An update on the Hirsch conjecture

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite scarce. Most notably, no polynomial upper bound is known for the diameters that are conjectured to be linear. In contrast, very few polytopes are known where the bound $n-d$ is attained. This paper collects known results and remarks both on the positive and on the negative side of the conjecture. Some proofs are included, but only those that we hope are accessible to a general mathematical audience without introducing too many technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2 and put into the appendix arXiv:0912.423

From error bounds to the complexity of first-order descent methods for convex functions

This paper shows that error bounds can be used as effective tools for deriving complexity results for first-order descent methods in convex minimization. In a first stage, this objective led us to revisit the interplay between error bounds and the Kurdyka-\L ojasiewicz (KL) inequality. One can show the equivalence between the two concepts for convex functions having a moderately flat profile near the set of minimizers (as those of functions with H\"olderian growth). A counterexample shows that the equivalence is no longer true for extremely flat functions. This fact reveals the relevance of an approach based on KL inequality. In a second stage, we show how KL inequalities can in turn be employed to compute new complexity bounds for a wealth of descent methods for convex problems. Our approach is completely original and makes use of a one-dimensional worst-case proximal sequence in the spirit of the famous majorant method of Kantorovich. Our result applies to a very simple abstract scheme that covers a wide class of descent methods. As a byproduct of our study, we also provide new results for the globalization of KL inequalities in the convex framework. Our main results inaugurate a simple methodology: derive an error bound, compute the desingularizing function whenever possible, identify essential constants in the descent method and finally compute the complexity using the one-dimensional worst case proximal sequence. Our method is illustrated through projection methods for feasibility problems, and through the famous iterative shrinkage thresholding algorithm (ISTA), for which we show that the complexity bound is of the form $O(q^{k})$ where the constituents of the bound only depend on error bound constants obtained for an arbitrary least squares objective with $\ell^1$ regularization

LRP-1 Promotes Cancer Cell Invasion by Supporting ERK and Inhibiting JNK Signaling Pathways

Background: The low-density lipoprotein receptor-related protein-1 (LRP-1) is an endocytic receptor mediating the clearance of various extracellular molecules involved in the dissemination of cancer cells. LRP-1 thus appeared as an attractive receptor for targeting the invasive behavior of malignant cells. However, recent results suggest that LRP-1 may facilitate the development and growth of cancer metastases in vivo, but the precise contribution of the receptor during cancer progression remains to be elucidated. The lack of mechanistic insights into the intracellular signaling networks downstream of LRP-1 has prevented the understanding of its contribution towards cancer. Methodology/Principal Findings: Through a short-hairpin RNA-mediated silencing approach, we identified LRP-1 as a main regulator of ERK and JNK signaling in a tumor cell context. Co-immunoprecipitation experiments revealed that LRP-1 constitutes an intracellular docking site for MAPK containing complexes. By using pharmacological agents, constitutively active and dominant-negative kinases, we demonstrated that LRP-1 maintains malignant cells in an adhesive state that is favorable for invasion by activating ERK and inhibiting JNK. We further demonstrated that the LRP-1-dependent regulation of MAPK signaling organizes the cytoskeletal architecture and mediates adhesive complex turnover in cancer cells. Moreover, we found that LRP-1 is tethered to the actin network and to focal adhesion sites and controls ERK and JNK targeting to talin-rich structures. Conclusions: We identified ERK and JNK as the main molecular relays by which LRP-1 regulates focal adhesion disassembly of malignant cells to support invasion

Artificial reefs: from ecological processes to fishing enhancement tools

info:eu-repo/semantics/publishedVersio

Free exopolysaccharide from Mycoplasma mycoides subsp. mycoides possesses anti-inflammatory properties

In this study we explored the immunomodulatory properties of highly purified free galactan, the soluble exopolysaccharide secreted by Mycoplasma mycoides subsp. mycoides (Mmm). Galactan was shown to bind to TLR2 but not TLR4 using HEK293 reporter cells and to induce the production of the anti-inflammatory cytokine IL-10 in bovine macrophages, whereas low IL-12p40 and no TNF-α, both pro-inflammatory cytokines, were induced in these cells. In addition, pre-treatment of macrophages with galactan substantially reduced lipopolysaccharide (LPS)-induced production of pro-inflammatory cytokines TNF- and IL-12p40 while increasing LPS-induced secretion of immunosuppressive IL-10. Also, galactan did not activate naïve lymphocytes and induced only low production of the Th1 cytokine IFN-γ in Mmm-experienced lymphocytes. Finally, galactan triggered weak recall proliferation of CD4+ T lymphocytes from contagious bovine pleuropneumonia-infected animals despite having a positive effect on the expression of co-stimulatory molecules on macrophages. All together, these results suggest that galactan possesses anti-inflammatory properties and potentially provides Mmm with a mechanism to evade host innate and adaptive cell-mediated immune responses. (Résumé d'auteur

Role of the hyporheic heterotrophic biofilm on transformation and toxicity of pesticides

The role of heterotrophic biofilm of water–sediment interface in detoxification processes was tested in abiotic and biotic conditions under laboratory conditions. Three toxicants, a herbicide (Diuron), a fungicide (Dimethomorph) and an insecticide (Chlorpyrifos-ethyl) have been tested in water percolating into columns reproducing hyporheic sediment. The detoxification processes were tested by comparing the water quality after 18 days of percolation with and without heterotrophic biofilm. Tested concentrations were 30 mg.Lx1 of Diuron diluted in 0.1% dimethyl sulfoxide (DMSO), 2 mg.Lx1 of Dimethomorph and 0.1 mg.Lx1 of Chlorpyrifos-ethyl. To characterise the detoxification efficiency of the system, we performed genotoxicity bioassays in amphibian larvae and rotifers and measured the respiration and denitrification of sediments. Although the presence of biofilm increased the production of N-(3,4 dichlorophenyl)-N-(methyl)-urea, a metabolite of diuron, the toxicity did not decrease irrespective of the bioassay. In the presence of biofilm, Dimethomorph concentrations decreased compared with abiotic conditions, from 2 mg.Lx1 to 0.4 mg.Lx1 after 18 days of percolation. For both Dimethomorph and Chlorpyrifos-ethyl additions, assessment of detoxification level by the biofilm depended on the test used: detoxification effect was found with amphibian larvae bioassay and no detoxification was observed with the rotifer test. Heterotrophic biofilm exerts a major influence in the biochemical transformation of contaminants such as pesticides, suggesting that the interface between running water and sediment plays a role in self-purification of stream reaches

Mycobacterium tuberculosis Lipolytic Enzymes as Potential Biomarkers for the Diagnosis of Active Tuberculosis

BACKGROUND: New diagnosis tests are urgently needed to address the global tuberculosis (TB) burden and to improve control programs especially in resource-limited settings. An effective in vitro diagnostic of TB based on serological methods would be regarded as an attractive progress because immunoassays are simple, rapid, inexpensive, and may offer the possibility to detect cases missed by standard sputum smear microscopy. However, currently available serology tests for TB are highly variable in sensitivity and specificity. Lipolytic enzymes have recently emerged as key factors in lipid metabolization during dormancy and/or exit of the non-replicating growth phase, a prerequisite step of TB reactivation. The focus of this study was to analyze and compare the potential of four Mycobacterium tuberculosis lipolytic enzymes (LipY, Rv0183, Rv1984c and Rv3452) as new markers in the serodiagnosis of active TB. METHODS: Recombinant proteins were produced and used in optimized ELISA aimed to detect IgG and IgM serum antibodies against the four lipolytic enzymes. The capacity of the assays to identify infection was evaluated in patients with either active TB or latent TB and compared with two distinct control groups consisting of BCG-vaccinated blood donors and hospitalized non-TB individuals. RESULTS: A robust humoral response was detected in patients with active TB whereas antibodies against lipolytic enzymes were infrequently detected in either uninfected groups or in subjects with latent infection. High specifity levels, ranging from 93.9% to 97.5%, were obtained for all four antigens with sensitivity values ranging from 73.4% to 90.5%, with Rv3452 displaying the highest performances. Patients with active TB usually exhibited strong IgG responses but poor IgM responses. CONCLUSION: These results clearly indicate that the lipolytic enzymes tested are strongly immunogenic allowing to distinguish active from latent TB infections. They appear as potent biomarkers providing high sensitivity and specificity levels for the immunodiagnosis of active TB

Feasibility, reliability and validity of a questionnaire on healthcare consumption and productivity loss in patients with a psychiatric disorder (TiC-P)

Background: Patient self-report allows collecting comprehensive data for the purpose of performing economic evaluations. The aim of the current study was to assess the feasibility, reliability and a part of the construct validity of a commonly applied questionnaire on healthcare utilization and productivity losses in patients with a psychiatric disorder (TiC-P). Methods. Data were derived alongside two clinical trials performed in the Netherlands in patients with mental health problems. The response rate, average time of filling out the questionnaire and proportions of missing values were used as indicators of feasibility of the questionnaire. Test-retest analyses were performed including Cohen's kappa and intra class correlation coefficients to assess reliability of the data. The construct validity was assessed by comparing patient reported data on contacts with psychotherapists and reported data on long-term absence from work with data derived from registries. Results: The response rate was 72%. The mean time needed for filling out the first TiC-P was 9.4 minutes. The time needed for filling out the questionnaire was 2.3 minutes less for follow up measurements. Proportions of missing values were limited (< 2.4%) except for medication for which in 10% of the cases costs could not be calculated. Cohen's kappa was satisfactory to almost perfect for most items related to healthcare consumption and satisfactory for items on absence from work and presenteeism. Comparable results were shown by the ICCs on variables measuring volumes of medical consumption and productivity losses indicating good reliability of the questionnaire. Absolute agreement between patient-reported data and data derived from medical registrations of the psychotherapists was satisfactory. Accepting a margin o