On the Banach lattice structure of L-w(1) of a vector measure on a delta-ring

We study some Banach lattice properties of the space L-w(1)(v) of weakly integrable functions with respect to a vector measure v defined on a delta-ring. Namely, we analyze order continuity, order density and Fatou type properties. We will see that the behavior of L-w(1)(v) differs from the case in which is defined on a sigma-algebra whenever does not satisfy certain local sigma-finiteness property.J. M. Calabuig and M. A. Juan were supported by the Ministerio de Economia y Competitividad (project MTM2008-04594). O. Delgado was supported by the Ministerio de Economia y Competitividad (project MTM2009-12740-C03-02). E. A. Sanchez Perez was supported by the Ministerio de Economia y Competitividad (project MTM2009-14483-C02-02).Calabuig Rodriguez, JM.; Delgado Garrido, O.; Juan Blanco, MA.; Sánchez Pérez, EA. (2014). On the Banach lattice structure of L-w(1) of a vector measure on a delta-ring. Collectanea Mathematica. 65(1):67-85. doi:10.1007/s13348-013-0081-8S6785651Brooks, J.K., Dinculeanu, N.: Strong additivity, absolute continuity and compactness in spaces of measures. J. Math. Anal. Appl. 45, 156–175 (1974)Calabuig, J.M., Delgado, O., Sánchez Pérez, E.A.: Factorizing operators on Banach function spaces through spaces of multiplication operators. J. Math. Anal. Appl. 364, 88–103 (2010)Calabuig, J.M., Juan, M.A., Sánchez Pérez, E.A.: Spaces of $$p$$ -integrable functions with respect to a vector measure defined on a $$\delta$$ -ring. Oper. Matrices 6, 241–262 (2012)Curbera, G.P.: El espacio de funciones integrables respecto de una medida vectorial. Ph. D. thesis, University of Sevilla, Sevilla (1992)Curbera, G.P.: Operators into $$L^1$$ of a vector measure and applications to Banach lattices. Math. Ann. 293, 317–330 (1992)Curbera, G.P., Ricker, W.J.: Banach lattices with the Fatou property and optimal domains of kernel operators. Indag. Math. (N.S.) 17, 187–204 (2006)G. P. Curbera and W. J. Ricker, Vector measures, integration and applications. In: Positivity (in Trends Math.), Birkhäuser, Basel, pp. 127–160 (2007)Curbera, G.P., Ricker, W.J.: The Fatou property in $$p$$ -convex Banach lattices. J. Math. Anal. Appl. 328, 287–294 (2007)Delgado, O.: $$L^1$$ -spaces of vector measures defined on $$\delta$$ -rings. Arch. Math. 84, 432–443 (2005)Delgado, O.: Optimal domains for kernel operators on $$[0,\infty )\times [0,\infty )$$ . Studia Math. 174, 131–145 (2006)Delgado, O., Soria, J.: Optimal domain for the Hardy operator. J. Funct. Anal. 244, 119–133 (2007)Delgado, O., Juan, M.A.: Representation of Banach lattices as $$L_w^1$$ spaces of a vector measure defined on a $$\delta$$ -ring. Bull. Belg. Math. Soc. Simon Stevin 19(2), 239–256 (2012)Diestel, J., Uhl, J.J.: Vector measures (Am. Math. Soc. surveys 15). American Mathematical Society, Providence (1997)Dinculeanu, N.: Vector measures, Hochschulbcher fr Mathematik, vol. 64. VEB Deutscher Verlag der Wissenschaften, Berlin (1966)Fernández, A., Mayoral, F., Naranjo, F., Sáez, C., Sánchez Pérez, E.A.: Spaces of $$p$$ -integrable functions with respect to a vector measure. Positivity 10, 1–16 (2006)Fremlin, D.H.: Measure theory, broad foundations, vol. 2. Torres Fremlin, Colchester (2001)Jiménez Fernández, E., Juan, M.A., Sánchez Pérez, E.A.: A Komlós theorem for abstract Banach lattices of measurable functions. J. Math. Anal. Appl. 383, 130–136 (2011)Lewis, D.R.: On integrability and summability in vector spaces. Ill. J. Math. 16, 294–307 (1972)Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces II. Springer, Berlin (1979)Luxemburg, W.A.J., Zaanen, A.C.: Riesz spaces I. North-Holland, Amsterdam (1971)Masani, P.R., Niemi, H.: The integration theory of Banach space valued measures and the Tonelli-Fubini theorems. I. Scalar-valued measures on $$\delta$$ -rings. Adv. Math. 73, 204–241 (1989)Masani, P.R., Niemi, H.: The integration theory of Banach space valued measures and the Tonelli-Fubini theorems. II. Pettis integration. Adv. Math. 75, 121–167 (1989)Thomas, E.G.F.: Vector integration (unpublished) (2013)Turpin, Ph.: Intégration par rapport à une mesure à valeurs dans un espace vectoriel topologique non supposé localement convexe, Intègration vectorielle et multivoque, (Colloq., University Caen, Caen, 1975), experiment no. 8, Dèp. Math., UER Sci., University Caen, Caen (1975)Okada, S., Ricker, W.J., Sánchez Pérez, E.A.: Optimal domain and integral extension of operators acting in function spaces (Oper. Theory Adv. Appl.), vol. 180. Birkhäuser, Basel (2008)Zaanen, A.C.: Riesz spaces II. North-Holland, Amsterdam (1983

Identifying the Machine Learning Family from Black-Box Models

[EN] We address the novel question of determining which kind of machine learning model is behind the predictions when we interact with a black-box model. This may allow us to identify families of techniques whose models exhibit similar vulnerabilities and strengths. In our method, we first consider how an adversary can systematically query a given black-box model (oracle) to label an artificially-generated dataset. This labelled dataset is then used for training different surrogate models (each one trying to imitate the oracle¿s behaviour). The method has two different approaches. First, we assume that the family of the surrogate model that achieves the maximum Kappa metric against the oracle labels corresponds to the family of the oracle model. The other approach, based on machine learning, consists in learning a meta-model that is able to predict the model family of a new black-box model. We compare these two approaches experimentally, giving us insight about how explanatory and predictable our concept of family is.This material is based upon work supported by the Air Force Office of Scientific Research under award number FA9550-17-1-0287, the EU (FEDER), and the Spanish MINECO under grant TIN 2015-69175-C4-1-R, the Generalitat Valenciana PROMETEOII/2015/013. F. Martinez-Plumed was also supported by INCIBE under grant INCIBEI-2015-27345 (Ayudas para la excelencia de los equipos de investigacion avanzada en ciberseguridad). J. H-Orallo also received a Salvador de Madariaga grant (PRX17/00467) from the Spanish MECD for a research stay at the CFI, Cambridge, and a BEST grant (BEST/2017/045) from the GVA for another research stay at the CFI.Fabra-Boluda, R.; Ferri Ramírez, C.; Hernández-Orallo, J.; Martínez-Plumed, F.; Ramírez Quintana, MJ. (2018). Identifying the Machine Learning Family from Black-Box Models. Lecture Notes in Computer Science. 11160:55-65. https://doi.org/10.1007/978-3-030-00374-6_6S556511160Angluin, D.: Queries and concept learning. Mach. Learn. 2(4), 319–342 (1988)Benedek, G.M., Itai, A.: Learnability with respect to fixed distributions. Theor. Comput. Sci. 86(2), 377–389 (1991)Biggio, B., et al.: Security Evaluation of support vector machines in adversarial environments. In: Ma, Y., Guo, G. (eds.) Support Vector Machines Applications, pp. 105–153. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-02300-7_4Blanco-Vega, R., Hernández-Orallo, J., Ramírez-Quintana, M.J.: Analysing the trade-off between comprehensibility and accuracy in mimetic models. In: Suzuki, E., Arikawa, S. (eds.) DS 2004. LNCS (LNAI), vol. 3245, pp. 338–346. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30214-8_29Dalvi, N., Domingos, P., Sanghai, S., Verma, D., et al.: Adversarial classification. In: Proceedings of the 10th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 99–108. ACM (2004)Dheeru, D., Karra Taniskidou, E.: UCI machine learning repository (2017). http://archive.ics.uci.edu/mlDomingos, P.: Knowledge discovery via multiple models. Intell. Data Anal. 2(3), 187–202 (1998)Duin, R.P.W., Loog, M., Pȩkalska, E., Tax, D.M.J.: Feature-based dissimilarity space classification. In: Ünay, D., Çataltepe, Z., Aksoy, S. (eds.) ICPR 2010. LNCS, vol. 6388, pp. 46–55. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17711-8_5Fernández-Delgado, M., Cernadas, E., Barro, S., Amorim, D.: Do we need hundreds of classifiers to solve real world classification problems. J. Mach. Learn. Res. 15(1), 3133–3181 (2014)Ferri, C., Hernández-Orallo, J., Modroiu, R.: An experimental comparison of performance measures for classification. Pattern Recognit. 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Maharam-type kernel representation for operators with a trigonometric domination

[EN] Consider a linear and continuous operator T between Banach function spaces. We prove that under certain requirements an integral inequality for T is equivalent to a factorization of T through a specific kernel operator: in other words, the operator T has what we call a Maharam-type kernel representation. In the case that the inequality provides a domination involving trigonometric functions, a special factorization through the Fourier operator is given. We apply this result to study the problem that motivates the paper: the approximation of functions in L2[0, 1] by means of trigonometric series whose Fourier coefficients are given by weighted trigonometric integrals.This research has been supported by MTM2016-77054-C2-1-P (Ministerio de Economia, Industria y Competitividad, Spain).Sánchez Pérez, EA. (2017). Maharam-type kernel representation for operators with a trigonometric domination. Aequationes Mathematicae. 91(6):1073-1091. https://doi.org/10.1007/s00010-017-0507-6S10731091916Calabuig, J.M., Delgado, O., Sánchez Pérez, E.A.: Generalized perfect spaces. Indag. Math. 19(3), 359–378 (2008)Calabuig, J.M., Delgado, O., Sánchez Pérez, E.A.: Factorizing operators on Banach function spaces through spaces of multiplication operators. J. Math. Anal. Appl. 364, 88–103 (2010)Delgado, O., Sánchez Pérez, E.A.: Strong factorizations between couples of operators on Banach function spaces. J. Convex Anal. 20(3), 599–616 (2013)Dodds, P.G., Huijsmans, C.B., de Pagter, B.: Characterizations of conditional expectation type operators. Pacific J. Math. 141(1), 55–77 (1990)Flores, J., Hernández, F.L., Tradacete, P.: Domination problems for strictly singular operators and other related classes. Positivity 15(4), 595–616 (2011). 2011Fremlin, D.H.: Tensor products of Banach lattices. Math. Ann. 211, 87–106 (1974)Hu, G.: Weighted norm inequalities for bilinear Fourier multiplier operators. Math. Ineq. Appl. 18(4), 1409–1425 (2015)Halmos, P., Sunder, V.: Bounded Integral Operators on $$L^2$$ L 2 Spaces. Springer, Berlin (1978)Kantorovitch, L., Vulich, B.: Sur la représentation des opérations linéaires. Compositio Math. 5, 119–165 (1938)Kolwicz, P., Leśnik, K., Maligranda, L.: Pointwise multipliers of Calderón- Lozanovskii spaces. Math. Nachr. 286, 876–907 (2013)Kolwicz, P., Leśnik, K., Maligranda, L.: Pointwise products of some Banach function spaces and factorization. J. Funct. Anal. 266(2), 616–659 (2014)Kuo, W.-C., Labuschagne, C.C.A., Watson, B.A.: Conditional expectations on Riesz spaces. J. Math. Anal. Appl. 303, 509–521 (2005)Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces II. Springer, Berlin (1979)Maharam, D.: The representation of abstract integrals. Trans. Am. Math. Soc. 75, 154–184 (1953)Maharam, D.: On kernel representation of linear operators. Trans. Am. Math. Soc. 79, 229–255 (1955)Maligranda, L., Persson, L.E.: Generalized duality of some Banach function spaces. Indag. Math. 51, 323–338 (1989)Neugebauer, C.J.: Weighted norm inequalities for averaging operators of monotone functions. Publ. Mat. 35, 429–447 (1991)Okada, S., Ricker, W.J., Sánchez Pérez, E.A.: Optimal Domain and Integral Extension of Operators Acting in Function Spaces. Operator Theory: Adv. Appl., vol. 180. Birkhäuser, Basel (2008)Rota, G.C.: On the representation of averaging operators. Rend. Sem. Mat. Univ. Padova. 30, 52–64 (1960)Sánchez Pérez, E.A.: Factorization theorems for multiplication operators on Banach function spaces. Integr. Equ. Oper. Theory 80(1), 117–135 (2014)Schep, A.R.: Factorization of positive multilinear maps. Ill. J. Math. 28(4), 579–591 (1984)Schep, A.R.: Products and factors of Banach function spaces. Positivity 14(2), 301–319 (2010

Direct effects of doxorubicin on skeletal muscle contribute to fatigue

Chemotherapy-induced fatigue is a multidimensional symptom. Oxidative stress has been proposed as a working mechanism for anthracycline-induced cardiotoxicity. In this study, doxorubicin (DOX) was tested on skeletal muscle function. Doxorubicin induced impaired ex vivo skeletal muscle relaxation followed in time by contraction impediment, which could be explained by DOX-induced changes in Ca2+ responses of myotubes in vitro. The Ca2+ responses in skeletal muscle, however, could not be explained by oxidative stress

A 20-year multicentre outcome analysis of salvage mechanical circulatory support for refractory cardiogenic shock after cardiac surgery

Abstract Background Refractory post-cardiotomy cardiogenic shock (PCCS) is a relatively rare phenomenon that can lead to rapid multi-organ dysfunction syndrome and is almost invariably fatal without advanced mechanical circulatory support (AMCS), namely extra-corporeal membrane oxygenation (ECMO) or ventricular assist devices (VAD). In this multicentre observational study we retrospectively analyzed the outcomes of salvage venoarterial ECMO (VA ECMO) and VAD for refractory PCCS in the 3 adult cardiothoracic surgery centres in Scotland over a 20-year period. Methods The data was obtained through the Edinburgh, Glasgow and Aberdeen cardiac surgery databases. Our inclusion criteria included any adult patient from April 1995 to April 2015 who had received salvage VA ECMO or VAD for PCCS refractory to intra-aortic balloon pump (IABP) and maximal inotropic support following adult cardiac surgery. Results A total of 27 patients met the inclusion criteria. Age range was 34–83 years (median 51 years). There was a large male predominance (n = 23, 85 %). Overall 23 patients (85 %) received VA ECMO of which 14 (61 %) had central ECMO and 9 (39 %) had peripheral ECMO. Four patients (15 %) were treated with short-term VAD (BiVAD = 1, RVAD = 1 and LVAD = 2). The most common procedure-related complication was major haemorrhage (n = 10). Renal failure requiring renal replacement therapy (n = 7), fatal stroke (n = 5), septic shock (n = 2), and a pseudo-aneurysm at the femoral artery cannulation site (n = 1) were also observed. Overall survival to hospital discharge was 40.7 %. All survivors were NYHA class I-II at 12 months’ follow-up. Conclusion AMCS for refractory PCCS carries a survival benefit and achieves acceptable functional recovery despite a significant complication rate

Product factorability of integral bilinear operators on Banach function spaces

[EN] This paper deals with bilinear operators acting in pairs of Banach function spaces that factor through the pointwise product. We find similar situations in different contexts of the functional analysis, including abstract vector lattices¿orthosymmetric maps, C¿-algebras¿zero product preserving operators, and classical and harmonic analysis¿integral bilinear operators. Bringing together the ideas of these areas, we show new factorization theorems and characterizations by means of norm inequalities. The objective of the paper is to apply these tools to provide new descriptions of some classes of bilinear integral operators, and to obtain integral representations for abstract classes of bilinear maps satisfying certain domination properties.The first author was supported by TUBITAK-The Scientific and Technological Research Council of Turkey, Grant No. 2211/E. The second author was supported by Ministerio de Economia y Competitividad (Spain) and FEDER, Grant MTM2016-77054-C2-1-P.Erdogan, E.; Sánchez Pérez, EA.; Gok, O. (2019). Product factorability of integral bilinear operators on Banach function spaces. Positivity. 23(3):671-696. https://doi.org/10.1007/s11117-018-0632-zS671696233Abramovich, Y.A., Kitover, A.K.: Inverses of Disjointness Preserving Operators. American Mathematical Society, Providence (2000)Abramovich, Y.A., Wickstead, A.W.: When each continuous operator is regular II. Indag. Math. (N.S.) 8(3), 281–294 (1997)Alaminos, J., Brešar, M., Extremera, J., Villena, A.R.: Maps preserving zero products. Studia Math. 193(2), 131–159 (2009)Alaminos, J., Brešar, M., Extremera, J., Villena, A.R.: On bilinear maps determined by rank one idempotents. Linear Algebra Appl. 432, 738–743 (2010)Alaminos, J., Extremera, J., Villena, A.R.: Orthogonality preserving linear maps on group algebras. Math. Proc. Camb. Philos. 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Studia Math. 24, 113–190 (1964)Defant, A.: Variants of the Maurey-Rosenthal theorem for quasi Köthe function spaces. Positivity 5, 153–175 (2001)Delgado Garrido, O., Sánchez Pérez, E.A.: Strong factorizations between couples of operators on Banach function spaces. J. Convex Anal. 20(3), 599–616 (2013)Diestel, J., Jarchow, H., Tonge, A.: Absolutely Summing Operators, vol. 43. Cambridge University Press, Cambridge (1995)Erdoğan, E., Calabuig, J.M., Sánchez Pérez, E.A.: Convolution-continuous bilinear operators acting in Hilbert spaces of integrable functions. Ann. Funct. Anal. 9(2), 166–179 (2018)Diestel, J., Uhl, J.J.: Vector Measures. American Mathematical Society, Providence (1977)Fremlin, D.H.: Tensor products of Archimedean vector lattices. Am. J. Math. 94, 778–798 (1972)Gillespie, T.A.: Factorization in Banach function spaces. Nederl. Akad. Wetensch. Indag. Math. 43(3), 287–300 (1981)Grafakos, L., Li, X.: Uniform bounds for the bilinear Hilbert transforms I. Ann. 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Inference Engine Based on a Hierarchical Structure for Detecting Everyday Activities within the Home

One of the key objectives of an ambient assisted living environment is to enable elderly people to lead a healthy and independent life. These assisted environments have the capability to capture and infer activities performed by individuals, which can be useful for providing assistance and tracking functional decline among the elderly community. This paper presents an activity recognition engine based on a hierarchal structure, which allows modelling, representation and recognition of ADLs, their associated tasks, objects, relationships and dependencies. The structure of this contextual information plays a vital role in conducting accurate ADL recognition. The recognition performance of the inference engine has been validated with a series of experiments based on object usage data collected within the home environment

Evaluation of a Fotonovela to Increase Depression Knowledge and Reduce Stigma Among Hispanic Adults

Fotonovelas—small booklets that portray a dramatic story using photographs and captions— represent a powerful health education tool for low-literacy and ethnic minority audiences. This study evaluated the effectiveness of a depression fotonovela in increasing depression knowledge, decreasing stigma, increasing self-efficacy to recognize depression, and increasing intentions to seek treatment, relative to a text pamphlet. Hispanic adults attending a community adult school (N = 157, 47.5 % female, mean age = 35.8 years, 84 % immigrants, 63 % with less than high school education) were randomly assigned to read the fotonovela or a low-literacy text pamphlet about depression. They completed surveys before reading the material, immediately after reading the material, and 1 month later. The fotonovela and text pamphlet both produced significant improvements in depression knowledge and self-efficacy to identify depression, but the fotonovela produced significantly larger reductions in antidepressant stigma and mental health care stigma. The fotonovela also was more likely to be passed on to family or friends after the study, potentially increasing its reach throughout the community. Results indicate that fotonovelas can be useful for improving health literacy among underserved populations, which could reduce health disparities