Linear recurrences and asymptotic behavior of exponential sums of symmetric boolean functions

In this paper we give an improvement of the degree of the homogeneous linear recurrence with integer coefficients that exponential sums of symmetric Boolean functions satisfy. This improvement is tight. We also compute the asymptotic behavior of symmetric Boolean functions and provide a formula that allows us to determine if a symmetric boolean function is asymptotically not balanced. In particular, when the degree of the symmetric function is a power of two, then the exponential sum is much smaller than $2^n$.Comment: 18 pages, 3 figure

Systemic intervention for computer-supported collaborative learning

This paper presents a systemic intervention approach as a means to overcome the methodological challenges involved in research into computer-supported collaborative learning applied to the promotion of mathematical problem-solving (CSCL-MPS) skills in schools. These challenges include how to develop an integrated analysis of several aspects of the learning process; and how to reflect on learning purposes, the context of application and participants' identities. The focus of systemic intervention is on processes for thinking through whose views and what issues and values should be considered pertinent in an analysis. Systemic intervention also advocates mixing methods from different traditions to address the purposes of multiple stakeholders. Consequently, a design for CSCL-MPS research is presented that includes several methods. This methodological design is used to analyse and reflect upon both a CSCL-MPS project with Colombian schools, and the identities of the participants in that project

Dynamics of quantum correlations and linear entropy in a multi-qubit-cavity system

We present a theoretical study of the relationship between entanglement and entropy in multi-qubit quantum optical systems. Specifically we investigate quantitative relations between the concurrence and linear entropy for a two-qubit mixed system, implemented as two two-level atoms interacting with a single-mode cavity field. The dynamical evolutions of the entanglement and entropy, are controlled via time-dependent cavity-atom couplings. Our theoretical findings lead us to propose an alternative measure of entanglement, which could be used to develop a much needed correlation measure for more general multi-partite quantum systems.Comment: New discussions on the generality of entanglement-entropy relationship, one new reference, and other minor changes. 10 pages, 6 figures, accepted for publication in J.Opt. B: "Special Issue on Fluctuations & Noise in Photonics & Quantum Optics.

La historia política a través de sus actores, historias con sentido

A riesgo de caer en la anécdota, pero con la convicción de que el camino recorrido es útil para quienes empiezan, el presente escrito intentará mostrar los aportes y las enseñanzas que dos investigaciones ofrecen con respecto a las teorías, miradas y métodos con que puede abordarse el análisis de la violencia en un contexto regional y próximo. El propósito de su publicación en este texto no es otro que participar en la discusión que el Grupo de Investigación de la Universidad Pedagógica Nacional, Sujetos y nuevas narrativas, pretende promover en torno al tema. Su conclusión más importante constituye una propuesta en desafío: además de ubicar a los actores en la historia, indagar sobre la producción de situaciones históricas por actores

2b-RAD genotyping for population genomic studies of Chagas disease vectors: Rhodnius ecuadoriensis in Ecuador

Background: Rhodnius ecuadoriensis is the main triatomine vector of Chagas disease, American trypanosomiasis, in Southern Ecuador and Northern Peru. Genomic approaches and next generation sequencing technologies have become powerful tools for investigating population diversity and structure which is a key consideration for vector control. Here we assess the effectiveness of three different 2b restriction site-associated DNA (2b-RAD) genotyping strategies in R. ecuadoriensis to provide sufficient genomic resolution to tease apart microevolutionary processes and undertake some pilot population genomic analyses. Methodology/Principal findings: The 2b-RAD protocol was carried out in-house at a non-specialized laboratory using 20 R. ecuadoriensis adults collected from the central coast and southern Andean region of Ecuador, from June 2006 to July 2013. 2b-RAD sequencing data was performed on an Illumina MiSeq instrument and analyzed with the STACKS de novo pipeline for loci assembly and Single Nucleotide Polymorphism (SNP) discovery. Preliminary population genomic analyses (global AMOVA and Bayesian clustering) were implemented. Our results showed that the 2b-RAD genotyping protocol is effective for R. ecuadoriensis and likely for other triatomine species. However, only BcgI and CspCI restriction enzymes provided a number of markers suitable for population genomic analysis at the read depth we generated. Our preliminary genomic analyses detected a signal of genetic structuring across the study area. Conclusions/Significance: Our findings suggest that 2b-RAD genotyping is both a cost effective and methodologically simple approach for generating high resolution genomic data for Chagas disease vectors with the power to distinguish between different vector populations at epidemiologically relevant scales. As such, 2b-RAD represents a powerful tool in the hands of medical entomologists with limited access to specialized molecular biological equipment. Author summary: Understanding Chagas disease vector (triatomine) population dispersal is key for the design of control measures tailored for the epidemiological situation of a particular region. In Ecuador, Rhodnius ecuadoriensis is a cause of concern for Chagas disease transmission, since it is widely distributed from the central coast to southern Ecuador. Here, a genome-wide sequencing (2b-RAD) approach was performed in 20 specimens from four communities from Manabí (central coast) and Loja (southern) provinces of Ecuador, and the effectiveness of three type IIB restriction enzymes was assessed. The findings of this study show that this genotyping methodology is cost effective in R. ecuadoriensis and likely in other triatomine species. In addition, preliminary population genomic analysis results detected a signal of population structure among geographically distinct communities and genetic variability within communities. As such, 2b-RAD shows significant promise as a relatively low-tech solution for determination of vector population genomics, dynamics, and spread