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To test if an unknown matrix M0 has a given rank (null hypothesis noted H0), we consider a statistic that is a squared distance between an estimator and the submanifold of fixed-rank matrix. Under H0, this statistic converges to a weighted chi-squared distribution. We introduce the constrained bootstrap (CS bootstrap) to estimate the law of this statistic under H0. An important point is that even if H0 fails, the CS bootstrap reproduces the behavior of the statistic under H0. As a consequence, the CS bootstrap is employed to estimate the nonasymptotic quantile for testing the rank. We provide the consistency of the procedure and the simulations shed light on the accuracy of the CS bootstrap with respect to the traditional asymptotic comparison. More generally, the results are extended to test whether an unknown parameter belongs to a submanifold of the Euclidean space. Finally, the CS bootstrap is easy to compute, it handles a large family of tests and it works under mild assumptions.

BACKGROUND: A wide range of techniques is now available for analyzing regulatory networks. Nonetheless, most of these techniques fail to interpret large-scale transcriptional data at the post-translational level. RESULTS: We address the question of using large-scale transcriptomic observation of a system perturbation to analyze a regulatory network which contained several types of interactions - transcriptional and post-translational. Our method consisted of post-processing the outputs of an open-source tool named BioQuali - an automatic constraint-based analysis mimicking biologist's local reasoning on a large scale. The post-processing relied on differences in the behavior of the transcriptional and post-translational levels in the network. As a case study, we analyzed a network representation of the genes and proteins controlled by an oncogene in the context of Ewing's sarcoma. The analysis allowed us to pinpoint active interactions specific to this cancer. We also identified the parts of the network which were incomplete and should be submitted for further investigation. CONCLUSIONS: The proposed approach is effective for the qualitative analysis of cancer networks. It allows the integrative use of experimental data of various types in order to identify the specific information that should be considered a priority in the initial - and possibly very large - experimental dataset. Iteratively, new dataset can be introduced into the analysis to improve the network representation and make it more specific.

BACKGROUND: A wide range of techniques is now available for analyzing regulatory networks. Nonetheless, most of these techniques fail to interpret large-scale transcriptional data at the post-translational level. RESULTS: We address the question of using large-scale transcriptomic observation of a system perturbation to analyze a regulatory network which contained several types of interactions - transcriptional and post-translational. Our method consisted of post-processing the outputs of an open-source tool named BioQuali - an automatic constraint-based analysis mimicking biologist's local reasoning on a large scale. The post-processing relied on differences in the behavior of the transcriptional and post-translational levels in the network. As a case study, we analyzed a network representation of the genes and proteins controlled by an oncogene in the context of Ewing's sarcoma. The analysis allowed us to pinpoint active interactions specific to this cancer. We also identified the parts of the network which were incomplete and should be submitted for further investigation. CONCLUSIONS: The proposed approach is effective for the qualitative analysis of cancer networks. It allows the integrative use of experimental data of various types in order to identify the specific information that should be considered a priority in the initial - and possibly very large - experimental dataset. Iteratively, new dataset can be introduced into the analysis to improve the network representation and make it more specific.

Estuarine areas are sensitive to rapid and punctual contamination linked to heavy rainfall inducing rapid fresh water input. Thus, the increase of seawater contamination may be linked to a salinity decrease. The objective of this study was to measure salinity variation as a proxy to evaluate the risk of faecal contamination. Salinity sensors were set up on shellfish beds in Daoulas estuary (Bay of Brest) and monitored every 10 min over a four year period. Precipitation and river flows were also recorded. Moreover E. coli concentrations and salinity were measured in the estuarine surface water during different hydrodynamic conditions and seasons. The results indicated a significant relationship between E. coli concentration and salinity in the estuary. Mathematical models were then selected and validated to assess and predict salinity variations. In the upper estuary, statistical analysis shows that variation in salinity is a function of the rainfall of the previous day (first model with r2= 0.66). The second model established a relationship between salinity and precipitation which reproduced 95% of the events, but failed to reproduce salinity variations during low rainfall (<1mm/day).

Estuarine areas are sensitive to rapid and punctual contamination linked to heavy rainfall inducing rapid fresh water input. Thus, the increase of seawater contamination may be linked to a salinity decrease. The objective of this study was to measure salinity variation as a proxy to evaluate the risk of faecal contamination. Salinity sensors were set up on shellfish beds in Daoulas estuary (Bay of Brest) and monitored every 10 min over a four year period. Precipitation and river flows were also recorded. Moreover E. coli concentrations and salinity were measured in the estuarine surface water during different hydrodynamic conditions and seasons. The results indicated a significant relationship between E. coli concentration and salinity in the estuary. Mathematical models were then selected and validated to assess and predict salinity variations. In the upper estuary, statistical analysis shows that variation in salinity is a function of the rainfall of the previous day (first model with r2= 0.66). The second model established a relationship between salinity and precipitation which reproduced 95% of the events, but failed to reproduce salinity variations during low rainfall (<1mm/day).

Estuarine areas are sensitive to rapid and punctual contamination linked to heavy rainfall inducing rapid fresh water input. Thus, the increase of seawater contamination may be linked to a salinity decrease. The objective of this study was to measure salinity variation as a proxy to evaluate the risk of faecal contamination. Salinity sensors were set up on shellfish beds in Daoulas estuary (Bay of Brest) and monitored every 10 min over a four year period. Precipitation and river flows were also recorded. Moreover E. coli concentrations and salinity were measured in the estuarine surface water during different hydrodynamic conditions and seasons. The results indicated a significant relationship between E. coli concentration and salinity in the estuary. Mathematical models were then selected and validated to assess and predict salinity variations. In the upper estuary, statistical analysis shows that variation in salinity is a function of the rainfall of the previous day (first model with r2= 0.66). The second model established a relationship between salinity and precipitation which reproduced 95% of the events, but failed to reproduce salinity variations during low rainfall (<1mm/day).

Estuarine areas are sensitive to rapid and punctual contamination linked to heavy rainfall inducing rapid fresh water input. Thus, the increase of seawater contamination may be linked to a salinity decrease. The objective of this study was to measure salinity variation as a proxy to evaluate the risk of faecal contamination. Salinity sensors were set up on shellfish beds in Daoulas estuary (Bay of Brest) and monitored every 10 min over a four year period. Precipitation and river flows were also recorded. Moreover E. coli concentrations and salinity were measured in the estuarine surface water during different hydrodynamic conditions and seasons. The results indicated a significant relationship between E. coli concentration and salinity in the estuary. Mathematical models were then selected and validated to assess and predict salinity variations. In the upper estuary, statistical analysis shows that variation in salinity is a function of the rainfall of the previous day (first model with r2= 0.66). The second model established a relationship between salinity and precipitation which reproduced 95% of the events, but failed to reproduce salinity variations during low rainfall (<1mm/day).

Caption title. "August 1988.", Includes bibliographical references., Work supported by the Army Research Office. DAAL03-86-K-0171, B. Delyon.

Caption title., Bibliography: leaf 14., Supported, in part, by a grant from the Air Force Office of Scientific Research. AFOSR-85-0227B Supported, in part, by the Weizmann Postdoctoral Fellowship., by Bernard Delyon, Ofer Zeitouni.

Caption title. "August 1988.", Includes bibliographical references., Work supported by the Army Research Office. DAAL03-86-K-0171, B. Delyon.

Caption title., Bibliography: leaf 14., Supported, in part, by a grant from the Air Force Office of Scientific Research. AFOSR-85-0227B Supported, in part, by the Weizmann Postdoctoral Fellowship., by Bernard Delyon, Ofer Zeitouni.

The dependence of the optimal nonlinear filter on it's initial conditions is considered for continuous time linear filtering and for finite state space nonlinear filtering. Partial results are obtained in the high signal to noise ration case, together with a characterization of the Lyapunov exponent in the (easier) low SNR case.