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

A cluster randomized trial to assess the impact of clinical pathways for patients with stroke: rationale and design of the Clinical Pathways for Effective and Appropriate Care Study [NCT00673491]

<p>Abstract</p> <p>Background</p> <p>Patients with stroke should have access to a continuum of care from organized stroke units in the acute phase, to appropriate rehabilitation and secondary prevention measures. Moreover to improve the outcomes for acute stroke patients from an organizational perspective, the use of multidisciplinary teams and the delivery of continuous stroke education both to the professionals and to the public, and the implementation of evidence-based stroke care are recommended. Clinical pathways are complex interventions that can be used for this purpose. However in stroke care the use of clinical pathways remains questionable because little prospective controlled data has demonstrated their effectiveness. The purpose of this study is to determine whether clinical pathways could improve the quality of the care provided to the patients affected by stroke in hospital and through the continuum of the care.</p> <p>Methods</p> <p>Two-arm, cluster-randomized trial with hospitals and rehabilitation long-term care facilities as randomization units. 14 units will be randomized either to arm 1 (clinical pathway) or to arm 2 (no intervention, usual care). The sample will include 238 in each group, this gives a power of 80%, at 5% significance level. The primary outcome measure is 30-days mortality. The impact of the clinical pathways along the continuum of care will also be analyzed by comparing the length of hospital stay, the hospital re-admissions rates, the institutionalization rates after hospital discharge, the patients' dependency levels, and complication rates. The quality of the care provided to the patients will be assessed by monitoring the use of diagnostic and therapeutic procedures during hospital stay and rehabilitation, and by the use of key quality indicators at discharge. The implementation of organized care will be also evaluated.</p> <p>Conclusion</p> <p>The management of patients affected by stroke involves the expertise of several professionals, which can result in poor coordination or inefficiencies in patient treatment, and clinical pathways can significantly improve the outcomes of these patients. It is proposed that this study will test a new hypothesis and provide evidence of how clinical pathways can work.</p> <p>Trial Registration</p> <p>ClinicalTrials.gov ID [NCT00673491]</p

LHC and lepton flavour violation phenomenology of a left-right extension of the MSSM

We study the phenomenology of a supersymmetric left-right model, assuming minimal supergravity boundary conditions. Both left-right and (B-L) symmetries are broken at an energy scale close to, but significantly below the GUT scale. Neutrino data is explained via a seesaw mechanism. We calculate the RGEs for superpotential and soft parameters complete at 2-loop order. At low energies lepton flavour violation (LFV) and small, but potentially measurable mass splittings in the charged scalar lepton sector appear, due to the RGE running. Different from the supersymmetric 'pure seesaw' models, both, LFV and slepton mass splittings, occur not only in the left- but also in the right slepton sector. Especially, ratios of LFV slepton decays, such as Br(${\tilde\tau}_R \to \mu \chi^0_1$)/Br(${\tilde\tau}_L \to \mu \chi^0_1$) are sensitive to the ratio of (B-L) and left-right symmetry breaking scales. Also the model predicts a polarization asymmetry of the outgoing positrons in the decay $\mu^+ \to e^+ \gamma$, A ~ [0,1], which differs from the pure seesaw 'prediction' A=1$. Observation of any of these signals allows to distinguish this model from any of the three standard, pure (mSugra) seesaw setups.Comment: 43 pages, 17 figure

Interplay of LFV and slepton mass splittings at the LHC as a probe of the SUSY seesaw

We study the impact of a type-I SUSY seesaw concerning lepton flavour violation (LFV) both at low-energies and at the LHC. The study of the di-lepton invariant mass distribution at the LHC allows to reconstruct some of the masses of the different sparticles involved in a decay chain. In particular, the combination with other observables renders feasible the reconstruction of the masses of the intermediate sleptons involved in $\chi_2^0\to \tilde \ell \,\ell \to \ell \,\ell\,\chi_1^0$ decays. Slepton mass splittings can be either interpreted as a signal of non-universality in the SUSY soft breaking-terms (signalling a deviation from constrained scenarios as the cMSSM) or as being due to the violation of lepton flavour. In the latter case, in addition to these high-energy processes, one expects further low-energy manifestations of LFV such as radiative and three-body lepton decays. Under the assumption of a type-I seesaw as the source of neutrino masses and mixings, all these LFV observables are related. Working in the framework of the cMSSM extended by three right-handed neutrino superfields, we conduct a systematic analysis addressing the simultaneous implications of the SUSY seesaw for both high- and low-energy lepton flavour violation. We discuss how the confrontation of slepton mass splittings as observed at the LHC and low-energy LFV observables may provide important information about the underlying mechanism of LFV.Comment: 50 pages, 42 eps Figures, typos correcte

El cómic es cosa seria. El cómic como mediación para la enseñanza en la educación superior Caso Universidad Nacional, Universidad de Medellín y Universidad Pontificia Bolivariana

El problema planteado en esta investigación es estudiar el posible uso del cómiccomo mediación para la enseñanza en la educación superior. Su objetivo es establecerlas condiciones y características que debe tener el cómic para enseñar. El trabajoconsidera una muestra referenciada de informantes, y se desarrolla por medio deobservaciones, entrevistas en profundidad, redacción de diarios de campo y estudio defuentes documentales. Las principales conclusiones son que el cómic tiene potencialdidáctico, que ha sido poco utilizado para enseñar, y que las instituciones de educaciónsuperior deben propiciar su uso, e investigar para validar este potencial. Se plantea unapropuesta didáctica para fomentar la utilización del cómic en la educación superior.Los tres proponentes de esta investigación son docentes y utilizan la imagen en suslabores educativas

Intraspecies Transmission of BASE Induces Clinical Dullness and Amyotrophic Changes

The disease phenotype of bovine spongiform encephalopathy (BSE) and the molecular/ biological properties of its prion strain, including the host range and the characteristics of BSE-related disorders, have been extensively studied since its discovery in 1986. In recent years, systematic testing of the brains of cattle coming to slaughter resulted in the identification of at least two atypical forms of BSE. These emerging disorders are characterized by novel conformers of the bovine pathological prion protein (PrPTSE), named high-type (BSE-H) and low-type (BSE-L). We recently reported two Italian atypical cases with a PrPTSE type identical to BSE-L, pathologically characterized by PrP amyloid plaques and known as bovine amyloidotic spongiform encephalopathy (BASE). Several lines of evidence suggest that BASE is highly virulent and easily transmissible to a wide host range. Experimental transmission to transgenic mice overexpressing bovine PrP (Tgbov XV) suggested that BASE is caused by a prion strain distinct from the BSE isolate. In the present study, we experimentally infected Friesian and Alpine brown cattle with Italian BSE and BASE isolates via the intracerebral route. BASE-infected cattle developed amyotrophic changes accompanied by mental dullness. The molecular and neuropathological profiles, including PrP deposition pattern, closely matched those observed in the original cases. This study provides clear evidence of BASE as a distinct prion isolate and discloses a novel disease phenotype in cattle

How Are the Interests of Incapacitated Research Participants Protected through Legislation? An Italian Study on Legal Agency for Dementia Patients

Patients with dementia may have limited capacity to give informed consent to participate in clinical research. One possible way to safeguard the patients' interests in research is the involvement of a proxy in the recruitment process. In Italy, the system of proxy is determined by the courts. In this study we evaluate the timing for appointment of a legal proxy in Italy and identify predictive variables of appointment.Subjects were recruited among the outpatients seeking medical advice for cognitive complaints at the Centre for Research and Treatment of Cognitive Dysfunctions, University of Milan, "Luigi Sacco" Hospital. The Centre was participating to the AdCare Study, a no-profit randomised clinical trial coordinated by the Italian National Institute of Health. The requirement that informed consent be given by a legal representative dramatically slowed down the recruitment process in AdCare, which was prematurely interrupted. The Centre for Research and Treatment of Cognitive Dysfunctions collected data on the timing required to appoint the legal representatives. Patients diagnosed with dementia and their caregivers were provided information on the Italian law on legal agency (law 6/2004). At each scheduled check-up the caregiver was asked whether she/he had applied to appoint a legal proxy for the patient and the time interval between the presentation of the law, the registration of the application at the law court chancellery and the sentence of appointment was registered. The study involved 169 demented patients. Seventy-eight patients (46.2%) applied to appoint a legal proxy. These subjects were usually younger, had been suffering from dementia for a longer time, had less than two children and made more use of memantine. The mean interval time between the presentation of the law and the patients' application to the law court chancellery was two months. The mean interval time between the patient's application to the law court chancellery and the sentence of appointment was four months.In Italy the requirement that legal representatives be appointed by the courts slows down subjects' participation in research. Other procedures for legal agency of the incapacitated patients may be adopted, taking as examples other EU countries' systems

CXCR3 Antagonism of SDF-1(5-67) Restores Trabecular Function and Prevents Retinal Neurodegeneration in a Rat Model of Ocular Hypertension

Glaucoma, the most common cause of irreversible blindness, is a neuropathy commonly initiated by pathological ocular hypertension due to unknown mechanisms of trabecular meshwork degeneration. Current antiglaucoma therapy does not target the causal trabecular pathology, which may explain why treatment failure is often observed. Here we show that the chemokine CXCL12, its truncated form SDF-1(5-67), and the receptors CXCR4 and CXCR3 are expressed in human glaucomatous trabecular tissue and a human trabecular cell line. SDF-1(5-67) is produced under the control of matrix metallo-proteinases, TNF-α, and TGF-β2, factors known to be involved in glaucoma. CXCL12 protects in vitro trabecular cells from apoptotic death via CXCR4 whereas SDF-1(5-67) induces apoptosis through CXCR3 and caspase activation. Ocular administration of SDF-1(5-67) in the rat increases intraocular pressure. In contrast, administration of a selective CXCR3 antagonist in a rat model of ocular hypertension decreases intraocular pressure, prevents retinal neurodegeneration, and preserves visual function. The protective effect of CXCR3 antagonism is related to restoration of the trabecular function. These data demonstrate that proteolytic cleavage of CXCL12 is involved in trabecular pathophysiology, and that local administration of a selective CXCR3 antagonist may be a beneficial therapeutic strategy for treating ocular hypertension and subsequent retinal degeneration