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.     

A habituating blood glucose control strategy for the critically ill

In the intensive care unit patients benefit from being fed and from having well controlled glucose levels. Insulin and glucose infusion serves as manipulated inputs to regulate blood glucose, while glucose infusion serves as a sole nutritional input. In this paper, a model predictive control strategy, based on simultaneously manipulating glucose and insulin infusion, is developed to improve blood glucose regulation in intensive care unit patients. In the short term, glucose infusion is used for tighter glucose control, particularly for disturbance rejection, while, in the long-term (24 h period), glucose infusion is used to meet nutritional needs. The “habituating control” algorithm is proposed and tested against a model predictive control (MPC) strategy that only manipulates insulin. The simulation results indicate that the Habituating MPC strategy outperforms the single input–single output MPC by providing faster setpoint tracking and tighter glucose control for a patient population, and producing less glucose variability while rejecting disturbances in insulin infusion and insulin sensitivity.     

A study on the rate of degradation of the bioabsorbable polymer polyglycolic acid (PGA)

As part of a study to characterise bioabsorbable scaffolds for tissue engineering an investigation has been conducted into the rate of degradation of polyglycolic acid (PGA). This is one of the most commonly used bioabsorbable materials and has been used in sutures since the 60s and more recently in cell scaffolds, drug delivery devices and bone fixation pins. This study looks at the influence that surface-to-volume ratio i.e. thickness of material, has on degradation. By degrading various thicknesses of PGA in a buffer saline solution over 24 days and testing their properties at regular intervals, a knowledge of how surface-to-volume ratio affects degradation was developed. Properties such as weight loss, crystallinity, molecular weight and structural integrity were measured. Results showed that rate of mass loss was dependent on sample thickness but crystallinity, melting point and molecular weight were independent of thickness.     

Adherence to antiretroviral therapy and its impact on clinical outcome in HIV-infected patients.

We analyse data on patient adherence to prescribed regimens and surrogate markers of clinical outcome for 168 human immunodeficiency virus infected patients treated with antiretroviral therapy. Data on patient adherence consisted of dose-timing measurements collected for an average of 12 months per patient via electronic monitoring of bottle opening events. We first discuss how such data can be presented to highlight suboptimal adherence patterns and between-patient differences, before introducing two novel methods by which such data can be statistically modelled. Correlations between adherence and subsequent measures of viral load and CD4+T-cell counts are then evaluated. We show that summary measures of short-term adherence, which incorporate pharmacokinetic and pharmacodynamic data on the monitored regimen, predict suboptimal trends in viral load and CD4+T-cell counts better than measures based on adherence data alone.     

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.