems in image processing.     

Registration of Anatomical Images Using Paths of Diffeomorphisms Parameterized with Stationary Vector Field Flows

Computational Anatomy aims for the study of variability in anatomical structures from images. Variability is encoded by the spatial transformations existing between anatomical images and a template selected as reference. In the absence of a more justified model for inter-subject variability, transformations are considered to belong to a convenient family of diffeomorphisms which provides a suitable mathematical setting for the analysis of anatomical variability. One of the proposed paradigms for diffeomorphic registration is the Large Deformation Diffeomorphic Metric Mapping (LDDMM). In this framework, transformations are characterized as end points of paths parameterized by time-varying flows of vector fields defined on the tangent space of a Riemannian manifold of diffeomorphisms and computed from the solution of the non-stationary transport equation associated to these flows. With this characterization, optimization in LDDMM is performed on the space of non-stationary vector field flows resulting into a time and memory consuming algorithm. Recently, an alternative characterization of paths of diffeomorphisms based on constant-time flows of vector fields has been proposed in the literature. With this parameterization, diffeomorphisms constitute solutions of stationary ODEs. In this article, the stationary parameterization is included for diffeomorphic registration in the LDDMM framework. We formulate the variational problem related to this registration scenario and derive the associated Euler-Lagrange equations. Moreover, the performance of the non-stationary vs the stationary parameterizations in real and simulated 3D-MRI brain datasets is evaluated. Compared to the non-stationary parameterization, our proposal provides similar results in terms of image matching and local differences between the diffeomorphic transformations while drastically reducing memory and time requirements.     

Tripartite entanglement of a spin star model with Dzialoshinski–Moriya interaction

The effect of Dzialoshinski–Moriya (DM) interaction on the tripartite thermal entanglement of a spin-star model with four spins has been analyzed by an entanglement measure of the tripartite negativity. Our results imply that the tripartite thermal entanglement can be established among the three surrounding parties which do not interact with each other but interact with the central party independently. From the results, we find that the strong DM interaction can enhance the tripartite thermal entanglement while the high temperature can shrink it. The effect of the inhomogeneous coupling on the tripartite thermal entanglement is also discussed.     

Topological and Variational Properties of a Model for the Reconstruction of Three-Dimensional Transparent Images with Self-Occlusions

We introduce and study a two-dimensional variational model for the reconstruction of a smooth generic solid shape E, which may handle the self-occlusions and that can be considered as an improvement of the 2.1D sketch of Nitzberg and Mumford (Proceedings of the Third International Conference on Computer Vision, Osaka, 1990). We characterize from the topological viewpoint the apparent contour of E, namely, we characterize those planar graphs that are apparent contours of some shape E. This is the classical problem of recovering a three-dimensional layered shape from its apparent contour, which is of interest in theoretical computer vision. We make use of the so-called Huffman labeling (Machine Intelligence, vol. 6, Am. Elsevier, New York, 1971), see also the papers of Williams (Ph.D. Dissertation, 1994 and Int. J. Comput. Vis. 23:93–108, 1997) and the paper of Karpenko and Hughes (Preprint, 2006) for related results. Moreover, we show that if E and F are two shapes having the same apparent contour, then E and F differ by a global homeomorphism which is strictly increasing on each fiber along the direction of the eye of the observer. These two topological theorems allow to find the domain of the functional ℱ describing the model. Compactness, semicontinuity and relaxation properties of ℱ are then studied, as well as connections of our model with the problem of completion of hidden contours.

Optimal control of distributed parameter systems with discrete constrained inputs†

The optimal control of linear distributed parameter systems, which are represent able by a linear vector integral equation, is investigated. Restricting the control action to be discrete in time, the problem of minimizing the mean-square error, between specified desired final state functions and the actual state functions at a prescribed final time, subject to an energy constraint on the controlling functions, is treated. A necessary and sufficient condition from functional analysis is used to derive an equation whose solution yields the optimal control vector. Two convergence properties for the discrete problem are established which can be used to determine a good approximate solution to the corresponding measurable optimal control problem. An illustrative example is given.     

Optimal Error Estimates of the Legendre Tau Method for Second-Order Differential Equations

In this paper, we prove that the Legendre tau method has the optimal rate of convergence in L ²-norm, H ¹-norm and H ²-norm for one-dimensional second-order steady differential equations with three kinds of boundary conditions and in C([0,T];L ²(I))-norm for the corresponding evolution equation with the Dirichlet boundary condition. For the generalized Burgers equation, we develop a Legendre tau-Chebyshev collocation method, which can also be optimally convergent in C([0,T];L ²(I))-norm. Finally, we give some numerical examples.     

Preemption-light multiprocessor scheduling of sporadic tasks with high utilisation bound

Known algorithms capable of scheduling implicit-deadline sporadic tasks over identical processors at up to 100% utilisation invariably involve numerous preemptions and migrations. To the challenge of devising a scheduling scheme with as few preemptions and migrations as possible, for a given guaranteed utilisation bound, we respond with the algorithm NPS-F. It is configurable with a parameter, trading off guaranteed schedulable utilisation (up to 100%) vs preemptions. For any possible configuration, NPS-F introduces fewer preemptions than any other known algorithm matching its utilisation bound.     

Simulation of a helicopter’s main gearbox semiactive suspension with bond graphs

This paper presents a bond graph model of a helicopter’s semiactive suspension and the associated simulations. The structural and modular approach proposed with bond graph permits a systematic modeling of mechatronic multibody systems. This approach was carried out thanks to the use of the singular perturbation method, which is a variant of penalty formulation. The model is then built as an assembly of components or modules (rigid bodies and compliant kinematic joints) by following the structure of the actual system.The bond graph model of the passive suspension with fixed flapping masses has been verified with another multibody tool for three different excitations (pumping, roll, and yaw). Next, the passive model, augmented with electrical actuators and controllers, is called the semiactive suspension model. Simulations on the semiactive suspension model have been conducted.     

Fault diagnosis for a class of active suspension systems with dynamic actuators’ faults

In this paper, a new fault diagnosis and fault-tolerant control method for a class of active suspension systems with actuator faults is proposed. The considered actuators have uncertain dynamic characteristics, which are the electromagnetic actuators made up with a motor control system and a ball screw transmission mechanism. To detect such suspension system actuator faults, dynamic fault diagnosis observers are designed for the actuators to estimate the possible faults. The actuators are analyzed to first and second order dynamic models, respectively, whose output can be measured but the rate is non-measurable. Then, the fault diagnosis method is developed for these two kinds of models to obtain the fault information. Using the fault estimation and adaptive control technique, a robust fault-tolerant controller is constructed to guarantee the performance of the rail vehicles in the faulty case. Finally, using the parameters of a practical suspension system, a simulation study is conducted to show the effectiveness of the proposed method.     

On the application of the minimum polynomial extrapolation method to incompressible flows with heat transfer

In this paper, the Minimum Polynomial Extrapolation method (MPE) is used to accelerate the convergence of the Characteristic–Based–Split (CBS) scheme for the numerical solution of steady state incompressible flows with heat transfer. The CBS scheme is a fractional step method for the solution of the Navier–Stokes equations while the MPE method is a vector extrapolation method which transforms the original sequence into another sequence converging to the same limit faster then the original one without the explicit knowledge of the sequence generator. The developed algorithm is tested on a two-dimensional benchmark problem (buoyancy–driven convection problem) where the Navier–Stokes equations are coupled with the temperature equation. The obtained results show the feature of the extrapolation procedure to the CBS scheme and the reduction of the computational time of the simulation.     

Optimal Management of a Bioreactor for Eutrophicated Water Treatment: A Numerical Approach

This paper presents a numerical algorithm for computing the optimal design variables in the management of a bioreactor for the treatment of eutrophicated water: initial and distributed quantities of phytoplankton added along the process, and total duration of the process. This real-world problem is formulated as a state-control constrained optimal control problem, whose numerical resolution is the main aim of this study. After discretizing the control problem, we present a structured algorithm for solving the discrete state systems, computing the corresponding derivatives, and minimizing the objective function. Finally, the good performance of the algorithm is shown by applying it to a realistic example with two pre-reservoirs.     

Energetically consistent simulation of simultaneous impacts and contacts in multibody systems with friction

This paper presents a methodology for treating energy consistency when considering simultaneous impacts and contacts with friction in the simulation of systems of interconnected bodies. Hard impact and contact is considered where deformation of the impacting surfaces is negligible. The proposed approach uses a discrete algebraic model of impact in conjunction with moment and tangential coefficients of restitution (CORs) to develop a general impact law for determining post-impact velocities. This process depends on impulse–momentum theory, the complementarity conditions, a principle of maximum dissipation, and the determination of contact forces and post-impact accelerations. The proposed methodology also uses an energy-modifying COR to directly control the system’s energy profile over time. The key result is that different energy profiles yield different results and thus energy consistency should be considered carefully in the development of dynamic simulations. The approach is illustrated on a double pendulum, considered to be a benchmark case, and a bicycle structure.