Unsupervised machine learning approach for building composite indicators with fuzzy metrics

[EN] This study aims at developing a new methodological approach for building composite indicators, focusingon the weight schemes through an unsupervised machine learning technique. The composite indicatorproposed is based on fuzzy metrics to capture multidimensional concepts that do not have boundaries, suchas competitiveness, development, corruption or vulnerability. This methodology is designed for formativemeasurement models using a set of indicators measured on different scales (quantitative, ordinal and binary)and it is partially compensatory. Under a benchmarking approach, the single indicators are synthesized.The optimization method applied manages to remove the overlapping information provided for the singleindicators, so that the composite indicator provides a more realistic and faithful approximation to the conceptwhich would be studied. It has been quantitatively and qualitatively validated with a set of randomizeddatabases covering extreme and usual cases.This work was supported by the project FEDER-University of Granada (B-SEJ-242.UGR20), 2021-2023: An innovative methodological approach for measuring multidimensional poverty in Andalusia (COMPOSITE). Eduardo Jimenez-Fernandez would also like to thank the support received from Universitat Jaume I under the grant E-2018-03.Jiménez Fernández, E.; Sánchez, A.; Sánchez Pérez, EA. (2022). Unsupervised machine learning approach for building composite indicators with fuzzy metrics. Expert Systems with Applications. 200:1-11. https://doi.org/10.1016/j.eswa.2022.11692711120

Positive Representations of L1 of a Vector Measure

We characterize the vector measures n on a Banach lattice such that the map |·|dn provides a quasi-norm which is equivalent to the canonical norm · n of the space L1(n) of integrable functions as an specific type of transformations of positive vector measures that we call cone-open transformations. We also prove that a vector measure m on a Banach space X constructed as a cone-open transformation of a positive vector measure can be considered in some sense as a positive vector measure by defining a new order on X.Ministerio de Educación y Ciencia MTM2006-11690-C0

Translation invariant maps on function spaces over locally compact groups

[EN] We prove that under adequate geometric requirements, translation invariant mappings between vector-valued quasi-Banach function spaces on a locally compact group G have a bounded extension between Kothe-Bochner spaces L-r (G, E). The class of mappings for which our results apply includes polynomials and multilinear operators. We develop an abstract approach based on some new tools as abstract convolution and matching among Banach function lattices, and also on some classical techniques as Maurey-Rosenthal factorization of operators. As a by-product we show when Haar measures which appear in certain factorization theorems for nonlinear mappings are in fact Pietsch measures. We also give applications to operators between Kothe-Bochner spaces. (C) 2018 Elsevier Inc. All rights reserved.The second named author was supported by National Science Centre, Poland, project, no. 2015/17/B/ST1/00064. The third named author was supported by Ministerio de Economia, Industria y Competitividad (Spain) and FEDER, (project MTM2016-77054-C2-1-P2). We thank the referee for careful reading of the paper and useful remarks.Defant, A.; Mastylo, M.; Sánchez Pérez, EA.; Steinwart, I. (2019). Translation invariant maps on function spaces over locally compact groups. Journal of Mathematical Analysis and Applications. 470(2):795-820. https://doi.org/10.1016/j.jmaa.2018.10.033S795820470

Tensor Characterizations of Summing Polynomials

[EN] Operators T that belong to some summing operator ideal, can be characterized by means of the continuity of an associated tensor operator T that is de¿ned between tensor products of sequences spaces. In this paper we provide a unifying treatment of these tensor product characterizations of summing operators. We work in the more general frame provided by homogeneous polynomials, where an associated ¿ten-sor¿ polynomial ¿which plays the role of T ¿, needs to be determined ¿rst. Examples of applications are shown.The third and fourth authors acknowledge with thanks the Ministerio de Economia, Industria y Competitividad and FEDER Grant MTM2016-77054-C2-1-P. The authors thank the referee for his valuable suggestions that improved the final presentation of the paper.Achour, D.; Alouani, A.; Rueda, P.; Sánchez Pérez, EA. (2018). Tensor Characterizations of Summing Polynomials. Mediterranean Journal of Mathematics. 15(3):127-139. https://doi.org/10.1007/s00009-018-1175-zS127139153Achour, D.: Multilinear extensions of absolutely (p;q;r)-summing operators. Rend. Circ. Mat. Palermo (2) 60(3), 337–350 (2011)Achour, D., Alouani, A.: On multilinear generalizations of the concept of nuclear operators. Colloq. Math. 120(1), 85–102 (2010)Achour, D., Saadi, K.: A polynomial characterization of Hilbert spaces. Collectanea. Math. 61(3), 291–301 (2010)Aron, R.M., Rueda, P.: p-Compact homogeneous polynomials from an ideal point of view. Function spaces in modern analysis, Contemp. Math., vol. 547. American Mathematical Society, Providence, RI, pp. 61–71 (2011)Botelho, G.: Ideals of polynomials generated by weakly compact operators. Note di Mat. 25, 69–102 (2005)Botelho, G.: Type, cotype and generalized Rademacher functions. Rocky Mt. J. Math. 28, 1227–1250 (1998)Botelho, G., Campos, J.: On the transformation of vector-valued sequences by linear and multilinear operators. Monatsh. Math. 183(2017), 415–435 (2015)Botelho, G., Campos, J., Santos, J.: Operator ideals related to absolutely summing and Cohen strongly summing operators. Pac. J. Math. 287, 1–17 (2017)Botelho, G., Pellegrino, D., Rueda, P.: Preduals of spaces of homogeneous polynomials on $$L_p$$ L p -spaces. Linear Multilinear Algebra 60(5), 565–571 (2012)Botelho, G., Pellegrino, D., Rueda, P.: Dominated polynomials on infinite dimensional spaces. Proc. Am. Math. Soc. 138(1), 209–216 (2010)Botelho, G., Pellegrino, D., Rueda, P.: Pietsch’s factorization theorem for dominated polynomials. J. Funct. Anal. 243(1), 257–269 (2007)Çalişkan, E., Pellegrino, D.M.: On the multilinear generalizations of the concept of absolutely summing operators. Rocky Mt. J. Math. 37(4), 1137–1154 (2007)Çalişkan, E., Rueda, P.: On distinguished polynomials and their projections. Ann. Acad. Sci. Fenn. Math. 37, 595–603 (2012)Cilia, R., Gutiérrez, J.: Dominated, diagonal polynomials on $$\ell _p$$ ℓ p spaces. Arch. Math. 84, 421–431 (2005)Cohen, J.S.: Absolutely p-summing, p-nuclear operators and their conjugates. Math. Ann. 201, 177–200 (1973)Defant, A., Floret, K.: Tensor norms and operator ideals. North-Holland Mathematics Studies, vol. 176. North-Holland Publishing Co., Amsterdam (1993)Diestel, J., Jarchow, H., Tonge, A.:, Absolutely summing operators. Cambridge Studies in Advanced Mathematics, vol. 43. Cambridge University Press, Cambridge (1995)Dimant, V.: Strongly p-summing multilinear operators. J. Math. Anal. Appl. 278, 182–193 (2003)Matos, M., Floret, K.: Application of a Khintchine inequality to holomorphic mappings. Math. Nachr. 176, 65–72 (1995)Mujica, J.: Complex Analysis in Banach spaces. Dover Publications Inc., New York (2010)Pérez-García, D.: Comparing different classes of absolutely summing multilinear operators. Arch. Math. 85, 258–267 (2005)Pellegrino, D., Rueda, P., Sánchez-Pérez, E.A.: Surveying the spirit of absolute summability on multilinear operators and homogeneous polynomials. Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM 110(1), 285–302 (2016)Pietsch, A.: Operator ideals. North-Holland Mathematical Library, vol. 20. North-Holland Publishing Co, Amsterdam-New York (1980)Rueda, P., Sánchez-Pérez, E.A.: Factorization of p-dominated polynomials through $$L_p$$ L p -spaces. Mich. Math. J. 63(2), 345–353 (2014)Rueda, P., Sánchez-Pérez, E.A., Tallab, A.: Traced tensor norms and multiple summing multilinear operators. Linear Multilinear Algebra 65(4), 768–786 (2017

A considerable fraction of soil-respired CO2 is not emitted directly to the atmosphere

All data used in this study are freely available (http://criticalzone.org/ catalina-jemez/data/datasets/). The authors wish to thank Rebecca Larkin Minor and Nate Abramson for their careful operation and maintenance of the field measurement devices. The program “Unidades de Excelencia Científica del Plan Propio de Investigación de la Universidad de Granada” funded the cost of this publicationSoil CO2 efflux (Fsoil) is commonly considered equal to soil CO2 production (Rsoil), and both terms are used interchangeably. However, a non-negligible fraction of Rsoil can be consumed in the subsurface due to a host of disparate, yet simultaneous processes. The ratio between CO2 efflux/O2 influx, known as the apparent respiratory quotient (ARQ), enables new insights into CO2 losses from Rsoil not previously captured by Fsoil. We present the first study using continuous ARQ estimates to evaluate annual CO2 losses of carbon produced from Rsoil. We found that up to 1/3 of Rsoil was emitted directly to the atmosphere, whereas 2/3 of Rsoil was removed by subsurface processes. These subsurface losses are attributable to dissolution in water, biological activities and chemical reactions. Having better estimates of Rsoil is key to understanding the true influence of ecosystem production on Rsoil, as well as the role of soil CO2 production in other connected processes within the critical zoneThis project and data were supported by NSF awards 1417101 and 1331408, as well as by the European Commission project DIESEL (FP7-PEOPLE-2013-IOF, 625988) and the Spanish Ministry of Economy and Competitiveness (IJCI-2016-30822)

The pp-Daugavet property for function spaces

A natural extension of the Daugavet property for $p$-convex Banach function spaces and related classes is analysed. As an application, we extend the arguments given in the setting of the Daugavet property to show that no reflexive space falls into this class