Hilbert number for a family of piecewise nonautonomous equations

For family $x'=(a_0+a_1\cos t+a_2 \sin t)|x|+b_0+b_1 \cos t+b_2 \sin t$, we solve three basic problems related with its dynamics. First, we characterize when it has a center (Poincar\'e center focus problem). Second, we show that each equation has a finite number of limit cycles (finiteness problem), and finally we give a uniform upper bound for the number of limit cycles (Hilbert's 16th problem).Comment: 16 pages, no figure

Resonant transmission of light through finite chains of subwavelength holes

In this paper we show that the extraordinary optical transmission phenomenon found before in 2D hole arrays is already present in a linear chain of subwavelength holes, which can be considered as the basic geometrical unit showing this property. In order to study this problem we have developed a new theoretical framework, able to analyze the optical properties of finite collections of subwavelength apertures and/or dimples (of any shape and placed in arbitrary positions) drilled in a metallic film.Comment: Accepted for publication in Phys. Rev. Let

Dispersal by cattle of salt-marsh and dune species into salt-marsh and dune communities

Seed dispersal via ingestion and defecation by large herbivores (endozoochory) plays a potentially important role in structuring plant communities. In the present study we tested whether cattle disperse seeds between different plant communities in a heterogeneous coastal habitat. We surveyed the seed contents of cattle dung collected from two habitat types within a grazing system, one in dunes and the other in salt-marsh. The dunes are characterized by sandy soil, and infrequent inundation by the sea, whereas the salt-marsh features clay deposited during inundations. Seeds of both salt-marsh and dune species were dispersed into salt-marsh and dune habitats. The seed content of cattle dung collected in salt-marsh and dunes was similar with respect to species composition and seed density. However, dispersal of dune species into salt-marsh and vice-versa did not result in establishment in those communities. Seed traits per se did not differ between dune species and salt-marsh species. Species abundance in the established vegetation and seed density in dung were positively correlated. Seed abundance for most species found in dung was consistent with the availability of viable seeds during the growing season. Seed mass, seed 'roundness' and seed release height were all negatively correlated with seed numbers in dung. An indirect factor, namely, forage quality of the plant, and hence attractiveness for herbivores, could explain the higher likelihood of seed dispersal of salt-marsh species than of dune species. The salt-marsh harbours species with higher forage quality than the dune species, as derived from Ellenberg nitrogen indicator values

Systematically Asymmetric Heliospheric Magnetic Field: Evidence for a Quadrupole Mode and Non-axisymmetry with Polarity Flip-flops

Recent studies of the heliospheric magnetic field (HMF) have detected interesting, systematic hemispherical and longitudinal asymmetries which have a profound significance for the understanding of solar magnetic fields. The in situ HMF measurements since 1960s show that the heliospheric current sheet (HCS) is systematically shifted (coned) southward during solar minimum times, leading to the concept of a bashful ballerina. While temporary shifts can be considerably larger, the average HCS shift (coning) angle is a few degrees, less than the $7.2^{\circ}$ tilt of the solar rotation axis. Recent solar observations during the last two solar cycles verify these results and show that the magnetic areas in the northern solar hemisphere are larger and their intensity weaker than in the south during long intervals in the late declining to minimum phase. The multipole expansion reveals a strong quadrupole term which is oppositely directed to the dipole term. These results imply that the Sun has a symmetric quadrupole S0 dynamo mode that oscillates in phase with the dominant dipole A0 mode. Moreover, the heliospheric magnetic field has a strong tendency to produce solar tilts that are roughly opposite in longitudinal phase. This implies is a systematic longitudinal asymmetry and leads to a "flip-flop" type behaviour in the dominant HMF sector whose period is about 3.2 years. This agrees very well with the similar flip-flop period found recently in sunspots, as well as with the observed ratio of three between the activity cycle period and the flip-flop period of sun-like stars. Accordingly, these results require that the solar dynamo includes three modes, A0, S0 and a non-axisymmetric mode. Obviously, these results have a great impact on solar modelling.Comment: 13 pages, 4 figures, Solar Physics, Topical Issue of Space Climate Symposium, in pres

Comparison of Metaheuristic Optimization Algorithms for Electromechanical Actuator Fault Detection

Model-based Fault Detection and Identification (FDI) for prognostics rely on the comparison between the response of the monitored system and that of a digital twin. Discrepancies among the behavior of the two systems are analyzed to filter out the effect of uncertainties of the model and identify failure precursors. A possible solution to identify faults is to leverage a model able to simulate faults: an optimization algorithm varies the faults magnitude parameters within the model to achieve the matching between the responses of the model and the actual system. When the algorithm converges, we can assume that the fault parameters that produce the best match between the system and its digital twin approximate the actual faults affecting the equipment. The choice of an optimization algorithm appropriate for the task is highly problem dependent. Algorithms for FDI are required to deal with multimodal objective functions characterized by poor regularity and a relatively high computational cost. Additionally, the derivatives of the objective function are not usually available and must be obtained numerically if needed. Then, we restrict our search for a suitable optimization algorithm to metaheuristic gradient-free ones, testing Genetic Algorithm, Particle Swarm Optimization, Differential Evolution, Grey Wolf Optimization, Dragonfly Algorithm, and Whale Optimization Algorithm. Their performances on the considered problem were assessed and compared, in terms of accuracy and computational time

Effect of tiotropium on health-related quality of life as a primary efficacy endpoint in COPD

Clinical manifestations of chronic obstructive pulmonary disease (COPD), including airflow limitation, dyspnea, and activity limitation, ultimately lead to impaired health-related quality of life (HRQoL). This 9-month, randomized, double-blind, multicenter study compared the effect of once-daily tiotropium 18 μg and placebo on HRQoL, spirometric parameters, and exacerbations in 554 patients with moderate-to-severe COPD. HRQoL was assessed using the St. George’s Respiratory Questionnaire (SGRQ) and the new 8-item Visual Simplified Respiratory Questionnaire (VSRQ), which is currently being validated. The primary efficacy endpoint was the proportion of patients achieving a reduction of at least 4 units in the SGRQ total score at study end (Month 9). Mean ± SD baseline SGRQ total score was 47.4 ± 18.1. Significantly more tiotropium-treated patients achieved a reduction of at least 4 units in the SGRQ score vs placebo at study end (59.1% vs 48.2%, respectively; p = 0.029). Tiotropium significantly improved spirometric parameters (forced expiratory volume in 1 second [FEV1]: 0.11 ± 0.02 L vs 0.01 ± 0.02 L; between-group difference: 0.10 ± 0.03 L, p = 0.0001) and reduced exacerbations vs placebo. Maintenance treatment with tiotropium provided significant and clinically relevant improvements in HRQoL, as measured by the SGRQ

Fluoxetine: a case history of its discovery and preclinical development

Introduction: Depression is a multifactorial mood disorder with a high prevalence worldwide. Until now, treatments for depression have focused on the inhibition of monoaminergic reuptake sites, which augment the bioavailability of monoamines in the CNS. Advances in drug discovery have widened the therapeutic options with the synthesis of so-called selective serotonin reuptake inhibitors (SSRIs), such as fluoxetine. Areas covered: The aim of this case history is to describe and discuss the pharmacokinetic and pharmacodynamic profiles of fluoxetine, including its acute effects and the adaptive changes induced after long-term treatment. Furthermore, the authors review the effect of fluoxetine on neuroplasticity and adult neurogenesis. In addition, the article summarises the preclinical behavioural data available on fluoxetine’s effects on depressive-like behaviour, anxiety and cognition as well as its effects on other diseases. Finally, the article describes the seminal studies validating the antidepressant effects of fluoxetine. Expert opinion: Fluoxetine is the first selective SSRI that has a recognised clinical efficacy and safety profile. Since its discovery, other molecules that mimic its mechanism of action have been developed, commencing a new age in the treatment of depression. Fluoxetine has also demonstrated utility in the treatment of other disorders for which its prescription has now been approved