On the Set of Locally Convex Topologies Compatible with a Given Topology on a Vector Space: Cardinality Aspects

For a topological vector space (X, τ ), we consider the family LCT (X, τ ) of all locally convex topologies defined on X, which give rise to the same continuous linear functionals as the original topology τ . We prove that for an infinite-dimensional reflexive Banach space (X, τ ), the cardinality of LCT (X, τ ) is at least c.

Mackey topology on locally convex spaces and on locally quasi-convex groups. Similarities and historical remarks

A counterpart of the Mackey–Arens Theorem for the class of locally quasi-convex topological Abelian groups (LQC-groups) was initiated in Chasco et al. (Stud Math 132(3):257–284, 1999). Several authors have been interested in the problems posed there and have done clarifying contributions, although the main question of that source remains open. Some differences between the Mackey Theory for locally convex spaces and for locally quasi-convex groups, stem from the following fact: The supremum of all compatible locally quasi-convex topologies for a topological abelian group G may not coincide with the topology of uniform convergence on the weak quasi-convex compact subsets of the dual groupG∧. Thus, a substantial part of the classical Mackey–Arens Theorem cannot be generalized to LQC-groups. Furthermore, the mentioned fact gives rise to a grading in the property of “being a Mackey group”, as defined and thoroughly studied in Díaz Nieto and Martín-Peinador (Proceedings in Mathematics and Statistics 80:119–144, 2014). At present it is not known—and this is the main open question—if the supremum of all the compatible locally quasi-convex topologies on a topological group is in fact a compatible topology. In the present paper we do a sort of historical review on the Mackey Theory, and we compare it in the two settings of locally convex spaces and of locally quasi-convex groups. We point out some general questions which are still open, under the name of Problems.

EACS: Effective Avoidance Combination Strategy

International audience

HBsAg seroclearance or seroconversion induced by peg-interferon alpha and lamivudine or adefovir combination therapy in chronic hepatitis B treatment: a meta-analysis and systematic review

Background and aims: Seroclearance or seroconversion of hepatitis B surface antigen (HBsAg) is generally considered as a clinical endpoint. The purpose of the present meta-analysis was to evaluate the effect of combined therapy with pegylated interferon alpha (PEG-IFNα) with or without lamivudine (LAM) or adefovir (ADV) on HBsAg seroclearance or seroconversion in subjects with chronic hepatitis B (CHB). Methods: Randomized controlled trials performed through May 30th 2015 in adults with CHB receiving PEG-IFNα and LAM or ADV combination therapy or monotherapy for 48-52 weeks were included. The Review Manager Software 5.2.0 was used for the meta-analysis. Results: No statistical differences in HBsAg seroclearance (9.9% vs. 7.1%, OR = 1.47, 95% CI: 0.75, 2.90; p = 0.26) or HBsAg seroconversion (4.2% vs. 3.7%, OR = 1.17, 95% CI: 0.57, 2.37; p = 0.67) rates were noticed between PEG-IFNα + LAM and PEG-IFN α + placebo during post-treatment follow-up for 24-26-weeks in subjects with hepatitis Be antigen (HBeAg)-positive CHB. No statistical differences in HBsAg clearance (10.5% vs. 6.4%, OR = 1.68, 95% CI: 0.75, 3.76; p = 0.21) were seen, but statistical differences in HBsAg seroconversion (6.3% vs. 0%, OR = 7.22, 95% CI: 1.23, 42.40; p = 0.03) were observed, between PEG-IFNα + ADV and PEG-IFNα for 48-52 weeks of treatment in subjects with HBeAg-positive CHB. A systematic evaluation showed no differences in HBsAg disappearance and seroconversion rates between PEG-IFNα + placebo and PEG-IFNα + LAM for 48-52 weeks in subjects with HBeAg-positive CHB. A systematic assessment found no differences in HBsAg disappearance and seroconversion rates between PEG-IFNα + placebo and PEG-IFNα + LAM during 24 weeks' to 3 years' follow-up after treatment in subjects with HBeAg-negative CHB. Conclusion: Combined therapy with PEG-IFNα and LAM or ADV was not superior to monotherapy with PEG-IFNα in terms of HBsAg seroclearance or seroconversion.

Using a Combination of Phylogenetic Comparative and Paleobotanical Methods to Elucidate Patterns of Lineage Selection in Rosales (Plantae: Anthophyta)

An increasing focus in evolutionary biology is on the interplay between mesoscale ecological and evolutionary processes such as population demographics, habitat tolerance, and especially geographic distribution, as potential drivers responsible for patterns of diversification and extinction over geologic time. However, few studies to date connect organismal processes such as survival and reproduction through mesoscale patterns to long-term macroevolutionary trends. In my dissertation, I investigate how mechanism of seed dispersal, mediated through geographic range size, influences diversification rates in the Rosales (Plantae: Anthophyta). In my first chapter, I validate the phylogenetic comparative methods that I use in my second and third chapters. Available state speciation and extinction (SSE) models assumptions about evolution known to be false through fossil data. I show, however, that as long as net diversification rates remain positive – a condition likely true for the Rosales – these violations of SSE’s assumptions do not cause significantly biased results. With SSE methods validated, my second chapter reconstructs three associations that appear to increase diversification rate for Rosalean genera: (1) herbaceous habit; (2) a three-way interaction combining animal dispersal, high within-genus species richness, and geographic range on multiple continents; (3) a four-way interaction combining woody habit with the other three characteristics of (2). I suggest that the three- and four-way interactions represent colonization ability and resulting extinction resistance in the face of late Cenozoic climate change; however, there are other possibilities as well that I hope to investigate in future research. My third chapter reconstructs the phylogeographic history of the Rosales using both non-fossil-assisted SSE methods as well as fossil-informed traditional phylogeographic analysis. Ancestral state reconstructions indicate that the Rosaceae diversified in North America while the other Rosalean families diversified elsewhere, possibly in Eurasia. SSE is able to successfully identify groups of genera that were likely to have been ancestrally widespread, but has poorer taxonomic resolution than methods that use fossil data. In conclusion, these chapters together suggest several potential causal links between organismal, mesoscale, and geologic scale processes, but further work will be needed to test the hypotheses that I raise here.

EFFECT OF BAP, NAA AND GA3, EITHER ALONE OR IN COMBINATION, ON MERISTEM CULTURE AND PLANTLET ESTABLISHMENT IN SWEET POTATO (CV BRONDAL)

In Zimbabwe, the average sweet potato yield (6 t/ha) is relatively low when compared to Asian counterparts (17 t/ha). These low crop yields have been blamed on weevil infestations and viral infections which account for 60-90% of sweet potato yield losses in Africa. Meristem tip culture, a Centre for Potato Improvement (CIP) initiated tissue culture technique, has been widely used to eradicate viruses from clonally propagated crops and has been noted to be one of the instrumental techniques that helped China to increase sweet potato yields. In an effort to adopt the meristem tip culture technique for the production of virus-free planting material of a local sweet potato (cv Brondal), a study was conducted to evaluate the effect of Benzylamino purine (BAP), 1-Naphthaleneacetic acid (NAA) and Gibberellic acid (GA3) (either alone or in combination) on cultured Brondal meristems. The different hormonal treatments were assessed on the following parameters: plantlet regenerative capacity, multiple plantlet production, shoot height, average leaf number per shoot and average node number per shoot, ten weeks after meristem culture. All treatments containing a combination of BAP (1 mg-L) and GA3 (at either 5 mg-L, 10 mg-L, or 20 mg-L) had a significantly (p<0.01) higher plantlet regenerative capacity of 33-66% when compared to other treatment combinations. Only treatments, 10 mg-L GA3 + 1 mg-L BAP and 20 mg-L GA3 + 1 mg-L BAP were capable of inducing multiple plantlet formation, producing an average of three plantlets/meristem and two plantlets/meristem respectively. Overall, treatment 10 mg-L GA3 + 1 mg-L BAP gave rise to significantly (p<0.01) taller shoots (20 mm) compared to the rest of the treatments used. For average leaf number per shoot, all GA3 treatments (5 mg-L, 10 mg-L, or 20 mg-L) supplemented with 1 mg-L BAP gave significantly (p<0.01) higher numbers of leaves (six leaves/shoot) than the rest of the treatments. Treatments 10 mg-L GA3 + 1 mg-L BAP and 20 mg-L GA3 + 1 mg-L BAP gave rise to the highest number of nodes per shoot, producing an average of three nodes per shoot. In sharp contrast to treatments containing a combination of BAP and GA3, all treatments containing a combination of BAP and NAA performed poorly in all parameters tested for plant regeneration of Brondal sweet potato variety. In conclusion, the best hormonal treatment for culturing Brondal meristems proved to be 10 mg-L GA3 + 1 mg-L BAP.

POSITIVE FILTERED P_N METHOD FOR LINEAR TRANSPORT EQUATIONS AND THE ASSOCIATED OPTIMIZATION ALGORITHM

We propose a positive, accurate moment closure for linear kinetic transport equations based on a filtered spherical harmonic (FP_N) expansion in the angular variable. The FP_N moment equations are accurate approximations to linear kinetic equations, but they are known to suffer from the occurrence of unphysical, negative particle concentrations. The new positive filtered P_N (FP_N+) closure is developed to address this issue. The FP_N+ closure approximates the kinetic distribution by a spherical harmonic expansion that is non-negative on a finite, predetermined set of quadrature points. With an appropriate numerical PDE solver, the FP_N+ closure generates particle concentrations that are guaranteed to be non-negative. Under an additional, mild regularity assumption, we prove that as the moment order tends to infinity, the FP_N+ approximation converges, in the L2 sense, at the same rate as the FP_N approximation; numerical tests suggest that this assumption may not be necessary. By numerical experiments on the challenging line source benchmark problem, we confirm that the FP_N+ method indeed produces accurate and non-negative solutions. To apply the FP_N+ closure on problems at large temporal-spatial scales, we develop a positive asymptotic preserving (AP) numerical PDE solver. We prove that the propose AP scheme maintains stability and accuracy with standard mesh sizes at large temporal-spatial scales, while, for generic numerical schemes, excessive refinements on temporal-spatial meshes are required. We also show that the proposed scheme preserves positivity of the particle concentration, under some time step restriction. Numerical results confirm that the proposed AP scheme is capable for solving linear transport equations at large temporal-spatial scales, for which a generic scheme could fail. Constrained optimization problems are involved in the formulation of the FP_N+ closure to enforce non-negativity of the FP_N+ approximation on the set of quadrature points. These optimization problems can be written as strictly convex quadratic programs (CQPs) with a large number of inequality constraints. To efficiently solve the CQPs, we propose a constraint-reduced variant of a Mehrotra-predictor-corrector algorithm, with a novel constraint selection rule. We prove that, under appropriate assumptions, the proposed optimization algorithm converges globally to the solution at a locally q-quadratic rate. We test the algorithm on randomly generated problems, and the numerical results indicate that the combination of the proposed algorithm and the constraint selection rule outperforms other compared constraint-reduced algorithms, especially for problems with many more inequality constraints than variables.

Arsenic bioleaching in medical realgar ore and arsenicbearing refractory gold ore by combination of Acidithiobacillus ferrooxidans and Acidithiobacillus thiooxidans

Purpose: To develop a novel biotechnological method for removing toxic arsenic from two kinds of representative arsenic-containing ores using different mixed mesophilic acidophiles. Methods: Bioleaching of the two types of arsenic-containing ores by mixed arsenic-unadapted Acidithiobacillus ferrooxidans and Acidithiobacillus thiooxidans or mixed arsenic-adapted cultures, were carried out. Arsenic bioleaching ratios in the various leachates were determined and compared. Results: The results showed that the maximum arsenic leaching ratio obtained from realgar in the presence of mixed adapted cultures was 28.6 %. However, the maximum arsenic leaching ratio from realgar in the presence of mixed unadapted strains was only 12.4 %. Besides, maximum arsenic leaching ratios from arsenic-bearing refractory gold ore by mixed adapted strains or unadapted strains were 45.0 and 22.9 %, respectively. Oxidation of these two ores by sulfuric acid was insignificant, as maximum arsenic leaching ratios of realgar and arsenic-bearing refractory gold ore in the absence of any bacterium were only 2.8 and 11.2 %, respectively. Conclusion: Arsenic leaching ratio of realgar and refractory gold ore can be enhanced significantly in the presence of arsenic-adapted mesophilic acidophiles.

Corrigendum to “The envelope theorem for multiobjective convex programming via contingent derivatives” [J. Math. Anal. Appl. 372 (1) (2010) 197–207]

The aim of this note is to formulate an envelope theorem for vector convex programs. This version corrects an earlier work, “The envelope theorem for multiobjective convex programming via contingent derivatives” by Jiménez Guerra et al. (2010) [3]. We first propose a necessary and sufficient condition allowing to restate the main result proved in the alluded paper. Second, we introduce a new Lagrange multiplier in order to obtain an envelope theorem avoiding the aforementioned error.

Sensitivity Analysis in Convex Optimization through the Circatangent Derivative

The main goal of this paper is to analyse the sensitivity of a vector convex optimization problem according to variations in the right-hand side. We measure the quantitative behavior of a certain set of Pareto optimal points characterized to become minimum when the objective function is composed with a positive function. Its behavior is analysed quantitatively using the circatangent derivative for set-valued maps. Particularly, it is shown that the sensitivity is closely related to a Lagrange multiplier solution of a dual program.

Therapeutic effects of ciprofloxacin/bushenhuazhuo combination on chronic prostatitis

Purpose: To evaluate the clinical effect of bushenhuazhuo (a Chinese traditional medicine) in combination with ciprofloxacin (an orthodox medicine) in chronic prostatitis (CP) therapy. Methods: A total of 160 patients who suffered from CP and received treatment in the People’s Hospital of Zhengzhou between April 2012 and June 2014 were selected and divided randomly into treatment and control groups, with 80 patients in each group. Control group was given 0.25 g ciprofloxacin hydrochloride tablets twice a day for 4 weeks. In addition to ciprofloxacin administration, patients in the treatment group also received a dose of bushenhuazhuo preparation twice daily for 4 weeks. Clinical outcomes, quality of life as well as lecithin body and white blood cell (WBC) count in expressed prostatic secretions (EPS-WBC) were evaluated. Results: Cure rates in the treatment and control groups were 90 and 72.50 %, respectively; this difference was significant (p < 0.05). Scores for National Institutes of Health Chronic Prostatitis Symptom Index (NIH-CPSI), WBC, and lecithin bodies in the treatment group (8.20 ± 2.20 points, 4.50 ± 1.20 points, and 28.10 ± 2.10 points, respectively) were higher (p < 0.05) than for the control group (12.20 ± 2.20, 6.30 ± 2.20, and 23.30 ± 2.90 points, respectively). The levels of interferon (IFN)-γ and tumour necrosis factor (TNF)-α in the treatment group (26.20 ± 3.30 and 33.80 ± 5.40 mg/L, respectively) were lower than those in the control group (37.70 ± 3.90 and 48.40 ± 3.70 mg/L, respectively), whereas the level of interleukin (IL)-10 in the treatment group (292.60 ± 23.70 mg/L) was higher (p < 0.05) than that in control group (235.80 ± 25.90 mg/L). Conclusion: Ciprofloxacin combined with the Chinese traditional medicine, bushenhuazhuo preparation, demonstrates a marked therapeutic effect in CP. Its mechanism of action may be related to decreased levels of IFN-γ and TNF-α and increased IL-10.

More favorable combination of circumstances could hardly have been desired : a bottom to top examination of the Pittsburgh and Boston Mining Company's Cliff Mine

The Cliff Mine, an archaeological site situated on the Keweenaw Peninsula of Michigan, is the location of the first successful attempt to mine native copper in North America. Under the management of the Pittsburgh & Boston Mining Company from 1845-1879, two-third of the Cliff’s mineral output was in the form of mass copper, some pieces of which weighed over 5 tons when removed from the ground. The unique nature of mass copper and the Cliff Mine’s handling of it make it one of the best examples of early mining processes in the Keweenaw District. Mass copper only constituted 2% of the entire product of the Lake Superior copper districts, and the story of early mining on the Peninsula is generally overshadowed by later, longer running mines such as the Calumet & Helca and Quincy Mining Companies. Operating into the mid-twentieth century, the size and duration of these later mines would come to define the region, though they would not have been possible without the Cliff’s early success. Research on the Cliff Mine has previously focused on social and popular history, neglecting the structural remains. However, these remains are physical clues to the technical processes that defined early mining on the Keweenaw. Through archaeological investigations, these processes and their associated networks were documented as part of the 2010 Michigan Technological Archaeology Field School’s curriculum. The project will create a visual representation of these processes utilizing Geographic Information Systems software. This map will be a useful aid in future research, community engagement and possible future interpretive planning.

Gravimetric and density profiling using the combination of surface acoustic waves and neutron reflectivity

A new approach is described herein, where neutron reflectivity measurements that probe changes in the density profile of thin films as they absorb material from the gas phase have been combined with a Love wave based gravimetric assay that measures the mass of absorbed material. This combination of techniques not only determines the spatial distribution of absorbed molecules, but also reveals the amount of void space within the thin film (a quantity that can be difficult to assess using neutron reflectivity measurements alone). The uptake of organic solvent vapours into spun cast films of polystyrene has been used as a model system with a view to this method having the potential for extension to the study of other systems. These could include, for example, humidity sensors, hydrogel swelling, biomolecule adsorption or transformations of electroactive and chemically reactive thin films. This is the first ever demonstration of combined neutron reflectivity and Love wave-based gravimetry and the experimental caveats, limitations and scope of the method are explored and discussed in detail.

Investigation of the enhanced antimicrobial activity of combination dry powder inhaler formulations of lactoferrin

The airways of most people with cystic fibrosis are colonized with biofilms of the Gram-negative, opportunistic pathogen Pseudomonas aeruginosa. Delivery of antibiotics directly to the lung in the form of dry powder aerosols offers the potential to achieve high local concentrations directly to the biofilms. Unfortunately, current aerosolised antibiotic regimes are unable to efficiently eradicate these biofilms from the airways. We investigated the ability of the innate antimicrobial, lactoferrin, to enhance the activity of two aminoglycoside antibiotics (tobramycin and gentamicin) against biofilms of P. aeruginosa strain PAO1. Biofilms were prepared in 96 well polystyrene plates. Combinations of the antibiotics and various lactoferrin preparations were spray dried. The bacterial cell viability of the various spray dried combinations was determined. Iron-free lactoferrin (apo lactoferrin) induced a 3-log reduction in the killing of planktonic cell by the aminoglycoside antibiotics (p < 0.01) and also reduced both the formation and persistence of P. aeruginosa biofilms (p < 0.01). Combinations of lactoferrin and an aminoglycoside displays potential as an effective new therapeutic strategy in the treatment of P. aeruginosa biofilms infections such as those typical of the CF lungs.