Lineability within probability theory settings

[EN] The search of lineability consists on finding large vector spaces of mathematical objects with special properties. Such examples have arisen in the last years in a wide range of settings such as in real and complex analysis, sequence spaces, linear dynamics, norm-attaining functionals, zeros of polynomials in Banach spaces, Dirichlet series, and non-convergent Fourier series, among others. In this paper we present the novelty of linking this notion of lineability to the area of Probability Theory by providing positive (and negative) results within the framework of martingales, random variables, and certain stochastic processes.This work was partially supported by Ministerio de Educacion, Cultura y Deporte, projects MTM2013-47093-P and MTM2015-65825-P, by the Basque Government through the BERC 2014-2017 program and by the Spanish Ministerio de Economia y Competitividad: BCAM Severo Ochoa excellence accreditation SEV-2013-0323.Conejero, JA.; Fenoy, M.; Murillo Arcila, M.; Seoane Sepúlveda, JB. (2017). Lineability within probability theory settings. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 111(3):673-684. https://doi.org/10.1007/s13398-016-0318-yS6736841113Aizpuru, A., Pérez-Eslava, C., García-Pacheco, F.J., Seoane-Sepúlveda, J.B.: Lineability and coneability of discontinuous functions on $$\mathbb{R}$$ R . Publ. Math. Debrecen 72(1–2), 129–139 (2008)Aron, R., Gurariy, V.I., Seoane, J.B.: Lineability and spaceability of sets of functions on $$\mathbb{R}$$ R . Proc. Am. Math. Soc. 133(3), 795–803 (2005, electronic)Aron, R.M., González, L.B., Pellegrino, D.M., Sepúlveda J.B.S.: Lineability: the search for linearity in mathematics. Monographs and Research Notes in Mathematics. CRC Press, Boca Raton (2016)Ash, R.B.: Real analysis and probability. Probability and mathematical statistics, No. 11. Academic Press, New York-London (1972)Barbieri, G., García-Pacheco, F.J., Puglisi, D.: Lineability and spaceability on vector-measure spaces. Stud. Math. 219(2), 155–161 (2013)Bernal-González, L., Cabrera, M.O.: Lineability criteria, with applications. J. Funct. Anal. 266(6), 3997–4025 (2014)Bernal-González, L., Pellegrino, D., Seoane-Sepúlveda, J.B.: Linear subsets of nonlinear sets in topological vector spaces. Bull. Am. Math. Soc. (N.S.), 51(1), 71–130 (2014)Berndt, B.C.: What is a $$q$$ q -series? In: Ramanujan rediscovered, Ramanujan Math. Soc. Lect. Notes Ser., vol. 14, pp. 31–51. Ramanujan Math. Soc., Mysore (2010)Bertoloto, F.J., Botelho, G., Fávaro, V.V., Jatobá, A.M.: Hypercyclicity of convolution operators on spaces of entire functions. Ann. Inst. Fourier (Grenoble) 63(4), 1263–1283 (2013)Billingsley, P.: Probability and measure. Wiley Series in Probability and Mathematical Statistics, 3rd edn, A Wiley-Interscience Publication. Wiley, New York (1995)Botelho, G., Fávaro, V.V.: Constructing Banach spaces of vector-valued sequences with special properties. Mich. Math. J. 64(3), 539–554 (2015)Cariello, D., Seoane-Sepúlveda, J.B.: Basic sequences and spaceability in $$\ell _p$$ ℓ p spaces. J. Funct. Anal. 266(6), 3797–3814 (2014)Drewnowski, L., Lipecki, Z.: On vector measures which have everywhere infinite variation or noncompact range. Dissertationes Math. (Rozprawy Mat.) 339, 39 (1995)Dugundji, J.: Topology. Allyn and Bacon, Inc., Boston, Mass.-London-Sydney (1978, Reprinting of the 1966 original, Allyn and Bacon Series in Advanced Mathematics)Enflo, P.H., Gurariy, V.I., Seoane-Sepúlveda, J.B.: Some results and open questions on spaceability in function spaces. Trans. Am. Math. Soc. 366(2), 611–625 (2014)Fonf, V.P., Zanco, C.: Almost overcomplete and almost overtotal sequences in Banach spaces. J. Math. Anal. Appl. 420(1), 94–101 (2014)Gámez-Merino, J.L., Seoane-Sepúlveda, J.B.: An undecidable case of lineability in $$\mathbb{R}^{\mathbb{R}}$$ R R . J. Math. Anal. Appl. 401(2), 959–962 (2013)Gurariĭ, V.I.: Linear spaces composed of everywhere nondifferentiable functions. C. R. Acad. Bulgare Sci. 44(5), 13–16 (1991)Muñoz-Fernández, G.A., Palmberg, N., Puglisi, D., Seoane-Sepúlveda, J.B.: Lineability in subsets of measure and function spaces. Linear Algebra Appl. 428(11–12), 2805–2812 (2008)Walsh, J.B.: Martingales with a multidimensional parameter and stochastic integrals in the plane. In: Lectures in probability and statistics (Santiago de Chile, 1986), Lecture Notes in Math., vol. 1215, pp. 329–491. Springer, Berlin (1986)Wise, G.L., Hall, E.B.: Counterexamples in probability and real analysis. The Clarendon Press, Oxford University Press, New York (1993

Estudio de la botica de la Alhambra en el siglo XVI

Stock inventories are a very useful source of information in the study of the history of pharmaceutical science. Thisarticle reports on two accounts from the XVI century related to this subject, which on analysis provide interestingand relevant information on the functioning of a pharmacy in the citadel of the Alhambra Palace in Granada,during the early modern age.Los inventarios que recogen las existencias de las boticas son documentos de gran interés para la Historia de laFarmacia. Se informa en este artículo del hallazgo de dos relaciones de este tipo, fechadas en el siglo XVI, cuyoanálisis ofrece interesantes datos sobre la botica de la Alhambra de Granada en la Edad Moderna

pH-triggered endosomal escape of pore-forming Listeriolysin O toxin-coated gold nanoparticles

The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (ERC grant agreement n° 338133)Background: A major bottleneck in drug delivery is the breakdown and degradation of the delivery system through the endosomal/lysosomal network of the host cell, hampering the correct delivery of the drug of interest. In nature, the bacterial pathogen Listeria monocytogenes has developed a strategy to secrete Listeriolysin O (LLO) toxin as a tool to escape the eukaryotic lysosomal system upon infection, allowing it to grow and proliferate unharmed inside the host cell. Results: As a “proof of concept”, we present here the use of purifed His-LLO H311A mutant protein and its conjuga tion on the surface of gold nanoparticles to promote the lysosomal escape of 40 nm-sized nanoparticles in mouse embryonic fbroblasts. Surface immobilization of LLO was achieved after specifc functionalization of the nanoparti cles with nitrile acetic acid, enabling the specifc binding of histidine-tagged proteins. Conclusions: Endosomal acidifcation leads to release of the LLO protein from the nanoparticle surface and its self-assembly into a 300 Å pore that perforates the endosomal/lysosomal membrane, enabling the escape of nanoparticles.Depto. de Química FísicaFac. de Ciencias QuímicasTRUEUnión Europea. FP7Ministerio de Ciencia e Innovación (MICINN)Comunidad de MadridUniversidad Complutense de Madridpu

Food allergy, airborne allergies, and allergic sensitisation among adolescents living in two disparate socioeconomic regions in Ecuador: A cross-sectional study

Background Allergic diseases are under-investigated and overlooked health conditions in developing countries. We measured the prevalence of food allergy (FA), airborne allergic disease, and allergic sensitisation among adolescents living in 2 socio-demographically disparate regions in Ecuador. We investigated which risk factors are associated with these conditions. Methods A cross-sectional study involved 1338 students (mean age: 13 ± 0.9 years old) living in Cuenca (n = 876) and Santa Isabel (n = 462). History of allergic symptoms (noted by parents or doctor) to food, house dust mites (HDM), pollen, and pets were recorded. Sociodemographic characteristics, environmental exposures, and parental history of allergic disorders data were collected. Sensitisation to 19 food and 20 aeroallergens was measured by skin-prick testing (SPT). FA and airborne allergic diseases (to HDM, pollen, cat, or dog) were defined as a report of allergic symptoms noted by doctor, together with a positive SPT (wheal size ≥3 mm). Logistic regression models were used to identify environmental and parental factors associated with allergic conditions. Results FA was prevalent among 0.4% (95% CI 0.2%–0.9%), and food sensitisation among 19.1% of the adolescents. Shrimp was the most frequent food linked with FA and food sensitisation. Risk factors associated with FA could not be evaluated due to the low prevalence. Food sensitisation was higher among adolescents exposed to family smoking (OR 1.63, 95% CI 1.14–2.34, p = 0.008) and those with parental history of allergic disorders (OR 1.68, 95% CI 1.13–2.49, p = 0.01), but less common among adolescents owning dogs (OR 0.59, 95% CI 0.41–0.84, p = 0.003). Airborne allergic diseases were prevalent amongst 12.0% of the adolescents (95% CI: 10.4–13.9, n = 1321), with HDM as the primary allergen (11.2%). Airborne allergic diseases were less common among adolescents with more siblings (OR 0.79, 95% CI 0.65–0.96, p = 0.02) and those who lived with farm animals in the first year of life (OR 0.47, 95% CI 0.23–0.95, p = 0.04), but, most common among adolescents with a smoking family (OR 1.67, 95% CI 1.04–2.70, p = 0.03) and with a parental history of allergic disorders (OR self-perceived: 2.62, 95% CI 1.46–4.71, p = 0.001; OR diagnosed by a doctor: 4.07, 95% CI 2.44–6.80, p < 0.001). Conclusions FA and airborne allergies are less prevalent in Ecuador than in developed regions; there is a great dissociation between the prevalence of allergic disease and allergic sensitisation. Shrimp and HDM were the most prevalent allergens. Risk factors identified in this study to be related to allergic diseases should be considered by physicians, health practitioners, and epidemiologists in Ecuador

Effects of highly active antiretroviral therapy with nelfinavir in vertically HIV-1 infected children: 3 years of follow-up. Long-term response to nelfinavir in children

BACKGROUND: Antiretroviral treatment (ART) in children has special features and consequently, results obtained from clinical trials with antiretroviral drugs in adults may not be representative of children. Nelfinavir (NFV) is an HIV-1 Protease Inhibitor (PI) which has become as one of the first choices of PI for ART in children. We studied during a 3-year follow-up period the effects of highly active antiretroviral therapy with nelfinavir in vertically HIV-1 infected children. METHODS: Forty-two vertically HIV-infected children on HAART with NFV were involved in a multicentre prospective study. The children were monitored at least every 3 months with physical examinations, and blood sample collection to measure viral load (VL) and CD4+ cell count. We performed a logistic regression analysis to determinate the odds ratio of baseline characteristics on therapeutic failure. RESULTS: Very important increase in CD4+ was observed and VL decreased quickly and it remained low during the follow-up study. Children with CD4+ <25% at baseline achieved CD4+ >25% at 9 months of follow-up. HIV-infected children who achieved undetectable viral load (uVL) were less than 40% in each visit during follow-up. Nevertheless, HIV-infected children with VL >5000 copies/ml were less than 50% during the follow-up study. Only baseline VL was an important factor to predict VL control during follow-up. Virological failure at defined end-point was confirmed in 30/42 patients. Along the whole of follow-up, 16/42 children stopped HAART with NFV. Baseline characteristics were not associated with therapeutic change. CONCLUSION: NFV is a safe drug with a good profile and able to achieve an adequate response in children

Capturing phenotypic heterogeneity in MPS I: results of an international consensus procedure

<p>Abstract</p> <p>Background</p> <p>Mucopolysaccharidosis type I (MPS I) is traditionally divided into three phenotypes: the severe Hurler (MPS I-H) phenotype, the intermediate Hurler-Scheie (MPS I-H/S) phenotype and the attenuated Scheie (MPS I-S) phenotype. However, there are no clear criteria for delineating the different phenotypes. Because decisions about optimal treatment (enzyme replacement therapy or hematopoietic stem cell transplantation) need to be made quickly and depend on the presumed phenotype, an assessment of phenotypic severity should be performed soon after diagnosis. Therefore, a numerical severity scale for classifying different MPS I phenotypes at diagnosis based on clinical signs and symptoms was developed.</p> <p>Methods</p> <p>A consensus procedure based on a combined modified Delphi method and a nominal group technique was undertaken. It consisted of two written rounds and a face-to-face meeting. Sixteen MPS I experts participated in the process. The main goal was to identify the most important indicators of phenotypic severity and include these in a numerical severity scale. The correlation between the median subjective expert MPS I rating and the scores derived from this severity scale was used as an indicator of validity.</p> <p>Results</p> <p>Full consensus was reached on six key clinical items for assessing severity: age of onset of signs and symptoms, developmental delay, joint stiffness/arthropathy/contractures, kyphosis, cardiomyopathy and large head/frontal bossing. Due to the remarkably large variability in the expert MPS I assessments, however, a reliable numerical scale could not be constructed. Because of this variability, such a scale would always result in patients whose calculated severity score differed unacceptably from the median expert severity score, which was considered to be the 'gold standard'.</p> <p>Conclusions</p> <p>Although consensus was reached on the six key items for assessing phenotypic severity in MPS I, expert opinion on phenotypic severity at diagnosis proved to be highly variable. This subjectivity emphasizes the need for validated biomarkers and improved genotype-phenotype correlations that can be incorporated into phenotypic severity assessments at diagnosis.</p

Children’s experiences following a CBT intervention to reduce dental anxiety: one year on

Objective: To investigate children’s ongoing experiences of dental care and use of strategies to manage their dental anxiety following cognitive behavioural therapy (CBT). Design: A child self-completed postal questionnaire. Settings: Hospital, community and general dental practice. Subjects: Questionnaires were sent to 44 children, aged 10-17 years who had been referred to specialist services due to their dental anxiety. Intervention: Children had all previously received a guided CBT self-help intervention to reduce their dental anxiety and, on completion of treatment, had been discharged to their referring dentist. Questionnaires were sent out 12-18 months later to ascertain dental attendance patterns and application of any strategies learnt from the previous CBT intervention. Results: 22 responses (50%) were received from 16 girls and 6 boys. 82% had subsequently accessed follow up care with a general dental practitioner and over half of these had undergone a dental procedure, other than a check-up. 91% reported feeling less worried about dental visits, than previously, and described a change in cognition, behaviours, and feelings that allowed them to manage their anxiety better. Conclusions: CBT has positive immediate and longitudinal effects in reducing children’s dental anxiety. The challenge of adopting this evidence-based approach within primary care settings remains

Armed Rollers: Does Nestling’s Vomit Function as a Defence against Predators?

Chemical defences against predators are widespread in the animal kingdom although have been seldom reported in birds. Here, we investigate the possibility that the orange liquid that nestlings of an insectivorous bird, the Eurasian roller (Coracias garrulus), expel when scared at their nests acts as a chemical defence against predators. We studied the diet of nestling rollers and vomit origin, its chemical composition and deterrent effect on a mammal generalist predator. We also hypothesized that nestling rollers, as their main prey (i.e. grasshoppers) do from plants, could sequester chemicals from their prey for their use. Grasshoppers, that also regurgitate when facing to a threat, store the harmful substances used by plants to defend themselves against herbivores. We found that nestling rollers only vomit after being grasped and moved. The production of vomit depended on food consumption and the vomit contained two deterrent chemicals (hydroxycinnamic and hydroxybenzoic acids) stored by grasshoppers and used by plants to diminish herbivory, suggesting that they originate from the rollers’ prey. Finally, we showed for the first time that the oral secretion of a vertebrate had a deterrent effect on a model predator because vomit of nestling rollers made meat distasteful to dogs. These results support the idea that the vomit of nestling rollers is a chemical defence against predators.Financial support was provided by the Junta de Andalucía (project P06-RNM-02177) and the Spanish Ministry of Science and Education/FEDER (projects CGL2008-00718 and CGL2011-27561)