Choreographic Three Bodies on the Lemniscate

We show that choreographic three bodies {x(t), x(t+T/3), x(t-T/3)} of period T on the lemniscate, x(t) = (x-hat+y-hat cn(t))sn(t)/(1+cn^2(t)) parameterized by the Jacobi's elliptic functions sn and cn with modulus k^2 = (2+sqrt{3})/4, conserve the center of mass and the angular momentum, where x-hat and y-hat are the orthogonal unit vectors defining the plane of the motion. They also conserve the moment of inertia, the kinetic energy, the sum of square of the curvature, the product of distance and the sum of square of distance between bodies. We find that they satisfy the equation of motion under the potential energy sum_{i<j}(1/2 ln r_{ij} -sqrt{3}/24 r_{ij}^2) or sum_{i<j}1/2 ln r_{ij} -sum_{i}sqrt{3}/8 r_{i}^2, where r_{ij} the distance between the body i and j, and r_{i} the distance from the origin. The first term of the potential energies is the Newton's gravity in two dimensions but the second term is the mutual repulsive force or a repulsive force from the origin, respectively. Then, geometric construction methods for the positions of the choreographic three bodies are given

Generic Twistless Bifurcations

We show that in the neighborhood of the tripling bifurcation of a periodic orbit of a Hamiltonian flow or of a fixed point of an area preserving map, there is generically a bifurcation that creates a ``twistless'' torus. At this bifurcation, the twist, which is the derivative of the rotation number with respect to the action, vanishes. The twistless torus moves outward after it is created, and eventually collides with the saddle-center bifurcation that creates the period three orbits. The existence of the twistless bifurcation is responsible for the breakdown of the nondegeneracy condition required in the proof of the KAM theorem for flows or the Moser twist theorem for maps. When the twistless torus has a rational rotation number, there are typically reconnection bifurcations of periodic orbits with that rotation number.Comment: 29 pages, 9 figure

Measuring the mixing efficiency in a simple model of stirring:some analytical results and a quantitative study via Frequency Map Analysis

We prove the existence of invariant curves for a $T$--periodic Hamiltonian system which models a fluid stirring in a cylindrical tank, when $T$ is small and the assigned stirring protocol is piecewise constant. Furthermore, using the Numerical Analysis of the Fundamental Frequency of Laskar, we investigate numerically the break down of invariant curves as $T$ increases and we give a quantitative estimate of the efficiency of the mixing.Comment: 10 figure

Proteomic analysis of early diabetic retinopathy reveals mediators of neurodegenerative brain diseases

© 2018 The Authors. PURPOSE. Current evidence suggests that retinal neurodegeneration is an early event in the pathogenesis of diabetic retinopathy. Our main goal was to examine whether, in the diabetic human retina, common proteins and pathways are shared with brain neurodegenerative diseases. METHODS. A proteomic analysis was performed on three groups of postmortem retinas matched by age: nondiabetic control retinas (n = 5), diabetic retinas without glial activation (n = 5), and diabetic retinas with glial activation (n = 5). Retinal lysates from each group were pooled and run on an SDS-PAGE gel. Bands were analyzed sequentially by liquid chromatography-mass spectrometry (LC/MS) using an Orbitrap Mass Spectrometer. RESULTS. A total of 2190 proteins were identified across all groups. To evaluate the association of the identified proteins with neurological signaling, significant signaling pathways belonging to the category ‘‘Neurotransmitters and Other Nervous System Signaling” were selected for analysis. Pathway analysis revealed that ‘‘Neuroprotective Role of THOP1 in Alzheimer’s Disease” and ‘‘Unfolded Protein Response” pathways were uniquely enriched in control retinas. By contrast, ‘‘Dopamine Degradation” and ‘‘Parkinson’s Signaling” were enriched only in diabetic retinas with glial activation. The ‘‘Neuregulin Signaling,” “Synaptic Long Term Potentiation,” and “Amyloid Processing” pathways were enriched in diabetic retinas with no glial activation. CONCLUSIONS. Diabetes-induced retinal neurodegeneration and brain neurodegenerative diseases, such as Alzheimer’s and Parkinson’s diseases, share common pathogenic pathways. These findings suggest that the study of neurodegeneration in the diabetic retina could be useful to further understand the neurodegenerative processes that occur in the brain of persons with diabetes

El gasto sanitario en España en comparación con el de la Europa desarrollada, 1985–2001. La atención primaria española, Cenicienta europea

ObjetivoDescribir la evolución de la distribución de fondos en nuestro sistema sanitario desde el inicio de la reforma de atención primaria hasta 2001, en comparación con la de los países europeos de la Organización para la Cooperación y el Desarrollo Económico (OCDE)DiseñoEstudio descriptivo longitudinal y retrospectivoEmplazamientoPaíses de la OCDEParticipantesPaíses europeos de la OCDEMedicionesSe utilizan datos de la base Health Data 2003 (OCDE) referidos al período 1985–2001 respecto a variables de gasto sanitario por sectores y de renta. Se comparan los datos españoles con los del conjunto de los 22 países europeos de la OCDEResultadosEuropa aumentó el gasto ambulatorio público, tanto como porcentaje del gasto sanitario público como del producto interior bruto (PIB). España redujo el gasto ambulatorio público en ambos sentidos. Nuestro gasto hospitalario público recuperó gran parte del retraso respecto a Europa y desde 1995 se encuentra, como parte del PIB, en la media europea y, en términos per cápita, acorde con nuestra renta. Sin embargo, nuestro gasto ambulatorio público como parte del PIB es muy inferior al promedio europeo y, per capita, muy inferior a nuestra renta. Nuestro gasto ambulatorio privado es de los más altos de Europa y, en relación con ella, muy superior a nuestra renta, al contrario que su homónimo público. Nuestro gasto privado hospitalario es de los más bajos de Europa y, en relación con ella, muy inferior a nuestra rentaConclusionesRespecto a los recursos públicos comprometidos, la reforma de la atención primaria española no ha servido para aproximarla a Europa, tal y como sí lo ha hecho nuestro nivel hospitalario. La distancia entre España y Europa en el esfuerzo público ambulatorio es incluso mayor que la que había al inicio de la reformaObjetiveTo describe the evolution of the funds distribution in our health care system since the start of the primary care reform to 2001, in comparison with the European countries members of the Organisation for Economic Co-operation andDevelopment (OECD)DesignA longitudinal descriptive and retrospective studyParticipantsEuropean countries members of the OECDSettingCountries members of the OECDMethodsThe data come from the OECD database Health Data 2003. The data refer to period 1985–2001, and to a group of variables of health care expenditure by sectors and of income (Gross Domestic Product [GDP] per capita). We compare Spanish data series with those of the group of 22 European members countries of the OECDResultsEurope increased public expenditure on outpatient care both as a percentage of public health care expenditure and as a percentage of GDP. Spain reduced public expenditure on outpatient care in both senses. Spanish publicexpenditure on in-patient care reduced a great partof its difference with Europe so that since 1995 it isfound, as a percentage of GDP, in the Europeanaverage and, as per capita, it is according with theSpanish income. In contrast, public expenditure onout-patient care as a percentage of GDP in Spain isvery much lower than the European average and, asper capita, is very much lower than the Spanishincome. The Spanish private expenditure on outpatient is found among the highest in Europe and, compared with Europe, exceeds very much Spanish income, in contrast with his homonymous public. The Spanish private expenditure on in-patient care is found among the lowest in Europe and, compared with Europe, is very much lower than Spanish income levelConclusionsWith respect to public resources assigned, the reform of primary care in Spain has not been useful to approach Spanish primary health care level to Europe, in contrast with the Spanish hospital level. The difference between Spain and Europe in public expenditure on out-patient care as a percentage of GDP is, even, bigger than the one there was when the reform of Spanish primary care starte

uDDS: A Middleware for Real-time Wireless Embedded Systems

[EN] A Real-Time Wireless Distributed Embedded System (RTWDES) is formed by a large quantity of small devices with certain computing power, wireless communication and sensing/actuators capabilities. These types of networks have become popular as they have been developed for applications which can carry out a vast quantity of tasks, including home and building monitoring, object tracking, precision agriculture, military applications, disaster recovery, industry applications, among others. For this type of applications a middleware is used in software systems to bridge the gap between the application and the underlying operating system and networks. As a result, a middleware system can facilitate the development of applications and is designed to provide common services to the applications. The development of a middleware for sensor networks presents several challenges due to the limited computational resources and energy of the different nodes. This work is related with the design, implementation and test of a micro middleware for RTWDES; the proposal incorporates characteristics of a message oriented middleware thus allowing the applications to communicate by employing the publish/subscribe model. Experimental evaluation shows that the proposed middleware provides a stable and timely service to support different Quality of Service (QoS) levels. © 2011 Springer Science+Business Media B.V.This work was developed as a part of the D2ARS Project supported by CYTED. UNESCO code 120325;330417;120314;120305.González, A.; Mata, W.; Villaseñor, L.; Aquino, R.; Simó Ten, JE.; Chávez, M.; Crespo Lorente, A. (2011). uDDS: A Middleware for Real-time Wireless Embedded Systems. Journal of Intelligent and Robotic Systems. 64(3-4):489-503. https://doi.org/10.1007/s10846-011-9550-zS489503643-4Akyildiz, I.F., Su, W., Sankarasubramaniam, Y., Cayirci, E.: A survey on sensor networks. IEEE Commun. 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Physical chemical properties and kinetics of redox processes in water/soybean oil microemulsions

Water/oil microemulsions (w/o ME) constituted by water, soybean oil, SDS (sodium dodecyl sulfate) and several short-chain alcohols were characterized from the viewpoint of its physical-chemical and electroanalytical properties. Different co-surfactants and surfactant:co-surfactant ratios were used, and the ME with the most favourable composition was used to study the kinetics of redox processes. For this purpose, cyclic voltammetry measurements using a Pt disk working ultramicroelectrode, an Ag/AgCl reference electrode and a Pt auxiliary electrode, and ferrocene as a probe, were performed. It was verified that the thermodynamic stability of the MEs increases with the co-surfactant content. The molecular structure and water solubility of the co-surfactant affect the electrical conductivity and the hydrodynamic radio of the MEs. Owing to the low diffusion coefficients verified in the MEs, measurements in transient state using conventional sweeping rates could be performed. Ferrocene oxidation in the ME has been demonstrated to proceed in quasi-reversibility conditions. Thus, the possibility of carrying out studies of cyclic voltammetry in vegetable oils under the w/o ME form was demonstrated

Distribution and drivers of marine isoprene concentration across the Southern Ocean

© 2020 by the authors. Isoprene is a biogenic trace gas produced by terrestrial vegetation and marine phytoplankton. In the remote oceans, where secondary aerosols are mostly biogenic, marine isoprene emissions affect atmospheric chemistry and influence cloud formation and brightness. Here, we present the first compilation of new and published measurements of isoprene concentrations in the Southern Ocean and explore their distribution patterns. Surface ocean isoprene concentrations in November through April span 1 to 94 pM. A band of higher concentrations is observed around a latitude of ≈40° S and a surface sea temperature of 15 °C. High isoprene also occurs in high productivity waters near islands and continental coasts. We use concurrent measurements of physical, chemical, and biological variables to explore the main potential drivers of isoprene concentration by means of paired regressions and multivariate analysis. Isoprene is best explained by phytoplankton-related variables like the concentrations of chlorophyll-a, photoprotective pigments and particulate organic matter, photosynthetic efficiency (influenced by iron availability), and the chlorophyll-a shares of most phytoplankton groups, and not by macronutrients or bacterial abundance. A simple statistical model based on chlorophyll-a concentration and a sea surface temperature discontinuity accounts for half of the variance of isoprene concentrations in surface waters of the Southern Ocean