Fat handles and phase portraits of Non Singular Morse-Smale flows on S^3 with unknotted saddle orbits

In this paper we build Non-singular Morse-Smale flows on S^3 with unknotted and unlinked saddle orbits by identifying fat round handles along their boundaries. This way of building the flows enables to get their phase portraits. We also show that the presence of heteroclinic trajectories imposes an order in the round handle decomposition of these flows; this order is total for NMS flows composed of one repulsive, one attractive and n unknotted saddle orbits, for n >1.Comment: 15 page

Non equivalence of NMS flows on S3S^{3}

summary:We build the flows of non singular Morse-Smale systems on the 3-sphere from its round handle decomposition. We show the existence of flows corresponding to the same link of periodic orbits that are non equivalent. So, the link of periodic orbits is not in a 1-1 correspondence with this type of flows and we search for other topological invariants such as the associated dual graph

Behavior of fixed and critical points of the (alpha,c)-family of iterative methods

In this paper we study the dynamical behavior of the -family of iterative methods for solving nonlinear equations, when we apply the fixed point operator associated to this family on quadratic polynomials. This is a family of third-order iterative root-finding methods depending on two parameters; so, as we show throughout this paper, its dynamics is really interesting, but complicated. In fact, we have found in the real -plane a line in which the corresponding elements of the family have a lower number of free critical points. As this number is directly related with the quantity of basins of attraction, it is probable to find more stable behavior between the elements of the family in this region.Supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02. The first and fourth authors were also partially supported by P11B2011-30 (Universitat Jaume I), the second and third authors were also partially supported by Vicerrectorado de Investigacion, Universitat Politecnica de Valencia SP20120474.Campos, B.; Cordero Barbero, A.; Torregrosa Sánchez, JR.; P. Vindel (2015). Behavior of fixed and critical points of the (alpha,c)-family of iterative methods. Journal of Mathematical Chemistry. 53(3):807-827. https://doi.org/10.1007/s10910-014-0465-3S807827533A.F. Beardon, Iteration of Rational Functions, Graduate Texts in Mathematics, vol. 132 (Springer, New York, 1991)B. Campos, A. Cordero, A. Magreñan, J.R. Torregrosa, P. Vindel, Study of a bi-parametric family of iterative methods, Abstra. Appl. Anal. (2014). doi: 10.1155/2014/141643B. Campos, A. Cordero, A. Magreñan, J.R. Torregrosa, P. Vindel, Bifurcations of the roots of a 6-degree symmetric polynomial coming from the fixed point operator of a class of iterative methods. in Proceedings of the 14th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE, ed. by J. Vigo-Aguiar (2014), pp. 253–264B. Campos, A. Cordero, J.R. Torregrosa, P. Vindel, Dynamics of the family of c-iterative methods. Int. J. Compt. Math. (2014). doi: 10.1080/00207160.2014.893608F. Chicharro, A. Cordero, J.R. Torregrosa, Drawing dynamical and parameter planes of iterative families and methods. Sci. World J. (2013). doi: 10.1155/2013/780153A. Cordero, J. García-Maimó, J.R. Torregrosa, M.P. Vassileva, P. Vindel, Chaos in King’s iterative family. Appl. Math. Lett. 26, 842–848 (2013)A. Cordero, J.R. Torregrosa, P. Vindel, Dynamics of a family of Chebyshev–Halley type method. Appl. Math. Comput. 219, 8568–8583 (2013)C.G. Jesudason, I. Numerical nonlinear analysis: differential methods and optimization applied to chemical reaction rate determination. J. Math. Chem. 49(7), 1384–1415 (2011)P.G. Logrado, J.D.M. Vianna, Partitioning technique procedure revisited: formalism and first applications to atomic problems. J. Math. Chem. 22, 107–116 (1997)M. Mahalakshmi, G. Hariharan, K. Kannan, The wavelet methods to linear and nonlinear reaction-diffusion model arising in mathematical chemistry. J. Math. Chem. 51(9), 2361–2385 (2013)K. Maleknejad, M. Alizadeh, An efficient numerical sheme for solving Hammerstein integral equation arisen in chemical phenomenon. Proc. Comput. Sci. 3, 361–364 (2011)J. Milnor, Dynamics in One Complex Variable (Princeton University Press, New Jersey, 2006

Study of the dynamics of third-order iterative methods on quadratic polynomials

In this paper, we analyse the dynamical behaviour of the operators associated with multi-point interpolation iterative methods and frozen derivative methods, for solving nonlinear equations, applied on second-degree complex polynomials. We obtain that, in both cases, the Julia set is connected and separates the basins of attraction of the roots of the polynomial. Moreover, the Julia set of the operator associated with multi-point interpolation methods is the same as the Newton operator, although it is more complicated for the frozen derivative operator. We explain these differences by obtaining the conjugacy function of each method and by showing that the operators associated with Newton's method and multi-point interpolation methods are both conjugate to powers of z.The authors thank Professors X. Jarque and A. Garijo for their help. The authors also thank the referees for their valuable comments and suggestions that have improved the content of this paper. This research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02 and by Vicerrectorado de Invetigacion, Universitat Politecnica de Valencia, PAID-06-2010-2285Cordero Barbero, A.; Torregrosa Sánchez, JR.; Vindel Cañas, P. (2012). Study of the dynamics of third-order iterative methods on quadratic polynomials. International Journal of Computer Mathematics. 89(13):1826-1836. https://doi.org/10.1080/00207160.2012.687446S182618368913Amat, S., Busquier, S., & Plaza, S. (2006). A construction of attracting periodic orbits for some classical third-order iterative methods. Journal of Computational and Applied Mathematics, 189(1-2), 22-33. doi:10.1016/j.cam.2005.03.049Amat, S., Bermúdez, C., Busquier, S., & Plaza, S. (2008). On the dynamics of the Euler iterative function. Applied Mathematics and Computation, 197(2), 725-732. doi:10.1016/j.amc.2007.08.086Amat, S., Busquier, S., & Plaza, S. (2010). Chaotic dynamics of a third-order Newton-type method. Journal of Mathematical Analysis and Applications, 366(1), 24-32. doi:10.1016/j.jmaa.2010.01.047Blanchard, P. (1995). The dynamics of Newton’s method. Proceedings of Symposia in Applied Mathematics, 139-154. doi:10.1090/psapm/049/1315536Cordero, A., & Torregrosa, J. R. (2010). On interpolation variants of Newton’s method for functions of several variables. Journal of Computational and Applied Mathematics, 234(1), 34-43. doi:10.1016/j.cam.2009.12.002Cordero, A., Hueso, J. L., Martínez, E., & Torregrosa, J. R. (2009). Multi-Point Iterative Methods for Systems of Nonlinear Equations. Lecture Notes in Control and Information Sciences, 259-267. doi:10.1007/978-3-642-02894-6_25Cordero, A., Hueso, J. L., Martínez, E., & Torregrosa, J. R. (2010). Iterative methods for use with nonlinear discrete algebraic models. Mathematical and Computer Modelling, 52(7-8), 1251-1257. doi:10.1016/j.mcm.2010.02.028Curry, J. H., Garnett, L., & Sullivan, D. (1983). On the iteration of a rational function: Computer experiments with Newton’s method. Communications in Mathematical Physics, 91(2), 267-277. doi:10.1007/bf01211162Douady, A., & Hubbard, J. H. (1985). On the dynamics of polynomial-like mappings. Annales scientifiques de l’École normale supérieure, 18(2), 287-343. doi:10.24033/asens.1491Frontini, M., & Sormani, E. (2003). Some variant of Newton’s method with third-order convergence. Applied Mathematics and Computation, 140(2-3), 419-426. doi:10.1016/s0096-3003(02)00238-2Gutiérrez, J. M., Hernández, M. A., & Romero, N. (2010). Dynamics of a new family of iterative processes for quadratic polynomials. Journal of Computational and Applied Mathematics, 233(10), 2688-2695. doi:10.1016/j.cam.2009.11.017Özban, A. . (2004). Some new variants of Newton’s method. Applied Mathematics Letters, 17(6), 677-682. doi:10.1016/s0893-9659(04)90104-8PLAZA, S. (2001). CONJUGACIES CLASSES OF SOME NUMERICAL METHODS. Proyecciones (Antofagasta), 20(1). doi:10.4067/s0716-09172001000100001Plaza, S., & Romero, N. (2011). Attracting cycles for the relaxed Newton’s method. Journal of Computational and Applied Mathematics, 235(10), 3238-3244. doi:10.1016/j.cam.2011.01.010F.A. Potra and V. Pták,Nondiscrete Introduction and Iterative Processes, Research Notes in Mathematics Vol. 103, Pitman, Boston, MA, 1984

Dynamics of the family of c-iterative methods

In this paper, the dynamics of the family of c-iterative methods for solving nonlinear equations are studied on quadratic polynomials. A singular parameter space is presented to show the complexity of the family. The analysis of the parameter space allows us to find elements of the family that have bad convergence properties and also other ones with very stable behaviour. These schemes correspond to values of c in different small regions of the parameter space.Supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02. The first and fourth authors were also partially supported by P11B2011-30 (Universitat Jaume I), the second and third authors were also partially supported by Vicerrectorado de Investigacion, Universitat Politecnica de Valencia PAID-06-2010-2285.Campos, B.; Cordero Barbero, A.; Torregrosa Sánchez, JR.; Vindel, P. (2015). Dynamics of the family of c-iterative methods. International Journal of Computer Mathematics. 92(9):1815-1825. https://doi.org/10.1080/00207160.2014.893608S1815182592

The Peña do Seo W-Sn deposit, NW Iberia: Petrology, fluid inclusions and O-H-S isotopes

The Peña do Seo W-Sn ore deposit in NW Iberia consists mainly of quartz veins hosted in schists. Vein mineralogy comprises wolframite, cassiterite and minor molybdenite. Peraluminous S-type granites and minor metaluminous granitoid breccias crop out in the same location. Whole rock geochemistry, mineral characterization, fluid inclusions and stable isotope geochemistry have been combined to infer hydrothermal mineralization conditions. A pre-ore stage (0) involving the alteration of host rocks, three stages of mineralization (I, II and III), and a supergene stage (IV) have been identified. Stage I (oxide-halide-sulfide stage) consisted of a cassiterite-pyrite-fluorite mineralization in granitoid breccias. Stage II (main oxide stage) involved wolframite-rich selvages and wolframite-cassiterite-(molybdenite) quartz veins. Stage III (main sulfide stage) consisted of a sulfide mineralization in quartz veins comprising pyrite and minor arsenopyrite and chalcopyrite. Three types of fluid inclusions were found in vein quartz: (1) aqueous two-phase inclusions, with homogenization temperatures (Th) between 445 °C and 280 °C and moderate salinities (9–14 wt% NaCl eq.), (2) aqueous-carbonic three-phase fluid inclusions, with Th from 340 °C to 260 °C and low salinities (2–7 wt% NaCl eq.), and (3) aqueous two-phase fluid inclusions, with Th from 270 °C to 155 °C and low salinities (0–6 wt% NaCl eq.). δ18O values in quartz from mineralized veins range from +11.2‰ to +13.4‰, and between +15.0‰ and +15.4% in quartz from mineralized granitoid breccias. δ34S values in sulfides (pyrite, arsenopyrite and chalcopyrite) range between +13.0 ‰ and +37.1 ‰, thus suggesting a marine source of sulfate and possible equilibration with host-rock sulfides. δD values in muscovite and chlorite from quartz veins range between −105.7 ‰ and −71.5 ‰ and between −69.4 ‰ and −67.1 ‰, respectively, indicating a transition from magmatic to magmatic-metamorphic conditions. An aqueous (H2O–NaCl) magmatic-hydrothermal fluid led to the W-Sn mineralization, as deduced from the studied fluid inclusions and isotopic signatures. High W and Sn contents in the peraluminous granites indicate that the W-Sn mineralization in Peña do Seo could partially be related to the granites and granitoid breccias. Whereas the Sn (±W) likely derived from hydrothermal fluids exsolving from the crystallizing magmas, host quartz schists would have supplied other elements required for wolframite deposition such as Fe and Mn. Sulfide mineralization in stage III was probably driven by fluid dilution.Depto. de Mineralogía y PetrologíaFac. de Ciencias GeológicasTRUEINTERREG V-A Spain-Portugal Cooperation Programme, 2014-20Junta de Castilla y Leónpu

Disability and perceived stress in primary care patients with major depression

Background: Major depressive disorder (MDD) is highly prevalent in the Spanish primary care (PC) setting and the leading cause of disability in Spain. The aim of this study was to evaluate several key psychometric properties of the Sheehan Disability Scale (SDS) in patients with or without MDD and varying degrees of symptom severity using the Patient Health Questionnaire-9 (PHQ-9). Method: A total of 1, 704 PC patients participating in the PsicAP clinical trial completed the SDS and PHQ-9. We evaluated the factor structure, measurement invariance across gender, internal consistency, and the discriminative and predictive validity. Results: Confirmatory factor analyses revealed a unifactorial model of the SDS containing 4 items (SDS-4) with the best model fit (CFI: .99; GFI: .99; TLI: 96; RMSEA: .10). This model contained the three life domain items (work, family, and social life) plus perceived stress (PS) with significant loadings. The internal consistency of the SDS-4 was acceptable in patients with or without MDD, regardless of symptom severity. The SDS-4 also showed good discriminative capacity and acceptable predictive validity in all subsamples. Conclusions: These findings support the use of the SDS-4 to assess depression-related disability in patients at Spanish primary care centres

Heterogeneous vancomycin-intermediate susceptibility in a community-associated methicillin-resistant Staphylococcus aureus epidemic clone, in a case of Infective Endocarditis in Argentina

BACKGROUND: Community-Associated Methicillin Resistant Staphylococcus aureus (CA-MRSA) has traditionally been related to skin and soft tissue infections in healthy young patients. However, it has now emerged as responsible for severe infections worldwide, for which vancomycin is one of the mainstays of treatment. Infective endocarditis (IE) due to CA-MRSA with heterogeneous vancomycin-intermediate susceptibility-(h-VISA) has been recently reported, associated to an epidemic USA 300 CA-MRSA clone. CASE PRESENTATION: We describe the occurrence of h-VISA phenotype in a case of IE caused by a strain belonging to an epidemic CA-MRSA clone, distinct from USA300, for the first time in Argentina. The isolate h-VISA (SaB2) was recovered from a patient with persistent bacteraemia after a 7-day therapy with vancomycin, which evolved to fatal case of IE complicated with brain abscesses. The initial isolate-(SaB1) was fully vancomycin susceptible (VSSA). Although MRSA SaB2 was vancomycin susceptible (≤ 2 μg/ml) by MIC (agar and broth dilution, E-test and VITEK 2), a slight increase of MIC values between SaB1 and SaB2 isolates was detected by the four MIC methods, particularly for teicoplanin. Moreover, Sab2 was classified as h-VISA by three different screening methods [MHA5T-screening agar, Macromethod-E-test-(MET) and by GRD E-test] and confirmed by population analysis profile-(PAP). In addition, a significant increase in cell-wall thickness was revealed for SaB2 by electron microscopy. Molecular typing showed that both strains, SaB1 and SaB2, belonged to ST5 lineage, carried SCCmecIV, lacked Panton-Valentine leukocidin-(PVL) genes and had indistinguishable PFGE patterns (subtype I2), thereby confirming their isogenic nature. In addition, they were clonally related to the epidemic CA-MRSA clone (pulsotype I) detected in our country. CONCLUSIONS: This report demonstrates the ability of this epidemic CA-MRSA clone, disseminated in some regions of Argentina, to produce severe and rapidly fatal infections such as IE, in addition to its ability to acquire low-level vancomycin resistance; for these reasons, it constitutes a new challenge for the Healthcare System of this country.This study was supported by the National Council for Scientific Research and Technology of Argentina (CONICET), Agencia Nacional de Promoción Científica y Tecnológica (ANPCyT - PICT 01630 to JLB), Secretaría de Ciencia y Técnica-Universidad Nacional de Córdoba (SECyT-UNC) and Agencia Córdoba Ciencia.S

Vaccines as alternatives to antibiotics for food producing animals. Part 2:new approaches and potential solutions

Vaccines and other alternative products are central to the future success of animal agriculture because they can help minimize the need for antibiotics by preventing and controlling infectious diseases in animal populations. To assess scientific advancements related to alternatives to antibiotics and provide actionable strategies to support their development, the United States Department of Agriculture, with support from the World Organisation for Animal Health, organized the second International Symposium on Alternatives to Antibiotics. It focused on six key areas: vaccines; microbial-derived products; non-nutritive phytochemicals; immune-related products; chemicals, enzymes, and innovative drugs; and regulatory pathways to enable the development and licensure of alternatives to antibiotics. This article, the second part in a two-part series, highlights new approaches and potential solutions for the development of vaccines as alternatives to antibiotics in food producing animals; opportunities, challenges and needs for the development of such vaccines are discussed in the first part of this series. As discussed in part 1 of this manuscript, many current vaccines fall short of ideal vaccines in one or more respects. Promising breakthroughs to overcome these limitations include new biotechnology techniques, new oral vaccine approaches, novel adjuvants, new delivery strategies based on bacterial spores, and live recombinant vectors; they also include new vaccination strategies in-ovo, and strategies that simultaneously protect against multiple pathogens. However, translating this research into commercial vaccines that effectively reduce the need for antibiotics will require close collaboration among stakeholders, for instance through public–private partnerships. Targeted research and development investments and concerted efforts by all affected are needed to realize the potential of vaccines to improve animal health, safeguard agricultural productivity, and reduce antibiotic consumption and resulting resistance risks