Modelos epidemiológicos en redes: una presentación introductoria

El propósito de este texto es presentar de manera precisa, aunque introductoria, los conceptos básicos de algunos modelos epidemiológicos en redes que al tomar en cuenta los patrones de contacto entre individuos contrastan con el modelo SIR, en el cual la transmisión sólo depende de la densidad de individuos en cada uno de los estadios de la enfermedad. Observamos que el modelo SIR sobrestima el máximo de prevalencia con respecto al modelo de red completa y que epidemias sobre redes más homogéneas presentan una mayor prevalencia. Adicionalmente, estudiamos mediante simulaciones el efecto onda que tienen las reconexiones en el modelo de mundo pequeño y mencionamos algunas aplicaciones de los modelos en redes a la epidemiologíaThe purpose of this paper is to present the basic concepts of some epidemiological network models in an accurate, although introductory way. By taking into account the contact patterns between individuals, these models contrast with the sir model, in which transmission depends only on the density of individuals in each stage of the disease. We observe that the sir model overestimates the maximum of prevalence as compared to the complete network model, and that epidemics over more homogeneous networks present higher prevalence. In addition we used simulations to study the effect of the wave-like spread of infection induced by the reconnections present in a smallworld network model. Finally we mention some applications of network models in epidemiology

Matemáticas y computación: miradas al desarrollo: capítulo 48

En Colombia actualmente existe una oferta de pregrados que comprenden matemáticas puras o ingeniería matemática…Este programa, va dirigido a quienes quieren comprender o estudiar las matemáticas con el apoyo de las ciencias de la computación, lo cual supone un acercamiento a las ingenierías y al análisis de problemas reales

Practical key recovery attacks on two McEliece variants

Abstract. The McEliece cryptosystem is a promising alternative to conventional public key encryption systems like RSA and ECC. In particular, it is supposed to resist even attackers equipped with quantum computers. Moreover, the encryption process requires only simple binary operations making it a good candidate for low cost devices like RFID tags. However, McEliece’s original scheme has the drawback that the keys are very large. Two promising variants have been proposed to overcome this disadvantage. The first one is due to Berger et al. presented at AFRICACRYPT 2009 and the second is due to Barreto and Misoczki presented at SAC 2009. In this paper we first present a general attack framework and apply it to both schemes subsequently. Our framework allows us to recover the private key for most parameters proposed by the authors of both schemes within at most a few days on a single PC

¡No necesitas ser un genio! Una mirada al programa de Matemáticas Aplicadas y Ciencias de la Computación (MACC)

Valérie Gauthier Umaña es la directora del programa de Matemáticas Aplicadas y Ciencias de la Computación (MACC), una carrera que, además de responder a los retos actuales de la revolución 4.0 y de la economía naranja, está al servicio de las personas. Los retos y avances que este programa ha tenido desde su inicio, hace dos años y medio, son sorprendentes; por esto Valérie habla con pasión e invita a estudiantes de todas las regiones del país a que sean parte de la generación que va a crear y liderar la transformación digital en Colombia.Valérie Gauthier Umaña is the director of the Applied Mathematics and Computer Science (MACC) program, a career that, in addition to responding to the current challenges of the 4.0 revolution and the orange economy, is at the service of people. The challenges and advances that this program has had since its inception, two and a half years ago, are surprising; That is why Valérie speaks with passion and invites students from all regions of the country to be part of the generation that will create and lead the digital transformation in Colombia

Mujeres en la revolución 4.0 y ciberseguridad

Estamos viviendo una transformación digital que impacta casi toda nuestra cotidianidad, desde la forma en la que nos comunicamos y trabajamos hasta la manera en cómo tomamos decisiones. El mundo ya no está limitado por fronteras geográficas y el Internet de las Cosas, la Inteligencia Artificial, la analítica de los grandes datos, entre otros, están cambiando el mundo en el que vivimos. Esta revolución crea nuevos retos, como por ejemplo la ciberseguridad, si toda la información y las comunicaciones están digitalizadas, debemos proteger tanto los datos como las comunicaciones y el no hacerlo puede tener un impacto muy costoso para la sociedad, desde el punto de vista del derecho a la privacidad y a la honra y el buen nombre, los derechos de propiedad intelectual, la protección de los ciudadanos, entre otros

An introduction to epidemiological network models

El propósito de este texto es presentar de manera precisa, aunque introductoria, los conceptos básicos de algunos modelos epidemiológicos en redes que al tomar en cuenta los patrones de contacto entre individuos contrastan con el modelo sir, en el cual la transmisión sólo depende de la densidad de individuos en cada uno de los estadios de la enfermedad. Observamos que el modelo sir sobrestima el máximo de prevalencia con respecto al modelo de red completa y que epidemias sobre redes más homogéneas presentan una mayor prevalencia. Adicionalmente, estudiamos mediante simulaciones el efecto onda que tienen las reconexiones en el modelo de mundo pequeño y mencionamos algunas aplicaciones de los modelos en redes a la epidemiologíaThe purpose of this paper is to present the basic concepts of some epidemiological network models in an accurate, although introductory way. By taking into account the contact patterns between individuals, these models contrast with the sir model, in which transmission depends only on the density of individuals in each stage of the disease. We observe that the sir model overestimates the maximum of prevalence as compared to the complete network model, and that epidemics over more homogeneous networks present higher prevalence. In addition we used simulations to study the effect of the wave-like spread of infection induced by the reconnections present in a smallworld network model. Finally we mention some applications of network models in epidemiology

El curso 'Ideas Matemáticas' como Proyecto de Innovación para Ciudadanos Matemáticos Críticos

In the context of a pedagogical innovation project of the Universidad del Rosario, the specific needs of the School of Human Sciences were initially addressed to incorporate different spaces where the students of some programs of this School could learn mathematics and explain their use in each one of the sub-disciplines. After these needs were collected, the course in question was designed and developed and is currently in an evaluation and sustainability stage. Traditionally, mathematics has been part of the factors of dropout in Colombian Higher Education. There is also the imaginary that mathematics turns out to be useless in different disciplines. As an institutional effort, we have proposed technology-mediated innovations that bring students closer to the applicability of what they have learned (from the mathematical context) to break down these beliefs that lead to obstacles in the learning of mathematics. The subject of 'mathematical ideas' is aimed at students of programs that do not have a mathematical focus. In this sense, it seeks to enable an approach, a reunion environment, and in some cases 'reconciliation' with mathematics. In class, basic concepts are addressed with important applications in everyday life, in order to have a more critical view of situations that involve using mathematics. That is, the use of mathematics as a tool to analyze and make decisions that positively impact their lives and society. In addition, there is a series of virtual support activities that have proved to be very useful as a complement to face-to-face classes and in accompanying the student's extra class work, that is, using a blended-based learning methodology. There is constant discussion about the implications of knowing how to use mathematics and the responsibility that this entails, always focusing on a use, let's say, fair. In this way we work in the formation of mathematically critical citizens, an idea that is closely related to what Paul Ernest (2002) names as 'critical mathematical citizenship'. On the other hand, students learn through projects facilitated by the teacher, where they can solve real tensions in society. With this, we seek to raise the levels of social sensitivity of our students, in the mobilization of content and skills for the solution of real problems. In this communication we will show the motivations that allowed the creation of the subject. We will describe in detail the scope of the course, the use of different disruptive methodologies and virtual scenarios, and a reflection from qualitative perspectives (through a case study), which gives prominence to the voice of students who have taken the course. There is evidence of the positive effect of this subject in front of the imaginaries that students had about mathematics. Students who have taken this course have been empowered and managed to mobilize the contents and skills learned for the solution of real problems that they have detected and modeled, and that they have solved with the use of mathematics. This is based on a project that works from the beginning of the course and that is nurtured as it progresses. Then, the results of their research are made public in the framework of the Pi Day, an activity that seeks to give visibility to mathematics within the university, and that allows them to connect with their intrinsic motivations

An introduction to epidemiological network models

El propósito de este texto es presentar de manera precisa, aunque introductoria, los conceptos básicos de algunos modelos epidemiológicos en redes que al tomar en cuenta los patrones de contacto entre individuos contrastan con el modelo sir, en el cual la transmisión sólo depende de la densidad de individuos en cada uno de los estadios de la enfermedad. Observamos que el modelo sir sobrestima el máximo de prevalencia con respecto al modelo de red completa y que epidemias sobre redes más homogéneas presentan una mayor prevalencia. Adicionalmente, estudiamos mediante simulaciones el efecto onda que tienen las reconexiones en el modelo de mundo pequeño y mencionamos algunas aplicaciones de los modelos en redes a la epidemiologíaThe purpose of this paper is to present the basic concepts of some epidemiological network models in an accurate, although introductory way. By taking into account the contact patterns between individuals, these models contrast with the sir model, in which transmission depends only on the density of individuals in each stage of the disease. We observe that the sir model overestimates the maximum of prevalence as compared to the complete network model, and that epidemics over more homogeneous networks present higher prevalence. In addition we used simulations to study the effect of the wave-like spread of infection induced by the reconnections present in a smallworld network model. Finally we mention some applications of network models in epidemiology

Modelos epidemiológicos en redes: una presentación introductoria

The purpose of this paper is to present the basic concepts of some epidemiological network models in an accurate, although introductory way. By taking into account the contact patterns between individuals, these models contrast with the sir model, in which transmission depends only on the density of individuals in each stage of the disease. We observe that the sir model overestimates the maximum of prevalence as compared to the complete network model, and that epidemics over more homogeneous networks present higher prevalence. In addition we used simulations to study the effect of the wave-like spread of infection induced by the reconnections present in a smallworld network model. Finally we mention some applications of network models in epidemiology.El propósito de este texto es presentar de manera precisa, aunque introductoria, los conceptos básicos de algunos modelos epidemiológicos en redes que al tomar en cuenta los patrones de contacto entre individuos contrastan con el modelo SIR, en el cual la transmisión sólo depende de la densidad de individuos en cada uno de los estadios de la enfermedad. Observamos que el modelo SIR sobrestima el máximo de prevalencia con respecto al modelo de red completa y que epidemias sobre redes más homogéneas presentan una mayor prevalencia. Adicionalmente, estudiamos mediante simulaciones el efecto onda que tienen las reconexiones en el modelo de mundo pequeño y mencionamos algunas aplicaciones de los modelos en redes a la epidemiologí