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

Application of the lumped age-class technique to studying the dynamics of malaria-mosquito-human interactions

A series of models of malaria-mosquito-human interactions using the Lumped Age-Class technique of Gurney & Nisbet are developed. The models explicitly include sub-adult mosquito dynamics and assume that population regulation occurs at the larval stage. A challenge for modelling mosquito dynamics in continuous time is that the insect has discrete life-history stages (egg, larva, pupa & adult), the sub-adult stages of relatively fixed duration, which are subject to very different demographic rates. The Lumped Age-Class technique provides a natural way to treat this type of population structure. The resulting model, phrased as a system of delay-differential equations, is only slightly harder to analyse than traditional ordinary differential equations and much easier than the alternative partial differential equation approach. The Lumped Age-Class technique also allows the natural treatment of the relatively fixed time delay between the mosquito ingesting Plasmodium and it becoming infective. Three models are developed to illustrate the application of this approach: one including just the mosquito dynamics, the second including Plasmodium but no human dynamics, and the third including the interaction of the malaria pathogen and the human population (though only in a simple classical Ross-Macdonald manner). A range of epidemiological quantities used in studying malaria such as the vectorial capacity, the entomological inoculation rate and the basic reproductive number (R0) are derived, and examples given of the analysis and simulation of model dynamics. Assumptions and extensions are discussed. It is suggested that this modelling framework may be a natural and useful tool for exploring a variety of issues in malaria-vector epidemiology, especially in circumstances where a dynamic representation of mosquito recruitment is required

Brief report:effects of sensory sensitivity and intolerance of uncertainty on anxiety in mothers of children with autism spectrum disorder

This study examined the relations between anxiety and individual characteristics of sensory sensitivity (SS) and intolerance of uncertainty (IU) in mothers of children with ASD. The mothers of 50 children completed the Hospital Anxiety and Depression Scale, the Highly Sensitive Person Scale and the IU Scale. Anxiety was associated with both SS and IU and IU was also associated with SS. Mediation analyses showed direct effects between anxiety and both IU and SS but a significant indirect effect was found only in the model in which IU mediated between SS. This is the first study to characterize the nature of the IU and SS interrelation in predicting levels of anxiety

Omentalisation as adjunctive treatment of an infected femoral nonunion fracture: a case report

A three-year-old male working border collie with an infected femoral nonunion fracture was managed in a two-stage procedure involving debridement and omentalisation, followed by stabilisation with a bone plate and an autogenous cancellous bone graft. Osseous union was documented radiographically 16 weeks after surgery. Telephone follow-up one year later revealed the dog had returned to full working function without evidence of lameness. To the authors' knowledge, this is the first clinical case described in the veterinary literature using omentalisation as an adjunct to the management of an infected, biologically inactive nonunion fracture

Effect of within-session breaks in play on responsible gambling behaviour during sustained monetary losses

Rapid, continuous gambling formats are associated with higher risks for gambling-related harm in terms of excessive monetary and time expenditure. The current study investigated the effect on gambling response latency and persistence, of a new form of within-game intervention that required players to actively engage in response inhibition via monitoring for stop signals. Seventy-four experienced electronic gaming machine gamblers, with a mean age of 35.28 years, were recruited to participate in a rapid, continuous gambling task where real money could be won and lost. Participants were randomly allocated to either the control condition where no intervention was presented, or either a condition with a passive three minute break in play or a condition with a three minute intervention that required participants to engage in response inhibition. Although there was no main effect for experimental condition on gambling persistence, both interventions were effective in elevating response latency during a period of sustained losses. It was concluded that within-game interventions that create an enforced break in play are effective in increasing response latency between bets during periods of sustained losses. Furthermore, within-game interventions that require active involvement appear to be more effective in increasing response latency than standard, passive breaks in play

Risk adjustment for inter-hospital comparison of primary cesarean section rates: need, validity and parsimony

BACKGROUND: Cesarean section rates is often used as an indicator of quality of care in maternity hospitals. The assumption is that lower rates reflect in developed countries more appropriate clinical practice and general better performances. Hospitals are thus often ranked on the basis of caesarean section rates. The aim of this study is to assess whether the adjustment for clinical and sociodemographic variables of the mother and the fetus is necessary for inter-hospital comparisons of cesarean section (c-section) rates and to assess whether a risk adjustment model based on a limited number of variables could be identified and used. METHODS: Discharge abstracts of labouring women without prior cesarean were linked with abstracts of newborns discharged from 29 hospitals of the Emilia-Romagna Region (Italy) from 2003 to 2004. Adjusted ORs of cesarean by hospital were estimated by using two logistic regression models: 1) a full model including the potential confounders selected by a backward procedure; 2) a parsimonious model including only actual confounders identified by the "change-in-estimate" procedure. Hospital rankings, based on ORs were examined. RESULTS: 24 risk factors for c-section were included in the full model and 7 (marital status, maternal age, infant weight, fetopelvic disproportion, eclampsia or pre-eclampsia, placenta previa/abruptio placentae, malposition/malpresentation) in the parsimonious model. Hospital ranking using the adjusted ORs from both models was different from that obtained using the crude ORs. The correlation between the rankings of the two models was 0.92. The crude ORs were smaller than ORs adjusted by both models, with the parsimonious ones producing more precise estimates. CONCLUSION: Risk adjustment is necessary to compare hospital c-section rates, it shows differences in rankings and highlights inappropriateness of some hospitals. By adjusting for only actual confounders valid and more precise estimates could be obtained

A Sub-Microscopic Gametocyte Reservoir Can Sustain Malaria Transmission

Novel diagnostic tools, including PCR and high field gradient magnetic fractionation (HFGMF), have improved detection of asexual Plasmodium falciparum parasites and especially infectious gametocytes in human blood. These techniques indicate a significant number of people carry gametocyte densities that fall below the conventional threshold of detection achieved by standard light microscopy (LM).To determine how low-level gametocytemia may affect transmission in present large-scale efforts for P. falciparum control in endemic areas, we developed a refinement of the classical Ross-Macdonald model of malaria transmission by introducing multiple infective compartments to model the potential impact of highly prevalent, low gametocytaemic reservoirs in the population. Models were calibrated using field-based data and several numerical experiments were conducted to assess the effect of high and low gametocytemia on P. falciparum transmission and control. Special consideration was given to the impact of long-lasting insecticide-treated bed nets (LLIN), presently considered the most efficient way to prevent transmission, and particularly LLIN coverage similar to goals targeted by the Roll Back Malaria and Global Fund malaria control campaigns. Our analyses indicate that models which include only moderate-to-high gametocytemia (detectable by LM) predict finite eradication times after LLIN introduction. Models that include a low gametocytemia reservoir (requiring PCR or HFGMF detection) predict much more stable, persistent transmission. Our modeled outcomes result in significantly different estimates for the level and duration of control needed to achieve malaria elimination if submicroscopic gametocytes are included.It will be very important to complement current methods of surveillance with enhanced diagnostic techniques to detect asexual parasites and gametocytes to more accurately plan, monitor and guide malaria control programs aimed at eliminating malaria

Plasma antibodies against heat shock protein 70 correlate with the incidence and severity of asthma in a Chinese population

BACKGROUND: The heat shock proteins (Hsps) are induced by stresses such as allergic factors and inflammatory responses in bronchi epithelial cells and therefore may be detectable in patients with asthma. However, the etiologic link between anti-Hsps and asthma (its severity and related inflammatory responses such as interleukin-4 and immunoglobulin E) has not been established. We determined whether antibodies against Hsp60 and Hsp70 were present in patients with asthma and evaluated their associations with risk and severity of asthma. METHODS: We determined the levels of anti-Hsp60 and anti-Hsp70 by immunoblot and their associations with risk and symptom severity of asthma in 95 patients with asthma and 99 matched non-symptomatic controls using multivariate logistic regression analysis. RESULTS: Compared to the controls, asthma patients were more likely to have detectable anti-Hsp60 (17.2% vs 5.1%) and anti-Hsp70 (33.7% vs 8.1%) (p ≤ 0.001). In particular, the presence of anti-Hsp70 was associated with a greater than 2 fold risk for asthma (adjusted OR = 2.21; 95% CI = 1.35~3.59). Furthermore, both anti-Hsp60 and anti-Hsp70 levels were positively correlated with symptom severity (p < 0.05) as well as interleukin-4 and immunoglobulin E (p < 0.05). Individuals with antibodies against anti-Hsp60 and anti-Hsp70 were more likely to have a family history of asthma (p < 0.001) and higher plasma concentrations of total immunoglobulin E (p = 0.001) and interleukin-4 (p < 0.05) than those without antibodies. CONCLUSIONS: These data suggest that anti-Hsp60 and especially anti-Hsp70 correlate with the attacks and severity of asthma. The underlying molecular mechanisms linking antibodies to heat shock proteins and asthma remain to be investigated

A case report and brief review of the literature on bilateral retinal infarction following cardiopulmonary bypass for coronary artery bypass grafting

Postoperative visual loss is a devastating perioperative complication. The commonest aetiologies are anterior ischaemic optic neuropathy (AION), posterior ischaemic optic neuropathy (PION), and central retinal artery occlusion (CRAO). These appear to be related to certain types of operation, most commonly spinal and cardiac bypass procedures; with the rest divided between: major trauma causing excessive blood loss; head/neck and nasal or sinus surgery; major vascular procedures (aortic aneurysm repair, aorto-bifemoral bypass); general surgery; urology; gynaecology; liposuction; liver transplantation and duration of surgery. The non-surgical risk factors are multifactorial: advanced age, prolonged postoperative anaemia, positioning (supine v prone), alteration of venous drainage of the retina, hypertension, smoking, atherosclerosis, hyperlipidaemia, diabetes, hypercoagulability, hypotension, blood loss and large volume resuscitation. Other important cardiac causes are septic emboli from bacterial endocarditis and emboli caused by atrial myxomata. The majority of AION cases occur during CPB followed by head/neck surgery and prone spine surgery. CPB is used to allow coronary artery bypass grafting on a motionless heart. It has many side-effects and complications associated with its use and we report here a case of bilateral retinal infarction during routine coronary artery bypass grafting in a young male patient with multiple risk factors for developing this complication despite steps to minimise its occurrence