First--order continuous models of opinion formation

We study certain nonlinear continuous models of opinion formation derived from a kinetic description involving exchange of opinion between individual agents. These models imply that the only possible final opinions are the extremal ones, and are similar to models of pure drift in magnetization. Both analytical and numerical methods allow to recover the final distribution of opinion between the two extremal ones.Comment: 17 pages, 4 figure

A well-posedness theory in measures for some kinetic models of collective motion

We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the behavior of large groups of animals, such as flocks of birds, swarms, or schools of fish. Our aim is to give a well-posedness theory for general models which possibly include a variety of effects: an interaction through a potential, such as a short-range repulsion and long-range attraction; a velocity-averaging effect where individuals try to adapt their own velocity to that of other individuals in their surroundings; and self-propulsion effects, which take into account effects on one individual that are independent of the others. We develop our theory in a space of measures, using mass transportation distances. As consequences of our theory we show also the convergence of particle systems to their corresponding kinetic equations, and the local-in-time convergence to the hydrodynamic limit for one of the models

Structure preserving schemes for mean-field equations of collective behavior

In this paper we consider the development of numerical schemes for mean-field equations describing the collective behavior of a large group of interacting agents. The schemes are based on a generalization of the classical Chang-Cooper approach and are capable to preserve the main structural properties of the systems, namely nonnegativity of the solution, physical conservation laws, entropy dissipation and stationary solutions. In particular, the methods here derived are second order accurate in transient regimes whereas they can reach arbitrary accuracy asymptotically for large times. Several examples are reported to show the generality of the approach.Comment: Proceedings of the XVI International Conference on Hyperbolic Problem

La plataforma virtual trastolillo como estrategia para fortalecer el proceso lector en los estudiantes de los grados primero, segundo y tercero del colegio Jorge Isaacs

173 p. Recurso Electr?nicoEste proyecto es el producto de una pr?ctica investigativa, la cual se basa en la creaci?n y aplicaci?n de una plataforma virtual como herramienta did?ctica para fortalecer procesos lectores en los estudiantes de primer ciclo. Se utiliz? como m?todo, la investigaci?n acci?n participativa, por cuanto permite establecer relaci?n directa entre los conocimientos y la acci?n. De igual manera, se utiliz? el enfoque etnogr?fico para, en primer lugar, tener un acercamiento a la poblaci?n abordada y, segundo para establecer las acciones tendientes a la transformaci?n de las problem?ticas en oportunidades de mejoramiento. Para sustentar lo expuesto anteriormente se implementaron antecedentes a nivel internacional, nacional y local en donde cada uno da cuenta de los beneficios y resultados que se proveen al implementar nuevos h?bitos de lectura mediante el uso de las TIC, adicional se abordaron diferentes teor?as coma la comprensi?n del texto vista desde Van Dijk (2006), el aprendizaje significativo y el enfoque constructivista visto por C?sar Coll (2008) desde la educaci?n y la tecnolog?a y enfocadas en la ley del ministerio de la TIC , los lineamientos curriculares y los est?ndares de educaci?n, lo anterior se referenci? desde el marco psicol?gico, epistemol?gico, pedag?gico y legal. Finalmente se implementan cuatro fases de intervenci?n: fase 1 .Reconozco y exploro, me reconocen y me exploran, fase 2.Formando y creando ideas, fase 3. Te va a interesar y te va a gustar, fase 4. Con nuevas herramientas mejores resultados, seguido a esto se realiza el an?lisis cualitativo de los resultados obtenidos por medio de r?bricas.This project is the product of an investigative practice, which is based on the creation and application of a virtual platform as a didactic tool to develop reading processes in first cycle students. Participatory action investigation was used as a method, because it allows a direct relationship between knowledge and action. Besides, the ethnographic approach was used to firstly have a close up with the population and, secondly, to establish actions aimed to transforming the problems in opportunities for improvement. To explain the foregoing were implemented international, national and local backgrounds where each or them give account of the benefits and results provided by the implementation of new reading habits through the use of ITC, as well as different theories such as understanding of the text from Van Dijk (2006), the significant learning and constructivist approach seen by C?sar Coll (2008) from education and technology and focused on the law of the Ministry of ICT, curricular guidelines and education standards. The above was referenced from the Psychological, epistemological, pedagogical and legal framework. Finally, four phases of intervention were implemented: phase 1. I recognize and explore, recognize and explore me, phase 2. Forming and creating ideas, phase 3. It will interest you and you will like it, phase 4. With new tools better results. According to this the qualitative analysis of the results obtained by means of rubrics is carried out. KEY WORDS: didactic, ICT, reading habits, theory, reading processes, virtual platfor