Solving large sparse linear systems in a grid environment: the GREMLINS code versus the PETSc library

Solving large sparse linear systems is essential in numerous scientific domains. Several algorithms, based on direct or iterative methods, have been developed for parallel architectures. On distributed grids consisting of processors located in distant geographical sites, their performance may be unsatisfactory because they suffer from too many synchronizations and communications. The GREMLINS code has been developed for solving large sparse linear systems on distributed grids. It implements the multisplitting method that consists in splitting the original linear system into several subsystems that can be solved independently. In this paper, the performance of the GREMLINS code obtained with several libraries for solving the linear subsystems is analyzed. Its performance is also compared with that of the widely used PETSc library that enables one to develop portable parallel applications. Numerical experiments have been carried out both on local clusters and on distributed grids.     

ISS-Lyapunov functions for time-varying hyperbolic systems of balance laws

A family of time-varying hyperbolic systems of balance laws is considered. The partial differential equations of this family can be stabilized by selecting suitable boundary conditions. For the stabilized systems, the classical technique of construction of Lyapunov functions provides a function which is a weak Lyapunov function in some cases, but is not in others. We transform this function through a strictification approach to obtain a time-varying strict Lyapunov function. It allows us to establish asymptotic stability in the general case and a robustness property with respect to additive disturbances of input-to-state stability (ISS) type. Two examples illustrate the results.     

A state dependent sampling for linear state feedback

In this work, a new state-dependent sampling control enlarges the sampling intervals of state feedback control. We consider the case of linear time invariant systems and guarantee the exponential stability of the system origin for a chosen decay rate. The approach is based on LMIs obtained thanks to sufficient Lyapunov–Razumikhin stability conditions and follows two steps. In the first step, we compute a Lyapunov–Razumikhin function that guarantees exponential stability for all time-varying sampling intervals up to some given bound. This value can be used as a lower-bound of the state-dependent sampling function. In a second step, an off-line computation provides a mapping from the state-space into the set of sampling intervals: the state is divided into a finite number of regions, and to each of these regions is associated an allowable upper-bound of the sampling intervals that will guarantee the global (exponential or asymptotic) stability of the system. The results are based on sufficient conditions obtained using convex polytopes. Therefore, they involve some conservatism with respect to necessary and sufficient conditions. However, at each of the two steps, an optimization on the sampling upper-bounds is proposed. The approach is illustrated with numerical examples from the literature for which the number of actuations is shown to be reduced with respect to the periodic sampling case.     

Genetic programming for multibiometrics

Biometric systems suffer from some drawbacks: a biometric system can provide in general good performances except with some individuals as its performance depends highly on the quality of the capture… One solution to solve some of these problems is to use multibiometrics where different biometric systems are combined together (multiple captures of the same biometric modality, multiple feature extraction algorithms, multiple biometric modalities…). In this paper, we are interested in score level fusion functions application (i.e., we use a multibiometric authentication scheme which accept or deny the claimant for using an application). In the state of the art, the weighted sum of scores (which is a linear classifier) and the use of an SVM (which is a non linear classifier) provided by different biometric systems provide one of the best performances. We present a new method based on the use of genetic programming giving similar or better performances (depending on the complexity of the database). We derive a score fusion function by assembling some classical primitives functions (+, ∗, −, … ). We have validated the proposed method on three significant biometric benchmark datasets from the state of the art.     

On the probabilistic-deterministic transition involved in a fragmentation process of brittle materials

Dynamic loadings produce high stress waves leading to the fragmentation of brittle materials such as ceramics, concrete, glass and rocks. The main mechanism used to explain the change of the number of fragments with stress rate is a shielding phenomenon. However, under quasi-static loading conditions, a weakest link hypothesis may be applicable. Therefore, depending on the local strain or stress rate, different fragmentation regimes are observed. One regime corresponds to single fragmentation for which a probabilistic approach is needed. Conversely, the multiple fragmentation regime may be described by a deterministic approach. The transition between the two fragmentation regimes is discussed for high performance concrete, glass and SiC ceramics.     

Monitoring of slow ground deformation by ERS radar interferometry on the Vauvert salt mine (France): Comparison with ground-based measurement

The differential SAR Interferometry (DInSAR) technique has been applied to a test site near Vauvert (France) to detect and monitor ground deformation. This site corresponds to the location of an industrial exploitation of underground salt using the solution mining technique. An area of subsidence has been observed using in situ measurements. Despite conditions unfavorable for InSAR because of the vegetal cover, we show that radar remote sensing observations provide valuable information which substantially improves our knowledge of the phenomenon. An adaptive phase filtering process has been used to improve the coherence level. In particular, our study shows that the geometry of the subsidence bowl is different to that previously assumed using ground-based techniques only. The size of the subsidence bowl (8 km) is larger than expected. This information will be useful for further modeling of the deformation and to improve the coverage of the in situ measurement networks. It also shows that radar interferometry can be used for the long-term monitoring of such sites and to predict potential environmental issues.     

A note on finding all homogeneous set sandwiches

A module is a set of vertices H of a graph G=(V,E) such that each vertex of V?H is either adjacent to all vertices of H or to none of them. A homogeneous set is a nontrivial module. A graph G_s=(V,E_s) is a sandwich for a pair of graphs G_t=(V,E_t) and G=(V,E) if E_t⊆E_s⊆E. In a recent paper, Tang et al. [Inform. Process. Lett. 77 (2001) 17-22] described an O(Δn²) algorithm for testing the existence of a homogeneous set in sandwich graphs of G_t=(V,E_t) and G=(V,E) and then extended it to an enumerative algorithm computing all these possible homogeneous sets. In this paper, we invalidate this latter algorithm by proving there are possibly exponentially many such sets, even if we restrict our attention to strong modules. We then give a correct characterization of a homogeneous set of a sandwich graph.     

Experience with a Hybrid Processor: K-Means Clustering

We discuss hardware/software co-processing on a hybrid processor for a compute- and data-intensive multispectral imaging algorithm, k-means clustering. The experiments are performed on two models of the Altera Excalibur board, the first using the soft IP core 32-bit NIOS 1.1 RISC processor, and the second with the hard IP core ARM processor. In our experiments, we compare performance of the sequential k-means algorithm with three different accelerated versions. We consider granularity and synchronization issues when mapping an algorithm to a hybrid processor. Our results show that speedup of 11.8X is achieved by migrating computation to the Excalibur ARM hardware/software as compared to software only on a Gigahertz Pentium III. Speedup on the Excalibur NIOS is limited by the communication cost of transferring data from external memory through the processor to the customized circuits. This limitation is overcome on the Excalibur ARM, in which dual-port memories, accessible to both the processor and configurable logic, have the biggest performance impact of all the techniques studied.     

Combining FDI and AI approaches within causal-model-based diagnosis.

This paper presents a model-based diagnostic method designed in the context of process supervision. It has been inspired by both artificial intelligence and control theory. AI contributes tools for qualitative modeling, including causal modeling, whose aim is to split a complex process into elementary submodels. Control theory, within the framework of fault detection and isolation (FDI), provides numerical models for generating and testing residuals, and for taking into account inaccuracies in the model, unknown disturbances and noise. Consistency-based reasoning provides a logical foundation for diagnostic reasoning and clarifies fundamental assumptions, such as single fault and exoneration. The diagnostic method presented in the paper benefits from the advantages of all these approaches. Causal modeling enables the method to focus on sufficient relations for fault isolation, which avoids combinatorial explosion. Moreover, it allows the model to be modified easily without changing any aspect of the diagnostic algorithm. The numerical submodels that are used to detect inconsistency benefit from the precise quantitative analysis of the FDI approach. The FDI models are studied in order to link this method with DX component-oriented reasoning. The recursive on-line use of this algorithm is explained and the concept of local exoneration is introduced.