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

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

Activation of PKR Causes Amyloid ß-Peptide Accumulation via De-Repression of BACE1 Expression

BACE1 is a key enzyme involved in the production of amyloid ß-peptide (Aß) in Alzheimer's disease (AD) brains. Normally, its expression is constitutively inhibited due to the presence of the 5′untranslated region (5′UTR) in the BACE1 promoter. BACE1 expression is activated by phosphorylation of the eukaryotic initiation factor (eIF)2-alpha, which reverses the inhibitory effect exerted by BACE1 5′UTR. There are four kinases associated with different types of stress that could phosphorylate eIF2-alpha. Here we focus on the double-stranded (ds) RNA-activated protein kinase (PKR). PKR is activated during viral infection, including that of herpes simplex virus type 1 (HSV1), a virus suggested to be implicated in the development of AD, acting when present in brains of carriers of the type 4 allele of the apolipoprotein E gene. HSV1 is a dsDNA virus but it has genes on both strands of the genome, and from these genes complementary RNA molecules are transcribed. These could activate BACE1 expression by the PKR pathway. Here we demonstrate in HSV1-infected neuroblastoma cells, and in peripheral nervous tissue from HSV1-infected mice, that HSV1 activates PKR. Cloning BACE1 5′UTR upstream of a luciferase (luc) gene confirmed its inhibitory effect, which can be prevented by salubrinal, an inhibitor of the eIF2-alpha phosphatase PP1c. Treatment with the dsRNA analog poly (I∶C) mimicked the stimulatory effect exerted by salubrinal over BACE1 translation in the 5′UTR-luc construct and increased Aß production in HEK-APPsw cells. Summarizing, our data suggest that PKR activated in brain by HSV1 could play an important role in the development of AD

Identification of sixteen novel candidate genes for late onset Parkinson’s disease

Background Parkinson’s disease (PD) is a neurodegenerative movement disorder affecting 1–5% of the general population for which neither effective cure nor early diagnostic tools are available that could tackle the pathology in the early phase. Here we report a multi-stage procedure to identify candidate genes likely involved in the etiopathogenesis of PD. Methods The study includes a discovery stage based on the analysis of whole exome data from 26 dominant late onset PD families, a validation analysis performed on 1542 independent PD patients and 706 controls from different cohorts and the assessment of polygenic variants load in the Italian cohort (394 unrelated patients and 203 controls). Results Family-based approach identified 28 disrupting variants in 26 candidate genes for PD including PARK2, PINK1, DJ-1(PARK7), LRRK2, HTRA2, FBXO7, EIF4G1, DNAJC6, DNAJC13, SNCAIP, AIMP2, CHMP1A, GIPC1, HMOX2, HSPA8, IMMT, KIF21B, KIF24, MAN2C1, RHOT2, SLC25A39, SPTBN1, TMEM175, TOMM22, TVP23A and ZSCAN21. Sixteen of them have not been associated to PD before, were expressed in mesencephalon and were involved in pathways potentially deregulated in PD. Mutation analysis in independent cohorts disclosed a significant excess of highly deleterious variants in cases (p = 0.0001), supporting their role in PD. Moreover, we demonstrated that the co-inheritance of multiple rare variants (≥ 2) in the 26 genes may predict PD occurrence in about 20% of patients, both familial and sporadic cases, with high specificity (> 93%; p = 4.4 × 10− 5). Moreover, our data highlight the fact that the genetic landmarks of late onset PD does not systematically differ between sporadic and familial forms, especially in the case of small nuclear families and underline the importance of rare variants in the genetics of sporadic PD. Furthermore, patients carrying multiple rare variants showed higher risk of manifesting dyskinesia induced by levodopa treatment. Conclusions Besides confirming the extreme genetic heterogeneity of PD, these data provide novel insights into the genetic of the disease and may be relevant for its prediction, diagnosis and treatment

A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)

Meeting abstrac

Guidelines for the use and interpretation of assays for monitoring autophagy (4th edition)1.

In 2008, we published the first set of guidelines for standardizing research in autophagy. Since then, this topic has received increasing attention, and many scientists have entered the field. Our knowledge base and relevant new technologies have also been expanding. Thus, it is important to formulate on a regular basis updated guidelines for monitoring autophagy in different organisms. Despite numerous reviews, there continues to be confusion regarding acceptable methods to evaluate autophagy, especially in multicellular eukaryotes. Here, we present a set of guidelines for investigators to select and interpret methods to examine autophagy and related processes, and for reviewers to provide realistic and reasonable critiques of reports that are focused on these processes. These guidelines are not meant to be a dogmatic set of rules, because the appropriateness of any assay largely depends on the question being asked and the system being used. Moreover, no individual assay is perfect for every situation, calling for the use of multiple techniques to properly monitor autophagy in each experimental setting. Finally, several core components of the autophagy machinery have been implicated in distinct autophagic processes (canonical and noncanonical autophagy), implying that genetic approaches to block autophagy should rely on targeting two or more autophagy-related genes that ideally participate in distinct steps of the pathway. Along similar lines, because multiple proteins involved in autophagy also regulate other cellular pathways including apoptosis, not all of them can be used as a specific marker for bona fide autophagic responses. Here, we critically discuss current methods of assessing autophagy and the information they can, or cannot, provide. Our ultimate goal is to encourage intellectual and technical innovation in the field