Mean Li-Yorke chaos in Banach spaces

We investigate the notion of mean Li-Yorke chaos for operators on Banach spaces. We show that it differs from the notion of distributional chaos of type 2, contrary to what happens in the context of topological dynamics on compact metric spaces. We prove that an operator is mean Li-Yorke chaotic if and only if it has an absolutely mean irregular vector. As a consequence, absolutely Ces\`aro bounded operators are never mean Li-Yorke chaotic. Dense mean Li-Yorke chaos is shown to be equivalent to the existence of a dense (or residual) set of absolutely mean irregular vectors. As a consequence, every mean Li-Yorke chaotic operator is densely mean Li-Yorke chaotic on some infinite-dimensional closed invariant subspace. A (Dense) Mean Li-Yorke Chaos Criterion and a sufficient condition for the existence of a dense absolutely mean irregular manifold are also obtained. Moreover, we construct an example of an invertible hypercyclic operator $T$ such that every nonzero vector is absolutely mean irregular for both $T$ and $T^{-1}$. Several other examples are also presented. Finally, mean Li-Yorke chaos is also investigated for $C_0$-semigroups of operators on Banach spaces.Comment: 26 page

Probing quantum fluctuation theorems in engineered reservoirs

Fluctuation Theorems are central in stochastic thermodynamics, as they allow for quantifying the irreversibility of single trajectories. Although they have been experimentally checked in the classical regime, a practical demonstration in the framework of quantum open systems is still to come. Here we propose a realistic platform to probe fluctuation theorems in the quantum regime. It is based on an effective two-level system coupled to an engineered reservoir, that enables the detection of the photons emitted and absorbed by the system. When the system is coherently driven, a measurable quantum component in the entropy production is evidenced. We quantify the error due to photon detection inefficiency, and show that the missing information can be efficiently corrected, based solely on the detected events. Our findings provide new insights into how the quantum character of a physical system impacts its thermodynamic evolution.Comment: 9 pages, 4 figure

Why are Diverticula of the Rectum Uncommon? Angiomorphological Hypothesis

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Entanglement properties of optical coherent states under amplitude damping

Through concurrence, we characterize the entanglement properties of optical coherent-state qubits subject to an amplitude damping channel. We investigate the distillation capabilities of known error correcting codes and obtain upper bounds on the entanglement depending on the non-orthogonality of the coherent states and the channel damping parameter. This work provides a first, full quantitative analysis of these photon-loss codes which are naturally reminiscent of the standard qubit codes against Pauli errors.Comment: 7 pages, 6 figures. Revised version with small corrections; main results remain unaltere

Mean Li-Yorke chaos in Banach spaces

[EN] We investigate the notion of mean Li-Yorke chaos for operators on Banach spaces. We show that it differs from the notion of distributional chaos of type 2, contrary to what happens in the context of topological dynamics on compact metric spaces. We prove that an operator is mean Li-Yorke chaotic if and only if it has an absolutely mean irregular vector. As a consequence, absolutely Cesaro bounded operators are never mean Li-Yorke chaotic. Dense mean Li-Yorke chaos is shown to be equivalent to the existence of a dense (or residual) set of absolutely mean irregular vectors. As a consequence, every mean Li-Yorke chaotic operator is densely mean Li-Yorke chaotic on some infinite-dimensional closed invariant subspace. A (Dense) Mean Li-Yorke Chaos Criterion and a sufficient condition for the existence of a dense absolutely mean irregular manifold are also obtained. Moreover, we construct an example of an invertible hypercyclic operator T such that every nonzero vector is absolutely mean irregular for both T and T-1. Several other examples are also presented. Finally, mean Li-Yorke chaos is also investigated for C-0-semigroups of operators on Banach spaces.This work was partially done on a visit of the first author to the Institut Universitari de Matematica Pura i Aplicada at Universitat Politecnica de Valencia, and he is very grateful for the hospitality and support. The first author was partially supported by project #304207/2018-7 of CNPq and by grant #2017/22588-0 of Sao Paulo Research Foundation (FAPESP). The second and third authors were supported by MINECO, Project MTM2016-75963-P. The third author was also supported by Generalitat Valenciana, Project PROMETEO/2017/102. We thank Frederic Bayart for providing us Theorem 27, which answers a previous question of us. We also thank the referee whose careful comments produced an improvement in the presentation of the article.Bernardes, NCJ.; Bonilla, A.; Peris Manguillot, A. (2020). Mean Li-Yorke chaos in Banach spaces. Journal of Functional Analysis. 278(3):1-31. https://doi.org/10.1016/j.jfa.2019.108343S1312783Albanese, A., Barrachina, X., Mangino, E. M., & Peris, A. (2013). Distributional chaos for strongly continuous semigroups of operators. Communications on Pure and Applied Analysis, 12(5), 2069-2082. doi:10.3934/cpaa.2013.12.2069Barrachina, X., & Conejero, J. A. (2012). Devaney Chaos and Distributional Chaos in the Solution of Certain Partial Differential Equations. Abstract and Applied Analysis, 2012, 1-11. doi:10.1155/2012/457019Barrachina, X., & Peris, A. (2012). Distributionally chaotic translation semigroups. Journal of Difference Equations and Applications, 18(4), 751-761. doi:10.1080/10236198.2011.625945Bayart, F., & Grivaux, S. (2006). Frequently hypercyclic operators. Transactions of the American Mathematical Society, 358(11), 5083-5117. doi:10.1090/s0002-9947-06-04019-0BAYART, F., & RUZSA, I. Z. (2013). Difference sets and frequently hypercyclic weighted shifts. Ergodic Theory and Dynamical Systems, 35(3), 691-709. doi:10.1017/etds.2013.77Bermúdez, T., Bonilla, A., Martínez-Giménez, F., & Peris, A. (2011). Li–Yorke and distributionally chaotic operators. Journal of Mathematical Analysis and Applications, 373(1), 83-93. doi:10.1016/j.jmaa.2010.06.011Bernal-González, L., & Bonilla, A. (2016). Order of growth of distributionally irregular entire functions for the differentiation operator. Complex Variables and Elliptic Equations, 61(8), 1176-1186. doi:10.1080/17476933.2016.1149820Bernardes, N. C., Bonilla, A., Müller, V., & Peris, A. (2013). Distributional chaos for linear operators. Journal of Functional Analysis, 265(9), 2143-2163. doi:10.1016/j.jfa.2013.06.019BERNARDES, N. C., BONILLA, A., MÜLLER, V., & PERIS, A. (2014). Li–Yorke chaos in linear dynamics. Ergodic Theory and Dynamical Systems, 35(6), 1723-1745. doi:10.1017/etds.2014.20Bernardes, N. C., Peris, A., & Rodenas, F. (2017). Set-Valued Chaos in Linear Dynamics. Integral Equations and Operator Theory, 88(4), 451-463. doi:10.1007/s00020-017-2394-6Bernardes, N. C., Bonilla, A., Peris, A., & Wu, X. (2018). Distributional chaos for operators on Banach spaces. Journal of Mathematical Analysis and Applications, 459(2), 797-821. doi:10.1016/j.jmaa.2017.11.005Bès, J., Menet, Q., Peris, A., & Puig, Y. (2015). Recurrence properties of hypercyclic operators. Mathematische Annalen, 366(1-2), 545-572. doi:10.1007/s00208-015-1336-3Conejero, J. A., Müller, V., & Peris, A. (2007). Hypercyclic behaviour of operators in a hypercyclic C0-semigroup. Journal of Functional Analysis, 244(1), 342-348. doi:10.1016/j.jfa.2006.12.008Alberto Conejero, J., Rodenas, F., & Trujillo, M. (2015). Chaos for the Hyperbolic Bioheat Equation. Discrete & Continuous Dynamical Systems - A, 35(2), 653-668. doi:10.3934/dcds.2015.35.653Downarowicz, T. (2013). Positive topological entropy implies chaos DC2. Proceedings of the American Mathematical Society, 142(1), 137-149. doi:10.1090/s0002-9939-2013-11717-xFeldman, N. S. (2002). Hypercyclicity and supercyclicity for invertible bilateral weighted shifts. Proceedings of the American Mathematical Society, 131(2), 479-485. doi:10.1090/s0002-9939-02-06537-1Foryś-Krawiec, M., Oprocha, P., & Štefánková, M. (2017). Distributionally chaotic systems of type 2 and rigidity. Journal of Mathematical Analysis and Applications, 452(1), 659-672. doi:10.1016/j.jmaa.2017.02.056Garcia-Ramos, F., & Jin, L. (2016). Mean proximality and mean Li-Yorke chaos. Proceedings of the American Mathematical Society, 145(7), 2959-2969. doi:10.1090/proc/13440Grivaux, S., & Matheron, É. (2014). Invariant measures for frequently hypercyclic operators. Advances in Mathematics, 265, 371-427. doi:10.1016/j.aim.2014.08.002Hou, B., Cui, P., & Cao, Y. (2009). Chaos for Cowen-Douglas operators. Proceedings of the American Mathematical Society, 138(3), 929-936. doi:10.1090/s0002-9939-09-10046-1Huang, W., Li, J., & Ye, X. (2014). Stable sets and mean Li–Yorke chaos in positive entropy systems. Journal of Functional Analysis, 266(6), 3377-3394. doi:10.1016/j.jfa.2014.01.005León-Saavedra, F. (2002). Operators with hypercyclic Cesaro means. Studia Mathematica, 152(3), 201-215. doi:10.4064/sm152-3-1LI, J., TU, S., & YE, X. (2014). Mean equicontinuity and mean sensitivity. Ergodic Theory and Dynamical Systems, 35(8), 2587-2612. doi:10.1017/etds.2014.41Martínez-Giménez, F., Oprocha, P., & Peris, A. (2009). Distributional chaos for backward shifts. Journal of Mathematical Analysis and Applications, 351(2), 607-615. doi:10.1016/j.jmaa.2008.10.049Martínez-Giménez, F., Oprocha, P., & Peris, A. (2012). Distributional chaos for operators with full scrambled sets. Mathematische Zeitschrift, 274(1-2), 603-612. doi:10.1007/s00209-012-1087-8Menet, Q. (2017). Linear chaos and frequent hypercyclicity. Transactions of the American Mathematical Society, 369(7), 4977-4994. doi:10.1090/tran/6808Müller, V., & Vrs˘ovský, J. (2009). Orbits of Linear Operators Tending to Infinity. Rocky Mountain Journal of Mathematics, 39(1). doi:10.1216/rmj-2009-39-1-219Wu, X. (2013). Li–Yorke chaos of translation semigroups. Journal of Difference Equations and Applications, 20(1), 49-57. doi:10.1080/10236198.2013.809712Wu, X., Oprocha, P., & Chen, G. (2016). On various definitions of shadowing with average error in tracing. Nonlinearity, 29(7), 1942-1972. doi:10.1088/0951-7715/29/7/1942Wu, X., Wang, L., & Chen, G. (2017). Weighted backward shift operators with invariant distributionally scrambled subsets. Annals of Functional Analysis, 8(2), 199-210. doi:10.1215/20088752-3802705Yin, Z., & Yang, Q. (2017). Distributionally n-Scrambled Set for Weighted Shift Operators. Journal of Dynamical and Control Systems, 23(4), 693-708. doi:10.1007/s10883-017-9359-6Yin, Z., & Yang, Q. (2017). Distributionally n-chaotic dynamics for linear operators. Revista Matemática Complutense, 31(1), 111-129. doi:10.1007/s13163-017-0226-

Direct Percutaneous Endoscopic Jejunostomy Using Single-Balloon Enteroscopy without Fluoroscopy: a Case Series

BACKGROUND: Direct percutaneous endoscopic jejunostomy (DPEJ) is a useful method to provide enteral nutrition to individuals when gastric feeding is not possible or contraindicated. The aim of this study was to analyze the efficacy and safety of DPEJ tube placement with the Gauderer-Ponsky technique by the pull method, using single-balloon enteroscopy (SBE) without fluoroscopy. METHODS: This is a retrospective analysis of patients undergoing SBE for DPEJ placement in a referral hospital between January 2010 and March 2016. Technical success, clinical success and procedure related complications were recorded. RESULTS: Twenty-three patients were included (17 males, median age 71 years, range 37-93 years). The most frequent indications for DPEJ were gastroesophageal cancer (n = 10) and neurological disease (n = 8). Eighty-seven percent of the patients had a contraindication to percutaneous endoscopic gastrostomy (PEG) and PEG was unsuccessful in the remaining patients. The technical success rate was 83% (19/23), transillumination was not possible in three patients and an accidental exteriorization of the bumper resulting in a jejunal perforation occurred in one patient. The clinical success was 100% (19/19). The median follow-up was five months (range 1-35 months). Apart from the case of jejunal perforation and the two cases of accidental exteriorization, there were no other complications during follow-up. The 6-month survival was 65.8% and the 1-year survival was 49.3%. CONCLUSION: DPEJ can be carried out successfully via SBE without fluoroscopy with a low rate of significant adverse events. Although, leaving the overtube in place during the bumper pulling can be useful for distal jejunal loops, it can be safely removed in proximal loops to minimize complications.info:eu-repo/semantics/publishedVersio

Cholesterol affects African swine fever virus infection

African swine fever virus (ASFV) enters cells by receptor mediated endocytosis and requires a fusion event between the viral envelope and the limiting membrane of the endosome at low pH. In order to investigate the role of cholesterol in the early stages of ASFV infection, we have studied the effect of the removal of cell and viral membrane cholesterol by cholesterol oxidase treatment of cells and virions, as well as the effect of some inhibitors of cholesterol synthesis on the infectious pathway. In addition, we have investigated viral infection in cholesterol-depleted Vero cells. Both cholesterol-depleted and cholesterol oxidase-treated Vero cells were unaltered in their ability to bind or internalize the virus, but were blocked in ASFV fusion and subsequent virus replication. Our results indicate that ASFV infection is affected by cholesterol in the target membrane.http://www.sciencedirect.com/science/article/B6T1X-3V3N06F-2/1/e52e3430df628f470dc4b0b8400b4b2

Obtenção de Imagens de Algas por Microscopia de Força Atômica.

bitstream/CNPDIA/10457/1/CT63_2004.pd

Direct Percutaneous Endoscopic Jejunostomy Using Single-Balloon Enteroscopy without Fluoroscopy: a Case Series

BACKGROUND: Direct percutaneous endoscopic jejunostomy (DPEJ) is a useful method to provide enteral nutrition to individuals when gastric feeding is not possible or contraindicated. The aim of this study was to analyze the efficacy and safety of DPEJ tube placement with the Gauderer-Ponsky technique by the pull method, using single-balloon enteroscopy (SBE) without fluoroscopy. METHODS: This is a retrospective analysis of patients undergoing SBE for DPEJ placement in a referral hospital between January 2010 and March 2016. Technical success, clinical success and procedure related complications were recorded. RESULTS: Twenty-three patients were included (17 males, median age 71 years, range 37-93 years). The most frequent indications for DPEJ were gastroesophageal cancer (n = 10) and neurological disease (n = 8). Eighty-seven percent of the patients had a contraindication to percutaneous endoscopic gastrostomy (PEG) and PEG was unsuccessful in the remaining patients. The technical success rate was 83% (19/23), transillumination was not possible in three patients and an accidental exteriorization of the bumper resulting in a jejunal perforation occurred in one patient. The clinical success was 100% (19/19). The median follow-up was five months (range 1-35 months). Apart from the case of jejunal perforation and the two cases of accidental exteriorization, there were no other complications during follow-up. The 6-month survival was 65.8% and the 1-year survival was 49.3%. CONCLUSION: DPEJ can be carried out successfully via SBE without fluoroscopy with a low rate of significant adverse events. Although, leaving the overtube in place during the bumper pulling can be useful for distal jejunal loops, it can be safely removed in proximal loops to minimize complications.info:eu-repo/semantics/publishedVersio