Differentiability of L-p of a vector measure and applications to the Bishop-Phelps-Bollobas property

[EN] We study the properties of Gâteaux, Fréchet, uniformly Fréchet and uniformly Gâteaux smoothness of the space Lp(m) of scalar p-integrable functions with respect to a positive vector measure m with values in a Banach lattice. Applications in the setting of the Bishop-Phelps-Bollobás property (both for operators and bilinear forms) are also given.Research supported by Ministerio de Economia y Competitividad and FEDER under projects MTM2012-36740-c02-02 (L. Agud and E.A. Sanchez-Perez), MTM201453009-P (J.M. Calabuig) and MTM2014-54182-P (S. Lajara). S. Lajara was also supported by project 19275/PI/14 funded by Fundacion Seneca-Agencia de Ciencia y Tecnologia de la Region de Murcia within the framework of PCTIRM 2011-2014.Agud Albesa, L.; Calabuig, JM.; Lajara, S.; Sánchez Pérez, EA. (2017). Differentiability of L-p of a vector measure and applications to the Bishop-Phelps-Bollobas property. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 111(3):735-751. https://doi.org/10.1007/s13398-016-0327-xS7357511113Acosta, M.D., Aron, R.M., García, D., Maestre, M.: The Bishop–Phelps–Bollobás theorem for operators. J. Funct. Anal. 254(11), 2780–2799 (2008)Acosta, M.D., Becerra-Guerrero, J., Choi, Y.S., García, D., Kim, S.K., Lee, H.J., Maestre, M.: The Bishop–Phelps–Bollobás theorem for bilinear forms and polinomials. J. Math. Soc. Jpn 66(3), 957–979 (2014)Acosta, M.D., Becerra-Guerrero, J., García, D., Maestre, M.: The Bishop–Phelps–Bollobás theorem for bilinear forms. Trans. Am. Math. Soc. 11, 5911–5932 (2013)Agud, L., Calabuig, J.M., Sánchez Pérez, E.A.: On the smoothness of $$L^p$$ L p of a positive vector measure. Monatsh. Math. 178(3), 329–343 (2015)Aron, R.M., Cascales, B., Kozhushkina, O.: The Bishop–Phelps–Bollobás theorem and Asplund operators. Proc. Am. Math. Soc. 139, 3553–3560 (2011)Bishop, E., Phelps, R.R.: A proof that every Banach space is subreflexive. Bull. Am. Math. Soc. 67, 97–98 (1961)Bollobás, B.: An extension to the theorem of Bishop and Phelps. Bull. Lond. Math. Soc. 2, 181–182 (1970)Cascales, B., Guirao, A.J., Kadets, V.: A Bishop–Phelps–Bollobás theorem type theorem for uniform algebras. Adv. Math. 240, 370–382 (2013)Choi, Y.S., Song, H.G.: The Bishop–Phelps–Bollobás theorem fails for bilinear forms on $$\ell _1\times \ell _1$$ ℓ 1 × ℓ 1 . J. Math. Anal. Appl. 360, 752–753 (2009)Deville, R., Godefroy, G., Zizler, V.: Smoothness and renormings in Banach spaces. Pitman Monographs and Surveys in Pure and Appl. Math., vol. 64, Longman, Harlow (1993)Diestel, J., Uhl, J.J.: Vector Measures. Math. Surveys, vol. 15, AMS, Providence, RI (1977)Fabian, M., Godefroy, G., Montesinos, V., Zizler, V.: Inner characterizations of weakly compactly generated Banach spaces and their relatives. J. Math. Anal. Appl. 297, 419–455 (2004)Fabian, M., Godefroy, G., Zizler, V.: The structure of uniformly Gâteaux smooth Banach spaces. Israel J. Math. 124, 243–252 (2001)Fabian, M., Habala, P., Hájek, P., Montesinos, V., Zizler, V.: Banach Space Theory: The Basis for Linear and Nonlinear Analysis. CMS Books in Mathematics, Springer, New York (2011)Fabian, M., Lajara, S.: Smooth renormings of the Lebesgue–Bochner function space $$L^1(\mu, X)$$ L 1 ( μ , X ) . Stud. Math. 209(3), 247–265 (2012)Ferrando, I., Rodríguez, J.: The weak topology on $$L^p$$ L p of a vector measure. Top. Appl. 155(13), 1439–1444 (2008)Hájek, P., Johanis, M.: Smooth analysis in Banach spaces. De Gruyter Series in Nonlinear Analysis and Applications, De Gruyter (2014)Kim, S.K.: The Bishop–Phelps–Bollobás theorem for operators from $$c_0$$ c 0 to uniformly convex spaces. Israel J. Math. 197, 425–435 (2013)Kim, S.K., Lee, H.J.: The Bishop–Phelps–Bollobás theorem for operators from $$C(K)$$ C ( K ) to uniformly convex spaces. J. Math. Anal. Appl. 421(1), 51–58 (2015)Hudzik, H., Kamińska, A., Mastylo, M.: Monotonocity and rotundity properties in Banach lattices. Rock. Mount J. Math. 30(3), 933–950 (2000)Kutzarova, D., Troyanski, S.L.: On equivalent norms which are uniformly convex or uniformly differentiable in every direction in symmetric function spaces. Serdica 11, 121–134 (1985)Okada, S., Ricker, W.J., Sánchez-Pérez, E.A.: Optimal Domain and Integral Extension of Operators Acting in Function Spaces. Operator Theory: Advances and Applications, vol. 180. Birkhäuser Verlag, Basel (2008

Omega-3 fatty acids and vitamin D in immobilisation: Part A - Modulation of appendicular mass content, composition and structure

Objectives: Muscle size decreases in response to short-term limb immobilisation. This study set out to determine whether two potential protein-sparing modulators (eicosapentaenoic acid and vitamin D) would attenuate immobilisation-induced changes in muscle characteristics. Design: The study used a randomised, double-blind, placebo-controlled design. Setting: The study took part in a laboratory setting. Participants: Twenty-four male and female healthy participants, aged 23.0±5.8 years. Intervention: The non-dominant arm was immobilised in a sling for a period of nine waking hours a day over two continuous weeks. Participants were randomly assigned to one of three groups: placebo (n=8, Lecithin, 2400 mg daily), omega-3 (ω-3) fatty acids (n=8, eicosapentaenoic acid (EPA); 1770 mg, and docosahexaenoic acid (DHA); 390 mg, daily) or vitamin D (n=8, 1,000 IU daily). Measurements: Muscle and sub-cutaneous adipose thickness (B-mode ultrasonography), body composition (DXA) and arm girth (anthropometry) were measured before immobilisation, immediately on removal of the sling and two weeks after re-mobilisation. Results: Muscle thickness (-5.4±4.3%), upper and lower arm girth (-1.3±0.4 and -0.8±0.8%, respectively), lean mass (-3.6±3.7%) and bone mineral content (BMC) (-2.3±1.5%) decreased significantly with limb immobilisation in the placebo group (P0.05) towards attenuating the decreases in muscle thickness, upper/lower arm girths and BMC observed in the placebo group. The ω-3 supplementation group demonstrated a non-significant attenuation of the decrease in DXA quantified lean mass observed in the placebo group. Sub-cutaneous adipose thickness increased in the placebo group (P<0.05). ω-3 and vitamin D both blunted this response, with ω-3 having a greater effect (P<0.05). All parameters had returned to baseline values at the re-mobilisation phase of the study. Conclusion: Overall, at the current doses, ω-3 and vitamin D supplementation only attenuated one of the changes associated with non-injurious limb immobilisation. These findings would necessitate further research into either a) supplementation linked to injury-induced immobilisation, or b) larger doses of these supplements to confirm/refute the physiological reserve potential of the two supplements

Double blind randomized placebo-controlled trial on the effects of testosterone supplementation in elderly men with moderate to low testosterone levels: design and baseline characteristics [ISRCTN23688581]

In ageing men testosterone levels decline, while cognitive function, muscle and bone mass, sexual hair growth, libido and sexual activity decline and the risk of cardiovascular diseases increase. We set up a double-blind, randomized placebo-controlled trial to investigate the effects of testosterone supplementation on functional mobility, quality of life, body composition, cognitive function, vascular function and risk factors, and bone mineral density in older hypogonadal men. We recruited 237 men with serum testosterone levels below 13.7 nmol/L and ages 60–80 years. They were randomized to either four capsules of 40 mg testosterone undecanoate (TU) or placebo daily for 26 weeks. Primary endpoints are functional mobility and quality of life. Secondary endpoints are body composition, cognitive function, aortic stiffness and cardiovascular risk factors and bone mineral density. Effects on prostate, liver and hematological parameters will be studied with respect to safety. Measure of effect will be the difference in change from baseline visit to final visit between TU and placebo. We will study whether the effect of TU differs across subgroups of baseline waist girth (< 100 cm vs. ≥ 100 cm; testosterone level (<12 versus ≥ 12 nmol/L), age (< median versus ≥ median), and level of outcome under study (< median versus ≥ median). At baseline, mean age, BMI and testosterone levels were 67 years, 27 kg/m(2 )and 10.72 nmol/L, respectively

Jet energy measurement with the ATLAS detector in proton-proton collisions at root s=7 TeV

The jet energy scale and its systematic uncertainty are determined for jets measured with the ATLAS detector at the LHC in proton-proton collision data at a centre-of-mass energy of √s = 7TeV corresponding to an integrated luminosity of 38 pb-1. Jets are reconstructed with the anti-kt algorithm with distance parameters R=0. 4 or R=0. 6. Jet energy and angle corrections are determined from Monte Carlo simulations to calibrate jets with transverse momenta pT≥20 GeV and pseudorapidities {pipe}η{pipe}<4. 5. The jet energy systematic uncertainty is estimated using the single isolated hadron response measured in situ and in test-beams, exploiting the transverse momentum balance between central and forward jets in events with dijet topologies and studying systematic variations in Monte Carlo simulations. The jet energy uncertainty is less than 2. 5 % in the central calorimeter region ({pipe}η{pipe}<0. 8) for jets with 60≤pT<800 GeV, and is maximally 14 % for pT<30 GeV in the most forward region 3. 2≤{pipe}η{pipe}<4. 5. The jet energy is validated for jet transverse momenta up to 1 TeV to the level of a few percent using several in situ techniques by comparing a well-known reference such as the recoiling photon pT, the sum of the transverse momenta of tracks associated to the jet, or a system of low-pT jets recoiling against a high-pT jet. More sophisticated jet calibration schemes are presented based on calorimeter cell energy density weighting or hadronic properties of jets, aiming for an improved jet energy resolution and a reduced flavour dependence of the jet response. The systematic uncertainty of the jet energy determined from a combination of in situ techniques is consistent with the one derived from single hadron response measurements over a wide kinematic range. The nominal corrections and uncertainties are derived for isolated jets in an inclusive sample of high-pT jets. Special cases such as event topologies with close-by jets, or selections of samples with an enhanced content of jets originating from light quarks, heavy quarks or gluons are also discussed and the corresponding uncertainties are determined. © 2013 CERN for the benefit of the ATLAS collaboration

Measurement of the inclusive and dijet cross-sections of b-jets in pp collisions at sqrt(s) = 7 TeV with the ATLAS detector

The inclusive and dijet production cross-sections have been measured for jets containing b-hadrons (b-jets) in proton-proton collisions at a centre-of-mass energy of sqrt(s) = 7 TeV, using the ATLAS detector at the LHC. The measurements use data corresponding to an integrated luminosity of 34 pb^-1. The b-jets are identified using either a lifetime-based method, where secondary decay vertices of b-hadrons in jets are reconstructed using information from the tracking detectors, or a muon-based method where the presence of a muon is used to identify semileptonic decays of b-hadrons inside jets. The inclusive b-jet cross-section is measured as a function of transverse momentum in the range 20 < pT < 400 GeV and rapidity in the range |y| < 2.1. The bbbar-dijet cross-section is measured as a function of the dijet invariant mass in the range 110 < m_jj < 760 GeV, the azimuthal angle difference between the two jets and the angular variable chi in two dijet mass regions. The results are compared with next-to-leading-order QCD predictions. Good agreement is observed between the measured cross-sections and the predictions obtained using POWHEG + Pythia. MC@NLO + Herwig shows good agreement with the measured bbbar-dijet cross-section. However, it does not reproduce the measured inclusive cross-section well, particularly for central b-jets with large transverse momenta.Comment: 10 pages plus author list (21 pages total), 8 figures, 1 table, final version published in European Physical Journal

Measurement of the cross-section of high transverse momentum vector bosons reconstructed as single jets and studies of jet substructure in pp collisions at √s = 7 TeV with the ATLAS detector

This paper presents a measurement of the cross-section for high transverse momentum W and Z bosons produced in pp collisions and decaying to all-hadronic final states. The data used in the analysis were recorded by the ATLAS detector at the CERN Large Hadron Collider at a centre-of-mass energy of √s = 7 TeV;{\rm Te}{\rm V}$and correspond to an integrated luminosity of$4.6\;{\rm f}{{{\rm b}}^{-1}}$. The measurement is performed by reconstructing the boosted W or Z bosons in single jets. The reconstructed jet mass is used to identify the W and Z bosons, and a jet substructure method based on energy cluster information in the jet centre-of-mass frame is used to suppress the large multi-jet background. The cross-section for events with a hadronically decaying W or Z boson, with transverse momentum${{p}_{{\rm T}}}\gt 320\;{\rm Ge}{\rm V}$and pseudorapidity$|\eta |\lt 1.9$, is measured to be${{\sigma }_{W+Z}}=8.5\pm 1.7$ pb and is compared to next-to-leading-order calculations. The selected events are further used to study jet grooming techniques

Observation of associated near-side and away-side long-range correlations in √sNN=5.02 TeV proton-lead collisions with the ATLAS detector

Two-particle correlations in relative azimuthal angle (Δϕ) and pseudorapidity (Δη) are measured in √sNN=5.02  TeV p+Pb collisions using the ATLAS detector at the LHC. The measurements are performed using approximately 1  μb-1 of data as a function of transverse momentum (pT) and the transverse energy (ΣETPb) summed over 3.1<η<4.9 in the direction of the Pb beam. The correlation function, constructed from charged particles, exhibits a long-range (2<|Δη|<5) “near-side” (Δϕ∼0) correlation that grows rapidly with increasing ΣETPb. A long-range “away-side” (Δϕ∼π) correlation, obtained by subtracting the expected contributions from recoiling dijets and other sources estimated using events with small ΣETPb, is found to match the near-side correlation in magnitude, shape (in Δη and Δϕ) and ΣETPb dependence. The resultant Δϕ correlation is approximately symmetric about π/2, and is consistent with a dominant cos⁡2Δϕ modulation for all ΣETPb ranges and particle pT

The emergence and diversification of a zoonotic pathogen from within the microbiota of intensively farmed pigs

The expansion and intensification of livestock production is predicted to promote the emergence of pathogens. As pathogens sometimes jump between species, this can affect the health of humans as well as livestock. Here, we investigate how livestock microbiota can act as a source of these emerging pathogens through analysis of Streptococcus suis, a ubiquitous component of the respiratory microbiota of pigs that is also a major cause of disease on pig farms and an important zoonotic pathogen. Combining molecular dating, phylogeography, and comparative genomic analyses of a large collection of isolates, we find that several pathogenic lineages of S. suis emerged in the 19th and 20th centuries, during an early period of growth in pig farming. These lineages have since spread between countries and continents, mirroring trade in live pigs. They are distinguished by the presence of three genomic islands with putative roles in metabolism and cell adhesion, and an ongoing reduction in genome size, which may reflect their recent shift to a more pathogenic ecology. Reconstructions of the evolutionary histories of these islands reveal constraints on pathogen emergence that could inform control strategies, with pathogenic lineages consistently emerging from one subpopulation of S. suis and acquiring genes through horizontal transfer from other pathogenic lineages. These results shed light on the capacity of the microbiota to rapidly evolve to exploit changes in their host population and suggest that the impact of changes in farming on the pathogenicity and zoonotic potential of S. suis is yet to be fully realized

Search for direct pair production of the top squark in all-hadronic final states in proton-proton collisions at s√=8 TeV with the ATLAS detector

The results of a search for direct pair production of the scalar partner to the top quark using an integrated luminosity of 20.1fb−1 of proton–proton collision data at √s = 8 TeV recorded with the ATLAS detector at the LHC are reported. The top squark is assumed to decay via t˜→tχ˜01 or t˜→ bχ˜±1 →bW(∗)χ˜01 , where χ˜01 (χ˜±1 ) denotes the lightest neutralino (chargino) in supersymmetric models. The search targets a fully-hadronic final state in events with four or more jets and large missing transverse momentum. No significant excess over the Standard Model background prediction is observed, and exclusion limits are reported in terms of the top squark and neutralino masses and as a function of the branching fraction of t˜ → tχ˜01 . For a branching fraction of 100%, top squark masses in the range 270–645 GeV are excluded for χ˜01 masses below 30 GeV. For a branching fraction of 50% to either t˜ → tχ˜01 or t˜ → bχ˜±1 , and assuming the χ˜±1 mass to be twice the χ˜01 mass, top squark masses in the range 250–550 GeV are excluded for χ˜01 masses below 60 GeV

Search for pair-produced long-lived neutral particles decaying to jets in the ATLAS hadronic calorimeter in ppcollisions at √s=8TeV

The ATLAS detector at the Large Hadron Collider at CERN is used to search for the decay of a scalar boson to a pair of long-lived particles, neutral under the Standard Model gauge group, in 20.3fb−1of data collected in proton–proton collisions at √s=8TeV. This search is sensitive to long-lived particles that decay to Standard Model particles producing jets at the outer edge of the ATLAS electromagnetic calorimeter or inside the hadronic calorimeter. No significant excess of events is observed. Limits are reported on the product of the scalar boson production cross section times branching ratio into long-lived neutral particles as a function of the proper lifetime of the particles. Limits are reported for boson masses from 100 GeVto 900 GeV, and a long-lived neutral particle mass from 10 GeVto 150 GeV