Recurrence properties of hypercyclic operators

[EN] We generalize the notions of hypercyclic operators, U-frequently hypercyclic operators and frequently hypercyclic operators by introducing a new concept in linear dynamics, namely A-hypercyclicity. We then state an A-hypercyclicity criterion, inspired by the hypercyclicity criterion and the frequent hypercyclicity criterion, and we show that this criterion characterizes the A-hypercyclicity for weighted shifts. We also investigate which density properties can the sets N(x, U) = {n is an element of N; T-n x is an element of U} have for a given hypercyclic operator, and we study the new notion of reiteratively hypercyclic operators.This work is supported in part by MEC and FEDER, Project MTM2013-47093-P, and by GVA, Projects PROMETEOII/2013/013 and ACOMP/2015/005. The second author was a postdoctoral researcher of the Belgian FNRS.Bès, JP.; Menet, Q.; Peris Manguillot, A.; Puig-De Dios, Y. (2016). Recurrence properties of hypercyclic operators. Mathematische Annalen. 366(1):545-572. https://doi.org/10.1007/s00208-015-1336-3S5455723661Badea, C., Grivaux, S.: Unimodular eigenvalues, uniformly distributed sequences and linear dynamics. Adv. Math. 211, 766–793 (2007)Bayart, F., Grivaux, S.: Frequently hypercyclic operators. Trans. Amer. Math. Soc. 358, 5083–5117 (2006)Bayart, F., Grivaux, S.: Invariant Gaussian measures for operators on Banach spaces and linear dynamics. Proc. Lond. Math. Soc. 94, 181–210 (2007)Bayart, F., Matheron, É.: Dynamics of linear operators, Cambridge Tracts in Mathematics, 179. Cambridge University Press, Cambridge (2009)Bayart, F., Matheron, É.: (Non-)weakly mixing operators and hypercyclicity sets. Ann. Inst. Fourier 59, 1–35 (2009)Bayart, F., Ruzsa, I.: Difference sets and frequently hypercyclic weighted shifts. Ergodic Theory Dynam. Syst. 35, 691–709 (2015)Bergelson, V.: Ergodic Ramsey Theory- an update, Ergodic Theory of $$\mathbb{Z}^d$$ Z d -actions. Lond. Math. Soc. Lecture Note Ser. 28, 1–61 (1996)Bernal-González, L., Grosse-Erdmann, K.-G.: The Hypercyclicity Criterion for sequences of operators. Studia Math. 157, 17–32 (2003)Bès, J., Peris, A.: Hereditarily hypercyclic operators. J. Funct. Anal. 167, 94–112 (1999)Bonilla, A., Grosse-Erdmann, K.-G.: Frequently hypercyclic operators and vectors. Ergodic Theory Dynam. Syst. 27, 383–404 (2007)Bonilla, A., Grosse-Erdmann, K.-G.: Erratum: Ergodic Theory Dynam. Systems 29, 1993–1994 (2009)Chan, K., Seceleanu, I.: Hypercyclicity of shifts as a zero-one law of orbital limit points. J. Oper. Theory 67, 257–277 (2012)Costakis, G., Sambarino, M.: Topologically mixing hypercyclic operators. Proc. Amer. Math. Soc. 132, 385–389 (2004)Furstenberg, H.: Recurrence in ergodic theory and combinatorial number theory. Princeton University Press, Princeton (1981)Giuliano, R., Grekos, G., Mišík, L.: Open problems on densities II, Diophantine Analysis and Related Fields 2010. AIP Conf. Proc. 1264, 114–128 (2010)Grosse-Erdmann, K.-G.: Hypercyclic and chaotic weighted shifts. Studia Math. 139, 47–68 (2000)Grosse-Erdmann, K.-G., Peris, A.: Frequently dense orbits. C. R. Math. Acad. Sci. Paris 341, 123–128 (2005)Grosse-Erdmann, K.G., Peris, A.: Weakly mixing operators on topological vector spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, 104, 413–426 (2010)Grosse-Erdmann, K.G., Peris Manguillot, A.: Linear chaos, Universitext. Springer, London (2011)Menet, Q.: Linear chaos and frequent hypercyclicity. Trans. Amer. Math. Soc. arXiv:1410.7173Puig, Y.: Linear dynamics and recurrence properties defined via essential idempotents of $$\beta {\mathbb{N}}$$ β N (2014) arXiv:1411.7729 (preprint)Salas, H.N.: Hypercyclic weighted shifts. Trans. Amer. Math. Soc. 347, 993–1004 (1995)Salat, T., Toma, V.: A classical Olivier’s theorem and statistical convergence. Ann. Math. Blaise Pascal 10, 305–313 (2003)Shkarin, S.: On the spectrum of frequently hypercyclic operators. Proc. Am. Math. Soc. 137, 123–134 (2009

Concurrent sampling of transitional and coastal waters by Diffusive Gradient in Thin-films (DGT) and spot sampling for trace metals analysis

This protocol was developed based on the knowledge acquired in the framework of the Interreg MONITOOL project (EAPA_565/2016) where extensive sampling campaigns were performed in transitional and coastal waters covering eight European countries. It provides detailed procedures and guidelines for the sampling of these waterbodies by concurrent collection of discrete water samples and the deployment of Diffusive Gradient in Thin-films (DGT) passive samplers for the measurement of trace metal concentrations. In order to facilitate the application of this protocol by end-users, it presents steps to follow in the laboratory prior to sampling campaigns, explains the procedures for field campaigns (including in situ measurement of supporting parameters) and subsequent sample processing in the laboratory in preparation for trace metal analyze by inductively coupled plasma-mass spectrometry (ICP-MS) and voltammetry. The protocol provides a systematic, coherent field sampling and sample preparation strategy that was developed in order to ensure comparability and reproducibility of the data obtained from each project Partner in different regions. • Standardization of the concurrent sampling of transitional and coastal waters by DGT passive samplers and spot sampling. • Robust procedures and tips based on existing international standards and comprehensive practical experience. • Links to demonstration videos produced within the MONITOOL project

Assessing variability in the ratio of metal concentrations measured by DGT-type passive samplers and spot sampling in European seawaters

The current study evaluates the effect of seawater physico-chemical characteristics on the relationship between the concentration of metals measured by Diffusive Gradients in Thin films (DGT) passive samplers (i.e., DGT-labile concentration) and the concentrations measured in discrete water samples. Accordingly, Inductively Coupled Plasma Mass Spectrometry (ICP-MS) was used to measure the total dissolved metal concentrations in the discrete water samples and the labile metal concentrations obtained by DGT samplers; additionally, lead and cadmium conditional labile fractions were determined by Anodic Stripping Voltammetry (ASV) and total dissolved nickel was measured by Cathodic Stripping Voltammetry (CSV). It can be concluded that, in general, the median ratios of DGT/ICP and DGT/ASV(CSV) were lower than 1, except for Ni (median ratio close to 1) and Zn (higher than 1). This indicates the importance of speciation and time-integrated concentrations measured using passive sampling techniques, which is in line with the WFD suggestions for improving the chemical assessment of waterbodies. It is the variability in metal content in waters rather than environmental conditions to which the variability of the ratios can be attributed. The ratios were not significantly affected by the temperature, salinity, pH, oxygen, DOC or SPM, giving a great confidence for all the techniques used. Within a regulatory context such as the EU Water Framework Directive this is a great advantage, since the simplicity of not needing to use corrections to minimize the effects of environmental variables could help in implementing DGTs within monitoring networks

Adult Circadian Behavior in Drosophila Requires Developmental Expression of cycle, But Not period

Circadian clocks have evolved as internal time keeping mechanisms that allow anticipation of daily environmental changes and organization of a daily program of physiological and behavioral rhythms. To better examine the mechanisms underlying circadian clocks in animals and to ask whether clock gene expression and function during development affected subsequent daily time keeping in the adult, we used the genetic tools available in Drosophila to conditionally manipulate the function of the CYCLE component of the positive regulator CLOCK/CYCLE (CLK/CYC) or its negative feedback inhibitor PERIOD (PER). Differential manipulation of clock function during development and in adulthood indicated that there is no developmental requirement for either a running clock mechanism or expression of per. However, conditional suppression of CLK/CYC activity either via per over-expression or cyc depletion during metamorphosis resulted in persistent arrhythmic behavior in the adult. Two distinct mechanisms were identified that may contribute to this developmental function of CLK/CYC and both involve the ventral lateral clock neurons (LNvs) that are crucial to circadian control of locomotor behavior: (1) selective depletion of cyc expression in the LNvs resulted in abnormal peptidergic small-LNv dorsal projections, and (2) PER expression rhythms in the adult LNvs appeared to be affected by developmental inhibition of CLK/CYC activity. Given the conservation of clock genes and circuits among animals, this study provides a rationale for investigating a possible similar developmental role of the homologous mammalian CLOCK/BMAL1 complex

CRTC Potentiates Light-independent timeless Transcription to Sustain Circadian Rhythms in Drosophila

Light is one of the strongest environmental time cues for entraining endogenous circadian rhythms. Emerging evidence indicates that CREB-regulated transcription co-activator 1 (CRTC1) is a key player in this pathway, stimulating light-induced Period1 (Per1) transcription in mammalian clocks. Here, we demonstrate a light-independent role of Drosophila CRTC in sustaining circadian behaviors. Genomic deletion of the crtc locus causes long but poor locomotor rhythms in constant darkness. Overexpression or RNA interference-mediated depletion of CRTC in circadian pacemaker neurons similarly impairs the free-running behavioral rhythms, implying that Drosophila clocks are sensitive to the dosage of CRTC. The crtc null mutation delays the overall phase of circadian gene expression yet it remarkably dampens light-independent oscillations of TIMELESS (TIM) proteins in the clock neurons. In fact, CRTC overexpression enhances CLOCK/CYCLE (CLK/CYC)-activated transcription from tim but not per promoter in clock-less S2 cells whereas CRTC depletion suppresses it. Consistently, TIM overexpression partially but significantly rescues the behavioral rhythms in crtc mutants. Taken together, our data suggest that CRTC is a novel co-activator for the CLK/CYC-activated tim transcription to coordinate molecular rhythms with circadian behaviors over a 24-hour time-scale. We thus propose that CRTC-dependent clock mechanisms have co-evolved with selective clock genes among different species.ope

Adult Circadian Behavior in Drosophila Requires Developmental Expression of cycle, But Not period

Circadian clocks have evolved as internal time keeping mechanisms that allow anticipation of daily environmental changes and organization of a daily program of physiological and behavioral rhythms. To better examine the mechanisms underlying circadian clocks in animals and to ask whether clock gene expression and function during development affected subsequent daily time keeping in the adult, we used the genetic tools available in Drosophila to conditionally manipulate the function of the CYCLE component of the positive regulator CLOCK/CYCLE (CLK/CYC) or its negative feedback inhibitor PERIOD (PER). Differential manipulation of clock function during development and in adulthood indicated that there is no developmental requirement for either a running clock mechanism or expression of per. However, conditional suppression of CLK/CYC activity either via per over-expression or cyc depletion during metamorphosis resulted in persistent arrhythmic behavior in the adult. Two distinct mechanisms were identified that may contribute to this developmental function of CLK/CYC and both involve the ventral lateral clock neurons (LNvs) that are crucial to circadian control of locomotor behavior: (1) selective depletion of cyc expression in the LNvs resulted in abnormal peptidergic small-LNv dorsal projections, and (2) PER expression rhythms in the adult LNvs appeared to be affected by developmental inhibition of CLK/CYC activity. Given the conservation of clock genes and circuits among animals, this study provides a rationale for investigating a possible similar developmental role of the homologous mammalian CLOCK/BMAL1 complex

Distributionally chaotic families of operators on Fréchet spaces

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Communications on Pure and Applied Analysis (CPAA) following peer review. The definitive publisher-authenticated version Conejero, J. A., Kostić, M., Miana, P. J., & Murillo-Arcila, M. (2016). Distributionally chaotic families of operators on Fréchet spaces.Communications on Pure and Applied Analysis, 2016, vol. 15, no 5, p. 1915-1939, is available online at: http://dx.doi.org/10.3934/cpaa.2016022The existence of distributional chaos and distributional irregular vectors has been recently considered in the study of linear dynamics of operators and C-0-semigroups. In this paper we extend some previous results on both notions to sequences of operators, C-0-semigroups, C-regularized semigroups, and alpha-timesintegrated semigroups on Frechet spaces. We also add a study of rescaled distributionally chaotic C-0-semigroups. Some examples are provided to illustrate all these results.The first and fourth authors are supported in part by MEC Project MTM2010-14909, MTM2013-47093-P, and Programa de Investigacion y Desarrollo de la UPV, Ref. SP20120700. The second author is partially supported by grant 174024 of Ministry of Science and Technological Development, Republic of Serbia. The third author has been partially supported by Project MTM2013-42105-P, DGI-FEDER, of the MCYTS; Project E-64, D.G. Aragon, and Project UZCUD2014-CIE-09, Universidad de Zaragoza. The fourth author is supported by a grant of the FPU Program of Ministry of education of Spain.Conejero, JA.; Kostic, M.; Miana Sanz, PJ.; Murillo Arcila, M. (2016). Distributionally chaotic families of operators on Fréchet spaces. Communications on Pure and Applied Analysis. 15(5):1915-1939. https://doi.org/10.3934/cpaa.2016022S1915193915

Predictions of total and total reaction cross sections for nucleon-nucleus scattering up to 300 MeV

Total reaction cross sections are predicted for nucleons scattering from various nuclei. Projectile energies to 300 MeV are considered. So also are mass variations of those cross sections at selected energies. All predictions have been obtained from coordinate space optical potentials formed by full folding effective two-nucleon (NN) interactions with one body density matrix elements (OBDME) of the nuclear ground states. Good comparisons with data result when effective NN interactions defined by medium modification of free NN t matrices are used. Coupled with analyses of differential cross sections, these results are sensitive to details of the model ground states used to describe nuclei

CNF1 Improves Astrocytic Ability to Support Neuronal Growth and Differentiation In vitro

Modulation of cerebral Rho GTPases activity in mice brain by intracerebral administration of Cytotoxic Necrotizing Factor 1 (CNF1) leads to enhanced neurotransmission and synaptic plasticity and improves learning and memory. To gain more insight into the interactions between CNF1 and neuronal cells, we used primary neuronal and astrocytic cultures from rat embryonic brain to study CNF1 effects on neuronal differentiation, focusing on dendritic tree growth and synapse formation, which are strictly modulated by Rho GTPases. CNF1 profoundly remodeled the cytoskeleton of hippocampal and cortical neurons, which showed philopodia-like, actin-positive projections, thickened and poorly branched dendrites, and a decrease in synapse number. CNF1 removal, however, restored dendritic tree development and synapse formation, suggesting that the toxin can reversibly block neuronal differentiation. On differentiated neurons, CNF1 had a similar effacing effect on synapses. Therefore, a direct interaction with CNF1 is apparently deleterious for neurons. Since astrocytes play a pivotal role in neuronal differentiation and synaptic regulation, we wondered if the beneficial in vivo effect could be mediated by astrocytes. Primary astrocytes from embryonic cortex were treated with CNF1 for 48 hours and used as a substrate for growing hippocampal neurons. Such neurons showed an increased development of neurites, in respect to age-matched controls, with a wider dendritic tree and a richer content in synapses. In CNF1-exposed astrocytes, the production of interleukin 1β, known to reduce dendrite development and complexity in neuronal cultures, was decreased. These results demonstrate that astrocytes, under the influence of CNF1, increase their supporting activity on neuronal growth and differentiation, possibly related to the diminished levels of interleukin 1β. These observations suggest that the enhanced synaptic plasticity and improved learning and memory described in CNF1-injected mice are probably mediated by astrocytes

Genome-Wide and Phase-Specific DNA-Binding Rhythms of BMAL1 Control Circadian Output Functions in Mouse Liver

Temporal mapping during a circadian day of binding sites for the BMAL1 transcription factor in mouse liver reveals genome-wide daily rhythms in DNA binding and uncovers output functions that are controlled by the circadian oscillator