Wicked Problems and the Invention of Calculus

Since the 1980s, wicked problems have represented a category of challenges that defy clear description, cannot be addressed with existing models or theories, and resist experimentation in trying to solve them. This class of problems existed before they were identified and have been unsuccessfully addressed with Thomas Kuhn’s model of scientific discovery, an expectation that requires the identification of a new object and the development of its correct interpretation. This paper proposes an alternative view of scientific discovery using the invention of Calculus as a case study that describes a successful process addressing wicked-like problems from a philosophical perspective, develops ideas that have an epistemological objective and are multidisciplinary in their applications, and results in additions to the Body of Knowledge that permeate human language and understanding. Leibniz’s wicked problem was to produce a universal method of discovery at the centre of his idea of a ‘General Science’ and the compilation of an encyclopaedia of all knowledge available at the time. From the existing paradigm of geometrical arguments and deductive processes, there is a gestalt shift in Leibniz’s leap in understanding mathematical methods and the language used in describing and solving problems that was rooted in the idea of infinitesimals and in a more general method of analysis. In doing so, the transition that began with his methods and notation became the first stage in a Kuhnian paradigm shift and the incorporation of Calculus and its applications into the mainstream of science. I will start by giving some background on wicked problems and describing the concept of discovery associated with Kuhn’s ideas, and I will then introduce the process of additions to knowledge advocated in this essay. These ideas will form the antecedent to summarise the paradigm in 17th century mathematics and from there I will proceed to describe Leibniz’s leap and the inherent gestalt shift that occurred in the mathematics of the 18th century. That gestalt shift was not exempt from acrimonious discussions over alternate formulations and I will present some differences between the views of Newton and Leibniz and of two of their supporters; Maclaurin and l’Hôpital. I will then describe some of the efforts that helped to expand the acceptance of Calculus and to embed it in the mainstream of science. I will conclude by proposing that there are other examples from the History and Philosophy of Science that follow a similar process of additions to the Body of Knowledge

Slim SUSY

The new SM-like Higgs boson discovered recently at the LHC, with mass $m_h \simeq$ 125 GeV, as well as the direct LHC bounds on the mass of superpartners, which are entering into the TeV range, suggest that the minimal surviving supersymmetric extension of the SM (MSSM), should be characterized by a heavy SUSY-breaking scale. Several variants of the MSSM have been proposed to account for this result, which vary according to the accepted degree of fine-tuning. We propose an alternative scenario here, Slim SUSY, which contains sfermions with multi-TeV masses and gauginos/higgsinos near the EW scale, but it includes the heavy MSSM Higgs bosons ($H^0$, $A^0$, $H^\pm$) near the EW scale too. We discuss first the formulation and constraints of the Slim SUSY scenario, and then identify distinctive heavy Higgs signals that could be searched at the LHC, within scenarios with the minimal number of superpartners with masses near the EW scale.Comment: 16 pages, 6 figures. Section 2 has been restructured, with a new subsection and some comments added. This version matches the manuscript accepted in Physics Letters

Decays of H0/A0H^0/A^0 in supersymmetric scenarios with heavy sfermions

The recent discovery of a new boson at the LHC, which resembles a SM-like Higgs boson with $m_h=125$ GeV, is starting to provide strong guidelines into SUSY model building. For instance, the identification of such a state with the lightest CP-even Higgs boson of the MSSM ($h^0$), requires large values of $\tan\beta$ and/or heavy sfermions. One outcome of this result is the possibility to solve the SUSY flavor and CP problems by decoupling, which points towards some realization of Split-inspired SUSY scenarios, in which scalars are much heavier than gauginos and higgsinos. However, we argue here that the remaining Higgs bosons of the MSSM ($H^0$, $A^0$, $H^{\pm}$) do not have to be as heavy as the sfermions, and having them with masses near the EW scale does not pose any conflict with current MSSM constraints. We discuss then some SUSY scenarios with heavy sfermions, from a bottom-up approach, which contain the full Higgs sector, as well as a possible dark matter candidate, with masses near the EW scale, and identify distinctive signals from these scenarios that could be searched at the LHC.Comment: 25 pages, 12 figures. Title modified, one figure and some comments added, overall conclusions remained as previous versions. This last version matches the manuscript accepted in EPJ

Living analytics methods for the social web

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Diplomado de profundización cisco ccnp solución de dos escenarios presentes en entornos corporativos bajo el uso de tecnología cisco

En el primer escenario se usan dos tipos de enrutamiento que permiten convivir dos protocolos como son OSPF Y EIGRP, esto con el fin que se aprendan las rutas de los dos protocolos y puedan compartir recursos, además de admitir la conexión entre áreas con sistemas autónomos, igualmente de permitir la redistribución de los protocolos usando técnicas donde se aplican las mediciones de ancho de banda, demora, confiabilidad, carga y MTU, el único problema es que consume recursos. En el segundo escenario aplicamos las configuraciones de etherchannel donde LACP Y PAGP se pueden agrupar, los enlaces ethernetchannel y port trunking logran combinar las interfaces de forma múltiple, permitiendo así un ancho de banda disponible y proporciona una medida de la redundancia física, el LACP puede proteger sobre los loops y el PAGP es meramente de negociación permitiendo a este en conjunto funcionar estrechamente el uno con el otro. CISCO, CCNP, Conmutación, Enrutamiento, Redes, Electrónica.The first scenario uses two types of routing that allow two protocols such as OSPF and EIGRP to coexist, this in order to learn the routes of the two protocols and share resources, as well as to support the connection between areas with autonomous systems, as well as to allow the redistribution of protocols using techniques where bandwidth measurements are applied , delay, reliability, load and MTU, the only problem is that it consumes resources. In the second scenario we apply etherchannel configurations where LACP and PAGP can be grouped, ethernetchannel and port trunking links manage to combine the interfaces multiplely, thus allowing an available bandwidth and provides a measure of physical redundancy, the LACP can protect over loops and paging is merely negotiation allowing it together to work closely with each other. CISCO, CCNP, Switching, Routing, Networking, Electronics

Jesuit Education and Mathematics: Review of the Literature on Jesuit Education and Mathematics

The purpose of the thesis is to review recent literature on diverse aspects of Jesuit cation including its historiography, pedagogy, teaching, philosophy, and its contributions to Id of Mathematics. The time frame studied has been divided in four main periods. Origins; encompassing the founding of the Society of Jesus in 1540 to the publication of the Ratio Studiorum in 1599. Expansion; covering from the publication of the Ratio to the suppression of Society in 1773. Restoration: covers the period between the 1814 Restoration, until the ginning of the Vatican II Council. Renewal; the Society in the post-Vatican area to the present day. In creating their educational system, the Jesuits combined their fundamental documents and the ‘best practices” available. The Spiritual Exercises from Ignatius inspired their mission d the Pedagogical process they implemented in their methods. The modus Parisiensis gave them a model for an educational institution, and the Italian Humanists an orientation for their Nation. The Constitutions gave them the focus and direction to implement their network of schools. Together with the product of local experiences and consultations for over fifty years y produced the Ratio Studiorum, a manual for the operation of a school, to be used everywhere. The Ratio has provisions for mathematics instruction that survive to the present, as well as for the foundation of the Collegio Romano. Mathematics and the Coliegio Romano played an Portant role in the beginning of the Scientific Revolution, and it affected the work of influential minds of the sixteenth, seventeenth and eighteenth centuries, and declined after that. Behind the mathematics of the Ratio and generations of Jesuit mathematicians is the influence of Christoph Clavius, his work, educational strategies and textbooks. The characteristics of Jesuit pedagogy, mathematical work and its influence in philosophical thinking in the Seventeenth century are examined. After the Restoration of the Society the Ratio was no longer the universal norm for their schools. Jesuit education in the eighteenth and nineteenth centuries had the most success in those areas were education was under the control of Protestants. The mission and current documents on educational pedagogy, characteristics and methodology are also reviewed. In the last several years, there has been a renewed interest the Jesuits, their influence and their educational system, but scholarly work is rare and the areas of study focus mostly in the Counter-Reformation period. Further work is suggested in using the tradition, experience and methodology of Jesuit education, particularly in the role of Mathematics and its teaching