Carry a big stick, or no stick at all: punishment and endowment heterogeneity in the trust game

We investigate the effect of costly punishment in a trust game with endowment heterogeneity. Our findings indicate that the difference between the investor and the allocator’s initial endowments determines the effect of punishment on trust and trustworthiness. Punishment fosters trust only when the investor is wealthier than the allocator. Otherwise, punishment fails to promote trusting behavior. As for trustworthiness, the effect is just the opposite. The higher the difference between the investor and the allocator’s initial endowments, the less willing allocators are to pay back. We discuss the consistency of our findings with social preference models (like inequality aversion, reciprocity), the capacity of punishment (i.e., the deterrence hypothesis) and hidden costs of punishment (i.e., models of intrinsic and extrinsic motivation). Our results are hardly coherent with the first two (inequality aversion and deterrence), but roughly consistent with the latter

Factorizing operators on Banach function spaces through spaces of multiplication operators

In order to extend the theory of optimal domains for continuous operators on a Banach function space X(μ) over a finite measure μ, we consider operators T satisfying other type of inequalities than the one given by the continuity which occur in several well-known factorization theorems (for instance, Pisier Factorization Theorem through Lorentz spaces, pth-power factorable operators . . . ). We prove that such a T factorizes through a space of multiplication operators which can be understood in a certain sense as the optimal domain for T . Our extended optimal domain technique does not need necessarily the equivalence between μ and the measure defined by the operator T and, by using δ-rings, μ is allowed to be infinite. Classical and new examples and applications of our results are also given, including some new results on the Hardy operator and a factorization theorem through Hilbert spaces.Generalitat Valenciana TSGD-07Ministerio de Educación y Ciencia MTM2006-13000-C03-0

Tensor product representation of Kothe-Bochner spaces and their dual spaces

We provide a tensor product representation of Kothe-Bochner function spaces of vector valued integrable functions. As an application, we show that the dual space of a Kothe-Bochner function space can be understood as a space of operators satisfying a certain extension property. We apply our results in order to give an alternate representation of the dual of the Bochner spaces of p-integrable functions and to analyze some properties of the natural norms that are defined on the associated tensor products.First and third authors are supported by grant MTM201453009-P of the Ministerio de Economia y Competitividad (Spain). Second and fourth authors are supported by grant MTM2012-36740-C02-02 of the Ministerio de Economia y Competitividad (Spain).Calabuig, JM.; Jiménez Fernández, E.; Juan Blanco, MA.; Sánchez Pérez, EA. (2016). Tensor product representation of Kothe-Bochner spaces and their dual spaces. Positivity. 20(1):155-169. https://doi.org/10.1007/s11117-015-0347-3S155169201Bochner, S.: Integration von Funktionen, deren Werte die Elemente eines Vectorraumes sind. Fundamenta Mathematicae 20, 262–276 (1933)Calabuig, J.M., Delgado, O., Juan, M.A., Sánchez, E.A.: Pérez, On the Banach lattice structure of $$L^1_w$$ L w 1 of a vector measure on a $$\delta$$ δ -ring. Collect. Math. 65, 6567–85 (2014)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(1), 88–103 (2010)Calabuig, J.M., Gregori, P., Sánchez, E.A.: Pérez, Radon-Nikodým derivatives for vector measures belonging to Köthe function spaces. J. Math. Anal. Appl. 348, 469–479 (2008)Cerdà, J., Hudzik, H., Mastyło, M.: Geometric properties of Köthe-Bochner spaces. Math. Proc. Cambridge Philos. Soc. 120(3), 521–533 (1996)Chakraborty, N.D., Basu, S.: Spaces of p-tensor integrable functions and related Banach space properties. Real Anal. Exchange 34, 87–104 (2008)Chakraborty, N.D., Basu, S.: Integration of vector-valued functions with respect to vector measures defined on $$\delta$$ δ -rings. Ill. J. Math. 55(2), 495–508 (2011)Defant, A., Floret, K.: Tensor norms and operator ideals. North-Holland, Amsterdam (1993)Delgado, O., Juan, M.A.: Representation of Banach lattices as $$L^{1}_{w}$$ L w 1 spaces of a vector measure defined on a $$\delta -$$ δ - ring. Bull. Belgian Math. Soc. 19, 239–256 (2012)Diestel, J., Uhl, J.J.: Vector measures. Am. Math. Soc, Providence (1977)Dobrakov, I.: On integration in Banach spaces, VII. Czechoslovak Math. J. 38, 434–449 (1988)García-Raffi, L.M., Jefferies, B.: An application of bilinear integration to quantum scattering. J. Math. Anal. Appl. 415, 394–421 (2014)Gregori Huerta, P.: Espacios de medidas vectoriales. Thesis, Universidad de Valencia, ISBN:8437060591 (2005)Jefferies, B., Okada, S.: Bilinear integration in tensor products. Rocky Mt. J. Math. 28, 517–545 (1998)Lewis, D.R.: On integrability and summability in vector spaces. Ill. J. Math. 16, 294–307 (1972)Lin, P.-K.: Köthe-Bochner function spaces. Birkhauser, Boston (2004)Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces II. Springer, Berlin (1979)Okada, S., Ricker, W.J., Sánchez Pérez, E.A.: Optimal Domains and integral extensions of operators acting in function spaces. Operator Theory Advances and Applications, vol. 180. Birkhäuser, Basel (2008)Pallu de La Barriére, R.: Integration of vector functions with respect to vector measures. Studia Univ. Babes-Bolyai Math. 43, 55–93 (1998)Rodríguez, J.: On integration of vector functions with respect to vector measures. Czechoslovak Math. J. 56, 805–825 (2006

Kaplan-Meier type survival curves for COVID-19: a health data based decision-making tool

Countries are recording health information on the global spread of COVID-19 using different methods, sometimes changing the rules after a few days. They are all publishing the number of new individuals infected, cured and dead, along with some supplementary data. These figures are often recorded in a non-uniform manner and do not match the standard definitions of these variables. However, in this paper we show that the Kaplan-Meier curves calculated with them could provide useful information about the dynamics of the disease in different countries. Our aim is to present a robust and simple model to show certain characteristics of the evolution of the dynamic process, showing that the differences of evolution among the countries is reflected in the corresponding Kaplan-Meier-type curves. We compare the curves obtained for the most affected countries so far, proposing possible interpretations of the properties that distinguish them.Comment: 12 pages, 6 figure

Factorization of operators through subspaces of L-1-spaces

[EN] We analyze domination properties and factorization of operators in Banach spaces through subspaces of L1-spaces. Using vector measure integration and extending classical arguments based on scalar integral bounds, we provide characterizations of operators factoring through subspaces of L1-spaces of finite measures. Some special cases involving positivity and compactness of the operators are considered.Research supported by MINECO/FEDER under projects MTM2014-53009-P (J.M Calabuig), MTM2014-54182-P (J. Rodriguez) and MTM2012-36740-C02-02 (E. A. Sanchez-Perez).Calabuig, JM.; Rodríguez, J.; Sánchez Pérez, EA. (2017). Factorization of operators through subspaces of L-1-spaces. Journal of the Australian Mathematical Society. 103(3):313-328. https://doi.org/10.1017/S1446788716000513S3133281033Lindenstrauss, J., & Tzafriri, L. (1979). Classical Banach Spaces II. doi:10.1007/978-3-662-35347-9Pisier, G. (1986). Factorization of Linear Operators and Geometry of Banach Spaces. CBMS Regional Conference Series in Mathematics. doi:10.1090/cbms/060Okada, S., Ricker, W. J., & Sánchez Pérez, E. A. (2008). Optimal Domain and Integral Extension of Operators. doi:10.1007/978-3-7643-8648-1Lacey, H. E. (1974). The Isometric Theory of Classical Banach Spaces. doi:10.1007/978-3-642-65762-7Fernández, A., Mayoral, F., Naranjo, F., Sáez, C., & Sánchez-Pérez, E. A. (2005). Vector measure Maurey–Rosenthal-type factorizations and ℓ-sums of L1-spaces. Journal of Functional Analysis, 220(2), 460-485. doi:10.1016/j.jfa.2004.06.010Juan, M. A., & Sánchez Pérez, E. A. (2013). Maurey-Rosenthal domination for abstract Banach lattices. Journal of Inequalities and Applications, 2013(1). doi:10.1186/1029-242x-2013-213Avilés, A., Cabello Sánchez, F., Castillo, J. M. F., González, M., & Moreno, Y. (2013). On separably injective Banach spaces. Advances in Mathematics, 234, 192-216. doi:10.1016/j.aim.2012.10.013Defant, A., & Sánchez Pérez, E. A. (2004). Maurey–Rosenthal factorization of positive operators and convexity. Journal of Mathematical Analysis and Applications, 297(2), 771-790. doi:10.1016/j.jmaa.2004.04.047DEFANT, A., & PÉREZ, E. A. S. (2009). Domination of operators on function spaces. Mathematical Proceedings of the Cambridge Philosophical Society, 146(1), 57-66. doi:10.1017/s0305004108001734Bartle, R. G., Dunford, N., & Schwartz, J. (1955). Weak Compactness and Vector Measures. Canadian Journal of Mathematics, 7, 289-305. doi:10.4153/cjm-1955-032-1Rosenthal, H. P. (1974). A Characterization of Banach Spaces Containing l1. Proceedings of the National Academy of Sciences, 71(6), 2411-2413. doi:10.1073/pnas.71.6.2411Diestel, J., Jarchow, H., & Tonge, A. (1995). Absolutely Summing Operators. doi:10.1017/cbo9780511526138Rueda, P., & Sánchez-Pérez, E. A. (2015). Compactness in spaces of p-integrable functions with respect to a vector measure. Topological Methods in Nonlinear Analysis, 45(2), 641. doi:10.12775/tmna.2015.030Rosenthal, H. P. (1973). On Subspaces of L p. The Annals of Mathematics, 97(2), 344. doi:10.2307/1970850Diestel, J., & Uhl, J. (1977). Vector Measures. Mathematical Surveys and Monographs. doi:10.1090/surv/015[16] M. Mastyło and E. A. Sánchez-Pérez , ‘Factorization of operators through Orlicz spaces’, Bull. Malays. Math. Sci. Soc. doi:10.1007/s40840-015-0158-5, to appear.Calabuig, J. M., Lajara, S., Rodríguez, J., & Sánchez-Pérez, E. A. (2014). Compactness in L1of a vector measure. Studia Mathematica, 225(3), 259-282. doi:10.4064/sm225-3-6Defant, A. (2001). Positivity, 5(2), 153-175. doi:10.1023/a:1011466509838Fabian, M., Habala, P., Hájek, P., Montesinos, V., & Zizler, V. (2011). Banach Space Theory. CMS Books in Mathematics. doi:10.1007/978-1-4419-7515-

Greenhouse effect gases emission implications on sustainability of the Campus of Vegazana, University of León

En este trabajo se presentan los resultados del estudio de emisiones de CO2, uno de los gases más importantes de efecto invernadero, debido a la actividad desarrollada en el Campus de Vegazana de la Universidad de León, para el año 2006. El estudio se enmarca en un proyecto más amplio de cálculo del indicador Huella Ecológica (HE), desarrollado para conocer en qué medida se alcanzan los objetivos de sostenibilidad establecidos para el Campus, así como para el desarrollo de propuestas encaminadas a la reducción de las emisiones de CO2. Los resultados obtenidos reflejan como el área de superficie biológicamente productiva necesaria para absorber las emisiones del Campus constituyen cerca del 99% del área total de HE. La mayor parte de estas emisiones proceden del gasto energético para electricidad (38%) y uso térmico (24%, seguido del transporte (19%) y la construcción del propio complejo universitario (16%, el cual hace referencia únicamente al año 2006, considerando una vida útil de 27 años para los edificios e instalaciones del Campus, inaugurado en 1979. Una vez analizadas cualitativa y cuantitativamente las emisiones producidas, se ha buscado conocer el total de superficie forestal necesaria para absorber dichas emisiones, considerando los datos del Tercer Inventario Forestal Nacional (2003) sobre cobertura de las masas forestales para el territorio nacional, y los aportados por Bravo (2007) en relación a las tasas de fijación del gas por parte de éstas. Como conclusión, puede estimarse que del total de la superficie forestal de la provincia de León, un 0.46% es necesaria como depósito y sumidero del CO2 emitido por el Campus de Vegazana (8.470.168 toneladas. Esta estimación se ha realizado considerando que las masas forestales son las únicas depositarias de CO2, tarea compartida en la naturaleza, no obstante, con el suelo, el agua y los cultivosIn this work, we present the results obtained about the CO2 emissions, one of the most important greenhouse gases, due to the normal activity developed in the Campus of Vegazana of the University of León for the year 2006. This study is all part of a wider project for evaluating the Fingerprint ecological indicator (HE, initially developed for assessing if the sustainability objectives established by the University policies for the Campus of Vegazana have been achieved, as well as the development of proposals and ideas directed towards the reduction of the emissions of CO2. Results obtained showed that the biologically productive area necessary for absorbing all emissions are close to the 99% of the total value of HE. The majority of these emissions come from the energy consumed for producing electricity (38%) and heating (24%), followed by the transport (19%) and the constructions of the buildings and infrastructures of the University (16%, which related just for the year 2006, considering a living period of 27 years as it was inaugurated in 1979. Once analyzed qualitatively and quantitatively the emissions produced, it was developed a method for estimating the total area covered necessary for absorbing them by considering data available from the Third National Forestry Inventory of Spain (2003), related with the forest cover of the territory, and data provided by Bravo(2007, about the absorption rate of the tree species. As a conclusion, we estimated that form the total area covered by forests of the Province of León, a 0.46% is necessary as sink of the CO2 produced in the Campus of Vegazana (8.470.168 ton. This assessment has been achieved considering that forests are the only warehouse of CO2, when actually soil, water and crops are in nature.Peer Reviewe

Zeb2 regulates myogenic differentiation in pluripotent stem cells

Skeletal muscle differentiation is triggered by a unique family of myogenic basic helix-loop-helix transcription factors, including MyoD, MRF-4, Myf-5, and Myogenin. These transcription factors bind promoters and distant regulatory regions, including E-box elements, of genes whose expression is restricted to muscle cells. Other E-box binding zinc finger proteins target the same DNA response elements, however, their function in muscle development and regeneration is still unknown. Here, we show that the transcription factor zinc finger E-box-binding homeobox 2 (Zeb2, Sip-1, Zfhx1b) is present in skeletal muscle tissues. We investigate the role of Zeb2 in skeletal muscle differentiation using genetic tools and transgenic mouse embryonic stem cells, together with single-cell RNA-sequencing and in vivo muscle engraftment capability. We show that Zeb2 over-expression has a positive impact on skeletal muscle differentiation in pluripotent stem cells and adult myogenic progenitors. We therefore propose that Zeb2 is a novel myogenic regulator and a possible target for improving skeletal muscle regeneration. The non-neural roles of Zeb2 are poorly understood

GRADIENTE LONGITUDINAL DE DISTRIBUCIÓN DE LA VEGETACIÓN RIBERENA DEL RIO BERNESGA (LEÓN) EN SU TRAMO DE MONTANA

The distribution of macrophytic vegetation associated to the mountain stretch of the Bernesga river (León, Spain) is anaiysed on the basis of the data coliected in 36 transects distributed on both banks and perpendicular to the river bed. The similarity among the sarnples placed along the river is on the whole low, except in those having an outstanding presence of Carex acuta subsp. broteriana; nevertheless, the strongest affinity among close transects allows to taik o€ a continous change in the vegetation. The best delimited areas embrace, on the one hand, the first kilometers where there are no real banks and both sides o€ the river are covered mainly by swampy meadows and harvest grassland with a high degree of dampness; and, on the other, the lower part where the riparian community gets its own physiognomy and Agrostis stolonifera, Mentha longifolia and mostly Carex acuta subsp. broteriana constitute the most important species.Se analiza la distribución de la vegetación macrofitica asociada al tramo de montaña del no Bernesga (León) a partir de los datos recogidos en 36 transectos distribuidos en ambas márgenes y perpendiculares al cauce. El grado de semejanza entre las muestras situadas a lo largo del no es generalmente bajo, salvo en aquellas que tienen una presencia destacada de Carex acuta subsp. broteriana; sin embargo, la mayor afmidad entre transectos próximos permite hablar de un cambio continuo en la vegetación. Las áreas mejor delimitadas corresponden, por un lado, a los kilómetros iniciales, donde no se distingue una verdadera ribera y las márgenes del no están ocupadas esencialmente por pastizales higroturbosos y prados de siega con un elevado grado de humedad; y por otro, a la zona baja, donde la comunidad ribereña adquiere una fisonomía propia y Agrostis stolonifera, Mentha longifolia y especialmente Carex acuta subsp. brotenana constituyen las especies más importantes