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

Pichia pastoris versus Saccharomyces cerevisiae:a case study on the recombinant production of human granulocyte-macrophage colony-stimulating factor

BACKGROUND: Recombinant human granulocyte-macrophage colony-stimulating factor (rhGM-CSF) is a glycoprotein that has been approved by the FDA for the treatment of neutropenia and leukemia in combination with chemotherapies. Recombinant hGM-CSF is produced industrially using the baker's yeast, Saccharomyces cerevisiae, by large-scale fermentation. The methylotrophic yeast, Pichia pastoris, has emerged as an alternative host cell system due to its shorter and less immunogenic glycosylation pattern together with higher cell density growth and higher secreted protein yield than S. cerevisiae. In this study, we compared the pipeline from gene to recombinant protein in these two yeasts. RESULTS: Codon optimization in silico for both yeast species showed no difference in frequent codon usage. However, rhGM-CSF expressed from S. cerevisiae BY4742 showed a significant discrepancy in molecular weight from those of P. pastoris X33. Analysis showed purified rhGM-CSF species with molecular weights ranging from 30 to more than 60 kDa. Fed-batch fermentation over 72 h showed that rhGM-CSF was more highly secreted from P. pastoris than S. cerevisiae (285 and 64 mg total secreted protein/L, respectively). Ion exchange chromatography gave higher purity and recovery than hydrophobic interaction chromatography. Purified rhGM-CSF from P. pastoris was 327 times more potent than rhGM-CSF from S. cerevisiae in terms of proliferative stimulating capacity on the hGM-CSF-dependent cell line, TF-1. CONCLUSION: Our data support a view that the methylotrophic yeast P. pastoris is an effective recombinant host for heterologous rhGM-CSF production

On a Convex Set with Nondifferentiable Metric Projection

A remarkable example of a nonempty closed convex set in the Euclidean plane for which the directional derivative of the metric projection mapping fails to exist was constructed by A. Shapiro. In this paper, we revisit and modify that construction to obtain a convex set with smooth boundary which possesses the same property

Spatio-temporal Models of Lymphangiogenesis in Wound Healing

Several studies suggest that one possible cause of impaired wound healing is failed or insufficient lymphangiogenesis, that is the formation of new lymphatic capillaries. Although many mathematical models have been developed to describe the formation of blood capillaries (angiogenesis), very few have been proposed for the regeneration of the lymphatic network. Lymphangiogenesis is a markedly different process from angiogenesis, occurring at different times and in response to different chemical stimuli. Two main hypotheses have been proposed: 1) lymphatic capillaries sprout from existing interrupted ones at the edge of the wound in analogy to the blood angiogenesis case; 2) lymphatic endothelial cells first pool in the wound region following the lymph flow and then, once sufficiently populated, start to form a network. Here we present two PDE models describing lymphangiogenesis according to these two different hypotheses. Further, we include the effect of advection due to interstitial flow and lymph flow coming from open capillaries. The variables represent different cell densities and growth factor concentrations, and where possible the parameters are estimated from biological data. The models are then solved numerically and the results are compared with the available biological literature.Comment: 29 pages, 9 Figures, 6 Tables (39 figure files in total

Loss of interleukin-12 modifies the pro-inflammatory response but does not prevent duct obstruction in experimental biliary atresia

BACKGROUND: Livers of infants with biliary atresia and of neonatal mice infected with rotavirus (RRV) have increased expression of interferon-gamma (IFNγ) and interleukin (IL)-12. While the expression of IFNγ regulates the obstruction of extrahepatic bile ducts by lymphocytes, the role of IL-12 in the pathogenesis of biliary obstruction is unknown. Based on the role of IL-12 as a key proinflammatory cytokine, we hypothesized that loss of IL-12 prevents the obstruction of extrahepatic bile ducts. METHODS: IL12-knockout (IL-12KO) and wild type mice were injected with RRV or saline at day 1 of age and monitored for the development of symptoms. The cellular and molecular phenotypes were determined at days 3, 7, and 14 by real-time PCR and flow cytometry. RESULTS: RRV infection of IL-12KO mice resulted in growth failure, jaundice/acholic stools, and decreased survival similar to wild-type mice. IL-12KO mice had a remarkable neutrophil-rich portal inflammation and epithelial sloughing of extrahepatic bile ducts. Loss of IL-12 decreased but did not abolish the hepatic expression of IFNγ, displayed a remarkable increase in expression of TNFα, IFNα, IFNβ and decreased expression of IL-4 and IL-5. CONCLUSION: Loss of IL-12 did not modify the progression of bile duct obstruction in experimental biliary atresia. However, the inflammatory response was predominantly neutrophil-based and displayed a Th1 response in the absence of IL-12

How many is enough? Determining optimal count totals for ecological and palaeoecological studies of testate amoebae

Testate amoebae are increasingly used in ecological and palaeoecological studies of wetlands. To characterise the amoeba community a certain number of individuals need to be counted under the microscope. To date, most studies have aimed for 150 individuals, but that sample size is not based on adequate evidence. When testate amoeba concentrations are low, it can be difficult or impossible to reach this total. The impacts of lower count totals have never been seriously scrutinised. We investigated the impact of count size on number of taxa identified, quantitative inferences of environmental variables and the strength of the links between amoebae and environmental data in the context of predicting depth to water table. Low counts were simulated by random selection of individuals from four existing datasets. Results show progressively diminishing returns by all criteria as count size increases from low numbers to counts of 150. A higher count is required to identify all taxa than to adequately characterise the community for transfer function inference. We suggest that in most cases, it will be a more efficient use of time to count a greater number of samples to a lower count. While a count of 50 individuals may be sufficient for some samples from some sites we recommend that counts of 100 individuals should be sufficient for most samples. Counts need only be increased to 150 or more where the aim is to identify relatively minor, but still potentially ecologically relevant community changes. This approach will help reduce lack of replication and low resolution, which are common limitations in testate amoeba-based palaeoecological and ecological studies

Patterns of HIV prevalence among injecting drug users in the cross-border area of Lang Son Province, Vietnam, and Ning Ming County, Guangxi Province, China

BACKGROUND: To assess patterns of injecting drug use and HIV prevalence among injecting drug users (IDUs) in an international border area along a major heroin trans-shipment route. METHODS: Cross-sectional surveys of IDUs in 5 sites in Lang Son Province, Vietnam (n = 348) and 3 sites in Ning Ming County, Guangxi Province, China (n = 308). Respondents were recruited through peer referral ("snowball") methods in both countries, and also from officially recorded lists of IDUs in Vietnam. A risk behavior questionnaire was administered and HIV counseling and testing conducted. RESULTS: Participants in both countries were largely male, in their 20s, and unmarried. A majority of subjects in both countries were members of ethnic minority groups. There were strong geographic gradients for length of drug injecting and for HIV seroprevalence. Both mean years injecting and HIV seroprevalence declined from the Vietnamese site farthest from the border to the Chinese site farthest from the border. 10.6% of participants in China and 24.5% of participants in Vietnam reported crossing the international border in the 6 months prior to interview. Crossing the border by IDUs was associated with (1) distance from the border, (2) being a member of an ethnic minority group, and (3) being HIV seropositive among Chinese participants. CONCLUSION: Reducing the international spread of HIV among IDUs will require programs at the global, regional, national, and "local cross border" levels. At the local cross border level, the programs should be coordinated on both sides of the border and on a sufficient scale that IDUs will be able to readily obtain clean injection equipment on the other side of the border as well as in their country of residence

The role of thrombin and thrombin receptors in ischemic, hemorrhagic and traumatic brain injury: deleterious or protective?

In the last two decades it has become apparent that thrombin has many extravascular effects that are mediated by a family of protease-activated receptors (PARs). PAR-1, -3 and -4 are activated via cleavage by thrombin. The importance of extravascular thrombin in modulating ischemic, hemorrhagic and traumatic injury in brain has recently become clear. Thus, in vitro , thrombin at low concentration protects neurons and astrocytes from cell death caused by a number of different insults. In vivo , pretreating the brain with a low dose of thrombin (thrombin preconditioning), attenuates the brain injury induced by a large dose of thrombin, an intracerebral hemorrhage or by focal cerebral ischemia. Thrombin may also be an important mediator of ischemic preconditioning. In contrast, high doses of thrombin kill neurons and astrocytes in vitro and cause disruption of the blood–brain barrier, brain edema and seizures in vivo . This review examines the role of thrombin in brain injury and the molecular mechanisms and signaling cascades involved.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66277/1/j.1471-4159.2003.01268.x.pd

Testate amoeba response to acid deposition in a Scottish peatland

Peatlands around the world are exposed to anthropogenic or volcanogenic sulphur pollution. Impacts on peatland microbial communities have been inferred from changes in gas flux but have rarely been directly studied. In this study, the impacts of sulphuric acid deposition on peatland testate amoebae were investigated by analysis of experimental plots on a Scottish peatland almost 7 years after acid treatment. Results showed reduced concentration of live amoebae and changes in community structure which remained significant even when differences in pH were accounted for. Several possible explanations for the impacts can be proposed including taphonomic processes and changes in plant communities. Previous studies have inferred a shift from methanogenic archaea to sulphate-reducing bacteria in sulphate-treated peats; it is possible that the impacts detected here might relate to this change, perhaps through testate amoeba predation on methanotrophs