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

High CO2 permeability in supported molten-salt membranes with highly dense and aligned pores produced by directional solidification

Composite molten salt-ceramic membranes are promising devices for high-temperature CO2 separation. Intensive material properties impact on separation performance as do membrane geometry (thickness) and microstructure (pore volume fraction, size, connectivity, and tortuosity factor). Although controlling pore size is considered somewhat routine, achieving pore alignment and connectivity is still challenging. Here we report the production of the first gas separation membrane using a porous ceramic matrix obtained from a directionally-solidified magnesium-stabilised zirconia (MgSZ) - MgO fibrilar eutectic as the membrane support. MgO was removed from the parent material by acid-etching to create a porous matrix with highly aligned pores with diameters of similar to 1 mu m. X-ray nano-computed tomography of a central portion (similar to 32, 000 mu m(3)) of the support identified similar to 21% porosity, with all pores aligned within 10 degrees and similar to 76% percolating along the longest sampled length. Employing the matrix as a support for a carbonate molten salt, a high CO2 permeability of 1.41x10(-10) mol m(-1).s(-1).Pa-1 at 815 degrees C was achieved, among the highest reported for supported molten-carbonate membranes (typically 10(-12) to 10(-10) mol m(-1).s(-1).Pa-1 at similar temperatures). We suggest that the high permeability is attributable to the excellent pore characteristics resulting from directional solidification, namely a dense array of parallel, micron-scale pores connecting the feed and permeate sides of the membrane

Environmental and Parental Influences on Offspring Health and Growth in Great Tits (Parus major)

PMCID: PMC3728352This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

The Effect of Epstein-Barr Virus Latent Membrane Protein 2 Expression on the Kinetics of Early B Cell Infection

Infection of human B cells with wild-type Epstein-Barr virus (EBV) in vitro leads to activation and proliferation that result in efficient production of lymphoblastoid cell lines (LCLs). Latent Membrane Protein 2 (LMP2) is expressed early after infection and previous research has suggested a possible role in this process. Therefore, we generated recombinant EBV with knockouts of either or both protein isoforms, LMP2A and LMP2B (Δ2A, Δ2B, Δ2A/Δ2B) to study the effect of LMP2 in early B cell infection. Infection of B cells with Δ2A and Δ2A/Δ2B viruses led to a marked decrease in activation and proliferation relative to wild-type (wt) viruses, and resulted in higher percentages of apoptotic B cells. Δ2B virus infection showed activation levels comparable to wt, but fewer numbers of proliferating B cells. Early B cell infection with wt, Δ2A and Δ2B viruses did not result in changes in latent gene expression, with the exception of elevated LMP2B transcript in Δ2A virus infection. Infection with Δ2A and Δ2B viruses did not affect viral latency, determined by changes in LMP1/Zebra expression following BCR stimulation. However, BCR stimulation of Δ2A/Δ2B cells resulted in decreased LMP1 expression, which suggests loss of stability in viral latency. Long-term outgrowth assays revealed that LMP2A, but not LMP2B, is critical for efficient long-term growth of B cells in vitro. The lowest levels of activation, proliferation, and LCL formation were observed when both isoforms were deleted. These results suggest that LMP2A appears to be critical for efficient activation, proliferation and survival of EBV-infected B cells at early times after infection, which impacts the efficient long-term growth of B cells in culture. In contrast, LMP2B did not appear to play a significant role in these processes, and long-term growth of infected B cells was not affected by the absence of this protein. © 2013 Wasil et al

Variation and ethnic inequalities in treatment of common mental disorders before, during and after pregnancy : combined analysis of routine and research data in the Born in Bradford cohort

BACKGROUND: Common mental disorders (CMD) such as anxiety and depression during the maternal period can cause significant morbidity to the mother in addition to disrupting biological, attachment and parenting processes that affect child development. Pharmacological treatment is a first-line option for moderate to severe episodes. Many women prescribed pharmacological treatments cease them during pregnancy but it is unclear to what extent non-pharmacological options are offered as replacement. There are also concerns that treatments offered may not be proportionate to need in minority ethnic groups, but few data exist on treatment disparities in the maternal period. We examined these questions in a multi-ethnic cohort of women with CMD living in Bradford, England before, during and up to one year after pregnancy. METHODS: We searched the primary care records of women enrolled in the Born in Bradford cohort for diagnoses, symptoms, signs ('identification'), referrals for treatment, non-pharmacological and pharmacological treatment and monitoring ('treatment') related to CMD. Records were linked with maternity data to classify women identified with a CMD as treated prior to, and one year after, delivery. We examined rates and types of treatment during pregnancy, and analysed potential ethnic group differences using adjusted Poisson and multinomial logistic regression models. RESULTS: We analysed data on 2,234 women with indicators of CMD. Most women were discontinued from pharmacological treatment early in pregnancy, but this was accompanied by recorded access to non-drug treatments in only 15 % at the time of delivery. Fewer minority ethnic women accessed treatments compared to White British women despite minority ethnic women being 55-70 % more likely than White British women to have been identified with anxiety in their medical record. CONCLUSIONS: Very few women who discontinued pharmacological treatment early in their pregnancy were offered other non-pharmacological treatments as replacement, and most appeared to complete their pregnancy untreated. Further investigation is warranted to replicate the finding that minority ethnic women are more likely to be identified as being anxious or having anxiety and understand what causes the variation in access to treatments

Critical analysis of vendor lock-in and its impact on cloud computing migration: a business perspective

Vendor lock-in is a major barrier to the adoption of cloud computing, due to the lack of standardization. Current solutions and efforts tackling the vendor lock-in problem are predominantly technology-oriented. Limited studies exist to analyse and highlight the complexity of vendor lock-in problem in the cloud environment. Consequently, most customers are unaware of proprietary standards which inhibit interoperability and portability of applications when taking services from vendors. This paper provides a critical analysis of the vendor lock-in problem, from a business perspective. A survey based on qualitative and quantitative approaches conducted in this study has identified the main risk factors that give rise to lock-in situations. The analysis of our survey of 114 participants shows that, as computing resources migrate from on-premise to the cloud, the vendor lock-in problem is exacerbated. Furthermore, the findings exemplify the importance of interoperability, portability and standards in cloud computing. A number of strategies are proposed on how to avoid and mitigate lock-in risks when migrating to cloud computing. The strategies relate to contracts, selection of vendors that support standardised formats and protocols regarding standard data structures and APIs, developing awareness of commonalities and dependencies among cloud-based solutions. We strongly believe that the implementation of these strategies has a great potential to reduce the risks of vendor lock-in

Discovery of an Auto-Regulation Mechanism for the Maltose ABC Transporter MalFGK2

The maltose transporter MalFGK2, together with the substrate-binding protein MalE, is one of the best-characterized ABC transporters. In the conventional model, MalE captures maltose in the periplasm and delivers the sugar to the transporter. Here, using nanodiscs and proteoliposomes, we instead find that MalE is bound with high-affinity to MalFGK2 to facilitate the acquisition of the sugar. When the maltose concentration exceeds the transport capacity, MalE captures maltose and dissociates from the transporter. This mechanism explains why the transport rate is high when MalE has low affinity for maltose, and low when MalE has high affinity for maltose. Transporter-bound MalE facilitates the acquisition of the sugar at low concentrations, but also captures and dissociates from the transporter past a threshold maltose concentration. In vivo, this maltose-forced dissociation limits the rate of transport. Given the conservation of the substrate-binding proteins, this mode of allosteric regulation may be universal to ABC importers

The Hubbard model within the equations of motion approach

The Hubbard model has a special role in Condensed Matter Theory as it is considered as the simplest Hamiltonian model one can write in order to describe anomalous physical properties of some class of real materials. Unfortunately, this model is not exactly solved except for some limits and therefore one should resort to analytical methods, like the Equations of Motion Approach, or to numerical techniques in order to attain a description of its relevant features in the whole range of physical parameters (interaction, filling and temperature). In this manuscript, the Composite Operator Method, which exploits the above mentioned analytical technique, is presented and systematically applied in order to get information about the behavior of all relevant properties of the model (local, thermodynamic, single- and two- particle ones) in comparison with many other analytical techniques, the above cited known limits and numerical simulations. Within this approach, the Hubbard model is shown to be also capable to describe some anomalous behaviors of the cuprate superconductors.Comment: 232 pages, more than 300 figures, more than 500 reference

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

Search for new phenomena in final states with an energetic jet and large missing transverse momentum in pp collisions at √ s = 8 TeV with the ATLAS detector

Results of a search for new phenomena in final states with an energetic jet and large missing transverse momentum are reported. The search uses 20.3 fb−1 of √ s = 8 TeV data collected in 2012 with the ATLAS detector at the LHC. Events are required to have at least one jet with pT > 120 GeV and no leptons. Nine signal regions are considered with increasing missing transverse momentum requirements between Emiss T > 150 GeV and Emiss T > 700 GeV. Good agreement is observed between the number of events in data and Standard Model expectations. The results are translated into exclusion limits on models with either large extra spatial dimensions, pair production of weakly interacting dark matter candidates, or production of very light gravitinos in a gauge-mediated supersymmetric model. In addition, limits on the production of an invisibly decaying Higgs-like boson leading to similar topologies in the final state are presente