Non-linear Aggregation of Filters to Improve Image Denoising.

We introduce a novel aggregation method to efficiently perform image denoising. Preliminary filters are aggregated in a non-linear fashion, using a new metric of pixel proximity based on how the pool of filters reaches a consensus. We provide a theoretical bound to support our aggregation scheme, its numerical performance is illustrated and we show that the aggregate significantly outperforms each of the preliminary filters

Modeling the dynamics of biomarkers during primary HIV infection taking into account the uncertainty of infection date

During primary HIV infection, the kinetics of plasma virus concentrations and CD4+ cell counts is very complex. Parametric and nonparametric models have been suggested for fitting repeated measurements of these markers. Alternatively, mechanistic approaches based on ordinary differential equations have also been proposed. These latter models are constructed according to biological knowledge and take into account the complex nonlinear interactions between viruses and cells. However, estimating the parameters of these models is difficult. A main difficulty in the context of primary HIV infection is that the date of infection is generally unknown. For some patients, the date of last negative HIV test is available in addition to the date of first positive HIV test (seroconverters). In this paper we propose a likelihood-based method for estimating the parameters of dynamical models using a population approach and taking into account the uncertainty of the infection date. We applied this method to a sample of 761 HIV-infected patients from the Concerted Action on SeroConversion to AIDS and Death in Europe (CASCADE).Comment: Published in at http://dx.doi.org/10.1214/10-AOAS364 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotic confidence interval for R2 in multiple linear regression

Following White's approach of robust multiple linear regression, we give asymptotic confidence intervals for the multiple correlation coefficient R2 under minimal moment conditions. We also give the asymptotic joint distribution of the empirical estimators of the individual R2's. Through different sets of simulations, we show that the procedure is indeed robust (contrary to the procedure involving the near exact distribution of the empirical estimator of R2 is the multivariate Gaussian case) and can be also applied to count linear regression

Clinical trial simulation to evaluate power to compare the antiviral effectiveness of two hepatitis C protease inhibitors using nonlinear mixed effect models: a viral kinetic approach.

International audienceBACKGROUND: Models of hepatitis C virus (HCV) kinetics are increasingly used to estimate and to compare in vivo drug's antiviral effectiveness of new potent anti-HCV agents. Viral kinetic parameters can be estimated using non-linear mixed effect models (NLMEM). Here we aimed to evaluate the performance of this approach to precisely estimate the parameters and to evaluate the type I errors and the power of the Wald test to compare the antiviral effectiveness between two treatment groups when data are sparse and/or a large proportion of viral load (VL) are below the limit of detection (BLD). METHODS: We performed a clinical trial simulation assuming two treatment groups with different levels of antiviral effectiveness. We evaluated the precision and the accuracy of parameter estimates obtained on 500 replication of this trial using the stochastic approximation expectation-approximation algorithm which appropriately handles BLD data. Next we evaluated the type I error and the power of the Wald test to assess a difference of antiviral effectiveness between the two groups. Standard error of the parameters and Wald test property were evaluated according to the number of patients, the number of samples per patient and the expected difference in antiviral effectiveness. RESULTS: NLMEM provided precise and accurate estimates for both the fixed effects and the inter-individual variance parameters even with sparse data and large proportion of BLD data. However Wald test with small number of patients and lack of information due to BLD resulted in an inflation of the type I error as compared to the results obtained when no limit of detection of VL was considered. The corrected power of the test was very high and largely outperformed what can be obtained with empirical comparison of the mean VL decline using Wilcoxon test. CONCLUSION: This simulation study shows the benefit of viral kinetic models analyzed with NLMEM over empirical approaches used in most clinical studies. When designing a viral kinetic study, our results indicate that the enrollment of a large number of patients is to be preferred to small population sample with frequent assessments of VL

Green Currents for Meromorphic Maps of Compact K\"ahler Manifolds

We consider the dynamics of meromorphic maps of compact K\"ahler manifolds. In this work, our goal is to locate the non-nef locus of invariant classes and provide necessary and sufficient conditions for existence of Green currents in codimension one.Comment: Statement of Theorem 1.5 is slightly improved. Proposition 5.2 and Theorem 5.3 are adde

Univalent Foundations and the UniMath Library

We give a concise presentation of the Univalent Foundations of mathematics outlining the main ideas, followed by a discussion of the UniMath library of formalized mathematics implementing the ideas of the Univalent Foundations (section 1), and the challenges one faces in attempting to design a large-scale library of formalized mathematics (section 2). This leads us to a general discussion about the links between architecture and mathematics where a meeting of minds is revealed between architects and mathematicians (section 3). On the way our odyssey from the foundations to the "horizon" of mathematics will lead us to meet the mathematicians David Hilbert and Nicolas Bourbaki as well as the architect Christopher Alexander

Preparation, characterization, and safety evaluation of poly(lactide-co-glycolide) nanoparticles for protein delivery into macrophages.

International audienceFollowing infection, HIV establishes reservoirs within tissues that are inaccessible to optimal levels of antiviral drugs or within cells where HIV lies latent, thus escaping the action of anti-HIV drugs. Macrophages are a persistent reservoir for HIV and may contribute to the rebound viremia observed after antiretroviral treatment is stopped. In this study, we further investigate the potential of poly(lactic-co-glycolic) acid (PLGA)-based nanocarriers as a new strategy to enhance penetration of therapeutic molecules into macrophages. We have prepared stable PLGA nanoparticles (NPs) and evaluated their capacity to transport an active molecule into the human monocyte/macrophage cell line THP-1 using bovine serum albumin (BSA) as a proof-of-concept compound. Intracellular localization of fluorescent BSA molecules encapsulated into PLGA NPs was monitored in live cells using confocal microscopy, and cellular uptake was quantified by flow cytometry. In vitro and in vivo toxicological studies were performed to further determine the safety profile of PLGA NPs including inflammatory effects. The size of the PLGA NPs carrying BSA (PLGA-BSA) in culture medium containing 10% serum was ~126 nm in diameter, and they were negatively charged at their surface (zeta potential =-5.6 mV). Our confocal microscopy studies and flow cytometry data showed that these PLGA-BSA NPs are rapidly and efficiently taken up by THP-1 monocyte-derived macrophages (MDMs) at low doses. We found that PLGA-BSA NPs increased cellular uptake and internalization of the protein in vitro. PLGA NPs were not cytotoxic for THP-1 MDM cells, did not modulate neutrophil apoptosis in vitro, and did not show inflammatory effect in vivo in the murine air pouch model of acute inflammation. In contrast to BSA alone, BSA encapsulated into PLGA NPs increased leukocyte infiltration in vivo, suggesting the in vivo enhanced delivery and protection of the protein by the polymer nanocarrier. We demonstrated that PLGA-based nanopolymer carriers are good candidates to efficiently and safely enhance the transport of active molecules into human MDMs. In addition, we further investigated their inflammatory profile and showed that PLGA NPs have low inflammatory effects in vitro and in vivo. Thus, PLGA nanocarriers are promising as a drug delivery strategy in macrophages for prevention and eradication of intracellular pathogens such as HIV and Mycobacterium tuberculosis