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

On the exchange of intersection and supremum of sigma-fields in filtering theory

We construct a stationary Markov process with trivial tail sigma-field and a nondegenerate observation process such that the corresponding nonlinear filtering process is not uniquely ergodic. This settles in the negative a conjecture of the author in the ergodic theory of nonlinear filters arising from an erroneous proof in the classic paper of H. Kunita (1971), wherein an exchange of intersection and supremum of sigma-fields is taken for granted.Comment: 20 page

Estimating Granger causality from Fourier and wavelet transforms of time series data

Experiments in many fields of science and engineering yield data in the form of time series. The Fourier and wavelet transform-based nonparametric methods are used widely to study the spectral characteristics of these time series data. Here, we extend the framework of nonparametric spectral methods to include the estimation of Granger causality spectra for assessing directional influences. We illustrate the utility of the proposed methods using synthetic data from network models consisting of interacting dynamical systems.Comment: 6 pages, 2 figure

The South West Area Mesothelioma and Pemetrexed trial - A multi-centre prospective observational study evaluating novel markers of chemotherapy response and prognostication

Background:Robust markers that predict prognosis and detect early treatment response in malignant pleural mesothelioma (MPM) would enhance patient care.Methods:Consecutive patients with MPM who were considered fit for first-line chemotherapy were prospectively recruited. Patients of similar performance status opting for best supportive care were included as a comparator group. Baseline and interval CT, PET-CT and serum markers (mesothelin, fibulin-3 and neutrophil–lymphocyte ratio (NLR)) were obtained, and patients followed up for a minimum 12 months.Findings:Seventy-three patients were recruited (58 chemotherapy/15 comparator arm). Baseline TGV (total glycolytic volume on PET-CT) was an independent predictor of worse overall survival (OS) (P=0.001). Change in interval TGV(baseline/after two cycles of chemotherapy) did not predict OS or chemotherapy response on CT. Baseline NL

Dynamics of Simple Balancing Models with State Dependent Switching Control

Time-delayed control in a balancing problem may be a nonsmooth function for a variety of reasons. In this paper we study a simple model of the control of an inverted pendulum by either a connected movable cart or an applied torque for which the control is turned off when the pendulum is located within certain regions of phase space. Without applying a small angle approximation for deviations about the vertical position, we see structurally stable periodic orbits which may be attracting or repelling. Due to the nonsmooth nature of the control, these periodic orbits are born in various discontinuity-induced bifurcations. Also we show that a coincidence of switching events can produce complicated periodic and aperiodic solutions.Comment: 36 pages, 12 figure

Phylogenetic groups and cephalosporin resistance genes of Escherichia coli from diseased food-producing animals in Japan

A total of 318 Escherichia coli isolates obtained from different food-producing animals affected with colibacillosis between 2001 and 2006 were subjected to phylogenetic analysis: 72 bovine isolates, 89 poultry isolates and 157 porcine isolates. Overall, the phylogenetic group A was predominant in isolates from cattle (36/72, 50%) and pigs (101/157, 64.3%) whereas groups A (44/89, 49.4%) and D (40/89, 44.9%) were predominant in isolates from poultry. In addition, group B2 was not found among diseased food-producing animals except for a poultry isolate. Thus, the phylogenetic group distribution of E. coli from diseased animals was different by animal species. Among the 318 isolates, cefazolin resistance (minimum inhibitory concentrations: ≥32 μg/ml) was found in six bovine isolates, 29 poultry isolates and three porcine isolates. Of them, 11 isolates (nine from poultry and two from cattle) produced extended spectrum β-lactamase (ESBL). The two bovine isolates produced blaCTX-M-2, while the nine poultry isolates produced blaCTX-M-25 (4), blaSHV-2 (3), blaCTX-M-15 (1) and blaCTX-M-2 (1). Thus, our results showed that several types of ESBL were identified and three types of β-lactamase (SHV-2, CTX-M-25 and CTX-M-15) were observed for the first time in E. coli from diseased animals in Japan

Maurey-Rosenthal domination for abstract Banach lattices

We extend the Maurey-Rosenthal theorem on integral domination and factorization of p-concave operators from a p-convex Banach function space through Lp-spaces for the case of operators on abstract p-convex Banach lattices satisfying some essential lattice requirements - mainly order density of its order continuous part - that are shown to be necessary. We prove that these geometric properties can be characterized by means of an integral inequality giving a domination of the pointwise evaluation of the operator for a suitable weight also in the case of abstract Banach lattices. We obtain in this way what in a sense can be considered the most general factorization theorem of operators through Lp-spaces. In order to do this, we prove a new representation theorem for abstract p-convex Banach lattices with the Fatou property as spaces of p-integrable functions with respect to a vector measure.The authors are supported by grants MTM2011-23164 and MTM2012-36740-C02-02 of the Ministerio de Economia y Competitividad (Spain).Juan Blanco, MA.; Sánchez Pérez, EA. (2013). Maurey-Rosenthal domination for abstract Banach lattices. Journal of Inequalities and Applications. (213). https://doi.org/10.1186/1029-242X-2013-213S213Defant A: Variants of the Maurey-Rosenthal theorem for quasi Köthe function spaces. Positivity 2001, 5: 153–175. 10.1023/A:1011466509838Defant A, Sánchez Pérez EA: Maurey-Rosenthal factorization of positive operators and convexity. J. Math. Anal. Appl. 2004, 297: 771–790. 10.1016/j.jmaa.2004.04.047Defant A, Sánchez Pérez EA: Domination of operators on function spaces. Math. Proc. Camb. Philos. Soc. 2009, 146: 57–66. 10.1017/S0305004108001734Fernández A, Mayoral F, Naranjo F, Sáez C, Sánchez-Pérez EA: Vector measure Maurey-Rosenthal type factorizations and l -sums of L 1 -spaces. J. Funct. Anal. 2005, 220: 460–485. 10.1016/j.jfa.2004.06.010Palazuelos C, Sánchez Pérez EA, Tradacete P: Maurey-Rosenthal factorization for p -summing operators and Dodds-Fremlin domination. J. Oper. Theory 2012, 68(1):205–222.Luxemburg WAJ, Zaanen AC: Riesz Spaces I. North-Holland, Amsterdam; 1971.Zaanen AC: Riesz Spaces II. North-Holland, Amsterdam; 1983.Lindenstrauss J, Tzafriri L: Classical Banach Spaces II. Springer, Berlin; 1979.Aliprantis CD, Burkinshaw O: Positive Operators. Academic Press, New York; 1985.Curbera GP, Ricker WJ: Vector measures, integration and applications. Trends Math. In Positivity. Birkhäuser, Basel; 2007:127–160.Okada S, Ricker WJ, Sánchez Pérez EA: Optimal domains and integral extensions of operators acting in function spaces. 180. In Operator Theory Advances and Applications. Birkhäuser, Basel; 2008.Delgado O: L 1 -spaces of vector measures defined on δ -rings. Arch. Math. 2005, 84: 432–443. 10.1007/s00013-005-1128-1Calabuig, JM, Delgado, O, Juan, MA, Sánchez Pérez, EA: On the Banach lattice structure of L w 1 of a vector measure on a δ-ring. Collect. Math. doi:10.1007/s13348–013–0081–8Calabuig JM, Delgado O, Sánchez Pérez EA: Factorizing operators on Banach function spaces through spaces of multiplication operators. J. Math. Anal. Appl. 2010, 364: 88–103. 10.1016/j.jmaa.2009.10.034Delgado O:Optimal domains for kernel operators on [ 0 , ∞ ) × [ 0 , ∞ ) .Stud. Math. 2006, 174: 131–145. 10.4064/sm174-2-2Delgado O, Soria J: Optimal domain for the Hardy operator. J. Funct. Anal. 2007, 244: 119–133. 10.1016/j.jfa.2006.12.011Jiménez Fernández E, Juan MA, Sánchez Pérez EA: A Komlós theorem for abstract Banach lattices of measurable functions. J. Math. Anal. Appl. 2011, 383: 130–136. 10.1016/j.jmaa.2011.05.010Curbera, GP: El espacio de funciones integrables respecto de una medida vectorial. PhD thesis, Univ. of Sevilla (1992)Sánchez Pérez EA: Compactness arguments for spaces of p -integrable functions with respect to a vector measure and factorization of operators through Lebesgue-Bochner spaces. Ill. J. Math. 2001, 45(3):907–923.Fernández A, Mayoral F, Naranjo F, Sáez C, Sánchez-Pérez EA: Spaces of p -integrable functions with respect to a vector measure. Positivity 2006, 10: 1–16. 10.1007/s11117-005-0016-zCalabuig JM, Juan MA, Sánchez Pérez EA: Spaces of p -integrable functions with respect to a vector measure defined on a δ -ring. Oper. Matrices 2012, 6: 241–262.Lewis DR: On integrability and summability in vector spaces. Ill. J. Math. 1972, 16: 294–307.Masani PR, Niemi H: The integration theory of Banach space valued measures and the Tonelli-Fubini theorems. I. Scalar-valued measures on δ -rings. Adv. Math. 1989, 73: 204–241. 10.1016/0001-8708(89)90069-8Masani PR, Niemi H: The integration theory of Banach space valued measures and the Tonelli-Fubini theorems. II. Pettis integration. Adv. Math. 1989, 75: 121–167. 10.1016/0001-8708(89)90035-2Brooks JK, Dinculeanu N: Strong additivity, absolute continuity and compactness in spaces of measures. J. Math. Anal. Appl. 1974, 45: 156–175. 10.1016/0022-247X(74)90130-9Curbera GP:Operators into L 1 of a vector measure and applications to Banach lattices.Math. Ann. 1992, 293: 317–330. 10.1007/BF01444717Delgado O, Juan MA: Representation of Banach lattices as L w 1 spaces of a vector measure defined on a δ -ring. Bull. Belg. Math. Soc. Simon Stevin 2012, 19: 239–256.Curbera GP, Ricker WJ: Banach lattices with the Fatou property and optimal domains of kernel operators. Indag. Math. 2006, 17: 187–204. 10.1016/S0019-3577(06)80015-7Curbera GP, Ricker WJ: The Fatou property in p -convex Banach lattices. J. Math. Anal. Appl. 2007, 328: 287–294. 10.1016/j.jmaa.2006.04.086Aliprantis CD, Border KC: Infinite Dimensional Analysis. Springer, Berlin; 1999.Delgado, O: Optimal extension for positive order continuous operators on Banach function spaces. Glasg. Math. J. (to appear

The effect of chemotherapy on health-related quality of life in mesothelioma: Results from the SWAMP trial

© 2015 Cancer Research UK. All rights reserved. Background: The effect of chemotherapy on health-related quality of life (HRQoL) in malignant pleural mesothelioma (MPM) is poorly understood. Patient-individualised prognostication and prediction of treatment response from chemotherapy is useful but little evidence exists to guide practice. Method: Consecutive patients with MPM who were fit for first-line chemotherapy with pemetrexed and cisplatin\carboplatin were recruited and followed up for a minimum of 12 months. This study focussed on the HRQoL outcomes of these patients using the EQ-5D, EORTC QLQ-C30 and LC13. Results: Seventy-three patients were recruited of which 58 received chemotherapy and 15 opted for best supportive care (BSC). Compliance with HRQoL questionnaires was 98% at baseline. The chemotherapy group maintained HRQoL compared with the BSC group whose overall HRQoL fell (P=0.006) with worsening dyspnoea and pain. The impact of chemotherapy was irrespective of histological subtype although those with non-epithelioid disease had worse HRQoL at later time points (P=0.012). Additionally, those with a falling mesothelin or improvement on modified-RECIST CT at early follow-up had a better HRQoL at 16 weeks. Conclusions: HRQoL was maintained following chemotherapy compared with a self-selected BSC group. Once chemotherapy is initiated, a falling mesothelin or improved RECIST CT findings infer a quality-of-life advantage

New high precision orbital and physical parameters of the double-lined low-mass spectroscopic binary BY Draconis

We present the most precise to date orbital and physical parameters of the well known short period (P=5.975 d), eccentric (e=0.3) double-lined spectroscopic binary BY Draconis, a prototype of a class of late-type, active, spotted flare stars. We calculate the full spectroscopic/astrometric orbital solution by combining our precise radial velocities (RVs) and the archival astrometric measurements from the Palomar Testbed Interferometer (PTI). The RVs were derived based on the high resolution echelle spectra taken between 2004 and 2008 with the Keck I/HIRES, Shane/CAT/HamSpec and TNG/SARG telescopes/spectrographs using our novel iodine-cell technique for double-lined binary stars. The RVs and available PTI astrometric data spanning over 8 years allow us to reach 0.2-0.5% level of precision in M sin3(i) and the parallax but the geometry of the orbit (i=154 deg) hampers the absolute mass precision to 3.3%, which is still an order of magnitude better than for previous studies. We compare our results with a set of Yonsei-Yale theoretical stellar isochrones and conclude that BY Dra is probably a main sequence system more metal-rich than the Sun. Using the orbital inclination and the available rotational velocities of the components, we also conclude that the rotational axes of the components are likely misaligned with the orbital angular momentum. Given BY Dra's main sequence status, late spectral type and the relatively short orbital period, its high orbital eccentricity and probable spin-orbit misalignment are not in agreement with the tidal theory. This disagreement may possibly be explained by smaller rotational velocities of the components and the presence of a substellar mass companion to BY Dra AB.Comment: 10 pages, 7 figures, 4 tables, to appear in MNRA