Maharam-type kernel representation for operators with a trigonometric domination

[EN] Consider a linear and continuous operator T between Banach function spaces. We prove that under certain requirements an integral inequality for T is equivalent to a factorization of T through a specific kernel operator: in other words, the operator T has what we call a Maharam-type kernel representation. In the case that the inequality provides a domination involving trigonometric functions, a special factorization through the Fourier operator is given. We apply this result to study the problem that motivates the paper: the approximation of functions in L2[0, 1] by means of trigonometric series whose Fourier coefficients are given by weighted trigonometric integrals.This research has been supported by MTM2016-77054-C2-1-P (Ministerio de Economia, Industria y Competitividad, Spain).Sánchez Pérez, EA. (2017). Maharam-type kernel representation for operators with a trigonometric domination. Aequationes Mathematicae. 91(6):1073-1091. https://doi.org/10.1007/s00010-017-0507-6S10731091916Calabuig, J.M., Delgado, O., Sánchez Pérez, E.A.: Generalized perfect spaces. Indag. Math. 19(3), 359–378 (2008)Calabuig, J.M., Delgado, O., Sánchez Pérez, E.A.: Factorizing operators on Banach function spaces through spaces of multiplication operators. J. Math. Anal. Appl. 364, 88–103 (2010)Delgado, O., Sánchez Pérez, E.A.: Strong factorizations between couples of operators on Banach function spaces. J. Convex Anal. 20(3), 599–616 (2013)Dodds, P.G., Huijsmans, C.B., de Pagter, B.: Characterizations of conditional expectation type operators. Pacific J. Math. 141(1), 55–77 (1990)Flores, J., Hernández, F.L., Tradacete, P.: Domination problems for strictly singular operators and other related classes. Positivity 15(4), 595–616 (2011). 2011Fremlin, D.H.: Tensor products of Banach lattices. Math. Ann. 211, 87–106 (1974)Hu, G.: Weighted norm inequalities for bilinear Fourier multiplier operators. Math. Ineq. Appl. 18(4), 1409–1425 (2015)Halmos, P., Sunder, V.: Bounded Integral Operators on $$L^2$$ L 2 Spaces. Springer, Berlin (1978)Kantorovitch, L., Vulich, B.: Sur la représentation des opérations linéaires. Compositio Math. 5, 119–165 (1938)Kolwicz, P., Leśnik, K., Maligranda, L.: Pointwise multipliers of Calderón- Lozanovskii spaces. Math. Nachr. 286, 876–907 (2013)Kolwicz, P., Leśnik, K., Maligranda, L.: Pointwise products of some Banach function spaces and factorization. J. Funct. Anal. 266(2), 616–659 (2014)Kuo, W.-C., Labuschagne, C.C.A., Watson, B.A.: Conditional expectations on Riesz spaces. J. Math. Anal. Appl. 303, 509–521 (2005)Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces II. Springer, Berlin (1979)Maharam, D.: The representation of abstract integrals. Trans. Am. Math. Soc. 75, 154–184 (1953)Maharam, D.: On kernel representation of linear operators. Trans. Am. Math. Soc. 79, 229–255 (1955)Maligranda, L., Persson, L.E.: Generalized duality of some Banach function spaces. Indag. Math. 51, 323–338 (1989)Neugebauer, C.J.: Weighted norm inequalities for averaging operators of monotone functions. Publ. Mat. 35, 429–447 (1991)Okada, S., Ricker, W.J., Sánchez Pérez, E.A.: Optimal Domain and Integral Extension of Operators Acting in Function Spaces. Operator Theory: Adv. Appl., vol. 180. Birkhäuser, Basel (2008)Rota, G.C.: On the representation of averaging operators. Rend. Sem. Mat. Univ. Padova. 30, 52–64 (1960)Sánchez Pérez, E.A.: Factorization theorems for multiplication operators on Banach function spaces. Integr. Equ. Oper. Theory 80(1), 117–135 (2014)Schep, A.R.: Factorization of positive multilinear maps. Ill. J. Math. 28(4), 579–591 (1984)Schep, A.R.: Products and factors of Banach function spaces. Positivity 14(2), 301–319 (2010

Bone Is Not Essential for Osteoclast Activation

Background: The mechanism whereby bone activates resorptive behavior in osteoclasts, the cells that resorb bone, is unknown. It is known that avb3 ligands are important, because blockade of avb3 receptor signaling inhibits bone resorption, but this might be through inhibition of adhesion or migration rather than resorption itself. Nor is it known whether avb3 ligands are sufficient for resorption the consensus is that bone mineral is essential for the recognition of bone as the substrate appropriate for resorption. Methodology/Principal Findings: Vitronectin- but not fibronectin-coated coverslips induced murine osteoclasts to secrete tartrate-resistant acid phosphatase, as they do on bone. Osteoclasts incubated on vitronectin, unlike fibronectin, formed podosome belts on glass coverslips, and these were modulated by resorption-regulating cytokines. Podosome belts formed on vitronectin-coated surfaces whether the substrates were rough or smooth, rigid or flexible. We developed a novel approach whereby the substrate-apposed surface of cells can be visualized in the scanning electron microscope. With this approach, supported by transmission electron microscopy, we found that osteoclasts on vitronectin-coated surfaces show ruffled borders and clear zones characteristic of resorbing osteoclasts. Ruffles were obscured by a film if cells were incubated in the cathepsin inhibitor E64, suggesting that removal of the film represents substrate-degrading behavior. Analogously, osteoclasts formed resorption-like trails on vitronectin-coated substrates. Like bone resorption, these trails were dependent upon resorbogenic cytokines and were inhibited by E64. Bone mineral induced actin rings and surface excavation only if first coated with vitronectin. Fibronectin could not substitute in any of these activities, despite enabling adhesion and cell spreading. Conclusions/Significance: Our results show that ligands avb3 are not only necessary but sufficient for the induction of resorptive behavior in osteoclasts; and suggest that bone is recognized through its affinity for these ligands, rather than by its mechanical or topographical attributes, or through a putative ‘mineral receptor’

Patient adherence to medical treatment: a review of reviews

BACKGROUND: Patients' non-adherence to medical treatment remains a persistent problem. Many interventions to improve patient adherence are unsuccessful and sound theoretical foundations are lacking. Innovations in theory and practice are badly needed. A new and promising way could be to review the existing reviews of adherence to interventions and identify the underlying theories for effective interventions. That is the aim of our study. METHODS: The study is a review of 38 systematic reviews of the effectiveness of adherence interventions published between 1990 and 2005. Electronic literature searches were conducted in Medline, Psychinfo, Embase and the Cochrane Library. Explicit inclusion and exclusion criteria were applied. The scope of the study is patient adherence to medical treatment in the cure and care sector. RESULTS: Significant differences in the effectiveness of adherence interventions were found in 23 of the 38 systematic reviews. Effective interventions were found in each of four theoretical approaches to adherence interventions: technical, behavioural, educational and multi-faceted or complex interventions. Technical solutions, such as a simplification of the regimen, were often found to be effective, although that does not count for every therapeutic regimen.Overall, our results show that, firstly, there are effective adherence interventions without an explicit theoretical explanation of the operating mechanisms, for example technical solutions. Secondly, there are effective adherence interventions, which clearly stem from the behavioural theories, for example incentives and reminders. Thirdly, there are other theoretical models that seem plausible for explaining non-adherence, but not very effective in improving adherence behaviour. Fourthly, effective components within promising theories could not be identified because of the complexity of many adherence interventions and the lack of studies that explicitly compare theoretical components. CONCLUSION: There is a scarcity of comparative studies explicitly contrasting theoretical models or their components. The relative weight of these theories and the effective components in the interventions designed to improve adherence, need to be assessed in future studies. (aut.ref.

Simultaneous Mutations in Multi-Viral Proteins Are Required for Soybean mosaic virus to Gain Virulence on Soybean Genotypes Carrying Different R Genes

BACKGROUND: Genetic resistance is the most effective and sustainable approach to the control of plant pathogens that are a major constraint to agriculture worldwide. In soybean, three dominant R genes, i.e., Rsv1, Rsv3 and Rsv4, have been identified and deployed against Soybean mosaic virus (SMV) with strain-specificities. Molecular identification of virulent determinants of SMV on these resistance genes will provide essential information for the proper utilization of these resistance genes to protect soybean against SMV, and advance knowledge of virus-host interactions in general. METHODOLOGY/PRINCIPAL FINDINGS: To study the gain and loss of SMV virulence on all the three resistance loci, SMV strains G7 and two G2 isolates L and LRB were used as parental viruses. SMV chimeras and mutants were created by partial genome swapping and point mutagenesis and then assessed for virulence on soybean cultivars PI96983 (Rsv1), L-29 (Rsv3), V94-5152 (Rsv4) and Williams 82 (rsv). It was found that P3 played an essential role in virulence determination on all three resistance loci and CI was required for virulence on Rsv1- and Rsv3-genotype soybeans. In addition, essential mutations in HC-Pro were also required for the gain of virulence on Rsv1-genotype soybean. To our best knowledge, this is the first report that CI and P3 are involved in virulence on Rsv1- and Rsv3-mediated resistance, respectively. CONCLUSIONS/SIGNIFICANCE: Multiple viral proteins, i.e., HC-Pro, P3 and CI, are involved in virulence on the three resistance loci and simultaneous mutations at essential positions of different viral proteins are required for an avirulent SMV strain to gain virulence on all three resistance loci. The likelihood of such mutations occurring naturally and concurrently on multiple viral proteins is low. Thus, incorporation of all three resistance genes in a soybean cultivar through gene pyramiding may provide durable resistance to SMV

Insights into the innate immunity of the Mediterranean mussel Mytilus galloprovincialis

<p>Abstract</p> <p>Background</p> <p>Sessile bivalves of the genus <it>Mytilus </it>are suspension feeders relatively tolerant to a wide range of environmental changes, used as sentinels in ecotoxicological investigations and marketed worldwide as seafood. Mortality events caused by infective agents and parasites apparently occur less in mussels than in other bivalves but the molecular basis of such evidence is unknown. The arrangement of Mytibase, interactive catalogue of 7,112 transcripts of <it>M. galloprovincialis</it>, offered us the opportunity to look for gene sequences relevant to the host defences, in particular the innate immunity related genes.</p> <p>Results</p> <p>We have explored and described the Mytibase sequence clusters and singletons having a putative role in recognition, intracellular signalling, and neutralization of potential pathogens in <it>M. galloprovincialis</it>. Automatically assisted searches of protein signatures and manually cured sequence analysis confirmed the molecular diversity of recognition/effector molecules such as the antimicrobial peptides and many carbohydrate binding proteins. Molecular motifs identifying complement C1q, C-type lectins and fibrinogen-like transcripts emerged as the most abundant in the Mytibase collection whereas, conversely, sequence motifs denoting the regulatory cytokine MIF and cytokine-related transcripts represent singular and unexpected findings. Using a cross-search strategy, 1,820 putatively immune-related sequences were selected to design oligonucleotide probes and define a species-specific Immunochip (DNA microarray). The Immunochip performance was tested with hemolymph RNAs from mussels injected with <it>Vibrio splendidus </it>at 3 and 48 hours post-treatment. A total of 143 and 262 differentially expressed genes exemplify the early and late hemocyte response of the <it>Vibrio</it>-challenged mussels, respectively, with AMP trends confirmed by qPCR and clear modulation of interrelated signalling pathways.</p> <p>Conclusions</p> <p>The Mytibase collection is rich in gene transcripts modulated in response to antigenic stimuli and represents an interesting window for looking at the mussel immunome (transcriptomes mediating the mussel response to non-self or abnormal antigens). On this basis, we have defined a new microarray platform, a mussel Immunochip, as a flexible tool for the experimental validation of immune-candidate sequences, and tested its performance on <it>Vibrio</it>-activated mussel hemocytes. The microarray platform and related expression data can be regarded as a step forward in the study of the adaptive response of the <it>Mytilus </it>species to an evolving microbial world.</p

Variability in organic carbon reactivity across lake residence time and trophic gradients

The transport of dissolved organic carbon from land to ocean is a large dynamic component of the global carbon cycle. Inland waters are hotspots for organic matter turnover, via both biological and photochemical processes, and mediate carbon transfer between land, oceans and atmosphere. However, predicting dissolved organic carbon reactivity remains problematic. Here we present in situ dissolved organic carbon budget data from 82 predominantly European and North American water bodies with varying nutrient concentrations and water residence times ranging from one week to 700 years. We find that trophic status strongly regulates whether water bodies act as net dissolved organic carbon sources or sinks, and that rates of both dissolved organic carbon production and consumption can be predicted from water residence time. Our results suggest a dominant role of rapid light-driven removal in water bodies with a short water residence time, whereas in water bodies with longer residence times, slower biotic production and consumption processes are dominant and counterbalance one another. Eutrophication caused lakes to transition from sinks to sources of dissolved organic carbon. We conclude that rates and locations of dissolved organic carbon processing and associated CO2 emissions in inland waters may be misrepresented in global carbon budgets if temporal and spatial reactivity gradients are not accounted for

Inhaled furosemide for relief of air hunger versus sense of breathing effort: a randomized controlled trial

Background. Inhaled furosemide offers a potentially novel treatment for dyspnoea, which may reflect modulation of pulmonary stretch receptor feedback to the brain. Specificity of relief is unclear because different neural pathways may account for different components of clinical dyspnoea. Our objective was to evaluate if inhaled furosemide relieves the air hunger component (uncomfortable urge to breathe) but not the sense of breathing work/effort of dyspnoea. Methods. A randomised, double blind, placebo-controlled crossover trial in 16 healthy volunteers studied in a university research laboratory. Each participant received 3 mist inhalations (either 40 mg furosemide or 4 ml saline) separated by 30–60 min on 2 test days. Each participant was randomised to mist order ‘furosemide-saline-furosemide’ (n- = 8) or ‘saline-furosemide-saline’ (n = 8) on both days. One day involved hypercapnic air hunger tests (mean ± SD PCO2 = 50 ± 3.7 mmHg; constrained ventilation = 9 ± 1.5 L/min), the other involved work/effort tests with targeted ventilation (17 ± 3.1 L/min) and external resistive load (20cmH2O/L/s). Primary outcome was ratings of air hunger or work/effort every 15 s on a visual analogue scale. During saline inhalations, 1.5 mg furosemide was infused intravenously to match the expected systemic absorption from the lungs when furosemide is inhaled. Corresponding infusions of saline during furosemide inhalations maintained procedural blinding. Average visual analogue scale ratings (%full scale) during the last minute of air hunger or work/effort stimuli were analysed using Linear Mixed Methods. Results. Data from all 16 participants were analysed. Inhaled furosemide relative to inhaled saline significantly improved visual analogues scale ratings of air hunger (Least Squares Mean ± SE − 9.7 ± 2%; p = 0.0015) but not work/effort (+ 1.6 ± 2%; p = 0.903). There were no significant adverse events. Conclusions. Inhaled furosemide was effective at relieving laboratory induced air hunger but not work/effort in healthy adults; this is consistent with the notion that modulation of pulmonary stretch receptor feedback by inhaled furosemide leads to dyspnoea relief that is specific to air hunger, the most unpleasant quality of dyspnoea