Papers by Mauricio Rene Herrera Marin
Europhysics Letters (epl), 2003
An exact integro-differential equation for the conformal map from the unit circle to the boundary... more An exact integro-differential equation for the conformal map from the unit circle to the boundary of an evolving cavity in a stressed 2-dimensional solid is derived. This equation provides an accurate description of the dynamics of precursors to fracture when surface diffusion is important. The solution predicts the creation of sharp grooves that eventually lead to material failure via rapid fracture. Solutions of the new equation are demonstrated for the dynamics of an elliptical cavity and the stability of a circular cavity under biaxial stress, including the effects of surface stress.
We address the problem of long-term dynamics of tuberculosis (TB) and latent tuberculosis (LTB) i... more We address the problem of long-term dynamics of tuberculosis (TB) and latent tuberculosis (LTB) in semiclosed communities. These communities are congregate settings with the potential for sustained daily contact for weeks, months, and even years between their members. Basic examples of these communities are prisons, but certain urban/rural communities, some schools, among others could possibly fit well into this definition. These communities present a sort of ideal conditions for TB spread. In order to describe key relevant dynamics of the disease in these communities, we consider a five compartments SEIR model with five possible routes toward TB infection: primary infection after a contact with infected and infectious individuals (fast TB), endogenous reactivation after a period of latency (slow TB), relapse by natural causes after a cure, exogenous reinfection of latently infected, and exogenous reinfection of recovered individuals. We discuss the possible existence of multiple endemic equilibrium states and the role that the two types of exogenous reinfections in the long-term dynamics of the disease could play.
Arxiv preprint math-ph/0008019, 2000
Examples of non-standard construction of Hamiltonian structures for dynamical systems and the res... more Examples of non-standard construction of Hamiltonian structures for dynamical systems and the respective Hamilton-Jacobi (H-J) equations, without using Lagrangians, are presented. Alternative H-J equations for Euler top are explicitly exhibited and solved. We demonstrate that the stability criterion used by Bridges in [16], relating the slope of a Casimir function parametrized by the Lagrange multiplier to critical point type, depends on the used Hamiltonian structure and it is inadequate for this reason.
Behavioural Neurology, 2018
We have developed a new methodology for examining and extracting patterns from brain electric act... more We have developed a new methodology for examining and extracting patterns from brain electric activity by using data mining and machine learning techniques. Data was collected from experiments focused on the study of cognitive processes that might evoke different specific strategies in the resolution of math problems. A binary classification problem was constructed using correlations and phase synchronization between different electroencephalographic channels as characteristics and, as labels or classes, the math performances of individuals participating in specially designed experiments. The proposed methodology is based on using well-established procedures of feature selection, which were used to determine a suitable brain functional network size related to math problem solving strategies and also to discover the most relevant links in this network without including noisy connections or excluding significant connections.
International Journal of Emerging Technologies in Learning (iJET), 2019
In mathematics education, studies reveal difficulties in the teaching-learning of trigonometry in... more In mathematics education, studies reveal difficulties in the teaching-learning of trigonometry in secondary and higher education, due to the fact that students are not encouraged to achieve a deep conceptual understanding of abstract concepts. Several studies demonstrate that incorporating digital technologies has a positive impact on students’ learning. However, most of the existing technologies do not consider the use of the body and multiple senses. Tangible User Interfaces (TUIs) in contrast, can host bodily interactions that have the potential of enhancing learning. Nonetheless, there is a lack of applications of TUIs for trigonometry education. This study consisted of designing and validating a tangible interface for the teaching-learning of basic concepts of trigonometry. The interface hosts a pedagogical experience that privileges exploration through physical manipulation and fosters intuitive and collaborative learning. A Pre-Test was applied to 121 students to determine previous knowledge, yielding a 29.1% performance. After two sessions using the interface, the results of a Post-Test reveal an increase of 37.1%, confirming the educational effectiveness of the interface, and the pedagogical experience to facilitate the learning of basic concepts of trigonometry.
WATER INTERNATIONAL, 2019
This article provides a multidimensional study based on data and text mining of prosecuted disput... more This article provides a multidimensional study based on data and text mining of prosecuted disputes on water rights in Chile, and an analysis of the state’s capacity, particularly of the institutions related to water regulation. This study shows not only a substantial increase of legal disputes regarding water rights over the years (1981–2014), but also clear patterns in the geographic location of these conflicts, as well as in the types of legal actions, arguments and strategies used in their pursuit. Through a topic analysis, we find a growing diversification over time of the subjects contained in the legal claims, suggesting an increase in structure and complexity.
Beyond obvious increase of conflicts due to scarcity of water resources there is a problem of gov... more Beyond obvious increase of conflicts due to scarcity of water resources there is a problem of governance, which prevents that water use become a source of conflicts Data show not only a substantial increase in legal disputes over years, but also clear patterns in geographic locations of conflicts, and types of used legal resources, arguments and strategies. It is also show, an increased diversification over time of the topics contained in legal claims, suggesting also an increase in the complexity of conflicts.
There are many studies in the marketing and diffusion literature of the conditions in which socia... more There are many studies in the marketing and diffusion literature of the conditions in which social contagion affects adoption processes. Yet most of these studies assume that social interactions do not change over time, even though actors in social networks exhibit different likelihoods of being influenced across the diffusion period. Rooted in physics and epidemiol- ogy theories, this study proposes a Susceptible Infectious Susceptible (SIS) model to assess the role of social contagion in adoption processes, which takes changes in social dynamics over time into account. To study the adoption over a span of ten years, the authors used detailed data sets from a community of consumers and determined the impor- tance of social contagion, as well as how the interplay of social and non-social influences from outside the community drives adoption processes. Although social contagion matters for diffusion, it is less relevant in shaping adoption when the study also includes social dynamics among members of the community. This finding is relevant for managers and entrepreneurs who trust in word-of-mouth marketing campaigns whose effect may be over- estimated if marketers fail to acknowledge variations in social interactions.
In this work, we apply a new methodology using SVM (with and without uncer- tainties) for examini... more In this work, we apply a new methodology using SVM (with and without uncer- tainties) for examining and extracting patterns in brain electric activity that result from analysing the synchronization between different electroencephalographic channels (EEG). We use datasets obtained from some experiments focused on the cognitive pro- cesses that may promote specific strategies in the resolution of mathematical problems. We use SVM to measure and classify patterns of synchrony in brain functional network constructed from the EEGs of a group of healthy individuals while they are solving mathematical problems. These patterns are related with the math performance of the participants and errors by them committed.
In this paper we address the problem of dynamics of tuberculosis spread, inside prisons. Prisons ... more In this paper we address the problem of dynamics of tuberculosis spread, inside prisons. Prisons are congregate settings with potential for sustained daily contact for weeks, months and years between people. We consider a five compartments SEIR model with four possible routes toward TB infection: primary infection after a contact with infected and infectious individuals (fast TB), endogenous reactivation after a period of latency (slow TB), relapse by natural causes after a cure and exogenous reinfection of recovered individuals. Besides, we will consider the physical constraints imposed by the structure of the prison premises on the infection spread.
The probability of transmission of tuberculosis (TB) per contact, per unit of time is in general ... more The probability of transmission of tuberculosis (TB) per contact, per unit of time is in general quite low and the risk of infection is very small during a single encounter with an infectious individual. But, the risk of TB transmission is particularly high in some congregate settings with poorly ventilated areas in which people are in close and frequent contact. Prisons are examples of these high-risk areas, in which incidence and prevalence of TB are very high. The transmission dynamics between prisoners and the general population, through prison staff, visitors and close contacts of prisoners, has been hypothesized to play a key role in driving overall population-level TB incidence, prevalence and mortality rates. Prisons represent a reservoir for TB transmission to the population at large and should be a source of public concern. In this paper, we use two-patch model, also known as - metapopulation model - to provide a simple framework within which the role of prisons as reservoirs for TB transmission can be examined. The population is subdivided into a two discrete patches -imprisoned population and general population- each of which is treated as being well-mixed.
En esta presentación se abordan preguntas tales como:
¿Por qué surgen diferencias individuales en... more En esta presentación se abordan preguntas tales como:
¿Por qué surgen diferencias individuales en la adquisición de habilidades matemáticas tempranas?. ¿Por qué la aritmética es importante?.
La adquisición de competencias matemáticas tempranas determinan en gran medida el éxito académico e incluso el éxito en la vida de un individuo y se correlacionan positivamente incluso con el crecimiento del bienestar económico de todo un país
¿Por qué se cometen tantos errores en la resolución de problemas matemáticos? y en general ¿Por qué aprender implica cometer errores?
¿Qué aportes ofrece la Neurociencia en la educación y en particular en la educación matemática? Reportes de una investigación.
Marketing research on diffusion of innovations contains an important debate about how the social ... more Marketing research on diffusion of innovations contains an important debate about how the social contagion could affect the adoption of innovations and whether the spread of such innovations is driven by opinion leaders or by regular consumers. To contribute to this debate, in this paper we study the innovation adoption dynamics in a span of ten years using detailed data sets from a community of consumers. We use a network contagion model to estimate the extent to which the social contagion is really important and how the interplay between complementary social and nonsocial influences from outside the community gives shape to the innovation adoption dynamics. We use a network model to represent the social interactions among community members. Because of a long-term observation period, the social network of the community do not remain static and the number and nature of contacts between individuals change over time. So, we keep track of both the temporal changes of the community social network and the innovation adoption dynamics propagating through this evolving network.
... Parcial de los Requisitos para la Obtención del Grado de Doctor en Ciencias (Mención Fısica) ... more ... Parcial de los Requisitos para la Obtención del Grado de Doctor en Ciencias (Mención Fısica) Agosto de 2001 ... En la sección 4.4 consideramos la estructura Multi Lagrangiana de la ecuación KdV , determinada según la receta dada en [7], con la correspondiente general-...
In this paper we address the problem of long-term dynamics of tuberculosis (TB) and latent tuberc... more In this paper we address the problem of long-term dynamics of tuberculosis (TB) and latent tuberculosis (LTB) in semi-closed communities. These communities are congregate settings with the potential for sustained daily contact for weeks, months and even years between its members. Basic examples of these communities are prisons, but certain urban/rural communities, some schools, among others could possibly fit well into this definition. These communities present a sort of ideal conditions for TB spread. In order to describe key relevant dynamics of the disease in these communities we consider a five compartments SEIR model with five possible routes toward TB infection: primary infection after a contact with infected and infectious individuals (fast TB), endogenous reactivation after a period of latency (slow TB), relapse by natural causes after a cure, exogenous reinfection of latently infected and exogenous reinfection of recovered individuals. We discuss the possible existence of multiple endemic equilibrium states and the role that could play the two types of exogenous reinfections in the long term dynamics of the disease.
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Papers by Mauricio Rene Herrera Marin
¿Por qué surgen diferencias individuales en la adquisición de habilidades matemáticas tempranas?. ¿Por qué la aritmética es importante?.
La adquisición de competencias matemáticas tempranas determinan en gran medida el éxito académico e incluso el éxito en la vida de un individuo y se correlacionan positivamente incluso con el crecimiento del bienestar económico de todo un país
¿Por qué se cometen tantos errores en la resolución de problemas matemáticos? y en general ¿Por qué aprender implica cometer errores?
¿Qué aportes ofrece la Neurociencia en la educación y en particular en la educación matemática? Reportes de una investigación.
¿Por qué surgen diferencias individuales en la adquisición de habilidades matemáticas tempranas?. ¿Por qué la aritmética es importante?.
La adquisición de competencias matemáticas tempranas determinan en gran medida el éxito académico e incluso el éxito en la vida de un individuo y se correlacionan positivamente incluso con el crecimiento del bienestar económico de todo un país
¿Por qué se cometen tantos errores en la resolución de problemas matemáticos? y en general ¿Por qué aprender implica cometer errores?
¿Qué aportes ofrece la Neurociencia en la educación y en particular en la educación matemática? Reportes de una investigación.